| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T171 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $C_2^2$ |
12T171 x 7, 18T190 x 8, 18T192 x 8, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
| 18T190 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$ x 2 |
12T171 x 8, 18T190 x 7, 18T192 x 8, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
| 18T192 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$ |
12T171 x 8, 18T190 x 8, 18T192 x 7, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
| 24T1523 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_3^4:(C_2\times C_4)$ |
12T171 x 8, 18T190 x 8, 18T192 x 8, 24T1523 x 7, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
| 36T1082 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $C_2^2$, $C_3^2:C_4$ x 2, $C_2\times C_3^2:C_4$ x 2, $C_3^4:(C_2\times C_4)$, $C_3^4:(C_2\times C_4)$ |
12T171 x 8, 18T190 x 8, 18T192 x 8, 24T1523 x 8, 36T1082 x 7, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
| 36T1083 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_4$, $C_3^2:C_4$ x 2, $(C_3\times C_3):C_4$, $C_2\times C_3^2:C_4$, $C_3^4:(C_2\times C_4)$ |
12T171 x 8, 18T190 x 8, 18T192 x 8, 24T1523 x 8, 36T1082 x 8, 36T1083 x 15, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
| 36T1087 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $C_2^2$, $C_3^4:(C_2\times C_4)$ x 2, $C_3^4:(C_2\times C_4)$ |
12T171 x 8, 18T190 x 8, 18T192 x 8, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 7, 36T1198 x 16, 36T1233 x 8 |
| 36T1198 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $C_2^2$, $C_3^2:C_4$, $C_2\times C_3^2:C_4$, $C_3^4:(C_2\times C_4)$ x 3 |
12T171 x 8, 18T190 x 8, 18T192 x 8, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 15, 36T1233 x 8 |
| 36T1233 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $C_2^2$, $C_3^4:(C_2\times C_4)$ x 4 |
12T171 x 8, 18T190 x 8, 18T192 x 8, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 7 |
Results are complete for degrees $\leq 23$.
