## Results (1-50 of at least 5000)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
24T1 $C_{24}$ $24$ $-1$ yes $C_2$, $C_3$, $C_4$, $C_6$, $C_8$, $C_{12}$
24T2 $C_2\times C_{12}$ $24$ $1$ yes $C_2$ x 3, $C_3$, $C_4$ x 2, $C_2^2$, $C_6$ x 3, $C_4\times C_2$, $C_{12}$ x 2, $C_6\times C_2$
24T3 $C_2^2\times C_6$ $24$ $1$ yes $C_2$ x 7, $C_3$, $C_2^2$ x 7, $C_6$ x 7, $C_2^3$, $C_6\times C_2$ x 7
24T4 $C_3\times Q_8$ $24$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8$, $C_6\times C_2$
24T5 $C_3:Q_8$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8$, $D_6$
24T6 $C_2\times C_3:C_4$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $S_3$, $D_{6}$ x 2, $C_4\times C_2$, $D_6$, $C_3 : C_4$ x 2
24T7 $\SL(2,3)$ $24$ $1$ yes $C_3$, $A_4$, $A_4$, $\SL(2,3)$, $A_4$ 8T12
24T8 $C_3:C_8$ $24$ $-1$ yes $C_2$, $S_3$, $C_4$, $S_3$, $C_8$, $C_3 : C_4$
24T9 $C_2\times A_4$ $24$ $1$ yes $C_2$, $C_3$, $A_4$, $C_6$, $A_4$, $A_4\times C_2$, $A_4\times C_2$, $A_4$, $A_4\times C_2$, $A_4 \times C_2$ 6T6, 8T13, 12T6, 12T7
24T10 $S_4$ $24$ $1$ yes $C_2$, $S_3$, $S_4$, $S_3$, $S_4$, $S_4$, $S_4$, $S_4$, $S_4$ 4T5, 6T7, 6T8, 8T14, 12T8, 12T9
24T11 $C_2^2\times S_3$ $24$ $1$ yes $C_2$ x 7, $S_3$, $C_2^2$ x 7, $S_3$, $D_{6}$ x 6, $C_2^3$, $D_6$ x 3, $S_3 \times C_2^2$ x 4 12T10 x 4
24T12 $C_4\times S_3$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $S_3$, $D_{6}$ x 2, $C_4\times C_2$, $D_6$, $S_3 \times C_4$ x 2 12T11 x 2
24T13 $D_{12}$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4$, $D_6$, $D_{12}$ x 2 12T12 x 2
24T14 $C_3:D_4$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4$, $D_6$, $(C_6\times C_2):C_2$, $(C_6\times C_2):C_2$ 12T13, 12T15
24T15 $C_3\times D_4$ $24$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $D_{4}$ x 2, $C_6$ x 3, $D_4$, $C_6\times C_2$, $D_4 \times C_3$ x 2 12T14 x 2
24T16 $C_3\times OD_{16}$ $48$ $-1$ yes $C_2$, $C_3$, $C_4$, $C_6$, $C_8:C_2$, $C_{12}$
24T17 $C_3\times D_4:C_2$ $48$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8:C_2$, $C_6\times C_2$ 24T17 x 2
24T18 $D_4:S_3$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8:C_2$, $D_6$ 24T18, 24T23
24T19 $D_{12}:C_2$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8:C_2$, $D_6$ 24T24 x 2
24T20 $C_3:OD_{16}$ $48$ $-1$ yes $C_2$, $S_3$, $C_4$, $S_3$, $C_8:C_2$, $C_3 : C_4$
24T21 $\SL(2,3):C_2$ $48$ $1$ yes $C_3$, $A_4$, $A_4\times C_2$, $A_4\times C_2$ 16T60
24T22 $\GL(2,3)$ $48$ $-1$ yes $S_3$, $S_4$, $S_4$, $\textrm{GL(2,3)}$ x 2, $S_4$ 8T23 x 2, 16T66
24T23 $D_4:S_3$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ 24T18 x 2
24T24 $D_{12}:C_2$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ 24T19, 24T24
24T25 $C_2\times C_3:D_4$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $D_{6}$ x 3, $D_4\times C_2$, $S_3 \times C_2^2$, $(C_6\times C_2):C_2$ x 2 24T25, 24T45 x 2
24T26 $S_3\times Q_8$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8$, $S_3 \times C_2^2$ 24T26
24T27 $C_2\times C_4\times S_3$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $D_{6}$ x 3, $C_4\times C_2$, $S_3 \times C_2^2$, $S_3 \times C_4$ x 2 24T27 x 3
24T28 $D_6.C_2^2$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ 24T28 x 2
24T29 $C_2\times D_{12}$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $D_{6}$ x 3, $D_4\times C_2$, $S_3 \times C_2^2$, $D_{12}$ x 2 24T29 x 3
24T30 $C_2^3\times S_3$ $48$ $1$ yes $C_2$ x 7, $S_3$, $C_2^2$ x 7, $D_{6}$ x 7, $C_2^3$, $S_3 \times C_2^2$ x 7 24T30 x 7
24T31 $C_{24}:C_2$ $48$ $-1$ yes $C_2$, $S_3$, $C_4$, $D_{6}$, $C_8:C_2$, $S_3 \times C_4$
24T32 $C_8\times S_3$ $48$ $-1$ yes $C_2$, $S_3$, $C_4$, $D_{6}$, $C_8$, $S_3 \times C_4$ 24T32
24T33 $D_6:C_4$ $48$ $1$ yes $C_2$, $S_3$, $C_4$, $D_{4}$ x 2, $D_{6}$, $C_2^2:C_4$, $S_3 \times C_4$, $D_{12}$, $(C_6\times C_2):C_2$ 24T33
24T34 $D_{24}$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{8}$, $D_{12}$ 24T34
24T35 $C_8:S_3$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $QD_{16}$, $D_{12}$
24T36 $Q_8:S_3$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $QD_{16}$, $(C_6\times C_2):C_2$
24T37 $C_3:D_8$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{8}$, $(C_6\times C_2):C_2$ 24T43
24T38 $C_6\times D_4$ $48$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $D_{4}$ x 2, $C_6$ x 3, $D_4\times C_2$, $C_6\times C_2$, $D_4 \times C_3$ x 2 24T38 x 3
24T39 $C_3\times C_2^2:C_4$ $48$ $1$ yes $C_2$, $C_3$, $C_4$, $D_{4}$ x 2, $C_6$, $C_2^2:C_4$, $C_{12}$, $D_4 \times C_3$ x 2 24T39
24T40 $C_3\times D_8$ $48$ $-1$ yes $C_2$, $C_3$, $D_{4}$, $C_6$, $D_{8}$, $D_4 \times C_3$ 24T40
24T41 $C_3\times SD_{16}$ $48$ $-1$ yes $C_2$, $C_3$, $D_{4}$, $C_6$, $QD_{16}$, $D_4 \times C_3$
24T42 $C_3:SD_{16}$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $S_3$, $QD_{16}$, $(C_6\times C_2):C_2$
24T43 $C_3:D_8$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $S_3$, $D_{8}$, $(C_6\times C_2):C_2$ 24T37
24T44 $C_6.D_4$ $48$ $1$ yes $C_2$, $S_3$, $C_4$, $D_{4}$ x 2, $S_3$, $C_2^2:C_4$, $C_3 : C_4$, $(C_6\times C_2):C_2$ x 2 24T44
24T45 $C_2\times C_3:D_4$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4\times C_2$, $D_6$, $(C_6\times C_2):C_2$ x 2 24T25 x 2, 24T45
24T46 $C_2\times S_4$ $48$ $1$ yes $C_2$, $S_3$, $S_3$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $S_4$, $C_2\times S_4$, $C_2 \times S_4$ 6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T47, 24T48 x 2
24T47 $C_2\times S_4$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $S_4$, $S_4$, $S_4\times C_2$ x 2, $D_6$, $S_4$, $C_2\times S_4$, $C_2 \times S_4$ x 2, $C_2 \times S_4$ x 2 6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T48 x 2
24T48 $C_2\times S_4$ $48$ $1$ yes $C_2$, $S_3$, $S_4$, $D_{6}$, $S_4$, $S_4\times C_2$, $S_4\times C_2$, $S_4$, $C_2 \times S_4$, $C_2 \times S_4$ 6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48
24T49 $C_2^2\times A_4$ $48$ $1$ yes $C_2$, $C_3$, $C_6$, $A_4$, $A_4\times C_2$ x 3, $A_4\times C_2$ x 2, $A_4 \times C_2$, $C_2^2 \times A_4$, $C_2^2 \times A_4$ x 2 12T25 x 3, 12T26 x 2, 16T58, 24T49 x 2, 24T50
24T50 $C_2^2\times A_4$ $48$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $A_4$, $A_4\times C_2$ x 3, $C_6\times C_2$, $A_4 \times C_2$ x 3, $C_2^2 \times A_4$ x 3 12T25 x 3, 12T26 x 2, 16T58, 24T49 x 3
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Results are complete for degrees $\leq 23$.