We have measured the orbital parameters of seven close binaries, including six new objects, in a radial velocity survey of 38 objects comprising a hot subdwarf star with orbital periods ranging from ∼0.17 to 3 d. One new system, GALEX J2205−3141, shows reflection on an M dwarf companion. Three other objects show significant short-period variations, but their orbital parameters could not be constrained. Two systems comprising a hot subdwarf paired with a bright main-sequence/giant companion display short-period photometric variations possibly due to irradiation or stellar activity and are also short-period candidates. All except two candidates were drawn from a selection of subluminous stars in the Galaxy Evolution Explorer ultraviolet sky survey. Our new identifications also include a low-mass subdwarf B star and likely progenitor of a low-mass white dwarf (GALEX J0805−1058) paired with an unseen, possibly substellar, companion. The mass functions of the newly identified binaries imply minimum secondary masses ranging from 0.03 to 0.39 M⊙. Photometric time series suggest that, apart from GALEX J0805−1058 and J2205−3141, the companions are most likely white dwarfs. We update the binary population statistics: close to 40 per cent of hot subdwarfs have a companion. Also, we found that the secondary mass distribution shows a low-mass peak attributed to late-type dwarfs, and a higher mass peak and tail distribution attributed to white dwarfs and a few spectroscopic composites. Also, we found that the population kinematics imply an old age and include a few likely halo population members.