| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 41T7 |
$C_{41}:C_{20}$ |
$820$ |
$1$ |
✓ |
$-1$ |
$22$ |
|
|
| 42T104 |
$C_{14}^2:C_3$ |
$588$ |
$1$ |
✓ |
$-1$ |
$68$ |
$C_3$, $A_4$, $C_7^2:C_3$ |
42T104 x 5 |
| 42T105 |
$C_{14}^2:C_3$ |
$588$ |
$1$ |
✓ |
$-1$ |
$84$ |
$C_3$, $A_4$, $C_7:C_{21}$ |
42T105 x 5 |
| 42T106 |
$C_{14}:F_7$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$44$ |
$C_2$, $C_3$, $C_6$, $C_7:F_7$ |
42T106 x 3 |
| 42T107 |
$C_7^2:D_6$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$40$ |
$C_2$, $S_3$, $D_{6}$, $C_7^2:S_3$ |
28T74, 42T107, 42T108 x 2 |
| 42T108 |
$C_7^2:D_6$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$40$ |
$C_2$, $S_3$, $D_{6}$, $C_7^2:S_3$ |
28T74, 42T107 x 2, 42T108 |
| 42T109 |
$C_{14}:F_7$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $C_3$, $C_6$, $C_7:F_7$ |
42T109 x 3 |
| 42T110 |
$C_7^2:D_6$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $S_3$, $S_3$, $C_7^2:D_6$ |
14T25, 21T23 x 2, 28T78, 42T110, 42T111 x 2, 42T112 x 2, 42T122 |
| 42T111 |
$C_7^2:D_6$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $S_3$, $D_{6}$, $C_7^2:D_6$ |
14T25, 21T23 x 2, 28T78, 42T110 x 2, 42T111, 42T112 x 2, 42T122 |
| 42T112 |
$C_7^2:D_6$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $S_3$, $D_{6}$, $C_7^2:D_6$ |
14T25, 21T23 x 2, 28T78, 42T110 x 2, 42T111 x 2, 42T112, 42T122 |
| 42T113 |
$C_{21}:D_{14}$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$105$ |
$C_2$, $S_3$, $D_{6}$, $C_7 \wr C_2$ |
42T113 x 2 |
| 42T114 |
$(C_7\times C_{21}):C_4$ |
$588$ |
$1$ |
✓ |
$-1$ |
$42$ |
$C_2$, $S_3$, $S_3$, $C_7^2:C_4$ |
42T114 x 3 |
| 42T115 |
$C_7^2:C_{12}$ |
$588$ |
$1$ |
✓ |
$-1$ |
$48$ |
$C_2$, $C_3$, $C_6$, $C_7^2:C_4$ |
42T115 x 3 |
| 42T116 |
$C_3\times D_7^2$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$75$ |
$C_2$, $C_3$, $C_6$, $D_7^2$ |
42T116 x 2 |
| 42T117 |
$C_{21}:D_{14}$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$51$ |
$C_2$, $S_3$, $S_3$, $D_7^2$ |
42T117 x 2 |
| 42T118 |
$D_7\times D_{21}$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$60$ |
$C_2$, $S_3$, $D_{6}$, $D_7^2$ |
42T118 x 2 |
| 42T119 |
$C_7^2:C_3:C_4$ |
$588$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_3$, $C_7^2:C_3:C_4$ |
14T22, 28T75, 42T125 |
| 42T120 |
$C_7^2:C_{12}$ |
$588$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_3$, $C_6$, $C_7^2:C_{12}$ |
14T23 x 4, 28T76 x 4, 42T120 x 3 |
| 42T121 |
$D_7:F_7$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $C_3$, $C_6$, $D_7:F_7$ |
14T24 x 3, 28T77 x 3, 42T121 x 2 |
| 42T122 |
$C_7^2:D_6$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $S_3$, $S_3$, $C_7^2:D_6$ |
14T25, 21T23 x 2, 28T78, 42T110 x 2, 42T111 x 2, 42T112 x 2 |
| 42T123 |
$D_7:F_7$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $C_3$, $C_6$ |
|
| 42T124 |
$D_7\times F_7$ |
$588$ |
$-1$ |
✓ |
$-1$ |
$35$ |
$C_2$, $C_3$, $C_6$ |
|
| 42T125 |
$C_7^2:C_3:C_4$ |
$588$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $S_3$, $S_3$ |
14T22, 28T75, 42T119 |
| 42T126 |
$A_4\times F_8$ |
$672$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $C_7$, $C_{21}$ |
32T34611 |
| 42T127 |
$F_8:A_4$ |
$672$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$, $C_7:C_3$, $C_7:C_3$ |
28T89 x 3, 32T34610 |
| 42T128 |
$D_6\times F_8$ |
$672$ |
$-1$ |
✓ |
$-1$ |
$48$ |
$S_3$, $C_7$, $C_2\times F_8$, $S_3\times C_7$ |
42T128 |
| 42T129 |
$S_4\times D_{14}$ |
$672$ |
$-1$ |
✓ |
$-1$ |
$50$ |
$S_3$, $S_4\times C_2$, $D_{7}$, $S_3\times D_7$ |
42T129 x 3 |
| 42T130 |
$C_2\times \PGL(2,7)$ |
$672$ |
$-1$ |
|
$-1$ |
$18$ |
$C_2$, $\PGL(2,7)$ |
16T1035 x 2, 28T80, 28T81, 32T34612, 42T130, 42T131 x 2 |
| 42T131 |
$C_2\times \PGL(2,7)$ |
$672$ |
$-1$ |
|
$-1$ |
$18$ |
$\PGL(2,7)$ |
16T1035 x 2, 28T80, 28T81, 32T34612, 42T130 x 2, 42T131 |
| 42T132 |
$(C_3\times C_{21}):C_{12}$ |
$756$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$, $F_7$, $F_7$ |
42T132 |
| 42T133 |
$C_{21}:(C_6\times S_3)$ |
$756$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3^2$, $F_7$, $F_7$ |
|
| 42T134 |
$C_{21}:C_6\times S_3$ |
$756$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $S_3^2$, $C_7:C_3$, $(C_7:C_3) \times C_2$ |
|
| 42T135 |
$(C_3\times C_{21}):C_{12}$ |
$756$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $C_3^2:C_4$, $C_7:C_3$, $(C_7:C_3) \times C_2$ |
42T135 |
| 42T136 |
$C_{21}:C_6\times S_3$ |
$756$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3^2$, $F_7$, $F_7 \times C_2$ |
|
| 42T137 |
$C_{21}:C_6^2$ |
$756$ |
$-1$ |
✓ |
$-1$ |
$63$ |
$C_2$, $S_3\times C_3$, $F_7$, $F_7 \times C_2$ |
42T137 x 2 |
| 42T138 |
$C_7\times S_5$ |
$840$ |
$-1$ |
|
$-1$ |
$49$ |
$\PGL(2,5)$, $C_7$ |
35T17 |
| 42T139 |
$D_7\times A_5$ |
$840$ |
$1$ |
|
$-1$ |
$25$ |
$\PSL(2,5)$, $D_{7}$ |
35T18 |
| 42T140 |
$C_7:S_5$ |
$840$ |
$-1$ |
|
$-1$ |
$22$ |
$\PGL(2,5)$, $D_{7}$ |
35T19 |
| 42T141 |
$C_2\times C_7^2:C_3^2$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$50$ |
$C_2$, $C_3$, $C_6$, $C_7^2:C_3^2$ |
42T141 |
| 42T142 |
$C_7:(C_3\times F_7)$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_3$, $C_6$, $C_7:(C_3\times F_7)$ |
21T24 x 2, 42T142 |
| 42T143 |
$C_7^2:(C_3\times S_3)$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $S_3$, $C_7^2:(C_3\times S_3)$ |
14T26, 21T25, 21T26, 42T144, 42T152, 42T153, 42T154, 42T155 |
| 42T144 |
$C_7^2:(C_3\times S_3)$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $S_3$, $C_7^2:(C_3\times S_3)$ |
14T26, 21T25, 21T26, 42T143, 42T152, 42T153, 42T154, 42T155 |
| 42T145 |
$C_{21}\times D_{21}$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$252$ |
$C_2$, $S_3\times C_3$, $C_7 \wr C_2$ |
42T145 x 5 |
| 42T146 |
$C_{21}:F_7$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$51$ |
$C_2$, $C_3$, $C_6$, $C_7:F_7$ |
42T146 x 8 |
| 42T147 |
$C_{21}:F_7$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3$, $S_3$, $C_7:F_7$ |
42T147 x 2, 42T148 x 6 |
| 42T148 |
$C_{21}:F_7$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3\times C_3$, $C_7:F_7$ |
42T147 x 3, 42T148 x 5 |
| 42T149 |
$(C_7\times C_{21}):S_3$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$39$ |
$C_2$, $S_3$, $S_3$, $C_7^2:S_3$ |
42T149 x 2 |
| 42T150 |
$C_3\times C_7^2:S_3$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$60$ |
$C_2$, $C_3$, $C_6$, $C_7^2:S_3$ |
42T151 x 2 |
| 42T151 |
$C_3\times C_7^2:S_3$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$60$ |
$C_2$, $S_3\times C_3$, $C_7^2:S_3$ |
42T150, 42T151 |
| 42T152 |
$C_7^2:(C_3\times S_3)$ |
$882$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3\times C_3$, $C_7^2:(C_3\times S_3)$ |
14T26, 21T25, 21T26, 42T143, 42T144, 42T153, 42T154, 42T155 |
Results are complete for degrees $\leq 23$.
