Lord of the Flies, by William Golding, is replete with conflict. The types of conflict found in literary works generally fall into three categories: man vs. man, man vs. nature, and man vs. society. This novel contains all three.
The man vs. man conflicts are many. Consider the fact that every boy on the island is against Piggy at first. Soon Ralph and Simon accept him as a friend and tribe member; however, most of the other boys are his active enemies throughout the story, and one of them (Roger) deliberately kills him. From the beginning, Jack is in conflict with Ralph for leadership of the boys and the island. While they have an uneasy working relationship for a few chapters, as soon as Jack begins painting his face, things change dramatically.
[T]he mask was a thing on its own, behind which Jack hid, liberated from shame and self-consciousness.
Jack's animosity for Ralph turns into hatred; by the end of the novel he has ordered everyone on the island to kill Ralph--and he means it. Simon is not really anyone's enemy, but when he crawls out of the forest one dark night, the rest of the boys kill him.
There are also some obvious man vs. nature conflicts in this novel. The boys are unexpectedly living on this island, and they are obviously not prepared to do so. They do not have enough to eat, they struggle to make fire--and when they do it turns into a deadly conflagration. The most obvious conflict is between the boys and the beast; of course, the beast is actually them, so this is a false conflict which the boys maintain throughout the story.
The man vs. society conflicts in this novel are, perhaps, Golding's most significant thematic elements. These boys turn from civilized, proper, disciplined British boarding-school boys into savages who are anything but civilized. Their behavior would not be acceptable anywhere off the island, which of course is Golding's point: without the restraints of law and authority, man would, because of his nature, revert to savagery. The backdrop of the entire novel is the war (World War II) which is raging around the world. Clearly this is the greatest societal conflict in the novel, though we do not actually see it happening.