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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{48}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_4.D_4^2$ | 1A | $1$ | $1$ | $C_4.D_4^2$ | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_4.D_4^2$ | 2A | $2$ | $1$ | $C_4.D_4^2$ | 1A | $ \left(\begin{array}{rr} 23 & 24 \\ 24 & 23 \end{array}\right) $ |
| $C_4.D_4^2$ | 2B | $2$ | $1$ | $C_4.D_4^2$ | 1A | $ \left(\begin{array}{rr} 1 & 24 \\ 24 & 1 \end{array}\right) $ |
| $C_4.D_4^2$ | 2C | $2$ | $1$ | $C_4.D_4^2$ | 1A | $ \left(\begin{array}{rr} 17 & 24 \\ 24 & 17 \end{array}\right) $ |
| $C_4.D_4^2$ | 2D | $2$ | $1$ | $C_4.D_4^2$ | 1A | $ \left(\begin{array}{rr} 7 & 24 \\ 24 & 7 \end{array}\right) $ |
| $C_4.D_4^2$ | 2E | $2$ | $1$ | $C_4.D_4^2$ | 1A | $ \left(\begin{array}{rr} 17 & 0 \\ 0 & 17 \end{array}\right) $ |
| $C_4.D_4^2$ | 2F | $2$ | $1$ | $C_4.D_4^2$ | 1A | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_4.D_4^2$ | 2G | $2$ | $1$ | $C_4.D_4^2$ | 1A | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 7 \end{array}\right) $ |
| $C_4.D_4^2$ | 2H | $2$ | $2$ | $C_2^4:D_4$ | 1A | $ \left(\begin{array}{rr} 41 & 24 \\ 24 & 25 \end{array}\right) $ |
| $C_4.D_4^2$ | 2I | $2$ | $2$ | $C_2^4:D_4$ | 1A | $ \left(\begin{array}{rr} 41 & 0 \\ 0 & 25 \end{array}\right) $ |
| $C_4.D_4^2$ | 2J | $2$ | $2$ | $C_2^4:D_4$ | 1A | $ \left(\begin{array}{rr} 47 & 0 \\ 0 & 31 \end{array}\right) $ |
| $C_4.D_4^2$ | 2K | $2$ | $2$ | $C_2^4:D_4$ | 1A | $ \left(\begin{array}{rr} 47 & 24 \\ 24 & 31 \end{array}\right) $ |
| $C_4.D_4^2$ | 2L | $2$ | $4$ | $C_2^4\times C_4$ | 1A | $ \left(\begin{array}{rr} 20 & 9 \\ 9 & 44 \end{array}\right) $ |
| $C_4.D_4^2$ | 2M | $2$ | $4$ | $C_2^4\times C_4$ | 1A | $ \left(\begin{array}{rr} 28 & 9 \\ 9 & 4 \end{array}\right) $ |
| $C_4.D_4^2$ | 2N | $2$ | $4$ | $D_4\times C_2^3$ | 1A | $ \left(\begin{array}{rr} 25 & 36 \\ 12 & 31 \end{array}\right) $ |
| $C_4.D_4^2$ | 2O | $2$ | $4$ | $C_2^4\times C_4$ | 1A | $ \left(\begin{array}{rr} 28 & 33 \\ 33 & 20 \end{array}\right) $ |
| $C_4.D_4^2$ | 2P | $2$ | $4$ | $D_4\times C_2^3$ | 1A | $ \left(\begin{array}{rr} 17 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_4.D_4^2$ | 2Q | $2$ | $4$ | $D_4\times C_2^3$ | 1A | $ \left(\begin{array}{rr} 41 & 12 \\ 36 & 47 \end{array}\right) $ |
| $C_4.D_4^2$ | 2R | $2$ | $4$ | $D_4\times C_2^3$ | 1A | $ \left(\begin{array}{rr} 33 & 8 \\ 32 & 33 \end{array}\right) $ |
| $C_4.D_4^2$ | 2S | $2$ | $4$ | $C_2^4\times C_4$ | 1A | $ \left(\begin{array}{rr} 4 & 33 \\ 33 & 44 \end{array}\right) $ |
| $C_4.D_4^2$ | 2T | $2$ | $4$ | $D_4\times C_2^3$ | 1A | $ \left(\begin{array}{rr} 1 & 24 \\ 24 & 7 \end{array}\right) $ |
| $C_4.D_4^2$ | 2U | $2$ | $4$ | $D_4\times C_2^3$ | 1A | $ \left(\begin{array}{rr} 39 & 32 \\ 8 & 39 \end{array}\right) $ |
| $C_4.D_4^2$ | 2V | $2$ | $8$ | $C_2^3\times C_4$ | 1A | $ \left(\begin{array}{rr} 24 & 17 \\ 17 & 24 \end{array}\right) $ |
| $C_4.D_4^2$ | 2W | $2$ | $8$ | $C_2^5$ | 1A | $ \left(\begin{array}{rr} 17 & 12 \\ 36 & 7 \end{array}\right) $ |
| $C_4.D_4^2$ | 2X | $2$ | $8$ | $C_2^5$ | 1A | $ \left(\begin{array}{rr} 25 & 24 \\ 24 & 47 \end{array}\right) $ |
| $C_4.D_4^2$ | 2Y | $2$ | $8$ | $C_2^5$ | 1A | $ \left(\begin{array}{rr} 33 & 16 \\ 40 & 39 \end{array}\right) $ |
| $C_4.D_4^2$ | 2Z | $2$ | $8$ | $C_2^5$ | 1A | $ \left(\begin{array}{rr} 9 & 44 \\ 44 & 15 \end{array}\right) $ |
| $C_4.D_4^2$ | 4A | $4$ | $2$ | $C_4^2:C_2^3$ | 2B | $ \left(\begin{array}{rr} 41 & 12 \\ 12 & 41 \end{array}\right) $ |
| $C_4.D_4^2$ | 4B | $4$ | $2$ | $C_4^2:C_2^3$ | 2B | $ \left(\begin{array}{rr} 25 & 36 \\ 36 & 25 \end{array}\right) $ |
| $C_4.D_4^2$ | 4C | $4$ | $2$ | $C_4^2:C_2^3$ | 2B | $ \left(\begin{array}{rr} 47 & 12 \\ 12 & 47 \end{array}\right) $ |
| $C_4.D_4^2$ | 4D | $4$ | $2$ | $C_4^2:C_2^3$ | 2B | $ \left(\begin{array}{rr} 31 & 36 \\ 36 & 31 \end{array}\right) $ |
| $C_4.D_4^2$ | 4E | $4$ | $4$ | $C_4:C_4^2$ | 2C | $ \left(\begin{array}{rr} 33 & 20 \\ 28 & 33 \end{array}\right) $ |
| $C_4.D_4^2$ | 4F | $4$ | $4$ | $C_2^2:C_4^2$ | 2D | $ \left(\begin{array}{rr} 32 & 39 \\ 33 & 8 \end{array}\right) $ |
| $C_4.D_4^2$ | 4G | $4$ | $4$ | $C_4^2:C_2^2$ | 2E | $ \left(\begin{array}{rr} 9 & 16 \\ 8 & 9 \end{array}\right) $ |
| $C_4.D_4^2$ | 4H | $4$ | $4$ | $C_4:C_4^2$ | 2C | $ \left(\begin{array}{rr} 39 & 20 \\ 28 & 39 \end{array}\right) $ |
| $C_4.D_4^2$ | 4I | $4$ | $4$ | $C_2^2:C_4^2$ | 2D | $ \left(\begin{array}{rr} 4 & 15 \\ 9 & 4 \end{array}\right) $ |
| $C_4.D_4^2$ | 4J | $4$ | $4$ | $C_2^2:C_4^2$ | 2D | $ \left(\begin{array}{rr} 40 & 39 \\ 33 & 16 \end{array}\right) $ |
| $C_4.D_4^2$ | 4K | $4$ | $4$ | $C_2^4\times C_4$ | 2B | $ \left(\begin{array}{rr} 16 & 33 \\ 33 & 40 \end{array}\right) $ |
| $C_4.D_4^2$ | 4L | $4$ | $4$ | $C_2^4\times C_4$ | 2B | $ \left(\begin{array}{rr} 1 & 36 \\ 36 & 17 \end{array}\right) $ |
| $C_4.D_4^2$ | 4M | $4$ | $4$ | $C_4^2:C_2^2$ | 2B | $ \left(\begin{array}{rr} 9 & 28 \\ 4 & 9 \end{array}\right) $ |
| $C_4.D_4^2$ | 4N | $4$ | $4$ | $C_4^2:C_2^2$ | 2E | $ \left(\begin{array}{rr} 15 & 40 \\ 32 & 15 \end{array}\right) $ |
| $C_4.D_4^2$ | 4O | $4$ | $4$ | $C_2^2:C_4^2$ | 2D | $ \left(\begin{array}{rr} 44 & 15 \\ 9 & 44 \end{array}\right) $ |
| $C_4.D_4^2$ | 4P | $4$ | $4$ | $C_2^4\times C_4$ | 2B | $ \left(\begin{array}{rr} 8 & 33 \\ 33 & 32 \end{array}\right) $ |
| $C_4.D_4^2$ | 4Q | $4$ | $4$ | $C_2^4\times C_4$ | 2B | $ \left(\begin{array}{rr} 7 & 36 \\ 36 & 23 \end{array}\right) $ |
| $C_4.D_4^2$ | 4R | $4$ | $4$ | $C_4^2:C_2^2$ | 2B | $ \left(\begin{array}{rr} 15 & 28 \\ 4 & 15 \end{array}\right) $ |
| $C_4.D_4^2$ | 4S1 | $4$ | $4$ | $C_2^4\times C_4$ | 2B | $ \left(\begin{array}{rr} 8 & 9 \\ 9 & 16 \end{array}\right) $ |
| $C_4.D_4^2$ | 4S-1 | $4$ | $4$ | $C_2^4\times C_4$ | 2B | $ \left(\begin{array}{rr} 32 & 9 \\ 9 & 40 \end{array}\right) $ |
| $C_4.D_4^2$ | 4T | $4$ | $8$ | $C_2\times C_4^2$ | 2F | $ \left(\begin{array}{rr} 36 & 7 \\ 17 & 12 \end{array}\right) $ |
| $C_4.D_4^2$ | 4U | $4$ | $8$ | $C_2\times C_4^2$ | 2E | $ \left(\begin{array}{rr} 0 & 25 \\ 41 & 0 \end{array}\right) $ |
| $C_4.D_4^2$ | 4V | $4$ | $8$ | $C_2^3\times C_4$ | 2D | $ \left(\begin{array}{rr} 40 & 15 \\ 9 & 32 \end{array}\right) $ |