While it would seem obvious at first glance to assume that Antigone is the tragic hero of the play of which she is the titular character, she does not fit the strictest definition of a tragic hero given that she does not have a readily apparent tragic flaw. She is, compared to other characters in the play, a paradigm of virtue, and she sacrifices herself for what she knows is right by the gods. Though she meets a grim and miserable fate, she meets it with her spirit unbesmirched and is a victim of external forces rather than herself.

Creon more readily fits the archetype of the tragic hero, as his eventual fall from grace is due to his excessive pride. He believes himself above the will of the gods and doubles down on his poor decisions even when evidence of his error overwhelms him. Creon no doubt has good intentions and wants to lead well, but by the time he abandons his pride to do right by those he has wronged, it is far too late.

This question is interesting because it brings to light just how much heroism and tragedy's definitions have shifted in the last couple thousand years.

In Aristotle's definition of tragedy, a character experiences a reversal of fortune, leading to events which inspire pity and fear in the audience. This certainly happens to both Antigone and Creon, who are both high-born characters that lose everything. Antigone loses her life, and Creon loses the people he loves most.

However, Aristotle's definition goes farther than this. A tragic hero's fall comes from an error in judgment—a mistake. No matter what one might think of Antigone's principled actions, it is clear from the moral perspective of the play that she is not making a mistake in choosing to bury her brothers properly. Rather, it is Creon who makes a mistake in acting against the will of the gods by trying to enforce his monstrous decree. His execution of Antigone is the final straw, leading to the deaths of his son and wife. So from the classical perspective, Creon is the tragic hero of the play, not Antigone.

Although what happens to Antigone in Sophocles' play is certainly tragic (she commits suicide as a result of an unjust decree) and she is considered a heroine in the modern sense of the word (i.e., we admire her because she stands up for what she believes is right in the face of adversity), I'm not sure Antigone is what Aristotle had in mind in the Poetics when he tried to define the hero of a tragedy.

For Aristotle (Poetics 13), the hero of a tragedy was a noble male, who was neither "eminently good and just, yet whose misfortune is brought about not by vice or depravity, but by some error or frailty" (S.H. Butcher translation). This description fits the character of Creon rather than Antigone.

Creon is nobleman whose misfortune is caused not because he is a wicked and vile human being, but because he makes an error in judgement that he does not decide to rectify until it is too late. His failure to reverse course on the decision to execute Antigone, results not only in Antigone's death, but also in the deaths of Haemon and Creon's wife.

We also need to keep in mind that our modern definition of hero is different from the ancient definition of hero. In modern times, we think of heroes as people that we admire and would wish to be like. In literary terms, however, the hero can be the focal point of a story without being someone that we would admire or want to be like.

So, while Antigone is certainly an admirable and heroic person in the modern sense, she may not be the sort of tragic hero that Aristotle had in mind in the Poetics. On the other hand, surely no one would want to be like Creon, but he probably fits the bill for the literary definition of a tragic hero.