We study the abundance of satellite galaxies as a function of primary stellar mass using the SDSS/DR7 spectroscopic catalogue. In contrast with previous studies, which focussed mainly on bright primaries, our central galaxies span a wide range of stellar mass, 10^7.5 < M_*^pri/M_sun < 10^11, from dwarfs to central cluster galaxies. Our analysis confirms that the average number of satellites around bright primaries, when expressed in terms of satellite-to-primary stellar mass ratio (m_*^sat/M_*^pri), is a strong function of M_*^pri. On the other hand, satellite abundance is largely independent of primary mass for dwarf primaries (M_*^pri<10^10 M_sun). These results are consistent with galaxy formation models in the LCDM scenario. We find excellent agreement between SDSS data and semi-analytic mock galaxy catalogues constructed from the Millennium-II Simulation. Satellite galaxies trace dark matter substructure in LCDM, so satellite abundance reflects the dependence on halo mass, M_200, of both substructure and galaxy stellar mass (M_*). Since dark matter substructure is almost scale-free, the dependence of satellite abundance on primary mass results solely from the well-defined characteristic mass in the galaxy mass-halo mass relation. On dwarf galaxy scales, where models predict a power-law scaling, M_* \propto M_200^2.5, similarity is preserved and satellite abundance is independent of primary mass. For primaries brighter than the characteristic mass of the M_*-M_200 relation, satellite abundance increases strongly with primary mass. Our results provide strong support for the steep, approximately power-law dependence of dwarf galaxy mass on halo mass envisioned in LCDM galaxy formation models.

7 pages, 3 figures, updated version accepted for MNRAS main journal. Added extended discussion with respect to first submission. Conclusions unchanged