Magnetoresistance measurements and theoretical calculations for two-dimensional electron systems under a perpendicular magnetic field are presented which illuminate transport effects due to a periodic electrostatic potential modulation. We focus on features arising from the resolution of the magnetic miniband structure which are beyond the perturbative regime governed by the dispersion of Landau bands. Our non-perturbative quantum-mechanical calculations reveal that the dispersion of individual minibands is responsible for the complicated behaviour of the magnetoresistance in the regime of intermediate modulation strength. In particular, the interplay between miniband and scattering contributions to the conductivity leads to an almost structureless magnetoresistance in this regime followed by the formation of antidot peaks due to the miniband conductivity.