Sophocles' Antigone is very different from traditional plays or tragedies. Not only does the play have two characters that function as protagonists, they also both function as the tragic hero ("Antigone--Whose Tragedy Is It?"). Since formatting limits us in how many characters we can discuss, below is a discussion of both of these tragic heroes.
As the play's title suggests, one of the protagonists of the story is Antigone, and she is also one of the tragic heroes. According to Aristotle's definition of a tragic hero found in his Poetics, a tragic hero must be of high social status and his/her downfall must be brought on by some fatal character flaw. Antigone fits this picture because as daughter of the late King Oedipus, she is a princess; also, her tragic character flaws are her headstrong nature and her stubbornness. Antigone sets the tragic outcome of the play in motion by rebelling against Creon's new decree that her brother Polynices shall be left unburied as a traitor to the city. Antigone decides to secretly bury her brother regardless because she feels she ought to honor her brother and because she feels that the gods' laws to pay respect to the dead are far higher than Creon's laws.
The second protagonist and tragic hero is Creon. In fact, some would argue that he really is the main tragic hero; although others would argue that he functions as more of an antagonist until the very end of the play. The antagonist is the character that the protagonist struggles against. Since Antigone struggles against Creon's law, and Creon even causes trouble for his son Haemon, we can easily view Creon as the play's antagonist. However, others view Creon as the true tragic hero in the play, and the reason is that, according to Aristotle's definition, a tragic hero must have a moment of development, a moment of revelation (McGee, "Creon: A Tragic Hero"). While Antigone is lead to the tomb believing that she is being mocked by the citizens for foolishly being headstrong enough to break a law, she never has a moment in which she decides that what she has done is right or wrong. Instead, it is Creon who undergoes a moment of revelation. After Tiresias prophecies doom, including not only the destruction of the city, but the death of Creon's own son, Creon finally relents and changes his mind. Contrary to his initial characterization, he even asks the chorus, "What should I do? Tell me, and I will obey," whereas before he accepted no one's counsel but his own. Since Creon finally relents and sees that he should not have passed a decree that broke a commandment of the gods, we see that Creon is really the character that has the moment of revelation. Not only that, since his revelation comes too late and what he has done already brings death and destruction, we can say that Creon is a tragic hero.