Summary: This work develops the geometry and dynamics for discrete-continuous systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics. The basic methodology is that of geometric mechanics of discrete-continuous type, applied to the formulation of Lagrange-d’Alembert for these systems, generalizing the momentum maps associated with a given symmetry group to this case. One of the purposes is to derive a discrete-continuous evolution equation for the momentum, and to distinguish geometrically and mechanically the cases where the momentum is conserved. We give detailed examples which illustrate this theory.