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This paper is devoted to define a characteristic homomorphism for a subfoliation $(F_1,F_2)$ and to study its relation with the usual characteristic homomorphism for each foliation (as defined by Bott). Moreover, two applications are given: 1) the Yamato’s 2-codimensional foliation is shown to be no homotopic to $F_2$ in a (1,2)-codimensional subfoliation; 2) an obstruction to the existence of $d$ everywhere independent and transverse infinitesimal transformations of a foliation $F_2$ is obtained, when $F_2$ and these...