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Label Name Order Parity Solvable Subfields Low Degree Siblings
42T1 $C_{42}$ $42$ $-1$ $C_2$, $C_3$, $C_6$, $C_7$, $C_{14}$, $C_{21}$
42T2 $C_7:C_6$ $42$ $-1$ $C_2$, $C_3$, $C_6$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $C_7:C_3$ 14T5
42T3 $C_3\times D_7$ $42$ $-1$ $C_2$, $C_3$, $C_6$, $D_{7}$, $D_{7}$, $C_3\times D_7$ 21T3
42T4 $F_7$ $42$ $-1$ $C_2$, $C_3$, $C_6$, $F_7$, $F_7$, $F_7$ 7T4, 14T4, 21T4
42T5 $D_{21}$ $42$ $-1$ $C_2$, $S_3$, $S_3$, $D_{7}$, $D_{7}$, $D_{21}$ 21T5
42T6 $S_3\times C_7$ $42$ $-1$ $C_2$, $S_3$, $S_3$, $C_7$, $C_{14}$, $S_3\times C_7$ 21T6
42T7 $C_7\times A_4$ $84$ $1$ $C_3$, $A_4$, $C_7$, $C_{21}$ 28T17
42T8 $C_7:A_4$ $84$ $1$ $C_3$, $A_4$, $C_7:C_3$, $C_7:C_3$ 28T16
42T9 $C_3\times D_{14}$ $84$ $-1$ $C_2$, $C_3$, $C_6$, $D_{7}$, $D_{14}$, $C_3\times D_7$ 42T9
42T10 $C_2\times F_7$ $84$ $-1$ $C_2$, $C_3$, $C_6$, $F_7$, $F_7 \times C_2$, $F_7$ 14T7 x 2, 28T15, 42T10
42T11 $D_{42}$ $84$ $-1$ $C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{14}$, $D_{21}$ 42T11
42T12 $S_3\times C_{14}$ $84$ $-1$ $C_2$, $S_3$, $D_{6}$, $C_7$, $C_{14}$, $S_3\times C_7$ 42T12
42T13 $S_3\times D_7$ $84$ $-1$ $C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{14}$, $S_3\times D_7$ 21T8, 42T14, 42T15
42T14 $S_3\times D_7$ $84$ $-1$ $C_2$, $S_3$, $S_3$, $D_{7}$, $D_{14}$, $S_3\times D_7$ 21T8, 42T13, 42T15
42T15 $S_3\times D_7$ $84$ $-1$ $C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{7}$, $S_3\times D_7$ 21T8, 42T13, 42T14
42T16 $C_{21}:C_6$ $126$ $-1$ $C_2$, $C_3$, $C_6$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $C_{21}:C_3$ 42T16 x 2
42T17 $C_3\times F_7$ $126$ $-1$ $C_2$, $C_3$, $C_6$, $F_7$, $F_7$, $C_3\times F_7$ 21T9 x 3, 42T17 x 2
42T18 $C_{21}:C_6$ $126$ $-1$ $C_2$, $S_3$, $S_3$, $F_7$, $F_7$, $C_{21}:C_6$ 21T10, 42T22
42T19 $C_{21}:C_6$ $126$ $-1$ $C_2$, $S_3$, $S_3$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $C_{21}:C_6$ 21T11, 42T23
42T20 $S_3\times C_{21}$ $126$ $-1$ $C_2$, $S_3\times C_3$, $C_7$, $C_{14}$
42T21 $C_3\times D_{21}$ $126$ $-1$ $C_2$, $S_3\times C_3$, $D_{7}$, $D_{7}$
42T22 $C_{21}:C_6$ $126$ $-1$ $C_2$, $S_3\times C_3$, $F_7$, $F_7$ 21T10, 42T18
42T23 $C_{21}:C_6$ $126$ $-1$ $C_2$, $S_3\times C_3$, $C_7:C_3$, $(C_7:C_3) \times C_2$ 21T11, 42T19
42T24 $A_4\times C_{14}$ $168$ $-1$ $C_3$, $A_4\times C_2$, $C_7$, $C_{21}$
42T25 $C_3\times F_8$ $168$ $1$ $C_3$, $C_7$, $F_8$, $C_{21}$ 24T282
42T26 $F_8:C_3$ $168$ $1$ $C_3$, $C_7:C_3$, $F_8:C_3$, $C_7:C_3$ 8T36, 14T11, 24T283, 28T27
42T27 $C_{14}:A_4$ $168$ $-1$ $C_3$, $A_4\times C_2$, $C_7:C_3$, $C_7:C_3$
42T28 $A_4\times D_7$ $168$ $1$ $C_3$, $A_4$, $D_{7}$, $C_3\times D_7$ 28T29, 42T29
42T29 $A_4\times D_7$ $168$ $-1$ $C_3$, $A_4\times C_2$, $D_{7}$, $C_3\times D_7$ 28T29, 42T28
42T30 $D_7:A_4$ $168$ $-1$ $C_3$, $A_4\times C_2$, $F_7$, $F_7$ 28T28, 42T31
42T31 $D_7:A_4$ $168$ $1$ $C_3$, $A_4$, $F_7$, $F_7$ 28T28, 42T30
42T32 $C_7:S_4$ $168$ $1$ $S_3$, $S_4$, $D_{7}$, $D_{21}$ 28T30, 42T33
42T33 $C_7:S_4$ $168$ $-1$ $S_3$, $S_4$, $D_{7}$, $D_{21}$ 28T30, 42T32
42T34 $C_7\times S_4$ $168$ $-1$ $S_3$, $S_4$, $C_7$, $S_3\times C_7$ 28T31, 42T35
42T35 $C_7\times S_4$ $168$ $1$ $S_3$, $S_4$, $C_7$, $S_3\times C_7$ 28T31, 42T34
42T36 $S_3\times D_{14}$ $168$ $-1$ $C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{14}$, $S_3\times D_7$ 42T36 x 3
42T37 $\PSL(2,7)$ $168$ $1$ $\GL(3,2)$ x 2, $\PSL(2,7)$ 7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T38 x 2
42T38 $\PSL(2,7)$ $168$ $1$ $\GL(3,2)$ x 2, $\PSL(2,7)$, $\PSL(2,7)$ 7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38
42T39 $A_4\times C_7:C_3$ $252$ $1$ $C_3$, $A_4$, $C_7:C_3$, $C_{21}:C_3$ 28T40
42T40 $C_6\times F_7$ $252$ $-1$ $C_2$, $C_3$, $C_6$, $F_7$, $F_7 \times C_2$, $C_3\times F_7$ 42T40 x 5
42T41 $C_{42}:C_6$ $252$ $-1$ $C_2$, $S_3$, $D_{6}$, $F_7$, $F_7 \times C_2$, $C_{21}:C_6$ 42T41
42T42 $C_{42}:C_6$ $252$ $-1$ $C_2$, $S_3$, $D_{6}$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $C_{21}:C_6$ 42T42
42T43 $S_3\times F_7$ $252$ $-1$ $C_2$, $S_3$, $D_{6}$, $F_7$, $F_7 \times C_2$, $S_3\times F_7$ 21T15, 42T44, 42T45, 42T52
42T44 $S_3\times F_7$ $252$ $-1$ $C_2$, $S_3$, $D_{6}$, $F_7$, $F_7$, $S_3\times F_7$ 21T15, 42T43, 42T45, 42T52
42T45 $S_3\times F_7$ $252$ $-1$ $C_2$, $S_3$, $S_3$, $F_7$, $F_7 \times C_2$, $S_3\times F_7$ 21T15, 42T43, 42T44, 42T52
42T46 $C_7\times S_3^2$ $252$ $-1$ $C_2$, $S_3^2$, $C_7$, $C_{14}$
42T47 $C_3^2:C_{28}$ $252$ $1$ $C_2$, $C_3^2:C_4$, $C_7$, $C_{14}$ 42T47
42T48 $(C_3\times C_{21}):C_4$ $252$ $1$ $C_2$, $C_3^2:C_4$, $D_{7}$, $D_{7}$ 42T48
42T49 $C_{21}:D_6$ $252$ $-1$ $C_2$, $S_3^2$, $D_{7}$, $D_{7}$
42T50 $C_{21}:D_6$ $252$ $-1$ $C_2$, $S_3\times C_3$, $D_{7}$, $D_{14}$
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Results are complete for degrees $\leq 23$.