  We study the strong gravitational lens statistics of triaxial cold dark
matter (CDM) halos occupied by central early-type galaxies. We calculate the
image separation distribution for double, cusp and quad configurations. The
ratios of image multiplicities at large separations are consistent with the
triaxial NFW model, and at small separations are consistent with the singular
isothermal ellipsoid (SIE) model. At all separations, the total lensing
probability is enhanced by adiabatic contraction. If no adiabatic contraction
is assumed, naked cusp configurations become dominant at approximately 2.5'',
which is inconsistent with the data. We also show that at small-to-moderate
separations, the image multiplicities depend sensitively on the alignment of
the shapes of the luminous and dark matter projected density profiles. In
constrast to other properties that affect these ratios, the degree of alignment
does not have a significant effect on the total lensing probability. These
correlations may therefore be constrained by comparing the theoretical image
separation distribution to a sufficiently large lens sample from future wide
and deep sky surveys such as Pan-Starrs, LSST and JDEM. Understanding the
correlations in the shapes of galaxies and their dark matter halo is important
for future weak lensing surveys.
