This talk is about joint work with F. Bleher. We answer a question of M. Flach by constructing representations of Galois groups whose deformation rings are not complete intersections. In this first talk I will discuss the background and then capping groups, which are quotients of a profinite group which control the deformations of mod p representations of the group. I will then show that the symmetric group S_4 is a capping group for infinitely many real quadratic fields when p=2.