Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1473 conjugacy classes of subgroups.
The subgroup lattice has 459 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Q8×#126 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #36166 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #33267 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #33083 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33082 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #28016 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #27841 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #27565 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #27551 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #27533 | C2 | 1 | 3 | yes | maximal |
| 11 | #27519 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #22678 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #22444 | C2 | 1 | 3 | yes | maximal |
| 14 | #21666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C42×SD16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×#137 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#440 | C22 | 1 | 3 | yes | — |
| 18 | C2×C4×SD16 | C22 | 1 | 3 | yes | — |
| 19 | #2863 | — | 2 | 1 | no | — |
| 20 | #2863 | C22 | 1 | 1 | yes | characteristic |
| 21 | #2863 | C22 | 1 | 1 | yes | characteristic |
| 22 | #2852 | — | 2 | 1 | no | — |
| 23 | #2514 | C22 | 1 | 3 | yes | — |
| 24 | #2511 | — | 2 | 3 | no | — |
| 25 | #2511 | C22 | 1 | 3 | yes | — |
| 26 | #2510 | — | 2 | 3 | no | — |
| 27 | #2497 | — | 2 | 3 | no | — |
| 28 | #2497 | C22 | 1 | 3 | yes | — |
| 29 | #2495 | C22 | 1 | 3 | yes | — |
| 30 | #2493 | — | 2 | 3 | no | — |
| 31 | Q8×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 32 | #2349 | C22 | 1 | 3 | yes | — |
| 33 | Q8×C22⋊C4 | C22 | 1 | 3 | yes | — |
| 34 | #2339 | C22 | 1 | 3 | yes | — |
| 35 | C4×#126 | — | 2 | 1 | no | — |
| 36 | C4×#126 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#383 | — | 2 | 1 | no | — |
| 38 | C42×Q8 | C22 | 1 | 1 | yes | characteristic |
| 39 | C42×D4 | C22 | 1 | 1 | yes | characteristic |
| 40 | #2101 | C22 | 1 | 3 | yes | — |
| 41 | #2099 | C22 | 1 | 3 | yes | — |
| 42 | #2077 | C22 | 1 | 3 | yes | — |
| 43 | #2075 | C22 | 1 | 3 | yes | — |
| 44 | #2074 | C22 | 1 | 3 | yes | — |
| 45 | #2072 | C22 | 1 | 3 | yes | — |
| 46 | #2068 | C22 | 1 | 3 | yes | — |
| 47 | #2066 | C22 | 1 | 3 | yes | — |
| 48 | #1971 | C22 | 1 | 3 | yes | — |
| 49 | #1969 | C22 | 1 | 3 | yes | — |
| 50 | #1943 | C22 | 1 | 3 | yes | — |
| 51 | #1942 | C22 | 1 | 3 | yes | — |
| 52 | #1933 | C22 | 1 | 3 | yes | — |
| 53 | #1933 | C22 | 1 | 3 | yes | — |
| 54 | #1928 | C22 | 1 | 3 | yes | — |
| 55 | #1927 | C22 | 1 | 3 | yes | — |
| 56 | #1923 | C22 | 1 | 3 | yes | — |
| 57 | #1921 | C22 | 1 | 3 | yes | — |
| 58 | #1920 | C22 | 1 | 3 | yes | — |
| 59 | #1916 | C22 | 1 | 3 | yes | — |
| 60 | #1878 | C22 | 1 | 3 | yes | — |
| 61 | #1878 | C22 | 1 | 3 | yes | — |
| 62 | #1877 | C22 | 1 | 3 | yes | — |
| 63 | #1877 | C22 | 1 | 3 | yes | — |
| 64 | #1865 | C22 | 1 | 3 | yes | — |
| 65 | #1864 | C22 | 1 | 3 | yes | — |
| 66 | #1863 | C22 | 1 | 3 | yes | — |
| 67 | #1862 | C22 | 1 | 3 | yes | — |
| 68 | #1847 | C22 | 1 | 3 | yes | — |
| 69 | #1839 | C22 | 1 | 1 | yes | characteristic |
| 70 | #1809 | C22 | 1 | 3 | yes | — |
| 71 | #1805 | C22 | 1 | 3 | yes | — |
| 72 | #1802 | C22 | 1 | 3 | yes | — |
| 73 | #1788 | C22 | 1 | 3 | yes | — |
| 74 | #1787 | C22 | 1 | 3 | yes | — |
| 75 | C4×#106 | C22 | 1 | 3 | yes | — |
| 76 | #1771 | C22 | 1 | 3 | yes | — |
| 77 | C4×#103 | C22 | 1 | 3 | yes | — |
| 78 | C4×#102 | C22 | 1 | 3 | yes | — |
| 79 | #1753 | C22 | 1 | 3 | yes | — |
| 80 | C42×C8 | C22 | 1 | 1 | yes | characteristic |
| 81 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 82 | C23×Q8 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×#137 | — | 2 | 12 | no | — |
| 84 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 86 | C22×SD16 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×SD16 | C23 | 1 | 1 | yes | characteristic |
| 88 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×#126 | D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 91 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 92 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 93 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 94 | C22×C42 | — | 2 | 1 | no | — |
| 95 | #440 | — | 2 | 12 | no | — |
| 96 | C4×SD16 | — | 2 | 12 | no | — |
| 97 | C2×#107 | C23 | 1 | 3 | yes | — |
| 98 | C2×#107 | C23 | 1 | 3 | yes | — |
| 99 | C2×#106 | C23 | 1 | 3 | yes | — |
| 100 | C2×#106 | C23 | 1 | 3 | yes | — |
| 101 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 102 | C2×#103 | C23 | 1 | 3 | yes | — |
| 103 | C2×#103 | C23 | 1 | 3 | yes | — |
| 104 | C2×#103 | C23 | 1 | 3 | yes | — |
| 105 | C2×#103 | C23 | 1 | 3 | yes | — |
| 106 | C2×#103 | C23 | 1 | 3 | yes | — |
| 107 | C2×#103 | C23 | 1 | 3 | yes | — |
| 108 | C2×#102 | C23 | 1 | 3 | yes | — |
| 109 | C2×#102 | C23 | 1 | 3 | yes | — |
| 110 | C2×C22⋊C8 | C23 | 1 | 3 | yes | — |
| 111 | C2×#97 | C23 | 1 | 3 | yes | — |
| 112 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 113 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 114 | #401 | — | 2 | 3 | no | — |
| 115 | #400 | — | 2 | 3 | no | — |
| 116 | #400 | — | 2 | 3 | no | — |
| 117 | #400 | — | 2 | 3 | no | — |
| 118 | #400 | — | 2 | 3 | no | — |
| 119 | #400 | — | 2 | 3 | no | — |
| 120 | #397 | — | 2 | 3 | no | — |
| 121 | #396 | — | 2 | 3 | no | — |
| 122 | #391 | — | 2 | 3 | no | — |
| 123 | #391 | — | 2 | 3 | no | — |
| 124 | #391 | C23 | 1 | 3 | yes | — |
| 125 | #391 | C23 | 1 | 3 | yes | — |
| 126 | #391 | C23 | 1 | 3 | yes | — |
| 127 | #391 | C23 | 1 | 3 | yes | — |
| 128 | #389 | — | 2 | 3 | no | — |
| 129 | #389 | — | 2 | 3 | no | — |
| 130 | #389 | C23 | 1 | 3 | yes | — |
| 131 | #389 | C23 | 1 | 3 | yes | — |
| 132 | #389 | C23 | 1 | 3 | yes | — |
| 133 | #389 | C23 | 1 | 3 | yes | — |
| 134 | #388 | — | 2 | 3 | no | — |
| 135 | #388 | — | 2 | 3 | no | — |
| 136 | #388 | D4 | 1 | 3 | yes | — |
| 137 | #387 | — | 2 | 3 | no | — |
| 138 | #387 | — | 2 | 3 | no | — |
| 139 | #387 | — | 2 | 3 | no | — |
| 140 | #387 | — | 2 | 3 | no | — |
| 141 | #387 | — | 2 | 3 | no | — |
| 142 | #387 | — | 2 | 3 | no | — |
| 143 | #387 | D4 | 1 | 3 | yes | — |
| 144 | #386 | — | 2 | 3 | no | — |
| 145 | #386 | — | 2 | 3 | no | — |
| 146 | #385 | — | 2 | 3 | no | — |
| 147 | #385 | — | 2 | 3 | no | — |
| 148 | #384 | — | 2 | 3 | no | — |
| 149 | #384 | C23 | 1 | 3 | yes | — |
| 150 | #383 | — | 2 | 1 | no | — |
| 151 | #383 | — | 2 | 1 | no | — |
| 152 | #383 | — | 2 | 3 | no | — |
| 153 | #383 | — | 2 | 3 | no | — |
| 154 | #383 | D4 | 1 | 1 | yes | characteristic |
| 155 | #382 | C23 | 1 | 3 | yes | — |
| 156 | #381 | — | 2 | 3 | no | — |
| 157 | #380 | — | 2 | 3 | no | — |
| 158 | #380 | — | 2 | 3 | no | — |
| 159 | #380 | C23 | 1 | 3 | yes | — |
| 160 | #380 | C23 | 1 | 3 | yes | — |
| 161 | C4×C4⋊C4 | — | 2 | 3 | no | — |
| 162 | C4×C4⋊C4 | — | 2 | 3 | no | — |
| 163 | C4×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 164 | C4×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 165 | C4×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 166 | C4×C22⋊C4 | — | 2 | 3 | no | — |
| 167 | C4×C22⋊C4 | — | 2 | 3 | no | — |
| 168 | C4×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 169 | C2×#95 | — | 2 | 3 | no | — |
| 170 | C2×#95 | — | 2 | 3 | no | — |
| 171 | C43 | — | 2 | 1 | no | — |
| 172 | C43 | C23 | 1 | 1 | yes | characteristic |
| 173 | #340 | C23 | 1 | 3 | yes | — |
| 174 | #340 | C23 | 1 | 3 | yes | — |
| 175 | #340 | C23 | 1 | 3 | yes | — |
| 176 | #340 | C23 | 1 | 3 | yes | — |
| 177 | #340 | C23 | 1 | 3 | yes | — |
| 178 | #340 | C23 | 1 | 3 | yes | — |
| 179 | #340 | C23 | 1 | 3 | yes | — |
| 180 | #340 | C23 | 1 | 3 | yes | — |
| 181 | #336 | C23 | 1 | 3 | yes | — |
| 182 | #336 | C23 | 1 | 3 | yes | — |
| 183 | #336 | C23 | 1 | 3 | yes | — |
| 184 | #336 | C23 | 1 | 3 | yes | — |
| 185 | C2×#41 | — | 2 | 6 | no | — |
| 186 | C2×#41 | — | 4 | 3 | no | — |
| 187 | C22×Q8 | — | 2 | 1 | no | — |
| 188 | C22×Q8 | — | 2 | 6 | no | — |
| 189 | C22×Q8 | — | 4 | 3 | no | — |
| 190 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 191 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 192 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 193 | C22×D4 | — | 2 | 1 | no | — |
| 194 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 195 | C23×C4 | — | 2 | 1 | no | — |
| 196 | C23×C4 | — | 2 | 1 | no | — |
| 197 | C23×C4 | — | 2 | 3 | no | — |
| 198 | C23×C4 | — | 2 | 3 | no | — |
| 199 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 200 | #137 | — | 4 | 16 | no | — |
| 201 | C2×Q16 | — | 2 | 6 | no | — |
| 202 | C2×Q16 | — | 2 | 6 | no | — |
| 203 | C2×SD16 | — | 2 | 6 | no | — |
| 204 | C2×SD16 | #41 | 1 | 12 | yes | — |
| 205 | C2×M16 | — | 2 | 6 | no | — |
| 206 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 207 | C22×C8 | C24 | 1 | 3 | yes | — |
| 208 | C22×C8 | C24 | 1 | 3 | yes | — |
| 209 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 210 | #126 | — | 2 | 4 | no | — |
| 211 | C4×Q8 | — | 2 | 6 | no | — |
| 212 | C4×Q8 | — | 2 | 6 | no | — |
| 213 | C4×Q8 | — | 4 | 3 | no | — |
| 214 | C4×Q8 | — | 4 | 3 | no | — |
| 215 | C4×D4 | — | 2 | 6 | no | — |
| 216 | C4×D4 | — | 2 | 6 | no | — |
| 217 | C4×D4 | — | 4 | 3 | no | — |
| 218 | C4×D4 | — | 4 | 3 | no | — |
| 219 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 220 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 221 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 222 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 223 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 224 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 225 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 226 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 227 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 228 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 229 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 230 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 231 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 232 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 233 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 234 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 235 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 236 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 237 | C2×C22⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 238 | C2×C22⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 239 | C2×C42 | — | 2 | 3 | no | — |
| 240 | C2×C42 | — | 2 | 3 | no | — |
| 241 | C2×C42 | — | 2 | 3 | no | — |
| 242 | C2×C42 | — | 2 | 3 | no | — |
| 243 | C2×C42 | — | 4 | 4 | no | — |
| 244 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 245 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C42 | C24 | 1 | 3 | yes | — |
| 247 | C2×C42 | C24 | 1 | 3 | yes | — |
| 248 | #107 | — | 2 | 6 | no | — |
| 249 | #107 | — | 4 | 3 | no | — |
| 250 | #106 | — | 2 | 6 | no | — |
| 251 | #106 | — | 4 | 3 | no | — |
| 252 | C4⋊C8 | — | 4 | 3 | no | — |
| 253 | #103 | — | 2 | 6 | no | — |
| 254 | #103 | — | 2 | 6 | no | — |
| 255 | #103 | — | 4 | 3 | no | — |
| 256 | #103 | — | 4 | 3 | no | — |
| 257 | #103 | — | 4 | 3 | no | — |
| 258 | #103 | — | 4 | 3 | no | — |
| 259 | #102 | — | 2 | 6 | no | — |
| 260 | #102 | — | 2 | 6 | no | — |
| 261 | C22⋊C8 | — | 4 | 3 | no | — |
| 262 | #97 | — | 2 | 6 | no | — |
| 263 | C4×C8 | — | 2 | 6 | no | — |
| 264 | C4×C8 | — | 4 | 3 | no | — |
| 265 | #95 | — | 2 | 3 | no | — |
| 266 | #95 | — | 2 | 3 | no | — |
| 267 | #95 | — | 2 | 3 | no | — |
| 268 | #95 | — | 2 | 3 | no | — |
| 269 | #95 | — | 2 | 3 | no | — |
| 270 | #95 | — | 2 | 3 | no | — |
| 271 | #95 | — | 2 | 3 | no | — |
| 272 | #95 | — | 2 | 3 | no | — |
| 273 | #95 | — | 2 | 3 | no | — |
| 274 | #95 | — | 2 | 3 | no | — |
| 275 | #95 | — | 2 | 3 | no | — |
| 276 | #95 | — | 2 | 3 | no | — |
| 277 | #95 | — | 2 | 3 | no | — |
| 278 | #95 | — | 2 | 3 | no | — |
| 279 | #95 | — | 2 | 3 | no | — |
| 280 | #95 | — | 2 | 3 | no | — |
| 281 | #95 | — | 2 | 3 | no | — |
| 282 | #95 | — | 2 | 3 | no | — |
| 283 | #95 | C2×D4 | 1 | 3 | yes | — |
| 284 | #95 | C2×D4 | 1 | 3 | yes | — |
| 285 | #95 | C2×D4 | 1 | 3 | yes | — |
| 286 | #95 | C2×D4 | 1 | 3 | yes | — |
| 287 | C24 | — | 2 | 1 | no | — |
| 288 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 289 | #41 | — | 4 | 4 | no | — |
| 290 | #41 | — | 8 | 6 | no | — |
| 291 | C2×Q8 | — | 2 | 3 | no | — |
| 292 | C2×Q8 | — | 2 | 3 | no | — |
| 293 | C2×Q8 | — | 2 | 3 | no | — |
| 294 | C2×Q8 | — | 2 | 3 | no | — |
| 295 | C2×Q8 | — | 2 | 3 | no | — |
| 296 | C2×Q8 | — | 4 | 6 | no | — |
| 297 | C2×Q8 | — | 4 | 4 | no | — |
| 298 | C2×Q8 | — | 8 | 6 | no | — |
| 299 | C2×Q8 | C2×#41 | 1 | 6 | yes | — |
| 300 | C2×D4 | — | 2 | 3 | no | — |
| 301 | C2×D4 | — | 4 | 6 | no | — |
| 302 | C2×D4 | C2×#41 | 1 | 6 | yes | — |
| 303 | C22×C4 | — | 2 | 1 | no | — |
| 304 | C22×C4 | — | 2 | 3 | no | — |
| 305 | C22×C4 | — | 2 | 3 | no | — |
| 306 | C22×C4 | — | 2 | 1 | no | — |
| 307 | C22×C4 | — | 2 | 1 | no | — |
| 308 | C22×C4 | — | 2 | 3 | no | — |
| 309 | C22×C4 | — | 2 | 3 | no | — |
| 310 | C22×C4 | — | 2 | 3 | no | — |
| 311 | C22×C4 | — | 2 | 3 | no | — |
| 312 | C22×C4 | — | 4 | 6 | no | — |
| 313 | C22×C4 | — | 4 | 6 | no | — |
| 314 | C22×C4 | — | 4 | 6 | no | — |
| 315 | C22×C4 | — | 4 | 6 | no | — |
| 316 | C22×C4 | — | 4 | 6 | no | — |
| 317 | C22×C4 | — | 8 | 3 | no | — |
| 318 | C22×C4 | — | 8 | 3 | no | — |
| 319 | C22×C4 | — | 8 | 3 | no | — |
| 320 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 321 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 322 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 323 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 324 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 325 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 326 | Q16 | — | 4 | 4 | no | — |
| 327 | Q16 | — | 4 | 4 | no | — |
| 328 | SD16 | — | 4 | 4 | no | — |
| 329 | SD16 | #126 | 1 | 16 | yes | complemented |
| 330 | M16 | — | 4 | 4 | no | — |
| 331 | C2×C8 | — | 2 | 3 | no | — |
| 332 | C2×C8 | — | 2 | 3 | no | — |
| 333 | C2×C8 | — | 2 | 3 | no | — |
| 334 | C2×C8 | — | 2 | 3 | no | — |
| 335 | C2×C8 | — | 2 | 3 | no | — |
| 336 | C2×C8 | — | 2 | 3 | no | — |
| 337 | C2×C8 | — | 2 | 3 | no | — |
| 338 | C2×C8 | C2×#41 | 1 | 6 | yes | — |
| 339 | C4⋊C4 | — | 2 | 6 | no | — |
| 340 | C4⋊C4 | — | 2 | 3 | no | — |
| 341 | C4⋊C4 | — | 2 | 3 | no | — |
| 342 | C4⋊C4 | — | 2 | 3 | no | — |
| 343 | C4⋊C4 | — | 2 | 3 | no | — |
| 344 | C4⋊C4 | — | 2 | 3 | no | — |
| 345 | C4⋊C4 | — | 2 | 3 | no | — |
| 346 | C4⋊C4 | — | 2 | 3 | no | — |
| 347 | C4⋊C4 | — | 2 | 3 | no | — |
| 348 | C4⋊C4 | — | 4 | 3 | no | — |
| 349 | C4⋊C4 | — | 4 | 6 | no | — |
| 350 | C4⋊C4 | — | 4 | 6 | no | — |
| 351 | C4⋊C4 | — | 8 | 3 | no | — |
| 352 | C4⋊C4 | — | 8 | 3 | no | — |
| 353 | C4⋊C4 | — | 8 | 3 | no | — |
| 354 | C4⋊C4 | — | 8 | 3 | no | — |
| 355 | C4⋊C4 | — | 8 | 3 | no | — |
| 356 | C4⋊C4 | — | 8 | 3 | no | — |
| 357 | C22⋊C4 | — | 2 | 6 | no | — |
| 358 | C22⋊C4 | — | 4 | 3 | no | — |
| 359 | C22⋊C4 | — | 4 | 6 | no | — |
| 360 | C22⋊C4 | — | 4 | 6 | no | — |
| 361 | C22⋊C4 | — | 8 | 3 | no | — |
| 362 | C22⋊C4 | — | 8 | 3 | no | — |
| 363 | C42 | — | 2 | 3 | no | — |
| 364 | C42 | — | 2 | 3 | no | — |
| 365 | C42 | — | 2 | 3 | no | — |
| 366 | C42 | — | 2 | 3 | no | — |
| 367 | C42 | — | 4 | 3 | no | — |
| 368 | C42 | — | 4 | 6 | no | — |
| 369 | C42 | — | 4 | 6 | no | — |
| 370 | C42 | — | 4 | 6 | no | — |
| 371 | C42 | — | 8 | 3 | no | — |
| 372 | C42 | #137 | 1 | 4 | yes | complemented |
| 373 | C23 | — | 2 | 6 | no | — |
| 374 | C23 | — | 2 | 3 | no | — |
| 375 | C23 | — | 2 | 3 | no | — |
| 376 | C23 | — | 2 | 1 | no | — |
| 377 | C23 | — | 4 | 3 | no | — |
| 378 | C23 | — | 4 | 1 | no | — |
| 379 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 380 | Q8 | — | 2 | 6 | no | — |
| 381 | Q8 | — | 4 | 1 | no | — |
| 382 | Q8 | — | 4 | 1 | no | — |
| 383 | Q8 | — | 4 | 3 | no | — |
| 384 | Q8 | — | 4 | 3 | no | — |
| 385 | Q8 | — | 8 | 4 | no | — |
| 386 | Q8 | C2×#126 | 1 | 4 | yes | — |
| 387 | D4 | — | 2 | 6 | no | — |
| 388 | D4 | — | 8 | 4 | no | — |
| 389 | D4 | C2×#126 | 1 | 4 | yes | — |
| 390 | C2×C4 | — | 2 | 3 | no | — |
| 391 | C2×C4 | — | 2 | 3 | no | — |
| 392 | C2×C4 | — | 2 | 6 | no | — |
| 393 | C2×C4 | — | 2 | 3 | no | — |
| 394 | C2×C4 | — | 2 | 3 | no | — |
| 395 | C2×C4 | — | 2 | 3 | no | — |
| 396 | C2×C4 | — | 2 | 3 | no | — |
| 397 | C2×C4 | — | 2 | 3 | no | — |
| 398 | C2×C4 | — | 2 | 3 | no | — |
| 399 | C2×C4 | — | 2 | 3 | no | — |
| 400 | C2×C4 | — | 2 | 3 | no | — |
| 401 | C2×C4 | — | 2 | 3 | no | — |
| 402 | C2×C4 | — | 2 | 3 | no | — |
| 403 | C2×C4 | — | 4 | 1 | no | — |
| 404 | C2×C4 | — | 4 | 3 | no | — |
| 405 | C2×C4 | — | 4 | 3 | no | — |
| 406 | C2×C4 | — | 4 | 3 | no | — |
| 407 | C2×C4 | — | 4 | 3 | no | — |
| 408 | C2×C4 | — | 4 | 3 | no | — |
| 409 | C2×C4 | — | 4 | 3 | no | — |
| 410 | C2×C4 | — | 4 | 3 | no | — |
| 411 | C2×C4 | — | 4 | 3 | no | — |
| 412 | C2×C4 | — | 4 | 3 | no | — |
| 413 | C2×C4 | — | 4 | 3 | no | — |
| 414 | C2×C4 | — | 4 | 3 | no | — |
| 415 | C2×C4 | — | 4 | 3 | no | — |
| 416 | C2×C4 | — | 4 | 3 | no | — |
| 417 | C2×C4 | — | 4 | 3 | no | — |
| 418 | C2×C4 | — | 4 | 3 | no | — |
| 419 | C2×C4 | — | 8 | 4 | no | — |
| 420 | C2×C4 | — | 8 | 12 | no | — |
| 421 | C2×C4 | — | 8 | 4 | no | — |
| 422 | C2×C4 | — | 16 | 6 | no | — |
| 423 | C2×C4 | C2×#137 | 1 | 6 | yes | — |
| 424 | C2×C4 | C22×#41 | 1 | 3 | yes | — |
| 425 | C2×C4 | #585 | 1 | 3 | yes | — |
| 426 | C8 | — | 4 | 1 | no | — |
| 427 | C8 | — | 4 | 3 | no | — |
| 428 | C8 | — | 4 | 3 | no | — |
| 429 | C8 | C2×#126 | 1 | 4 | yes | — |
| 430 | C22 | — | 2 | 4 | no | — |
| 431 | C22 | — | 4 | 6 | no | — |
| 432 | C22 | — | 4 | 6 | no | — |
| 433 | C22 | — | 4 | 1 | no | — |
| 434 | C22 | — | 4 | 3 | no | — |
| 435 | C22 | — | 4 | 3 | no | — |
| 436 | C22 | D4×#41 | 1 | 3 | yes | — |
| 437 | C22 | C22×#137 | 1 | 1 | yes | characteristic |
| 438 | C22 | #3584 | 1 | 3 | yes | — |
| 439 | C4 | — | 2 | 4 | no | — |
| 440 | C4 | — | 2 | 6 | no | — |
| 441 | C4 | — | 4 | 1 | no | — |
| 442 | C4 | — | 4 | 3 | no | — |
| 443 | C4 | — | 4 | 3 | no | — |
| 444 | C4 | — | 4 | 3 | no | — |
| 445 | C4 | — | 8 | 1 | no | — |
| 446 | C4 | — | 8 | 1 | no | — |
| 447 | C4 | — | 8 | 3 | no | — |
| 448 | C4 | — | 8 | 3 | no | — |
| 449 | C4 | — | 8 | 3 | no | — |
| 450 | C4 | — | 8 | 3 | no | — |
| 451 | C4 | C22×#126 | 1 | 1 | yes | characteristic |
| 452 | C4 | #3521 | 1 | 3 | yes | — |
| 453 | C2 | — | 4 | 4 | no | — |
| 454 | C2 | — | 8 | 1 | no | — |
| 455 | C2 | D4×#126 | 1 | 1 | yes | characteristic |
| 456 | C2 | #61438 | 1 | 3 | yes | — |
| 457 | C2 | #61500 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C23×D4 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | C22×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×#126 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#126 | C2 | semidirect |
| 3. #33267 | C2 | semidirect |
| 4. #33083 | C2 | semidirect |
| 5. #33082 | C2 | semidirect |
| 6. #28016 | C2 | semidirect |
| 7. #27841 | C2 | semidirect |
| 8. #27565 | C2 | semidirect |
| 9. #27551 | C2 | semidirect |
| 11. #27519 | C2 | semidirect |
| 12. #22678 | C2 | semidirect |
| 14. #21666 | C2 | semidirect |
| 15. C42×SD16 | C2 | semidirect |
| 329. SD16 | #126 | semidirect |
| 372. C42 | #137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#126 | 2 |
| #36166 | 2 |
| #33267 | 2 |
| #33083 | 2 |
| #33082 | 2 |
| #28016 | 2 |
| #27841 | 2 |
| #27565 | 2 |
| #27551 | 2 |
| #27533 | 2 |
| #27519 | 2 |
| #22678 | 2 |
| #22444 | 2 |
| #21666 | 2 |
| C42×SD16 | 2 |