  We investigate the statistics of flux anomalies in gravitationally lensed
QSOs as a function of dark matter halo properties such as substructure content
and halo ellipticity. We do this by creating a very large number of simulated
lenses with finite source sizes to compare with the data. After analyzing these
simulations, our conclusions are: 1) The finite size of the source is
important. The point source approximation commonly used can cause biased
results. 2) The widely used R_cusp statistic is sensitive to halo ellipticity
as well as the lens' substructure content. 3) For compact substructure, we find
new upper bounds on the amount of substructure from the the fact that no simple
single-galaxy lenses have been observed with a single source having more than
four well separated images. 4) The frequency of image flux anomalies is largely
dependent on the total surface mass density in substructures and the size--mass
relation for the substructures, and not on the range of substructure masses. 5)
Substructure models with the same size--mass relation produce similar numbers
of flux anomalies even when their internal mass profiles are different. 6) The
lack of high image multiplicity lenses puts a limit on a combination of the
substructures' size--mass relation, surface density and mass. 7) Substructures
with shallower mass profiles and/or larger sizes produce less extra images. 8)
The constraints that we are able to measure here with current data are roughly
consistent with \LambdaCDM Nbody simulations.
