  We prove a superposition principle for Riesz potentials of nonnegative
continuous functions on Lie groups of Heisenberg type. More precisely, we show
that the Riesz potential $$ R_\alpha(\rho)(g) = \int_{\G} N(g^{-1}
g')^{\alpha-Q} \rho(g') dg', \qquad 0<\alpha<Q, $$ of a nonnegative function
$\rho\in C_0(\G)$ on a group $\G$ of Heisenberg type is necessarily either
$p$-subharmonic or $p$-superharmonic, depending on $p$ and $\alpha$. Here $N$
denotes the non-isotropic homogeneous norm on such groups, as introduced by
Kaplan. This result extends to a wide class of nonabelian stratified Lie groups
a recent remarkable superposition result of Lindqvist and Manfredi.
