  The hierarchical growth of dark matter haloes, in which galaxies are hosted,
has been studied and modeled using various approaches. In this paper we use a
modified version the Sheth & Lemson algorithm for a $\mathrm{\Lambda}$ cold
dark matter power spectrum, and model the growth of a Milky-Way sized halo with
microsolar mass resolution, corresponding to the typical Jeans mass for a dark
matter Weakly Interacting Massive Particle with mass of 100 GeV. We then
compute the \emph{unevolved} subhalo mass function and build-up a Milky-Way
halo placing and evolving its satellites. This subhalo population is used to
study the $\gamma$-ray emission from dark matter annihilation. In this case,
the subhaloes which populate the host halo have been computed considering only
progenitor haloes accreted by the main branch of the tree, so as to correctly
treat the embedding of sub-subhaloes inside subhaloes. Each subhalo will indeed
host atthe present-time sub-subhaloes accreted when it was an isolated system.
In order to compute the sub-subhalo population of a Milky-Way dwarf galaxy,
like Draco, and to study its $\gamma$-ray emission, we first estimate the Draco
virial mass at merging redshift $z_m$ and then we run the merger tree from
$z_m$ following the halo down to the dark matter Jeans mass. We then study the
effect on the Fermi-LAT (GLAST) detectability for both subhaloes in the
Milky-Way and in Draco, and we show how subhaloes cannot be responsible for the
boost factor needed for detection.
