Lifts of Brauer characters in characteristic two, II

In 2007, J. P. Cossey conjectured that if $G$ is a finite $p$-solvable group and $\phi$ is an irreducible Brauer character of $G$ with vertex $Q$, then the number of lifts of $\phi$ is at most $\mathrm{\mid }Q:Q^{\mathrm{\prime }}\mathrm{\mid }$. In this paper we revisited Cossey’s conjecture for $p=2$ from the perspective of Navarro vertices and obtained a new way to count the number of lifts of $\phi$. Some applications were given.