Let $G$ be a finite simple group in which there is no element of order $p^2$ for all primes $p\mid\vert G\vert$. Suppose that $H$ is a finite group whose number of nontrivial proper subgroups is as same as $G$ and there is a bijection $\phi$ from the set of nontrivial subgroups of $G$ to the set of nontrivial subgroups of $H$ such that for every two subgroups of $G$ say $K_{1}, K_{2}$ we have $K_{1}\leq K_{2}$ if and only if $\phi(K_{1})\leq \phi(K_{2})$(i.e. $\phi$ preserves inclusions)

Can we say that $G\cong H$?