daughter Mariane is completely dominated by her father, also.  In Act 2, Scene 1, for instance, she comes to Organ in response to his demand to see her,

MARIANE I'm deeply grateful, Father, for your love.
ORGON    That's well said, Daughter; and you can repay me it in all things, you'll cheerfully obey me.
MARIANE  To please you, Sir, is what delights me best.
ORGON     Good, good!  Now, what d'you think of Tartuffe, our guest?....In being his wife, if that should be my choice.
MARIANE  You can't mean, father...
ORGON     Yes, Tartuffe shall be
Allied by marriage to this family,
And he's to be your husband, is that clear?
It's a father privilege...

This announcement is so emotionally devastating to Mariane, who loves Valere whom her father has previously approved as her fiance, that she contemplates suicide as the only alternative to a miserable fate.

Elmire, too, is subservient to Orgon. For instance, when Tartuffe proposes his sexual advances, Elmire politely tells him that she will not report Tartuffe's inappropriate conduct to her husband in an attempt to bargain with him in return for her silence. She requests of him

ELMIRE  To advocate as forcefully as you can
The marriage of Valere and Mariane,
Renouncing all desire to dispossess
Another of his rightful happiness,....

In his male arrogance, Tartuffe refuses Elmire's request. So, she devises a trap in order to expose the religious hypocrite for the philanderer that he is.  Convincing her husband to hear for himself since he believes that she is "impudent," Elmire has Orgon hide himself under the table in the room where Tartuffe again makes his lascivious advances. It is not until she is nearly assaulted that Orgon emerges from underneath the table, and Elmire sarcastically asks, "What, coming out so soon? How premature!"  Thus, it is only because his pride is insulted by Tartuffe's advances to his wife, that Orgon takes offense against the impostor.

Classical comedy is strongly normative. It is by its nature conservative, making fun of people who transgress social norms and expectations and coming to a happy ending or resolution when the normal order is restored. Written in 1684,  the normative gender expectations were that men were dominant and females subordinate. Men were also expected to be rational and women more pious, and more prone to gullibility and superstition. 

The first violation of conventional gender roles is seen in the character of Orgon. He tends to be a follower rather than a leader, weak and easily manipulated, superstitious and irrational, characteristics that almost seem effeminate. His relationship with Tartuffe also violated gender codes in having an intensity that seems almost to carry homosexual overtones, with Orgon in a feminized role, worrying about Tartuffe's health and appetite, as would a wife. 

Madame Pernelle is a figure like the "matrona" of Roman comedy who is overbearing and matriarchal, and thus violates the norm of the female as subordinate. Elmire also needs to step out of the traditional female role in order to devise a plot to save her family.  She is sensible, decisive, and rational.

The play as a whole subverts gender roles by suggesting that the absolute power of the male head of a household can be problematic, as Orgon is clearly undeserving of his power. 

The question is basically asking how characters in the play act in a different way than society would expect them to act.  In this case, it is really asking about women and how they are behaving in a way that would have shocked society in their day.  Remember, we are talking about a very long time ago.  What Moliere does is show us one character that does act as society would expect (Mariane) and then shows a contrast with other female characters, such as Elmire and Dorine. 

Mariane is the perfect young woman of the time.  She is very obedient to her parents; in fact, when her father tells her she has to give up the fiancé she loves in order to marry the man of his choice, she does not argue with him.  She is upset, but even so, when Dorine suggests she argue with her father, she is shocked and tells her she could never do that.  In the end, she marries the man she loves, but only because others in the play intervened.

Elmire is a good example of a woman who does not act as her gender should in the play.  In her marriage to Orgon, it is clear that Elmire is in charge.  This may even be why Tartuffe ends up in the house in the first place—Orgon is trying to assert his authority that was lost long ago. 

Dorine is also an excellent example of a woman who does not “know her place.”  Dorine talks back, not only to her bosses, but to everyone around her.  As our perfect example of a woman is Mariane, it is obvious that Dorine is not acting like the other girls of her day.  When she should close her mouth, she opens it.  When she should not argue, she argues.  An example of this is when she is trying to explain to Orgon that he should not marry Mariane to Tartuffe, and she tells him, proudly, that she would never let a man choose who she married. 

In short, Mariane is the best example of the girl of the day—sweet and obedient.  The other two women are representing girls in that society who are trying to break free.

The first version of Tartuffe, by Jean Baptiste Poquelin, better known as Moliere, was performed at the Palace of Versailles in 1664, during the reign of King Louis XIV of France, who promptly banned the play from public performance.

A second version of the play, titled L'Imposteur (The Imposter), was performed in 1667 in the Théâtre du Palais-Royal in Paris and was also banned.

The third version of the play, Le Tartuffe, was performed in 1669, also at the Théâtre du Palais-Royal in Paris. The third version was not banned, and this is the version of the play which has come down to us.

Moliere changed the title from Tartuffe in 1664 to Le Tartuffe in 1669 partly because the term "tartuffe" was in common use in France and England as a synonym for "hypocrite," and Moliere shifted the title from "Tartuffe," the title character in the play, to "the Tartuffe," meaning someone who acts like Tartuffe.

In relation to the question of gender roles, Tartuffe wasn't banned because of any controversy concerning the portrayal of men or women in the play, but because influential Roman Catholic Church leaders strongly objected to what they considered Moliere's attack on religion. They also objected to the portrayal of Tartuffe as an outwardly pious person who is actually a lecherous, deceitful hypocrite.

Instead of directly undermining gender roles by portraying all of the female characters in ways that are adverse to societal norms, Moliere established one character, Mariane, as the cultural standard of the time. Mariane is quiet (seen but not heard, like a child), passive, and obedient to her father, Orgon, even to the point of agreeing to marry Tartuffe, even though she's in love with Valère.

Having established Mariane as the perfect woman (and perfect daughter), Moliere uses two other female characters, Elmire and Dorine, to satirize and criticize society's fixation with the perfect woman.

Elmire, Orgon's second wife and Marian's stepmother, is strong-minded, intelligent, and independent. Elmire actually "wears the pants" in the household. Except when bullying his daughter, Mariane, Orgon defers to Elmire, which is a definite role reversal.

Tartuffe attempts to seduce Elmire, and, not being as easily misled as Orgon is by Tartuffe's feigned virtue, Elmire rejects Tartuffe and eventually helps expose him for what he is.

Moliere's portrayal of Dorine is even more revolutionary than his portrayal of Elmire. A "henpecked husband" like Orgon is a well-known character in comic plays, but Dorine's character goes well beyond Elmire in terms of her relationship with men and her place in society.

Dorine is a servant. Of all the woman in the play, Dorine is the one person who should "know her place." Of all the woman in the play, however, Dorine is the most outspoken, both as a character in the play and as a commentator on the role of women in the play.

Dorine doesn't know her place. She has opinions, and she expresses them in no uncertain terms. She argues with men, and she encourages Mariane to argue with Orgon and stand up for herself. Dorine tells Orgon that she would never let a man choose who she married. Even though Dorine is a servant, she's definitely not subservient to any man.

In his first appeal to Louis XIV to lift the ban on Tartuffe, Moliere wrote that “the purpose of the comedy is to correct the faults of men.” In Tartuffe, Moliere shows that the prevailing attitude regarding a woman's role in French society is one of the "faults of men" that needs to be corrected.