line graph characterization of the order supergraph of a finite group

The power graph ${mathcal{p}(g)}$ is the simple undirected graph with group elements as a vertex set and two elements are adjacent if one of them is a power of the other. the order supergraph ${mathcal{s}(g)}$ of the power graph ${mathcal{p}(g)}$ is the simple undirected graph with vertex set $g$ in which two vertices $x$ and $y$ are adjacent if $o(x)vert o(y)$ or $o(y)vert o(x)$. in this paper, we classify all the finite groups $g$ such that the order supergraph ${mathcal{s}(g)}$ is the line graph of some graph. moreover, we characterize finite groups whose order supergraphs are the complement of line graphs.