let $G$ be a finite group and $\Phi(G)=1$. ($\Phi(G)$ denotes the frattini subgroup of $G$)
Could we find two non-trivial subgroups $H_1$ and $H_2$ of $G$ with this property "both $H_1$ and $H_2$ are contained in the same maximal subgroup $M$ of $G$ and for each maximal subgroup $M^'$ of $G$ where $M^' \neq M$, if $H_i\nleq M^'$ then $H_j\leq M^'$; 
$1\geq i,j\leq 2 $?"\\ 
If it is hard to answer the question in general, could we answer it on certain classes of finite groups (say finite simple groups, symmetric groups,...)?