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Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
4T3 | $D_{4}$ | $8$ | $-1$ | ✓ | $C_2$ | 4T3, 8T4 |
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, $C_2^2$ | |
8T7 | $C_8:C_2$ | $16$ | $-1$ | ✓ | $C_2$, $C_4$ | 16T6 |
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 |
8T18 | $C_2^2 \wr C_2$ | $32$ | $1$ | ✓ | $C_2$, $D_{4}$ x 3 | 8T18 x 7, 16T39 x 6, 16T46, 32T24 |
8T22 | $Q_8:C_2^2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$ | 8T22 x 5, 16T23 x 9, 32T9 |
9T6 | $C_9:C_3$ | $27$ | $1$ | ✓ | $C_3$ | 27T5 |
9T7 | $C_3^2:C_3$ | $27$ | $1$ | ✓ | $C_3$ | 9T7 x 3, 27T3 |
12T14 | $D_4 \times C_3$ | $24$ | $-1$ | ✓ | $C_2$, $C_3$, $D_{4}$, $C_6$ | 12T14, 24T15 |
16T6 | $C_8: C_2$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_8:C_2$ | 8T7 |
16T7 | $Q_8\times C_2$ | $16$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8$ x 2 | |
16T8 | $C_4:C_4$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$ | |
16T9 | $D_4\times C_2$ | $16$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4 | 8T9 x 4 |
16T10 | $C_2^2 : C_4$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $C_2^2:C_4$ x 2 | 8T10 x 2 |
16T11 | $Q_8 : C_2$ | $16$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 3 | 8T11 x 3 |
16T15 | $C_2 \times (C_8:C_2)$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_8:C_2$ x 2 | 16T15, 32T1 |
16T16 | $(C_8:C_2):C_2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$ | 16T16 x 2, 32T2 |
16T17 | $C_4^2:C_2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $Q_8:C_2$ x 2 | 16T17, 32T3 |
16T18 | $C_2 \times (C_4\times C_2):C_2$ | $32$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 2 | 16T18 x 5, 32T4 |
16T19 | $C_4 \times D_4$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4\times C_2$, $Q_8:C_2$ | 16T19 x 3, 32T5 |
16T20 | $(C_2 \times Q_8):C_2$ | $32$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $C_2^3$ | 16T20 x 4, 32T6 |
16T21 | $C_2 \times (C_2^2:C_4)$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4 | 16T21 x 3, 32T7 |
16T22 | $C_{16} : C_2$ | $32$ | $-1$ | ✓ | $C_2$, $C_4$, $C_8$ | 32T8 |
16T23 | $Q_8 : C_2^2$ | $32$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 2 | 8T22 x 6, 16T23 x 8, 32T9 |
16T24 | $C_2^2 : C_8$ | $32$ | $1$ | ✓ | $C_2$, $C_4$, $D_{4}$ x 2, $C_8$, $C_8:C_2$, $C_2^2:C_4$ | 16T24, 32T10 |
16T25 | $C_2^2 \times D_4$ | $32$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6 | 16T25 x 7, 32T11 |
16T27 | $C_4^2:C_2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $Q_8:C_2$ x 3 | 32T13 |
16T30 | $C_4^2:C_2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2$ x 2 | 16T30, 32T16 |
16T31 | $C_2^2:Q_8$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $Q_8$, $D_4\times C_2$, $Q_8:C_2$ | 16T31, 32T17 |
16T34 | $C_4:D_4$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 4, $D_4\times C_2$ x 2, $Q_8:C_2$ | 16T34, 16T43 x 2, 32T20 |
16T37 | $C_2^2.D_4$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2$ x 2 | 16T54 x 2, 32T23 |
16T39 | $C_2^2\wr C_2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4$, $D_4\times C_2$ x 2, $C_2^2 \wr C_2$ x 4 | 8T18 x 8, 16T39 x 5, 16T46, 32T24 |
16T43 | $C_4:D_4$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 4, $D_4$, $D_4\times C_2$, $Q_8:C_2$ | 16T34 x 2, 16T43, 32T20 |
16T46 | $C_2^2\wr C_2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3 | 8T18 x 8, 16T39 x 6, 32T24 |
16T51 | $C_4^2:C_2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3 | 16T51 x 3, 32T29 |
16T54 | $C_2^2.D_4$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $Q_8:C_2$ x 2 | 16T37, 16T54, 32T23 |
16T67 | $C_4.C_2^4$ | $64$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $C_2^3$ | 16T67 x 14, 32T52 x 15 |
16T68 | $C_4^2:C_2^2$ | $64$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $Q_8:C_2^2$ x 2 | 16T68 x 7, 32T53 x 8, 32T54 x 2 |
16T69 | $D_4:C_2^3$ | $64$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 2 | 16T69 x 23, 32T55 x 18 |
16T70 | $C_8.C_2^3$ | $64$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$ | 16T70 x 2, 32T56 x 6, 32T57 |
16T73 | $C_4^2:C_2^2$ | $64$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2^2$ x 2 | 16T73 x 7, 32T62 x 4, 32T63 x 2, 32T269 x 2 |
16T74 | $C_4^2:C_4$ | $64$ | $1$ | ✓ | $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ | 16T74 x 3, 16T123, 32T64 x 2, 32T131 |
16T79 | $C_2^4:C_4$ | $64$ | $1$ | ✓ | $C_2$, $C_4$, $D_{4}$ x 6, $C_2^2:C_4$ x 3, $C_2^2 \wr C_2$ x 4 | 16T79 x 31, 32T72 x 12 |
16T81 | $C_4^2:C_2^2$ | $64$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $Q_8:C_2$ x 2, $Q_8:C_2^2$ | 16T81 x 3, 32T75 x 4, 32T76, 32T233 |
16T82 | $C_4^2:C_2^2$ | $64$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $Q_8:C_2$, $Q_8:C_2^2$ x 2 | 16T82 x 3, 32T77 x 2, 32T78 x 2, 32T234 x 2 |
16T83 | $C_4^2:C_2^2$ | $64$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $Q_8:C_2^2$ x 3 | 16T83 x 3, 32T79 x 2, 32T80, 32T270 x 3 |
16T87 | $C_2^3:D_4$ | $64$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2^2$ x 2 | 16T87 x 7, 16T119 x 4, 32T85 x 4, 32T86 x 4, 32T128 x 2 |
Results are complete for degrees $\leq 23$.