Finite almost simple implies 3-generated

Definition
Suppose $$G$$ is a finite fact about::almost simple group. Then, the fact about::minimum size of generating set for $$G$$ is at most $$3$$.

Related facts

 * Finite minimal simple implies 2-generated
 * Finite simple implies 2-generated
 * Every finite group is generated by a solvable subgroup and one element
 * Solvability is 2-local for finite groups