Energetic electrons are a common feature of interplanetary shocks and planetary bow shocks, and they are invoked as a key component of models of nonthermal radio emission, such as solar radio bursts. A simulation study is carried out of electron acceleration for high Mach number, quasi-perpendicular shocks, typical of the shocks in the solar wind. Two-dimensional self-consistent hybrid shock simulations provide the electric and magnetic fields in which test particle electrons are followed. A range of different shock types, shock normal angles, and injection energies are studied. When the Mach number is low, or the simulation configuration suppresses fluctuations along the magnetic field direction, the results agree with theory assuming magnetic moment conserving reflection (or fast Fermi acceleration), with electron energy gains of a factor only 2-3. For high Mach numbers, with a realistic simulation configuration, the shock front has a dynamic rippled character. The corresponding electron energization is radically different: energy spectra display (1) considerably higher maximum energies than fast Fermi acceleration; (2) a plateau or shallow sloped region at intermediate energies 2-5 times the injection energy; (3) power-law falloff with increasing energy, for both upstream and downstream particles, with a slope decreasing as the shock normal angle approaches perpendicular; (4) sustained flux levels over a broader region of shock normal angle than for adiabatic reflection. All these features are in good qualitative agreement with observations, and show that dynamic structure in the shock surface at ion scales produces effective scattering and can be responsible for making high Mach number shocks effective sites for electron acceleration.