The predicted abundance and properties of the low-mass substructures embedded inside larger dark matter haloes differ sharply among alternative dark matter models. Too small to host galaxies themselves, these subhaloes may still be detected via gravitational lensing or via perturbations of the Milky Way's globular cluster streams and its stellar disc. Here, we use the APOSTLE cosmological simulations to predict the abundance and the spatial and velocity distributions of subhaloes in the range 10(6.5)-10(8.5)M(circle dot) inside haloes of mass similar to 10(12) M-circle dot in Lambda cold dark matter. Although these subhaloes are themselves devoid of baryons, we find that baryonic effects are important. Compared to corresponding dark matter only simulations, the loss of baryons from subhaloes and stronger tidal disruption due to the presence of baryons near the centre of the main halo reduce the number of subhaloes by similar to 1/4 to 1/2, independently of subhalo mass, but increasingly towards the host halo centre. We also find that subhaloes have non-Maxwellian orbital velocity distributions, with centrally rising velocity anisotropy and positive velocity bias that reduces the number of low-velocity subhaloes, particularly near the halo centre. We parametrize the predicted population of subhaloes in terms of mass, galactocentric distance and velocities. We discuss implications of our results for the prospects of detecting dark matter substructures and for possible inferences about the nature of dark matter.