Let $G$ be a group of 35 elements. Then the largest possible size of a subgroup of $G$ other than $G$ itself is ________.

According to Lagrange's Theorem, the order (size) of any subgroup $H$ of a finite group $G$ must divide the order of $G$, denoted by $|G|$.

Given $|G| = 35$, the positive divisors of $35$ are:

A proper subgroup of $G$ is any subgroup other than $G$ itself, so its size must be a divisor strictly less than $35$, i.e., $1, 5,$ or $7$.

The largest possible size among these proper divisors is 7.