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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{8}\Z)$.

Group Label Order Size Centralizer Powers Representative
2P
$C_2^3.C_4^2$ 1A $1$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 2A $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 5 & 0 \\ 4 & 5 \end{array}\right) $
$C_2^3.C_4^2$ 2B $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 3 & 4 \\ 4 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 2C $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 7 & 4 \\ 0 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 2D $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 5 & 0 \\ 0 & 5 \end{array}\right) $
$C_2^3.C_4^2$ 2E $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 1 & 4 \\ 4 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 2F $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 3 & 4 \\ 0 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 2G $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 7 & 4 \\ 0 & 7 \end{array}\right) $
$C_2^3.C_4^2$ 2H $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 3 & 0 \\ 4 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 2I $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 7 & 4 \\ 4 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 2J $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 3 & 4 \\ 4 & 7 \end{array}\right) $
$C_2^3.C_4^2$ 2K $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 2L $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 5 & 0 \\ 4 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 2M $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 5 & 4 \\ 0 & 5 \end{array}\right) $
$C_2^3.C_4^2$ 2N $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 7 & 4 \\ 4 & 7 \end{array}\right) $
$C_2^3.C_4^2$ 2O $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 3 & 0 \\ 0 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 2P $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 7 \end{array}\right) $
$C_2^3.C_4^2$ 2Q $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 3 & 4 \\ 0 & 7 \end{array}\right) $
$C_2^3.C_4^2$ 2R $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 7 & 0 \\ 4 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 2S $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 3 & 0 \\ 4 & 7 \end{array}\right) $
$C_2^3.C_4^2$ 2T $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 5 & 0 \\ 0 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 2U $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 5 \end{array}\right) $
$C_2^3.C_4^2$ 2V $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 5 & 4 \\ 4 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 2W $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 7 & 0 \\ 4 & 7 \end{array}\right) $
$C_2^3.C_4^2$ 2X $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 3 & 0 \\ 0 & 7 \end{array}\right) $
$C_2^3.C_4^2$ 2Y $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 1 & 0 \\ 4 & 5 \end{array}\right) $
$C_2^3.C_4^2$ 2Z $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 5 & 4 \\ 0 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 2AA $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 1 & 4 \\ 0 & 5 \end{array}\right) $
$C_2^3.C_4^2$ 2AB $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 1 & 4 \\ 4 & 5 \end{array}\right) $
$C_2^3.C_4^2$ 2AC $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 1 & 0 \\ 4 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 2AD $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 1 & 4 \\ 0 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 2AE $2$ $1$ $C_2^3.C_4^2$ 1A $ \left(\begin{array}{rr} 5 & 4 \\ 4 & 5 \end{array}\right) $
$C_2^3.C_4^2$ 4A1 $4$ $2$ $C_2^4\times C_4$ 2AC $ \left(\begin{array}{rr} 5 & 4 \\ 6 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 4A-1 $4$ $2$ $C_2^4\times C_4$ 2AC $ \left(\begin{array}{rr} 5 & 4 \\ 2 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 4B1 $4$ $2$ $C_2^4\times C_4$ 2AD $ \left(\begin{array}{rr} 3 & 2 \\ 4 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4B-1 $4$ $2$ $C_2^4\times C_4$ 2AD $ \left(\begin{array}{rr} 3 & 6 \\ 4 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4C1 $4$ $2$ $C_2^4\times C_4$ 2AC $ \left(\begin{array}{rr} 5 & 0 \\ 6 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 4C-1 $4$ $2$ $C_2^4\times C_4$ 2AC $ \left(\begin{array}{rr} 5 & 0 \\ 2 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 4D1 $4$ $2$ $C_2^4\times C_4$ 2AD $ \left(\begin{array}{rr} 3 & 2 \\ 0 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4D-1 $4$ $2$ $C_2^4\times C_4$ 2AD $ \left(\begin{array}{rr} 3 & 6 \\ 0 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4E1 $4$ $2$ $C_2^4\times C_4$ 2AE $ \left(\begin{array}{rr} 3 & 6 \\ 6 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4E-1 $4$ $2$ $C_2^4\times C_4$ 2AE $ \left(\begin{array}{rr} 3 & 2 \\ 2 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4F1 $4$ $2$ $C_2^4\times C_4$ 2AC $ \left(\begin{array}{rr} 7 & 0 \\ 6 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4F-1 $4$ $2$ $C_2^4\times C_4$ 2AC $ \left(\begin{array}{rr} 7 & 0 \\ 2 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4G1 $4$ $2$ $C_2^4\times C_4$ 2AD $ \left(\begin{array}{rr} 1 & 2 \\ 0 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 4G-1 $4$ $2$ $C_2^4\times C_4$ 2AD $ \left(\begin{array}{rr} 1 & 6 \\ 0 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 4H1 $4$ $2$ $C_2^4\times C_4$ 2AC $ \left(\begin{array}{rr} 3 & 0 \\ 2 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4H-1 $4$ $2$ $C_2^4\times C_4$ 2AC $ \left(\begin{array}{rr} 3 & 0 \\ 6 & 3 \end{array}\right) $
$C_2^3.C_4^2$ 4I1 $4$ $2$ $C_2^4\times C_4$ 2AD $ \left(\begin{array}{rr} 5 & 2 \\ 4 & 1 \end{array}\right) $
$C_2^3.C_4^2$ 4I-1 $4$ $2$ $C_2^4\times C_4$ 2AD $ \left(\begin{array}{rr} 5 & 6 \\ 4 & 1 \end{array}\right) $
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