| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 16T1068 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$ x 3, $C_2^2$ |
16T1068, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T1632 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $S_3$, $S_4$, $S_4$, $S_4$ |
16T1068 x 2, 24T1632, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T1639 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_2 \times S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 3, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2199 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $D_6$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2248 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$ x 3, $C_2^2:S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2355 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $C_2^3:S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2357 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $C_2^3:S_4$, $C_2^3:S_4$, $C_2^3:S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 3, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2365 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $C_2^3:S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2373 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $S_4\times C_2$ x 2, $C_2^3:S_4$, $C_2^3:S_4$, $C_2^3:S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 3, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2378 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $S_4\times C_2$ x 2, $C_2^3:S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2382 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $S_4\times C_2$ x 2, $C_2^3:S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2392 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $S_4\times C_2$ x 2, $C_2^3:S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2405 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_2 \times S_4$, $C_2^3:S_4$, $C_2^3:S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 7, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2406 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_2 \times S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 3, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2407 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $C_2^3:S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 7, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2408 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_2 \times S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 3, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2417 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $S_4$ x 2, $C_2^2:S_4$, $C_2^3:S_4$, $C_2^3:S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 3, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2419 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$ x 3, $C_2^2:S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2421 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $C_2^2:S_4$, $C_2^3:S_4$, $C_2^3:S_4$ |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 3, 24T2423 x 2, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2423 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $C_2^2:S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423, 24T2426 x 2, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2426 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$, $C_2^2:S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426, 24T2429 x 2, 32T34622 x 4, 32T34628 |
| 24T2429 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4$ x 3, $C_2^2:S_4$, $C_2^3:S_4$ x 2 |
16T1068 x 2, 24T1632 x 2, 24T1639 x 4, 24T2199 x 2, 24T2248 x 2, 24T2355 x 2, 24T2357 x 4, 24T2365 x 2, 24T2373 x 4, 24T2378 x 2, 24T2382 x 2, 24T2392 x 2, 24T2405 x 8, 24T2406 x 4, 24T2407 x 8, 24T2408 x 4, 24T2417 x 4, 24T2419 x 2, 24T2421 x 4, 24T2423 x 2, 24T2426 x 2, 24T2429, 32T34622 x 4, 32T34628 |
Results are complete for degrees $\leq 23$.
