  We show that unconventional nematic superconductors with multi-component
order parameter in lattices with three-fold and six-fold rotational symmetries
support a charge-$4e$ vestigial superconducting phase above $T_c$. The
charge-$4e$ state, which is a condensate of four-electron bound states that
preserve the rotational symmetry of the lattice, is nearly degenerate with a
competing vestigial nematic state, which is non-superconducting and breaks the
rotational symmetry. This robust result is the consequence of a hidden discrete
symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge
sector and in the crystalline sector of the symmetry group. We argue that
random strain generally favors the charge-$4e$ state over the nematic phase, as
it acts as a random-mass to the former but as a random-field to the latter.
Thus, we propose that two-dimensional inhomogeneous systems displaying nematic
superconductivity, such as twisted bilayer graphene, provide a promising
platform to realize the elusive charge-$4e$ superconducting phase.
