Here SU(3)$_C$ denotes the color interaction responsible for the strong force, SU(2)$_L$ the isospin coupling of left-handed fermions and U(1)$_Y$ the hypercharge group. The spontaneous breaking of the electroweak symmetry by the Higgs mechanism suggested the possibility of higher symmetries at yet higher scales that would also be spontaneously broken, providing strong and electroweak force unification at higher scales; these symmetries would also have to be spontaneously broken.
‡( ‡ It is usually and superficially stated that the gauge symmetry SU$(2)_L\times U(1)_Y$ is spontaneously broken; this, however cannot be, as dictated by Elitzur's theorem.
[1] Gauge symmetries must be broken explicitly by a gauge fixing term leaving only the global symmetry and then this remaining symmetry can be spontaneously broken. The modern viewpoint is that gauge symmetries are just a redundancy in the description of the theory on which expectation values of observables must not depend. The actual symmetry from which consecuences such as degeneracies in the spectrum, couplings or conserved currents appear is the true global symmetry. We will continue using "spontaneous symmetry breaking'' without specifying, though in the understanding that it is the global group, which is affected.)