| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 42T1 |
$C_{42}$ |
$42$ |
$-1$ |
✓ |
$1$ |
$42$ |
$C_2$, $C_3$, $C_6$, $C_7$, $C_{14}$, $C_{21}$ |
|
| 42T2 |
$C_2\times C_7:C_3$ |
$42$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_3$, $C_6$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $C_7:C_3$ |
14T5 |
| 42T3 |
$C_3\times D_7$ |
$42$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $C_3$, $C_6$, $D_{7}$, $D_{7}$, $C_3\times D_7$ |
21T3 |
| 42T4 |
$F_7$ |
$42$ |
$-1$ |
✓ |
$-1$ |
$7$ |
$C_2$, $C_3$, $C_6$, $F_7$, $F_7$, $F_7$ |
7T4, 14T4, 21T4 |
| 42T5 |
$D_{21}$ |
$42$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $S_3$, $D_{7}$, $D_{7}$, $D_{21}$ |
21T5 |
| 42T6 |
$C_7\times S_3$ |
$42$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $S_3$, $C_7$, $C_{14}$, $C_7\times S_3$ |
21T6 |
| 42T7 |
$C_7\times A_4$ |
$84$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_3$, $A_4$, $C_7$, $C_{21}$ |
28T17 |
| 42T8 |
$C_7:A_4$ |
$84$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $A_4$, $C_7:C_3$, $C_7:C_3$ |
28T16 |
| 42T9 |
$C_6\times D_7$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $C_3$, $C_6$, $D_{7}$, $D_{14}$, $C_3\times D_7$ |
42T9 |
| 42T10 |
$C_2\times F_7$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $C_3$, $C_6$, $F_7$, $F_7 \times C_2$, $F_7$ |
14T7 x 2, 28T15, 42T10 |
| 42T11 |
$D_{42}$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{14}$, $D_{21}$ |
42T11 |
| 42T12 |
$C_{14}\times S_3$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$42$ |
$C_2$, $S_3$, $D_{6}$, $C_7$, $C_{14}$, $C_7\times S_3$ |
42T12 |
| 42T13 |
$S_3\times D_7$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{14}$, $S_3\times D_7$ |
21T8, 42T14, 42T15 |
| 42T14 |
$S_3\times D_7$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $S_3$, $D_{7}$, $D_{14}$, $S_3\times D_7$ |
21T8, 42T13, 42T15 |
| 42T15 |
$S_3\times D_7$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{7}$, $S_3\times D_7$ |
21T8, 42T13, 42T14 |
| 42T16 |
$C_6\times C_7:C_3$ |
$126$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $C_3$, $C_6$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $C_3\times C_7:C_3$ |
42T16 x 2 |
| 42T17 |
$C_3\times F_7$ |
$126$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $C_3$, $C_6$, $F_7$, $F_7$, $C_3\times F_7$ |
21T9 x 3, 42T17 x 2 |
| 42T18 |
$D_{21}:C_3$ |
$126$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $S_3$, $F_7$, $F_7$, $D_{21}:C_3$ |
21T10, 42T22 |
| 42T19 |
$S_3\times C_7:C_3$ |
$126$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $S_3$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $S_3\times C_7:C_3$ |
21T11, 42T23 |
| 42T20 |
$C_{21}\times S_3$ |
$126$ |
$-1$ |
✓ |
$-1$ |
$63$ |
$C_2$, $S_3\times C_3$, $C_7$, $C_{14}$ |
|
| 42T21 |
$C_3\times D_{21}$ |
$126$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3\times C_3$, $D_{7}$, $D_{7}$ |
|
| 42T22 |
$D_{21}:C_3$ |
$126$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3\times C_3$, $F_7$, $F_7$ |
21T10, 42T18 |
| 42T23 |
$S_3\times C_7:C_3$ |
$126$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3\times C_3$, $C_7:C_3$, $(C_7:C_3) \times C_2$ |
21T11, 42T19 |
| 42T24 |
$C_{14}\times A_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$56$ |
$C_3$, $A_4\times C_2$, $C_7$, $C_{21}$ |
|
| 42T25 |
$C_3\times F_8$ |
$168$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $C_7$, $F_8$, $C_{21}$ |
24T282 |
| 42T26 |
$F_8:C_3$ |
$168$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_3$, $C_7:C_3$, $F_8:C_3$, $C_7:C_3$ |
8T36, 14T11, 24T283, 28T27 |
| 42T27 |
$C_2\times C_7:A_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $A_4\times C_2$, $C_7:C_3$, $C_7:C_3$ |
|
| 42T28 |
$A_4\times D_7$ |
$168$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$, $D_{7}$, $C_3\times D_7$ |
28T29, 42T29 |
| 42T29 |
$A_4\times D_7$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4\times C_2$, $D_{7}$, $C_3\times D_7$ |
28T29, 42T28 |
| 42T30 |
$D_7:A_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $A_4\times C_2$, $F_7$, $F_7$ |
28T28, 42T31 |
| 42T31 |
$D_7:A_4$ |
$168$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $A_4$, $F_7$, $F_7$ |
28T28, 42T30 |
| 42T32 |
$C_7:S_4$ |
$168$ |
$1$ |
✓ |
$-1$ |
$17$ |
$S_3$, $S_4$, $D_{7}$, $D_{21}$ |
28T30, 42T33 |
| 42T33 |
$C_7:S_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_3$, $S_4$, $D_{7}$, $D_{21}$ |
28T30, 42T32 |
| 42T34 |
$C_7\times S_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$35$ |
$S_3$, $S_4$, $C_7$, $C_7\times S_3$ |
28T31, 42T35 |
| 42T35 |
$C_7\times S_4$ |
$168$ |
$1$ |
✓ |
$-1$ |
$35$ |
$S_3$, $S_4$, $C_7$, $C_7\times S_3$ |
28T31, 42T34 |
| 42T36 |
$C_2\times S_3\times D_7$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{14}$, $S_3\times D_7$ |
42T36 x 3 |
| 42T37 |
$\PSL(2,7)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$ |
7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T38 x 2 |
| 42T38 |
$\PSL(2,7)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$, $\PSL(2,7)$ |
7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 |
| 42T39 |
$A_4\times C_7:C_3$ |
$252$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$, $C_7:C_3$, $C_3\times C_7:C_3$ |
28T40 |
| 42T40 |
$C_6\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$42$ |
$C_2$, $C_3$, $C_6$, $F_7$, $F_7 \times C_2$, $C_3\times F_7$ |
42T40 x 5 |
| 42T41 |
$C_2\times D_{21}:C_3$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $S_3$, $D_{6}$, $F_7$, $F_7 \times C_2$, $D_{21}:C_3$ |
42T41 |
| 42T42 |
$C_2\times S_3\times C_7:C_3$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $S_3\times C_7:C_3$ |
42T42 |
| 42T43 |
$S_3\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{6}$, $F_7$, $F_7 \times C_2$, $S_3\times F_7$ |
21T15, 42T44, 42T45, 42T52 |
| 42T44 |
$S_3\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{6}$, $F_7$, $F_7$, $S_3\times F_7$ |
21T15, 42T43, 42T45, 42T52 |
| 42T45 |
$S_3\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $S_3$, $F_7$, $F_7 \times C_2$, $S_3\times F_7$ |
21T15, 42T43, 42T44, 42T52 |
| 42T46 |
$C_7\times S_3^2$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$63$ |
$C_2$, $S_3^2$, $C_7$, $C_{14}$ |
|
| 42T47 |
$C_7\times C_3:S_3.C_2$ |
$252$ |
$1$ |
✓ |
$-1$ |
$42$ |
$C_2$, $C_3^2:C_4$, $C_7$, $C_{14}$ |
42T47 |
| 42T48 |
$C_3^2:(C_7:C_4)$ |
$252$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$, $D_{7}$, $D_{7}$ |
42T48 |
| 42T49 |
$D_{21}:S_3$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $S_3^2$, $D_{7}$, $D_{7}$ |
|
| 42T50 |
$C_3\times S_3\times D_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $S_3\times C_3$, $D_{7}$, $D_{14}$ |
|
Results are complete for degrees $\leq 23$.
