{\mathcal{R}}_{q-4}^2 & {\mathcal{R}}_{q-4}^4
    \\ \hline\hline
    \mathrm{AI}     & 0     & {\mathbb{Z}}& 0         & {\mathbb{Z}}& {\mathbb{Z}}^2     & 0         & {\mathbb{Z}}^2     & {\mathbb{Z}}^4                     
    \\ \hline
    \mathrm{BDI}    & 0     & 0     & 0         & 0     & 0         & 0         & 0         & 0                                 
    \\ \hline
    \mathrm{D}      & 0     & 0     & 0         & 0     & 0         & 0         & 0         & 0                     
    \\ \hline
    \mathrm{DIII}   & {\mathbb{Z}}& 0     & {\mathbb{Z}}^2     & 0     & 0         & {\mathbb{Z}}^4     & 0         & 0                     
    \\ \hline
    \mathrm{AII}    & {\mathbb{Z}}_2 & {\mathbb{Z}}& {\mathbb{Z}}_2^2   & {\mathbb{Z}}& {\mathbb{Z}}^2     & {\mathbb{Z}}_2^4   & {\mathbb{Z}}^2     & {\mathbb{Z}}^4 
    \\ \hline
    \mathrm{CII}    & {\mathbb{Z}}_2 & {\mathbb{Z}}_2 & {\mathbb{Z}}_2^2   & {\mathbb{Z}}_2 & {\mathbb{Z}}_2^2   & {\mathbb{Z}}_2^4   & {\mathbb{Z}}_2^2   & {\mathbb{Z}}_2^4                                       
    \\ \hline
    \mathrm{C}      & 0     & {\mathbb{Z}}_2 & 0         & {\mathbb{Z}}_2 & {\mathbb{Z}}_2^2   & 0         & {\mathbb{Z}}_2^2   & {\mathbb{Z}}_2^4                       
    \\ \hline
    \mathrm{CI}     & {\mathbb{Z}}& 0     & {\mathbb{Z}}^2     & 0     & 0         & {\mathbb{Z}}^4     & 0         & 0                                     
    \end{array}$$

\[tab:o2\]

$$\begin{array}{l||c||c|c|c|c|c|c|c||}
    \multicolumn{2}{l||}{} &
    \parbox{\fgw}{\includegraphics[height=\fgb]{C4_3D.png}} & 
    \parbox{\fgw}{\includegraphics[height=\fgb]{S4_3D.png}} & 
    \parbox{\fgw}{\includegraphics[height=\fgb]{C4h_3D.png}} & 
    \parbox{\fgw}{\includegraphics[height=\fgb]{D4_3D.png}} & 
    \parbox{\fgw}{\includegraphics[height=\fgb]{C4v_3D.png}} & 
    \parbox{\fgw}{\includegraphics[height=\fgb]{D2d_3D.png}} & 
    \parbox{\fgw}{\includegraphics[height=\fgb]{D4h_3D.png}}
    \\ \hline\hline
    \mathrm{Sch\ddot{o}n.}  & C_1 & C_4 & S_4 & C_{4h} & D_4 & C_{4v} & D_{2d} & D_{4h}
    \\ \hline
    \mathrm{HM} & 1 & 4 & \bar 4 & 4/\mathrm{m} & 422 