  We perform a theoretical study of the leading pairing instabilities and the
associated superconducting gap functions within the spin-fluctuation mediated
pairing scenario in the presence of spin-orbit coupling (SOC). Focussing on
iron-based superconductors (FeSCs), our model Hamiltonian consists of a
realistic density functional theory (DFT)-derived ten-band hopping term,
spin-orbit coupling, and electron-electron interactions included via the
multi-orbital Hubbard-Hund Hamiltonian. We perform an extensive parameter sweep
and investigate different doping regimes including cases with only hole- or
only electron Fermi pockets. In addition, we explore two different
bandstructures: a rather generic band derived for LaFeAsO but known to
represent standard DFT-obtained bands for iron-based superconductors, and a
band specifically tailored for FeSe which exhibits a notably different Fermi
surface compared to the generic case. It is found that for the generic FeSCs
band, even rather large SOC has negligible effect on the resulting gap
structure; the $s_{+-}$ (pseudo-)spin singlet pairing remains strongly favored
and SOC does not lead to any SOC-characteristic gap oscillations along the
various Fermi surfaces. By contrast in the strongly hole-doped case featuring
only hole-pockets around the $\Gamma$-point, the leading solution is $d$-wave
pseudo-spin singlet, but with a notable SOC-driven tendency towards helical
pseudo-spin triplet pairing, which may even become the leading instability. In
the heavily electron doped situation, featuring only electron pockets centered
around the $M$-point, the leading superconducting instabilities are pseudo-spin
singlets with SOC favoring the $s$-wave case as compared to $d$-wave pairing,
which is the favored gap symmetry for vanishing SOC.
