| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 17T5 |
$F_{17}$ |
$272$ |
$-1$ |
✓ |
$-1$ |
$17$ |
|
|
| 18T109 |
$C_2\times A_4^2$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_3$ x 4, $C_3^2$ |
24T579 x 2, 24T684 x 2, 32T9309, 36T314, 36T345 x 2, 36T346 x 2, 36T368, 36T369 x 4, 36T427 x 2 |
| 18T110 |
$F_9:C_2^2$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $(C_3^2:C_8):C_2$ |
18T110 x 3, 24T681 x 2, 24T682 x 2, 36T442, 36T444 x 2, 36T450 x 2, 36T453, 36T455 x 2 |
| 18T111 |
$D_6\times S_4$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$S_3$ x 2, $S_4\times C_2$, $S_3^2$ |
18T111 x 3, 24T679 x 4, 36T350 x 2, 36T354 x 2, 36T358 x 2, 36T374 x 4, 36T375 x 4, 36T376 x 4, 36T377 x 4, 36T451 x 2 |
| 18T112 |
$A_4\wr C_2$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_3$, $S_3$, $S_3\times C_3$ |
8T42, 12T126, 12T128, 12T129, 16T708, 18T113, 24T692, 24T694, 24T695, 24T702, 24T703, 24T704, 32T9306, 36T316, 36T318, 36T456, 36T457, 36T458, 36T459 |
| 18T113 |
$A_4\wr C_2$ |
$288$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_3$, $S_3$, $S_3\times C_3$ |
8T42, 12T126, 12T128, 12T129, 16T708, 18T112, 24T692, 24T694, 24T695, 24T702, 24T703, 24T704, 32T9306, 36T316, 36T318, 36T456, 36T457, 36T458, 36T459 |
| 18T114 |
$A_4\times S_4$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $S_3$, $S_3\times C_3$ |
16T709, 18T115, 24T634, 24T635, 24T638, 24T639, 24T705, 32T9307, 36T321, 36T380, 36T381, 36T388, 36T389, 36T390, 36T392, 36T393 x 2, 36T399 |
| 18T115 |
$A_4\times S_4$ |
$288$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $S_3$, $S_3\times C_3$ |
16T709, 18T114, 24T634, 24T635, 24T638, 24T639, 24T705, 32T9307, 36T321, 36T380, 36T381, 36T388, 36T389, 36T390, 36T392, 36T393 x 2, 36T399 |
| 18T116 |
$\PSOPlus(4,3)$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$ x 4, $C_3^2:C_2$ |
12T127 x 2, 16T710, 18T117, 24T636 x 2, 24T637 x 2, 24T693 x 2, 32T9308, 36T324, 36T403 x 2, 36T404 x 2, 36T405, 36T420, 36T460 x 2 |
| 18T117 |
$\PSOPlus(4,3)$ |
$288$ |
$1$ |
✓ |
$-1$ |
$14$ |
$S_3$ x 4, $C_3^2:C_2$ |
12T127 x 2, 16T710, 18T116, 24T636 x 2, 24T637 x 2, 24T693 x 2, 32T9308, 36T324, 36T403 x 2, 36T404 x 2, 36T405, 36T420, 36T460 x 2 |
| 18T118 |
$C_3^3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3^2$ |
18T118, 18T126 x 2, 27T125 x 2, 36T493 x 2, 36T499 x 2 |
| 18T119 |
$C_3^3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$44$ |
$C_2$, $S_3$, $D_{6}$, $C_3 \wr S_3 $ |
18T119 x 5, 36T486 x 3 |
| 18T120 |
$C_3\wr C_2^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $S_3\times C_3$, $S_3^2$ |
12T130 x 2, 18T120 x 5, 36T494 x 6, 36T517, 36T523 x 3, 36T530 x 6, 36T535 x 6, 36T541 x 2 |
| 18T121 |
$C_3^2:S_3^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$ |
18T124, 27T115, 27T119, 36T495, 36T498, 36T533 |
| 18T122 |
$C_3^2.S_3^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$ |
27T116, 36T496 |
| 18T123 |
$C_3\wr C_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3\times C_3$, $C_3^2:C_4$ |
12T131 x 4, 18T123 x 3, 36T497 x 4, 36T514 x 2, 36T527 x 2, 36T532 x 4, 36T536 x 4, 36T543 x 4, 36T544 x 8 |
| 18T124 |
$C_3^2:S_3^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $C_3$, $C_6$ |
18T121, 27T115, 27T119, 36T495, 36T498, 36T533 |
| 18T125 |
$\He_3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_3$, $C_6$, $(C_3^3:C_3):C_2$ |
18T125 x 5, 36T484 x 3 |
| 18T126 |
$C_3^3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3$, $D_{6}$ |
18T118 x 2, 18T126, 27T125 x 2, 36T493 x 2, 36T499 x 2 |
| 18T127 |
$C_3^3:A_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$44$ |
$C_3$, $A_4$, $C_3 \wr C_3 $ |
18T127 x 8, 36T500 x 3 |
| 18T128 |
$C_3^4:C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$ x 4 |
18T128 x 59, 36T501 x 60 |
| 18T129 |
$C_3^3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $S_3$, $S_3$, $((C_3^3:C_3):C_2):C_2$ |
9T24 x 3, 18T129 x 2, 18T136 x 3, 18T137 x 3, 27T121, 27T128 x 3, 27T129, 36T502 x 3 |
| 18T130 |
$C_9^2:C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$ |
18T130 x 5, 36T503 x 6 |
| 18T131 |
$(C_3\times \He_3):C_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$ |
18T131 x 3, 36T504 x 4 |
| 18T132 |
$C_3^2:D_{18}$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{6}$ |
27T126, 36T505 |
| 18T133 |
$C_3^2:S_3^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $S_3$ |
18T139, 27T117 x 3, 27T127, 36T506, 36T509, 36T528 |
| 18T134 |
$C_3^3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $S_3$, $D_{6}$, $(C_3^3:C_3):C_2$ |
18T134 x 5, 36T490 x 3 |
| 18T135 |
$C_3^2:S_3^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$ |
18T135 x 3, 27T118 x 4, 36T507 x 4 |
| 18T136 |
$C_3^3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $S_3$, $D_{6}$, $((C_3^3:C_3):C_2):C_2$ |
9T24 x 3, 18T129 x 3, 18T136 x 2, 18T137 x 3, 27T121, 27T128 x 3, 27T129, 36T502 x 3 |
| 18T137 |
$C_3^3:D_6$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $S_3$, $D_{6}$, $((C_3^3:C_3):C_2):C_2$ |
9T24 x 3, 18T129 x 3, 18T136 x 3, 18T137 x 2, 27T121, 27T128 x 3, 27T129, 36T502 x 3 |
| 18T138 |
$C_3^2:S_3^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3^2$ x 4 |
18T138 x 23, 36T508 x 24 |
| 18T139 |
$C_3^2:S_3^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{6}$ |
18T133, 27T117 x 3, 27T127, 36T506, 36T509, 36T528 |
| 18T140 |
$D_9^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3^2$ |
18T140 x 2, 36T510 x 3 |
| 18T141 |
$C_3^3:A_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_3$, $A_4$, $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
9T25, 12T132 x 2, 12T133, 18T141, 18T142, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
| 18T142 |
$C_3^3:A_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_3$, $A_4$ |
9T25, 12T132 x 2, 12T133, 18T141 x 2, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
| 18T143 |
$C_3^3:A_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_3$, $A_4$, $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
9T25, 12T132 x 2, 12T133, 18T141 x 2, 18T142, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
| 18T144 |
$C_3\times S_5$ |
$360$ |
$-1$ |
|
$-1$ |
$21$ |
$C_3$, $\PGL(2,5)$ |
15T24, 30T90, 30T98, 30T103, 36T550, 45T44 |
| 18T145 |
$S_3\times A_5$ |
$360$ |
$1$ |
|
$-1$ |
$15$ |
$S_3$, $\PSL(2,5)$ |
15T23, 30T85, 30T94, 30T102, 36T551, 36T552, 36T553, 45T40 |
| 18T146 |
$C_3:S_5$ |
$360$ |
$-1$ |
|
$-1$ |
$12$ |
$S_3$, $\PGL(2,5)$ |
15T21 x 2, 15T22, 30T89, 30T93 x 2, 30T101, 36T554, 45T45 |
| 18T147 |
$C_6^2.D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$38$ |
$S_3$, $S_4\times C_2$, $(C_9:C_3):C_2$ |
18T147, 36T565, 36T566, 36T595 x 2, 36T596 x 2, 36T660 |
| 18T148 |
$C_2\times C_6^2:C_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $A_4\times C_2$, $C_3^2 : S_3 $ |
18T148 x 5, 36T571 x 3, 36T586 x 6, 36T587 x 6, 36T659 x 6, 36T661 x 6 |
| 18T149 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$38$ |
$S_3$, $S_4\times C_2$, $C_3^2 : C_6$ |
18T149, 36T573, 36T575, 36T583 x 2, 36T584 x 2, 36T658 |
| 18T150 |
$S_3^3:C_2$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $S_3$, $D_{6}$, $C_3^2:D_4$ |
12T156 x 2, 18T150, 24T1322 x 2, 24T1323 x 2, 24T1324 x 2, 27T137, 36T680 x 2, 36T681 x 2, 36T682 x 2, 36T683 x 2, 36T684 x 2, 36T685 x 2, 36T686 x 2, 36T699 x 2 |
| 18T151 |
$C_2\times \PGU(3,2)$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $(C_3^2:Q_8):C_3$ |
24T1320, 24T1321 |
| 18T152 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $C_3^2 : D_{6} $ |
18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 18T153 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4\times C_2$, $C_3^2 : D_{6} $ |
18T152, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 18T154 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $C_3^2 : D_{6} $ |
18T152, 18T153, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 18T155 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4\times C_2$, $C_3^2 : D_{6} $ |
18T152, 18T153, 18T154, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 18T156 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$38$ |
$S_3$, $S_4\times C_2$, $(C_3^2:C_3):C_2$ |
18T156, 36T579, 36T581, 36T614 x 2, 36T615 x 2, 36T679 |
| 18T157 |
$C_3^2:\GL(2,3)$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$11$ |
$C_2$, $((C_3^2:Q_8):C_3):C_2$ |
9T26, 12T157, 24T1325, 24T1326, 24T1327, 24T1334, 27T139, 36T689, 36T709 |
Results are complete for degrees $\leq 23$.
