  We construct a moduli space for the connected subgroups of an algebraic group
and the corresponding universal family. Morphisms from an algebraic variety to
this moduli space correspond to flat families of connected algebraic subgroups
parametrised by this variety. This moduli space is obtained by gluing together
infinitely many irreducible projective varieties of bounded dimension along
closed subvarieties.
  Regarding families of non-connected subgroups of an algebraic group, we show
that, given sich a family, the corresponding family of identity components is
an irreducible component of the former, and the quotient of a family of groups
group by the family of their identity components exists.
