Let $G$ be a solvable group in which all non-trivial subgroups are supplemented. (A subgroup $H$ of a group $G$ is called supplemented if $G=HK$ for some proper subgroup $K$. Such a subgroup $K$ is called a supplement of $H$ in $G$). Suppose further that $G$ has a maximal subgroup $M$ having only finitely many supplements in $G$.

Is $G$ necessarily finite?