  The author establishes some geometric criteria for a domain of ${\mathbb
R}^n$ with $n\ge2$ to support a
$(pn/(n-ps),\,p)_s$-Haj{\l}asz-Sobolev-Poincar\'e imbedding with $s\in(0,\,1]$
and $p\in(n/(n+s),\,n/s)$ or an $s$-Haj{\l}asz-Trudinger imbedding with
$s\in(0,\,1]$.
