  It is widely recognized that cold dark matter models predict abundant dark
matter substructure in halos of all sizes. Galaxy-galaxy lensing provides a
unique opportunity to directly measure the presence and the mass of such
substructures in clusters of galaxies. Here we present the mass function of
substructures obtained from lensing in massive HST cluster lenses, and compare
it with that obtained from high-resolution cosmological N-body simulations. We
find excellent agreement in the slope and amplitude in the mass range 10^{11} -
10^{12.5} solar masses probed by the observations, highlighting a significant
success of the CDM theory. At lower mass scales, the simulations predict a
large abundance of small substructures below our detection threshold with
galaxy-galaxy lensing, with many of them being plausibly associated with faint
cluster galaxies. Our results suggest that the CDM substructure abundance on
the scale of clusters is in good agreement with present observational data.
