| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 18T1 |
$C_{18}$ |
$18$ |
$-1$ |
✓ |
$1$ |
$18$ |
$C_2$, $C_3$, $C_6$, $C_9$ |
|
| 18T2 |
$C_6 \times C_3$ |
$18$ |
$-1$ |
✓ |
$1$ |
$18$ |
$C_2$, $C_3$ x 4, $C_6$ x 4, $C_3^2$ |
|
| 18T3 |
$S_3 \times C_3$ |
$18$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $C_3$, $S_3$, $C_6$, $S_3$, $S_3\times C_3$, $S_3\times C_3$ |
6T5, 9T4 |
| 18T4 |
$C_3^2 : C_2$ |
$18$ |
$-1$ |
✓ |
$-1$ |
$6$ |
$C_2$, $S_3$ x 4, $S_3$ x 4, $C_3^2:C_2$ |
9T5 |
| 18T5 |
$D_9$ |
$18$ |
$-1$ |
✓ |
$-1$ |
$6$ |
$C_2$, $S_3$, $S_3$, $D_{9}$ |
9T3 |
| 18T6 |
$S_3 \times C_6$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_3$, $S_3$, $C_6$, $D_{6}$, $S_3\times C_3$ |
12T18, 18T6, 36T6 |
| 18T7 |
$C_2^2 : C_9$ |
$36$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $A_4$, $C_9$ |
36T11 |
| 18T8 |
$A_4 \times C_3$ |
$36$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$ x 4, $A_4$, $C_3^2$ |
12T20 x 3, 36T12 |
| 18T9 |
$S_3^2$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$ x 2, $D_{6}$ x 2, $S_3^2$, $S_3^2$ |
6T9, 9T8, 12T16, 18T11 x 2, 36T13 |
| 18T10 |
$C_3^2 : C_4$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$6$ |
$C_2$, $C_3^2:C_4$ x 2, $C_3^2:C_4$ |
6T10 x 2, 9T9, 12T17 x 2, 36T14 |
| 18T11 |
$S_3^2$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$ x 2, $S_3$, $D_{6}$, $S_3^2$ |
6T9, 9T8, 12T16, 18T9, 18T11, 36T13 |
| 18T12 |
$C_6:S_3$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$ x 4, $D_{6}$ x 4, $C_3^2:C_2$ |
18T12, 36T8 |
| 18T13 |
$D_{18}$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $D_{6}$, $D_{9}$ |
18T13, 36T10 |
| 18T14 |
$C_9:C_6$ |
$54$ |
$-1$ |
✓ |
$2$ |
$22$ |
$C_2$, $C_3$, $C_6$, $C_9:C_3$ |
|
| 18T15 |
$C_2\times \He_3$ |
$54$ |
$-1$ |
✓ |
$2$ |
$22$ |
$C_2$, $C_3$, $C_6$, $C_3^2:C_3$ |
18T15 x 3 |
| 18T16 |
$C_9\times S_3$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3$, $C_6$ |
27T12 |
| 18T17 |
$C_3^2\times S_3$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3$, $C_6$, $S_3\times C_3$ x 3 |
18T17 x 3, 27T15 |
| 18T18 |
$C_9:C_6$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_3$, $(C_9:C_3):C_2$ |
9T10, 27T14 |
| 18T19 |
$C_3\times D_9$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $S_3$ |
27T9 |
| 18T20 |
$C_3^2:C_6$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_3$, $C_6$, $C_3^2 : S_3 $ |
9T11, 9T13, 18T21, 18T22, 27T11 |
| 18T21 |
$C_3^2:C_6$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_3$, $C_3^2 : C_6$ |
9T11, 9T13, 18T20, 18T22, 27T11 |
| 18T22 |
$C_3^2:C_6$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3\times C_3$ |
9T11, 9T13, 18T20, 18T21, 27T11 |
| 18T23 |
$C_3^2:C_6$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $S_3$, $S_3\times C_3$ x 3 |
18T23 x 3, 27T13 |
| 18T24 |
$C_3^2:S_3$ |
$54$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_3$, $(C_3^2:C_3):C_2$ |
9T12 x 4, 18T24 x 3, 27T6 |
| 18T25 |
$C_6\times A_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_3$ x 4, $A_4\times C_2$, $C_3^2$ |
24T71 x 3, 36T18, 36T31 |
| 18T26 |
$C_2^2:C_{18}$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $A_4\times C_2$, $C_9$ |
36T16, 36T30 |
| 18T27 |
$C_2\times C_3^2:C_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $C_3^2:C_4$ |
12T40 x 2, 12T41 x 2, 18T27, 24T76 x 2, 36T35, 36T36 |
| 18T28 |
$F_9$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $C_3^2:C_8$ |
9T15, 12T46, 24T81, 36T49 |
| 18T29 |
$S_3\times D_6$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$ x 2, $D_{6}$ x 2, $S_3^2$ |
12T37 x 2, 18T29 x 3, 24T73, 36T34 x 2, 36T40 x 4 |
| 18T30 |
$C_3\times S_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_3$, $S_3$, $S_4$, $S_3\times C_3$ |
12T45, 18T33, 24T80, 24T84, 36T20, 36T52 |
| 18T31 |
$S_3\times A_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $S_3$, $A_4$, $S_3\times C_3$ |
12T43, 18T32, 24T78, 24T83, 36T21, 36T50, 36T51 |
| 18T32 |
$S_3\times A_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $S_3$, $A_4\times C_2$, $S_3\times C_3$ |
12T43, 18T31, 24T78, 24T83, 36T21, 36T50, 36T51 |
| 18T33 |
$C_3\times S_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_3$, $S_3$, $S_4$, $S_3\times C_3$ |
12T45, 18T30, 24T80, 24T84, 36T20, 36T52 |
| 18T34 |
$\SOPlus(4,2)$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $C_3^2:D_4$, $S_3^2:C_2$ |
6T13 x 2, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
| 18T35 |
$\PSU(3,2)$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$6$ |
$C_2$, $C_3^2:Q_8$ |
9T14, 12T47, 18T35 x 2, 24T82, 36T55 |
| 18T36 |
$\SOPlus(4,2)$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3^2:C_2$ |
6T13 x 2, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 24T72 x 2, 36T53, 36T54 x 2 |
| 18T37 |
$C_3:S_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$9$ |
$S_3$ x 4, $S_4$, $C_3^2:C_2$ |
12T44 x 3, 18T40, 24T79 x 3, 36T23, 36T56 |
| 18T38 |
$C_2^2:D_9$ |
$72$ |
$1$ |
✓ |
$-1$ |
$9$ |
$S_3$, $S_4$, $D_{9}$ |
18T39, 36T25, 36T57 |
| 18T39 |
$C_2^2:D_9$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$S_3$, $S_4$, $D_{9}$ |
18T38, 36T25, 36T57 |
| 18T40 |
$C_3:S_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$S_3$ x 4, $S_4$, $C_3^2:C_2$ |
12T44 x 3, 18T37, 24T79 x 3, 36T23, 36T56 |
| 18T41 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $C_3^2 : C_6$ |
18T41, 18T42 x 2, 36T71, 36T73, 36T75 |
| 18T42 |
$C_3^2:D_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3$, $C_6$, $C_3^2 : S_3 $ |
18T41 x 2, 18T42, 36T71, 36T73, 36T75 |
| 18T43 |
$C_3\times S_3^2$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3$, $C_6$, $S_3^2$ |
12T70, 18T46 x 2, 27T36, 36T80, 36T82 x 2, 36T92 |
| 18T44 |
$C_3^2:C_{12}$ |
$108$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_3$, $C_6$, $C_3^2:C_4$ |
12T73 x 2, 18T44, 27T33, 36T81 x 2, 36T95 x 2 |
| 18T45 |
$C_{18}:C_6$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $(C_9:C_3):C_2$ |
18T45, 36T67 |
| 18T46 |
$C_3\times S_3^2$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $S_3$, $D_{6}$, $S_3\times C_3$ |
12T70, 18T43, 18T46, 27T36, 36T80, 36T82 x 2, 36T92 |
| 18T47 |
$C_3^2.A_4$ |
$108$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$, $C_9:C_3$ |
18T47 x 2, 36T83 |
| 18T48 |
$C_3^2:A_4$ |
$108$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$, $C_3^2:C_3$ |
18T48 x 2, 36T84, 36T97 x 3 |
| 18T49 |
$\He_3:C_4$ |
$108$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $C_3^2:C_4$ |
18T49, 27T32, 36T85 x 2 |
| 18T50 |
$S_3\times D_9$ |
$108$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $D_{6}$ |
27T30, 36T86 |
Results are complete for degrees $\leq 23$.
