On $\mathfrak{U}\Phi$-hypercentrally embedded subgroups of finite groups

A subgroup $M$ of a group $G$ is a modular subgroup in $G$ if the following conditions are true:

• $\langle X, M\cap Z\rangle=\langle X, M\rangle\cap Z$ for all $X\leqslant G$, $Z\leqslant G$ with $X\leqslant Z$, and
• $\langle M, Y\cap Z\rangle=\langle M, Y\rangle\cap Z$ for all $Y\leqslant G$, $Z\leqslant G$ with $M\leqslant Z$.

Conditions for $\mathfrak{U}\Phi$-embedding of hypercentral subgroups of finite groups with given modular primary subgroups are found.