Strong Gelfand Pairs of the Dihedral and Dicyclic Groups

A strong Gelfand pair $(G,H)$ is a finite group $G$ and a subgroup $H$ where every irreducible character of $H$ induces to a multiplicity-free character of $G$. We determine the strong Gelfand pairs of the dihedral groups $D_{2n}$ and the dicyclic groups $Di{c}_{4n}$ for all $n$.