  Discovering a selection principle and the origin of flavor symmetries from an
ultraviolet completion of particle physics is an interesting open task. As a
step in this direction, we classify all possible flavor symmetries of 4D
massless spectra emerging from supersymmetric Abelian orbifold
compactifications, including roto-translations and non-factorizable compact
spaces, for generic moduli values. Although these symmetries are valid in all
string theories, we focus on the E8 x E8 heterotic string. We perform the
widest known search of E8 x E8 Abelian orbifold compactifications, yielding
over 121,000 models with MSSM-like features. About 75.4% of these models
exhibit flavor symmetries containing D4 factors and only nearly 1.2% have
Delta(54) factors. The remaining models are furnished with purely Abelian
flavor symmetries. Our findings suggest that, should particle phenomenology
arise from a heterotic orbifold, it could accommodate only one of these flavor
symmetries.
