Question

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

• A. 42

Answer 1

The correct option is A 42
Given $|G|=84$
By Lagrang's theorem any subgroup size is a divisior of 84.
But a proper subgroup cannot have same size as group.
So largest divisor of 84, other than 84 is 42.
So, largest proper subgroup can have in size of 42.