Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is    

Q. Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is                 .

Ans: 42

According to Lagrange’s theorem, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G.

Therefore, possible subgroups of group on 84 elements are : 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

Subgroups with element 1 and 84 are trivial groups.