The principal affine W-algebras enjoy the Feigin-Frenkel duality and the Goddard-Kent-Olive construction if associated with simply-laced Lie algebras. Recently, Gaiotto and Rapcak proposed a generalization of this triality (or dualities) among W-superalgebras（and their affine cosets) by using the 4-dimensional N=4 super Yang-Mills theories. In this talk, we prove the Feigin-Frenkel type duality between the Heisenberg cosets of the subregular W-algebras and the principal W-superalgebras for A and B-types. This is a joint work with T. Creutzig and N. Genra.

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