The free streaming motion of dark matter particles imprints a cutoff in the matter power spectrum and set the scale of the smallest dark matter halo .
Recent cosmological N -body simulations have shown that the central density cusp is much steeper in haloes near the free streaming scale than in more massive haloes .
Here , we study the abundance and structure of subhaloes near the free streaming scale at very high redshift using a suite of unprecedentedly large cosmological N -body simulations , over a wide range of the host halo mass .
The subhalo abundance is suppressed strongly below the free streaming scale , but the ratio between the subhalo mass function in the cutoff and no cutoff simulations is well fitted by a single correction function regardless of the host halo mass and the redshift .
In subhaloes , the central slopes are considerably shallower than in field haloes , however , are still steeper than that of the NFW profile .
Contrary , the concentrations are significantly larger in subhaloes than haloes and depend on the subhalo mass .
We compare two methods to extrapolate the mass-concentration relation of haloes and subhaloes to z=0 and provide a new simple fitting function for subhaloes , based on a suite of large cosmological N -body simulations .
Finally , we estimate the annihilation boost factor of a Milky-Way sized halo to be between 1.8 and 6.2 .