  We investigate the spatial distribution of galactic satellites in high
resolution simulations of structure formation in the LCDM model: the Aquarius
dark matter simulations of individual halos and the Millennium II simulation of
a large cosmological volume. To relate the simulations to observations of the
Milky Way we use two alternative models to populate dark halos with "visible"
galaxies: a semi-analytic model of galaxy formation and an abundance matching
technique. We find that the radial density profile of massive satellites
roughly follows that of the dark matter halo (unlike the distribution of dark
matter subhalos). Furthermore, our two galaxy formation models give results
consistent with the observed profile of the 11 classical satellites of the
Milky Way. Our simulations predict that larger, fainter samples of satellites
should still retain this profile at least up to samples of 100 satellites. The
angular distribution of the classical satellites of the Milky Way is known to
be highly anisotropic. Depending on the exact measure of flattening, 5--10 per
cent of satellite systems in our simulations are as flat as the Milky Way's and
this fraction does not change when we correct for possible obscuration of
satellites by the Galactic disk. A moderate flattening of satellite systems is
a general property of LCDM, best understood as the consequence of preferential
accretion along filaments of the cosmic web. Accretion of a single rich group
of satellites can enhance the flattening due to such anisotropic accretion. We
verify that a typical Milky Way-mass CDM halo does not acquire its 11 most
massive satellites from a small number of rich groups. Single--group accretion
becomes more likely for less massive satellites. Our model predictions should
be testable with forthcoming studies of satellite systems in other galaxies and
surveys of fainter satellites in the Milky Way.
