Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
18T175 |
$A_4^2:C_2^2$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_3$, $S_3$, $S_3\times C_3$ |
12T158, 16T1028, 18T175, 24T1481 x 2, 24T1484 x 2, 24T1485, 24T1486, 32T34599 x 2, 36T720, 36T723, 36T743 x 2, 36T744 x 2, 36T948 x 2, 36T949, 36T950, 36T951 x 2 |
18T176 |
$A_4^2:C_2^2$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$40$ |
$C_3$, $S_3$, $S_3\times C_3$ |
18T176, 24T1362 x 2, 24T1366 x 2, 32T34601 x 2, 36T722, 36T741 x 2, 36T742 x 2, 36T813 x 2, 36T824 x 2, 36T825 x 2, 36T832 x 2, 36T833 x 2, 36T842, 36T843 x 2, 36T875 x 2, 36T876 x 2, 36T877 x 4, 36T878 x 4 |
18T177 |
$C_2^6:C_9$ |
$576$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$, $C_9$ |
12T166 x 7, 18T177 x 6, 36T954 x 7, 36T955 x 21, 36T956 x 7, 36T957 x 42 |
18T178 |
$C_2^2:A_4^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$ x 4, $C_3^2$ |
12T164 x 3, 18T178 x 2, 24T1470 x 9, 36T753 x 9, 36T754 x 9, 36T882 x 9, 36T883 x 9, 36T884 x 3, 36T885 x 18, 36T958 x 3, 36T959 x 3 |
18T179 |
$\PGOPlus(4,3)$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$S_3$ x 2, $S_3^2$ |
8T45, 12T161, 12T163, 12T165 x 2, 16T1032, 16T1034, 18T180, 18T185 x 2, 24T1490, 24T1492, 24T1493 x 2, 24T1494 x 2, 24T1495 x 2, 24T1503, 24T1504 x 2, 32T34597 x 2, 32T34598, 36T759, 36T760, 36T762, 36T763, 36T774 x 2, 36T775 x 2, 36T960, 36T961, 36T962 x 2, 36T963 x 2 |
18T180 |
$\PGOPlus(4,3)$ |
$576$ |
$1$ |
✓ |
$-1$ |
$16$ |
$S_3$ x 2, $S_3^2$ |
8T45, 12T161, 12T163, 12T165 x 2, 16T1032, 16T1034, 18T179, 18T185 x 2, 24T1490, 24T1492, 24T1493 x 2, 24T1494 x 2, 24T1495 x 2, 24T1503, 24T1504 x 2, 32T34597 x 2, 32T34598, 36T759, 36T760, 36T762, 36T763, 36T774 x 2, 36T775 x 2, 36T960, 36T961, 36T962 x 2, 36T963 x 2 |
18T181 |
$S_4^2$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$25$ |
$S_3$ x 2, $S_3^2$ |
16T1033, 18T186, 18T187 x 2, 24T1465 x 2, 24T1466 x 2, 24T1467 x 2, 24T1468 x 2, 24T1507, 32T34595 x 2, 32T34596, 36T757, 36T758, 36T776 x 2, 36T777 x 2, 36T892 x 2, 36T893, 36T894 x 2, 36T895 x 2, 36T906 x 2, 36T907, 36T908 x 2, 36T912, 36T913 x 2, 36T932 x 2, 36T933 x 2, 36T934 |
18T182 |
$A_4^2:C_4$ |
$576$ |
$1$ |
✓ |
$-1$ |
$13$ |
$C_3^2:C_4$ |
8T46, 12T160, 12T162, 16T1030, 16T1031, 18T184, 24T1489, 24T1491, 24T1505, 24T1506 x 2, 24T1508, 32T34594, 36T764, 36T765, 36T766, 36T767, 36T964, 36T965 |
18T183 |
$A_4^2:C_2^2$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$ x 4, $C_3^2:C_2$ |
18T183, 24T1364 x 4, 24T1480 x 4, 32T34605 x 2, 36T730, 36T781 x 2, 36T782 x 2, 36T844 x 2, 36T845 x 4, 36T871 x 4, 36T898 x 2, 36T899 x 2, 36T953 x 2 |
18T184 |
$A_4^2:C_4$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$13$ |
$C_3^2:C_4$ |
8T46, 12T160, 12T162, 16T1030, 16T1031, 18T182, 24T1489, 24T1491, 24T1505, 24T1506 x 2, 24T1508, 32T34594, 36T764, 36T765, 36T766, 36T767, 36T964, 36T965 |
18T185 |
$\PGOPlus(4,3)$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$S_3$ x 2, $S_3^2$ |
8T45, 12T161, 12T163, 12T165 x 2, 16T1032, 16T1034, 18T179, 18T180, 18T185, 24T1490, 24T1492, 24T1493 x 2, 24T1494 x 2, 24T1495 x 2, 24T1503, 24T1504 x 2, 32T34597 x 2, 32T34598, 36T759, 36T760, 36T762, 36T763, 36T774 x 2, 36T775 x 2, 36T960, 36T961, 36T962 x 2, 36T963 x 2 |
18T186 |
$S_4^2$ |
$576$ |
$1$ |
✓ |
$-1$ |
$25$ |
$S_3$ x 2, $S_3^2$ |
16T1033, 18T181, 18T187 x 2, 24T1465 x 2, 24T1466 x 2, 24T1467 x 2, 24T1468 x 2, 24T1507, 32T34595 x 2, 32T34596, 36T757, 36T758, 36T776 x 2, 36T777 x 2, 36T892 x 2, 36T893, 36T894 x 2, 36T895 x 2, 36T906 x 2, 36T907, 36T908 x 2, 36T912, 36T913 x 2, 36T932 x 2, 36T933 x 2, 36T934 |
18T187 |
$S_4^2$ |
$576$ |
$-1$ |
✓ |
$-1$ |
$25$ |
$S_3$ x 2, $S_3^2$ |
16T1033, 18T181, 18T186, 18T187, 24T1465 x 2, 24T1466 x 2, 24T1467 x 2, 24T1468 x 2, 24T1507, 32T34595 x 2, 32T34596, 36T757, 36T758, 36T776 x 2, 36T777 x 2, 36T892 x 2, 36T893, 36T894 x 2, 36T895 x 2, 36T906 x 2, 36T907, 36T908 x 2, 36T912, 36T913 x 2, 36T932 x 2, 36T933 x 2, 36T934 |
18T188 |
$C_6\wr C_3$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$88$ |
$C_3$, $A_4\times C_2$, $C_3 \wr C_3 $ |
18T188 x 8, 36T968 x 9, 36T1028 x 9 |
18T189 |
$C_3\wr D_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$54$ |
$C_2$, $S_3\times C_3$, $C_3^2:D_4$ |
12T167 x 2, 18T189, 24T1519 x 2, 24T1536, 36T1079 x 2, 36T1080 x 2, 36T1081 x 2, 36T1158, 36T1163, 36T1165, 36T1170, 36T1180, 36T1191 x 2, 36T1200 x 2, 36T1231 x 2 |
18T190 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$ x 2 |
12T171 x 8, 18T190 x 7, 18T192 x 8, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
18T191 |
$C_3.S_3^3$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $S_3$, $D_{6}$ |
18T191, 27T218 x 2, 36T1084 x 2, 36T1085 x 2, 36T1086 x 2, 36T1192 |
18T192 |
$C_3^4:(C_2\times C_4)$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$ |
12T171 x 8, 18T190 x 8, 18T192 x 7, 24T1523 x 8, 36T1082 x 8, 36T1083 x 16, 36T1087 x 8, 36T1198 x 16, 36T1233 x 8 |
18T193 |
$C_3:S_3^3$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$42$ |
$C_2$, $S_3^2$ x 2 |
12T168 x 2, 18T193 x 5, 24T1520 x 2, 36T1088 x 6, 36T1089 x 12, 36T1144 x 4, 36T1194 x 12, 36T1226 x 2 |
18T194 |
$C_2\times C_3^3:D_6$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$34$ |
$C_2$, $S_3$, $D_{6}$, $((C_3^3:C_3):C_2):C_2$ |
18T194 x 11, 36T1034 x 6, 36T1058 x 6, 36T1062 x 6 |
18T195 |
$C_3^3:(C_4\times S_3)$ |
$648$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3^2$, $C_3^2:C_4$ |
12T170 x 4, 18T195 x 3, 24T1522 x 4, 36T1090 x 4, 36T1091 x 4, 36T1092 x 4, 36T1149 x 4, 36T1196 x 4, 36T1199 x 4, 36T1228 x 4, 36T1229 x 8 |
18T196 |
$C_3^2:F_9$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$ |
12T173 x 8, 18T196 x 3, 24T1525 x 8, 36T1093 x 4, 36T1216 x 4, 36T1217 x 16, 36T1235 x 2, 36T1236 x 8 |
18T197 |
$S_3\wr C_3$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_3$, $A_4\times C_2$, $S_3 \wr C_3 $ |
9T28, 12T176, 18T197, 18T198 x 2, 18T202, 18T204, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
18T198 |
$S_3\wr C_3$ |
$648$ |
$1$ |
✓ |
$-1$ |
$17$ |
$C_3$, $A_4$, $S_3 \wr C_3 $ |
9T28, 12T176, 18T197 x 2, 18T198, 18T202, 18T204, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
18T199 |
$C_2\times C_3^3:A_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_3$, $A_4\times C_2$, $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
18T199, 18T201, 18T205, 24T1516 x 2, 24T1518, 36T1073 x 2, 36T1074 x 2, 36T1075, 36T1076, 36T1077, 36T1078 |
18T200 |
$(C_3\times C_6^2):C_6$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_3$, $A_4\times C_2$, $(C_3^3:C_3):C_2$ |
18T200 x 8, 18T209 x 9, 36T985 x 9, 36T1098 x 9, 36T1104 x 3 |
18T201 |
$C_2\times C_3^3:A_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_3$, $C_6$, $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
18T199 x 2, 18T205, 24T1516 x 2, 24T1518, 36T1073 x 2, 36T1074 x 2, 36T1075, 36T1076, 36T1077, 36T1078 |
18T202 |
$S_3\wr C_3$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $C_3$, $C_6$, $S_3 \wr C_3 $ |
9T28, 12T176, 18T197 x 2, 18T198 x 2, 18T204, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
18T203 |
$C_3^3:S_4$ |
$648$ |
$1$ |
✓ |
$-1$ |
$49$ |
$S_3$, $S_4$, $C_3 \wr S_3 $ |
18T203 x 2, 18T208 x 3, 36T986 x 3, 36T988 x 3, 36T1100 x 3 |
18T204 |
$S_3\wr C_3$ |
$648$ |
$1$ |
✓ |
$-1$ |
$17$ |
$C_3$, $A_4$, $S_3 \wr C_3 $ |
9T28, 12T176, 18T197 x 2, 18T198 x 2, 18T202, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
18T205 |
$C_2\times C_3^3:A_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_3$, $A_4\times C_2$, $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
18T199 x 2, 18T201, 24T1516 x 2, 24T1518, 36T1073 x 2, 36T1074 x 2, 36T1075, 36T1076, 36T1077, 36T1078 |
18T206 |
$S_3\wr C_3$ |
$648$ |
$1$ |
✓ |
$-1$ |
$17$ |
$C_3$, $A_4$ |
9T28, 12T176, 18T197 x 2, 18T198 x 2, 18T202, 18T204, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
18T207 |
$S_3\wr C_3$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_3$, $A_4\times C_2$, $S_3 \wr C_3 $ |
9T28, 12T176, 18T197 x 2, 18T198 x 2, 18T202, 18T204, 18T206, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
18T208 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$49$ |
$S_3$, $S_4$, $C_3 \wr S_3 $ |
18T203 x 3, 18T208 x 2, 36T986 x 3, 36T988 x 3, 36T1100 x 3 |
18T209 |
$(C_3\times C_6^2):C_6$ |
$648$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_3$, $A_4$, $(C_3^3:C_3):C_2$ |
18T200 x 9, 18T209 x 8, 36T985 x 9, 36T1098 x 9, 36T1104 x 3 |
18T210 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3^2$, $C_3^2:D_4$ |
12T169 x 2, 18T210, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
18T211 |
$D_9\wr C_2$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3^2:D_4$ |
18T211, 36T1108 x 2, 36T1109 x 2, 36T1110 x 2, 36T1188 x 2 |
18T212 |
$C_3^4:Q_8$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$ |
12T174 x 6, 18T212 x 8, 24T1526 x 6, 36T1111 x 9, 36T1220 x 18, 36T1221, 36T1222 x 8 |
18T213 |
$C_3^4:D_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3^2:D_4$ x 4 |
12T172 x 6, 18T213, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3 |
18T214 |
$C_3^4:D_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$ |
12T172 x 6, 18T213 x 2, 18T214 x 2, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3 |
18T215 |
$C_3^2.\SOPlus(4,2)$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:D_4$ |
18T215, 36T1116 x 2, 36T1117 x 2, 36T1118 x 2, 36T1186 |
18T216 |
$C_3^4:D_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $C_3^2:D_4$ x 2 |
12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 11, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3 |
18T217 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $S_3$, $S_3$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
9T30, 12T177 x 2, 12T178, 18T218, 18T221, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
18T218 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4$ |
9T30, 12T177 x 2, 12T178, 18T217, 18T221, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
18T219 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_3$, $S_4$ |
9T29, 12T175, 18T220, 18T223, 18T224, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237 |
18T220 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_3$, $S_4$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
9T29, 12T175, 18T219, 18T223, 18T224, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237 |
18T221 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
9T30, 12T177 x 2, 12T178, 18T217, 18T218, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
18T222 |
$C_3^3:S_4$ |
$648$ |
$1$ |
✓ |
$-1$ |
$14$ |
$S_3$, $S_4$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
9T30, 12T177 x 2, 12T178, 18T217, 18T218, 18T221, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
18T223 |
$C_3^3:S_4$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $S_3$, $S_3$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
9T29, 12T175, 18T219, 18T220, 18T224, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237 |
18T224 |
$C_3^3:S_4$ |
$648$ |
$1$ |
✓ |
$-1$ |
$17$ |
$S_3$, $S_4$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
9T29, 12T175, 18T219, 18T220, 18T223, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237 |
Results are complete for degrees $\leq 23$.