Context : 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 ^ { -1 } } .
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 \sim 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 .

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