  We perform a projective symmetry group (PSG) classification of symmetric
quantum spin liquids with different gauge groups on the square-octagon lattice.
Employing the Abrikosov fermion representation for spin-$1/2$, we obtain $32$
$SU(2)$, $1808$ $U(1)$ and $384$ $\mathbb{Z}_{2}$ algebraic PSGs. Constraining
ourselves to mean-field parton ans\"atze with short-range amplitudes, the
classification reduces to a limited number, with 4 $SU(2)$, 24 $U(1)$ and 36
$\mathbb{Z}_{2}$, distinct phases. We discuss their ground state properties and
spinon dispersions within a self-consistent treatment of the Heisenberg
Hamiltonian with frustrating couplings.
