  We use large cosmological N-body simulations to study the subhalo population
in galaxy group sized halos. In particular, we look for fossil group candidates
with typical masses ~10-25% of Virgo cluster but with an order of magnitude
less substructure. We examine recent claims that the earliest systems to form
are deficient enough in substructure to explain the luminosity function found
in fossil groups. Although our simulations show a correlation between the halo
formation time and the number of subhalos, the maximum suppression of subhalos
is a factor of 2-2.5, whereas a factor of 6 is required to match fossil groups
and galaxies. While the number of subhalos depends weakly on the formation
time, the slope of the halo substructure velocity function does not. The
satellite population within Cold Dark Matter (CDM) halos is self-similar at
scales between galaxies and galaxy clusters regardless of mass, whereas current
observations show a break in self-similarity at a mass scale corresponding to
group of galaxies.
