Piggy is very clear with Ralph in the first chapter that he does not want to be called Piggy. Have you ever thought about the fact that we never even learn this kid's real name? This is the power of control. Throughout the rest of the text, we hear this boy called Fatty as well, but we never learn his true identity. The entire group then, never learns the truth about him either.
Furthermore, Piggy has great ideas to offer the group yet lacks the leadership abilities to ensure the group works together and completes tasks required for survival. Because of this the entire group suffers. They have to endure the leadership of Ralph, which could be good with the advisement of Piggy; or, they could join forces later with Jack.
Throughout the book, Piggy and his needs are viewed as expendable, yet what Piggy has to offer is what the rest of the group needs. The kids make fun of his ass-mar, obesity, and glasses. However, his glasses are their only ability to create fire, a much needed source of heat, food, and most importantly, rescue. Both Ralph and Jack use Piggy as a dispensible pawn, Jack more so than Ralph. This demonstrates that a leader can easily manipulate members of a group regardless of their ability to contribute. For these groups, Piggy's treatment is unfortunate.
What this demonstrates about groups in general in reference to power is a startling reality. We tend to choose people for leaders who look the part and can convince us they have something to offer even if they don't. It also demonstrates how quickly we conform to an idea just because a leader suggests it.