On Maximal Subgroups of a Finite Solvable Group
  The following result is received: Let $H$ be a non-normal maximal subgroup of a finite solvable group $G$ and let $q \in \pi(F(H/\mathrm{Core}_GH))$, then $G$ has a Sylow $q$-subgroup $Q$ such that $N_{G}(Q) \subseteq H$. 
D.V. Gritsuk, V.S. Monakhov
math.GR