Let $G$ be a group with order 12. Which of the following claims are false?
Does Lagrange's Theorem imply that there could exist a subgroup with order 6? I'm not sure where to begin. The question was taken from a past test with multiple choice answers, and the question asked which of the following claims were false:
• G must have an element of order 2.
• G must have a subgroup of order 6.
• G must have a subgroup of order 2.
• None of the above, they are all true.