One of the symbols that is used to invoke power and particularly power over a group is the conch. As Ralph and Piggy set it up as the object of power, the object that gives someone the right to speak and be heard, they are looking to inject the power of law and rules over the boys.
Another is the idea of the hunt, the path to satisfaction of both hunger and a desire to strike back. Jack represents this power and uses it and his charisma to lead boys to join him and to ignore the idea of civilization and law and the power of the conch.
A third is the power of fear over the boys, the power that only Simon sees and understands because it comes from within them. This power is shown to have the greatest effect as it leads the boys to murder each other and to turn to complete savages.