  In the past years several authors studied the abundance of satellites around
galaxies in order to better estimate the halo masses of host galaxies. To
investigate this connection, we analyze galaxies with
$M_\mathrm{star}\geq\,10^{10}\,M_{\odot}$ from the hydrodynamical cosmological
simulation Magneticum. We find that the satellite fraction of centrals is
independent of their morphology. With the exception of very massive galaxies at
low redshift, our results do not support the assumption that the dark matter
(DM) haloes of spheroidal galaxies are significantly more massive than those of
disc galaxies at fixed $M_\mathrm{star}$. We show that the
density-morphology-relation starts to build up at $z\sim2$ and is independent
of the star-formation properties of central galaxies. We conclude that
environmental quenching is more important for satellites than for centrals. Our
simulations indicate that conformity is already in place at $z=2$, where
formation redshift and current star-formation rate (SFR) of central and
satellite galaxies correlate. Centrals with low SFRs have formed earlier (at
fixed $M_\mathrm{star}$) while centrals with high SFR formed later, with
typical formation redshifts well in agreement with observations. However, we
confirm the recent observations that the apparent number of satellites of
spheroidal galaxies is significantly larger than for disc galaxies. This
difference completely originates from the inclusion of companion galaxies, i.e.
galaxies that do not sit in the potential minimum of a DM halo. Thus, due to
the density-morphological-relation the number of satellites is not a good
tracer for the halo mass, unless samples are restricted to the central galaxies
of DM haloes.
