I'm aware that the representatives of conjugacy classes of involutions of $G = PGL(4,\mathbb{C})$ which have a conjugate in a fixed maximal torus of $G$ are $\begin{bmatrix} -1 & 0 & 0\\ 0 & -1 & 0 \\ 0 & 0 & I_2 \end{bmatrix}, \begin{bmatrix} I_3 & 0 \\ 0 & -1 \end{bmatrix}$.
What are the representatives of conjugacy classes of involutions of $H = PSL(4,\mathbb{C})$ which have a conjugate in a fixed maximal torus of $H$. I thought at first they were $\begin{bmatrix} -1 & 0 & 0\\ 0 & -1 & 0 \\ 0 & 0 & I_2 \end{bmatrix}, \begin{bmatrix} 1 & 0 & 0 & 0\\ 0 & -1 &0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & -1 \end{bmatrix}$. But when I try to find the conjugacy classes of elementary abelian $2$-subgroups of rank $3$ of $H$, it didn't add up. And I got totally stuck for a long time now. I'm being silly here as this should not be too hard.. If I could get some direction or hint, I'd appreciate it!