The method of projective symmetry groups has established itself as one of the most powerful frameworks for classifying different types of quantum spin liquids — zero-temperature strongly correlated phases which do no feature any broken symmetries. This framework exploits the additional SU(2) or U(1) gauge symmetry present in the fermionic or bosonic representation of spin operators, respectively, to distinguish different types of spin liquids which cannot be distinguished by local order parameters. With the field of three-dimensional frustrated quantum magnetism poised with the arrival of promising new candidate quantum spin liquid materials, and recent availability of inelastic neutron scattering on high-quality single crystals, the question of identifying their precise microscopic nature constitutes one of the most pressing problems. This talk will present the work on classifying fermionic mean-field Ansatze on some three-dimensional non-symmorphic lattices. Here, we show that the presence of screw symmetries and glide planes considerably simplifies the classification by excluding Ansatze with nontrivial gauge flux patterns — and discuss explicitly the case for the diamond lattice, the structure of many promising quantum materials. The talk will conclude with a discussion on how one can achieve a complete classification of chiral spin liquids — states breaking time-reversal together with a lattice symmetry while preserving their product, by exploiting a construction of the space group whereby only the index-2 subgroup symmetries become chiral, and mention its connection with black and white magnetic space groups.