We prove that theories that arise by taking free hypermultiplets and gauging a subgroup of , the non-R global symmetry of the free theory, have a remaining global symmetry, which is a direct sum of unitary, symplectic, and special orthogonal factors. This implies that theories that have but not global symmetries, such as Gaiotto's theories, are not likely to arise as IR fixed points of RG flows from weakly coupled gauge theories.