| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 36T138 |
$C_2^2:C_6^2$ |
$144$ |
$1$ |
✓ |
$-1$ |
$48$ |
$C_3$ x 4, $A_4\times C_2$ x 3, $C_3^2$, $C_2^2 \times A_4$, $C_6\times A_4$ x 3 |
36T103 x 3, 36T138 |
| 36T139 |
$C_2^3:C_{18}$ |
$144$ |
$1$ |
✓ |
$-1$ |
$48$ |
$C_3$, $A_4\times C_2$ x 3, $C_9$, $C_2^2 \times A_4$, $C_2^2:C_{18}$ x 3 |
36T101 x 3, 36T139 |
| 36T154 |
$A_4\times D_6$ |
$144$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $S_3$, $A_4\times C_2$ x 3, $S_3\times C_3$, $C_2^2 \times A_4$, $S_3\times A_4$, $A_4\times D_6$ x 2 |
18T60 x 2, 24T250 x 2, 36T107, 36T115 x 2, 36T116 x 2, 36T153 x 2, 36T154 |
| 36T170 |
$A_4^2$ |
$144$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$ x 4, $C_3^2$, $A_4^2$, $A_4^2$ |
12T85 x 2, 16T414, 18T62, 24T212 x 2, 36T121, 36T122 x 2, 36T170 |
| 36T211 |
$C_3^2:D_{12}$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $C_3$, $D_{4}$, $C_6$, $S_3^2$, $D_4 \times C_3$, $C_3:D_{12}$, $C_3\times S_3^2$ |
24T543, 36T211, 36T219 x 2 |
| 36T227 |
$C_3:D_{36}$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{12}$, $S_3\times D_9$ |
36T227 |
| 36T229 |
$C_9:D_{12}$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $(C_6\times C_2):C_2$, $S_3\times D_9$ |
36T229 |
| 36T240 |
$C_3^2:D_{12}$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $S_3$, $D_{4}$, $S_3$, $S_3^2$, $(C_6\times C_2):C_2$, $C_3:D_{12}$, $C_3:S_3^2$ |
24T550, 36T240 x 3 |
| 36T249 |
$C_3^2:D_{12}$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $D_{4}$, $S_3^2$, $C_3:D_{12}$, $C_3^2:D_6$ |
36T231, 36T244, 36T249, 36T251, 36T252 |
| 36T256 |
$C_3^2:D_{12}$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $S_3^2$ x 3, $D_{12}$, $C_3:D_{12}$ x 3, $C_3:S_3^2$ |
36T256 x 7 |
| 36T257 |
$C_3^2:D_{12}$ |
$216$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $S_3^2$ x 3, $(C_6\times C_2):C_2$, $C_3:D_{12}$ x 3, $C_3:S_3^2$ |
36T257 x 7 |
| 36T338 |
$(C_2\times C_6).\SL(2,3)$ |
$288$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_3$, $A_4$, $C_9$, $C_2^3.A_4$, $C_2^2 : C_9$ |
36T338 |
| 36T343 |
$C_3\times C_2^3.A_4$ |
$288$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_3$ x 4, $A_4$, $C_3^2$, $C_2^3.A_4$, $A_4 \times C_3$ |
36T343 |
| 36T369 |
$C_2\times A_4^2$ |
$288$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_3$ x 4, $A_4\times C_2$, $C_3^2$, $C_6\times A_4$, $A_4^2$, $C_2\times A_4^2$ |
18T109, 24T579 x 2, 24T684 x 2, 32T9309, 36T314, 36T345 x 2, 36T346 x 2, 36T368, 36T369 x 3, 36T427 x 2 |
| 36T393 |
$A_4\times S_4$ |
$288$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $S_3$, $A_4\times C_2$, $S_3\times C_3$, $S_3\times A_4$, $A_4\times S_4$, $A_4\times S_4$ |
16T709, 18T114, 18T115, 24T634, 24T635, 24T638, 24T639, 24T705, 32T9307, 36T321, 36T380, 36T381, 36T388, 36T389, 36T390, 36T392, 36T393, 36T399 |
| 36T425 |
$C_2\times A_4\times D_6$ |
$288$ |
$1$ |
✓ |
$-1$ |
$48$ |
$C_3$, $S_3$, $A_4\times C_2$ x 3, $S_3\times C_3$, $C_2^2 \times A_4$, $A_4\times D_6$ x 3 |
36T334 x 12, 36T425 x 7 |
| 36T426 |
$C_3\times \GL(2,\mathbb{Z}/4)$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$42$ |
$C_3$, $S_3$, $S_4\times C_2$, $S_3\times C_3$, $\GL(2,\mathbb{Z}/4)$, $C_6\times S_4$ |
36T315, 36T327, 36T426 |
| 36T427 |
$C_2\times A_4^2$ |
$288$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_3$ x 4, $C_3^2$, $A_4^2$, $C_2\times A_4^2$ |
18T109, 24T579 x 2, 24T684 x 2, 32T9309, 36T314, 36T345 x 2, 36T346 x 2, 36T368, 36T369 x 4, 36T427 |
| 36T438 |
$D_6:S_4$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$S_3$ x 2, $S_4\times C_2$, $S_3^2$, $\GL(2,\mathbb{Z}/4)$, $S_3\times S_4$ |
36T352, 36T356, 36T438 |
| 36T439 |
$C_3:\GL(2,\mathbb{Z}/4)$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$S_3$ x 4, $S_4\times C_2$, $C_3^2:C_2$, $\GL(2,\mathbb{Z}/4)$, $C_6:S_4$ |
36T322, 36T360, 36T439 |
| 36T440 |
$C_2^4:D_9$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $S_4\times C_2$, $D_{9}$, $\GL(2,\mathbb{Z}/4)$, $C_2^2:D_{18}$ |
36T326, 36T364, 36T440 |
| 36T445 |
$D_6:S_4$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$S_3$ x 2, $S_4\times C_2$, $S_3^2$, $\GL(2,\mathbb{Z}/4)$, $S_3\times S_4$ |
36T348, 36T353, 36T445 |
| 36T460 |
$\PSOPlus(4,3)$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$ x 4, $C_3^2:C_2$, $\PSOPlus(4,3)$, $\PSOPlus(4,3)$ |
12T127 x 2, 16T710, 18T116, 18T117, 24T636 x 2, 24T637 x 2, 24T693 x 2, 32T9308, 36T324, 36T403 x 2, 36T404 x 2, 36T405, 36T420, 36T460 |
| 36T475 |
$C_3^3:C_{12}$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$60$ |
$C_2$, $C_4$, $S_3\times C_3$, $C_3\times (C_3 : C_4)$, $C_3^3:C_6$ |
36T466, 36T470, 36T475 |
| 36T476 |
$C_3^2:C_6^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$60$ |
$C_2$ x 3, $C_2^2$, $S_3\times C_3$, $C_6\times S_3$, $C_3^3:C_6$ |
36T465, 36T469, 36T476 |
| 36T493 |
$C_3^3:D_6$ |
$324$ |
$1$ |
✓ |
$-1$ |
$33$ |
$C_2$ x 3, $C_2^2$, $S_3^2$, $S_3^2$, $C_3^3:D_6$ |
18T118 x 2, 18T126 x 2, 27T125 x 2, 36T493, 36T499 x 2 |
| 36T504 |
$(C_3\times \He_3):C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_4$, $C_3^2:C_4$, $(C_3\times C_3):C_4$, $(C_3\times \He_3):C_4$ |
18T131 x 4, 36T504 x 3 |
| 36T541 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $C_2^2$, $C_3\times S_3^2$ x 3, $C_3:S_3^2$ |
12T130 x 2, 18T120 x 6, 36T494 x 6, 36T517, 36T523 x 3, 36T530 x 6, 36T535 x 6, 36T541 |
| 36T542 |
$C_3^4:C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $C_4$, $C_3^3:C_4$ x 4 |
36T526 x 8, 36T542 x 11 |
| 36T545 |
$C_3^3:C_{12}$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$54$ |
$C_2$, $C_4$, $C_3^2:C_{12}$ x 4 |
36T515 x 8, 36T545 x 11 |
| 36T655 |
$D_6:S_3^2$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $S_3^2$, $S_3\times D_4$, $C_3:D_{12}$, $S_3^3$ |
24T1295 x 2, 36T655 x 3 |
| 36T661 |
$C_2\times C_6^2:C_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $A_4\times C_2$ x 3, $C_3^2 : S_3 $, $C_2^2 \times A_4$, $C_6^2:C_6$, $C_2\times C_6^2:C_6$ x 2 |
18T148 x 6, 36T571 x 3, 36T586 x 6, 36T587 x 6, 36T659 x 6, 36T661 x 5 |
| 36T790 |
$(C_2^2\times C_{12}).A_4$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$54$ |
$C_3$ x 4, $A_4\times C_2$, $C_3^2$, $C_2^3.(C_2\times A_4)$, $C_6\times A_4$ |
36T790 x 3 |
| 36T793 |
$C_2^2\times A_4^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$64$ |
$C_3$ x 4, $A_4\times C_2$, $C_3^2$, $C_6\times A_4$, $C_2\times A_4^2$ x 2 |
36T718 x 3, 36T792 x 6, 36T793 x 11, 36T936 x 4 |
| 36T797 |
$(C_2^2\times C_{12}).A_4$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$54$ |
$C_3$, $A_4\times C_2$, $C_9$, $C_2^3.(C_2\times A_4)$, $C_2^2:C_{18}$ |
36T797 x 3 |
| 36T822 |
$S_3\times C_2^3.A_4$ |
$576$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_3$, $S_3$, $A_4$, $S_3\times C_3$, $C_2^3.A_4$, $S_3\times A_4$ |
36T822 x 3 |
| 36T830 |
$C_2^3.(S_3\times A_4)$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_3$, $S_3$, $A_4\times C_2$, $S_3\times C_3$, $C_2^3.(C_2\times A_4)$, $S_3\times A_4$ |
36T830 x 3 |
| 36T833 |
$A_4^2:C_2^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$40$ |
$C_3$, $S_3$, $A_4\times C_2$, $S_3\times C_3$, $S_3\times A_4$, $A_4^2:C_2^2$ x 2 |
18T176 x 2, 24T1362 x 2, 24T1366 x 2, 32T34601 x 2, 36T722, 36T741 x 2, 36T742 x 2, 36T813 x 2, 36T824 x 2, 36T825 x 2, 36T832 x 2, 36T833, 36T842, 36T843 x 2, 36T875 x 2, 36T876 x 2, 36T877 x 4, 36T878 x 4 |
| 36T877 |
$A_4^2:C_2^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$40$ |
$C_3$, $S_3$, $A_4\times C_2$, $S_3\times C_3$, $A_4\times D_6$, $A_4\times S_4$, $A_4^2:C_2^2$ |
18T176 x 2, 24T1362 x 2, 24T1366 x 2, 32T34601 x 2, 36T722, 36T741 x 2, 36T742 x 2, 36T813 x 2, 36T824 x 2, 36T825 x 2, 36T832 x 2, 36T833 x 2, 36T842, 36T843 x 2, 36T875 x 2, 36T876 x 2, 36T877 x 3, 36T878 x 4 |
| 36T878 |
$A_4^2:C_2^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$40$ |
$C_3$, $S_3$, $A_4\times C_2$, $S_3\times C_3$, $A_4\times D_6$, $A_4\times S_4$, $A_4^2:C_2^2$ |
18T176 x 2, 24T1362 x 2, 24T1366 x 2, 32T34601 x 2, 36T722, 36T741 x 2, 36T742 x 2, 36T813 x 2, 36T824 x 2, 36T825 x 2, 36T832 x 2, 36T833 x 2, 36T842, 36T843 x 2, 36T875 x 2, 36T876 x 2, 36T877 x 4, 36T878 x 3 |
| 36T881 |
$C_2^2:A_4^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_3$ x 4, $C_3^2$, $A_4^2$ x 3 |
36T752 x 30, 36T881 x 19 |
| 36T885 |
$C_2^2:A_4^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$ x 4, $C_3^2$, $A_4^2$ x 2, $C_2^2:A_4^2$ |
12T164 x 3, 18T178 x 3, 24T1470 x 9, 36T753 x 9, 36T754 x 9, 36T882 x 9, 36T883 x 9, 36T884 x 3, 36T885 x 17, 36T958 x 3, 36T959 x 3 |
| 36T945 |
$S_3\times \GL(2,\mathbb{Z}/4)$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$42$ |
$S_3$ x 2, $S_4\times C_2$, $S_3^2$, $\GL(2,\mathbb{Z}/4)$, $D_6\times S_4$ |
36T768 x 2, 36T803 x 2, 36T945 x 3 |
| 36T948 |
$A_4^2:C_2^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_3$, $S_3$, $S_3\times C_3$, $A_4\wr C_2$, $A_4^2:C_2^2$ x 2 |
12T158, 16T1028, 18T175 x 2, 24T1481 x 2, 24T1484 x 2, 24T1485, 24T1486, 32T34599 x 2, 36T720, 36T723, 36T743 x 2, 36T744 x 2, 36T948, 36T949, 36T950, 36T951 x 2 |
| 36T952 |
$A_4^2:C_4$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$ x 4, $C_3^2:C_2$, $\PSOPlus(4,3)$ |
36T729, 36T870 x 2, 36T952 |
| 36T953 |
$A_4^2:C_2^2$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$ x 4, $C_3^2:C_2$, $\PSOPlus(4,3)$ |
18T183 x 2, 24T1364 x 4, 24T1480 x 4, 32T34605 x 2, 36T730, 36T781 x 2, 36T782 x 2, 36T844 x 2, 36T845 x 4, 36T871 x 4, 36T898 x 2, 36T899 x 2, 36T953 |
| 36T957 |
$C_2^6:C_9$ |
$576$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$, $C_9$, $C_2^6:C_9$ x 3 |
12T166 x 7, 18T177 x 7, 36T954 x 7, 36T955 x 21, 36T956 x 7, 36T957 x 41 |
| 36T996 |
$C_6\times C_3^2:D_6$ |
$648$ |
$1$ |
✓ |
$-1$ |
$66$ |
$C_2$ x 3, $C_2^2$, $S_3^2$, $S_3\times D_6$, $C_3^3:D_6$ |
36T996 x 3, 36T1024 x 4 |
| 36T997 |
$C_3\times C_6.S_3^2$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$66$ |
$C_2$, $C_4$, $S_3^2$, $C_6.D_6$, $C_3^3:D_6$ |
36T997 x 3, 36T1026 x 4 |
| 36T998 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$57$ |
$C_2$, $D_{4}$, $S_3^2$, $C_3:D_{12}$, $C_3^3:D_6$ |
36T998 x 3, 36T1025 x 2, 36T1027 x 2 |
Results are complete for degrees $\leq 23$.
