  We study models with fracton-like order based on $\mathbb{Z}_2$ lattice gauge
theories with subsystem symmetries in $d=2$ and $d=3$ spatial dimensions. The
$3d$ model reduces to the $3$-dimensional Toric Code when subsystem symmetry is
broken, giving an example of a subsystem symmetry enriched topological phase
(SSET). Although not topologically protected, its ground state degeneracy has
as leading contribution a term which grows exponentially with the square of the
linear size of the system. Also, there are completely mobile gauge charges
living along with immobile fractons. Our method shows that fracton-like phases
are also present in more usual lattice gauge theories. We calculate the
entanglement entropy $S_A$ of these models in a sub-region $A$ of the lattice
and show that it is equal to the logarithm of the ground state degeneracy of a
particular restriction of the full model to $A$.
