| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 32T385 |
$D_4\times A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $A_4$, $D_4$, $A_4\times C_2$ x 3, $C_2^2\times A_4$, $D_4\times A_4$ x 2 |
12T51 x 2, 16T179 x 2, 24T160, 24T161 x 2, 24T162 x 2, 24T163 x 2, 24T164 x 2 |
| 32T386 |
$D_4.A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$19$ |
$C_2$ x 3, $C_2^2$, $A_4$, $A_4\times C_2$ x 3, $C_2^2\times A_4$, $D_4.A_4$ x 2 |
16T180 x 2 |
| 32T387 |
$C_4\times S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $S_4$, $C_4\times C_2$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $C_4\times S_4$ x 2 |
12T53 x 2, 16T181 x 2, 24T129, 24T130, 24T167, 24T168 x 2, 24T169 x 2 |
| 32T388 |
$C_2^2\times S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 7, $C_2^2$ x 7, $S_4$, $C_2^3$, $S_4$, $S_4\times C_2$ x 6, $C_2\times S_4$ x 3, $C_2^2\times S_4$ x 4 |
12T48 x 12, 16T182 x 4, 24T125, 24T126 x 6, 24T150 x 3, 24T151 x 4, 24T152 x 4 |
| 32T389 |
$C_2^3:A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $A_4$, $A_4\times C_2$, $C_2^4:C_6$ x 2, $C_2^3:A_4$ |
8T33 x 2, 12T58 x 2, 12T59 x 2, 16T183, 24T181 x 2, 24T182 x 2, 24T183 x 2, 24T184 x 2, 24T185, 24T186 |
| 32T390 |
$C_4^2:C_6$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $A_4$, $A_4\times C_2$, $C_4^2:C_6$ |
16T184, 24T120, 24T121, 24T122 |
| 32T391 |
$C_4^2:C_6$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $A_4$, $A_4\times C_2$, $C_4^2:C_6$ |
12T60 x 2, 12T61 x 2, 16T185, 24T187 x 2, 24T188 x 2, 24T189, 24T190 |
| 32T392 |
$\GL(2,\mathbb{Z}/4)$ |
$96$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $S_4$, $D_4$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $\GL(2,\mathbb{Z}/4)$, $\GL(2,\mathbb{Z}/4)$ |
12T49 x 2, 12T50, 12T52, 16T186, 16T193, 24T153, 24T154, 24T155 x 2, 24T156, 24T157, 24T158, 24T159, 24T165, 24T166 |
| 32T393 |
$\GL(2,3):C_2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $\GL(2,3):C_2$, $\GL(2,3):C_2$ |
16T187, 16T192 |
| 32T394 |
$C_2\times \GL(2,3)$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $\textrm{GL(2,3)}$ x 4, $S_4\times C_2$ x 2, $C_2\times S_4$, $\GL(2,3)$ x 2, $C_2\times \GL(2,3)$ x 4 |
16T188 x 4 |
| 32T395 |
$\GL(2,3):C_2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $\GL(2,3):C_2$ x 2 |
16T189 x 2 |
| 32T396 |
$\GL(2,3):C_2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $\GL(2,3):C_2$ x 2 |
16T190 x 2, 24T127 x 2 |
| 32T397 |
$C_4:S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $S_4$, $D_4$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $C_4:S_4$ x 2 |
12T54 x 2, 16T191 x 2, 24T128 x 2, 24T170, 24T171 x 2, 24T172 x 2 |
| 32T398 |
$C_2^2:S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_4$ x 3, $S_4$ x 3, $V_4^2:S_3$, $C_2^2:S_4$ |
8T34, 12T66 x 3, 12T67, 12T68 x 3, 12T69, 16T194, 24T195 x 3, 24T196 x 3, 24T197 x 3, 24T198, 24T199, 24T200 x 3 |
| 32T399 |
$C_4^2:S_3$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_4$, $S_4$, $C_4^2:S_3$ |
12T62, 12T63, 12T64, 12T65, 16T195, 24T191, 24T192, 24T193, 24T194 |
| 32T400 |
$C_2^3:C_{12}$ |
$96$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $A_4$, $C_4\times C_2$, $A_4\times C_2$ x 3, $C_4\times A_4$ x 2, $C_2^2\times A_4$ |
24T133 x 2, 24T134 x 2, 24T147 |
| 32T401 |
$C_8\times A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_2$, $C_4$, $A_4$, $C_8$, $A_4\times C_2$, $C_4\times A_4$ |
24T85 |
| 32T402 |
$C_8.A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $C_4$, $A_4$, $A_4\times C_2$, $C_4\times A_4$ |
|
| 32T403 |
$C_4\times \SL(2,3)$ |
$96$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $C_4$, $A_4$, $\SL(2,3)$ x 2, $A_4\times C_2$, $C_4\times A_4$, $C_2\times \SL(2,3)$, $\SL(2,3):C_2$ |
|
| 32T404 |
$C_2^3\times A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_2$ x 7, $C_2^2$ x 7, $A_4$, $C_2^3$, $A_4\times C_2$ x 7, $C_2^2\times A_4$ x 7 |
24T135 x 7, 24T136 x 14 |
| 32T405 |
$C_2^2\times \SL(2,3)$ |
$96$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$ x 3, $C_2^2$, $A_4$, $\SL(2,3)$ x 4, $A_4\times C_2$ x 3, $C_2^2\times A_4$, $C_2\times \SL(2,3)$ x 6 |
|
| 32T406 |
$Q_8\times A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $A_4$, $Q_8$, $A_4\times C_2$ x 3, $C_2^2\times A_4$ |
24T86 |
| 32T407 |
$\SL(2,3):C_2^2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$19$ |
$C_2$ x 3, $C_2^2$, $A_4$, $A_4\times C_2$ x 3, $C_2^2\times A_4$ |
24T137 x 2 |
| 32T408 |
$\SL(2,3):C_2^2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$ x 3, $C_2^2$, $A_4$, $A_4\times C_2$ x 3, $C_2^2\times A_4$, $\SL(2,3):C_2$ x 2 |
|
| 32T409 |
$C_2^2.S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $C_2.S_4$ x 2 |
|
| 32T410 |
$A_4:Q_8$ |
$96$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$ x 3, $C_2^2$, $S_4$, $Q_8$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$ |
24T87, 24T131 x 2 |
| 32T411 |
$C_2^2.S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $S_4$, $C_4\times C_2$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $A_4:C_4$ x 2 |
24T123, 24T124 x 2, 24T132 x 2, 24T148 |
| 32T412 |
$C_4.S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$ |
|
| 32T413 |
$A_4:C_8$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_4$, $S_4$, $C_8$, $S_4$, $A_4:C_4$ |
24T89 |
| 32T414 |
$\GU(2,3)$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_4$, $S_4$, $S_4$, $A_4:C_4$ |
24T138 x 2 |
| 32T415 |
$\SL(2,3):C_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_4$, $S_4$, $S_4$, $\textrm{GL(2,3)}$ x 2, $A_4:C_4$, $C_2.S_4$, $\GL(2,3)$ |
|
| 32T416 |
$C_4^2:C_6$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $A_4$, $A_4\times C_2$, $C_4^2:C_3$ |
12T55 x 2, 24T173, 24T174 x 2, 24T175 x 2 |
| 32T417 |
$C_2^3.A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$12$ |
$A_4$, $\SL(2,3)$, $C_4^2:C_3$ |
12T57 x 2, 24T179, 24T180 x 2 |
| 32T418 |
$C_2^3:A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $A_4$ x 5, $A_4\times C_2$ x 5, $C_2^2:A_4$ |
12T56 x 30, 24T176 x 5, 24T177 x 30, 24T178 x 10 |
| 32T419 |
$Q_8:A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$12$ |
$A_4$ x 5, $\SL(2,3)$, $C_2^2:A_4$ |
24T88 |
| 32T420 |
$Q_8:A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$11$ |
$A_4$ x 5, $((C_2 \times D_4): C_2):C_3$ x 3, $C_2^2:A_4$ |
8T32 x 3, 24T97 x 3, 24T149 |
| 32T2132 |
$C_2^4:D_5$ |
$160$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_2^4:D_5$ |
10T15 x 3, 10T16 x 3, 16T415, 20T38 x 6, 20T39, 20T43 x 3, 20T45 x 3, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146 |
| 32T2133 |
$C_2\wr C_5$ |
$160$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_2^4:C_5$ |
10T14 x 3, 20T40 x 12, 20T41 x 6, 20T44 x 3, 20T46 x 3, 40T121 x 6, 40T122 x 6, 40T123 x 12, 40T141, 40T142 x 3 |
| 32T2134 |
$C_2.C_2^4:C_5$ |
$160$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2^4:C_5$ |
|
| 32T2135 |
$C_2^4:A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $A_4$, $A_4\times C_2$, $C_2^4:A_4$ |
16T417, 16T419, 24T369, 24T371, 24T376 x 3, 24T381, 32T2135 x 2 |
| 32T2136 |
$C_2^4.A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $A_4$, $A_4\times C_2$, $C_2^4.A_4$ |
16T420, 24T368, 24T373 x 2, 24T377, 24T380, 24T382, 32T2136, 32T2137 |
| 32T2137 |
$C_2^4.A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $A_4$, $A_4\times C_2$, $C_2^4.A_4$ |
16T420, 24T368, 24T373 x 2, 24T377, 24T380, 24T382, 32T2136 x 2 |
| 32T2138 |
$D_4\times S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$25$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $S_4$, $D_4\times C_2$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $D_4\times S_4$ x 2 |
12T86 x 4, 16T421 x 4, 24T358 x 2, 24T393 x 2, 24T434 x 2, 24T435 x 2, 24T436 x 2, 24T437 x 4, 24T438 x 4, 24T439 x 4, 24T440 x 4, 32T2138, 32T2139 x 2, 32T2140 x 2 |
| 32T2139 |
$D_4\times S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$25$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $S_4$, $D_4\times C_2$, $S_4\times C_2$ x 3, $C_2^2\times S_4$, $D_4\times S_4$ x 2 |
12T86 x 4, 16T421 x 4, 24T358 x 2, 24T393 x 2, 24T434 x 2, 24T435 x 2, 24T436 x 2, 24T437 x 4, 24T438 x 4, 24T439 x 4, 24T440 x 4, 32T2138 x 2, 32T2139, 32T2140 x 2 |
| 32T2140 |
$D_4\times S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$25$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $S_4$, $D_4$, $S_4\times C_2$ x 3, $C_2^2\times S_4$, $D_4\times S_4$ x 2 |
12T86 x 4, 16T421 x 4, 24T358 x 2, 24T393 x 2, 24T434 x 2, 24T435 x 2, 24T436 x 2, 24T437 x 4, 24T438 x 4, 24T439 x 4, 24T440 x 4, 32T2138 x 2, 32T2139 x 2, 32T2140 |
| 32T2141 |
$\GL(2,3):C_2^2$ |
$192$ |
$1$ |
✓ |
$-1$ |
$23$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $C_2\times S_4$, $\GL(2,3):C_2^2$ x 2 |
16T422 x 4, 32T2141, 32T2142 x 2, 32T2143 x 2 |
| 32T2142 |
$\GL(2,3):C_2^2$ |
$192$ |
$1$ |
✓ |
$-1$ |
$23$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4\times C_2$ x 3, $C_2^2\times S_4$, $\GL(2,3):C_2^2$ x 2 |
16T422 x 4, 32T2141 x 2, 32T2142, 32T2143 x 2 |
| 32T2143 |
$\GL(2,3):C_2^2$ |
$192$ |
$1$ |
✓ |
$-1$ |
$23$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4\times C_2$ x 3, $C_2^2\times S_4$, $\GL(2,3):C_2^2$ x 2 |
16T422 x 4, 32T2141 x 2, 32T2142 x 2, 32T2143 |
| 32T2144 |
$C_2^3.S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$11$ |
$C_2$, $S_4$, $S_4$, $C_2^3.S_4$ |
16T430, 24T374, 24T378, 24T384, 24T387 |
| 32T2145 |
$C_4^2:D_6$ |
$192$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $S_4$, $S_4$, $C_4^2:D_6$ |
12T112 x 2, 12T113 x 2, 12T114 x 2, 12T115 x 2, 16T431, 24T530 x 2, 24T531 x 2, 24T532 x 2, 24T533 x 2, 24T534 x 2, 24T535, 24T536 x 2, 24T537 x 2, 24T538 x 2, 24T539, 24T540, 24T541, 32T2146 x 2 |
Results are complete for degrees $\leq 23$.
