Human influenza viruses are grown in chicken eggs for vaccine production. Sequences of these egg-passaged viruses give us the opportunity to examine the evolution that occurs when these human viruses are subjected to the selective pressure of growing in chicken eggs, which (among other things) express different sialic acid receptors. The repetition of this evolutionary experiment in hundreds of strains over the past several decades allows us to identify mutations that adapt the virus to eggs and epistatic constraints that influence them. We analyze influenza A/H3N2, A/H1N1pdm, B/Vic and B/Yam sequences that were passaged in eggs and find that almost all of the adaptive mutations are located around the receptor-binding pocket of hemagglutinin (HA). We observe epistatic interactions both between adaptive mutations and between these mutations and the continually-evolving human influenza HA background sequence. Our results show that this background dependence is greatest for influenza A/H3N2, then A/H1N1pdm, with B/Vic and B/Yam showing little-to-no background dependence. We find that the total number of adaptive mutations and the length of adaptive walk also follow the same pattern between the influenza subtypes, suggesting that background dependence, number of adaptive mutations, and extent of additive versus epistatic interactions may all be related features of the fitness landscape.