Refine search
Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
3T2 | $S_3$ | $6$ | $-1$ | ✓ | 6T2 | |
4T2 | $C_2^2$ | $4$ | $1$ | ✓ | $C_2$ x 3 | |
4T3 | $D_{4}$ | $8$ | $-1$ | ✓ | $C_2$ | 4T3, 8T4 |
4T4 | $A_4$ | $12$ | $1$ | ✓ | 6T4, 12T4 | |
4T5 | $S_4$ | $24$ | $-1$ | ✓ | 6T7, 6T8, 8T14, 12T8, 12T9, 24T10 | |
5T2 | $D_{5}$ | $10$ | $1$ | ✓ | 10T2 | |
5T3 | $F_5$ | $20$ | $-1$ | ✓ | 10T4, 20T5 | |
5T4 | $A_5$ | $60$ | $1$ | 6T12, 10T7, 12T33, 15T5, 20T15, 30T9 | ||
5T5 | $S_5$ | $120$ | $-1$ | 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 | ||
6T2 | $S_3$ | $6$ | $-1$ | ✓ | $C_2$, $S_3$ | 3T2 |
6T3 | $D_{6}$ | $12$ | $-1$ | ✓ | $C_2$, $S_3$ | 6T3, 12T3 |
6T4 | $A_4$ | $12$ | $1$ | ✓ | $C_3$ | 4T4, 12T4 |
6T5 | $S_3\times C_3$ | $18$ | $-1$ | ✓ | $C_2$ | 9T4, 18T3 |
6T6 | $A_4\times C_2$ | $24$ | $-1$ | ✓ | $C_3$ | 8T13, 12T6, 12T7, 24T9 |
6T7 | $S_4$ | $24$ | $1$ | ✓ | $S_3$ | 4T5, 6T8, 8T14, 12T8, 12T9, 24T10 |
6T8 | $S_4$ | $24$ | $-1$ | ✓ | $S_3$ | 4T5, 6T7, 8T14, 12T8, 12T9, 24T10 |
6T9 | $S_3^2$ | $36$ | $-1$ | ✓ | $C_2$ | 9T8, 12T16, 18T9, 18T11 x 2, 36T13 |
6T10 | $C_3^2:C_4$ | $36$ | $1$ | ✓ | $C_2$ | 6T10, 9T9, 12T17 x 2, 18T10, 36T14 |
6T11 | $S_4\times C_2$ | $48$ | $-1$ | ✓ | $S_3$ | 6T11, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2 |
6T12 | $\PSL(2,5)$ | $60$ | $1$ | 5T4, 10T7, 12T33, 15T5, 20T15, 30T9 | ||
6T13 | $C_3^2:D_4$ | $72$ | $-1$ | ✓ | $C_2$ | 6T13, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
6T14 | $\PGL(2,5)$ | $120$ | $-1$ | 5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 | ||
6T15 | $A_6$ | $360$ | $1$ | 6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 | ||
6T16 | $S_6$ | $720$ | $-1$ | 6T16, 10T32, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96 | ||
7T2 | $D_{7}$ | $14$ | $-1$ | ✓ | 14T2 | |
7T3 | $C_7:C_3$ | $21$ | $1$ | ✓ | 21T2 | |
7T4 | $F_7$ | $42$ | $-1$ | ✓ | 14T4, 21T4, 42T4 | |
7T5 | $\GL(3,2)$ | $168$ | $1$ | 7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2 | ||
7T6 | $A_7$ | $2520$ | $1$ | 15T47 x 2, 21T33, 35T28, 42T294, 42T299 | ||
7T7 | $S_7$ | $5040$ | $-1$ | 14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418 | ||
8T2 | $C_4\times C_2$ | $8$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$ | |
8T3 | $C_2^3$ | $8$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7 | |
8T4 | $D_4$ | $8$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2 | 4T3 x 2 |
8T5 | $Q_8$ | $8$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$ | |
8T6 | $D_{8}$ | $16$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T6, 16T13 |
8T7 | $C_8:C_2$ | $16$ | $-1$ | ✓ | $C_2$, $C_4$ | 16T6 |
8T8 | $QD_{16}$ | $16$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 16T12 |
8T9 | $D_4\times C_2$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2 | 8T9 x 3, 16T9 |
8T10 | $C_2^2:C_4$ | $16$ | $1$ | ✓ | $C_2$, $C_4$, $D_{4}$ x 2 | 8T10, 16T10 |
8T11 | $Q_8:C_2$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$ | 8T11 x 2, 16T11 |
8T12 | $\SL(2,3)$ | $24$ | $1$ | ✓ | $A_4$ | 24T7 |
8T13 | $A_4\times C_2$ | $24$ | $1$ | ✓ | $C_2$, $A_4$ | 6T6, 12T6, 12T7, 24T9 |
8T14 | $S_4$ | $24$ | $1$ | ✓ | $C_2$, $S_4$ | 4T5, 6T7, 6T8, 12T8, 12T9, 24T10 |
8T15 | $Z_8 : Z_8^\times$ | $32$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T15, 16T35, 16T38 x 2, 16T45, 32T21 |
8T16 | $(C_8:C_2):C_2$ | $32$ | $-1$ | ✓ | $C_2$, $C_4$ | 8T16, 16T36, 16T41 x 2, 32T22 |
8T17 | $C_4\wr C_2$ | $32$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T17, 16T28, 16T42, 32T14 |
8T18 | $C_2^2 \wr C_2$ | $32$ | $1$ | ✓ | $C_2$, $D_{4}$ x 3 | 8T18 x 7, 16T39 x 6, 16T46, 32T24 |
8T19 | $C_2^3 : C_4 $ | $32$ | $1$ | ✓ | $C_2$, $D_{4}$ | 8T19, 8T20, 8T21, 16T33 x 2, 16T52, 16T53, 32T19 |
8T20 | $C_2^3: C_4$ | $32$ | $1$ | ✓ | $C_2$, $C_4$ | 8T19 x 2, 8T21, 16T33 x 2, 16T52, 16T53, 32T19 |
8T21 | $C_2^3: C_4$ | $32$ | $-1$ | ✓ | $C_2$ x 3, $C_2^2$ | 8T19 x 2, 8T20, 16T33 x 2, 16T52, 16T53, 32T19 |
Results are complete for degrees $\leq 23$.