  Strong gravitational lensing by groups or clusters of galaxies provides a
powerful technique to measure the dark matter properties of individual lens
galaxies. We study in detail the mass distribution of the satellite lens galaxy
in the group-scale lens SL2S J08544-0121 by modelling simultaneously the
spatially extended surface brightness distribution of the source galaxy and the
lens mass distribution using Markov chain Monte Carlo methods. In particular,
we measure the dark matter halo size of the satellite lens galaxy to be
6.0^{+2.9}_{-2.0} kpc with a fiducial velocity dispersion of 127^{+21}_{-12}
km/s. This is the first time the size of an individual galaxy halo in a galaxy
group has been measured using strong gravitational lensing without assumptions
of mass following light. We verify the robustness of our halo size measurement
using mock data resembling our lens system. Our measurement of the halo size is
compatible with the estimated tidal radius of the satellite galaxy, suggesting
that halos of galaxies in groups experience significant tidal stripping, a
process that has been previously observed on galaxies in clusters. Our mass
model of the satellite galaxy is elliptical with its major axis misaligned with
that of the light by ~50 deg. The major axis of the total matter distribution
is oriented more towards the centre of the host halo, exhibiting the radial
alignment found in N-body simulations and observational studies of satellite
galaxies. This misalignment between mass and light poses a significant
challenge to modified Newtonian dynamics.
