| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 24T1932 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $D_{6}$, $S_4\times C_2$ x 2, $C_2^2\times S_4$, $\GL(2,\mathbb{Z}/4)$ x 2 |
24T1932 x 11, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 8, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T1974 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $S_3$, $S_4\times C_2$ x 2, $C_2\times S_4$, $\GL(2,\mathbb{Z}/4)$ x 2 |
24T1932 x 12, 24T1974 x 11, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 8, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T2204 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $S_3$, $\GL(2,\mathbb{Z}/4)$ x 2, $C_2^3:S_4$ |
24T1932 x 12, 24T1974 x 12, 24T2204 x 23, 24T2469 x 24, 24T2470 x 48, 24T2471 x 8, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T2469 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $S_3$, $\GL(2,\mathbb{Z}/4)$, $C_2^3:S_4$, $C_2\wr S_3$ |
24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 23, 24T2470 x 48, 24T2471 x 8, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T2470 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $S_3$, $S_4\times C_2$ x 2, $C_2\times S_4$, $\GL(2,\mathbb{Z}/4)$, $C_2\wr S_3$ |
24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 47, 24T2471 x 8, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T2471 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $S_3$, $C_2^3:S_4$, $C_2\wr S_3$ x 2 |
24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 7, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T2472 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $S_3$, $S_4\times C_2$ x 2, $C_2\times S_4$, $C_2\wr S_3$ x 2 |
24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 8, 24T2472 x 11, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T2475 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $D_6$, $C_2\wr S_3$ x 2 |
24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 8, 24T2472 x 12, 24T2475 x 3, 24T2476 x 8, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T2476 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $D_{4}$, $S_3$, $(C_6\times C_2):C_2$, $C_2^3:S_4$, $C_2\wr S_3$ |
24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 8, 24T2472 x 12, 24T2475 x 4, 24T2476 x 7, 24T2498 x 48, 24T2525 x 24, 32T34970 x 4 |
| 24T2498 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$S_3$, $S_4\times C_2$ x 3, $\GL(2,\mathbb{Z}/4)$, $C_2^2\wr S_3$, $C_2\wr S_3$ |
24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 8, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 47, 24T2525 x 24, 32T34970 x 4 |
| 24T2525 |
$C_2^3:\GL(2,\mathbb{Z}/4)$ |
$768$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_2$, $S_3$, $D_{6}$, $S_4\times C_2$ x 2, $C_2^2\times S_4$, $C_2\wr S_3$ x 2 |
24T1932 x 12, 24T1974 x 12, 24T2204 x 24, 24T2469 x 24, 24T2470 x 48, 24T2471 x 8, 24T2472 x 12, 24T2475 x 4, 24T2476 x 8, 24T2498 x 48, 24T2525 x 23, 32T34970 x 4 |
Results are complete for degrees $\leq 23$.
