| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T158 |
$A_4^2:C_2^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3\times C_3$ |
16T1028, 18T175 x 2, 24T1481 x 2, 24T1484 x 2, 24T1485, 24T1486, 32T34599 x 2, 36T720, 36T723, 36T743 x 2, 36T744 x 2, 36T948 x 2, 36T949, 36T950, 36T951 x 2 |
| 12T159 |
$A_4^2:C_4$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3\times C_3$ |
16T1027, 24T1487, 24T1488, 36T719, 36T724, 36T946, 36T947 |
| 12T160 |
$A_4^2:C_4$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$13$ |
$C_2$, $C_3^2:C_4$ |
8T46, 12T162, 16T1030, 16T1031, 18T182, 18T184, 24T1489, 24T1491, 24T1505, 24T1506 x 2, 24T1508, 32T34594, 36T764, 36T765, 36T766, 36T767, 36T964, 36T965 |
| 12T161 |
$\PGOPlus(4,3)$ |
$576$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $S_3^2$ |
8T45, 12T163, 12T165 x 2, 16T1032, 16T1034, 18T179, 18T180, 18T185 x 2, 24T1490, 24T1492, 24T1493 x 2, 24T1494 x 2, 24T1495 x 2, 24T1503, 24T1504 x 2, 32T34597 x 2, 32T34598, 36T759, 36T760, 36T762, 36T763, 36T774 x 2, 36T775 x 2, 36T960, 36T961, 36T962 x 2, 36T963 x 2 |
| 12T162 |
$A_4^2:C_4$ |
$576$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$, $C_3^2:C_4$ |
8T46, 12T160, 16T1030, 16T1031, 18T182, 18T184, 24T1489, 24T1491, 24T1505, 24T1506 x 2, 24T1508, 32T34594, 36T764, 36T765, 36T766, 36T767, 36T964, 36T965 |
| 12T163 |
$\PGOPlus(4,3)$ |
$576$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $S_3^2$ |
8T45, 12T161, 12T165 x 2, 16T1032, 16T1034, 18T179, 18T180, 18T185 x 2, 24T1490, 24T1492, 24T1493 x 2, 24T1494 x 2, 24T1495 x 2, 24T1503, 24T1504 x 2, 32T34597 x 2, 32T34598, 36T759, 36T760, 36T762, 36T763, 36T774 x 2, 36T775 x 2, 36T960, 36T961, 36T962 x 2, 36T963 x 2 |
| 12T164 |
$C_2^2:A_4^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$ |
12T164 x 2, 18T178 x 3, 24T1470 x 9, 36T753 x 9, 36T754 x 9, 36T882 x 9, 36T883 x 9, 36T884 x 3, 36T885 x 18, 36T958 x 3, 36T959 x 3 |
| 12T165 |
$\PGOPlus(4,3)$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$S_3$ |
8T45, 12T161, 12T163, 12T165, 16T1032, 16T1034, 18T179, 18T180, 18T185 x 2, 24T1490, 24T1492, 24T1493 x 2, 24T1494 x 2, 24T1495 x 2, 24T1503, 24T1504 x 2, 32T34597 x 2, 32T34598, 36T759, 36T760, 36T762, 36T763, 36T774 x 2, 36T775 x 2, 36T960, 36T961, 36T962 x 2, 36T963 x 2 |
| 12T166 |
$C_2^6:C_9$ |
$576$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$ |
12T166 x 6, 18T177 x 7, 36T954 x 7, 36T955 x 21, 36T956 x 7, 36T957 x 42 |
| 12T167 |
$C_3\wr D_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$54$ |
$C_2$, $D_{4}$ |
12T167, 18T189 x 2, 24T1519 x 2, 24T1536, 36T1079 x 2, 36T1080 x 2, 36T1081 x 2, 36T1158, 36T1163, 36T1165, 36T1170, 36T1180, 36T1191 x 2, 36T1200 x 2, 36T1231 x 2 |
| 12T168 |
$C_3:S_3^3$ |
$648$ |
$1$ |
✓ |
$-1$ |
$42$ |
$C_2$ x 3, $C_2^2$ |
12T168, 18T193 x 6, 24T1520 x 2, 36T1088 x 6, 36T1089 x 12, 36T1144 x 4, 36T1194 x 12, 36T1226 x 2 |
| 12T169 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $D_{4}$ |
12T169, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 12T170 |
$C_3^3:(C_4\times S_3)$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $C_4$ |
12T170 x 3, 18T195 x 4, 24T1522 x 4, 36T1090 x 4, 36T1091 x 4, 36T1092 x 4, 36T1149 x 4, 36T1196 x 4, 36T1199 x 4, 36T1228 x 4, 36T1229 x 8 |
| 12T171 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $C_2^2$ |
12T171 x 7, 18T190 x 8, 18T192 x 8, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
| 12T172 |
$C_3^4:D_4$ |
$648$ |
$1$ |
✓ |
$-1$ |
$27$ |
$C_2$ x 3, $C_2^2$ |
12T172 x 5, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3 |
| 12T173 |
$C_3^2:F_9$ |
$648$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_4$ |
12T173 x 7, 18T196 x 4, 24T1525 x 8, 36T1093 x 4, 36T1216 x 4, 36T1217 x 16, 36T1235 x 2, 36T1236 x 8 |
| 12T174 |
$C_3^4:Q_8$ |
$648$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_2$ x 3, $C_2^2$ |
12T174 x 5, 18T212 x 9, 24T1526 x 6, 36T1111 x 9, 36T1220 x 18, 36T1221, 36T1222 x 8 |
| 12T175 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_4$ |
9T29, 18T219, 18T220, 18T223, 18T224, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237 |
| 12T176 |
$S_3\wr C_3$ |
$648$ |
$1$ |
✓ |
$-1$ |
$17$ |
$A_4$ |
9T28, 18T197 x 2, 18T198 x 2, 18T202, 18T204, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
| 12T177 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_4$ |
9T30, 12T177, 12T178, 18T217, 18T218, 18T221, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
| 12T178 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_4$ |
9T30, 12T177 x 2, 18T217, 18T218, 18T221, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
| 12T179 |
$\PSL(2,11)$ |
$660$ |
$1$ |
|
$-1$ |
$8$ |
|
11T5 x 2 |
| 12T180 |
$C_2\times A_6$ |
$720$ |
$1$ |
|
$-1$ |
$14$ |
$C_2$, $A_6$ |
12T180, 20T151, 20T152, 30T172 x 2, 30T179 x 2, 40T587, 40T588 |
| 12T181 |
$A_6.C_2$ |
$720$ |
$1$ |
|
$-1$ |
$8$ |
$C_2$ |
10T31, 20T148, 20T150 x 2, 30T162, 36T1253, 40T591, 45T109 |
| 12T182 |
$\PGL(2,9)$ |
$720$ |
$1$ |
|
$-1$ |
$11$ |
$C_2$ |
10T30, 20T146, 30T171, 36T1254, 40T590, 45T110 |
| 12T183 |
$S_6$ |
$720$ |
$1$ |
|
$-1$ |
$11$ |
$C_2$, $S_6$ |
6T16 x 2, 10T32, 12T183, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96 |
| 12T184 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$23$ |
$S_3$, $S_4$ |
12T184 x 3, 12T190 x 4, 12T191 x 4, 24T1587 x 2, 24T2181, 24T2540 x 2, 24T2541 x 8, 24T2542 x 2, 24T2543 x 2, 24T2544 x 8, 24T2587 x 2, 24T2588 x 4, 24T2589 x 2, 24T2590 x 2, 24T2591 x 2, 32T35000 x 8 |
| 12T185 |
$C_4^3:D_6$ |
$768$ |
$-1$ |
✓ |
$-1$ |
$38$ |
$S_3$, $S_4\times C_2$ |
12T185 x 7, 24T1825 x 2, 24T1843 x 2, 24T1938 x 2, 24T2545 x 4, 24T2546 x 4, 24T2547 x 4, 24T2548 x 4, 24T2549 x 4, 24T2550 x 4, 24T2551 x 4 |
| 12T186 |
$C_2\wr D_6$ |
$768$ |
$-1$ |
✓ |
$-1$ |
$38$ |
$S_3$, $S_4\times C_2$ |
12T186 x 3, 12T193 x 4, 16T1053 x 4, 24T1557, 24T1598, 24T1767, 24T1844, 24T1882, 24T1911, 24T2208 x 2, 24T2209 x 2, 24T2487 x 2, 24T2488 x 2, 24T2552 x 2, 24T2553 x 4, 24T2554 x 2, 24T2555 x 2, 24T2556 x 2, 24T2557 x 2, 24T2558 x 2, 24T2595 x 2, 24T2596 x 2, 24T2597 x 4, 24T2598 x 4, 24T2599 x 4, 24T2600 x 4, 24T2601 x 4, 24T2602 x 4, 24T2603 x 4, 24T2604 x 4, 24T2605 x 2, 24T2606 x 2, 24T2607 x 2, 24T2608 x 2, 32T34686 x 2, 32T34687 x 2, 32T34688 x 2, 32T34803, 32T35039 |
| 12T187 |
$C_2\wr A_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $A_4\times C_2$ |
12T187 x 7, 12T188 x 8, 24T2559 x 8, 24T2560 x 4, 24T2561 x 8, 24T2562 x 8, 24T2563 x 4, 24T2564 x 8, 24T2565 x 8, 24T2566 x 8, 24T2567 x 8, 24T2568 x 4, 24T2569 x 4, 24T2570 x 8, 24T2571 x 8, 24T2572 x 8, 24T2573 x 8, 24T2574 x 4, 24T2575 x 4, 24T2576 x 4, 24T2577 x 4, 32T34825 x 8 |
| 12T188 |
$C_2\wr A_4$ |
$768$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $A_4$ |
12T187 x 8, 12T188 x 7, 24T2559 x 8, 24T2560 x 4, 24T2561 x 8, 24T2562 x 8, 24T2563 x 4, 24T2564 x 8, 24T2565 x 8, 24T2566 x 8, 24T2567 x 8, 24T2568 x 4, 24T2569 x 4, 24T2570 x 8, 24T2571 x 8, 24T2572 x 8, 24T2573 x 8, 24T2574 x 4, 24T2575 x 4, 24T2576 x 4, 24T2577 x 4, 32T34825 x 8 |
| 12T189 |
$C_4^3:A_4$ |
$768$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $A_4\times C_2$ |
12T189 x 15, 24T2578 x 16, 24T2579 x 8, 24T2580 x 16, 24T2581 x 16, 24T2582 x 16, 24T2583 x 16, 24T2584 x 8, 24T2585 x 16, 24T2586 x 8 |
| 12T190 |
$C_2^5:S_4$ |
$768$ |
$-1$ |
✓ |
$-1$ |
$23$ |
$S_3$, $S_4$ |
12T184 x 4, 12T190 x 3, 12T191 x 4, 24T1587 x 2, 24T2181, 24T2540 x 2, 24T2541 x 8, 24T2542 x 2, 24T2543 x 2, 24T2544 x 8, 24T2587 x 2, 24T2588 x 4, 24T2589 x 2, 24T2590 x 2, 24T2591 x 2, 32T35000 x 8 |
| 12T191 |
$C_2^5:S_4$ |
$768$ |
$1$ |
✓ |
$-1$ |
$23$ |
$S_3$, $S_4$ |
12T184 x 4, 12T190 x 4, 12T191 x 3, 24T1587 x 2, 24T2181, 24T2540 x 2, 24T2541 x 8, 24T2542 x 2, 24T2543 x 2, 24T2544 x 8, 24T2587 x 2, 24T2588 x 4, 24T2589 x 2, 24T2590 x 2, 24T2591 x 2, 32T35000 x 8 |
| 12T192 |
$C_2^5.S_4$ |
$768$ |
$-1$ |
✓ |
$-1$ |
$23$ |
$S_3$, $S_4$ |
12T192 x 3, 24T1588 x 2, 24T1593 x 2, 24T1594 x 2, 24T2187 x 2, 24T2189, 24T2592 x 2, 24T2593 x 2, 24T2594 x 2 |
| 12T193 |
$C_2\wr D_6$ |
$768$ |
$-1$ |
✓ |
$-1$ |
$38$ |
$C_2$, $S_3$, $D_{6}$ |
12T186 x 4, 12T193 x 3, 16T1053 x 4, 24T1557, 24T1598, 24T1767, 24T1844, 24T1882, 24T1911, 24T2208 x 2, 24T2209 x 2, 24T2487 x 2, 24T2488 x 2, 24T2552 x 2, 24T2553 x 4, 24T2554 x 2, 24T2555 x 2, 24T2556 x 2, 24T2557 x 2, 24T2558 x 2, 24T2595 x 2, 24T2596 x 2, 24T2597 x 4, 24T2598 x 4, 24T2599 x 4, 24T2600 x 4, 24T2601 x 4, 24T2602 x 4, 24T2603 x 4, 24T2604 x 4, 24T2605 x 2, 24T2606 x 2, 24T2607 x 2, 24T2608 x 2, 32T34686 x 2, 32T34687 x 2, 32T34688 x 2, 32T34803, 32T35039 |
| 12T194 |
$C_3\wr A_4$ |
$972$ |
$1$ |
✓ |
$-1$ |
$39$ |
$A_4$ |
12T194 x 5, 18T242, 27T262, 36T1502, 36T1549, 36T1552 x 2, 36T1585 x 3, 36T1586 x 6, 36T1597 x 4, 36T1598 x 2 |
Results are complete for degrees $\leq 23$.
