  Given $p \in (0,1)$, we let $Q_p= Q_p^d$ be the random subgraph of the
$d$-dimensional hypercube $Q^d$ where edges are present independently with
probability $p$. It is well known that, as $d \rightarrow \infty$, if
$p>\frac12$ then with high probability $Q_p$ is connected; and if $p<\frac12$
then with high probability $Q_p$ consists of one giant component together with
many smaller components which form the `fragment'. Here we fix $p \in
(0,\frac12)$, and investigate the fragment, and how it sits inside the
hypercube. In particular we give asymptotic estimates for the mean numbers of
components in the fragment of each size, and describe their asymptotic
distributions and indeed their joint distribution, much extending earlier work
of Weber.
