  We study the luminosity function of satellite galaxies around isolated
primaries using the Sloan Digital Sky Survey (SDSS) spectroscopic and
photometric galaxy samples. We select isolated primaries from the spectroscopic
sample and search for potential satellites in the much deeper photometric
sample. For primaries of similar luminosity to the Milky Way and M31, we are
able to stack as many as $\sim\negthinspace 20,000$ galaxy systems to obtain
robust statistical results. We derive the satellite luminosity function
extending almost 8 magnitudes fainter than the primary galaxy. We also
determine how the satellite luminosity function varies with the luminosity,
colour and concentration of the primary. We find that, in the mean, isolated
primaries of comparable luminosity to the Milky Way and M31 contain about a
factor of two fewer satellites brighter than $M_V=-14$ than the average of the
Milky Way and M31.
