  Motivated by Burillo, Cleary and Roever's summary on obstructions of
subgroups of Thompson's group $V,$ we explored the higher dimensional version
of the groups, Brin-Thompson groups $nV$ and $SV,$ a class of infinite
dimensional Brin-Thompson groups and an easy class of the twisted version of
the Brin-Thompson groups $SV_G$ with some certain condition. We found that they
have similar obstructions as Thompson's group $V$ on the torsion subgroups and
a selection of the interesting Baumslag-Solitor groups are excluded as the
subgroups of $SV$ and $SV_G.$ We also discuss a little on the group
$\mathscr{S}V,$ an even larger class relaxing some of the "finiteness
condition" and observe that some of the restrictions on subgroups disappear.
