| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 16T57 |
$C_4\times A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_4$, $A_4$, $A_4\times C_2$ |
12T29, 24T55, 24T56 |
| 16T58 |
$C_2^2\times A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_2^2$, $A_4$, $A_4\times C_2$ x 3 |
12T25 x 3, 12T26 x 2, 24T49 x 3, 24T50 |
| 16T59 |
$C_2\times \SL(2,3)$ |
$48$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $A_4$, $\SL(2,3)$ x 2, $A_4\times C_2$ |
|
| 16T60 |
$\SL(2,3):C_2$ |
$48$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $A_4$, $A_4\times C_2$ |
24T21 |
| 16T61 |
$C_2\times S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $S_4\times C_2$ x 2 |
6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 24T46, 24T47, 24T48 x 2 |
| 16T62 |
$A_4:C_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_4$, $S_4$, $S_4$ |
12T27, 12T30, 24T51, 24T57 |
| 16T63 |
$C_4^2:C_3$ |
$48$ |
$1$ |
✓ |
$-1$ |
$8$ |
$A_4$ |
12T31 x 2, 24T58 |
| 16T64 |
$C_2^2:A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$8$ |
$A_4$ x 5 |
12T32 x 10, 24T59 x 5 |
| 16T65 |
$C_2.S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_2$, $S_4$, $S_4$ |
|
| 16T66 |
$\GL(2,3)$ |
$48$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_2$, $S_4$, $S_4$, $\textrm{GL(2,3)}$ x 2 |
8T23 x 2, 24T22 |
| 16T178 |
$C_2^4:C_5$ |
$80$ |
$1$ |
✓ |
$-1$ |
$8$ |
|
10T8 x 3, 20T17 x 6, 20T23, 40T57 x 3 |
| 16T179 |
$D_4\times A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $D_{4}$, $A_4$, $A_4\times C_2$ |
12T51 x 2, 16T179, 24T160, 24T161 x 2, 24T162 x 2, 24T163 x 2, 24T164 x 2, 32T385 |
| 16T180 |
$D_4.A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $A_4$, $A_4\times C_2$ |
16T180, 32T386 |
| 16T181 |
$C_4\times S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_4$, $S_4$, $S_4\times C_2$ |
12T53 x 2, 16T181, 24T129, 24T130, 24T167, 24T168 x 2, 24T169 x 2, 32T387 |
| 16T182 |
$C_2^2\times S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4\times C_2$ x 3 |
12T48 x 12, 16T182 x 3, 24T125, 24T126 x 6, 24T150 x 3, 24T151 x 4, 24T152 x 4, 32T388 |
| 16T183 |
$C_2^3:A_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$A_4$ |
8T33 x 2, 12T58 x 2, 12T59 x 2, 24T181 x 2, 24T182 x 2, 24T183 x 2, 24T184 x 2, 24T185, 24T186, 32T389 |
| 16T184 |
$C_4^2:C_6$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$A_4$ |
24T120, 24T121, 24T122, 32T390 |
| 16T185 |
$C_4^2:C_6$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$A_4$ |
12T60 x 2, 12T61 x 2, 24T187 x 2, 24T188 x 2, 24T189, 24T190, 32T391 |
| 16T186 |
$\GL(2,\mathbb{Z}/4)$ |
$96$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $D_{4}$, $S_4$, $S_4\times C_2$ |
12T49 x 2, 12T50, 12T52, 16T193, 24T153, 24T154, 24T155 x 2, 24T156, 24T157, 24T158, 24T159, 24T165, 24T166, 32T392 |
| 16T187 |
$\GL(2,3):C_2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$, $S_4$, $S_4\times C_2$ |
16T192, 32T393 |
| 16T188 |
$C_2\times \GL(2,3)$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $S_4$, $\textrm{GL(2,3)}$ x 2, $S_4\times C_2$ |
16T188 x 3, 32T394 |
| 16T189 |
$\GL(2,3):C_2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $S_4$, $S_4\times C_2$ |
16T189, 32T395 |
| 16T190 |
$\GL(2,3):C_2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$, $S_4$, $S_4\times C_2$ |
16T190, 24T127 x 2, 32T396 |
| 16T191 |
$C_4:S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $D_{4}$, $S_4$, $S_4\times C_2$ |
12T54 x 2, 16T191, 24T128 x 2, 24T170, 24T171 x 2, 24T172 x 2, 32T397 |
| 16T192 |
$\GL(2,3):C_2$ |
$96$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$, $S_4$, $S_4$ |
16T187, 32T393 |
| 16T193 |
$\GL(2,\mathbb{Z}/4)$ |
$96$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $D_{4}$, $S_4$, $S_4$ |
12T49 x 2, 12T50, 12T52, 16T186, 24T153, 24T154, 24T155 x 2, 24T156, 24T157, 24T158, 24T159, 24T165, 24T166, 32T392 |
| 16T194 |
$C_2^2:S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$S_4$ x 3 |
8T34, 12T66 x 3, 12T67, 12T68 x 3, 12T69, 24T195 x 3, 24T196 x 3, 24T197 x 3, 24T198, 24T199, 24T200 x 3, 32T398 |
| 16T195 |
$C_4^2:S_3$ |
$96$ |
$1$ |
✓ |
$-1$ |
$10$ |
$S_4$ |
12T62, 12T63, 12T64, 12T65, 24T191, 24T192, 24T193, 24T194, 32T399 |
| 16T196 |
$C_2\times F_8$ |
$112$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_2^3:C_7$ |
14T9, 28T19 x 3, 28T20 |
| 16T414 |
$A_4^2$ |
$144$ |
$1$ |
✓ |
$-1$ |
$16$ |
$A_4$ x 2 |
12T85 x 2, 18T62, 24T212 x 2, 36T121, 36T122 x 2, 36T170 x 2 |
| 16T415 |
$C_2^4:D_5$ |
$160$ |
$1$ |
✓ |
$-1$ |
$10$ |
|
10T15 x 3, 10T16 x 3, 20T38 x 6, 20T39, 20T43 x 3, 20T45 x 3, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146 |
| 16T416 |
$C_2^4:A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $C_2^4:C_6$ |
12T87 x 2, 12T88 x 2, 16T416, 24T441 x 2, 24T442 x 2, 24T443 x 4, 24T444 x 2, 24T445 x 2, 24T446 x 2, 24T447 x 2, 24T448 x 4, 24T449, 24T450, 24T451 x 4, 24T452 x 4, 32T2183 x 2 |
| 16T417 |
$C_2^4:A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$17$ |
$C_2$ x 3, $C_2^2$ |
16T419, 24T369, 24T371, 24T376 x 3, 24T381, 32T2135 x 3 |
| 16T418 |
$C_2^4:C_{12}$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_4$, $C_2^4:C_6$ |
12T99 x 2, 12T105 x 2, 16T418, 24T483 x 2, 24T484 x 2, 24T501 x 2, 24T502 x 4, 24T503 x 2, 24T504 x 2, 24T505 x 2, 24T506 x 2, 24T507 x 4 |
| 16T419 |
$C_2^4:A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$17$ |
$A_4$ |
16T417, 24T369, 24T371, 24T376 x 3, 24T381, 32T2135 x 3 |
| 16T420 |
$C_2^4.A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$17$ |
$A_4$ |
24T368, 24T373 x 2, 24T377, 24T380, 24T382, 32T2136 x 2, 32T2137 |
| 16T421 |
$D_4\times S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$25$ |
$C_2$, $D_{4}$, $S_4$, $S_4\times C_2$ |
12T86 x 4, 16T421 x 3, 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 x 2 |
| 16T422 |
$\GL(2,3):C_2^2$ |
$192$ |
$1$ |
✓ |
$-1$ |
$23$ |
$C_2$, $S_4$, $S_4\times C_2$ |
16T422 x 3, 32T2141 x 2, 32T2142 x 2, 32T2143 x 2 |
| 16T423 |
$(C_2^2\times C_4):A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$22$ |
$C_2$, $A_4$, $A_4\times C_2$ |
16T423 x 2 |
| 16T424 |
$C_2^4:A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$22$ |
$C_2$, $A_4$, $A_4\times C_2$, $((C_2 \times D_4): C_2):C_3$ x 2 |
16T424 x 2 |
| 16T425 |
$C_2\wr A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_2^4:C_6$ |
8T38 x 2, 16T427, 24T288 x 2, 24T425 x 2, 32T2185 x 2 |
| 16T426 |
$(C_2^2\times C_4):A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $A_4$, $A_4\times C_2$ |
16T428 |
| 16T427 |
$C_2\wr A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $A_4$, $A_4\times C_2$, $C_2\wr A_4$ x 2 |
8T38 x 2, 16T425, 24T288 x 2, 24T425 x 2, 32T2185 x 2 |
| 16T428 |
$(C_2^2\times C_4):A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_2^4:C_6$ |
16T426 |
| 16T429 |
$C_2^3:S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $V_4^2:S_3$ |
12T100 x 3, 12T101 x 6, 12T103 x 6, 12T106, 24T432 x 3, 24T485 x 3, 24T486 x 6, 24T487 x 6, 24T488 x 3, 24T489 x 3, 24T490 x 3, 24T491 x 2, 24T492 x 6, 24T493 x 6, 24T508 x 3, 24T509 x 6, 24T510, 24T511, 32T2212 x 2 |
| 16T430 |
$C_2^3.S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$11$ |
$S_4$ |
24T374, 24T378, 24T384, 24T387, 32T2144 |
| 16T431 |
$C_4^2:D_6$ |
$192$ |
$1$ |
✓ |
$-1$ |
$14$ |
$S_4$ |
12T112 x 2, 12T113 x 2, 12T114 x 2, 12T115 x 2, 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, 32T2145, 32T2146 x 2 |
| 16T432 |
$C_2^3.S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$11$ |
$C_2$, $C_4$ |
16T433, 24T370, 24T375, 24T379, 24T383, 32T2147 |
| 16T433 |
$C_2^3.S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$11$ |
$S_4$ |
16T432, 24T370, 24T375, 24T379, 24T383, 32T2147 |
| 16T434 |
$C_2^3.S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_4$, $V_4^2:S_3$ |
12T102 x 3, 12T107, 24T386 x 3, 24T433 x 3, 24T494 x 3, 24T495 x 6, 24T512 x 3, 24T513 x 6, 24T514, 24T515 |
Results are complete for degrees $\leq 23$.
