| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T1 |
$C_{12}$ |
$12$ |
$-1$ |
✓ |
$1$ |
$12$ |
$C_2$, $C_3$, $C_4$, $C_6$ |
|
| 12T2 |
$C_6\times C_2$ |
$12$ |
$1$ |
✓ |
$1$ |
$12$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3 |
|
| 12T3 |
$D_6$ |
$12$ |
$1$ |
✓ |
$-1$ |
$6$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2 |
6T3 x 2 |
| 12T4 |
$A_4$ |
$12$ |
$1$ |
✓ |
$-1$ |
$4$ |
$C_3$, $A_4$, $A_4$ |
4T4, 6T4 |
| 12T5 |
$C_3 : C_4$ |
$12$ |
$-1$ |
✓ |
$-1$ |
$6$ |
$C_2$, $S_3$, $C_4$, $S_3$ |
|
| 12T6 |
$A_4\times C_2$ |
$24$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_3$, $A_4$, $A_4\times C_2$ |
6T6, 8T13, 12T7, 24T9 |
| 12T7 |
$A_4 \times C_2$ |
$24$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_2$, $C_3$, $C_6$, $A_4$, $A_4\times C_2$ |
6T6, 8T13, 12T6, 24T9 |
| 12T8 |
$S_4$ |
$24$ |
$-1$ |
✓ |
$-1$ |
$5$ |
$S_3$, $S_4$, $S_4$ |
4T5, 6T7, 6T8, 8T14, 12T9, 24T10 |
| 12T9 |
$S_4$ |
$24$ |
$1$ |
✓ |
$-1$ |
$5$ |
$C_2$, $S_3$, $S_3$, $S_4$, $S_4$ |
4T5, 6T7, 6T8, 8T14, 12T8, 24T10 |
| 12T10 |
$S_3 \times C_2^2$ |
$24$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3 |
12T10 x 3, 24T11 |
| 12T11 |
$S_3 \times C_4$ |
$24$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $C_4$, $D_{6}$ |
12T11, 24T12 |
| 12T12 |
$D_{12}$ |
$24$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$ |
12T12, 24T13 |
| 12T13 |
$(C_6\times C_2):C_2$ |
$24$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$ |
12T15, 24T14 |
| 12T14 |
$D_4 \times C_3$ |
$24$ |
$-1$ |
✓ |
$2$ |
$15$ |
$C_2$, $C_3$, $D_{4}$, $C_6$ |
12T14, 24T15 |
| 12T15 |
$(C_6\times C_2):C_2$ |
$24$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$, $D_{4}$, $S_3$ |
12T13, 24T14 |
| 12T16 |
$S_3^2$ |
$36$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$ x 3, $C_2^2$, $S_3^2$ |
6T9, 9T8, 18T9, 18T11 x 2, 36T13 |
| 12T17 |
$(C_3\times C_3):C_4$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$6$ |
$C_2$, $C_4$, $C_3^2:C_4$ |
6T10 x 2, 9T9, 12T17, 18T10, 36T14 |
| 12T18 |
$C_6\times S_3$ |
$36$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $C_2^2$, $S_3\times C_3$ |
18T6 x 2, 36T6 |
| 12T19 |
$C_3\times (C_3 : C_4)$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_4$, $S_3\times C_3$ |
36T5 |
| 12T20 |
$C_3\times A_4$ |
$36$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $A_4$ |
12T20 x 2, 18T8, 36T12 |
| 12T21 |
$C_2\times S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_3$, $S_4\times C_2$ x 2 |
6T11 x 2, 8T24 x 2, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2 |
| 12T22 |
$C_2 \times S_4$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$S_3$, $S_4$ |
6T11 x 2, 8T24 x 2, 12T21, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2 |
| 12T23 |
$C_2 \times S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$ |
6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2 |
| 12T24 |
$C_2 \times S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$ |
6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24, 16T61, 24T46, 24T47, 24T48 x 2 |
| 12T25 |
$C_2^2 \times A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_3$, $C_6$, $A_4\times C_2$ x 2 |
12T25 x 2, 12T26 x 2, 16T58, 24T49 x 3, 24T50 |
| 12T27 |
$A_4:C_4$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$S_3$, $S_4$ |
12T30, 16T62, 24T51, 24T57 |
| 12T28 |
$S_3\times D_4$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$ |
12T28 x 3, 24T52 x 2, 24T53 x 2, 24T54 x 2 |
| 12T29 |
$C_4\times A_4$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_3$, $C_6$ |
16T57, 24T55, 24T56 |
| 12T30 |
$A_4:C_4$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_3$ |
12T27, 16T62, 24T51, 24T57 |
| 12T31 |
$C_4^2:C_3$ |
$48$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_3$, $A_4$ |
12T31, 16T63, 24T58 |
| 12T32 |
$C_2^4:C_3$ |
$48$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_3$, $A_4$ x 3 |
12T32 x 9, 16T64, 24T59 x 5 |
| 12T33 |
$A_5$ |
$60$ |
$1$ |
|
$-1$ |
$5$ |
$\PSL(2,5)$ |
5T4, 6T12, 10T7, 15T5, 20T15, 30T9 |
| 12T34 |
$\SOPlus(4,2)$ |
$72$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$ x 3, $C_2^2$, $C_3^2:D_4$ |
6T13 x 2, 9T16, 12T34, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
| 12T35 |
$\SOPlus(4,2)$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $D_{4}$, $C_3^2:D_4$ |
6T13 x 2, 9T16, 12T34 x 2, 12T35, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
| 12T36 |
$\SOPlus(4,2)$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $D_{4}$, $C_3^2:D_4$ |
6T13 x 2, 9T16, 12T34 x 2, 12T35 x 2, 12T36, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
| 12T37 |
$S_3\times D_6$ |
$72$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $C_2^2$, $S_3^2$ |
12T37, 18T29 x 4, 24T73, 36T34 x 2, 36T40 x 4 |
| 12T39 |
$C_6.D_6$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_4$, $S_3^2$ |
12T39, 24T75, 36T32 x 2 |
| 12T40 |
$C_2\times C_3^2:C_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$ x 3, $C_2^2$, $C_3^2:C_4$ |
12T40, 12T41 x 2, 18T27 x 2, 24T76 x 2, 36T35, 36T36 |
| 12T41 |
$C_2\times C_3^2:C_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $C_4$, $C_3^2:C_4$ |
12T40 x 2, 12T41, 18T27 x 2, 24T76 x 2, 36T35, 36T36 |
| 12T42 |
$C_6\wr C_2$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $D_{4}$, $S_3\times C_3$ |
12T42, 24T77, 36T19, 36T26 |
| 12T43 |
$S_3\times A_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$12$ |
$S_3$, $A_4$ |
18T31, 18T32, 24T78, 24T83, 36T21, 36T50, 36T51 |
| 12T44 |
$C_3:S_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$S_3$, $S_4$ |
12T44 x 2, 18T37, 18T40, 24T79 x 3, 36T23, 36T56 |
| 12T45 |
$C_3\times S_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_3$, $S_4$ |
18T30, 18T33, 24T80, 24T84, 36T20, 36T52 |
| 12T46 |
$F_9$ |
$72$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $C_4$ |
9T15, 18T28, 24T81, 36T49 |
| 12T47 |
$\PSU(3,2)$ |
$72$ |
$1$ |
✓ |
$-1$ |
$6$ |
$C_2$ x 3, $C_2^2$ |
9T14, 18T35 x 3, 24T82, 36T55 |
| 12T48 |
$C_2^2\times S_4$ |
$96$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $S_4\times C_2$ x 2 |
12T48 x 11, 16T182 x 4, 24T125, 24T126 x 6, 24T150 x 3, 24T151 x 4, 24T152 x 4, 32T388 |
| 12T50 |
$\GL(2,\mathbb{Z}/4)$ |
$96$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $S_3$, $S_3$ |
12T49 x 2, 12T52, 16T186, 16T193, 24T153, 24T154, 24T155 x 2, 24T156, 24T157, 24T158, 24T159, 24T165, 24T166, 32T392 |
| 12T51 |
$D_4\times A_4$ |
$96$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3$, $C_6$ |
12T51, 16T179 x 2, 24T160, 24T161 x 2, 24T162 x 2, 24T163 x 2, 24T164 x 2, 32T385 |
| 12T52 |
$\GL(2,\mathbb{Z}/4)$ |
$96$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $S_3$, $D_{6}$ |
12T49 x 2, 12T50, 16T186, 16T193, 24T153, 24T154, 24T155 x 2, 24T156, 24T157, 24T158, 24T159, 24T165, 24T166, 32T392 |
| 12T53 |
$C_4\times S_4$ |
$96$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$ |
12T53, 16T181 x 2, 24T129, 24T130, 24T167, 24T168 x 2, 24T169 x 2, 32T387 |
Results are complete for degrees $\leq 23$.
