This is problem 2.7.15 from Hungerford's Algebra:
If $H$ is a maximal proper subgroup of a finite solvable group $G$, then $[G:H]$ is a prime power.
If $G$ is abelian, then it's easy to show that $[G:H]$ is a prime power. I'm stuck on the non-abelian case. Any hints how to proceed?