  We study the interplay of nematic and superconducting order in the
two-dimensional Hubbard model and show that they can coexist, especially when
superconductivity is not the energetically dominant phase. Due to a breaking of
the $C_4$ symmetry, the coexisting phase inherently contains admixture of the
$s$-wave pairing components. As a result, the superconducting gap exhibits very
non-standard features including changed nodal directions. Our results also show
that in the optimally doped regime the superconducting phase is typically
unstable towards developing nematicity (breaking of the $C_4$ symmetry). This
has implications for the cuprate high-$T_c$ superconductors, for which in this
regime the so-called intertwined orders have recently been observed. Namely,
the coexisting phase may be viewed as a precursor to such more involved
patterns of symmetry breaking.
