We examine the fraction of early-type (and spiral) galaxies found in groups and clusters of galaxies as a function of dark matter halo mass. We use morphological classifications from the Galaxy Zoo project matched to halo masses from both the C4 cluster catalogue and the Yang et al. group catalogue. We find that the fraction of early-type (or spiral) galaxies remains constant (changing by less than 10 per cent) over three orders of magnitude in halo mass (13 ≤ log MH/h−1 M⊙≤ 15.8). This result is insensitive to our choice of halo mass measure, from velocity dispersions or summed optical luminosity. Furthermore, we consider the morphology–halo mass relations in bins of galaxy stellar mass M*, and find that while the trend of constant fraction remains unchanged, the early-type fraction amongst the most massive galaxies (11 ≤ log M*/h−1 M⊙≤ 12) is a factor of 3 greater than lower mass galaxies (10 ≤ log M*/h−1 M⊙≤ 10.7). We compare our observational results with those of simulations presented in De Lucia et al., as well as previous observational analyses and semi-analytic bulge (or disc) dominated galaxies from the Millennium Simulation. We find the simulations recover similar trends as observed, but may overpredict the abundances of the most massive bulge-dominated (early-type) galaxies. Our results suggest that most morphological transformation is happening on the group scale before groups merge into massive clusters. However, we show that within each halo a morphology–density relation remains: it is summing the total fraction to a self-similar scaled radius which results in a flat morphology–halo mass relationship.