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Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
4T5 | $S_4$ | $24$ | $-1$ | ✓ | 6T7, 6T8, 8T14, 12T8, 12T9, 24T10 | |
5T3 | $F_5$ | $20$ | $-1$ | ✓ | 10T4, 20T5 | |
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 |
7T3 | $C_7:C_3$ | $21$ | $1$ | ✓ | 21T2 | |
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 |
9T3 | $D_{9}$ | $18$ | $1$ | ✓ | $S_3$ | 18T5 |
9T4 | $S_3\times C_3$ | $18$ | $-1$ | ✓ | $C_3$, $S_3$ | 6T5, 18T3 |
9T5 | $C_3^2:C_2$ | $18$ | $1$ | ✓ | $S_3$ x 4 | 18T4 |
9T6 | $C_9:C_3$ | $27$ | $1$ | ✓ | $C_3$ | 27T5 |
9T7 | $C_3^2:C_3$ | $27$ | $1$ | ✓ | $C_3$ | 9T7 x 3, 27T3 |
10T3 | $D_{10}$ | $20$ | $-1$ | ✓ | $C_2$, $D_{5}$ | 10T3, 20T4 |
10T4 | $F_5$ | $20$ | $-1$ | ✓ | $C_2$, $F_5$ | 5T3, 20T5 |
11T2 | $D_{11}$ | $22$ | $-1$ | ✓ | 22T2 | |
12T6 | $A_4\times C_2$ | $24$ | $1$ | ✓ | $C_3$, $A_4$, $A_4\times C_2$ | 6T6, 8T13, 12T7, 24T9 |
12T7 | $A_4 \times C_2$ | $24$ | $1$ | ✓ | $C_2$, $C_3$, $C_6$, $A_4$, $A_4\times C_2$ | 6T6, 8T13, 12T6, 24T9 |
12T8 | $S_4$ | $24$ | $-1$ | ✓ | $S_3$, $S_4$, $S_4$ | 4T5, 6T7, 6T8, 8T14, 12T9, 24T10 |
12T9 | $S_4$ | $24$ | $1$ | ✓ | $C_2$, $S_3$, $S_3$, $S_4$, $S_4$ | 4T5, 6T7, 6T8, 8T14, 12T8, 24T10 |
12T10 | $S_3 \times C_2^2$ | $24$ | $1$ | ✓ | $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3 | 12T10 x 3, 24T11 |
12T11 | $S_3 \times C_4$ | $24$ | $-1$ | ✓ | $C_2$, $S_3$, $C_4$, $D_{6}$ | 12T11, 24T12 |
12T12 | $D_{12}$ | $24$ | $-1$ | ✓ | $C_2$, $S_3$, $D_{4}$, $D_{6}$ | 12T12, 24T13 |
12T13 | $(C_6\times C_2):C_2$ | $24$ | $-1$ | ✓ | $C_2$, $S_3$, $D_{4}$, $D_{6}$ | 12T15, 24T14 |
12T14 | $D_4 \times C_3$ | $24$ | $-1$ | ✓ | $C_2$, $C_3$, $D_{4}$, $C_6$ | 12T14, 24T15 |
12T15 | $(C_6\times C_2):C_2$ | $24$ | $-1$ | ✓ | $C_2$, $S_3$, $D_{4}$, $S_3$ | 12T13, 24T14 |
13T2 | $D_{13}$ | $26$ | $1$ | ✓ | 26T2 | |
14T3 | $D_{14}$ | $28$ | $-1$ | ✓ | $C_2$, $D_{7}$ | 14T3, 28T4 |
15T2 | $D_{15}$ | $30$ | $-1$ | ✓ | $S_3$, $D_{5}$ | 30T3 |
15T3 | $D_5\times C_3$ | $30$ | $1$ | ✓ | $C_3$, $D_{5}$ | 30T4 |
15T4 | $S_3 \times C_5$ | $30$ | $-1$ | ✓ | $S_3$, $C_5$ | 30T2 |
16T1 | $C_{16}$ | $16$ | $-1$ | ✓ | $C_2$, $C_4$, $C_8$ | |
16T2 | $C_4\times C_2^2$ | $16$ | $1$ | ✓ | $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$ | |
16T3 | $C_2^4$ | $16$ | $1$ | ✓ | $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15 | |
16T4 | $C_4^2$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_4\times C_2$ x 3 | |
16T5 | $C_8\times C_2$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$ | |
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 |
Results are complete for degrees $\leq 23$.