1.  subgroup(n = noun.group) - a distinct and often subordinate group within a group;
is a kind of group, grouping
has particulars: bench

2.  subgroup(n = noun.cognition) - (mathematics) a subset (that is not empty) of a mathematical group;
is a kind of group, mathematical group

   A subdivision of a group, as of animals. Darwin. [1913 Webster]

subgroup, n. Math. etc. a subset of a group.