We estimate the HI mass function (HIMF) of galaxies in groups based on thousands of ALFALFA (Arecibo Legacy Fast ALFA survey) HI detections within the galaxy groups of four widely used SDSS (Sloan Digital Sky Survey) groups catalogues. Although differences between the catalogues mean that there is no one definitive group galaxy HIMF, in general we find that the low-mass slope is flat, in agreement with studies based on small samples of individual groups, and that the 'knee' mass is slightly higher than that of the global HIMF of the full ALFALFA sample. We find that the observed fraction of ALFALFA galaxies in groups is approximately 22 per cent. These group galaxies were removed from the full ALFALFA source catalogue to calculate the field HIMF using the remaining galaxies. Comparison between the field and group HIMFs reveals that group galaxies make only a small contribution to the global HIMF as most ALFALFA galaxies are in the field, but beyond the HIMF 'knee' group galaxies dominate. Finally we attempt to separate the group galaxy HIMF into bins of group halo mass, but find that too few low-mass galaxies are detected in the most massive groups to tightly constrain the slope, owing to the rarity of such groups in the nearby Universe where low-mass galaxies are detectable with existing HI surveys.