Order has only two prime factors implies solvable for Moufang loops

Statement
Suppose $$L$$ is a finite Moufang loop (i.e., a Moufang loop whose underlying set is finite). Suppose the order (i.e., the size of the underlying set) of $$L$$ has at most two distinct prime factors, i.e., it is of the form $$p^aq^b$$ where $$p,q$$ are primes and $$a,b$$ are nonnegative integers (possibly zero). Then, $$L$$ is a fact about::solvable Moufang loop (and in particular a finite solvable Moufang loop).

Related facts

 * Order has only two prime factors implies solvable (for finite groups)