  As an extension of the Standard Model (SM), the 3HDM (Three-Higgs-Doublet
Model) defines additional relationships among the fermions. In the visible
leptonic Yukawa sector of a minimal 3HDM, we determine and classify the
existing flavor symmetries under discrete non-abelian groups up to order 1032.
The three Higgs doublets form a flavor triplet, and the admission of unfaithful
representations enriches the set of candidate flavor transformations greatly.
The many existing symmetries give rise (after EWSB) to a large number of
inequivalent mass matrices that imply lepton properties, which in turn are
evaluated against experimental data. In the 3HDM the mass hierarchy of the
charged leptons leads to a too small $\Delta m^2_{21} / \Delta m^2_{32}$ ratio
of the neutrinos. More generally, it is proven that the lepton mass matrices
implied by discrete flavor symmetries are in disagreement with the observed
data for all groups investigated, both when it is assumed that the neutrinos
have the Dirac or Majorana nature.
