| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 6T15 |
$A_6$ |
$360$ |
$1$ |
|
$-1$ |
$7$ |
|
6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 |
| 8T42 |
$A_4\wr C_2$ |
$288$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$ |
12T126, 12T128, 12T129, 16T708, 18T112, 18T113, 24T692, 24T694, 24T695, 24T702, 24T703, 24T704, 32T9306, 36T316, 36T318, 36T456, 36T457, 36T458, 36T459 |
| 8T43 |
$\PGL(2,7)$ |
$336$ |
$-1$ |
|
$-1$ |
$9$ |
|
14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83 |
| 8T44 |
$C_2 \wr S_4$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_4$ |
8T44 x 3, 16T736 x 2, 16T743 x 2, 16T748 x 2, 16T752 x 2, 24T708 x 4, 24T1151 x 4, 32T9340, 32T9355, 32T9459 x 4 |
| 9T24 |
$((C_3^3:C_3):C_2):C_2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_3$ |
9T24 x 2, 18T129 x 3, 18T136 x 3, 18T137 x 3, 27T121, 27T128 x 3, 27T129, 36T502 x 3 |
| 9T25 |
$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
$324$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_3$ |
12T132 x 2, 12T133, 18T141 x 2, 18T142, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
| 9T26 |
$((C_3^2:Q_8):C_3):C_2$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$11$ |
|
12T157, 18T157, 24T1325, 24T1326, 24T1327, 24T1334, 27T139, 36T689, 36T709 |
| 9T27 |
$\PSL(2,8)$ |
$504$ |
$1$ |
|
$-1$ |
$9$ |
|
28T70, 36T712 |
| 10T23 |
$C_2\times (C_2^4 : D_5)$ |
$320$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$D_{5}$ |
10T23 x 5, 20T71 x 6, 20T73 x 6, 20T76 x 6, 20T81 x 3, 20T85 x 6, 20T87 x 6, 32T9313 x 2, 40T204 x 3, 40T270 x 12, 40T271 x 12, 40T272 x 3, 40T273 x 2, 40T284 x 6, 40T286 x 6, 40T288 x 3, 40T293 x 3, 40T295 x 6 |
| 10T24 |
$(C_2^4 : C_5):C_4$ |
$320$ |
$1$ |
✓ |
$-1$ |
$11$ |
$F_5$ |
10T25, 16T711, 20T77, 20T78, 20T79, 20T80, 20T83, 20T88, 32T9312, 40T206, 40T207, 40T296, 40T297, 40T298, 40T299, 40T300, 40T301, 40T302, 40T303 |
| 10T25 |
$(C_2^4 : C_5):C_4$ |
$320$ |
$-1$ |
✓ |
$-1$ |
$11$ |
$F_5$ |
10T24, 16T711, 20T77, 20T78, 20T79, 20T80, 20T83, 20T88, 32T9312, 40T206, 40T207, 40T296, 40T297, 40T298, 40T299, 40T300, 40T301, 40T302, 40T303 |
| 10T26 |
$\PSL(2,9)$ |
$360$ |
$1$ |
|
$-1$ |
$7$ |
|
6T15 x 2, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 |
| 10T27 |
$(D_5 \wr C_2):C_2$ |
$400$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_2$ |
10T27 x 2, 20T90 x 3, 20T96 x 3, 20T97 x 3, 25T30, 40T393 x 3, 40T394 x 3, 40T395 x 3 |
| 10T28 |
$(C_5^2 : C_8):C_2$ |
$400$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_2$ |
20T104, 20T107, 20T109, 20T115, 25T31, 40T397, 40T398, 40T399, 40T400 |
| 12T125 |
$D_6\wr C_2$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $D_{4}$, $C_3^2:D_4$ |
12T125 x 7, 24T594 x 2, 24T655 x 2, 24T686 x 4, 24T687 x 4, 24T688 x 8, 24T689 x 4, 24T690 x 4, 24T691 x 4, 36T400 x 4, 36T432 x 4 |
| 12T126 |
$A_4\wr C_2$ |
$288$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $S_3\times C_3$ |
8T42, 12T128, 12T129, 16T708, 18T112, 18T113, 24T692, 24T694, 24T695, 24T702, 24T703, 24T704, 32T9306, 36T316, 36T318, 36T456, 36T457, 36T458, 36T459 |
| 12T127 |
$\PSOPlus(4,3)$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$ |
12T127, 16T710, 18T116, 18T117, 24T636 x 2, 24T637 x 2, 24T693 x 2, 32T9308, 36T324, 36T403 x 2, 36T404 x 2, 36T405, 36T420, 36T460 x 2 |
| 12T128 |
$A_4\wr C_2$ |
$288$ |
$1$ |
✓ |
$-1$ |
$14$ |
$S_3$ |
8T42, 12T126, 12T129, 16T708, 18T112, 18T113, 24T692, 24T694, 24T695, 24T702, 24T703, 24T704, 32T9306, 36T316, 36T318, 36T456, 36T457, 36T458, 36T459 |
| 12T129 |
$A_4\wr C_2$ |
$288$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_3$ |
8T42, 12T126, 12T128, 16T708, 18T112, 18T113, 24T692, 24T694, 24T695, 24T702, 24T703, 24T704, 32T9306, 36T316, 36T318, 36T456, 36T457, 36T458, 36T459 |
| 12T130 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $C_2^2$ |
12T130, 18T120 x 6, 36T494 x 6, 36T517, 36T523 x 3, 36T530 x 6, 36T535 x 6, 36T541 x 2 |
| 12T131 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_4$ |
12T131 x 3, 18T123 x 4, 36T497 x 4, 36T514 x 2, 36T527 x 2, 36T532 x 4, 36T536 x 4, 36T543 x 4, 36T544 x 8 |
| 12T132 |
$C_3^3:A_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$13$ |
$A_4$ |
9T25, 12T132, 12T133, 18T141 x 2, 18T142, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
| 12T133 |
$C_3^3:A_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$13$ |
$A_4$ |
9T25, 12T132 x 2, 18T141 x 2, 18T142, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
| 12T134 |
$C_2\wr C_6$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $C_3$, $C_6$ |
12T134 x 3, 12T142 x 4, 16T719 x 4, 24T1156 x 4, 24T1157 x 4, 24T1158 x 8, 24T1159 x 4, 24T1160 x 8, 24T1161 x 8, 24T1162 x 8, 24T1163 x 4, 24T1164 x 4, 24T1165 x 4, 24T1166 x 4, 24T1167 x 4, 24T1168 x 4, 24T1169 x 4, 24T1170 x 4, 24T1171 x 2, 24T1172 x 2, 24T1220 x 4, 24T1221 x 4, 24T1222 x 2, 24T1223 x 2, 32T9328 x 2 |
| 12T135 |
$C_2\wr S_3$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $S_3$ |
12T135, 12T148 x 6, 16T765 x 2, 24T1003 x 6, 24T1004 x 3, 24T1005 x 3, 24T1008 x 3, 24T1010 x 3, 24T1123 x 6, 24T1173 x 6, 24T1174 x 6, 24T1175 x 2, 24T1176 x 12, 24T1177 x 12, 24T1178 x 2, 24T1179 x 6, 24T1180 x 3, 24T1181 x 2, 24T1182 x 2, 24T1183, 24T1250 x 12, 24T1251 x 12, 24T1252 x 3, 24T1253 x 3, 32T9368 |
| 12T136 |
$C_2^4:S_4$ |
$384$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $D_{6}$ |
12T136 x 3, 12T137 x 4, 16T724 x 4, 24T1143 x 2, 24T1144 x 2, 24T1184 x 2, 24T1185 x 4, 24T1186 x 2, 24T1187 x 4, 24T1188 x 4, 24T1189 x 4, 24T1190 x 4, 24T1191 x 2, 24T1192 x 4, 24T1193 x 2, 24T1194 x 4, 24T1195 x 8, 24T1196 x 8, 24T1197 x 8, 24T1198 x 8, 32T9332 x 2, 32T9457 x 4 |
| 12T137 |
$C_2^4:S_4$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4$ |
12T136 x 4, 12T137 x 3, 16T724 x 4, 24T1143 x 2, 24T1144 x 2, 24T1184 x 2, 24T1185 x 4, 24T1186 x 2, 24T1187 x 4, 24T1188 x 4, 24T1189 x 4, 24T1190 x 4, 24T1191 x 2, 24T1192 x 4, 24T1193 x 2, 24T1194 x 4, 24T1195 x 8, 24T1196 x 8, 24T1197 x 8, 24T1198 x 8, 32T9332 x 2, 32T9457 x 4 |
| 12T138 |
$C_2^4.S_4$ |
$384$ |
$1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4\times C_2$ |
12T138 x 3, 12T140 x 4, 24T1199 x 2, 24T1200 x 4, 24T1201 x 2, 24T1202 x 8, 24T1203 x 8, 24T1207 x 2, 24T1208 x 4, 24T1209 x 2, 24T1210 x 4, 24T1211 x 8, 24T1212 x 8, 24T1213 x 8, 24T1214 x 8, 32T9440 x 4 |
| 12T139 |
$C_2^2\wr S_3$ |
$384$ |
$1$ |
✓ |
$-1$ |
$40$ |
$S_3$, $S_4\times C_2$ x 3 |
12T139 x 23, 24T1114 x 36, 24T1115 x 18, 24T1124 x 2, 24T1125 x 9, 24T1126 x 18, 24T1130 x 3, 24T1204 x 6, 24T1205 x 36, 24T1206 x 36, 32T9428 |
| 12T140 |
$C_2^4.S_4$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4$ |
12T138 x 4, 12T140 x 3, 24T1199 x 2, 24T1200 x 4, 24T1201 x 2, 24T1202 x 8, 24T1203 x 8, 24T1207 x 2, 24T1208 x 4, 24T1209 x 2, 24T1210 x 4, 24T1211 x 8, 24T1212 x 8, 24T1213 x 8, 24T1214 x 8, 32T9440 x 4 |
| 12T141 |
$C_4^3:C_6$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_3$, $A_4\times C_2$ |
12T141 x 7, 24T1215 x 4, 24T1216 x 8, 24T1217 x 8, 24T1218 x 4, 24T1219 x 4 |
| 12T142 |
$C_2\wr C_6$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_3$, $A_4\times C_2$ |
12T134 x 4, 12T142 x 3, 16T719 x 4, 24T1156 x 4, 24T1157 x 4, 24T1158 x 8, 24T1159 x 4, 24T1160 x 8, 24T1161 x 8, 24T1162 x 8, 24T1163 x 4, 24T1164 x 4, 24T1165 x 4, 24T1166 x 4, 24T1167 x 4, 24T1168 x 4, 24T1169 x 4, 24T1170 x 4, 24T1171 x 2, 24T1172 x 2, 24T1220 x 4, 24T1221 x 4, 24T1222 x 2, 24T1223 x 2, 32T9328 x 2 |
| 12T143 |
$C_2^4.(C_2\times A_4)$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $A_4\times C_2$ |
12T143 x 7, 24T1224 x 4, 24T1225 x 4, 24T1226 x 4, 24T1227 x 4, 24T1228 x 4, 24T1229 x 4, 24T1230 x 4 |
| 12T144 |
$C_2^5:A_4$ |
$384$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$, $A_4$ |
12T144 x 7, 24T1231 x 4, 24T1232 x 8, 24T1233 x 8, 24T1234 x 4, 24T1235 x 4, 32T9464 x 8 |
| 12T145 |
$C_2^4:S_4$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$C_2$, $S_3$, $D_{6}$ |
12T145, 12T146 x 2, 16T744 x 2, 24T719, 24T803, 24T848, 24T1137, 24T1139, 24T1147, 24T1148, 24T1236, 24T1237 x 2, 24T1238, 24T1239 x 2, 24T1240 x 2, 24T1241 x 2, 24T1242 x 2, 24T1243, 24T1244, 32T9347, 32T9450 |
| 12T146 |
$C_2^4:S_4$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$S_3$, $S_4$ |
12T145 x 2, 12T146, 16T744 x 2, 24T719, 24T803, 24T848, 24T1137, 24T1139, 24T1147, 24T1148, 24T1236, 24T1237 x 2, 24T1238, 24T1239 x 2, 24T1240 x 2, 24T1241 x 2, 24T1242 x 2, 24T1243, 24T1244, 32T9347, 32T9450 |
| 12T147 |
$C_2^2.\GL(2,\mathbb{Z}/4)$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$S_3$, $S_4\times C_2$ |
12T147, 12T149 x 2, 24T759, 24T838, 24T852, 24T1245, 24T1246 x 2, 24T1247, 24T1248 x 4, 24T1249 x 4, 24T1254, 24T1255 |
| 12T148 |
$C_2\wr S_3$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4\times C_2$ |
12T135 x 2, 12T148 x 5, 16T765 x 2, 24T1003 x 6, 24T1004 x 3, 24T1005 x 3, 24T1008 x 3, 24T1010 x 3, 24T1123 x 6, 24T1173 x 6, 24T1174 x 6, 24T1175 x 2, 24T1176 x 12, 24T1177 x 12, 24T1178 x 2, 24T1179 x 6, 24T1180 x 3, 24T1181 x 2, 24T1182 x 2, 24T1183, 24T1250 x 12, 24T1251 x 12, 24T1252 x 3, 24T1253 x 3, 32T9368 |
| 12T149 |
$C_2^2.\GL(2,\mathbb{Z}/4)$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$S_3$, $S_4$ |
12T147 x 2, 12T149, 24T759, 24T838, 24T852, 24T1245, 24T1246 x 2, 24T1247, 24T1248 x 4, 24T1249 x 4, 24T1254, 24T1255 |
| 12T150 |
$C_4\wr S_3$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$40$ |
$S_3$, $S_4\times C_2$ |
12T150 x 3, 24T835, 24T857, 24T861, 24T1256 x 2, 24T1257 x 2, 24T1258 x 2 |
| 12T151 |
$C_4^2:D_{12}$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4\times C_2$ |
12T151 x 3, 24T837, 24T854 x 2, 24T1259 x 2, 24T1260 x 2, 24T1261 x 2 |
| 12T152 |
$C_2^4:D_{12}$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$S_3$, $S_4\times C_2$ |
12T152 x 3, 12T154 x 4, 16T742 x 4, 24T1149 x 2, 24T1150 x 2, 24T1262 x 2, 24T1263 x 2, 24T1264 x 4, 24T1268 x 2, 24T1269 x 2, 24T1270 x 4, 24T1271 x 4, 24T1272 x 4, 24T1273 x 4, 32T9346 x 2 |
| 12T153 |
$C_2^5.D_6$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4\times C_2$ |
12T153, 12T155 x 2, 16T725 x 2, 24T720, 24T836, 24T860, 24T1136, 24T1142, 24T1145, 24T1146, 24T1265 x 2, 24T1266, 24T1267, 24T1274, 24T1275, 24T1276 x 2, 24T1277 x 2, 24T1278 x 2, 24T1279 x 2, 32T9333, 32T9454 |
| 12T154 |
$C_2^4:D_{12}$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$C_2$, $S_3$, $D_{6}$ |
12T152 x 4, 12T154 x 3, 16T742 x 4, 24T1149 x 2, 24T1150 x 2, 24T1262 x 2, 24T1263 x 2, 24T1264 x 4, 24T1268 x 2, 24T1269 x 2, 24T1270 x 4, 24T1271 x 4, 24T1272 x 4, 24T1273 x 4, 32T9346 x 2 |
| 12T155 |
$C_2^5.D_6$ |
$384$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $D_{6}$ |
12T153 x 2, 12T155, 16T725 x 2, 24T720, 24T836, 24T860, 24T1136, 24T1142, 24T1145, 24T1146, 24T1265 x 2, 24T1266, 24T1267, 24T1274, 24T1275, 24T1276 x 2, 24T1277 x 2, 24T1278 x 2, 24T1279 x 2, 32T9333, 32T9454 |
| 12T156 |
$S_3^3:C_2$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $D_{4}$ |
12T156, 18T150 x 2, 24T1322 x 2, 24T1323 x 2, 24T1324 x 2, 27T137, 36T680 x 2, 36T681 x 2, 36T682 x 2, 36T683 x 2, 36T684 x 2, 36T685 x 2, 36T686 x 2, 36T699 x 2 |
| 12T157 |
$C_3^2:\GL(2,3)$ |
$432$ |
$1$ |
✓ |
$-1$ |
$11$ |
$S_4$ |
9T26, 18T157, 24T1325, 24T1326, 24T1327, 24T1334, 27T139, 36T689, 36T709 |
| 14T14 |
$C_7:F_7$ |
$294$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$ |
14T14 x 2, 42T61 x 3 |
| 14T15 |
$C_7^2:S_3$ |
$294$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$ |
21T17, 21T18, 42T56, 42T57, 42T62 |
| 14T16 |
$\PGL(2,7)$ |
$336$ |
$-1$ |
|
$-1$ |
$9$ |
$C_2$ |
8T43, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83 |
Results are complete for degrees $\leq 23$.
