| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T195 |
$A_4^2:C_2^3$ |
$1152$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_2$, $S_3^2$ |
12T195, 16T1288 x 2, 18T267 x 4, 24T2782, 24T2786 x 8, 24T2789, 24T2790 x 2, 24T2791 x 2, 32T96690, 32T96715 x 4, 36T1655 x 2, 36T1663 x 2, 36T1671 x 4, 36T1717 x 4, 36T1718 x 4, 36T1719 x 8, 36T1928 x 2, 36T1929 x 4 |
| 12T196 |
$A_4^2:D_4$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $S_3^2$ |
12T196, 16T1293 x 2, 24T2783, 24T2792, 24T2793 x 2, 24T2794 x 2, 32T96693, 36T1657 x 2, 36T1662, 36T1670, 36T1927 x 2, 36T1933 x 2 |
| 12T197 |
$C_2^5.S_3^2$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_2$, $S_3^2$ |
12T197, 16T1289 x 2, 24T2784, 24T2795, 24T2796 x 2, 24T2797 x 2, 32T96691, 36T1656 x 2, 36T1661 x 2, 36T1926 x 2 |
| 12T198 |
$C_2\times A_4^2:C_4$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_3^2:C_4$ |
12T199, 16T1287, 16T1290, 18T265 x 2, 24T2781, 24T2798, 24T2799, 24T2800, 24T2801, 24T2802, 32T96689, 32T96706 x 2, 36T1664, 36T1665, 36T1666, 36T1667, 36T1707 x 2, 36T1708 x 2, 36T1930, 36T1932 |
| 12T199 |
$C_2\times A_4^2:C_4$ |
$1152$ |
$1$ |
✓ |
$-1$ |
$26$ |
$C_2$, $C_3^2:C_4$ |
12T198, 16T1287, 16T1290, 18T265 x 2, 24T2781, 24T2798, 24T2799, 24T2800, 24T2801, 24T2802, 32T96689, 32T96706 x 2, 36T1664, 36T1665, 36T1666, 36T1667, 36T1707 x 2, 36T1708 x 2, 36T1930, 36T1932 |
| 12T200 |
$S_4\wr C_2$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3^2:D_4$ |
8T47, 12T201, 12T202, 12T203, 16T1292, 16T1294, 16T1295, 16T1296, 18T272, 18T273, 18T274, 18T275, 24T2803, 24T2804, 24T2805, 24T2806, 24T2807, 24T2808, 24T2809, 24T2810, 24T2821, 24T2826, 32T96692, 32T96694, 32T96695, 32T96696, 36T1758, 36T1759, 36T1760, 36T1761, 36T1762, 36T1763, 36T1764, 36T1765, 36T1766, 36T1767, 36T1768, 36T1769, 36T1943, 36T1944, 36T1945, 36T1946 |
| 12T201 |
$S_4\wr C_2$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3^2:D_4$ |
8T47, 12T200, 12T202, 12T203, 16T1292, 16T1294, 16T1295, 16T1296, 18T272, 18T273, 18T274, 18T275, 24T2803, 24T2804, 24T2805, 24T2806, 24T2807, 24T2808, 24T2809, 24T2810, 24T2821, 24T2826, 32T96692, 32T96694, 32T96695, 32T96696, 36T1758, 36T1759, 36T1760, 36T1761, 36T1762, 36T1763, 36T1764, 36T1765, 36T1766, 36T1767, 36T1768, 36T1769, 36T1943, 36T1944, 36T1945, 36T1946 |
| 12T202 |
$S_4\wr C_2$ |
$1152$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3^2:D_4$ |
8T47, 12T200, 12T201, 12T203, 16T1292, 16T1294, 16T1295, 16T1296, 18T272, 18T273, 18T274, 18T275, 24T2803, 24T2804, 24T2805, 24T2806, 24T2807, 24T2808, 24T2809, 24T2810, 24T2821, 24T2826, 32T96692, 32T96694, 32T96695, 32T96696, 36T1758, 36T1759, 36T1760, 36T1761, 36T1762, 36T1763, 36T1764, 36T1765, 36T1766, 36T1767, 36T1768, 36T1769, 36T1943, 36T1944, 36T1945, 36T1946 |
| 12T203 |
$S_4\wr C_2$ |
$1152$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_3^2:D_4$ |
8T47, 12T200, 12T201, 12T202, 16T1292, 16T1294, 16T1295, 16T1296, 18T272, 18T273, 18T274, 18T275, 24T2803, 24T2804, 24T2805, 24T2806, 24T2807, 24T2808, 24T2809, 24T2810, 24T2821, 24T2826, 32T96692, 32T96694, 32T96695, 32T96696, 36T1758, 36T1759, 36T1760, 36T1761, 36T1762, 36T1763, 36T1764, 36T1765, 36T1766, 36T1767, 36T1768, 36T1769, 36T1943, 36T1944, 36T1945, 36T1946 |
| 12T204 |
$C_2^2:\PSOPlus(4,3)$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$S_3$ |
18T276, 18T279, 24T2760 x 3, 24T2762 x 3, 24T2811, 24T2832, 36T1619, 36T1623, 36T1770 x 3, 36T1771 x 3, 36T1772 x 3, 36T1789 x 3, 36T1790 x 3, 36T1909 x 3, 36T1910 x 3, 36T1911 x 3, 36T1912, 36T1947, 36T1948 x 3 |
| 12T205 |
$C_2^4:(C_3\times S_4)$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_3$ |
18T269, 18T270, 24T2765, 24T2767, 24T2812, 24T2823, 24T2829, 24T2831, 32T96681, 36T1610, 36T1615, 36T1617, 36T1724, 36T1725, 36T1755, 36T1756, 36T1757, 36T1896 x 2, 36T1902, 36T1903, 36T1904, 36T1905, 36T1940, 36T1941, 36T1942 x 2 |
| 12T206 |
$C_2^4:(S_3\times A_4)$ |
$1152$ |
$1$ |
✓ |
$-1$ |
$24$ |
$S_3$ |
12T206 x 2, 18T268 x 3, 18T271 x 3, 24T2768 x 3, 24T2769 x 3, 24T2813 x 3, 24T2825, 24T2827, 32T96680, 36T1609, 36T1618 x 3, 36T1735 x 3, 36T1736 x 3, 36T1737 x 3, 36T1738 x 3, 36T1744 x 3, 36T1745 x 3, 36T1746 x 6, 36T1897 x 6, 36T1898 x 3, 36T1899 x 3, 36T1900 x 3, 36T1901 x 3, 36T1936 x 3, 36T1937 x 3, 36T1938 x 3, 36T1939 |
| 12T207 |
$C_2^6:D_9$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$ |
12T207 x 6, 18T277 x 7, 18T278 x 7, 24T2814 x 7, 36T1625 x 7, 36T1949 x 21, 36T1950 x 7, 36T1951 x 21, 36T1952 x 7 |
| 12T208 |
$A_4^2:D_4$ |
$1152$ |
$-1$ |
✓ |
$-1$ |
$44$ |
$C_2$, $S_3\times C_3$ |
12T208, 16T1286 x 2, 24T2815 x 2, 24T2816 x 2, 24T2817 x 2, 24T2818 x 2, 24T2819, 32T96688, 36T1607, 36T1613 x 2, 36T1635, 36T1914 x 2, 36T1915 x 2 |
| 12T209 |
$(C_3^2\times S_3^2):C_4$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $D_{4}$ |
12T209 x 3, 18T296 x 4, 24T2881 x 4, 24T2882 x 4, 24T2883 x 4, 24T2927 x 2, 36T2188 x 4, 36T2189 x 4, 36T2190 x 4, 36T2191 x 4, 36T2192 x 4, 36T2193 x 4, 36T2194 x 4, 36T2252 x 2, 36T2280 x 4, 36T2282 x 4, 36T2328 x 4 |
| 12T210 |
$C_3^4:(C_2\times D_4)$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_2$ x 3, $C_2^2$ |
12T210 x 3, 18T287 x 4, 18T292 x 4, 24T2884 x 4, 24T2885 x 4, 24T2886 x 4, 24T2926 x 2, 36T2159 x 4, 36T2160 x 4, 36T2161 x 4, 36T2162 x 8, 36T2163 x 8, 36T2179 x 4, 36T2180 x 8, 36T2254 x 2, 36T2277 x 8, 36T2318 x 2 |
| 12T211 |
$C_3^2\wr C_2.D_4$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$33$ |
$C_2$, $C_4$ |
12T211, 18T295 x 2, 24T2887 x 2, 24T2888 x 2, 24T2889 x 2, 24T2924, 24T2933 x 2, 36T2183 x 2, 36T2184 x 2, 36T2185 x 2, 36T2186 x 4, 36T2187 x 4, 36T2249, 36T2251 x 2, 36T2279 x 4, 36T2303 x 2 |
| 12T212 |
$C_3^4:\SD_{16}$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $D_{4}$ |
12T212, 18T307, 18T318, 24T2890 x 2, 24T2891 x 2, 24T2892 x 2, 24T2932 x 2, 24T2945, 36T2207, 36T2208 x 2, 36T2223, 36T2224 x 2, 36T2291, 36T2292 x 4, 36T2295, 36T2304, 36T2321, 36T2325, 36T2327 x 2 |
| 12T213 |
$S_3\wr S_3$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$S_4$ |
9T31, 18T300, 18T303, 18T311, 18T312, 18T314, 18T315, 18T319, 18T320, 24T2893, 24T2894, 24T2895, 24T2912, 27T296, 27T298, 36T2197, 36T2198, 36T2199, 36T2201, 36T2202, 36T2210, 36T2211, 36T2212, 36T2213, 36T2214, 36T2215, 36T2216, 36T2217, 36T2218, 36T2219, 36T2220, 36T2225, 36T2226, 36T2229, 36T2305 |
| 12T214 |
$C_3^4:D_4:C_2$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$ x 3, $C_2^2$ |
12T214 x 5, 18T290 x 6, 18T291 x 3, 18T294 x 2, 24T2896 x 6, 24T2897 x 6, 24T2898 x 6, 24T2941 x 2, 36T2174 x 6, 36T2175 x 12, 36T2176 x 3, 36T2177 x 3, 36T2178 x 3, 36T2182 x 6, 36T2306 x 6, 36T2317 |
| 12T215 |
$C_3^4:\OD_{16}$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $C_4$ |
12T215, 18T288, 18T297 x 2, 24T2899 x 2, 24T2900 x 2, 24T2901 x 2, 24T2928 x 2, 24T2939 x 2, 36T2164, 36T2165, 36T2166, 36T2195 x 2, 36T2307 x 2, 36T2308 x 2, 36T2313, 36T2314, 36T2319 |
| 12T216 |
$C_3^4:D_8$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $D_{4}$ |
12T216 x 7, 18T298, 18T304 x 4, 24T2902 x 8, 24T2903 x 8, 24T2904 x 8, 24T2944, 36T2196, 36T2203 x 4, 36T2204 x 8, 36T2309 x 4, 36T2310 x 8, 36T2311 x 2 |
| 12T217 |
$S_3^2:S_3^2$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $D_{4}$ |
12T217, 18T289 x 2, 24T2905 x 2, 24T2906 x 2, 24T2907 x 2, 24T2934, 36T2167 x 2, 36T2168 x 2, 36T2169 x 2, 36T2170 x 2, 36T2171 x 2, 36T2172 x 2, 36T2173 x 2, 36T2244 x 2, 36T2245 x 2, 36T2253, 36T2278 x 2, 36T2281 x 2, 36T2301 x 2 |
| 12T218 |
$\PGL(2,11)$ |
$1320$ |
$-1$ |
|
$-1$ |
$13$ |
|
22T14, 24T2949 |
| 12T219 |
$S_6\times C_2$ |
$1440$ |
$1$ |
|
$-1$ |
$22$ |
$C_2$, $S_6$ |
12T219 x 3, 20T198 x 2, 20T199 x 2, 24T2959 x 2, 30T260 x 4, 30T261 x 4, 40T1177, 40T1178, 40T1189 x 2, 40T1190 x 4 |
| 12T220 |
$S_6:C_2$ |
$1440$ |
$1$ |
|
$-1$ |
$13$ |
$C_2$ |
10T35, 20T201, 20T204, 20T208, 24T2960, 30T264, 36T2341, 40T1198, 40T1199, 40T1201, 45T187 |
| 12T221 |
$C_4^3:S_4$ |
$1536$ |
$-1$ |
✓ |
$-1$ |
$40$ |
$S_3$, $S_4\times C_2$ |
12T221 x 7, 24T3114 x 2, 24T3116 x 4, 24T3120 x 2, 24T3146 x 2, 24T3179 x 2, 24T4298 x 2, 24T4305 x 2, 24T4344 x 2, 24T4831 x 4, 24T4832 x 4, 24T4833 x 4, 24T4834 x 4, 24T4835 x 4, 24T4836 x 4, 24T4837 x 4 |
| 12T222 |
$D_4\wr C_3$ |
$1536$ |
$-1$ |
✓ |
$-1$ |
$55$ |
$C_3$, $A_4\times C_2$ |
12T222 x 31, 24T4838 x 32, 24T4839 x 16, 24T4840 x 32, 24T4841 x 16, 24T4842 x 16, 24T4843 x 32, 24T4844 x 32, 24T4845 x 32, 24T4846 x 32, 24T4847 x 32, 24T4848 x 32, 24T4849 x 32, 24T4850 x 32, 24T4851 x 16, 24T4852 x 32, 24T4853 x 16, 24T4854 x 32, 24T4855 x 16, 24T4856 x 16 |
| 12T223 |
$C_2\wr S_4$ |
$1536$ |
$-1$ |
✓ |
$-1$ |
$37$ |
$S_3$, $S_4\times C_2$ |
12T223 x 3, 12T224 x 4, 24T2996 x 2, 24T3106, 24T3107, 24T3112 x 2, 24T3117, 24T3122, 24T3149, 24T3170, 24T3176, 24T3180, 24T3560, 24T3600, 24T4285 x 2, 24T4287, 24T4357, 24T4857 x 2, 24T4858 x 2, 24T4859 x 4, 24T4860 x 2, 24T4861 x 2, 24T4862 x 2, 24T4863 x 2, 24T4864 x 2, 24T4865 x 2, 24T4866 x 2, 24T4867 x 2, 24T4868 x 2, 24T4869 x 2 |
| 12T224 |
$C_2\wr S_4$ |
$1536$ |
$-1$ |
✓ |
$-1$ |
$37$ |
$S_3$, $S_4$ |
12T223 x 4, 12T224 x 3, 24T2996 x 2, 24T3106, 24T3107, 24T3112 x 2, 24T3117, 24T3122, 24T3149, 24T3170, 24T3176, 24T3180, 24T3560, 24T3600, 24T4285 x 2, 24T4287, 24T4357, 24T4857 x 2, 24T4858 x 2, 24T4859 x 4, 24T4860 x 2, 24T4861 x 2, 24T4862 x 2, 24T4863 x 2, 24T4864 x 2, 24T4865 x 2, 24T4866 x 2, 24T4867 x 2, 24T4868 x 2, 24T4869 x 2 |
| 12T225 |
$C_4^3:S_4$ |
$1536$ |
$-1$ |
✓ |
$-1$ |
$37$ |
$S_3$, $S_4\times C_2$ |
12T225 x 15, 24T3113 x 4, 24T3143 x 4, 24T4284 x 4, 24T4870 x 8, 24T4871 x 8, 24T4872 x 8, 24T4873 x 8, 24T4874 x 8, 24T4875 x 8, 24T4876 x 8 |
| 12T226 |
$C_2\wr S_4$ |
$1536$ |
$1$ |
✓ |
$-1$ |
$40$ |
$S_3$, $S_4\times C_2$ |
12T226 x 7, 12T227 x 8, 24T3089 x 2, 24T3115 x 2, 24T3152 x 2, 24T3206 x 2, 24T3628 x 2, 24T4307 x 2, 24T4877 x 4, 24T4878 x 4, 24T4879 x 4, 24T4880 x 8, 24T4881 x 4, 24T4882 x 4, 24T4883 x 4, 24T4884 x 4, 24T4885 x 8, 24T4886 x 4, 24T4887 x 8, 24T4888 x 4, 24T4889 x 4, 24T4890 x 8, 24T4891 x 4, 24T4892 x 4, 24T4893 x 8, 32T97069 x 8 |
| 12T227 |
$C_2\wr S_4$ |
$1536$ |
$-1$ |
✓ |
$-1$ |
$40$ |
$S_3$, $S_4$ |
12T226 x 8, 12T227 x 7, 24T3089 x 2, 24T3115 x 2, 24T3152 x 2, 24T3206 x 2, 24T3628 x 2, 24T4307 x 2, 24T4877 x 4, 24T4878 x 4, 24T4879 x 4, 24T4880 x 8, 24T4881 x 4, 24T4882 x 4, 24T4883 x 4, 24T4884 x 4, 24T4885 x 8, 24T4886 x 4, 24T4887 x 8, 24T4888 x 4, 24T4889 x 4, 24T4890 x 8, 24T4891 x 4, 24T4892 x 4, 24T4893 x 8, 32T97069 x 8 |
| 12T228 |
$C_2^6:C_9:C_3$ |
$1728$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$ |
18T335, 36T2584, 36T2600, 36T2601 x 2, 36T2605, 36T2607, 36T2608 |
| 12T229 |
$C_2^6:\He_3$ |
$1728$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$ |
12T229 x 3, 18T334 x 4, 36T2583 x 4, 36T2602 x 4, 36T2603 x 8, 36T2604, 36T2609 x 4 |
| 12T230 |
$C_2^5:A_5$ |
$1920$ |
$1$ |
|
$-1$ |
$16$ |
$\PSL(2,5)$ |
12T230, 20T228 x 2, 24T4946, 32T97740 x 4, 40T1580, 40T1651, 40T1653 |
| 12T231 |
$C_3\wr S_4$ |
$1944$ |
$-1$ |
✓ |
$-1$ |
$51$ |
$S_4$ |
12T231, 18T349, 24T4949 x 2, 24T4955 x 2, 27T400, 36T2775, 36T2776 x 2, 36T2847, 36T2849 x 2, 36T2985 |
| 12T232 |
$C_3^4:\SL(2,3)$ |
$1944$ |
$1$ |
✓ |
$-1$ |
$21$ |
$A_4$ |
12T232 x 2, 24T4950 x 3, 24T4953 x 3, 27T416, 36T2831, 36T2833, 36T2835 x 3, 36T3013, 36T3014, 36T3016 |
| 12T233 |
$C_3^4:S_4$ |
$1944$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$S_4$ |
12T233 x 5, 18T359, 24T4951 x 6, 27T396, 36T2803 x 2, 36T2804, 36T2845, 36T2850 x 2, 36T2979 x 3, 36T2980 x 6 |
| 12T234 |
$C_3^3:(S_3\times A_4)$ |
$1944$ |
$1$ |
✓ |
$-1$ |
$30$ |
$A_4$ |
12T234, 18T348, 24T4952 x 2, 24T4954 x 2, 27T417, 36T2772, 36T2773, 36T2774, 36T2832, 36T2836 x 2, 36T2975, 36T3018 x 2 |
Results are complete for degrees $\leq 23$.
