  Motivated by the recent experiments on periodically modulated, two
dimensional electron systems placed in large transversal magnetic fields, we
investigate the interplay between the effects of disorder and periodic
potentials in the integer quantum Hall regime. In particular, we study the case
where disorder is larger than the periodic modulation, but both are small
enough that Landau level mixing is negligible. In this limit, the
self-consistent Born approximation is inadequate. We carry extensive numerical
calculations to understand the relevant physics in the lowest Landau level,
such as the spectrum and nature (localized or extended) of the wave functions.
Based on our results, we propose a qualitative explanation of the new features
uncovered recently in transport measurements.
