Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
936 conjugacy classes of subgroups.
The subgroup lattice has 710 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 | #72225419 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225172 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72223683 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72216424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72216258 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#13692 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×#13658 | — | 2 | 1 | no | — |
| 10 | #497829 | — | 2 | 1 | no | — |
| 11 | #496104 | C22 | 1 | 1 | yes | characteristic |
| 12 | #493242 | C22 | 1 | 1 | yes | characteristic |
| 13 | #483601 | — | 2 | 1 | no | — |
| 14 | #152994 | C4 | 1 | 1 | yes | characteristic |
| 15 | #152873 | C4 | 1 | 1 | yes | characteristic |
| 16 | #152824 | — | 2 | 1 | no | — |
| 17 | #152534 | — | 2 | 1 | no | — |
| 18 | #152282 | C4 | 1 | 1 | yes | characteristic |
| 19 | #151981 | C22 | 1 | 1 | yes | characteristic |
| 20 | #151969 | — | 2 | 1 | no | — |
| 21 | C4×#1398 | C22 | 1 | 1 | yes | characteristic |
| 22 | #150074 | — | 2 | 1 | no | — |
| 23 | C2×#7390 | — | 2 | 2 | no | — |
| 24 | #140849 | — | 2 | 1 | no | — |
| 25 | #140357 | — | 2 | 1 | no | — |
| 26 | #135910 | — | 2 | 2 | no | — |
| 27 | #135718 | C22 | 1 | 1 | yes | characteristic |
| 28 | #134373 | — | 2 | 1 | no | — |
| 29 | #129090 | C22 | 1 | 1 | yes | characteristic |
| 30 | #129051 | C22 | 1 | 1 | yes | characteristic |
| 31 | #124215 | — | 2 | 1 | no | — |
| 32 | #94058 | — | 2 | 1 | no | — |
| 33 | C2×#2263 | — | 2 | 1 | no | — |
| 34 | C2×#2246 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×#2179 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×#2178 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | #33451 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×#2177 | — | 2 | 1 | no | — |
| 39 | C2×#2177 | — | 2 | 1 | no | — |
| 40 | #33443 | — | 2 | 2 | no | — |
| 41 | #33401 | — | 4 | 1 | no | — |
| 42 | C4×#493 | — | 2 | 1 | no | — |
| 43 | C4×#443 | — | 2 | 1 | no | — |
| 44 | #13692 | — | 2 | 2 | no | — |
| 45 | #13692 | C8 | 1 | 4 | yes | complemented |
| 46 | #13658 | — | 4 | 2 | no | — |
| 47 | #13658 | — | 4 | 2 | no | — |
| 48 | C2×#1426 | — | 2 | 1 | no | — |
| 49 | C2×#1422 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×#1422 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×#1419 | — | 2 | 1 | no | — |
| 52 | C2×#1419 | — | 2 | 1 | no | — |
| 53 | C2×#1418 | — | 2 | 1 | no | — |
| 54 | #13617 | — | 2 | 1 | no | — |
| 55 | C2×#1398 | — | 2 | 1 | no | — |
| 56 | C2×#1398 | — | 2 | 1 | no | — |
| 57 | C2×#1398 | — | 2 | 1 | no | — |
| 58 | C4×M64 | — | 2 | 1 | no | — |
| 59 | #13239 | — | 2 | 1 | no | — |
| 60 | #13239 | — | 2 | 1 | no | — |
| 61 | #13202 | — | 2 | 1 | no | — |
| 62 | #13164 | — | 2 | 2 | no | — |
| 63 | #12918 | — | 4 | 2 | no | — |
| 64 | #12906 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | #12900 | — | 2 | 1 | no | — |
| 66 | #12792 | — | 4 | 1 | no | — |
| 67 | #12676 | D4 | 1 | 1 | yes | characteristic |
| 68 | #12671 | D4 | 1 | 1 | yes | characteristic |
| 69 | #12670 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C4×#364 | — | 2 | 1 | no | — |
| 71 | C4×#364 | D4 | 1 | 1 | yes | characteristic |
| 72 | #12642 | — | 2 | 1 | no | — |
| 73 | #12641 | — | 2 | 1 | no | — |
| 74 | #12640 | — | 2 | 1 | no | — |
| 75 | C4×#346 | C23 | 1 | 1 | yes | characteristic |
| 76 | #12068 | — | 4 | 2 | no | — |
| 77 | #12068 | — | 4 | 2 | no | — |
| 78 | C2×#1369 | — | 2 | 1 | no | — |
| 79 | C2×#1369 | — | 2 | 1 | no | — |
| 80 | C2×#1369 | D4 | 1 | 2 | yes | — |
| 81 | #11604 | — | 2 | 2 | no | — |
| 82 | #11599 | — | 4 | 1 | no | — |
| 83 | #11593 | — | 4 | 1 | no | — |
| 84 | #11405 | — | 2 | 1 | no | — |
| 85 | #8266 | D4 | 1 | 1 | yes | characteristic |
| 86 | #7477 | — | 2 | 1 | no | — |
| 87 | #7474 | — | 2 | 1 | no | — |
| 88 | #7468 | — | 2 | 1 | no | — |
| 89 | #7391 | — | 2 | 2 | no | — |
| 90 | #7390 | — | 2 | 2 | no | — |
| 91 | #7390 | — | 4 | 4 | no | — |
| 92 | #7180 | — | 2 | 2 | no | — |
| 93 | #7161 | — | 2 | 1 | no | — |
| 94 | #7140 | — | 2 | 1 | no | — |
| 95 | #7107 | — | 4 | 2 | no | — |
| 96 | C2×#508 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C22×D16 | — | 2 | 1 | no | — |
| 98 | C22×D16 | — | 2 | 1 | no | — |
| 99 | #3407 | — | 4 | 2 | no | — |
| 100 | C2×#493 | — | 2 | 1 | no | — |
| 101 | C2×#443 | — | 2 | 1 | no | — |
| 102 | C2×#443 | — | 2 | 1 | no | — |
| 103 | C4×#135 | — | 2 | 1 | no | — |
| 104 | C2×C4×D8 | — | 4 | 1 | no | — |
| 105 | C2×C4×D8 | — | 4 | 1 | no | — |
| 106 | C4×#131 | — | 4 | 1 | no | — |
| 107 | C4×#127 | — | 4 | 1 | no | — |
| 108 | #2263 | — | 2 | 4 | no | — |
| 109 | #2263 | — | 4 | 2 | no | — |
| 110 | C2×SD64 | — | 4 | 1 | no | — |
| 111 | C2×D32 | — | 4 | 1 | no | — |
| 112 | C2×M64 | — | 2 | 1 | no | — |
| 113 | C2×M64 | — | 2 | 1 | no | — |
| 114 | C2×M64 | — | 4 | 1 | no | — |
| 115 | #2246 | — | 2 | 1 | no | — |
| 116 | #2246 | — | 2 | 1 | no | — |
| 117 | #2246 | — | 2 | 1 | no | — |
| 118 | #2246 | C2×C8 | 1 | 2 | yes | — |
| 119 | #2179 | — | 2 | 1 | no | — |
| 120 | #2179 | — | 2 | 1 | no | — |
| 121 | #2179 | D8 | 1 | 2 | yes | — |
| 122 | #2179 | SD16 | 1 | 2 | yes | — |
| 123 | #2178 | — | 2 | 1 | no | — |
| 124 | #2178 | — | 2 | 1 | no | — |
| 125 | #2178 | C2×C8 | 1 | 2 | yes | — |
| 126 | #2178 | M16 | 1 | 2 | yes | — |
| 127 | #2177 | — | 2 | 1 | no | — |
| 128 | #2177 | — | 4 | 2 | no | — |
| 129 | #2177 | — | 4 | 2 | no | — |
| 130 | #2177 | — | 4 | 1 | no | — |
| 131 | #2177 | — | 4 | 1 | no | — |
| 132 | #2177 | — | 4 | 1 | no | — |
| 133 | #2177 | — | 4 | 1 | no | — |
| 134 | #2176 | — | 2 | 1 | no | — |
| 135 | #2175 | — | 4 | 1 | no | — |
| 136 | #2171 | — | 4 | 4 | no | — |
| 137 | #2170 | — | 8 | 2 | no | — |
| 138 | C2×#368 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C2×#368 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | #2158 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 141 | C2×#367 | — | 2 | 1 | no | — |
| 142 | C2×#367 | — | 2 | 1 | no | — |
| 143 | #2153 | — | 4 | 2 | no | — |
| 144 | #2153 | — | 8 | 2 | no | — |
| 145 | C2×#364 | — | 2 | 2 | no | — |
| 146 | C2×#364 | — | 2 | 1 | no | — |
| 147 | C2×#364 | — | 4 | 1 | no | — |
| 148 | C2×#364 | — | 4 | 1 | no | — |
| 149 | C2×#364 | — | 8 | 2 | no | — |
| 150 | #2150 | — | 4 | 1 | no | — |
| 151 | C2×#359 | — | 2 | 1 | no | — |
| 152 | C2×#359 | — | 2 | 1 | no | — |
| 153 | #2138 | — | 2 | 1 | no | — |
| 154 | C2×#357 | — | 4 | 1 | no | — |
| 155 | C2×#357 | — | 4 | 1 | no | — |
| 156 | #2117 | — | 4 | 2 | no | — |
| 157 | C4×M32 | — | 2 | 1 | no | — |
| 158 | C4×M32 | — | 4 | 1 | no | — |
| 159 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C16 | #41 | 1 | 1 | yes | characteristic |
| 165 | #1970 | — | 4 | 1 | no | — |
| 166 | #1970 | — | 4 | 1 | no | — |
| 167 | #1957 | — | 4 | 1 | no | — |
| 168 | #1845 | — | 2 | 1 | no | — |
| 169 | C4×#108 | — | 2 | 1 | no | — |
| 170 | #1772 | — | 2 | 1 | no | — |
| 171 | #1772 | — | 2 | 1 | no | — |
| 172 | #1764 | — | 4 | 1 | no | — |
| 173 | #1764 | — | 4 | 1 | no | — |
| 174 | C4×#104 | — | 4 | 1 | no | — |
| 175 | C42×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | #1564 | — | 2 | 1 | no | — |
| 177 | #1450 | — | 2 | 1 | no | — |
| 178 | #1426 | — | 4 | 2 | no | — |
| 179 | #1422 | — | 2 | 1 | no | — |
| 180 | #1422 | — | 2 | 1 | no | — |
| 181 | #1422 | — | 2 | 1 | no | — |
| 182 | #1422 | C2×C8 | 1 | 2 | yes | — |
| 183 | #1419 | — | 2 | 4 | no | — |
| 184 | #1419 | — | 4 | 2 | no | — |
| 185 | #1418 | — | 4 | 2 | no | — |
| 186 | #1415 | — | 4 | 2 | no | — |
| 187 | #1398 | — | 2 | 2 | no | — |
| 188 | #1398 | — | 2 | 2 | no | — |
| 189 | #1398 | — | 4 | 1 | no | — |
| 190 | #1398 | — | 4 | 1 | no | — |
| 191 | #1398 | — | 4 | 1 | no | — |
| 192 | #1398 | — | 4 | 1 | no | — |
| 193 | #1397 | — | 4 | 1 | no | — |
| 194 | C4×C32 | — | 2 | 2 | no | — |
| 195 | #1382 | — | 2 | 1 | no | — |
| 196 | #1382 | — | 2 | 1 | no | — |
| 197 | #1381 | — | 2 | 1 | no | — |
| 198 | #1378 | — | 4 | 2 | no | — |
| 199 | #1376 | — | 4 | 1 | no | — |
| 200 | #1376 | D8 | 1 | 2 | yes | — |
| 201 | #1369 | — | 2 | 2 | no | — |
| 202 | #1369 | — | 4 | 2 | no | — |
| 203 | #1369 | — | 4 | 1 | no | — |
| 204 | #1369 | — | 4 | 1 | no | — |
| 205 | #1369 | — | 4 | 1 | no | — |
| 206 | #1336 | — | 4 | 4 | no | — |
| 207 | #1333 | — | 8 | 2 | no | — |
| 208 | #1331 | — | 8 | 2 | no | — |
| 209 | #1313 | — | 4 | 1 | no | — |
| 210 | #1313 | — | 4 | 1 | no | — |
| 211 | #1276 | — | 2 | 1 | no | — |
| 212 | C2×#135 | — | 2 | 1 | no | — |
| 213 | C22×D8 | — | 4 | 1 | no | — |
| 214 | C22×D8 | — | 4 | 1 | no | — |
| 215 | C2×#131 | — | 4 | 1 | no | — |
| 216 | C2×#131 | — | 4 | 1 | no | — |
| 217 | C2×#127 | — | 4 | 1 | no | — |
| 218 | C4×#41 | — | 4 | 1 | no | — |
| 219 | C2×C4×D4 | — | 8 | 1 | no | — |
| 220 | C2×C4×D4 | — | 16 | 1 | no | — |
| 221 | #508 | — | 2 | 1 | no | — |
| 222 | #508 | — | 2 | 1 | no | — |
| 223 | #508 | C22⋊C8 | 1 | 2 | yes | — |
| 224 | #508 | #102 | 1 | 2 | yes | — |
| 225 | C2×Q32 | #104 | 1 | 1 | yes | characteristic |
| 226 | C2×SD32 | — | 2 | 1 | no | — |
| 227 | C2×D16 | — | 2 | 2 | no | — |
| 228 | C2×D16 | — | 2 | 2 | no | — |
| 229 | C2×D16 | — | 4 | 2 | no | — |
| 230 | C2×D16 | — | 4 | 2 | no | — |
| 231 | C2×D16 | — | 4 | 1 | no | — |
| 232 | C2×D16 | — | 4 | 1 | no | — |
| 233 | C2×D16 | — | 4 | 1 | no | — |
| 234 | C2×D16 | — | 4 | 1 | no | — |
| 235 | C2×D16 | — | 4 | 1 | no | — |
| 236 | C2×D16 | — | 4 | 1 | no | — |
| 237 | C2×D16 | #104 | 1 | 1 | yes | characteristic |
| 238 | #504 | — | 8 | 4 | no | — |
| 239 | #504 | — | 16 | 2 | no | — |
| 240 | C2×M32 | — | 2 | 2 | no | — |
| 241 | C2×M32 | — | 4 | 2 | no | — |
| 242 | C2×M32 | — | 8 | 4 | no | — |
| 243 | C2×M32 | — | 8 | 1 | no | — |
| 244 | C22×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 245 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 246 | C22×C16 | #121 | 1 | 1 | yes | characteristic |
| 247 | C22×C16 | #123 | 1 | 1 | yes | characteristic |
| 248 | #493 | — | 2 | 2 | no | — |
| 249 | #493 | — | 4 | 1 | no | — |
| 250 | #493 | — | 4 | 1 | no | — |
| 251 | #493 | — | 4 | 1 | no | — |
| 252 | #443 | — | 2 | 2 | no | — |
| 253 | #443 | — | 2 | 2 | no | — |
| 254 | #443 | — | 2 | 2 | no | — |
| 255 | #443 | — | 2 | 2 | no | — |
| 256 | #443 | — | 4 | 1 | no | — |
| 257 | #443 | — | 4 | 1 | no | — |
| 258 | #443 | — | 4 | 1 | no | — |
| 259 | #443 | — | 4 | 1 | no | — |
| 260 | C4×Q16 | — | 4 | 1 | no | — |
| 261 | C4×SD16 | — | 8 | 1 | no | — |
| 262 | C4×D8 | — | 4 | 1 | no | — |
| 263 | C4×D8 | — | 8 | 1 | no | — |
| 264 | C4×D8 | — | 8 | 1 | no | — |
| 265 | C4×D8 | — | 8 | 1 | no | — |
| 266 | C4×D8 | — | 8 | 1 | no | — |
| 267 | C4×D8 | — | 8 | 1 | no | — |
| 268 | C4×D8 | — | 8 | 1 | no | — |
| 269 | C4×D8 | — | 8 | 1 | no | — |
| 270 | C4×D8 | — | 8 | 1 | no | — |
| 271 | #431 | — | 4 | 1 | no | — |
| 272 | C2×#108 | — | 2 | 1 | no | — |
| 273 | C2×#108 | — | 2 | 1 | no | — |
| 274 | #427 | — | 2 | 1 | no | — |
| 275 | C2×#107 | — | 4 | 1 | no | — |
| 276 | C2×#107 | — | 4 | 1 | no | — |
| 277 | C2×#104 | — | 4 | 1 | no | — |
| 278 | C2×#104 | — | 4 | 1 | no | — |
| 279 | #416 | — | 4 | 1 | no | — |
| 280 | C2×#102 | — | 8 | 1 | no | — |
| 281 | C2×#102 | — | 8 | 1 | no | — |
| 282 | #405 | — | 4 | 1 | no | — |
| 283 | #405 | — | 4 | 1 | no | — |
| 284 | #405 | — | 8 | 1 | no | — |
| 285 | #405 | — | 8 | 1 | no | — |
| 286 | C4×M16 | — | 4 | 1 | no | — |
| 287 | C4×M16 | — | 8 | 1 | no | — |
| 288 | C2×C4×C8 | — | 8 | 1 | no | — |
| 289 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 290 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 291 | C2×C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 292 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 293 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 294 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 295 | #390 | — | 8 | 1 | no | — |
| 296 | #390 | — | 16 | 1 | no | — |
| 297 | #384 | — | 4 | 1 | no | — |
| 298 | C43 | #135 | 1 | 1 | yes | characteristic |
| 299 | SD64 | — | 4 | 4 | no | — |
| 300 | D32 | — | 4 | 4 | no | — |
| 301 | M64 | — | 2 | 2 | no | — |
| 302 | M64 | — | 4 | 2 | no | — |
| 303 | M64 | — | 4 | 2 | no | — |
| 304 | M64 | — | 4 | 1 | no | — |
| 305 | M64 | — | 4 | 1 | no | — |
| 306 | M64 | — | 4 | 1 | no | — |
| 307 | C2×C32 | — | 4 | 2 | no | — |
| 308 | C2×C32 | — | 4 | 1 | no | — |
| 309 | C2×C32 | — | 4 | 1 | no | — |
| 310 | #368 | — | 2 | 1 | no | — |
| 311 | #368 | — | 2 | 1 | no | — |
| 312 | #368 | C22⋊C8 | 1 | 2 | yes | — |
| 313 | #368 | #102 | 1 | 2 | yes | — |
| 314 | #367 | — | 2 | 1 | no | — |
| 315 | #367 | — | 4 | 2 | no | — |
| 316 | #367 | — | 4 | 1 | no | — |
| 317 | #367 | — | 4 | 1 | no | — |
| 318 | #366 | — | 2 | 1 | no | — |
| 319 | #364 | — | 4 | 1 | no | — |
| 320 | #364 | — | 4 | 1 | no | — |
| 321 | #364 | — | 4 | 2 | no | — |
| 322 | #364 | — | 4 | 2 | no | — |
| 323 | #364 | — | 4 | 2 | no | — |
| 324 | #364 | — | 8 | 1 | no | — |
| 325 | #364 | — | 8 | 1 | no | — |
| 326 | #364 | — | 8 | 1 | no | — |
| 327 | #364 | — | 8 | 4 | no | — |
| 328 | C4⋊C16 | — | 16 | 1 | no | — |
| 329 | #359 | — | 2 | 2 | no | — |
| 330 | #359 | — | 2 | 2 | no | — |
| 331 | #359 | — | 2 | 2 | no | — |
| 332 | #359 | — | 2 | 2 | no | — |
| 333 | #358 | — | 4 | 1 | no | — |
| 334 | #357 | — | 4 | 1 | no | — |
| 335 | #357 | — | 8 | 2 | no | — |
| 336 | #357 | — | 8 | 1 | no | — |
| 337 | #357 | — | 8 | 1 | no | — |
| 338 | #350 | — | 8 | 4 | no | — |
| 339 | #346 | — | 2 | 1 | no | — |
| 340 | #346 | — | 2 | 1 | no | — |
| 341 | #346 | — | 2 | 1 | no | — |
| 342 | #346 | — | 2 | 1 | no | — |
| 343 | #346 | — | 4 | 1 | no | — |
| 344 | #346 | — | 4 | 1 | no | — |
| 345 | #346 | — | 8 | 1 | no | — |
| 346 | #346 | C2×D8 | 1 | 1 | yes | characteristic |
| 347 | #346 | C2×SD16 | 1 | 1 | yes | characteristic |
| 348 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 349 | #346 | #137 | 1 | 1 | yes | characteristic |
| 350 | C4×C16 | — | 2 | 1 | no | — |
| 351 | C4×C16 | — | 2 | 1 | no | — |
| 352 | C4×C16 | — | 4 | 1 | no | — |
| 353 | C4×C16 | — | 8 | 1 | no | — |
| 354 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 355 | C4×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 356 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 357 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 358 | #341 | — | 4 | 1 | no | — |
| 359 | #339 | — | 4 | 1 | no | — |
| 360 | #339 | — | 4 | 1 | no | — |
| 361 | #335 | — | 4 | 1 | no | — |
| 362 | #334 | — | 4 | 1 | no | — |
| 363 | #322 | — | 4 | 1 | no | — |
| 364 | C82 | — | 4 | 1 | no | — |
| 365 | C2×#41 | — | 4 | 1 | no | — |
| 366 | C22×D4 | — | 8 | 1 | no | — |
| 367 | C22×D4 | — | 16 | 1 | no | — |
| 368 | C23×C4 | — | 16 | 1 | no | — |
| 369 | #135 | — | 2 | 2 | no | — |
| 370 | #135 | — | 2 | 2 | no | — |
| 371 | #135 | — | 4 | 1 | no | — |
| 372 | #135 | — | 4 | 1 | no | — |
| 373 | C2×Q16 | — | 2 | 1 | no | — |
| 374 | C2×SD16 | — | 4 | 1 | no | — |
| 375 | C2×D8 | — | 2 | 1 | no | — |
| 376 | C2×D8 | — | 4 | 2 | no | — |
| 377 | C2×D8 | — | 4 | 2 | no | — |
| 378 | C2×D8 | — | 8 | 1 | no | — |
| 379 | C2×D8 | — | 8 | 1 | no | — |
| 380 | C2×D8 | — | 8 | 1 | no | — |
| 381 | C2×D8 | — | 8 | 1 | no | — |
| 382 | C2×D8 | — | 8 | 1 | no | — |
| 383 | C2×D8 | — | 8 | 1 | no | — |
| 384 | C2×D8 | — | 8 | 1 | no | — |
| 385 | C2×D8 | — | 8 | 1 | no | — |
| 386 | C2×D8 | — | 8 | 1 | no | — |
| 387 | C2×D8 | — | 8 | 1 | no | — |
| 388 | #131 | — | 4 | 2 | no | — |
| 389 | #131 | — | 4 | 2 | no | — |
| 390 | #131 | — | 4 | 2 | no | — |
| 391 | #131 | — | 4 | 2 | no | — |
| 392 | #131 | — | 8 | 1 | no | — |
| 393 | #131 | — | 8 | 1 | no | — |
| 394 | #131 | — | 8 | 1 | no | — |
| 395 | #131 | — | 8 | 1 | no | — |
| 396 | C2×M16 | — | 4 | 1 | no | — |
| 397 | C2×M16 | — | 4 | 1 | no | — |
| 398 | C2×M16 | — | 8 | 1 | no | — |
| 399 | C2×M16 | — | 8 | 1 | no | — |
| 400 | C22×C8 | — | 8 | 1 | no | — |
| 401 | C22×C8 | — | 8 | 1 | no | — |
| 402 | C22×C8 | #386 | 1 | 1 | yes | characteristic |
| 403 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 404 | C22×C8 | #447 | 1 | 1 | yes | characteristic |
| 405 | C22×C8 | #459 | 1 | 1 | yes | characteristic |
| 406 | #127 | — | 4 | 2 | no | — |
| 407 | #127 | — | 8 | 1 | no | — |
| 408 | #127 | — | 16 | 1 | no | — |
| 409 | C4×Q8 | — | 8 | 1 | no | — |
| 410 | C4×D4 | — | 8 | 1 | no | — |
| 411 | C4×D4 | — | 16 | 1 | no | — |
| 412 | C4×D4 | — | 16 | 1 | no | — |
| 413 | C4×D4 | — | 16 | 1 | no | — |
| 414 | C4×D4 | — | 16 | 1 | no | — |
| 415 | C4×D4 | — | 16 | 1 | no | — |
| 416 | C4×D4 | — | 32 | 4 | no | — |
| 417 | #117 | — | 4 | 1 | no | — |
| 418 | #117 | — | 8 | 1 | no | — |
| 419 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 420 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 421 | C2×C22⋊C4 | — | 16 | 1 | no | — |
| 422 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 423 | C2×C42 | — | 4 | 1 | no | — |
| 424 | C2×C42 | — | 8 | 1 | no | — |
| 425 | C2×C42 | C4×D8 | 1 | 1 | yes | characteristic |
| 426 | C2×C42 | #449 | 1 | 1 | yes | characteristic |
| 427 | C2×C42 | #463 | 1 | 1 | yes | characteristic |
| 428 | Q32 | — | 2 | 1 | no | — |
| 429 | Q32 | D4⋊C8 | 1 | 2 | yes | — |
| 430 | SD32 | — | 2 | 2 | no | — |
| 431 | SD32 | — | 2 | 2 | no | — |
| 432 | D16 | — | 2 | 1 | no | — |
| 433 | D16 | — | 4 | 4 | no | — |
| 434 | D16 | — | 4 | 2 | no | — |
| 435 | D16 | — | 4 | 2 | no | — |
| 436 | D16 | — | 8 | 2 | no | — |
| 437 | D16 | — | 8 | 1 | no | — |
| 438 | D16 | — | 8 | 1 | no | — |
| 439 | D16 | D4⋊C8 | 1 | 2 | yes | — |
| 440 | M32 | — | 4 | 2 | no | — |
| 441 | M32 | — | 4 | 2 | no | — |
| 442 | M32 | — | 8 | 2 | no | — |
| 443 | M32 | — | 8 | 2 | no | — |
| 444 | M32 | — | 8 | 2 | no | — |
| 445 | M32 | — | 16 | 4 | no | — |
| 446 | M32 | — | 16 | 1 | no | — |
| 447 | C2×C16 | — | 2 | 1 | no | — |
| 448 | C2×C16 | — | 2 | 1 | no | — |
| 449 | C2×C16 | — | 2 | 1 | no | — |
| 450 | C2×C16 | — | 2 | 1 | no | — |
| 451 | C2×C16 | — | 2 | 1 | no | — |
| 452 | C2×C16 | — | 2 | 1 | no | — |
| 453 | C2×C16 | — | 2 | 1 | no | — |
| 454 | C2×C16 | — | 4 | 2 | no | — |
| 455 | C2×C16 | — | 8 | 2 | no | — |
| 456 | C2×C16 | — | 16 | 4 | no | — |
| 457 | C2×C16 | — | 16 | 1 | no | — |
| 458 | C2×C16 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 459 | C2×C16 | #408 | 1 | 1 | yes | characteristic |
| 460 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 461 | C2×C16 | #417 | 1 | 1 | yes | characteristic |
| 462 | C2×C16 | C2×#104 | 1 | 1 | yes | characteristic |
| 463 | C2×C16 | #421 | 1 | 1 | yes | characteristic |
| 464 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 465 | C2×C16 | #435 | 1 | 1 | yes | characteristic |
| 466 | C2×C16 | #480 | 1 | 1 | yes | characteristic |
| 467 | C2×C16 | #481 | 1 | 1 | yes | characteristic |
| 468 | #108 | — | 2 | 2 | no | — |
| 469 | #108 | — | 2 | 2 | no | — |
| 470 | #108 | — | 4 | 1 | no | — |
| 471 | #108 | — | 4 | 1 | no | — |
| 472 | #107 | — | 4 | 1 | no | — |
| 473 | #107 | — | 8 | 1 | no | — |
| 474 | #107 | — | 8 | 1 | no | — |
| 475 | #107 | — | 8 | 1 | no | — |
| 476 | #107 | — | 8 | 1 | no | — |
| 477 | #106 | — | 4 | 1 | no | — |
| 478 | C4⋊C8 | — | 8 | 1 | no | — |
| 479 | #104 | — | 4 | 2 | no | — |
| 480 | #104 | — | 4 | 2 | no | — |
| 481 | #104 | — | 4 | 2 | no | — |
| 482 | #104 | — | 4 | 2 | no | — |
| 483 | #103 | — | 8 | 1 | no | — |
| 484 | #102 | — | 8 | 1 | no | — |
| 485 | #102 | — | 16 | 1 | no | — |
| 486 | #102 | — | 16 | 1 | no | — |
| 487 | #102 | — | 16 | 1 | no | — |
| 488 | #102 | — | 16 | 1 | no | — |
| 489 | C22⋊C8 | — | 8 | 1 | no | — |
| 490 | #97 | — | 8 | 1 | no | — |
| 491 | #97 | — | 8 | 1 | no | — |
| 492 | #97 | — | 8 | 1 | no | — |
| 493 | C4×C8 | — | 2 | 1 | no | — |
| 494 | C4×C8 | — | 2 | 1 | no | — |
| 495 | C4×C8 | — | 2 | 1 | no | — |
| 496 | C4×C8 | — | 2 | 1 | no | — |
| 497 | C4×C8 | — | 2 | 1 | no | — |
| 498 | C4×C8 | — | 2 | 1 | no | — |
| 499 | C4×C8 | — | 4 | 1 | no | — |
| 500 | C4×C8 | — | 8 | 1 | no | — |
| 501 | C4×C8 | — | 8 | 1 | no | — |
| 502 | C4×C8 | — | 8 | 1 | no | — |
| 503 | C4×C8 | — | 8 | 1 | no | — |
| 504 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 505 | C4×C8 | #435 | 1 | 1 | yes | characteristic |
| 506 | C4×C8 | #443 | 1 | 1 | yes | characteristic |
| 507 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 508 | C4×C8 | #447 | 1 | 1 | yes | characteristic |
| 509 | C4×C8 | #448 | 1 | 1 | yes | characteristic |
| 510 | C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 511 | C4×C8 | #454 | 1 | 1 | yes | characteristic |
| 512 | C32 | — | 4 | 4 | no | — |
| 513 | C32 | — | 4 | 2 | no | — |
| 514 | C32 | — | 8 | 1 | no | — |
| 515 | C24 | — | 16 | 1 | no | — |
| 516 | #41 | — | 4 | 2 | no | — |
| 517 | #41 | — | 4 | 2 | no | — |
| 518 | #41 | — | 8 | 1 | no | — |
| 519 | #41 | — | 8 | 1 | no | — |
| 520 | C2×Q8 | — | 4 | 1 | no | — |
| 521 | C2×D4 | — | 4 | 1 | no | — |
| 522 | C2×D4 | — | 8 | 1 | no | — |
| 523 | C2×D4 | — | 8 | 2 | no | — |
| 524 | C2×D4 | — | 16 | 2 | no | — |
| 525 | C2×D4 | — | 16 | 2 | no | — |
| 526 | C2×D4 | — | 16 | 1 | no | — |
| 527 | C2×D4 | — | 16 | 1 | no | — |
| 528 | C2×D4 | — | 16 | 1 | no | — |
| 529 | C2×D4 | — | 16 | 1 | no | — |
| 530 | C2×D4 | — | 16 | 1 | no | — |
| 531 | C2×D4 | — | 32 | 2 | no | — |
| 532 | C2×D4 | — | 32 | 2 | no | — |
| 533 | C22×C4 | — | 2 | 1 | no | — |
| 534 | C22×C4 | — | 2 | 1 | no | — |
| 535 | C22×C4 | — | 2 | 1 | no | — |
| 536 | C22×C4 | — | 8 | 1 | no | — |
| 537 | C22×C4 | — | 16 | 1 | no | — |
| 538 | C22×C4 | — | 16 | 1 | no | — |
| 539 | C22×C4 | — | 32 | 1 | no | — |
| 540 | C22×C4 | — | 32 | 1 | no | — |
| 541 | C22×C4 | — | 32 | 4 | no | — |
| 542 | C22×C4 | #1879 | 1 | 1 | yes | characteristic |
| 543 | Q16 | — | 2 | 2 | no | — |
| 544 | Q16 | — | 4 | 1 | no | — |
| 545 | SD16 | — | 4 | 2 | no | — |
| 546 | SD16 | — | 4 | 2 | no | — |
| 547 | D8 | — | 2 | 2 | no | — |
| 548 | D8 | — | 4 | 1 | no | — |
| 549 | D8 | — | 8 | 2 | no | — |
| 550 | D8 | — | 8 | 2 | no | — |
| 551 | D8 | — | 8 | 2 | no | — |
| 552 | D8 | — | 8 | 2 | no | — |
| 553 | D8 | — | 16 | 1 | no | — |
| 554 | D8 | — | 16 | 1 | no | — |
| 555 | D8 | — | 16 | 1 | no | — |
| 556 | D8 | — | 16 | 1 | no | — |
| 557 | M16 | — | 4 | 2 | no | — |
| 558 | M16 | — | 4 | 2 | no | — |
| 559 | M16 | — | 8 | 2 | no | — |
| 560 | M16 | — | 8 | 2 | no | — |
| 561 | M16 | — | 8 | 1 | no | — |
| 562 | M16 | — | 8 | 1 | no | — |
| 563 | M16 | — | 8 | 2 | no | — |
| 564 | M16 | — | 8 | 2 | no | — |
| 565 | C2×C8 | — | 2 | 1 | no | — |
| 566 | C2×C8 | — | 2 | 1 | no | — |
| 567 | C2×C8 | — | 2 | 1 | no | — |
| 568 | C2×C8 | — | 2 | 1 | no | — |
| 569 | C2×C8 | — | 2 | 1 | no | — |
| 570 | C2×C8 | — | 8 | 2 | no | — |
| 571 | C2×C8 | — | 8 | 2 | no | — |
| 572 | C2×C8 | — | 8 | 1 | no | — |
| 573 | C2×C8 | — | 8 | 1 | no | — |
| 574 | C2×C8 | — | 8 | 2 | no | — |
| 575 | C2×C8 | — | 8 | 2 | no | — |
| 576 | C2×C8 | — | 16 | 1 | no | — |
| 577 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 578 | C2×C8 | #1586 | 1 | 1 | yes | characteristic |
| 579 | C2×C8 | #1619 | 1 | 1 | yes | characteristic |
| 580 | C2×C8 | #1627 | 1 | 1 | yes | characteristic |
| 581 | C2×C8 | #1869 | 1 | 1 | yes | characteristic |
| 582 | C2×C8 | #1871 | 1 | 1 | yes | characteristic |
| 583 | C2×C8 | #1874 | 1 | 1 | yes | characteristic |
| 584 | C2×C8 | #1876 | 1 | 1 | yes | characteristic |
| 585 | C2×C8 | #1881 | 1 | 1 | yes | characteristic |
| 586 | C2×C8 | #1883 | 1 | 1 | yes | characteristic |
| 587 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 588 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 589 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 590 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 591 | C4⋊C4 | — | 8 | 1 | no | — |
| 592 | C4⋊C4 | — | 16 | 1 | no | — |
| 593 | C4⋊C4 | — | 16 | 1 | no | — |
| 594 | C4⋊C4 | — | 16 | 1 | no | — |
| 595 | C4⋊C4 | — | 32 | 2 | no | — |
| 596 | C22⋊C4 | — | 8 | 1 | no | — |
| 597 | C22⋊C4 | — | 16 | 1 | no | — |
| 598 | C22⋊C4 | — | 32 | 1 | no | — |
| 599 | C22⋊C4 | — | 32 | 1 | no | — |
| 600 | C22⋊C4 | — | 32 | 4 | no | — |
| 601 | C42 | — | 2 | 1 | no | — |
| 602 | C42 | — | 2 | 1 | no | — |
| 603 | C42 | — | 2 | 1 | no | — |
| 604 | C42 | — | 2 | 1 | no | — |
| 605 | C42 | — | 8 | 2 | no | — |
| 606 | C42 | — | 8 | 1 | no | — |
| 607 | C42 | — | 16 | 1 | no | — |
| 608 | C42 | C8×D8 | 1 | 1 | yes | characteristic |
| 609 | C42 | #1581 | 1 | 1 | yes | characteristic |
| 610 | C42 | #1622 | 1 | 1 | yes | characteristic |
| 611 | C42 | #1625 | 1 | 1 | yes | characteristic |
| 612 | C16 | — | 2 | 1 | no | — |
| 613 | C16 | — | 2 | 1 | no | — |
| 614 | C16 | — | 2 | 1 | no | — |
| 615 | C16 | — | 2 | 1 | no | — |
| 616 | C16 | — | 4 | 1 | no | — |
| 617 | C16 | — | 8 | 2 | no | — |
| 618 | C16 | — | 16 | 2 | no | — |
| 619 | C16 | — | 16 | 2 | no | — |
| 620 | C16 | C2×D4⋊C8 | 1 | 1 | yes | characteristic |
| 621 | C16 | #1477 | 1 | 1 | yes | characteristic |
| 622 | C16 | #1480 | 1 | 1 | yes | characteristic |
| 623 | C16 | #1483 | 1 | 1 | yes | characteristic |
| 624 | C23 | — | 8 | 1 | no | — |
| 625 | C23 | — | 16 | 2 | no | — |
| 626 | C23 | — | 32 | 2 | no | — |
| 627 | C23 | — | 32 | 2 | no | — |
| 628 | C23 | — | 32 | 1 | no | — |
| 629 | C23 | — | 32 | 1 | no | — |
| 630 | C23 | #13032 | 1 | 1 | yes | characteristic |
| 631 | Q8 | — | 4 | 2 | no | — |
| 632 | Q8 | — | 8 | 1 | no | — |
| 633 | D4 | — | 4 | 2 | no | — |
| 634 | D4 | — | 8 | 2 | no | — |
| 635 | D4 | — | 8 | 2 | no | — |
| 636 | D4 | — | 8 | 1 | no | — |
| 637 | D4 | — | 16 | 2 | no | — |
| 638 | D4 | — | 16 | 2 | no | — |
| 639 | D4 | — | 32 | 4 | no | — |
| 640 | D4 | — | 32 | 4 | no | — |
| 641 | D4 | — | 32 | 1 | no | — |
| 642 | D4 | — | 32 | 1 | no | — |
| 643 | C2×C4 | — | 2 | 1 | no | — |
| 644 | C2×C4 | — | 2 | 1 | no | — |
| 645 | C2×C4 | — | 2 | 1 | no | — |
| 646 | C2×C4 | — | 2 | 1 | no | — |
| 647 | C2×C4 | — | 4 | 2 | no | — |
| 648 | C2×C4 | — | 4 | 1 | no | — |
| 649 | C2×C4 | — | 8 | 1 | no | — |
| 650 | C2×C4 | — | 8 | 1 | no | — |
| 651 | C2×C4 | — | 8 | 2 | no | — |
| 652 | C2×C4 | — | 8 | 2 | no | — |
| 653 | C2×C4 | — | 8 | 1 | no | — |
| 654 | C2×C4 | — | 16 | 1 | no | — |
| 655 | C2×C4 | — | 32 | 2 | no | — |
| 656 | C2×C4 | — | 32 | 2 | no | — |
| 657 | C2×C4 | — | 32 | 1 | no | — |
| 658 | C2×C4 | — | 64 | 2 | no | — |
| 659 | C2×C4 | — | 64 | 2 | no | — |
| 660 | C2×C4 | #8947 | 1 | 1 | yes | characteristic |
| 661 | C2×C4 | #8977 | 1 | 1 | yes | characteristic |
| 662 | C2×C4 | #8991 | 1 | 1 | yes | characteristic |
| 663 | C2×C4 | #13030 | 1 | 1 | yes | characteristic |
| 664 | C2×C4 | #13037 | 1 | 1 | yes | characteristic |
| 665 | C2×C4 | #13040 | 1 | 1 | yes | characteristic |
| 666 | C8 | — | 2 | 1 | no | — |
| 667 | C8 | — | 2 | 1 | no | — |
| 668 | C8 | — | 4 | 1 | no | — |
| 669 | C8 | — | 8 | 2 | no | — |
| 670 | C8 | — | 8 | 2 | no | — |
| 671 | C8 | — | 32 | 1 | no | — |
| 672 | C8 | #8939 | 1 | 1 | yes | characteristic |
| 673 | C8 | #8954 | 1 | 1 | yes | characteristic |
| 674 | C8 | #8969 | 1 | 1 | yes | characteristic |
| 675 | C8 | #8995 | 1 | 1 | yes | characteristic |
| 676 | C8 | #12067 | 1 | 1 | yes | characteristic |
| 677 | C8 | #12067 | 1 | 1 | yes | characteristic |
| 678 | C8 | #12078 | 1 | 1 | yes | characteristic |
| 679 | C8 | #12078 | 1 | 1 | yes | characteristic |
| 680 | C22 | — | 4 | 1 | no | — |
| 681 | C22 | — | 8 | 2 | no | — |
| 682 | C22 | — | 32 | 1 | no | — |
| 683 | C22 | — | 32 | 4 | no | — |
| 684 | C22 | — | 32 | 2 | no | — |
| 685 | C22 | — | 64 | 1 | no | — |
| 686 | C22 | — | 64 | 1 | no | — |
| 687 | C22 | — | 64 | 2 | no | — |
| 688 | C22 | #136700 | 1 | 1 | yes | characteristic |
| 689 | C22 | #136909 | 1 | 1 | yes | characteristic |
| 690 | C22 | #137039 | 1 | 1 | yes | characteristic |
| 691 | C4 | — | 2 | 2 | no | — |
| 692 | C4 | — | 4 | 1 | no | — |
| 693 | C4 | — | 4 | 1 | no | — |
| 694 | C4 | — | 4 | 1 | no | — |
| 695 | C4 | — | 8 | 1 | no | — |
| 696 | C4 | — | 8 | 2 | no | — |
| 697 | C4 | — | 32 | 1 | no | — |
| 698 | C4 | — | 64 | 1 | no | — |
| 699 | C4 | #99507 | 1 | 1 | yes | characteristic |
| 700 | C4 | #136707 | 1 | 1 | yes | characteristic |
| 701 | C4 | #136906 | 1 | 1 | yes | characteristic |
| 702 | C4 | #137035 | 1 | 1 | yes | characteristic |
| 703 | C2 | — | 2 | 1 | no | — |
| 704 | C2 | — | 2 | 1 | no | — |
| 705 | C2 | — | 2 | 1 | no | — |
| 706 | C2 | — | 16 | 2 | no | — |
| 707 | C2 | — | 64 | 2 | no | — |
| 708 | C2 | #72216590 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72216590 |
| commutator | C4×C16 | C22×C8 |
| Frattini, cosocle | C4×#346 | C23 |
| prime radical | C2×#13692 | 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. #72225419 | C2 | semidirect |
| 3. #72225349 | C2 | semidirect |
| 4. #72225172 | C2 | semidirect |
| 5. #72223683 | C2 | semidirect |
| 6. #72216424 | C2 | semidirect |
| 45. #13692 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225526 | 2 |
| #72225419 | 2 |
| #72225349 | 2 |
| #72225172 | 2 |
| #72223683 | 2 |
| #72216424 | 2 |
| #72216258 | 2 |