In chapter 15, there are three distinct groups: the lynch mob, Atticus, and the kids. Which group or person had the most power? Explain your answer.

This is based on opinion, but I believe this one belongs to the kids.

Explanation:

Scout recognizes Mr. Cunningham: she asks about his entailment and about Walter, which makes him look uncomfortable. Remembering Atticus's advice to talk to people about what they're interested in, Scout mentions the entailment again and realizes that everyone, including Atticus, is staring at her openmouthed. She asks what's wrong. Mr. Cunningham squats, tells Scout he'll say hi to Walter, and leads the men away. Mr. Cunningham smiles at her, and leads the men away. Scout's innocence contributes to this save, and uses this leverage to save Tom Robinson.

One could say it was Atticus, but the mob was already towards making a move against him, but it was Scout who saved him from this danger.

Again, this is my opinion, and is entirely up to debate.