Aristotle, in Poetics, outlined the characteristics of the tragic hero. In order to define a character as a tragic hero, he or she must possess numerous traits associated with the tragic hero. Yet here, you are asking about numerous characters' alignments with these characteristics.

The Captain, from August Strindberg's The Father, possesses two of the typical tragic hero characteristics: he possesses greatness (so a fall can come), and he cannot be held solely accountable for his fall (given his rejection by his mother—she is partly to blame).

Laura, the Captain's wife, possesses a tragic flaw. Although most would not identify Laura as a tragic hero, she does possess hubris (excessive pride). In her refusal to be claimed by the Captain, she plots against him and leads him down a path of inner destruction, forcing him to go mad. That said, since she does possess the intent to do wrong to her husband, Laura does not fully align with the typical characteristics of the tragic hero.

In the end, the Captain seems to be the character who comes closest to aligning with the characteristics of Aristotle's tragic hero. One would be hard-pressed to argue that the Captain does deserve his fate; essentially, the punishment does not seem worth the crime (which is true of the tragic hero). His history with his mother led him down a path to seeking out a replacement for her. Unfortunately, Laura is simply not going to bend to his will.