| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 42T1088 |
$D_{14}\wr C_3$ |
$65856$ |
$-1$ |
✓ |
$-1$ |
$360$ |
$C_3$, $A_4\times C_2$, $D_7\wr C_3$ |
42T1088 x 23 |
| 42T1089 |
$C_2^3:(C_7^3:S_4)$ |
$65856$ |
$-1$ |
✓ |
$-1$ |
$330$ |
$S_3$, $S_4\times C_2$, $C_7^3:S_4$ |
42T1089 x 3 |
| 42T1090 |
$C_2^3:(C_7^3:S_4)$ |
$65856$ |
$-1$ |
✓ |
$-1$ |
$222$ |
$S_3$, $S_4\times C_2$, $C_7^3:S_4$ |
42T1090 x 3 |
| 42T1091 |
$D_7^3:S_4$ |
$65856$ |
$1$ |
✓ |
$-1$ |
$165$ |
$S_3$, $S_4$, $D_7\wr S_3$ |
42T1091, 42T1092 x 2, 42T1093 x 2, 42T1094 x 2 |
| 42T1092 |
$D_7^3:S_4$ |
$65856$ |
$-1$ |
✓ |
$-1$ |
$165$ |
$S_3$, $S_4\times C_2$, $D_7\wr S_3$ |
42T1091 x 2, 42T1092, 42T1093 x 2, 42T1094 x 2 |
| 42T1093 |
$D_7^3:S_4$ |
$65856$ |
$-1$ |
✓ |
$-1$ |
$165$ |
$S_3$, $S_4\times C_2$, $D_7\wr S_3$ |
42T1091 x 2, 42T1092 x 2, 42T1093, 42T1094 x 2 |
| 42T1094 |
$D_7^3:S_4$ |
$65856$ |
$-1$ |
✓ |
$-1$ |
$165$ |
$S_3$, $S_4$, $D_7\wr S_3$ |
42T1091 x 2, 42T1092 x 2, 42T1093 x 2, 42T1094 |
| 42T1095 |
$\PGL(2,41)$ |
$68880$ |
$-1$ |
|
$-1$ |
$43$ |
|
|
| 42T1096 |
$C_7^3:(C_6^2:C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$216$ |
$C_3$, $A_4\times C_2$, $C_7^3:\He_3$ |
42T1096 x 2 |
| 42T1097 |
$C_2\times C_3^3.D_6^2$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$184$ |
$C_3$, $A_4\times C_2$, $C_7^3:C_9:C_3$ |
42T1097 x 2 |
| 42T1098 |
$C_7^3:(C_6^2:C_6)$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$84$ |
$C_3$, $A_4$, $C_7^3:(C_2\times \He_3)$ |
42T1098 x 2, 42T1099 x 3 |
| 42T1099 |
$C_7^3:(C_6^2:C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$84$ |
$C_3$, $A_4\times C_2$, $C_7^3:(C_2\times \He_3)$ |
42T1098 x 3, 42T1099 x 2 |
| 42T1100 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$69$ |
$S_3$, $S_4$, $C_7^3:C_3^2:S_3$ |
42T1101 |
| 42T1101 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$69$ |
$S_3$, $S_4$, $C_7^3:C_3^2:S_3$ |
42T1100 |
| 42T1102 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$111$ |
$S_3$, $S_4$, $C_7^3:C_3^2:S_3$ |
42T1103 |
| 42T1103 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$111$ |
$S_3$, $S_4$, $C_7^3:C_3^2:S_3$ |
42T1102 |
| 42T1104 |
$C_7^3.C_6^2.C_6$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$76$ |
$C_3$, $A_4$, $C_7^3:C_9:C_6$ |
42T1104 x 2, 42T1105 x 3 |
| 42T1105 |
$C_7^3.C_6^2.C_6$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$76$ |
$C_3$, $A_4\times C_2$, $C_7^3:C_9:C_6$ |
42T1104 x 3, 42T1105 x 2 |
| 42T1106 |
$C_7^3:C_6^2:S_3$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$84$ |
$C_2$, $S_3$, $D_{6}$, $C_7^3:C_3^2:D_6$ |
42T1106 x 15 |
| 42T1107 |
$C_7^3:(C_6^2.C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$58$ |
$C_2$, $C_3$, $C_6$, $C_7^3:C_3^2.A_4$ |
42T1108, 42T1109, 42T1110 |
| 42T1108 |
$C_7^3:(C_6^2.C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$58$ |
$C_3$, $A_4\times C_2$, $C_7^3:C_3^2.A_4$ |
42T1107, 42T1109, 42T1110 |
| 42T1109 |
$C_7^3:(C_6^2.C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$58$ |
$C_3$, $A_4\times C_2$, $C_7^3:C_3^2.A_4$ |
42T1107, 42T1108, 42T1110 |
| 42T1110 |
$C_7^3:(C_6^2.C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$58$ |
$C_3$, $A_4\times C_2$, $C_7^3:C_3^2.A_4$ |
42T1107, 42T1108, 42T1109 |
| 42T1111 |
$C_7^3:(C_6^2:C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$90$ |
$C_2$, $C_3$, $C_6$, $C_7^3:C_3^2:A_4$ |
42T1112, 42T1113 x 2 |
| 42T1112 |
$C_7^3:(C_6^2:C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$90$ |
$C_3$, $A_4\times C_2$, $C_7^3:C_3^2:A_4$ |
42T1111, 42T1113 x 2 |
| 42T1113 |
$C_7^3:(C_6^2:C_6)$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$90$ |
$C_3$, $A_4\times C_2$, $C_7^3:C_3^2:A_4$ |
42T1111, 42T1112, 42T1113 |
| 42T1114 |
$D_7^3:\He_3$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$63$ |
$C_2$, $C_3$, $C_6$, $D_7^3:\He_3$ |
21T94, 42T1115, 42T1116, 42T1117 x 2, 42T1118 x 2 |
| 42T1115 |
$D_7^3:\He_3$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$63$ |
$C_3$, $A_4\times C_2$, $D_7^3:\He_3$ |
21T94, 42T1114, 42T1116, 42T1117 x 2, 42T1118 x 2 |
| 42T1116 |
$D_7^3:\He_3$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$63$ |
$C_3$, $A_4$, $D_7^3:\He_3$ |
21T94, 42T1114, 42T1115, 42T1117 x 2, 42T1118 x 2 |
| 42T1117 |
$D_7^3:\He_3$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$63$ |
$C_3$, $A_4\times C_2$, $D_7^3:\He_3$ |
21T94, 42T1114, 42T1115, 42T1116, 42T1117, 42T1118 x 2 |
| 42T1118 |
$D_7^3:\He_3$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$63$ |
$C_3$, $A_4$, $D_7^3:\He_3$ |
21T94, 42T1114, 42T1115, 42T1116, 42T1117 x 2, 42T1118 |
| 42T1119 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$S_3$, $S_4$, $C_7^3:C_3^2:S_4$ |
21T95, 42T1120, 42T1121 |
| 42T1120 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3$, $S_3$, $C_7^3:C_3^2:S_4$ |
21T95, 42T1119, 42T1121 |
| 42T1121 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$36$ |
$S_3$, $S_4$, $C_7^3:C_3^2:S_4$ |
21T95, 42T1119, 42T1120 |
| 42T1122 |
$D_7^3:C_9:C_3$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$55$ |
$C_3$, $A_4$, $D_7^3:C_9:C_3$ |
21T96, 42T1123, 42T1124, 42T1125, 42T1126, 42T1127, 42T1128 |
| 42T1123 |
$D_7^3:C_9:C_3$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$55$ |
$C_3$, $A_4\times C_2$, $D_7^3:C_9:C_3$ |
21T96, 42T1122, 42T1124, 42T1125, 42T1126, 42T1127, 42T1128 |
| 42T1124 |
$D_7^3:C_9:C_3$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$55$ |
$C_3$, $A_4\times C_2$, $D_7^3:C_9:C_3$ |
21T96, 42T1122, 42T1123, 42T1125, 42T1126, 42T1127, 42T1128 |
| 42T1125 |
$D_7^3:C_9:C_3$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$55$ |
$C_3$, $A_4$, $D_7^3:C_9:C_3$ |
21T96, 42T1122, 42T1123, 42T1124, 42T1126, 42T1127, 42T1128 |
| 42T1126 |
$D_7^3:C_9:C_3$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$55$ |
$C_3$, $A_4$, $D_7^3:C_9:C_3$ |
21T96, 42T1122, 42T1123, 42T1124, 42T1125, 42T1127, 42T1128 |
| 42T1127 |
$D_7^3:C_9:C_3$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$55$ |
$C_2$, $C_3$, $C_6$, $D_7^3:C_9:C_3$ |
21T96, 42T1122, 42T1123, 42T1124, 42T1125, 42T1126, 42T1128 |
| 42T1128 |
$D_7^3:C_9:C_3$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$55$ |
$C_3$, $A_4\times C_2$, $D_7^3:C_9:C_3$ |
21T96, 42T1122, 42T1123, 42T1124, 42T1125, 42T1126, 42T1127 |
| 42T1129 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$S_3$, $S_4$, $C_7^3:C_3^2:S_4$ |
21T97, 42T1130, 42T1131 |
| 42T1130 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$1$ |
✓ |
$-1$ |
$45$ |
$S_3$, $S_4$, $C_7^3:C_3^2:S_4$ |
21T97, 42T1129, 42T1131 |
| 42T1131 |
$C_7^3:C_3^2:S_4$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $S_3$, $S_3$, $C_7^3:C_3^2:S_4$ |
21T97, 42T1129, 42T1130 |
| 42T1132 |
$C_7^3:(C_2\times \He_3):C_4$ |
$74088$ |
$-1$ |
✓ |
$-1$ |
$42$ |
$C_2$, $C_3^2:C_4$ |
42T1132 |
| 42T1133 |
$C_2^9:(C_7^2:C_3)$ |
$75264$ |
$1$ |
✓ |
$-1$ |
$48$ |
$C_3$, $C_7^2:C_3$ |
24T16555 |
| 42T1134 |
$C_2^9:(C_7:C_{21})$ |
$75264$ |
$1$ |
✓ |
$-1$ |
$48$ |
$C_3$, $C_7:C_{21}$ |
24T16556 |
| 42T1135 |
$\PSL(3,4):C_2^2$ |
$80640$ |
$-1$ |
|
$-1$ |
$28$ |
$C_2$, $\PSL(3,4).C_2$ |
42T1135 x 3 |
| 42T1136 |
$\PSL(3,4):C_2^2$ |
$80640$ |
$-1$ |
|
$-1$ |
$22$ |
$C_2$ |
|
| 42T1137 |
$C_2\times C_3^6:F_8$ |
$81648$ |
$-1$ |
✓ |
$-1$ |
$1680$ |
$C_7$, $C_2\times F_8$, $C_3^6:C_7$ |
42T1137 x 363 |
Results are complete for degrees $\leq 23$.
