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We explore the radial distribution of satellite galaxies in groups in the Galaxy and Mass Assembly (GAMA) survey and the IllustrisTNG simulations. Considering groups with masses $12.0 \leq \log_{10} (\mathcal{M}_h / h^{-1} \mathrm{M}_{\odot}) < 14.8$ at $z<0.267$, we find a good agreement between GAMA and a sample of TNG300 groups and galaxies designed to match the GAMA selection. Both display a flat profile in the centre of groups, followed by a decline that becomes steeper towards the group edge, and normalised profiles show no dependence on group mass. Using matched satellites from TNG and dark matter-only TNG-Dark runs we investigate the effect of baryons on satellite radial location. At $z=0$, we find that the matched subhaloes from the TNG-Dark runs display a much flatter radial profile: namely, satellites selected above a minimum stellar mass exhibit both smaller halo-centric distances and longer survival times in the full-physics simulations compared to their dark-matter only analogues. We then divide the TNG satellites into those which possess TNG-Dark counterparts and those which do not, and develop models for the radial positions of each. We find the satellites with TNG-Dark counterparts are displaced towards the halo centre in the full-physics simulations, and this difference has a power-law behaviour with radius. For the `orphan' galaxies without TNG-Dark counterparts, we consider the shape of their radial distribution and provide a model for their motion over time, which can be used to improve the treatment of satellite galaxies in semi-analytic and semi-empirical models of galaxy formation.