Number of Sylow subgroups in $p$-solvable groups

If $G$ is a finite group and $p$ is a prime number, let $\nu_p(G)$be the number of Sylow $p$-subgroups of $G$. If $H$ is a subgroup of a $p$-solvable group $G$, we prove that $\nu_p(H)$ divides $\nu_p(G)$.