## Maximal Subgroups [closed]

Let $U$ and $S$ be two maximal subgroups of a finite group $G$ such that $Core_G(U)\ne Core_G(S)$ and both $U$ and $S$ supplement a chief factor $H/K$.

Let $M=(U\cap S)H$. Prove that $M$ is maximal in $G$ and $Core_G(M)=(Core_G(U)\cap Core_G(S))H$.