  Microswimmers often exhibit surprising patterns due to the nonequilibrium
nature of their dynamics. Collectively, suspensions of microswimmers appear as
a liquid whose properties set it apart from its passive counterpart. To
understand the impact of hydrodynamic interactions on the basic statistical
features of a microswimmer's liquid, we investigate its structure by means of
the pair distribution function. We perform particle-based simulations of
microswimmers that include steric effects, shape anisotropy, and hydrodynamic
interactions. We find that hydrodynamic interactions considerably alter the
orientation-dependent pair distribution function compared to purely
excluded-volume models like active Brownian particles, and generally decrease
the structure of the liquid. Depletion regions are dominant at lower filling
fractions, while at larger filling fraction the microswimmer liquid develops a
stronger first shell of neighbors in specific directions, while losing
structure at larger distances. Our work is a first step towards a
statistico-mechanical treatment of the structure of microswimmer suspensions.
