Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1946 conjugacy classes of subgroups.
The subgroup lattice has 607 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5700 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10594589 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10594495 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10594492 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10594426 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10594404 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10594386 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #10593952 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10593921 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #87094 | — | 3 | 1 | no | maximal |
| 13 | #86286 | — | 3 | 1 | no | maximal |
| 14 | C32×#125 | C22 | 1 | 1 | yes | characteristic |
| 15 | #64099 | C22 | 1 | 4 | yes | — |
| 16 | #64098 | C22 | 1 | 4 | yes | — |
| 17 | #64098 | C22 | 1 | 4 | yes | — |
| 18 | #64079 | C22 | 1 | 2 | yes | — |
| 19 | C3×#896 | C22 | 1 | 4 | yes | — |
| 20 | C3×#896 | C22 | 1 | 4 | yes | — |
| 21 | C3×#895 | C22 | 1 | 4 | yes | — |
| 22 | C3×#894 | C22 | 1 | 4 | yes | — |
| 23 | C3×#892 | C22 | 1 | 2 | yes | — |
| 24 | C3×#888 | C22 | 1 | 2 | yes | — |
| 25 | C3×#887 | C22 | 1 | 4 | yes | — |
| 26 | C3×#875 | C22 | 1 | 2 | yes | — |
| 27 | C3×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 28 | C3×#870 | C22 | 1 | 1 | yes | characteristic |
| 29 | #63915 | C22 | 1 | 4 | yes | — |
| 30 | #63908 | C22 | 1 | 2 | yes | — |
| 31 | #63905 | C22 | 1 | 4 | yes | — |
| 32 | #63905 | C22 | 1 | 4 | yes | — |
| 33 | #63899 | C22 | 1 | 4 | yes | — |
| 34 | #63893 | C22 | 1 | 4 | yes | — |
| 35 | Dic3×D12 | C22 | 1 | 4 | yes | — |
| 36 | Dic3×D12 | C22 | 1 | 2 | yes | — |
| 37 | #63887 | C22 | 1 | 4 | yes | — |
| 38 | #63885 | C22 | 1 | 4 | yes | — |
| 39 | #63884 | C22 | 1 | 4 | yes | — |
| 40 | #63884 | C22 | 1 | 4 | yes | — |
| 41 | #63879 | C22 | 1 | 4 | yes | — |
| 42 | #63877 | C22 | 1 | 4 | yes | — |
| 43 | #63877 | C22 | 1 | 4 | yes | — |
| 44 | C4×D3×Dic3 | C22 | 1 | 4 | yes | — |
| 45 | #63870 | C22 | 1 | 4 | yes | — |
| 46 | #63863 | C22 | 1 | 4 | yes | — |
| 47 | #63861 | C22 | 1 | 4 | yes | — |
| 48 | #63861 | C22 | 1 | 4 | yes | — |
| 49 | #63861 | C22 | 1 | 4 | yes | — |
| 50 | #63859 | C22 | 1 | 4 | yes | — |
| 51 | #63858 | C22 | 1 | 4 | yes | — |
| 52 | #63856 | C22 | 1 | 2 | yes | — |
| 53 | #63856 | C22 | 1 | 4 | yes | — |
| 54 | #63851 | C22 | 1 | 4 | yes | — |
| 55 | Dic3×Dic6 | C22 | 1 | 2 | yes | — |
| 56 | #63839 | C22 | 1 | 4 | yes | — |
| 57 | #63839 | C22 | 1 | 4 | yes | — |
| 58 | #63837 | C22 | 1 | 4 | yes | — |
| 59 | C3×#562 | — | 3 | 1 | no | — |
| 60 | C3×#533 | — | 3 | 1 | no | — |
| 61 | #5735 | — | 3 | 4 | no | — |
| 62 | #5700 | D3 | 1 | 1 | yes | characteristic, complemented |
| 63 | #5699 | — | 3 | 2 | no | — |
| 64 | #5688 | D3 | 1 | 1 | yes | characteristic, complemented |
| 65 | C3⋊#564 | — | 3 | 1 | no | — |
| 66 | C3⋊#564 | — | 3 | 1 | no | — |
| 67 | C3⋊#564 | — | 6 | 1 | no | — |
| 68 | #5680 | — | 3 | 2 | no | — |
| 69 | #5672 | — | 3 | 2 | no | — |
| 70 | #5651 | — | 3 | 4 | no | — |
| 71 | #5649 | — | 3 | 4 | no | — |
| 72 | #5647 | — | 3 | 4 | no | — |
| 73 | #5646 | — | 3 | 4 | no | — |
| 74 | #5646 | — | 3 | 4 | no | — |
| 75 | #5622 | — | 3 | 4 | no | — |
| 76 | #5621 | — | 3 | 4 | no | — |
| 77 | #5600 | — | 3 | 4 | no | — |
| 78 | #5580 | — | 3 | 4 | no | — |
| 79 | #5578 | — | 3 | 4 | no | — |
| 80 | #5528 | — | 3 | 4 | no | — |
| 81 | #5479 | — | 3 | 2 | no | — |
| 82 | C2×C3×D12 | C23 | 1 | 4 | yes | — |
| 83 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 84 | C2×C3×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C3×C4×D3 | C23 | 1 | 4 | yes | — |
| 86 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 87 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 88 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 89 | C2×#627 | C23 | 1 | 4 | yes | — |
| 90 | C2×#625 | C23 | 1 | 4 | yes | — |
| 91 | C2×D3×Dic3 | C23 | 1 | 4 | yes | — |
| 92 | C2×D3×Dic3 | C23 | 1 | 4 | yes | — |
| 93 | C32×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 94 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 95 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 96 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 97 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 98 | C4⋊(C3⋊Dic3) | C23 | 1 | 4 | yes | — |
| 99 | #3750 | C23 | 1 | 4 | yes | — |
| 100 | #3750 | C23 | 1 | 4 | yes | — |
| 101 | #3750 | C23 | 1 | 4 | yes | — |
| 102 | #3750 | C23 | 1 | 4 | yes | — |
| 103 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 104 | C3×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 105 | C3×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 106 | C3×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 107 | C3×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 108 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 109 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 110 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 111 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 112 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 113 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 114 | C3×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 115 | #3724 | C23 | 1 | 4 | yes | — |
| 116 | #3724 | C23 | 1 | 4 | yes | — |
| 117 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 118 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 119 | (C2×D3)⋊Dic3 | C23 | 1 | 4 | yes | — |
| 120 | (C2×D3)⋊Dic3 | C23 | 1 | 4 | yes | — |
| 121 | (C2×D3)⋊Dic3 | C23 | 1 | 4 | yes | — |
| 122 | (C2×D3)⋊Dic3 | C23 | 1 | 4 | yes | — |
| 123 | (C2×D3)⋊Dic3 | C23 | 1 | 4 | yes | — |
| 124 | (C2×D3)⋊Dic3 | C23 | 1 | 4 | yes | — |
| 125 | Dic32 | C23 | 1 | 4 | yes | — |
| 126 | Dic32 | C23 | 1 | 4 | yes | — |
| 127 | #3531 | — | 9 | 1 | no | Sylow |
| 128 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 129 | C3×#125 | — | 2 | 1 | no | — |
| 130 | C3×#125 | — | 3 | 1 | no | — |
| 131 | C3×#125 | C2×D3 | 1 | 1 | yes | characteristic |
| 132 | C3×#125 | C2×D3 | 1 | 1 | yes | characteristic |
| 133 | C3×#124 | — | 3 | 2 | no | — |
| 134 | C3×#123 | — | 3 | 4 | no | — |
| 135 | C3×C22⋊Q8 | — | 3 | 4 | no | — |
| 136 | C3×C22⋊Q8 | — | 3 | 4 | no | — |
| 137 | C3×#121 | — | 3 | 4 | no | — |
| 138 | C3×C4×Q8 | — | 3 | 4 | no | — |
| 139 | C3×#117 | — | 3 | 2 | no | — |
| 140 | C2×C3×C42 | — | 3 | 1 | no | — |
| 141 | #947 | — | 3 | 4 | no | — |
| 142 | #946 | — | 3 | 2 | no | — |
| 143 | #946 | — | 3 | 4 | no | — |
| 144 | #946 | — | 3 | 4 | no | — |
| 145 | Q8×Dic3 | — | 3 | 2 | no | — |
| 146 | #944 | — | 3 | 4 | no | — |
| 147 | #944 | — | 3 | 4 | no | — |
| 148 | #939 | — | 3 | 4 | no | — |
| 149 | #938 | — | 3 | 2 | no | — |
| 150 | #936 | — | 3 | 4 | no | — |
| 151 | #935 | — | 3 | 4 | no | — |
| 152 | #935 | — | 3 | 4 | no | — |
| 153 | D4×Dic3 | — | 3 | 4 | no | — |
| 154 | D4×Dic3 | — | 3 | 2 | no | — |
| 155 | #930 | — | 3 | 2 | no | — |
| 156 | #929 | — | 3 | 4 | no | — |
| 157 | #929 | — | 3 | 4 | no | — |
| 158 | C4×#67 | — | 3 | 4 | no | — |
| 159 | #924 | — | 3 | 2 | no | — |
| 160 | #924 | — | 3 | 4 | no | — |
| 161 | #924 | — | 3 | 4 | no | — |
| 162 | C2×C4×Dic3 | — | 3 | 4 | no | — |
| 163 | #898 | — | 3 | 4 | no | — |
| 164 | #898 | — | 3 | 4 | no | — |
| 165 | #898 | — | 3 | 4 | no | — |
| 166 | #898 | — | 3 | 4 | no | — |
| 167 | #897 | — | 3 | 4 | no | — |
| 168 | #896 | — | 3 | 4 | no | — |
| 169 | #896 | — | 3 | 4 | no | — |
| 170 | #896 | C2×D3 | 1 | 4 | yes | — |
| 171 | #896 | C2×D3 | 1 | 4 | yes | — |
| 172 | #895 | C2×D3 | 1 | 4 | yes | — |
| 173 | #894 | — | 3 | 4 | no | — |
| 174 | #894 | — | 3 | 4 | no | — |
| 175 | #894 | C2×D3 | 1 | 4 | yes | — |
| 176 | #892 | C2×D3 | 1 | 2 | yes | — |
| 177 | #890 | — | 3 | 4 | no | — |
| 178 | #890 | — | 3 | 4 | no | — |
| 179 | #890 | — | 6 | 4 | no | — |
| 180 | #889 | — | 3 | 4 | no | — |
| 181 | #889 | — | 3 | 4 | no | — |
| 182 | #889 | — | 3 | 4 | no | — |
| 183 | #889 | — | 3 | 4 | no | — |
| 184 | #889 | — | 3 | 4 | no | — |
| 185 | #889 | — | 3 | 4 | no | — |
| 186 | #889 | — | 6 | 4 | no | — |
| 187 | #889 | — | 6 | 4 | no | — |
| 188 | #888 | — | 3 | 4 | no | — |
| 189 | #888 | — | 3 | 4 | no | — |
| 190 | #888 | C2×D3 | 1 | 2 | yes | — |
| 191 | #887 | — | 3 | 4 | no | — |
| 192 | #887 | C2×D3 | 1 | 4 | yes | — |
| 193 | #885 | — | 3 | 4 | no | — |
| 194 | #885 | — | 3 | 4 | no | — |
| 195 | #884 | — | 3 | 4 | no | — |
| 196 | #883 | — | 3 | 4 | no | — |
| 197 | #883 | — | 3 | 4 | no | — |
| 198 | #67⋊C4 | — | 3 | 4 | no | — |
| 199 | #879 | — | 3 | 4 | no | — |
| 200 | #879 | — | 3 | 4 | no | — |
| 201 | #879 | — | 3 | 4 | no | — |
| 202 | #879 | — | 3 | 4 | no | — |
| 203 | #879 | — | 3 | 4 | no | — |
| 204 | #878 | — | 3 | 4 | no | — |
| 205 | #878 | — | 3 | 4 | no | — |
| 206 | #878 | — | 3 | 4 | no | — |
| 207 | #877 | — | 3 | 4 | no | — |
| 208 | #877 | — | 3 | 4 | no | — |
| 209 | #876 | — | 3 | 4 | no | — |
| 210 | #875 | C2×D3 | 1 | 2 | yes | — |
| 211 | C4×D12 | — | 3 | 2 | no | — |
| 212 | C4×D12 | — | 3 | 4 | no | — |
| 213 | #872 | — | 3 | 4 | no | — |
| 214 | #872 | — | 3 | 4 | no | — |
| 215 | C42×D3 | — | 3 | 4 | no | — |
| 216 | C42×D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 217 | #870 | — | 3 | 2 | no | — |
| 218 | #870 | — | 3 | 2 | no | — |
| 219 | #870 | — | 6 | 2 | no | — |
| 220 | #870 | C2×D3 | 1 | 1 | yes | characteristic |
| 221 | C4×Dic6 | — | 3 | 2 | no | — |
| 222 | C4×Dic6 | — | 3 | 4 | no | — |
| 223 | C22×C3×D3 | C24 | 1 | 4 | yes | — |
| 224 | C22×C3×D3 | C24 | 1 | 1 | yes | characteristic |
| 225 | C2×C32×C4 | C24 | 1 | 4 | yes | — |
| 226 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 227 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 228 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 229 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 230 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 231 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 232 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 233 | C2×C3×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 234 | C3×D12 | — | 4 | 2 | no | — |
| 235 | C3×D12 | — | 4 | 4 | no | — |
| 236 | C3×C4×D3 | — | 2 | 2 | no | — |
| 237 | C3×C4×D3 | — | 4 | 4 | no | — |
| 238 | C3×C4×D3 | — | 4 | 2 | no | — |
| 239 | C3×Dic6 | — | 4 | 4 | no | — |
| 240 | C3×Dic6 | — | 4 | 2 | no | — |
| 241 | #627 | — | 4 | 4 | no | — |
| 242 | #625 | — | 4 | 4 | no | — |
| 243 | D3×Dic3 | — | 2 | 8 | no | — |
| 244 | D3×Dic3 | — | 4 | 4 | no | — |
| 245 | #564 | — | 9 | 1 | no | — |
| 246 | #563 | — | 9 | 4 | no | — |
| 247 | #563 | — | 9 | 4 | no | — |
| 248 | #563 | — | 9 | 2 | no | — |
| 249 | #562 | — | 3 | 1 | no | — |
| 250 | #562 | — | 9 | 4 | no | — |
| 251 | #533 | — | 3 | 1 | no | — |
| 252 | #533 | — | 9 | 4 | no | — |
| 253 | #529 | — | 9 | 2 | no | — |
| 254 | #529 | — | 9 | 4 | no | — |
| 255 | #529 | — | 9 | 4 | no | — |
| 256 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 257 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 258 | C2×C3×D4 | — | 3 | 2 | no | — |
| 259 | C2×C3×D4 | — | 3 | 4 | no | — |
| 260 | C22×C3×C4 | — | 3 | 1 | no | — |
| 261 | C22×C3×C4 | — | 3 | 4 | no | — |
| 262 | C22×C3×C4 | — | 3 | 2 | no | — |
| 263 | C2×#67 | — | 3 | 4 | no | — |
| 264 | C2×#67 | — | 3 | 4 | no | — |
| 265 | C22×Dic3 | — | 3 | 4 | no | — |
| 266 | C22×Dic3 | — | 3 | 4 | no | — |
| 267 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 268 | C2×D12 | C22×D3 | 1 | 4 | yes | — |
| 269 | C2×C4×D3 | — | 3 | 4 | no | — |
| 270 | C2×C4×D3 | — | 3 | 4 | no | — |
| 271 | C2×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 272 | C2×C4×D3 | C22×D3 | 1 | 4 | yes | — |
| 273 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 274 | C2×Dic6 | — | 3 | 4 | no | — |
| 275 | C2×Dic6 | — | 3 | 4 | no | — |
| 276 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 277 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 278 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 279 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 280 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 281 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 282 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 283 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 284 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 285 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 286 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 287 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 288 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 289 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 290 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 291 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 292 | C3×C42 | — | 2 | 1 | no | — |
| 293 | C3×C42 | — | 3 | 4 | no | — |
| 294 | C3×C42 | — | 3 | 2 | no | — |
| 295 | C3×C42 | — | 3 | 1 | no | — |
| 296 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 297 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 298 | #217 | — | 3 | 4 | no | — |
| 299 | #217 | — | 3 | 4 | no | — |
| 300 | #217 | — | 3 | 4 | no | — |
| 301 | #217 | — | 3 | 4 | no | — |
| 302 | #217 | — | 3 | 4 | no | — |
| 303 | #217 | — | 3 | 4 | no | — |
| 304 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 305 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 306 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 307 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 308 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 309 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 310 | (C2×D3)⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 311 | (C2×D3)⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 312 | (C2×D3)⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 313 | (C2×D3)⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 314 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 315 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 316 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 317 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 318 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 319 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 320 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 321 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 322 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 323 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 324 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 325 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 326 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 327 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 328 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 329 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 330 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 331 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 332 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 333 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 334 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 335 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 336 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 337 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 338 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 339 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 340 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 341 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 342 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 343 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 344 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 345 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 346 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 347 | C4×Dic3 | — | 3 | 4 | no | — |
| 348 | C4×Dic3 | — | 3 | 4 | no | — |
| 349 | C4×Dic3 | — | 3 | 4 | no | — |
| 350 | C4×Dic3 | — | 3 | 4 | no | — |
| 351 | C4×Dic3 | — | 3 | 4 | no | — |
| 352 | C4×Dic3 | — | 3 | 4 | no | — |
| 353 | C4×Dic3 | — | 6 | 4 | no | — |
| 354 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 355 | C4×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 356 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 357 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 358 | C2×C3×D3 | — | 2 | 4 | no | — |
| 359 | C2×C3×D3 | — | 2 | 1 | no | — |
| 360 | C2×C3×D3 | — | 2 | 4 | no | — |
| 361 | C2×C3×D3 | — | 2 | 2 | no | — |
| 362 | C2×C3×D3 | — | 2 | 4 | no | — |
| 363 | C32×C4 | — | 2 | 1 | no | — |
| 364 | C32×C4 | — | 2 | 4 | no | — |
| 365 | C32×C4 | — | 2 | 2 | no | — |
| 366 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 367 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 368 | C3×Dic3 | — | 2 | 4 | no | — |
| 369 | C3×Dic3 | — | 2 | 4 | no | — |
| 370 | C3×Dic3 | — | 2 | 2 | no | — |
| 371 | C3×Dic3 | 2−1+4 | 1 | 2 | yes | — |
| 372 | C4⋊Q8 | — | 3 | 2 | no | — |
| 373 | C4⋊Q8 | — | 9 | 4 | no | — |
| 374 | C4⋊Q8 | — | 9 | 4 | no | — |
| 375 | #126 | — | 9 | 4 | no | — |
| 376 | #126 | — | 9 | 4 | no | — |
| 377 | #126 | — | 9 | 4 | no | — |
| 378 | #126 | — | 9 | 4 | no | — |
| 379 | #126 | — | 9 | 4 | no | — |
| 380 | #125 | — | 3 | 1 | no | — |
| 381 | #125 | — | 9 | 4 | no | — |
| 382 | #125 | — | 9 | 4 | no | — |
| 383 | #125 | — | 9 | 4 | no | — |
| 384 | #125 | — | 9 | 4 | no | — |
| 385 | #125 | — | 9 | 2 | no | — |
| 386 | #125 | D32 | 1 | 1 | yes | characteristic |
| 387 | #124 | — | 3 | 2 | no | — |
| 388 | #124 | — | 9 | 4 | no | — |
| 389 | #124 | — | 9 | 4 | no | — |
| 390 | #123 | — | 3 | 4 | no | — |
| 391 | #123 | — | 9 | 4 | no | — |
| 392 | #123 | — | 9 | 4 | no | — |
| 393 | #123 | — | 9 | 4 | no | — |
| 394 | #123 | — | 9 | 4 | no | — |
| 395 | C22⋊Q8 | — | 3 | 4 | no | — |
| 396 | C22⋊Q8 | — | 3 | 4 | no | — |
| 397 | C22⋊Q8 | — | 9 | 4 | no | — |
| 398 | C22⋊Q8 | — | 9 | 4 | no | — |
| 399 | C22⋊Q8 | — | 9 | 4 | no | — |
| 400 | C22⋊Q8 | — | 9 | 4 | no | — |
| 401 | C22⋊Q8 | — | 9 | 2 | no | — |
| 402 | C22⋊Q8 | — | 9 | 4 | no | — |
| 403 | #121 | — | 3 | 4 | no | — |
| 404 | #121 | — | 9 | 4 | no | — |
| 405 | #121 | — | 9 | 2 | no | — |
| 406 | C4×Q8 | — | 3 | 4 | no | — |
| 407 | C4×Q8 | — | 9 | 4 | no | — |
| 408 | C4×Q8 | — | 9 | 2 | no | — |
| 409 | C4×D4 | — | 9 | 2 | no | — |
| 410 | C4×D4 | — | 9 | 4 | no | — |
| 411 | C4×D4 | — | 9 | 4 | no | — |
| 412 | #117 | — | 3 | 2 | no | — |
| 413 | #117 | — | 9 | 4 | no | — |
| 414 | #117 | — | 9 | 4 | no | — |
| 415 | C2×C42 | — | 3 | 1 | no | — |
| 416 | C2×C42 | — | 9 | 4 | no | — |
| 417 | C23×C3 | — | 3 | 4 | no | — |
| 418 | C23×C3 | — | 3 | 1 | no | — |
| 419 | C22×D3 | C23×D3 | 1 | 4 | yes | — |
| 420 | C22×D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 421 | C3×Q8 | — | 12 | 2 | no | — |
| 422 | C3×Q8 | — | 12 | 4 | no | — |
| 423 | C3×D4 | — | 12 | 4 | no | — |
| 424 | C3×D4 | — | 12 | 2 | no | — |
| 425 | C2×C3×C4 | — | 2 | 4 | no | — |
| 426 | C2×C3×C4 | — | 2 | 1 | no | — |
| 427 | C2×C3×C4 | — | 2 | 2 | no | — |
| 428 | C2×C3×C4 | — | 3 | 1 | no | — |
| 429 | C2×C3×C4 | — | 3 | 4 | no | — |
| 430 | C2×C3×C4 | — | 3 | 4 | no | — |
| 431 | C2×C3×C4 | — | 3 | 2 | no | — |
| 432 | C2×C3×C4 | — | 6 | 2 | no | — |
| 433 | C2×C3×C4 | — | 12 | 4 | no | — |
| 434 | C2×C3×C4 | — | 12 | 2 | no | — |
| 435 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 436 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 437 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 438 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 439 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 440 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 441 | #67 | — | 12 | 4 | no | — |
| 442 | #67 | — | 12 | 4 | no | — |
| 443 | C2×Dic3 | — | 3 | 4 | no | — |
| 444 | C2×Dic3 | — | 3 | 4 | no | — |
| 445 | C2×Dic3 | — | 3 | 4 | no | — |
| 446 | C2×Dic3 | — | 3 | 4 | no | — |
| 447 | C2×Dic3 | — | 6 | 4 | no | — |
| 448 | C2×Dic3 | — | 6 | 4 | no | — |
| 449 | C2×Dic3 | — | 6 | 8 | no | — |
| 450 | C2×Dic3 | — | 12 | 4 | no | — |
| 451 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 452 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 453 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 454 | C2×Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 455 | D12 | — | 4 | 2 | no | — |
| 456 | D12 | — | 4 | 4 | no | — |
| 457 | C4×D3 | — | 2 | 2 | no | — |
| 458 | C4×D3 | — | 4 | 2 | no | — |
| 459 | C4×D3 | — | 4 | 4 | no | — |
| 460 | C4×D3 | — | 6 | 8 | no | — |
| 461 | C4×D3 | — | 12 | 4 | no | — |
| 462 | Dic6 | — | 4 | 4 | no | — |
| 463 | Dic6 | — | 4 | 2 | no | — |
| 464 | Dic6 | — | 12 | 4 | no | — |
| 465 | Dic6 | — | 12 | 4 | no | — |
| 466 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 467 | C2×C32 | #585 | 1 | 2 | yes | — |
| 468 | C3×D3 | — | 4 | 1 | no | — |
| 469 | C3×D3 | — | 4 | 4 | no | — |
| 470 | C2×Q8 | — | 3 | 4 | no | — |
| 471 | C2×Q8 | — | 3 | 2 | no | — |
| 472 | C2×Q8 | — | 9 | 4 | no | — |
| 473 | C2×D4 | — | 3 | 4 | no | — |
| 474 | C2×D4 | — | 3 | 2 | no | — |
| 475 | C2×D4 | — | 9 | 4 | no | — |
| 476 | C22×C4 | — | 3 | 1 | no | — |
| 477 | C22×C4 | — | 3 | 2 | no | — |
| 478 | C22×C4 | — | 3 | 4 | no | — |
| 479 | C22×C4 | — | 9 | 4 | no | — |
| 480 | C22×C4 | — | 9 | 4 | no | — |
| 481 | C4⋊C4 | — | 3 | 2 | no | — |
| 482 | C4⋊C4 | — | 3 | 4 | no | — |
| 483 | C4⋊C4 | — | 3 | 4 | no | — |
| 484 | C4⋊C4 | — | 3 | 4 | no | — |
| 485 | C4⋊C4 | — | 9 | 4 | no | — |
| 486 | C4⋊C4 | — | 9 | 4 | no | — |
| 487 | C4⋊C4 | — | 9 | 4 | no | — |
| 488 | C4⋊C4 | — | 9 | 4 | no | — |
| 489 | C4⋊C4 | — | 9 | 4 | no | — |
| 490 | C4⋊C4 | — | 9 | 4 | no | — |
| 491 | C4⋊C4 | — | 9 | 4 | no | — |
| 492 | C4⋊C4 | — | 9 | 4 | no | — |
| 493 | C4⋊C4 | — | 9 | 2 | no | — |
| 494 | C4⋊C4 | — | 9 | 4 | no | — |
| 495 | C4⋊C4 | — | 9 | 2 | no | — |
| 496 | C4⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 497 | C4⋊C4 | C2×D32 | 1 | 4 | yes | — |
| 498 | C22⋊C4 | — | 3 | 4 | no | — |
| 499 | C22⋊C4 | — | 3 | 4 | no | — |
| 500 | C22⋊C4 | — | 3 | 4 | no | — |
| 501 | C22⋊C4 | — | 3 | 4 | no | — |
| 502 | C22⋊C4 | — | 9 | 4 | no | — |
| 503 | C22⋊C4 | — | 9 | 4 | no | — |
| 504 | C22⋊C4 | — | 9 | 4 | no | — |
| 505 | C22⋊C4 | — | 9 | 4 | no | — |
| 506 | C22⋊C4 | — | 9 | 4 | no | — |
| 507 | C22⋊C4 | — | 9 | 4 | no | — |
| 508 | C42 | — | 3 | 2 | no | — |
| 509 | C42 | — | 3 | 1 | no | — |
| 510 | C42 | — | 3 | 4 | no | — |
| 511 | C42 | — | 9 | 4 | no | — |
| 512 | C42 | — | 9 | 4 | no | — |
| 513 | C42 | — | 9 | 4 | no | — |
| 514 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 515 | C22×C3 | — | 2 | 1 | no | — |
| 516 | C22×C3 | — | 6 | 4 | no | — |
| 517 | C22×C3 | — | 6 | 4 | no | — |
| 518 | C22×C3 | — | 6 | 4 | no | — |
| 519 | C22×C3 | — | 6 | 2 | no | — |
| 520 | C22×C3 | — | 6 | 1 | no | — |
| 521 | C22×C3 | C24×D3 | 1 | 1 | yes | characteristic |
| 522 | C22×C3 | C24×D3 | 1 | 1 | yes | characteristic |
| 523 | C2×D3 | — | 2 | 1 | no | — |
| 524 | C2×D3 | — | 2 | 2 | no | — |
| 525 | C2×D3 | — | 2 | 4 | no | — |
| 526 | C2×D3 | — | 2 | 4 | no | — |
| 527 | C2×D3 | — | 2 | 4 | no | — |
| 528 | C3×C4 | — | 2 | 1 | no | — |
| 529 | C3×C4 | — | 2 | 4 | no | — |
| 530 | C3×C4 | — | 2 | 2 | no | — |
| 531 | C3×C4 | — | 2 | 2 | no | — |
| 532 | C3×C4 | — | 2 | 4 | no | — |
| 533 | C3×C4 | — | 2 | 1 | no | — |
| 534 | C3×C4 | — | 3 | 2 | no | — |
| 535 | C3×C4 | — | 4 | 1 | no | — |
| 536 | C3×C4 | — | 4 | 4 | no | — |
| 537 | C3×C4 | — | 4 | 2 | no | — |
| 538 | C3×C4 | — | 6 | 4 | no | — |
| 539 | C3×C4 | — | 6 | 4 | no | — |
| 540 | C3×C4 | — | 6 | 2 | no | — |
| 541 | Dic3 | — | 2 | 2 | no | — |
| 542 | Dic3 | — | 2 | 4 | no | — |
| 543 | Dic3 | — | 2 | 4 | no | — |
| 544 | Dic3 | — | 6 | 4 | no | — |
| 545 | Dic3 | — | 6 | 4 | no | — |
| 546 | Dic3 | — | 6 | 4 | no | — |
| 547 | Dic3 | — | 6 | 4 | no | — |
| 548 | Dic3 | — | 12 | 4 | no | — |
| 549 | Dic3 | — | 12 | 4 | no | — |
| 550 | Dic3 | #1007 | 1 | 2 | yes | — |
| 551 | C32 | #3531 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 552 | C23 | — | 3 | 1 | no | — |
| 553 | C23 | — | 3 | 4 | no | — |
| 554 | Q8 | — | 12 | 4 | no | — |
| 555 | Q8 | — | 12 | 2 | no | — |
| 556 | Q8 | — | 36 | 4 | no | — |
| 557 | D4 | — | 12 | 4 | no | — |
| 558 | D4 | — | 12 | 2 | no | — |
| 559 | D4 | — | 36 | 4 | no | — |
| 560 | C2×C4 | — | 3 | 1 | no | — |
| 561 | C2×C4 | — | 3 | 2 | no | — |
| 562 | C2×C4 | — | 3 | 4 | no | — |
| 563 | C2×C4 | — | 3 | 4 | no | — |
| 564 | C2×C4 | — | 6 | 2 | no | — |
| 565 | C2×C4 | — | 9 | 4 | no | — |
| 566 | C2×C4 | — | 9 | 4 | no | — |
| 567 | C2×C4 | — | 12 | 2 | no | — |
| 568 | C2×C4 | — | 12 | 4 | no | — |
| 569 | C2×C4 | — | 18 | 8 | no | — |
| 570 | C2×C4 | — | 36 | 4 | no | — |
| 571 | C2×C4 | C22×D32 | 1 | 4 | yes | — |
| 572 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 573 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 574 | C2×C3 | — | 2 | 1 | no | — |
| 575 | C2×C3 | — | 2 | 2 | no | — |
| 576 | C2×C3 | — | 12 | 4 | no | — |
| 577 | C2×C3 | — | 12 | 1 | no | — |
| 578 | C2×C3 | C2×#1007 | 1 | 1 | yes | characteristic |
| 579 | C2×C3 | #5964 | 1 | 2 | yes | — |
| 580 | C2×C3 | #5966 | 1 | 2 | yes | — |
| 581 | C2×C3 | D3×2−1+4 | 1 | 1 | yes | characteristic |
| 582 | D3 | — | 4 | 1 | no | — |
| 583 | D3 | — | 4 | 4 | no | — |
| 584 | C22 | — | 6 | 1 | no | — |
| 585 | C22 | — | 6 | 4 | no | — |
| 586 | C22 | — | 6 | 4 | no | — |
| 587 | C22 | — | 6 | 2 | no | — |
| 588 | C22 | — | 6 | 4 | no | — |
| 589 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 590 | C4 | — | 2 | 1 | no | — |
| 591 | C4 | — | 2 | 4 | no | — |
| 592 | C4 | — | 2 | 2 | no | — |
| 593 | C4 | — | 3 | 2 | no | — |
| 594 | C4 | — | 6 | 2 | no | — |
| 595 | C4 | — | 6 | 4 | no | — |
| 596 | C4 | — | 6 | 4 | no | — |
| 597 | C4 | — | 18 | 4 | no | — |
| 598 | C4 | — | 18 | 4 | no | — |
| 599 | C3 | — | 2 | 1 | no | — |
| 600 | C3 | #86286 | 1 | 1 | yes | characteristic, complemented |
| 601 | C3 | #87094 | 1 | 1 | yes | characteristic, complemented |
| 602 | C2 | — | 12 | 1 | no | — |
| 603 | C2 | — | 12 | 4 | no | — |
| 604 | C2 | D3×#1007 | 1 | 1 | yes | characteristic |
| 605 | C2 | #10596696 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#125 | C22 |
| hypercenter | #125 | D32 |
| hypocenter | C32 | #3531 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596157 | C2 | semidirect |
| 2. C3×#5700 | C2 | semidirect |
| 3. C3×#5688 | C2 | semidirect |
| 4. #10594589 | C2 | semidirect |
| 5. #10594495 | C2 | semidirect |
| 6. #10594492 | C2 | semidirect |
| 7. #10594426 | C2 | semidirect |
| 8. #10594404 | C2 | semidirect |
| 9. #10594386 | C2 | semidirect |
| 10. #10593952 | C2 | semidirect |
| 11. #10593921 | C2 | semidirect |
| 62. #5700 | D3 | semidirect |
| 64. #5688 | D3 | semidirect |
| 551. C32 | #3531 | semidirect |
| 600. C3 | #86286 | semidirect |
| 601. C3 | #87094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596157 | 2 |
| C3×#5700 | 2 |
| C3×#5688 | 2 |
| #10594589 | 2 |
| #10594495 | 2 |
| #10594492 | 2 |
| #10594426 | 2 |
| #10594404 | 2 |
| #10594386 | 2 |
| #10593952 | 2 |
| #10593921 | 2 |
| #87094 | 3 |
| #86286 | 3 |