Just insert "L" at the beginning and "Q" at the end of the following permutations:
{A, E, S} | {A, E, U} | {A, S, E} | {A, S, U} | {A, U, E} | {A, U, S} | {E, A, S} | {E, A, U} | {E, S, A} | {E, S, U} | {E, U, A} | {E, U, S} | {S, A, E} | {S, A, U} | {S, E, A} | {S, E, U} | {S, U, A} | {S, U, E} | {U, A, E} | {U, A, S} | {U, E, A} | {U, E, S} | {U, S, A} | {U, S, E} (total: 24)