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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{32}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_4^4.C_{24}$ | 1A | $1$ | $1$ | $C_4^4.C_{24}$ | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2A | $2$ | $1$ | $C_4^4.C_{24}$ | 1A | 2A | $ \left(\begin{array}{rr} 17 & 16 \\ 16 & 1 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2B | $2$ | $1$ | $C_4^4.C_{24}$ | 1A | 2B | $ \left(\begin{array}{rr} 17 & 0 \\ 0 & 17 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2C | $2$ | $1$ | $C_4^4.C_{24}$ | 1A | 2C | $ \left(\begin{array}{rr} 1 & 16 \\ 16 & 17 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2D | $2$ | $1$ | $C_4^4.C_{24}$ | 1A | 2D | $ \left(\begin{array}{rr} 31 & 0 \\ 0 & 31 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2E | $2$ | $1$ | $C_4^4.C_{24}$ | 1A | 2E | $ \left(\begin{array}{rr} 15 & 0 \\ 0 & 15 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2F | $2$ | $1$ | $C_4^4.C_{24}$ | 1A | 2F | $ \left(\begin{array}{rr} 15 & 16 \\ 16 & 31 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2G | $2$ | $1$ | $C_4^4.C_{24}$ | 1A | 2G | $ \left(\begin{array}{rr} 31 & 16 \\ 16 & 15 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2H | $2$ | $3$ | $C_4^4.C_8$ | 1A | 2H | $ \left(\begin{array}{rr} 31 & 16 \\ 16 & 31 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2I | $2$ | $3$ | $C_4^4.C_8$ | 1A | 2I | $ \left(\begin{array}{rr} 15 & 0 \\ 0 & 31 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2J | $2$ | $3$ | $C_4^4.C_8$ | 1A | 2J | $ \left(\begin{array}{rr} 15 & 16 \\ 16 & 15 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2K | $2$ | $3$ | $C_4^4.C_8$ | 1A | 2K | $ \left(\begin{array}{rr} 31 & 0 \\ 0 & 15 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2L | $2$ | $3$ | $C_4^4.C_8$ | 1A | 2L | $ \left(\begin{array}{rr} 1 & 16 \\ 16 & 1 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2M | $2$ | $3$ | $C_4^4.C_8$ | 1A | 2M | $ \left(\begin{array}{rr} 17 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2N | $2$ | $3$ | $C_4^4.C_8$ | 1A | 2N | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 17 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 2O | $2$ | $3$ | $C_4^4.C_8$ | 1A | 2O | $ \left(\begin{array}{rr} 17 & 16 \\ 16 & 17 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 3A1 | $3$ | $16$ | $C_2\times C_4\times C_{48}$ | 3A-1 | 1A | $ \left(\begin{array}{rr} 12 & 27 \\ 25 & 19 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 3A-1 | $3$ | $16$ | $C_2\times C_4\times C_{48}$ | 3A1 | 1A | $ \left(\begin{array}{rr} 19 & 5 \\ 7 & 12 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4A1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2B | 4A-1 | $ \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4A-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2B | 4A1 | $ \left(\begin{array}{rr} 25 & 0 \\ 0 & 25 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4B1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2B | 4B-1 | $ \left(\begin{array}{rr} 25 & 16 \\ 16 & 9 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4B-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2B | 4B1 | $ \left(\begin{array}{rr} 9 & 16 \\ 16 & 25 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4C1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2A | 4C-1 | $ \left(\begin{array}{rr} 23 & 24 \\ 8 & 15 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4C-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2A | 4C1 | $ \left(\begin{array}{rr} 7 & 8 \\ 24 & 15 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4D1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2A | 4D-1 | $ \left(\begin{array}{rr} 7 & 24 \\ 8 & 31 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4D-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2A | 4D1 | $ \left(\begin{array}{rr} 23 & 8 \\ 24 & 31 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4E1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2B | 4E-1 | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 7 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4E-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2B | 4E1 | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4F1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2C | 4F-1 | $ \left(\begin{array}{rr} 31 & 24 \\ 8 & 23 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4F-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2C | 4F1 | $ \left(\begin{array}{rr} 31 & 8 \\ 24 & 7 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4G1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2C | 4G-1 | $ \left(\begin{array}{rr} 15 & 8 \\ 24 & 23 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4G-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2C | 4G1 | $ \left(\begin{array}{rr} 15 & 24 \\ 8 & 7 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4H1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2A | 4H-1 | $ \left(\begin{array}{rr} 9 & 8 \\ 24 & 17 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4H-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2A | 4H1 | $ \left(\begin{array}{rr} 25 & 24 \\ 8 & 17 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4I1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2A | 4I-1 | $ \left(\begin{array}{rr} 25 & 8 \\ 24 & 1 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4I-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2A | 4I1 | $ \left(\begin{array}{rr} 9 & 24 \\ 8 & 1 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4J1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2B | 4J-1 | $ \left(\begin{array}{rr} 23 & 16 \\ 16 & 7 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4J-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2B | 4J1 | $ \left(\begin{array}{rr} 7 & 16 \\ 16 & 23 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4K1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2C | 4K-1 | $ \left(\begin{array}{rr} 1 & 8 \\ 24 & 9 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4K-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2C | 4K1 | $ \left(\begin{array}{rr} 1 & 24 \\ 8 & 25 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4L1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2C | 4L-1 | $ \left(\begin{array}{rr} 17 & 24 \\ 8 & 9 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4L-1 | $4$ | $1$ | $C_4^4.C_{24}$ | 2C | 4L1 | $ \left(\begin{array}{rr} 17 & 8 \\ 24 & 25 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4M1 | $4$ | $3$ | $C_4^4.C_8$ | 2A | 4M-1 | $ \left(\begin{array}{rr} 7 & 24 \\ 8 & 15 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4M-1 | $4$ | $3$ | $C_4^4.C_8$ | 2A | 4M1 | $ \left(\begin{array}{rr} 23 & 8 \\ 24 & 15 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4N1 | $4$ | $3$ | $C_4^4.C_8$ | 2A | 4N-1 | $ \left(\begin{array}{rr} 9 & 24 \\ 8 & 17 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4N-1 | $4$ | $3$ | $C_4^4.C_8$ | 2A | 4N1 | $ \left(\begin{array}{rr} 25 & 8 \\ 24 & 17 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4O1 | $4$ | $3$ | $C_4^4.C_8$ | 2A | 4O-1 | $ \left(\begin{array}{rr} 23 & 24 \\ 8 & 31 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4O-1 | $4$ | $3$ | $C_4^4.C_8$ | 2A | 4O1 | $ \left(\begin{array}{rr} 7 & 8 \\ 24 & 31 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4P1 | $4$ | $3$ | $C_4^4.C_8$ | 2B | 4P-1 | $ \left(\begin{array}{rr} 7 & 16 \\ 16 & 7 \end{array}\right) $ |
| $C_4^4.C_{24}$ | 4P-1 | $4$ | $3$ | $C_4^4.C_8$ | 2B | 4P1 | $ \left(\begin{array}{rr} 23 & 16 \\ 16 & 23 \end{array}\right) $ |