We report on magnetotransport of a two-dimensional electron system (2DES), located 32 nm below the surface, with a surface superlattice gate structure of periodicity 39 nm imposing a periodic modulation of its potential. For low Landau level fillings nu, the diagonal resistivity displays a rich pattern of fluctuations, even though the disorder dominates over the periodic modulation. Theoretical arguments based on the combined effects of the long-wavelength, strong disorder and the short-wavelength, weak periodic modulation present in the 2DES qualitatively explain the data.