Semi-analytic models (SAMs) are currently one of the primary tools with which we model statistically significant ensembles of galaxies. The underlying physical prescriptions inherent to each SAM are, in many cases, different from one another. Several SAMs have been applied to the dark matter merger trees extracted from the Millennium Run, including those associated with the well-known Munich and Durham lineages. We compare the predicted luminosity distributions of galaxy groups using four publicly available SAMs, in order to explore a galactic environment in which the models have not been explored to the same degree as they have in the field or in rich clusters. We identify a characteristic 'wiggle' in the group galaxy luminosity function generated using the De Lucia et al. SAM, which is not present in the Durham-based models, consistent to some degree with observations. However, a comparison between conditional luminosity functions of groups between the models and observations suggests that neither model is a particularly good match. The luminosity function wiggle is interpreted as the result of the two-mode active galactic nucleus feedback implementation used in the Munich models, which itself results in flattened magnitude gap distribution. An associated analysis of the magnitude gap distribution between first- and second-ranked group galaxies shows that while the Durham models yield distributions with approximately equal luminosity first- and second-ranked galaxies, in agreement with observations, the De Lucia et al. models favour the scenario in which the second-ranked galaxy is approximately 1 mag fainter than the primary, especially when the dynamic range of the mock data is limited to 3 mag.