Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1710 conjugacy classes of subgroups.
The subgroup lattice has 375 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61414 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #61284 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #30765 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #28220 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #28174 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26195 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #24180 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #23810 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22281 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22258 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #3506 | C22 | 1 | 4 | yes | — |
| 12 | #3401 | — | 2 | 8 | no | — |
| 13 | #3399 | — | 2 | 8 | no | — |
| 14 | #3355 | — | 2 | 4 | no | — |
| 15 | #3354 | — | 2 | 4 | no | — |
| 16 | #3341 | — | 2 | 2 | no | — |
| 17 | #3339 | — | 2 | 4 | no | — |
| 18 | #3334 | — | 2 | 2 | no | — |
| 19 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 20 | #3155 | C22 | 1 | 4 | yes | — |
| 21 | #3150 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3096 | C22 | 1 | 8 | yes | — |
| 23 | #3077 | C22 | 1 | 4 | yes | — |
| 24 | #3058 | C22 | 1 | 4 | yes | — |
| 25 | #3045 | C22 | 1 | 8 | yes | — |
| 26 | #3036 | C22 | 1 | 4 | yes | — |
| 27 | #2961 | C22 | 1 | 2 | yes | — |
| 28 | #2952 | C22 | 1 | 4 | yes | — |
| 29 | C2×#442 | C22 | 1 | 2 | yes | — |
| 30 | C2×C4×D8 | C22 | 1 | 2 | yes | — |
| 31 | #2931 | C22 | 1 | 2 | yes | — |
| 32 | #2913 | C22 | 1 | 4 | yes | — |
| 33 | #2328 | C22 | 1 | 2 | yes | — |
| 34 | #2092 | C22 | 1 | 4 | yes | — |
| 35 | #2090 | C22 | 1 | 4 | yes | — |
| 36 | #2078 | C22 | 1 | 4 | yes | — |
| 37 | #2045 | C22 | 1 | 4 | yes | — |
| 38 | #2037 | C22 | 1 | 8 | yes | — |
| 39 | #2018 | C22 | 1 | 4 | yes | — |
| 40 | #2011 | C22 | 1 | 4 | yes | — |
| 41 | #2002 | C22 | 1 | 8 | yes | — |
| 42 | #1995 | C22 | 1 | 2 | yes | — |
| 43 | #1963 | C22 | 1 | 2 | yes | — |
| 44 | #1931 | C22 | 1 | 8 | yes | — |
| 45 | #1922 | C22 | 1 | 8 | yes | — |
| 46 | #1907 | C22 | 1 | 8 | yes | — |
| 47 | #1883 | C22 | 1 | 8 | yes | — |
| 48 | #1876 | C22 | 1 | 8 | yes | — |
| 49 | #1860 | C22 | 1 | 8 | yes | — |
| 50 | #1838 | C22 | 1 | 1 | yes | characteristic |
| 51 | #1837 | C22 | 1 | 1 | yes | characteristic |
| 52 | #1800 | C22 | 1 | 4 | yes | — |
| 53 | #1746 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×AGL(1,ℤ/8) | C23 | 1 | 8 | yes | — |
| 55 | C2×#135 | C23 | 1 | 4 | yes | — |
| 56 | C22×D8 | C23 | 1 | 2 | yes | — |
| 57 | C22×D8 | C23 | 1 | 2 | yes | — |
| 58 | C2×#131 | C23 | 1 | 4 | yes | — |
| 59 | #559 | — | 2 | 8 | no | — |
| 60 | #556 | — | 2 | 4 | no | — |
| 61 | #555 | — | 2 | 4 | no | — |
| 62 | #553 | — | 2 | 8 | no | — |
| 63 | #550 | — | 2 | 4 | no | — |
| 64 | #547 | — | 2 | 4 | no | — |
| 65 | #538 | — | 4 | 4 | no | — |
| 66 | #535 | C23 | 1 | 8 | yes | — |
| 67 | #533 | C23 | 1 | 2 | yes | — |
| 68 | #532 | C23 | 1 | 2 | yes | — |
| 69 | C2×#127 | C23 | 1 | 2 | yes | — |
| 70 | #525 | — | 4 | 4 | no | — |
| 71 | #520 | C23 | 1 | 8 | yes | — |
| 72 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 73 | #500 | D4 | 1 | 2 | yes | complemented |
| 74 | #499 | D4 | 1 | 4 | yes | complemented |
| 75 | #498 | D4 | 1 | 2 | yes | complemented |
| 76 | #497 | D4 | 1 | 4 | yes | complemented |
| 77 | #496 | — | 2 | 8 | no | — |
| 78 | #496 | D4 | 1 | 4 | yes | complemented |
| 79 | #495 | — | 2 | 4 | no | — |
| 80 | #493 | — | 2 | 4 | no | — |
| 81 | #482 | — | 2 | 8 | no | — |
| 82 | #482 | — | 2 | 8 | no | — |
| 83 | #481 | — | 2 | 8 | no | — |
| 84 | #480 | — | 2 | 8 | no | — |
| 85 | #478 | — | 2 | 8 | no | — |
| 86 | #476 | — | 2 | 4 | no | — |
| 87 | #474 | — | 2 | 4 | no | — |
| 88 | #469 | — | 2 | 8 | no | — |
| 89 | #466 | — | 2 | 4 | no | — |
| 90 | #466 | — | 2 | 4 | no | — |
| 91 | #464 | — | 2 | 8 | no | — |
| 92 | #463 | — | 2 | 8 | no | — |
| 93 | #463 | — | 2 | 8 | no | — |
| 94 | #461 | — | 2 | 4 | no | — |
| 95 | #460 | — | 2 | 8 | no | — |
| 96 | #459 | — | 2 | 8 | no | — |
| 97 | #459 | — | 2 | 4 | no | — |
| 98 | #446 | — | 2 | 8 | no | — |
| 99 | #442 | — | 2 | 4 | no | — |
| 100 | #442 | — | 2 | 8 | no | — |
| 101 | #441 | — | 2 | 4 | no | — |
| 102 | C4×SD16 | — | 2 | 8 | no | — |
| 103 | C4×D8 | — | 2 | 2 | no | — |
| 104 | C4×D8 | — | 2 | 2 | no | — |
| 105 | C4×D8 | — | 2 | 2 | no | — |
| 106 | C4×D8 | — | 2 | 2 | no | — |
| 107 | #436 | — | 2 | 2 | no | — |
| 108 | #436 | — | 2 | 2 | no | — |
| 109 | C8×D4 | — | 2 | 2 | no | — |
| 110 | C8×D4 | — | 2 | 2 | no | — |
| 111 | #428 | — | 2 | 8 | no | — |
| 112 | #428 | C23 | 1 | 8 | yes | — |
| 113 | #427 | — | 2 | 4 | no | — |
| 114 | #427 | C23 | 1 | 4 | yes | — |
| 115 | C2×#107 | — | 2 | 4 | no | — |
| 116 | C2×#107 | C23 | 1 | 2 | yes | — |
| 117 | C2×#106 | C23 | 1 | 2 | yes | — |
| 118 | #424 | C23 | 1 | 4 | yes | — |
| 119 | #423 | C23 | 1 | 2 | yes | — |
| 120 | #423 | C23 | 1 | 2 | yes | — |
| 121 | C2×#104 | C23 | 1 | 8 | yes | — |
| 122 | #418 | C23 | 1 | 8 | yes | — |
| 123 | #417 | C23 | 1 | 8 | yes | — |
| 124 | C2×#102 | C23 | 1 | 4 | yes | — |
| 125 | C2×#102 | C23 | 1 | 4 | yes | — |
| 126 | C2×#100 | C23 | 1 | 8 | yes | — |
| 127 | #408 | C23 | 1 | 4 | yes | — |
| 128 | #405 | C23 | 1 | 4 | yes | — |
| 129 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 130 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 131 | #390 | C23 | 1 | 4 | yes | — |
| 132 | #386 | — | 4 | 4 | no | — |
| 133 | #382 | C23 | 1 | 2 | yes | — |
| 134 | #376 | C23 | 1 | 1 | yes | characteristic |
| 135 | #343 | C23 | 1 | 8 | yes | — |
| 136 | #341 | C23 | 1 | 4 | yes | — |
| 137 | #341 | C23 | 1 | 4 | yes | — |
| 138 | #339 | C23 | 1 | 8 | yes | — |
| 139 | #336 | C23 | 1 | 4 | yes | — |
| 140 | C2×#41 | — | 4 | 4 | no | — |
| 141 | C2×#41 | C24 | 1 | 4 | yes | — |
| 142 | C22×D4 | — | 4 | 2 | no | — |
| 143 | C22×D4 | C24 | 1 | 4 | yes | — |
| 144 | C23×C4 | — | 2 | 4 | no | — |
| 145 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 146 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 147 | #135 | — | 4 | 8 | no | — |
| 148 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 149 | C2×SD16 | — | 2 | 8 | no | — |
| 150 | C2×SD16 | C2×D4 | 1 | 8 | yes | — |
| 151 | C2×D8 | — | 2 | 8 | no | — |
| 152 | C2×D8 | — | 2 | 2 | no | — |
| 153 | C2×D8 | — | 2 | 2 | no | — |
| 154 | C2×D8 | — | 2 | 4 | no | — |
| 155 | C2×D8 | — | 4 | 4 | no | — |
| 156 | C2×D8 | — | 4 | 4 | no | — |
| 157 | C2×D8 | C2×D4 | 1 | 4 | yes | — |
| 158 | #131 | — | 4 | 8 | no | — |
| 159 | C2×M16 | — | 2 | 4 | no | — |
| 160 | C2×M16 | C24 | 1 | 4 | yes | — |
| 161 | C2×M16 | C24 | 1 | 4 | yes | — |
| 162 | C22×C8 | — | 2 | 4 | no | — |
| 163 | C22×C8 | C24 | 1 | 2 | yes | — |
| 164 | C22×C8 | C24 | 1 | 2 | yes | — |
| 165 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 166 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 167 | #127 | — | 2 | 8 | no | — |
| 168 | #127 | — | 4 | 4 | no | — |
| 169 | #127 | C2×D4 | 1 | 2 | yes | — |
| 170 | #126 | — | 4 | 8 | no | — |
| 171 | #125 | C2×D4 | 1 | 4 | yes | — |
| 172 | #124 | — | 2 | 8 | no | — |
| 173 | #124 | — | 4 | 8 | no | — |
| 174 | #124 | C2×D4 | 1 | 4 | yes | — |
| 175 | #123 | — | 4 | 8 | no | — |
| 176 | #123 | — | 4 | 8 | no | — |
| 177 | C22⋊Q8 | — | 2 | 4 | no | — |
| 178 | C22⋊Q8 | — | 4 | 4 | no | — |
| 179 | #121 | — | 2 | 2 | no | — |
| 180 | #121 | — | 2 | 2 | no | — |
| 181 | #121 | — | 2 | 8 | no | — |
| 182 | #121 | — | 2 | 8 | no | — |
| 183 | #121 | — | 4 | 4 | no | — |
| 184 | #121 | — | 4 | 8 | no | — |
| 185 | #120 | — | 4 | 8 | no | — |
| 186 | C4×Q8 | — | 2 | 4 | no | — |
| 187 | C4×Q8 | — | 2 | 8 | no | — |
| 188 | C4×D4 | — | 2 | 8 | no | — |
| 189 | C4×D4 | — | 2 | 2 | no | — |
| 190 | C4×D4 | — | 2 | 2 | no | — |
| 191 | C4×D4 | — | 2 | 4 | no | — |
| 192 | C4×D4 | — | 2 | 4 | no | — |
| 193 | C4×D4 | — | 2 | 4 | no | — |
| 194 | C4×D4 | — | 2 | 4 | no | — |
| 195 | C4×D4 | — | 4 | 8 | no | — |
| 196 | C4×D4 | — | 4 | 8 | no | — |
| 197 | #117 | — | 2 | 8 | no | — |
| 198 | #117 | — | 4 | 4 | no | — |
| 199 | #117 | C24 | 1 | 4 | yes | — |
| 200 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 201 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 202 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 203 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 204 | C2×C42 | C24 | 1 | 2 | yes | — |
| 205 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 206 | #107 | — | 2 | 2 | no | — |
| 207 | #107 | — | 2 | 2 | no | — |
| 208 | #107 | — | 2 | 8 | no | — |
| 209 | #107 | C2×D4 | 1 | 4 | yes | — |
| 210 | #107 | C2×D4 | 1 | 4 | yes | — |
| 211 | #106 | — | 2 | 4 | no | — |
| 212 | #106 | — | 2 | 8 | no | — |
| 213 | #106 | C2×D4 | 1 | 8 | yes | — |
| 214 | C4⋊C8 | — | 2 | 8 | no | — |
| 215 | C4⋊C8 | — | 2 | 2 | no | — |
| 216 | C4⋊C8 | — | 2 | 2 | no | — |
| 217 | C4⋊C8 | — | 2 | 4 | no | — |
| 218 | #104 | — | 4 | 8 | no | — |
| 219 | #103 | — | 2 | 8 | no | — |
| 220 | #102 | — | 2 | 8 | no | — |
| 221 | #102 | — | 2 | 4 | no | — |
| 222 | #102 | — | 2 | 4 | no | — |
| 223 | #102 | — | 2 | 8 | no | — |
| 224 | #102 | — | 2 | 8 | no | — |
| 225 | #102 | — | 2 | 8 | no | — |
| 226 | #100 | — | 4 | 8 | no | — |
| 227 | C22⋊C8 | — | 2 | 4 | no | — |
| 228 | C22⋊C8 | — | 2 | 4 | no | — |
| 229 | #97 | — | 2 | 4 | no | — |
| 230 | #97 | C2×D4 | 1 | 4 | yes | — |
| 231 | C4×C8 | — | 2 | 4 | no | — |
| 232 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 233 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 234 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | #95 | — | 2 | 2 | no | — |
| 236 | #95 | — | 4 | 2 | no | — |
| 237 | C24 | — | 2 | 4 | no | — |
| 238 | #41 | — | 2 | 8 | no | — |
| 239 | #41 | — | 2 | 8 | no | — |
| 240 | #41 | — | 16 | 8 | no | — |
| 241 | C2×Q8 | — | 2 | 4 | no | — |
| 242 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 243 | C2×D4 | — | 2 | 4 | no | — |
| 244 | C2×D4 | — | 2 | 2 | no | — |
| 245 | C2×D4 | — | 2 | 2 | no | — |
| 246 | C2×D4 | — | 2 | 4 | no | — |
| 247 | C2×D4 | — | 2 | 4 | no | — |
| 248 | C2×D4 | — | 2 | 4 | no | — |
| 249 | C2×D4 | — | 2 | 4 | no | — |
| 250 | C2×D4 | — | 2 | 4 | no | — |
| 251 | C2×D4 | — | 2 | 4 | no | — |
| 252 | C2×D4 | — | 4 | 8 | no | — |
| 253 | C2×D4 | — | 4 | 8 | no | — |
| 254 | C2×D4 | — | 4 | 8 | no | — |
| 255 | C2×D4 | — | 16 | 4 | no | — |
| 256 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 257 | C22×C4 | — | 2 | 4 | no | — |
| 258 | C22×C4 | — | 2 | 2 | no | — |
| 259 | C22×C4 | — | 2 | 4 | no | — |
| 260 | C22×C4 | — | 4 | 8 | no | — |
| 261 | C22×C4 | — | 4 | 4 | no | — |
| 262 | C22×C4 | — | 4 | 4 | no | — |
| 263 | C22×C4 | — | 16 | 4 | no | — |
| 264 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 265 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 266 | Q16 | — | 4 | 4 | no | — |
| 267 | SD16 | — | 4 | 8 | no | — |
| 268 | SD16 | — | 8 | 8 | no | — |
| 269 | D8 | — | 4 | 4 | no | — |
| 270 | D8 | — | 4 | 8 | no | — |
| 271 | D8 | — | 4 | 4 | no | — |
| 272 | D8 | — | 4 | 4 | no | — |
| 273 | D8 | — | 8 | 8 | no | — |
| 274 | M16 | — | 2 | 8 | no | — |
| 275 | M16 | — | 2 | 8 | no | — |
| 276 | M16 | — | 4 | 8 | no | — |
| 277 | C2×C8 | — | 2 | 4 | no | — |
| 278 | C2×C8 | — | 2 | 4 | no | — |
| 279 | C2×C8 | — | 2 | 4 | no | — |
| 280 | C2×C8 | — | 2 | 4 | no | — |
| 281 | C2×C8 | — | 4 | 8 | no | — |
| 282 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 283 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 284 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 285 | C4⋊C4 | — | 2 | 2 | no | — |
| 286 | C4⋊C4 | — | 2 | 4 | no | — |
| 287 | C4⋊C4 | — | 2 | 2 | no | — |
| 288 | C4⋊C4 | — | 2 | 8 | no | — |
| 289 | C4⋊C4 | — | 2 | 4 | no | — |
| 290 | C4⋊C4 | — | 2 | 4 | no | — |
| 291 | C4⋊C4 | — | 4 | 8 | no | — |
| 292 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 293 | C22⋊C4 | — | 2 | 4 | no | — |
| 294 | C22⋊C4 | — | 2 | 4 | no | — |
| 295 | C22⋊C4 | — | 2 | 4 | no | — |
| 296 | C22⋊C4 | — | 4 | 8 | no | — |
| 297 | C22⋊C4 | — | 4 | 8 | no | — |
| 298 | C22⋊C4 | — | 4 | 8 | no | — |
| 299 | C22⋊C4 | — | 4 | 4 | no | — |
| 300 | C22⋊C4 | — | 4 | 4 | no | — |
| 301 | C22⋊C4 | — | 16 | 4 | no | — |
| 302 | C42 | — | 2 | 4 | no | — |
| 303 | C42 | — | 2 | 4 | no | — |
| 304 | C42 | — | 4 | 8 | no | — |
| 305 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 306 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 307 | C42 | C22×D4 | 1 | 2 | yes | — |
| 308 | C23 | — | 2 | 4 | no | — |
| 309 | C23 | — | 4 | 4 | no | — |
| 310 | C23 | — | 4 | 4 | no | — |
| 311 | C23 | — | 4 | 4 | no | — |
| 312 | C23 | — | 8 | 4 | no | — |
| 313 | C23 | — | 8 | 4 | no | — |
| 314 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 315 | Q8 | — | 2 | 8 | no | — |
| 316 | Q8 | — | 8 | 4 | no | — |
| 317 | D4 | — | 2 | 8 | no | — |
| 318 | D4 | — | 4 | 4 | no | — |
| 319 | D4 | — | 4 | 8 | no | — |
| 320 | D4 | — | 4 | 4 | no | — |
| 321 | D4 | — | 4 | 4 | no | — |
| 322 | D4 | — | 4 | 4 | no | — |
| 323 | D4 | — | 4 | 4 | no | — |
| 324 | D4 | — | 8 | 2 | no | — |
| 325 | D4 | — | 16 | 8 | no | — |
| 326 | D4 | — | 16 | 8 | no | — |
| 327 | D4 | — | 16 | 8 | no | — |
| 328 | C2×C4 | — | 2 | 8 | no | — |
| 329 | C2×C4 | — | 2 | 4 | no | — |
| 330 | C2×C4 | — | 4 | 2 | no | — |
| 331 | C2×C4 | — | 4 | 4 | no | — |
| 332 | C2×C4 | — | 4 | 4 | no | — |
| 333 | C2×C4 | — | 4 | 4 | no | — |
| 334 | C2×C4 | — | 4 | 4 | no | — |
| 335 | C2×C4 | — | 4 | 2 | no | — |
| 336 | C2×C4 | — | 8 | 8 | no | — |
| 337 | C2×C4 | — | 8 | 4 | no | — |
| 338 | C2×C4 | — | 16 | 4 | no | — |
| 339 | C2×C4 | — | 16 | 8 | no | — |
| 340 | C2×C4 | D42 | 1 | 2 | yes | — |
| 341 | C2×C4 | D42 | 1 | 2 | yes | — |
| 342 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 343 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 344 | C2×C4 | #585 | 1 | 4 | yes | — |
| 345 | C8 | — | 2 | 4 | no | — |
| 346 | C8 | — | 2 | 2 | no | — |
| 347 | C8 | — | 2 | 2 | no | — |
| 348 | C8 | — | 4 | 4 | no | — |
| 349 | C8 | — | 4 | 4 | no | — |
| 350 | C22 | — | 2 | 2 | no | — |
| 351 | C22 | — | 4 | 4 | no | — |
| 352 | C22 | — | 4 | 4 | no | — |
| 353 | C22 | — | 4 | 4 | no | — |
| 354 | C22 | — | 8 | 8 | no | — |
| 355 | C22 | — | 8 | 4 | no | — |
| 356 | C22 | — | 8 | 4 | no | — |
| 357 | C22 | — | 8 | 4 | no | — |
| 358 | C22 | — | 16 | 4 | no | — |
| 359 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 360 | C22 | #3539 | 1 | 2 | yes | — |
| 361 | C4 | — | 2 | 2 | no | — |
| 362 | C4 | — | 2 | 2 | no | — |
| 363 | C4 | — | 4 | 4 | no | — |
| 364 | C4 | — | 4 | 8 | no | — |
| 365 | C4 | — | 8 | 2 | no | — |
| 366 | C4 | — | 8 | 4 | no | — |
| 367 | C4 | #3485 | 1 | 2 | yes | — |
| 368 | C4 | #3487 | 1 | 2 | yes | — |
| 369 | C2 | — | 2 | 2 | no | — |
| 370 | C2 | — | 8 | 4 | no | — |
| 371 | C2 | — | 16 | 4 | no | — |
| 372 | C2 | #45387 | 1 | 1 | yes | characteristic |
| 373 | C2 | #61106 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61414 | C2 | semidirect |
| 2. #61284 | C2 | semidirect |
| 3. #30765 | C2 | semidirect |
| 4. #28220 | C2 | semidirect |
| 5. #28174 | C2 | semidirect |
| 6. #26195 | C2 | semidirect |
| 7. #24180 | C2 | semidirect |
| 8. #23810 | C2 | semidirect |
| 9. #22281 | C2 | semidirect |
| 10. #22258 | C2 | semidirect |
| 73. #500 | D4 | semidirect |
| 74. #499 | D4 | semidirect |
| 75. #498 | D4 | semidirect |
| 76. #497 | D4 | semidirect |
| 78. #496 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61414 | 2 |
| #61284 | 2 |
| #30765 | 2 |
| #28220 | 2 |
| #28174 | 2 |
| #26195 | 2 |
| #24180 | 2 |
| #23810 | 2 |
| #22281 | 2 |
| #22258 | 2 |