Maximal subgroup has prime power index in finite solvable group

Statement
Let $$G$$ be a finite solvable group and $$M$$ be a maximal subgroup of $$G$$. Then, the index $$[G:M]$$ is a power of a prime.

Facts used

 * 1) Primitive implies Fitting-free or elementary Abelian Fitting subgroup

Textbook references

 * , Page 219, Theorem 1.5 (Section 6.1)
 * , Page 200, Exercise 32, Section 6.1 ($$p$$-groups, nilpotent groups and solvable groups)