  Using published data, we have compiled the circular velocity (Vc)
distribution function (VDF) of galaxy satellites in the Local Group. We find
that within the volumes of radius of 570 kpc (400/h kpc for h=0.7) centered on
the Milky Way and Andromeda, the average VDF is roughly approximated as n(>Vc)~
45(Vc/10 km/s)^{-1} h^3 Mpc^{-3} for Vc in the range ~10-70 km/s. The observed
VDF is compared with results of high-resolution cosmological simulations. We
find that the VDF in models is very different from the observed one:
n(>Vc)~1200(Vc/10 km/s)^{-2.75}h^3 Mpc^{-3}. Cosmological models thus predict
that a halo of the size of our Galaxy should have about 50 dark matter
satellites with circular velocity >20 km/s and mass >3x10^8/h Msun within a 570
kpc radius. This number is significantly higher than the approximate dozen
satellites actually observed around our Galaxy. The observed and predicted VDFs
cross at ~50 km/s, indicating that the predicted abundance of satellites with
Vc> 50 km/s is in reasonably good agreement with observations. We conclude,
therefore, that unless a large fraction of the Local Group satellites has been
missed in observations, there is a dramatic discrepancy between observations
and hierarchical models, regardless of the model parameters. We discuss several
possible explanations for this discrepancy including identification of some
satellites with the High Velocity Clouds observed in the Local Group, and the
existence of dark satellites that failed to accrete gas and form stars due
either to the expulsion of gas in the supernovae-driven winds or to gas heating
by the intergalactic ionizing background. (Abridged)
