Let $G$ be a non-nilpotent and supersoluble finite group.
$G=Q\ltimes P$ and $|Q: C_{Q}(P)|=q$ is prime, Where $P$ is a group of prime order $p\neq q$.
$Q$ is noncyclic group of order $|Q|=q^{\alpha}$ where $\alpha >2$ and all maximal subgroup of $Q$ diffrent from $C_{Q}(P)$ are cyclic Then every $2$-maximal subgroup of $G$ permutes with all $3$-maximal subgroup of $G$.
I dont have idea ? What i do? Maximal subgroup of $G$ is not clear for me.
A subgroup $H$ of a group $G$ is called $2$-maximal (or second maximal )in $G$ if $H$ is a maximal subgroup of some maximal subgroup $M$ of $G$.