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 |
36T15 |
$D_4\times C_9$ |
$72$ |
$-1$ |
✓ |
$2$ |
$45$ |
$C_2$, $C_3$, $D_{4}$, $C_6$, $C_9$, $D_4 \times C_3$, $C_{18}$ |
36T15 |
36T16 |
$C_2^2:C_{18}$ |
$72$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3$, $C_6$, $A_4$, $A_4\times C_2$, $C_9$, $A_4 \times C_2$, $C_{18}$, $C_2^2 : C_9$, $C_2^2:C_{18}$ |
18T26, 36T30 |
36T17 |
$D_4\times C_3^2$ |
$72$ |
$-1$ |
✓ |
$2$ |
$45$ |
$C_2$, $C_3$ x 4, $D_{4}$, $C_6$ x 4, $C_3^2$, $D_4 \times C_3$ x 4, $C_6 \times C_3$ |
36T17 |
36T18 |
$C_6\times A_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3$ x 4, $C_6$ x 4, $A_4$, $A_4\times C_2$, $C_3^2$, $A_4 \times C_2$, $C_6 \times C_3$, $A_4 \times C_3$, $C_6\times A_4$ |
18T25, 24T71 x 3, 36T31 |
36T19 |
$C_6\wr C_2$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3$, $S_3$, $D_{4}$, $C_6$, $S_3$, $S_3\times C_3$, $S_3\times C_3$, $D_4 \times C_3$, $(C_6\times C_2):C_2$, $C_6\wr C_2$ x 2, $S_3 \times C_3$ |
12T42 x 2, 24T77, 36T26 |
36T20 |
$C_3\times S_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $C_3$, $S_3$, $C_6$, $S_3$, $S_3\times C_3$, $S_4$, $S_4$, $S_3\times C_3$, $S_4$, $S_3 \times C_3$, $C_3\times S_4$, $C_3\times S_4$ |
12T45, 18T30, 18T33, 24T80, 24T84, 36T52 |
36T21 |
$S_3\times A_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $C_3$, $S_3$, $C_6$, $S_3$, $A_4$, $S_3\times C_3$, $A_4\times C_2$, $S_3\times C_3$, $A_4 \times C_2$, $S_3 \times C_3$, $S_3\times A_4$, $S_3\times A_4$ |
12T43, 18T31, 18T32, 24T78, 24T83, 36T50, 36T51 |
36T22 |
$C_6^2:C_2$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$ x 4, $D_{4}$, $S_3$ x 4, $C_3^2:C_2$, $(C_6\times C_2):C_2$ x 4, $C_3^2 : C_2$ |
36T42 |
36T23 |
$C_3:S_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$ x 4, $S_3$ x 4, $S_4$, $S_4$, $C_3^2:C_2$, $S_4$, $C_3^2 : C_2$, $C_3:S_4$, $C_3:S_4$ |
12T44 x 3, 18T37, 18T40, 24T79 x 3, 36T56 |
36T24 |
$C_9:D_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{4}$, $S_3$, $D_{9}$, $(C_6\times C_2):C_2$, $D_9$ |
36T46 |
36T25 |
$C_2^2:D_9$ |
$72$ |
$1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$, $S_3$, $S_4$, $S_4$, $D_{9}$, $S_4$, $D_9$, $C_2^2:D_9$, $C_2^2:D_9$ |
18T38, 18T39, 36T57 |
36T26 |
$C_6\wr C_2$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3$, $S_3$, $D_{4}$, $C_6$, $D_{6}$, $S_3\times C_3$, $(C_6\times C_2):C_2$, $D_4 \times C_3$, $S_3 \times C_6$ |
12T42 x 2, 24T77, 36T19 |
36T27 |
$S_3\times C_{12}$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_3$, $S_3$, $C_4$, $C_6$, $D_{6}$, $S_3\times C_3$, $C_{12}$, $S_3 \times C_4$, $S_3 \times C_6$ |
24T65, 36T27 |
36T28 |
$C_3\times D_{12}$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3$, $S_3$, $D_{4}$, $C_6$, $D_{6}$, $S_3\times C_3$, $D_{12}$, $D_4 \times C_3$, $S_3 \times C_6$ |
24T67, 36T28 |
36T29 |
$C_6\times D_6$ |
$72$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_2$ x 3, $C_3$, $S_3$, $C_2^2$, $C_6$ x 3, $D_{6}$ x 3, $S_3\times C_3$, $C_6\times C_2$, $S_3 \times C_2^2$, $S_3 \times C_6$ x 3 |
24T68, 36T29 x 3 |
36T30 |
$C_2^2:C_{18}$ |
$72$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $A_4$, $A_4\times C_2$, $C_9$, $A_4\times C_2$, $C_2^2 : C_9$, $C_2^2:C_{18}$ |
18T26, 36T16 |
36T31 |
$C_6\times A_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$ x 4, $A_4$, $A_4\times C_2$, $C_3^2$, $A_4\times C_2$, $A_4 \times C_3$, $C_6\times A_4$ |
18T25, 24T71 x 3, 36T18 |
36T32 |
$C_6.D_6$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$ x 2, $C_4$, $D_{6}$ x 2, $S_3^2$, $S_3^2$, $S_3 \times C_4$ x 2, $C_6.D_6$, $S_3^2$ |
12T39 x 2, 24T75, 36T32 |
36T33 |
$C_3:D_{12}$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$ x 2, $D_{4}$, $D_{6}$ x 2, $S_3^2$, $S_3^2$, $D_{12}$, $(C_6\times C_2):C_2$, $C_3:D_{12}$ x 2, $S_3^2$ |
12T38 x 2, 24T74, 36T38 |
36T34 |
$S_3\times D_6$ |
$72$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $S_3$ x 2, $C_2^2$, $D_{6}$ x 6, $S_3^2$, $S_3^2$, $S_3 \times C_2^2$ x 2, $S_3\times D_6$, $S_3^2$, $S_3\times D_6$ x 2 |
12T37 x 2, 18T29 x 4, 24T73, 36T34, 36T40 x 4 |
36T35 |
$C_2\times C_3^2:C_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $C_4$, $C_3^2:C_4$ x 2, $C_3^2:C_4$, $C_2\times C_3^2:C_4$ x 2, $C_3^2 : C_4$ |
12T40 x 2, 12T41 x 2, 18T27 x 2, 24T76 x 2, 36T36 |
36T36 |
$C_2\times C_3^2:C_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_2$ x 3, $C_2^2$, $C_3^2:C_4$ x 2, $C_3^2:C_4$, $C_2\times C_3^2:C_4$ x 2, $C_3^2 : C_4$, $C_2\times C_3^2:C_4$ x 2 |
12T40 x 2, 12T41 x 2, 18T27 x 2, 24T76 x 2, 36T35 |
36T37 |
$C_6.D_6$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$ x 2, $C_4$, $S_3$, $D_{6}$, $S_3^2$, $C_3 : C_4$, $S_3 \times C_4$, $S_3^2$ |
24T60, 36T37 |
36T38 |
$C_3:D_{12}$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$ x 2, $D_{4}$, $S_3$, $D_{6}$, $S_3^2$, $D_{12}$, $(C_6\times C_2):C_2$, $S_3^2$ |
12T38 x 2, 24T74, 36T33 |
36T39 |
$D_6:S_3$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$ x 2, $D_{4}$, $S_3$, $D_{6}$, $S_3^2$, $(C_6\times C_2):C_2$, $(C_6\times C_2):C_2$, $S_3^2$ |
24T61, 36T39 |
36T40 |
$S_3\times D_6$ |
$72$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$ x 3, $S_3$ x 2, $C_2^2$, $S_3$, $D_{6}$ x 5, $S_3^2$, $D_6$, $S_3 \times C_2^2$, $S_3^2$, $S_3\times D_6$ x 2 |
12T37 x 2, 18T29 x 4, 24T73, 36T34 x 2, 36T40 x 3 |
36T41 |
$C_{12}:S_3$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $S_3$ x 4, $C_4$, $D_{6}$ x 4, $C_3^2:C_2$, $S_3 \times C_4$ x 4, $C_6:S_3$ |
36T41 |
36T42 |
$C_6^2:C_2$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$ x 4, $D_{4}$, $D_{6}$ x 4, $C_3^2:C_2$, $(C_6\times C_2):C_2$ x 4, $C_6:S_3$ |
36T22 |
36T43 |
$C_3:D_{12}$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$ x 4, $D_{4}$, $D_{6}$ x 4, $C_3^2:C_2$, $D_{12}$ x 4, $C_6:S_3$ |
36T43 |
36T44 |
$C_6:D_6$ |
$72$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $S_3$ x 4, $C_2^2$, $D_{6}$ x 12, $C_3^2:C_2$, $S_3 \times C_2^2$ x 4, $C_6:S_3$ x 3 |
36T44 x 3 |
36T45 |
$C_4\times D_9$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $S_3$, $C_4$, $D_{6}$, $D_{9}$, $S_3 \times C_4$, $D_{18}$ |
36T45 |
36T46 |
$C_9:D_4$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{9}$, $(C_6\times C_2):C_2$, $D_{18}$ |
36T24 |
36T47 |
$D_{36}$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{9}$, $D_{12}$, $D_{18}$ |
36T47 |
36T48 |
$C_2\times D_{18}$ |
$72$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $D_{9}$, $S_3 \times C_2^2$, $D_{18}$ x 3 |
36T48 x 3 |
36T49 |
$F_9$ |
$72$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $C_4$, $C_3^2:C_8$, $F_9$, $F_9$ |
9T15, 12T46, 18T28, 24T81 |
36T50 |
$S_3\times A_4$ |
$72$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $S_3$, $A_4$, $A_4\times C_2$, $S_3\times C_3$, $A_4\times C_2$, $S_3\times A_4$, $S_3\times A_4$ |
12T43, 18T31, 18T32, 24T78, 24T83, 36T21, 36T51 |
Results are complete for degrees $\leq 23$.