Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
973 conjugacy classes of subgroups.
The subgroup lattice has 683 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72225526 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225428 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225354 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72216424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72216315 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72216297 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #513051 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×#13658 | — | 2 | 2 | no | — |
| 10 | #498550 | — | 2 | 1 | no | — |
| 11 | #496112 | C22 | 1 | 1 | yes | characteristic |
| 12 | #496104 | C22 | 1 | 1 | yes | characteristic |
| 13 | #483601 | — | 2 | 1 | no | — |
| 14 | #152984 | — | 2 | 2 | no | — |
| 15 | #152899 | C4 | 1 | 1 | yes | characteristic |
| 16 | #152896 | C4 | 1 | 1 | yes | characteristic |
| 17 | #152407 | C4 | 1 | 1 | yes | characteristic |
| 18 | #151981 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×#1398 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#7390 | — | 2 | 1 | no | — |
| 21 | C2×#7390 | — | 2 | 1 | no | — |
| 22 | #140849 | — | 2 | 1 | no | — |
| 23 | #140841 | — | 2 | 1 | no | — |
| 24 | #140752 | — | 2 | 1 | no | — |
| 25 | #136683 | — | 2 | 2 | no | — |
| 26 | #129090 | C22 | 1 | 1 | yes | characteristic |
| 27 | #129090 | C22 | 1 | 1 | yes | characteristic |
| 28 | #129051 | C22 | 1 | 1 | yes | characteristic |
| 29 | #124215 | — | 2 | 1 | no | — |
| 30 | #93926 | — | 2 | 2 | no | — |
| 31 | C2×#2263 | — | 2 | 2 | no | — |
| 32 | #33713 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C2×#2246 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×#2179 | — | 2 | 1 | no | — |
| 35 | C2×#2179 | D4 | 1 | 2 | yes | — |
| 36 | C2×#2177 | — | 2 | 1 | no | — |
| 37 | C2×#2177 | — | 2 | 1 | no | — |
| 38 | #33443 | — | 2 | 2 | no | — |
| 39 | #33443 | — | 4 | 1 | no | — |
| 40 | #21705 | — | 2 | 1 | no | — |
| 41 | C4×#493 | — | 2 | 1 | no | — |
| 42 | #13729 | — | 2 | 2 | no | — |
| 43 | #13727 | C8 | 1 | 2 | yes | complemented |
| 44 | #13725 | C8 | 1 | 2 | yes | complemented |
| 45 | #13658 | — | 4 | 4 | no | — |
| 46 | #13658 | — | 4 | 4 | no | — |
| 47 | C2×#1426 | — | 2 | 2 | no | — |
| 48 | C2×#1422 | — | 2 | 1 | no | — |
| 49 | C2×#1419 | — | 2 | 2 | no | — |
| 50 | C2×#1418 | — | 2 | 2 | no | — |
| 51 | C2×#1398 | — | 2 | 1 | no | — |
| 52 | C2×#1398 | — | 2 | 1 | no | — |
| 53 | C2×#1398 | — | 2 | 1 | no | — |
| 54 | C4×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C4×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | #13242 | — | 2 | 1 | no | — |
| 57 | #13242 | D4 | 1 | 2 | yes | — |
| 58 | #13239 | — | 2 | 1 | no | — |
| 59 | #13239 | — | 2 | 1 | no | — |
| 60 | #13208 | — | 2 | 1 | no | — |
| 61 | #13202 | — | 2 | 1 | no | — |
| 62 | #13197 | — | 2 | 2 | no | — |
| 63 | #13197 | — | 4 | 1 | no | — |
| 64 | #12982 | — | 4 | 2 | no | — |
| 65 | #12909 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | #12906 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | C4×#364 | — | 2 | 1 | no | — |
| 68 | C4×#364 | — | 2 | 1 | no | — |
| 69 | C4×#364 | D4 | 1 | 1 | yes | characteristic |
| 70 | C4×#346 | C23 | 1 | 1 | yes | characteristic |
| 71 | #12068 | — | 4 | 2 | no | — |
| 72 | #12068 | — | 4 | 2 | no | — |
| 73 | C2×#1369 | — | 2 | 1 | no | — |
| 74 | C2×#1369 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×#1369 | D4 | 1 | 1 | yes | characteristic |
| 76 | #11604 | — | 2 | 2 | no | — |
| 77 | #11602 | — | 2 | 2 | no | — |
| 78 | #11599 | — | 4 | 1 | no | — |
| 79 | #11593 | — | 4 | 1 | no | — |
| 80 | #11405 | — | 2 | 1 | no | — |
| 81 | #8266 | D4 | 1 | 1 | yes | characteristic |
| 82 | #7468 | — | 2 | 1 | no | — |
| 83 | #7390 | — | 4 | 2 | no | — |
| 84 | #7390 | — | 4 | 2 | no | — |
| 85 | #7161 | — | 2 | 1 | no | — |
| 86 | #7161 | — | 2 | 1 | no | — |
| 87 | #7140 | — | 2 | 1 | no | — |
| 88 | #7107 | — | 4 | 2 | no | — |
| 89 | C2×#508 | — | 2 | 1 | no | — |
| 90 | C2×#508 | C22⋊C4 | 1 | 2 | yes | — |
| 91 | C22×D16 | — | 2 | 1 | no | — |
| 92 | C22×D16 | — | 2 | 1 | no | — |
| 93 | #3407 | — | 4 | 2 | no | — |
| 94 | #3147 | — | 2 | 1 | no | — |
| 95 | C2×#493 | — | 2 | 1 | no | — |
| 96 | C2×#443 | — | 2 | 2 | no | — |
| 97 | C2×#443 | — | 4 | 1 | no | — |
| 98 | C2×C4×D8 | — | 4 | 1 | no | — |
| 99 | C2×C4×D8 | — | 4 | 1 | no | — |
| 100 | #2931 | — | 4 | 1 | no | — |
| 101 | C4×#127 | — | 4 | 1 | no | — |
| 102 | #2263 | — | 4 | 4 | no | — |
| 103 | #2263 | — | 4 | 4 | no | — |
| 104 | C2×SD64 | — | 2 | 4 | no | — |
| 105 | C2×D32 | — | 2 | 4 | no | — |
| 106 | C2×M64 | — | 2 | 1 | no | — |
| 107 | C2×M64 | — | 2 | 1 | no | — |
| 108 | C2×M64 | — | 4 | 1 | no | — |
| 109 | #2249 | — | 2 | 1 | no | — |
| 110 | #2249 | M16 | 1 | 2 | yes | — |
| 111 | #2248 | — | 2 | 1 | no | — |
| 112 | #2247 | C2×C8 | 1 | 1 | yes | characteristic |
| 113 | #2246 | — | 2 | 1 | no | — |
| 114 | #2246 | — | 2 | 1 | no | — |
| 115 | #2246 | — | 2 | 1 | no | — |
| 116 | #2246 | C2×C8 | 1 | 2 | yes | — |
| 117 | #2246 | C2×C8 | 1 | 1 | yes | characteristic |
| 118 | #2179 | — | 4 | 2 | no | — |
| 119 | #2179 | — | 4 | 2 | no | — |
| 120 | #2179 | — | 4 | 1 | no | — |
| 121 | #2179 | — | 4 | 1 | no | — |
| 122 | #2179 | — | 4 | 1 | no | — |
| 123 | #2179 | — | 4 | 1 | no | — |
| 124 | #2177 | — | 4 | 2 | no | — |
| 125 | #2177 | — | 4 | 2 | no | — |
| 126 | #2177 | — | 4 | 1 | no | — |
| 127 | #2177 | — | 4 | 1 | no | — |
| 128 | #2177 | — | 4 | 1 | no | — |
| 129 | #2177 | — | 4 | 1 | no | — |
| 130 | #2171 | — | 4 | 4 | no | — |
| 131 | #2171 | — | 8 | 2 | no | — |
| 132 | #2170 | — | 8 | 2 | no | — |
| 133 | #2170 | — | 8 | 2 | no | — |
| 134 | C2×#368 | — | 2 | 1 | no | — |
| 135 | C2×#368 | C22⋊C4 | 1 | 2 | yes | — |
| 136 | C2×#367 | — | 2 | 1 | no | — |
| 137 | C2×#367 | — | 2 | 1 | no | — |
| 138 | C2×#364 | — | 2 | 1 | no | — |
| 139 | C2×#364 | — | 2 | 1 | no | — |
| 140 | C2×#364 | — | 2 | 1 | no | — |
| 141 | C2×#364 | — | 4 | 1 | no | — |
| 142 | C2×#359 | — | 2 | 2 | no | — |
| 143 | C2×#359 | — | 2 | 2 | no | — |
| 144 | C2×#357 | — | 4 | 1 | no | — |
| 145 | C2×#357 | — | 4 | 1 | no | — |
| 146 | #2117 | — | 4 | 2 | no | — |
| 147 | #2117 | — | 4 | 2 | no | — |
| 148 | #2115 | — | 4 | 2 | no | — |
| 149 | C4×M32 | — | 2 | 1 | no | — |
| 150 | C4×M32 | — | 4 | 1 | no | — |
| 151 | C4×M32 | — | 4 | 1 | no | — |
| 152 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 157 | C2×C4×C16 | #41 | 1 | 1 | yes | characteristic |
| 158 | #1974 | — | 2 | 2 | no | — |
| 159 | #1974 | — | 4 | 1 | no | — |
| 160 | #1970 | — | 4 | 1 | no | — |
| 161 | #1970 | — | 4 | 1 | no | — |
| 162 | #1962 | — | 4 | 1 | no | — |
| 163 | #1957 | — | 4 | 1 | no | — |
| 164 | #1848 | — | 2 | 1 | no | — |
| 165 | #1845 | — | 2 | 1 | no | — |
| 166 | C42×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | #1564 | — | 2 | 1 | no | — |
| 168 | #1450 | — | 2 | 1 | no | — |
| 169 | #1426 | — | 4 | 4 | no | — |
| 170 | #1422 | — | 2 | 2 | no | — |
| 171 | #1422 | — | 4 | 1 | no | — |
| 172 | #1419 | — | 4 | 4 | no | — |
| 173 | #1418 | — | 4 | 4 | no | — |
| 174 | #1398 | — | 2 | 2 | no | — |
| 175 | #1398 | — | 2 | 2 | no | — |
| 176 | #1398 | — | 4 | 2 | no | — |
| 177 | #1398 | — | 4 | 1 | no | — |
| 178 | #1398 | — | 4 | 1 | no | — |
| 179 | #1397 | — | 2 | 1 | no | — |
| 180 | #1397 | — | 2 | 1 | no | — |
| 181 | C4×C32 | — | 2 | 1 | no | — |
| 182 | C4×C32 | C2×C8 | 1 | 2 | yes | — |
| 183 | #1376 | — | 4 | 1 | no | — |
| 184 | #1376 | — | 4 | 1 | no | — |
| 185 | #1376 | D8 | 1 | 2 | yes | — |
| 186 | #1369 | — | 2 | 2 | no | — |
| 187 | #1369 | — | 2 | 1 | no | — |
| 188 | #1369 | — | 2 | 1 | no | — |
| 189 | #1369 | — | 2 | 1 | no | — |
| 190 | #1369 | — | 4 | 1 | no | — |
| 191 | #1369 | D8 | 1 | 2 | yes | — |
| 192 | #1336 | — | 4 | 4 | no | — |
| 193 | #1335 | — | 8 | 2 | no | — |
| 194 | #1333 | — | 8 | 2 | no | — |
| 195 | #1331 | — | 8 | 2 | no | — |
| 196 | #1313 | — | 4 | 1 | no | — |
| 197 | #1313 | — | 4 | 1 | no | — |
| 198 | #1276 | — | 2 | 1 | no | — |
| 199 | C2×#135 | — | 2 | 2 | no | — |
| 200 | C2×#135 | — | 4 | 1 | no | — |
| 201 | C22×D8 | — | 4 | 1 | no | — |
| 202 | C22×D8 | — | 4 | 1 | no | — |
| 203 | C2×#131 | — | 4 | 2 | no | — |
| 204 | #532 | — | 4 | 1 | no | — |
| 205 | C2×#127 | — | 4 | 1 | no | — |
| 206 | C2×C4×D4 | — | 8 | 1 | no | — |
| 207 | C2×C4×D4 | — | 16 | 1 | no | — |
| 208 | #508 | — | 4 | 2 | no | — |
| 209 | #508 | — | 4 | 2 | no | — |
| 210 | #508 | — | 4 | 1 | no | — |
| 211 | #508 | — | 4 | 1 | no | — |
| 212 | #508 | — | 4 | 1 | no | — |
| 213 | #508 | — | 4 | 1 | no | — |
| 214 | C2×Q32 | — | 2 | 1 | no | — |
| 215 | C2×Q32 | C22⋊C8 | 1 | 2 | yes | — |
| 216 | C2×SD32 | — | 2 | 2 | no | — |
| 217 | C2×SD32 | — | 2 | 2 | no | — |
| 218 | C2×D16 | — | 2 | 2 | no | — |
| 219 | C2×D16 | — | 2 | 1 | no | — |
| 220 | C2×D16 | — | 2 | 2 | no | — |
| 221 | C2×D16 | — | 4 | 2 | no | — |
| 222 | C2×D16 | — | 4 | 2 | no | — |
| 223 | C2×D16 | — | 4 | 1 | no | — |
| 224 | C2×D16 | — | 4 | 1 | no | — |
| 225 | C2×D16 | — | 4 | 1 | no | — |
| 226 | C2×D16 | — | 4 | 1 | no | — |
| 227 | C2×D16 | — | 4 | 1 | no | — |
| 228 | C2×D16 | — | 4 | 1 | no | — |
| 229 | C2×D16 | C22⋊C8 | 1 | 2 | yes | — |
| 230 | #504 | — | 8 | 4 | no | — |
| 231 | #504 | — | 8 | 4 | no | — |
| 232 | C2×M32 | — | 2 | 2 | no | — |
| 233 | C2×M32 | — | 4 | 1 | no | — |
| 234 | C2×M32 | — | 4 | 1 | no | — |
| 235 | C2×M32 | — | 8 | 1 | no | — |
| 236 | C2×M32 | — | 16 | 2 | no | — |
| 237 | C22×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 238 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 239 | C22×C16 | #121 | 1 | 1 | yes | characteristic |
| 240 | C22×C16 | #123 | 1 | 1 | yes | characteristic |
| 241 | #495 | — | 2 | 2 | no | — |
| 242 | #495 | — | 4 | 1 | no | — |
| 243 | #494 | — | 2 | 1 | no | — |
| 244 | #493 | — | 2 | 1 | no | — |
| 245 | #493 | — | 2 | 2 | no | — |
| 246 | #493 | — | 4 | 1 | no | — |
| 247 | #493 | — | 4 | 1 | no | — |
| 248 | #493 | — | 4 | 1 | no | — |
| 249 | #492 | — | 4 | 1 | no | — |
| 250 | #443 | — | 4 | 2 | no | — |
| 251 | #443 | — | 4 | 2 | no | — |
| 252 | #443 | — | 4 | 2 | no | — |
| 253 | #443 | — | 4 | 2 | no | — |
| 254 | #443 | — | 8 | 1 | no | — |
| 255 | #443 | — | 8 | 1 | no | — |
| 256 | #443 | — | 8 | 1 | no | — |
| 257 | #443 | — | 8 | 1 | no | — |
| 258 | C4×D8 | — | 8 | 1 | no | — |
| 259 | C4×D8 | — | 8 | 1 | no | — |
| 260 | C4×D8 | — | 8 | 1 | no | — |
| 261 | C4×D8 | — | 8 | 1 | no | — |
| 262 | C4×D8 | — | 8 | 1 | no | — |
| 263 | C4×D8 | — | 8 | 1 | no | — |
| 264 | C4×D8 | — | 8 | 1 | no | — |
| 265 | C4×D8 | — | 8 | 1 | no | — |
| 266 | #436 | — | 16 | 1 | no | — |
| 267 | C8×D4 | — | 16 | 1 | no | — |
| 268 | #431 | — | 4 | 1 | no | — |
| 269 | C2×#108 | — | 2 | 2 | no | — |
| 270 | C2×#108 | — | 4 | 1 | no | — |
| 271 | C2×#107 | — | 4 | 1 | no | — |
| 272 | C2×#107 | — | 4 | 1 | no | — |
| 273 | #423 | — | 4 | 1 | no | — |
| 274 | C2×#104 | — | 4 | 2 | no | — |
| 275 | C2×#104 | — | 4 | 2 | no | — |
| 276 | C2×#102 | — | 8 | 1 | no | — |
| 277 | C2×#102 | — | 8 | 1 | no | — |
| 278 | #408 | — | 4 | 2 | no | — |
| 279 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 280 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 281 | C2×C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 282 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 283 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 284 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 285 | #390 | — | 8 | 1 | no | — |
| 286 | #390 | — | 16 | 1 | no | — |
| 287 | #384 | — | 4 | 1 | no | — |
| 288 | C43 | #135 | 1 | 1 | yes | characteristic |
| 289 | SD64 | — | 4 | 8 | no | — |
| 290 | D32 | — | 4 | 8 | no | — |
| 291 | M64 | — | 2 | 2 | no | — |
| 292 | M64 | — | 2 | 2 | no | — |
| 293 | M64 | — | 2 | 2 | no | — |
| 294 | M64 | — | 4 | 1 | no | — |
| 295 | M64 | — | 4 | 2 | no | — |
| 296 | M64 | — | 8 | 1 | no | — |
| 297 | C2×C32 | — | 2 | 2 | no | — |
| 298 | C2×C32 | — | 4 | 1 | no | — |
| 299 | C2×C32 | — | 8 | 1 | no | — |
| 300 | #368 | — | 4 | 1 | no | — |
| 301 | #368 | — | 4 | 1 | no | — |
| 302 | #368 | — | 4 | 2 | no | — |
| 303 | #367 | — | 4 | 2 | no | — |
| 304 | #367 | — | 4 | 1 | no | — |
| 305 | #367 | — | 4 | 1 | no | — |
| 306 | #364 | — | 2 | 2 | no | — |
| 307 | #364 | — | 4 | 1 | no | — |
| 308 | #364 | — | 4 | 1 | no | — |
| 309 | #364 | — | 4 | 2 | no | — |
| 310 | #364 | — | 4 | 1 | no | — |
| 311 | #364 | — | 4 | 1 | no | — |
| 312 | #364 | — | 4 | 1 | no | — |
| 313 | #364 | — | 8 | 1 | no | — |
| 314 | #359 | — | 4 | 2 | no | — |
| 315 | #359 | — | 4 | 2 | no | — |
| 316 | #359 | — | 8 | 2 | no | — |
| 317 | #357 | — | 8 | 2 | no | — |
| 318 | #357 | — | 8 | 1 | no | — |
| 319 | #357 | — | 8 | 1 | no | — |
| 320 | #350 | — | 8 | 4 | no | — |
| 321 | #350 | — | 8 | 4 | no | — |
| 322 | #349 | — | 16 | 2 | no | — |
| 323 | #346 | — | 2 | 1 | no | — |
| 324 | #346 | — | 2 | 1 | no | — |
| 325 | #346 | — | 2 | 1 | no | — |
| 326 | #346 | — | 2 | 1 | no | — |
| 327 | #346 | — | 4 | 1 | no | — |
| 328 | #346 | — | 4 | 1 | no | — |
| 329 | #346 | — | 8 | 1 | no | — |
| 330 | #346 | — | 8 | 1 | no | — |
| 331 | #346 | C2×D8 | 1 | 1 | yes | characteristic |
| 332 | #346 | #135 | 1 | 1 | yes | characteristic |
| 333 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 334 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 335 | C4×C16 | — | 2 | 1 | no | — |
| 336 | C4×C16 | — | 2 | 1 | no | — |
| 337 | C4×C16 | — | 4 | 1 | no | — |
| 338 | C4×C16 | — | 8 | 1 | no | — |
| 339 | C4×C16 | — | 8 | 1 | no | — |
| 340 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 341 | C4×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 342 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 343 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 344 | #335 | — | 4 | 1 | no | — |
| 345 | #334 | — | 4 | 1 | no | — |
| 346 | #322 | — | 4 | 1 | no | — |
| 347 | C82 | — | 4 | 1 | no | — |
| 348 | C2×#41 | — | 4 | 2 | no | — |
| 349 | C22×D4 | — | 8 | 1 | no | — |
| 350 | C22×D4 | — | 16 | 1 | no | — |
| 351 | C23×C4 | — | 16 | 1 | no | — |
| 352 | #135 | — | 4 | 2 | no | — |
| 353 | #135 | — | 4 | 2 | no | — |
| 354 | #135 | — | 4 | 2 | no | — |
| 355 | #135 | — | 4 | 2 | no | — |
| 356 | #135 | — | 8 | 1 | no | — |
| 357 | #135 | — | 8 | 1 | no | — |
| 358 | #135 | — | 8 | 1 | no | — |
| 359 | #135 | — | 8 | 1 | no | — |
| 360 | C2×Q16 | — | 2 | 2 | no | — |
| 361 | C2×Q16 | — | 4 | 1 | no | — |
| 362 | C2×SD16 | — | 4 | 2 | no | — |
| 363 | C2×SD16 | — | 4 | 2 | no | — |
| 364 | C2×D8 | — | 2 | 2 | no | — |
| 365 | C2×D8 | — | 4 | 1 | no | — |
| 366 | C2×D8 | — | 4 | 2 | no | — |
| 367 | C2×D8 | — | 4 | 2 | no | — |
| 368 | C2×D8 | — | 8 | 1 | no | — |
| 369 | C2×D8 | — | 8 | 1 | no | — |
| 370 | C2×D8 | — | 8 | 1 | no | — |
| 371 | C2×D8 | — | 8 | 1 | no | — |
| 372 | C2×D8 | — | 8 | 1 | no | — |
| 373 | C2×D8 | — | 8 | 1 | no | — |
| 374 | C2×D8 | — | 8 | 1 | no | — |
| 375 | C2×D8 | — | 8 | 1 | no | — |
| 376 | C2×D8 | — | 8 | 1 | no | — |
| 377 | C2×D8 | — | 8 | 1 | no | — |
| 378 | #131 | — | 8 | 2 | no | — |
| 379 | #131 | — | 8 | 2 | no | — |
| 380 | #131 | — | 8 | 2 | no | — |
| 381 | #131 | — | 8 | 2 | no | — |
| 382 | C2×M16 | — | 4 | 2 | no | — |
| 383 | C2×M16 | — | 8 | 2 | no | — |
| 384 | C22×C8 | — | 8 | 2 | no | — |
| 385 | C22×C8 | #386 | 1 | 1 | yes | characteristic |
| 386 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 387 | C22×C8 | #447 | 1 | 1 | yes | characteristic |
| 388 | C22×C8 | #459 | 1 | 1 | yes | characteristic |
| 389 | C4⋊Q8 | — | 4 | 1 | no | — |
| 390 | #127 | — | 4 | 1 | no | — |
| 391 | #127 | — | 4 | 2 | no | — |
| 392 | #127 | — | 8 | 1 | no | — |
| 393 | #127 | — | 16 | 1 | no | — |
| 394 | #124 | — | 4 | 2 | no | — |
| 395 | #121 | — | 16 | 1 | no | — |
| 396 | C4×D4 | — | 16 | 1 | no | — |
| 397 | C4×D4 | — | 16 | 1 | no | — |
| 398 | C4×D4 | — | 16 | 1 | no | — |
| 399 | C4×D4 | — | 16 | 1 | no | — |
| 400 | C4×D4 | — | 16 | 1 | no | — |
| 401 | C4×D4 | — | 32 | 4 | no | — |
| 402 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 403 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 404 | C2×C22⋊C4 | — | 16 | 1 | no | — |
| 405 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 406 | C2×C42 | — | 4 | 1 | no | — |
| 407 | C2×C42 | C4×D8 | 1 | 1 | yes | characteristic |
| 408 | C2×C42 | #449 | 1 | 1 | yes | characteristic |
| 409 | C2×C42 | #463 | 1 | 1 | yes | characteristic |
| 410 | Q32 | — | 4 | 2 | no | — |
| 411 | Q32 | — | 4 | 1 | no | — |
| 412 | Q32 | — | 4 | 1 | no | — |
| 413 | SD32 | — | 4 | 2 | no | — |
| 414 | SD32 | — | 4 | 2 | no | — |
| 415 | SD32 | — | 8 | 2 | no | — |
| 416 | D16 | — | 4 | 2 | no | — |
| 417 | D16 | — | 4 | 4 | no | — |
| 418 | D16 | — | 4 | 1 | no | — |
| 419 | D16 | — | 4 | 2 | no | — |
| 420 | D16 | — | 4 | 1 | no | — |
| 421 | D16 | — | 4 | 2 | no | — |
| 422 | D16 | — | 8 | 2 | no | — |
| 423 | D16 | — | 8 | 1 | no | — |
| 424 | D16 | — | 8 | 1 | no | — |
| 425 | M32 | — | 4 | 2 | no | — |
| 426 | M32 | — | 4 | 2 | no | — |
| 427 | M32 | — | 4 | 2 | no | — |
| 428 | M32 | — | 8 | 1 | no | — |
| 429 | M32 | — | 8 | 1 | no | — |
| 430 | M32 | — | 8 | 2 | no | — |
| 431 | M32 | — | 8 | 1 | no | — |
| 432 | M32 | — | 16 | 4 | no | — |
| 433 | M32 | — | 16 | 1 | no | — |
| 434 | C2×C16 | — | 2 | 1 | no | — |
| 435 | C2×C16 | — | 2 | 1 | no | — |
| 436 | C2×C16 | — | 2 | 1 | no | — |
| 437 | C2×C16 | — | 2 | 1 | no | — |
| 438 | C2×C16 | — | 2 | 1 | no | — |
| 439 | C2×C16 | — | 2 | 1 | no | — |
| 440 | C2×C16 | — | 2 | 1 | no | — |
| 441 | C2×C16 | — | 4 | 2 | no | — |
| 442 | C2×C16 | — | 8 | 1 | no | — |
| 443 | C2×C16 | — | 8 | 1 | no | — |
| 444 | C2×C16 | — | 16 | 4 | no | — |
| 445 | C2×C16 | — | 16 | 1 | no | — |
| 446 | C2×C16 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 447 | C2×C16 | #408 | 1 | 1 | yes | characteristic |
| 448 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 449 | C2×C16 | #435 | 1 | 1 | yes | characteristic |
| 450 | C2×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 451 | C2×C16 | #442 | 1 | 1 | yes | characteristic |
| 452 | C2×C16 | #443 | 1 | 1 | yes | characteristic |
| 453 | C2×C16 | #444 | 1 | 1 | yes | characteristic |
| 454 | C2×C16 | #459 | 1 | 1 | yes | characteristic |
| 455 | C2×C16 | #463 | 1 | 1 | yes | characteristic |
| 456 | #108 | — | 4 | 2 | no | — |
| 457 | #108 | — | 4 | 2 | no | — |
| 458 | #108 | — | 8 | 1 | no | — |
| 459 | #108 | — | 8 | 1 | no | — |
| 460 | #107 | — | 8 | 1 | no | — |
| 461 | #107 | — | 8 | 1 | no | — |
| 462 | #107 | — | 8 | 1 | no | — |
| 463 | #107 | — | 8 | 1 | no | — |
| 464 | C4⋊C8 | — | 8 | 1 | no | — |
| 465 | C4⋊C8 | — | 16 | 1 | no | — |
| 466 | #104 | — | 8 | 2 | no | — |
| 467 | #104 | — | 8 | 2 | no | — |
| 468 | #104 | — | 8 | 2 | no | — |
| 469 | #104 | — | 8 | 2 | no | — |
| 470 | #102 | — | 16 | 1 | no | — |
| 471 | #102 | — | 16 | 1 | no | — |
| 472 | #102 | — | 16 | 1 | no | — |
| 473 | #102 | — | 16 | 1 | no | — |
| 474 | C22⋊C8 | — | 8 | 1 | no | — |
| 475 | C22⋊C8 | — | 16 | 2 | no | — |
| 476 | C4×C8 | — | 2 | 1 | no | — |
| 477 | C4×C8 | — | 2 | 1 | no | — |
| 478 | C4×C8 | — | 2 | 1 | no | — |
| 479 | C4×C8 | — | 2 | 1 | no | — |
| 480 | C4×C8 | — | 2 | 1 | no | — |
| 481 | C4×C8 | — | 2 | 1 | no | — |
| 482 | C4×C8 | — | 4 | 1 | no | — |
| 483 | C4×C8 | — | 8 | 1 | no | — |
| 484 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 485 | C4×C8 | #435 | 1 | 1 | yes | characteristic |
| 486 | C4×C8 | #443 | 1 | 1 | yes | characteristic |
| 487 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 488 | C4×C8 | #447 | 1 | 1 | yes | characteristic |
| 489 | C4×C8 | #449 | 1 | 1 | yes | characteristic |
| 490 | C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 491 | C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 492 | C32 | — | 2 | 4 | no | — |
| 493 | C32 | — | 4 | 2 | no | — |
| 494 | C32 | — | 8 | 2 | no | — |
| 495 | C24 | — | 16 | 1 | no | — |
| 496 | #41 | — | 8 | 2 | no | — |
| 497 | #41 | — | 8 | 2 | no | — |
| 498 | #41 | — | 8 | 2 | no | — |
| 499 | #41 | — | 8 | 2 | no | — |
| 500 | C2×Q8 | — | 4 | 2 | no | — |
| 501 | C2×D4 | — | 4 | 2 | no | — |
| 502 | C2×D4 | — | 8 | 2 | no | — |
| 503 | C2×D4 | — | 8 | 2 | no | — |
| 504 | C2×D4 | — | 16 | 1 | no | — |
| 505 | C2×D4 | — | 16 | 2 | no | — |
| 506 | C2×D4 | — | 16 | 2 | no | — |
| 507 | C2×D4 | — | 16 | 1 | no | — |
| 508 | C2×D4 | — | 16 | 1 | no | — |
| 509 | C2×D4 | — | 16 | 1 | no | — |
| 510 | C2×D4 | — | 16 | 1 | no | — |
| 511 | C2×D4 | — | 16 | 1 | no | — |
| 512 | C2×D4 | — | 32 | 2 | no | — |
| 513 | C2×D4 | — | 32 | 2 | no | — |
| 514 | C22×C4 | — | 2 | 1 | no | — |
| 515 | C22×C4 | — | 2 | 1 | no | — |
| 516 | C22×C4 | — | 2 | 1 | no | — |
| 517 | C22×C4 | — | 8 | 2 | no | — |
| 518 | C22×C4 | — | 16 | 1 | no | — |
| 519 | C22×C4 | — | 32 | 1 | no | — |
| 520 | C22×C4 | — | 32 | 1 | no | — |
| 521 | C22×C4 | — | 32 | 4 | no | — |
| 522 | C22×C4 | #1879 | 1 | 1 | yes | characteristic |
| 523 | Q16 | — | 4 | 2 | no | — |
| 524 | Q16 | — | 4 | 2 | no | — |
| 525 | Q16 | — | 8 | 1 | no | — |
| 526 | Q16 | — | 8 | 1 | no | — |
| 527 | SD16 | — | 8 | 2 | no | — |
| 528 | SD16 | — | 8 | 2 | no | — |
| 529 | SD16 | — | 8 | 2 | no | — |
| 530 | SD16 | — | 8 | 2 | no | — |
| 531 | D8 | — | 4 | 2 | no | — |
| 532 | D8 | — | 4 | 2 | no | — |
| 533 | D8 | — | 8 | 1 | no | — |
| 534 | D8 | — | 8 | 1 | no | — |
| 535 | D8 | — | 8 | 2 | no | — |
| 536 | D8 | — | 8 | 2 | no | — |
| 537 | D8 | — | 8 | 2 | no | — |
| 538 | D8 | — | 8 | 2 | no | — |
| 539 | D8 | — | 16 | 1 | no | — |
| 540 | D8 | — | 16 | 1 | no | — |
| 541 | D8 | — | 16 | 1 | no | — |
| 542 | D8 | — | 16 | 1 | no | — |
| 543 | M16 | — | 8 | 2 | no | — |
| 544 | M16 | — | 8 | 2 | no | — |
| 545 | M16 | — | 16 | 2 | no | — |
| 546 | M16 | — | 16 | 2 | no | — |
| 547 | C2×C8 | — | 2 | 1 | no | — |
| 548 | C2×C8 | — | 2 | 1 | no | — |
| 549 | C2×C8 | — | 2 | 1 | no | — |
| 550 | C2×C8 | — | 2 | 1 | no | — |
| 551 | C2×C8 | — | 2 | 1 | no | — |
| 552 | C2×C8 | — | 8 | 2 | no | — |
| 553 | C2×C8 | — | 16 | 2 | no | — |
| 554 | C2×C8 | — | 16 | 2 | no | — |
| 555 | C2×C8 | — | 16 | 1 | no | — |
| 556 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 557 | C2×C8 | #1586 | 1 | 1 | yes | characteristic |
| 558 | C2×C8 | #1619 | 1 | 1 | yes | characteristic |
| 559 | C2×C8 | #1621 | 1 | 1 | yes | characteristic |
| 560 | C2×C8 | #1869 | 1 | 1 | yes | characteristic |
| 561 | C2×C8 | #1876 | 1 | 1 | yes | characteristic |
| 562 | C2×C8 | #1876 | 1 | 1 | yes | characteristic |
| 563 | C2×C8 | #1879 | 1 | 1 | yes | characteristic |
| 564 | C2×C8 | #1884 | 1 | 1 | yes | characteristic |
| 565 | C2×C8 | #1887 | 1 | 1 | yes | characteristic |
| 566 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 567 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 568 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 569 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 570 | C4⋊C4 | — | 16 | 1 | no | — |
| 571 | C4⋊C4 | — | 16 | 1 | no | — |
| 572 | C4⋊C4 | — | 16 | 1 | no | — |
| 573 | C4⋊C4 | — | 32 | 2 | no | — |
| 574 | C22⋊C4 | — | 16 | 2 | no | — |
| 575 | C22⋊C4 | — | 32 | 1 | no | — |
| 576 | C22⋊C4 | — | 32 | 1 | no | — |
| 577 | C22⋊C4 | — | 32 | 4 | no | — |
| 578 | C42 | — | 2 | 1 | no | — |
| 579 | C42 | — | 2 | 1 | no | — |
| 580 | C42 | — | 2 | 1 | no | — |
| 581 | C42 | — | 2 | 1 | no | — |
| 582 | C42 | — | 8 | 2 | no | — |
| 583 | C42 | C8×D8 | 1 | 1 | yes | characteristic |
| 584 | C42 | #1581 | 1 | 1 | yes | characteristic |
| 585 | C42 | #1620 | 1 | 1 | yes | characteristic |
| 586 | C42 | #1621 | 1 | 1 | yes | characteristic |
| 587 | C16 | — | 2 | 1 | no | — |
| 588 | C16 | — | 2 | 1 | no | — |
| 589 | C16 | — | 2 | 1 | no | — |
| 590 | C16 | — | 2 | 1 | no | — |
| 591 | C16 | — | 4 | 1 | no | — |
| 592 | C16 | — | 8 | 2 | no | — |
| 593 | C16 | — | 8 | 2 | no | — |
| 594 | C16 | — | 16 | 1 | no | — |
| 595 | C16 | — | 16 | 2 | no | — |
| 596 | C16 | C8×D8 | 1 | 1 | yes | characteristic |
| 597 | C16 | #1580 | 1 | 1 | yes | characteristic |
| 598 | C16 | #1581 | 1 | 1 | yes | characteristic |
| 599 | C16 | #1586 | 1 | 1 | yes | characteristic |
| 600 | C23 | — | 8 | 2 | no | — |
| 601 | C23 | — | 16 | 2 | no | — |
| 602 | C23 | — | 32 | 2 | no | — |
| 603 | C23 | — | 32 | 2 | no | — |
| 604 | C23 | — | 32 | 1 | no | — |
| 605 | C23 | — | 32 | 1 | no | — |
| 606 | C23 | #13036 | 1 | 1 | yes | characteristic |
| 607 | Q8 | — | 8 | 2 | no | — |
| 608 | Q8 | — | 8 | 2 | no | — |
| 609 | D4 | — | 8 | 2 | no | — |
| 610 | D4 | — | 8 | 2 | no | — |
| 611 | D4 | — | 16 | 2 | no | — |
| 612 | D4 | — | 16 | 2 | no | — |
| 613 | D4 | — | 16 | 2 | no | — |
| 614 | D4 | — | 16 | 2 | no | — |
| 615 | D4 | — | 32 | 2 | no | — |
| 616 | D4 | — | 32 | 4 | no | — |
| 617 | D4 | — | 32 | 4 | no | — |
| 618 | D4 | — | 32 | 1 | no | — |
| 619 | D4 | — | 32 | 1 | no | — |
| 620 | C2×C4 | — | 2 | 1 | no | — |
| 621 | C2×C4 | — | 2 | 1 | no | — |
| 622 | C2×C4 | — | 2 | 1 | no | — |
| 623 | C2×C4 | — | 2 | 1 | no | — |
| 624 | C2×C4 | — | 4 | 2 | no | — |
| 625 | C2×C4 | — | 4 | 1 | no | — |
| 626 | C2×C4 | — | 8 | 1 | no | — |
| 627 | C2×C4 | — | 8 | 1 | no | — |
| 628 | C2×C4 | — | 8 | 2 | no | — |
| 629 | C2×C4 | — | 16 | 2 | no | — |
| 630 | C2×C4 | — | 16 | 2 | no | — |
| 631 | C2×C4 | — | 32 | 2 | no | — |
| 632 | C2×C4 | — | 32 | 1 | no | — |
| 633 | C2×C4 | — | 64 | 2 | no | — |
| 634 | C2×C4 | — | 64 | 2 | no | — |
| 635 | C2×C4 | #8947 | 1 | 1 | yes | characteristic |
| 636 | C2×C4 | #9053 | 1 | 1 | yes | characteristic |
| 637 | C2×C4 | #9061 | 1 | 1 | yes | characteristic |
| 638 | C2×C4 | #13033 | 1 | 1 | yes | characteristic |
| 639 | C2×C4 | #13037 | 1 | 1 | yes | characteristic |
| 640 | C2×C4 | #13040 | 1 | 1 | yes | characteristic |
| 641 | C8 | — | 2 | 1 | no | — |
| 642 | C8 | — | 2 | 1 | no | — |
| 643 | C8 | — | 4 | 1 | no | — |
| 644 | C8 | — | 16 | 2 | no | — |
| 645 | C8 | — | 32 | 1 | no | — |
| 646 | C8 | #8947 | 1 | 1 | yes | characteristic |
| 647 | C8 | #8959 | 1 | 1 | yes | characteristic |
| 648 | C8 | #9053 | 1 | 1 | yes | characteristic |
| 649 | C8 | #9069 | 1 | 1 | yes | characteristic |
| 650 | C8 | #12067 | 1 | 1 | yes | characteristic |
| 651 | C8 | #12067 | 1 | 1 | yes | characteristic |
| 652 | C8 | #12078 | 1 | 1 | yes | characteristic |
| 653 | C8 | #12078 | 1 | 1 | yes | characteristic |
| 654 | C22 | — | 4 | 1 | no | — |
| 655 | C22 | — | 16 | 2 | no | — |
| 656 | C22 | — | 32 | 2 | no | — |
| 657 | C22 | — | 32 | 4 | no | — |
| 658 | C22 | — | 32 | 2 | no | — |
| 659 | C22 | — | 64 | 1 | no | — |
| 660 | C22 | — | 64 | 1 | no | — |
| 661 | C22 | — | 64 | 2 | no | — |
| 662 | C22 | #136703 | 1 | 1 | yes | characteristic |
| 663 | C22 | #137501 | 1 | 1 | yes | characteristic |
| 664 | C22 | #137549 | 1 | 1 | yes | characteristic |
| 665 | C4 | — | 2 | 2 | no | — |
| 666 | C4 | — | 4 | 1 | no | — |
| 667 | C4 | — | 4 | 1 | no | — |
| 668 | C4 | — | 4 | 1 | no | — |
| 669 | C4 | — | 8 | 1 | no | — |
| 670 | C4 | — | 16 | 2 | no | — |
| 671 | C4 | — | 64 | 1 | no | — |
| 672 | C4 | #99599 | 1 | 1 | yes | characteristic |
| 673 | C4 | #136707 | 1 | 1 | yes | characteristic |
| 674 | C4 | #137499 | 1 | 1 | yes | characteristic |
| 675 | C4 | #137546 | 1 | 1 | yes | characteristic |
| 676 | C2 | — | 2 | 1 | no | — |
| 677 | C2 | — | 2 | 1 | no | — |
| 678 | C2 | — | 2 | 1 | no | — |
| 679 | C2 | — | 32 | 2 | no | — |
| 680 | C2 | — | 64 | 2 | no | — |
| 681 | C2 | #72225244 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72225244 |
| commutator | C4×C16 | C22×C8 |
| Frattini, cosocle | C4×#346 | C23 |
| prime radical | #513051 | C4 |
| LCS | G ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C42×C8 ◁ #129051 ◁ G | |
| LECS | G ▷ C4×#346 ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225526 | C2 | semidirect |
| 2. #72225428 | C2 | semidirect |
| 3. #72225354 | C2 | semidirect |
| 4. #72225322 | C2 | semidirect |
| 5. #72216424 | C2 | semidirect |
| 7. #72216297 | C2 | semidirect |
| 43. #13727 | C8 | semidirect |
| 44. #13725 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225526 | 2 |
| #72225428 | 2 |
| #72225354 | 2 |
| #72225322 | 2 |
| #72216424 | 2 |
| #72216315 | 2 |
| #72216297 | 2 |