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Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
17T1 | $C_{17}$ | $17$ | $1$ | ✓ | ||
17T2 | $D_{17}$ | $34$ | $1$ | ✓ | ||
17T3 | $C_{17}:C_{4}$ | $68$ | $1$ | ✓ | ||
17T4 | $C_{17}:C_{8}$ | $136$ | $1$ | ✓ | ||
17T5 | $F_{17}$ | $272$ | $-1$ | ✓ | ||
17T6 | $\PSL(2,16)$ | $4080$ | $1$ | |||
17T7 | $\PSL(2,16):C_2$ | $8160$ | $1$ | |||
17T8 | $\PSL(2,16):C_4$ | $16320$ | $1$ | |||
17T9 | $A_{17}$ | $177843714048000$ | $1$ | |||
17T10 | $S_{17}$ | $355687428096000$ | $-1$ | |||
18T1 | $C_{18}$ | $18$ | $-1$ | ✓ | $C_2$, $C_3$, $C_6$, $C_9$ | |
18T2 | $C_6 \times C_3$ | $18$ | $-1$ | ✓ | $C_2$, $C_3$ x 4, $C_6$ x 4, $C_3^2$ | |
18T3 | $S_3 \times C_3$ | $18$ | $-1$ | ✓ | $C_2$, $C_3$, $S_3$, $C_6$, $S_3$, $S_3\times C_3$, $S_3\times C_3$ | 6T5, 9T4 |
18T4 | $C_3^2 : C_2$ | $18$ | $-1$ | ✓ | $C_2$, $S_3$ x 4, $S_3$ x 4, $C_3^2:C_2$ | 9T5 |
18T5 | $D_9$ | $18$ | $-1$ | ✓ | $C_2$, $S_3$, $S_3$, $D_{9}$ | 9T3 |
18T6 | $S_3 \times C_6$ | $36$ | $-1$ | ✓ | $C_2$, $C_3$, $S_3$, $C_6$, $D_{6}$, $S_3\times C_3$ | 12T18, 18T6, 36T6 |
18T7 | $C_2^2 : C_9$ | $36$ | $1$ | ✓ | $C_3$, $A_4$, $C_9$ | 36T11 |
18T8 | $A_4 \times C_3$ | $36$ | $1$ | ✓ | $C_3$ x 4, $A_4$, $C_3^2$ | 12T20 x 3, 36T12 |
18T9 | $S_3^2$ | $36$ | $-1$ | ✓ | $C_2$, $S_3$ x 2, $D_{6}$ x 2, $S_3^2$, $S_3^2$ | 6T9, 9T8, 12T16, 18T11 x 2, 36T13 |
18T10 | $C_3^2 : C_4$ | $36$ | $-1$ | ✓ | $C_2$, $C_3^2:C_4$ x 2, $C_3^2:C_4$ | 6T10 x 2, 9T9, 12T17 x 2, 36T14 |
18T11 | $S_3^2$ | $36$ | $-1$ | ✓ | $C_2$, $S_3$ x 2, $S_3$, $D_{6}$, $S_3^2$ | 6T9, 9T8, 12T16, 18T9, 18T11, 36T13 |
18T12 | $C_6:S_3$ | $36$ | $-1$ | ✓ | $C_2$, $S_3$ x 4, $D_{6}$ x 4, $C_3^2:C_2$ | 18T12, 36T8 |
18T13 | $D_{18}$ | $36$ | $-1$ | ✓ | $C_2$, $S_3$, $D_{6}$, $D_{9}$ | 18T13, 36T10 |
18T14 | $C_9:C_6$ | $54$ | $-1$ | ✓ | $C_2$, $C_3$, $C_6$, $C_9:C_3$ | |
18T15 | $C_2\times \He_3$ | $54$ | $-1$ | ✓ | $C_2$, $C_3$, $C_6$, $C_3^2:C_3$ | 18T15 x 3 |
18T16 | $C_9\times S_3$ | $54$ | $-1$ | ✓ | $C_2$, $C_3$, $C_6$ | 27T12 |
18T17 | $C_3^2\times S_3$ | $54$ | $-1$ | ✓ | $C_2$, $C_3$, $C_6$, $S_3\times C_3$ x 3 | 18T17 x 3, 27T15 |
18T18 | $C_9:C_6$ | $54$ | $-1$ | ✓ | $C_2$, $S_3$, $S_3$, $(C_9:C_3):C_2$ | 9T10, 27T14 |
18T19 | $C_3\times D_9$ | $54$ | $-1$ | ✓ | $C_2$, $S_3$, $S_3$ | 27T9 |
18T20 | $C_3^2:C_6$ | $54$ | $-1$ | ✓ | $C_2$, $C_3$, $C_6$, $C_3^2 : S_3 $ | 9T11, 9T13, 18T21, 18T22, 27T11 |
18T21 | $C_3^2:C_6$ | $54$ | $-1$ | ✓ | $C_2$, $S_3$, $S_3$, $C_3^2 : C_6$ | 9T11, 9T13, 18T20, 18T22, 27T11 |
18T22 | $C_3^2:C_6$ | $54$ | $-1$ | ✓ | $C_2$, $S_3\times C_3$ | 9T11, 9T13, 18T20, 18T21, 27T11 |
18T23 | $C_3^2:C_6$ | $54$ | $-1$ | ✓ | $C_2$, $S_3$, $S_3$, $S_3\times C_3$ x 3 | 18T23 x 3, 27T13 |
18T24 | $C_3^2:S_3$ | $54$ | $-1$ | ✓ | $C_2$, $S_3$, $S_3$, $(C_3^2:C_3):C_2$ | 9T12 x 4, 18T24 x 3, 27T6 |
18T25 | $C_6\times A_4$ | $72$ | $-1$ | ✓ | $C_3$ x 4, $A_4\times C_2$, $C_3^2$ | 24T71 x 3, 36T18, 36T31 |
18T26 | $C_2^2:C_{18}$ | $72$ | $-1$ | ✓ | $C_3$, $A_4\times C_2$, $C_9$ | 36T16, 36T30 |
18T27 | $C_2\times C_3^2:C_4$ | $72$ | $-1$ | ✓ | $C_2$, $C_3^2:C_4$ | 12T40 x 2, 12T41 x 2, 18T27, 24T76 x 2, 36T35, 36T36 |
18T28 | $F_9$ | $72$ | $-1$ | ✓ | $C_2$, $C_3^2:C_8$ | 9T15, 12T46, 24T81, 36T49 |
18T29 | $S_3\times D_6$ | $72$ | $-1$ | ✓ | $C_2$, $S_3$ x 2, $D_{6}$ x 2, $S_3^2$ | 12T37 x 2, 18T29 x 3, 24T73, 36T34 x 2, 36T40 x 4 |
18T30 | $C_3\times S_4$ | $72$ | $-1$ | ✓ | $C_3$, $S_3$, $S_4$, $S_3\times C_3$ | 12T45, 18T33, 24T80, 24T84, 36T20, 36T52 |
18T31 | $S_3\times A_4$ | $72$ | $1$ | ✓ | $C_3$, $S_3$, $A_4$, $S_3\times C_3$ | 12T43, 18T32, 24T78, 24T83, 36T21, 36T50, 36T51 |
18T32 | $S_3\times A_4$ | $72$ | $-1$ | ✓ | $C_3$, $S_3$, $A_4\times C_2$, $S_3\times C_3$ | 12T43, 18T31, 24T78, 24T83, 36T21, 36T50, 36T51 |
18T33 | $C_3\times S_4$ | $72$ | $1$ | ✓ | $C_3$, $S_3$, $S_4$, $S_3\times C_3$ | 12T45, 18T30, 24T80, 24T84, 36T20, 36T52 |
18T34 | $\SOPlus(4,2)$ | $72$ | $-1$ | ✓ | $C_2$, $C_3^2:D_4$, $S_3^2:C_2$ | 6T13 x 2, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
18T35 | $\PSU(3,2)$ | $72$ | $-1$ | ✓ | $C_2$, $C_3^2:Q_8$ | 9T14, 12T47, 18T35 x 2, 24T82, 36T55 |
18T36 | $\SOPlus(4,2)$ | $72$ | $-1$ | ✓ | $C_2$, $S_3^2:C_2$ | 6T13 x 2, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 24T72 x 2, 36T53, 36T54 x 2 |
18T37 | $C_3:S_4$ | $72$ | $1$ | ✓ | $S_3$ x 4, $S_4$, $C_3^2:C_2$ | 12T44 x 3, 18T40, 24T79 x 3, 36T23, 36T56 |
18T38 | $C_2^2:D_9$ | $72$ | $1$ | ✓ | $S_3$, $S_4$, $D_{9}$ | 18T39, 36T25, 36T57 |
18T39 | $C_2^2:D_9$ | $72$ | $-1$ | ✓ | $S_3$, $S_4$, $D_{9}$ | 18T38, 36T25, 36T57 |
18T40 | $C_3:S_4$ | $72$ | $-1$ | ✓ | $S_3$ x 4, $S_4$, $C_3^2:C_2$ | 12T44 x 3, 18T37, 24T79 x 3, 36T23, 36T56 |
Results are complete for degrees $\leq 23$.