Substructures, expected in cold dark matter haloes, have been proposed to explain the anomalous flux ratios in gravitational lenses. About 25% of lenses in the Cosmic Lens All-Sky Survey (CLASS) appear to have luminous satellites within ~ 5 kpc/h of the main lensing galaxies, which are usually at redshift z ~ 0.2-1. In this work we use the Millennium Simulation combined with galaxy catalogues from semi-analytical techniques to study the predicted frequency of such satellites in simulated haloes. The fraction of haloes that host bright satellites within the (projected) central regions is similar for red and blue hosts and is found to increase as a function of host halo mass and redshift. Specifically, at z = 1, about 11% of galaxy-sized haloes (with masses between 10^{12} M_sun/h and 10^{13} M_sun/h) host bright satellite galaxies within a projected radius of 5 kpc/h. This fraction increases to about 17% (25%) if we consider bright (all) satellites of only group-sized haloes (with masses between 10^{13} M_sun/h and 10^{14} M_sun/h). These results are roughly consistent with the fraction (~ 25%) of CLASS lensing galaxies observed to host luminous satellites. At z = 0, only ~ 3% of galaxy-sized haloes host bright satellite galaxies. The fraction rises to ~ 6%, (10%) if we consider bright (all) satellites of only group-sized haloes at z = 0. However, most of the satellites found in the inner regions are `orphan galaxies where the dark matter haloes have been completely stripped. Thus the agreement crucially depends on the true survival rate of these `orphan galaxies. We also discuss the effects of numerical resolution and cosmologies on our results.
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