  We investigate the notion of a subgroup of a quantum group. We suggest a
general definition, which takes into account the work that has been done for
quantum homogeneous spaces. We further restrict our attention to reductive
subgroups, where some faithful flatness conditions apply. Furthermore, we
proceed with a categorical approach to the problem of finding quantum
subgroups. We translate all existing results into the language of module and
monoidal categories and give another characterization of the notion of a
quantum subgroup.
