Finite groups with the same join graph as a finite nilpotent group

Given a finite group $G,$ we denote by $\mathrm{\Delta }(G)$ the graph whose vertices are the proper subgroups of $G$ and in which two vertices $H$ and $K$ are joined by an edge if and only if $G=⟨H,K⟩\mathrm{.}$ We prove that if there exists a finite nilpotent group $X$ with $\mathrm{\Delta }(G)\cong \mathrm{\Delta }(X),$ then $G$ is supersoluble.