  We present a statistical study of substructure within a sample of LCDM
clusters and galaxies simulated with up to 25 million particles. With thousands
of subhalos per object we can accurately measure their spatial clustering and
velocity distribution functions and compare these with observational data. The
substructure properties of galactic halos closely resembles those of galaxy
clusters with a small scatter in the mass and circular velocity functions. The
velocity distribution function is non-Maxwellian and flat topped with a
negative kurtosis of about -0.7. Within the virial radius the velocity bias
$b=\sigma_{\rm sub}/\sigma_{\rm DM}\sim 1.12 \pm 0.04$, increasing to b > 1.3
within the halo centers. Slow subhalos are much less common, due to physical
disruption by gravitational tides early in the merging history. This leads to a
spatially anti-biased subhalo distribution that is well fitted by a cored
isothermal. Observations of cluster galaxies do not show such biases which we
interpret as a limitation of pure dark matter simulations - we estimate that we
are missing half of the halo population which has been destroyed by physical
overmerging. High resolution hydrodynamical simulations are required to study
these issues further. If CDM is correct then the cluster galaxies must survive
the tidal field, perhaps due to baryonic inflow during elliptical galaxy
formation. Spirals can never exist near the cluster centers and the elliptical
galaxies there will have little remaining dark matter. This implies that the
morphology-density relation is set {\it before} the cluster forms, rather than
a subsequent transformation of disks to S0's by virtue of the cluster
environment.

Astrophysics