| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T77 |
$S_3^2:C_2^2$ |
$144$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $C_2^2$, $C_3^2:D_4$ |
12T77 x 3, 12T78 x 4, 18T63 x 4, 24T261 x 4, 24T262 x 4, 24T263 x 2, 24T264 x 2, 36T157 x 2, 36T159 x 4, 36T165 x 2 |
| 12T78 |
$S_3^2:C_2^2$ |
$144$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $D_{4}$, $C_3^2:D_4$ |
12T77 x 4, 12T78 x 3, 18T63 x 4, 24T261 x 4, 24T262 x 4, 24T263 x 2, 24T264 x 2, 36T157 x 2, 36T159 x 4, 36T165 x 2 |
| 12T79 |
$S_3^2:C_4$ |
$144$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_4$, $C_3^2:D_4$ |
12T79, 12T80 x 2, 24T213, 24T215, 24T265 x 2, 24T266 x 2, 24T267, 24T268, 36T156 x 2, 36T158, 36T164 |
| 12T80 |
$S_3^2:C_4$ |
$144$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $D_{4}$, $C_3^2:D_4$ |
12T79 x 2, 12T80, 24T213, 24T215, 24T265 x 2, 24T266 x 2, 24T267, 24T268, 36T156 x 2, 36T158, 36T164 |
| 12T81 |
$D_6:D_6$ |
$144$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $D_{4}$, $S_3^2$ |
12T81 x 3, 24T269 x 2, 24T270 x 2, 24T271 x 2, 36T123 x 2, 36T147 x 2 |
| 12T82 |
$C_6^2:C_4$ |
$144$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $D_{4}$, $C_3^2:C_4$ |
12T82 x 7, 24T272 x 4, 24T273 x 4, 24T274 x 4, 36T126 x 2, 36T141 x 2 |
| 12T83 |
$S_3\times S_4$ |
$144$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$S_3$, $S_4$ |
18T65, 18T69, 18T70, 18T72, 24T275, 24T276, 24T277, 24T281, 36T124, 36T125, 36T128, 36T129, 36T130, 36T131, 36T173, 36T174 |
| 12T84 |
$F_9:C_2$ |
$144$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $D_{4}$ |
9T19, 18T68, 18T71, 18T73, 24T278, 24T279, 24T280, 36T171, 36T172, 36T175 |
| 12T85 |
$A_4^2$ |
$144$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$ |
12T85, 16T414, 18T62, 24T212 x 2, 36T121, 36T122 x 2, 36T170 x 2 |
| 12T86 |
$D_4\times S_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$25$ |
$C_2$, $S_3$, $D_{6}$ |
12T86 x 3, 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 x 2 |
| 12T87 |
$C_2^4:A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3$, $C_6$ |
12T87, 12T88 x 2, 16T416 x 2, 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 |
| 12T88 |
$C_2^4:A_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$ |
12T87 x 2, 12T88, 16T416 x 2, 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 |
| 12T89 |
$C_2^4.A_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4\times C_2$ |
12T89, 12T92 x 2, 24T453 x 2, 24T454 x 2, 24T455 x 4, 24T456 x 4, 24T463, 24T464, 24T465 x 4, 24T466 x 4, 32T2188 x 2 |
| 12T90 |
$C_2^2\wr C_3$ |
$192$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $A_4\times C_2$ x 3 |
12T90 x 59, 24T457 x 90, 24T458 x 90, 24T459 x 120 |
| 12T91 |
$C_2^3.\SL(2,3)$ |
$192$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_3$, $A_4\times C_2$ |
12T91, 12T93 x 2, 24T460, 24T461 x 2, 24T462, 24T467, 24T468, 32T2187 x 2 |
| 12T92 |
$C_2^4.A_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$ |
12T89 x 2, 12T92, 24T453 x 2, 24T454 x 2, 24T455 x 4, 24T456 x 4, 24T463, 24T464, 24T465 x 4, 24T466 x 4, 32T2188 x 2 |
| 12T93 |
$C_2^3.\SL(2,3)$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_3$, $A_4$ |
12T91 x 2, 12T93, 24T460, 24T461 x 2, 24T462, 24T467, 24T468, 32T2187 x 2 |
| 12T94 |
$C_4\wr C_3$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $A_4\times C_2$ |
12T94 x 3, 24T469 x 4, 24T470 x 2 |
| 12T95 |
$C_4^2:D_6$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$ |
12T95, 12T96, 12T97, 24T471, 24T472 x 2, 24T473 x 2, 24T474 x 2, 24T475 x 2, 24T476, 24T477, 24T478, 24T479 x 2, 24T480 x 2, 32T2216 x 2 |
| 12T96 |
$C_4^2:D_6$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$ |
12T95 x 2, 12T97, 24T471, 24T472 x 2, 24T473 x 2, 24T474 x 2, 24T475 x 2, 24T476, 24T477, 24T478, 24T479 x 2, 24T480 x 2, 32T2216 x 2 |
| 12T97 |
$C_4^2:D_6$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$ |
12T95 x 2, 12T96, 24T471, 24T472 x 2, 24T473 x 2, 24T474 x 2, 24T475 x 2, 24T476, 24T477, 24T478, 24T479 x 2, 24T480 x 2, 32T2216 x 2 |
| 12T98 |
$C_2^3.S_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$ |
12T98, 24T317, 24T481, 24T482 x 2 |
| 12T99 |
$C_2^4:C_{12}$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4\times C_2$ |
12T99, 12T105 x 2, 16T418 x 2, 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 |
| 12T100 |
$C_2^3:S_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$ |
12T100 x 2, 12T101 x 6, 12T103 x 6, 12T106, 16T429, 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 |
| 12T101 |
$C_2^3:S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $S_4\times C_2$ x 2 |
12T100 x 3, 12T101 x 5, 12T103 x 6, 12T106, 16T429, 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 |
| 12T102 |
$C_2^3.S_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$ |
12T102 x 2, 12T107, 16T434, 24T386 x 3, 24T433 x 3, 24T494 x 3, 24T495 x 6, 24T512 x 3, 24T513 x 6, 24T514, 24T515 |
| 12T103 |
$C_2^3:S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $S_4\times C_2$ x 2 |
12T100 x 3, 12T101 x 6, 12T103 x 5, 12T106, 16T429, 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 |
| 12T104 |
$C_2^3.(C_2\times A_4)$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_3$, $A_4\times C_2$ |
12T104 x 3, 24T496 x 2, 24T497 x 2, 24T498 x 2, 24T499 x 4, 24T500 x 4 |
| 12T105 |
$C_2^4:C_{12}$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3$, $C_6$ |
12T99 x 2, 12T105, 16T418 x 2, 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 |
| 12T106 |
$C_2^3:S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $S_3$ |
12T100 x 3, 12T101 x 6, 12T103 x 6, 16T429, 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 |
| 12T107 |
$C_2^3.S_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $S_3$ |
12T102 x 3, 16T434, 24T386 x 3, 24T433 x 3, 24T494 x 3, 24T495 x 6, 24T512 x 3, 24T513 x 6, 24T514, 24T515 |
| 12T108 |
$C_2^3:S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $S_3$, $D_{6}$ |
8T41 x 2, 12T108, 12T109 x 2, 12T110 x 2, 12T111 x 2, 16T435 x 2, 16T436, 24T516 x 2, 24T517 x 2, 24T518 x 2, 24T519 x 2, 24T520 x 2, 24T521 x 2, 24T522 x 2, 24T523, 24T524 x 2, 24T525 x 2, 24T526 x 2, 24T527, 24T528, 24T529, 32T2148, 32T2149 x 2 |
| 12T109 |
$C_2^3:S_4$ |
$192$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $S_3$, $D_{6}$ |
8T41 x 2, 12T108 x 2, 12T109, 12T110 x 2, 12T111 x 2, 16T435 x 2, 16T436, 24T516 x 2, 24T517 x 2, 24T518 x 2, 24T519 x 2, 24T520 x 2, 24T521 x 2, 24T522 x 2, 24T523, 24T524 x 2, 24T525 x 2, 24T526 x 2, 24T527, 24T528, 24T529, 32T2148, 32T2149 x 2 |
| 12T110 |
$C_2^3:S_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4$ |
8T41 x 2, 12T108 x 2, 12T109 x 2, 12T110, 12T111 x 2, 16T435 x 2, 16T436, 24T516 x 2, 24T517 x 2, 24T518 x 2, 24T519 x 2, 24T520 x 2, 24T521 x 2, 24T522 x 2, 24T523, 24T524 x 2, 24T525 x 2, 24T526 x 2, 24T527, 24T528, 24T529, 32T2148, 32T2149 x 2 |
| 12T111 |
$C_2^3:S_4$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4$ |
8T41 x 2, 12T108 x 2, 12T109 x 2, 12T110 x 2, 12T111, 16T435 x 2, 16T436, 24T516 x 2, 24T517 x 2, 24T518 x 2, 24T519 x 2, 24T520 x 2, 24T521 x 2, 24T522 x 2, 24T523, 24T524 x 2, 24T525 x 2, 24T526 x 2, 24T527, 24T528, 24T529, 32T2148, 32T2149 x 2 |
| 12T112 |
$C_4^2:D_6$ |
$192$ |
$1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4\times C_2$ |
12T112, 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, 32T2145, 32T2146 x 2 |
| 12T113 |
$C_4^2:D_6$ |
$192$ |
$1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4\times C_2$ |
12T112 x 2, 12T113, 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, 32T2145, 32T2146 x 2 |
| 12T114 |
$C_4^2:D_6$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4$ |
12T112 x 2, 12T113 x 2, 12T114, 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, 32T2145, 32T2146 x 2 |
| 12T115 |
$C_4^2:D_6$ |
$192$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4$ |
12T112 x 2, 12T113 x 2, 12T114 x 2, 12T115, 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, 32T2145, 32T2146 x 2 |
| 12T116 |
$S_3^2:S_3$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $D_{4}$ |
12T120, 18T103, 18T106, 24T556, 24T560, 27T81, 36T271, 36T272, 36T273, 36T280, 36T281, 36T282, 36T291, 36T293 |
| 12T117 |
$S_3^3$ |
$216$ |
$1$ |
✓ |
$-1$ |
$27$ |
$C_2$ x 3, $C_2^2$ |
18T96 x 3, 24T557, 27T86, 36T264 x 3, 36T265 x 3, 36T266 x 3, 36T294 |
| 12T118 |
$C_3^2:D_{12}$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $D_{4}$ |
12T118, 18T104 x 2, 24T558 x 2, 27T79, 36T274 x 2, 36T275 x 2, 36T276 x 2, 36T290 x 2 |
| 12T119 |
$C_3^2:C_4\times S_3$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_4$ |
12T119, 18T95 x 2, 24T559 x 2, 27T85, 36T261 x 2, 36T262 x 2, 36T263 x 2, 36T295 x 2 |
| 12T120 |
$S_3^2:S_3$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $D_{4}$ |
12T116, 18T103, 18T106, 24T556, 24T560, 27T81, 36T271, 36T272, 36T273, 36T280, 36T281, 36T282, 36T291, 36T293 |
| 12T121 |
$S_3^2:C_6$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $D_{4}$ |
12T121, 18T93 x 2, 24T561 x 2, 27T84, 36T258 x 2, 36T259 x 2, 36T260 x 2, 36T292 x 2 |
| 12T122 |
$\PGU(3,2)$ |
$216$ |
$1$ |
✓ |
$-1$ |
$10$ |
$A_4$ |
9T23, 24T562, 24T569, 27T82, 36T287, 36T309 |
| 12T123 |
$C_2\times S_5$ |
$240$ |
$1$ |
|
$-1$ |
$14$ |
$C_2$, $\PGL(2,5)$ |
10T22 x 2, 12T123, 20T62 x 2, 20T65 x 2, 20T70, 24T570, 24T577, 30T58 x 2, 30T60 x 2, 40T173 x 2, 40T180, 40T181, 40T187 x 2 |
| 12T124 |
$A_5:C_4$ |
$240$ |
$-1$ |
|
$-1$ |
$14$ |
$\PGL(2,5)$ |
12T124, 20T66, 24T571, 24T578, 40T178, 40T179 |
Results are complete for degrees $\leq 23$.
