  We use the Millennium Simulation, a large, high resolution N-body simulation
of the evolution of structure in a LambdaCDM cosmology, to study the properties
and fate of substructures within a large sample of dark matter haloes. We find
that the subhalo mass function departs significantly from a power law at the
high mass end. We also find that the radial and angular distributions of
substructures depend on subhalo mass. In particular, high mass subhaloes tend
to be less radially concentrated and to have angular distributions closer to
the direction perpendicular to the spin of the host halo than their less
massive counterparts. We find that mergers between subhaloes occur. These tend
to be between substructures that were already dynamically associated before
accretion into the main halo. For subhaloes larger than 0.001 times the mass of
the host halo, it is more likely that the subhalo will merge with the central
or main subhalo than with another subhalo larger than itself. For lower masses,
subhalo-subhalo mergers become equally likely to mergers with the main subhalo.
Our results have implications for the variation of galaxy properties with
environment and for the treatment of mergers in galaxy formation models.
