| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 36T1 |
$C_{36}$ |
$36$ |
$-1$ |
✓ |
$1$ |
$36$ |
$C_2$, $C_3$, $C_4$, $C_6$, $C_9$, $C_{12}$, $C_{18}$ |
|
| 36T2 |
$C_2\times C_{18}$ |
$36$ |
$1$ |
✓ |
$1$ |
$36$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $C_9$, $C_6\times C_2$, $C_{18}$ x 3 |
|
| 36T3 |
$C_3\times C_{12}$ |
$36$ |
$-1$ |
✓ |
$1$ |
$36$ |
$C_2$, $C_3$ x 4, $C_4$, $C_6$ x 4, $C_3^2$, $C_{12}$ x 4, $C_6 \times C_3$ |
|
| 36T4 |
$C_6^2$ |
$36$ |
$1$ |
✓ |
$1$ |
$36$ |
$C_2$ x 3, $C_3$ x 4, $C_2^2$, $C_6$ x 12, $C_3^2$, $C_6\times C_2$ x 4, $C_6 \times C_3$ x 3 |
|
| 36T5 |
$C_3:C_{12}$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_3$, $S_3$, $C_4$, $C_6$, $S_3$, $S_3\times C_3$, $S_3\times C_3$, $C_{12}$, $C_3 : C_4$, $C_3\times (C_3 : C_4)$, $S_3 \times C_3$ |
12T19 |
| 36T6 |
$C_6\times S_3$ |
$36$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $C_3$, $S_3$, $C_2^2$, $C_6$ x 3, $S_3$, $D_{6}$ x 2, $S_3\times C_3$, $S_3\times C_3$, $C_6\times C_2$, $D_6$, $C_6\times S_3$, $S_3 \times C_3$, $S_3 \times C_6$ x 2 |
12T18, 18T6 x 2 |
| 36T7 |
$C_3^2:C_4$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$ x 4, $C_4$, $S_3$ x 4, $C_3^2:C_2$, $C_3 : C_4$ x 4, $C_3^2 : C_2$ |
|
| 36T8 |
$C_6:S_3$ |
$36$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$ x 3, $S_3$ x 4, $C_2^2$, $S_3$ x 4, $D_{6}$ x 8, $C_3^2:C_2$, $D_6$ x 4, $C_3^2 : C_2$, $C_6:S_3$ x 2 |
18T12 x 2 |
| 36T9 |
$C_9:C_4$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $C_4$, $S_3$, $D_{9}$, $C_3 : C_4$, $D_9$ |
|
| 36T10 |
$D_{18}$ |
$36$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $D_{9}$, $D_6$, $D_9$, $D_{18}$ x 2 |
18T13 x 2 |
| 36T11 |
$C_2^2:C_9$ |
$36$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $A_4$, $A_4$, $C_9$, $A_4$, $C_2^2 : C_9$ |
18T7 |
| 36T12 |
$C_3\times A_4$ |
$36$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$ x 4, $A_4$, $A_4$, $C_3^2$, $A_4$, $C_3\times A_4$ x 3, $A_4 \times C_3$ |
12T20 x 3, 18T8 |
| 36T13 |
$S_3^2$ |
$36$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$ x 3, $S_3$ x 2, $C_2^2$, $S_3$ x 2, $D_{6}$ x 4, $S_3^2$, $S_3^2$, $D_6$ x 2, $S_3^2$, $S_3^2$, $S_3^2$ x 2 |
6T9, 9T8, 12T16, 18T9, 18T11 x 2 |
| 36T14 |
$C_3^2:C_4$ |
$36$ |
$-1$ |
✓ |
$-1$ |
$6$ |
$C_2$, $C_4$, $C_3^2:C_4$ x 2, $C_3^2:C_4$, $(C_3\times C_3):C_4$ x 2, $C_3^2 : C_4$ |
6T10 x 2, 9T9, 12T17 x 2, 18T10 |
Results are complete for degrees $\leq 23$.
