| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 24T1 |
$C_{24}$ |
$24$ |
$-1$ |
✓ |
$1$ |
$24$ |
$C_2$, $C_3$, $C_4$, $C_6$, $C_8$, $C_{12}$ |
|
| 24T2 |
$C_2\times C_{12}$ |
$24$ |
$1$ |
✓ |
$1$ |
$24$ |
$C_2$ x 3, $C_3$, $C_4$ x 2, $C_2^2$, $C_6$ x 3, $C_4\times C_2$, $C_{12}$ x 2, $C_6\times C_2$ |
|
| 24T3 |
$C_2^2\times C_6$ |
$24$ |
$1$ |
✓ |
$1$ |
$24$ |
$C_2$ x 7, $C_3$, $C_2^2$ x 7, $C_6$ x 7, $C_2^3$, $C_6\times C_2$ x 7 |
|
| 24T4 |
$C_3\times Q_8$ |
$24$ |
$1$ |
✓ |
$2$ |
$15$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8$, $C_6\times C_2$ |
|
| 24T5 |
$C_3:Q_8$ |
$24$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8$, $D_6$ |
|
| 24T6 |
$C_6:C_4$ |
$24$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $S_3$, $D_{6}$ x 2, $C_4\times C_2$, $D_6$, $C_3 : C_4$ x 2 |
|
| 24T7 |
$\SL(2,3)$ |
$24$ |
$1$ |
✓ |
$-1$ |
$7$ |
$C_3$, $A_4$, $A_4$, $\SL(2,3)$, $A_4$ |
8T12 |
| 24T8 |
$C_3:C_8$ |
$24$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $C_4$, $S_3$, $C_8$, $C_3 : C_4$ |
|
| 24T9 |
$C_2\times A_4$ |
$24$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_2$, $C_3$, $A_4$, $C_6$, $A_4$, $A_4\times C_2$, $A_4\times C_2$, $A_4$, $A_4\times C_2$, $A_4 \times C_2$ |
6T6, 8T13, 12T6, 12T7 |
| 24T10 |
$S_4$ |
$24$ |
$1$ |
✓ |
$-1$ |
$5$ |
$C_2$, $S_3$, $S_4$, $S_3$, $S_4$, $S_4$, $S_4$, $S_4$, $S_4$ |
4T5, 6T7, 6T8, 8T14, 12T8, 12T9 |
| 24T11 |
$C_2\times D_6$ |
$24$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$ x 7, $S_3$, $C_2^2$ x 7, $S_3$, $D_{6}$ x 6, $C_2^3$, $D_6$ x 3, $S_3 \times C_2^2$ x 4 |
12T10 x 4 |
| 24T12 |
$C_4\times S_3$ |
$24$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $S_3$, $D_{6}$ x 2, $C_4\times C_2$, $D_6$, $S_3 \times C_4$ x 2 |
12T11 x 2 |
| 24T13 |
$D_{12}$ |
$24$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4$, $D_6$, $D_{12}$ x 2 |
12T12 x 2 |
| 24T14 |
$C_3:D_4$ |
$24$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4$, $D_6$, $(C_6\times C_2):C_2$, $(C_6\times C_2):C_2$ |
12T13, 12T15 |
| 24T15 |
$C_3\times D_4$ |
$24$ |
$1$ |
✓ |
$2$ |
$15$ |
$C_2$ x 3, $C_3$, $C_2^2$, $D_{4}$ x 2, $C_6$ x 3, $D_4$, $C_6\times C_2$, $D_4 \times C_3$ x 2 |
12T14 x 2 |
| 24T16 |
$C_3\times \OD_{16}$ |
$48$ |
$-1$ |
✓ |
$2$ |
$30$ |
$C_2$, $C_3$, $C_4$, $C_6$, $C_8:C_2$, $C_{12}$ |
|
| 24T17 |
$D_4:C_6$ |
$48$ |
$1$ |
✓ |
$2$ |
$30$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8:C_2$, $C_6\times C_2$ |
24T17 x 2 |
| 24T18 |
$D_4:S_3$ |
$48$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8:C_2$, $D_6$ |
24T18, 24T23 |
| 24T19 |
$D_{12}:C_2$ |
$48$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8:C_2$, $D_6$ |
24T24 x 2 |
| 24T20 |
$C_3:\OD_{16}$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $C_4$, $S_3$, $C_8:C_2$, $C_3 : C_4$ |
|
| 24T21 |
$\SL(2,3):C_2$ |
$48$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_3$, $A_4$, $A_4\times C_2$, $A_4\times C_2$ |
16T60 |
| 24T22 |
$\GL(2,3)$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$8$ |
$S_3$, $S_4$, $S_4$, $\textrm{GL(2,3)}$ x 2, $S_4$ |
8T23 x 2, 16T66 |
| 24T23 |
$D_4:S_3$ |
$48$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ |
24T18 x 2 |
| 24T24 |
$D_{12}:C_2$ |
$48$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ |
24T19, 24T24 |
| 24T25 |
$C_6:D_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $D_{6}$ x 3, $D_4\times C_2$, $S_3 \times C_2^2$, $(C_6\times C_2):C_2$ x 2 |
24T25, 24T45 x 2 |
| 24T26 |
$S_3\times Q_8$ |
$48$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8$, $S_3 \times C_2^2$ |
24T26 |
| 24T27 |
$C_4\times D_6$ |
$48$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $D_{6}$ x 3, $C_4\times C_2$, $S_3 \times C_2^2$, $S_3 \times C_4$ x 2 |
24T27 x 3 |
| 24T28 |
$D_{12}:C_2$ |
$48$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ |
24T28 x 2 |
| 24T29 |
$C_2\times D_{12}$ |
$48$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $D_{6}$ x 3, $D_4\times C_2$, $S_3 \times C_2^2$, $D_{12}$ x 2 |
24T29 x 3 |
| 24T30 |
$C_2^2\times D_6$ |
$48$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 7, $S_3$, $C_2^2$ x 7, $D_{6}$ x 7, $C_2^3$, $S_3 \times C_2^2$ x 7 |
24T30 x 7 |
| 24T31 |
$C_{24}:C_2$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $C_4$, $D_{6}$, $C_8:C_2$, $S_3 \times C_4$ |
|
| 24T32 |
$S_3\times C_8$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $S_3$, $C_4$, $D_{6}$, $C_8$, $S_3 \times C_4$ |
24T32 |
| 24T33 |
$D_6:C_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $C_4$, $D_{4}$ x 2, $D_{6}$, $C_2^2:C_4$, $S_3 \times C_4$, $D_{12}$, $(C_6\times C_2):C_2$ |
24T33 |
| 24T34 |
$D_{24}$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{8}$, $D_{12}$ |
24T34 |
| 24T35 |
$C_{24}:C_2$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $QD_{16}$, $D_{12}$ |
|
| 24T36 |
$Q_8:S_3$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $QD_{16}$, $(C_6\times C_2):C_2$ |
|
| 24T37 |
$C_3:D_8$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{8}$, $(C_6\times C_2):C_2$ |
24T43 |
| 24T38 |
$C_6\times D_4$ |
$48$ |
$1$ |
✓ |
$2$ |
$30$ |
$C_2$ x 3, $C_3$, $C_2^2$, $D_{4}$ x 2, $C_6$ x 3, $D_4\times C_2$, $C_6\times C_2$, $D_4 \times C_3$ x 2 |
24T38 x 3 |
| 24T39 |
$C_2^2:C_{12}$ |
$48$ |
$1$ |
✓ |
$2$ |
$30$ |
$C_2$, $C_3$, $C_4$, $D_{4}$ x 2, $C_6$, $C_2^2:C_4$, $C_{12}$, $D_4 \times C_3$ x 2 |
24T39 |
| 24T40 |
$C_3\times D_8$ |
$48$ |
$-1$ |
✓ |
$3$ |
$21$ |
$C_2$, $C_3$, $D_{4}$, $C_6$, $D_{8}$, $D_4 \times C_3$ |
24T40 |
| 24T41 |
$C_3\times \SD_{16}$ |
$48$ |
$-1$ |
✓ |
$3$ |
$21$ |
$C_2$, $C_3$, $D_{4}$, $C_6$, $QD_{16}$, $D_4 \times C_3$ |
|
| 24T42 |
$C_3:\SD_{16}$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $D_{4}$, $S_3$, $QD_{16}$, $(C_6\times C_2):C_2$ |
|
| 24T43 |
$C_3:D_8$ |
$48$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $D_{4}$, $S_3$, $D_{8}$, $(C_6\times C_2):C_2$ |
24T37 |
| 24T44 |
$C_6.D_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $C_4$, $D_{4}$ x 2, $S_3$, $C_2^2:C_4$, $C_3 : C_4$, $(C_6\times C_2):C_2$ x 2 |
24T44 |
| 24T45 |
$C_6:D_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4\times C_2$, $D_6$, $(C_6\times C_2):C_2$ x 2 |
24T25 x 2, 24T45 |
| 24T46 |
$C_2\times S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_3$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $S_4$, $C_2\times S_4$, $C_2 \times S_4$ |
6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T47, 24T48 x 2 |
| 24T47 |
$C_2\times S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $S_4$, $S_4$, $S_4\times C_2$ x 2, $D_6$, $S_4$, $C_2\times S_4$, $C_2 \times S_4$ x 2, $C_2 \times S_4$ x 2 |
6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T48 x 2 |
| 24T48 |
$C_2\times S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_4$, $D_{6}$, $S_4$, $S_4\times C_2$, $S_4\times C_2$, $S_4$, $C_2 \times S_4$, $C_2 \times S_4$ |
6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 |
| 24T49 |
$C_2^2\times A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_3$, $C_6$, $A_4$, $A_4\times C_2$ x 3, $A_4\times C_2$ x 2, $A_4 \times C_2$, $C_2^2 \times A_4$, $C_2^2 \times A_4$ x 2 |
12T25 x 3, 12T26 x 2, 16T58, 24T49 x 2, 24T50 |
| 24T50 |
$C_2^2\times A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $A_4$, $A_4\times C_2$ x 3, $C_6\times C_2$, $A_4 \times C_2$ x 3, $C_2^2 \times A_4$ x 3 |
12T25 x 3, 12T26 x 2, 16T58, 24T49 x 3 |
Results are complete for degrees $\leq 23$.
