To the theorem of K. Doerk

For a finite group $G$ and its maximal subgroup $M$ we proved that the generalized Fitting height of $G$ minus the generalized Fitting height of $M$ is not greater than $2$ and the non-$p$-soluble length of $G$ minus the non-$p$-soluble length of $M$ is not greater than $1$. We constructed a hereditary saturated formation $\mathfrak{F}$ such that $\{n_\sigma(G, \mathfrak{F})-n_\sigma(M, \mathfrak{F})\mid G$ is finite $\sigma$-soluble and $M$ is a maximal subgroup of $G\}=\mathbb{N}\cup\{0\}$ where $n_\sigma(G, \mathfrak{F})$ denotes the $\sigma$-nilpotent length of the $\mathfrak{F}$-residual of $G$. This construction shows the results about the generalized lengths of maximal subgroups published in Math. Nachr. (1994) and Mathematics (2020) are not correct.