Most of the characters in Flannery O'Connor's short story "A Good Man is Hard to Find" can be divided into two groups: those who are murdered and those who are not murderers.
O'Connor's story involves a family vacation in which a father, mother, their children, and their grandmother take a car trip through the southern part of the United States (O'Connor herself was from Georgia). A suggested detour by the Grandmother leads to the family car crashing off the road. Unfortunately, the first people on the scene are three outlaws, whose ringleader is known as the "Misfit".
To make matters worse, when the Grandmother recognizes the Misfit, he decides that he must kill the entire family. Aided by his two accomplices, he does just that. His accomplices kill most of the family, but the Misfit himself kills the Grandmother, who pleads with the Misfit not to do it.
Before the Misfit kills the old man, he tells her about the trials and tribulations that he has experienced in his own life.
As for which characters are sympathetic in the story, the simple answer would be that we feel sympathy for the murdered family. They happened to be in the wrong place at the wrong time and were savagely and callously murdered. Even the Grandmother, who ended up leading the family off their original route and whose recognition of the Misfit contributed to his decision to kill the family, must be viewed in a sympathetic light.
The Misfit himself did have events in his past that evoke sympathy, but in the end it seems difficult to have sympathy for someone who is responsible for the deaths of six people, three of whom were children (one was a baby) and one of whom was a helpless old woman.