Modular symmetry and non-Abelian discrete flavor symmetries in string compactification

We study the modular symmetry in magnetized D-brane models on T-2. Non-Abelian flavor symmetry D-4 in the model with magnetic flux M = 2 ( in a certain unit) is a subgroup of the modular symmetry. We also study the modular symmetry in heterotic orbifold models. The T-2=Z(4) orbifold model has the same modular symmetry as the magnetized brane model with M = 2, and its flavor symmetry D-4 is a subgroup of the modular symmetry