Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
837 conjugacy classes of subgroups.
The subgroup lattice has 596 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72225599 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225401 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225344 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225339 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72216535 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#93752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72216251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #512928 | — | 2 | 1 | no | — |
| 9 | #497894 | — | 2 | 1 | no | — |
| 10 | #497857 | — | 2 | 1 | no | — |
| 11 | #491465 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#12046 | C22 | 1 | 1 | yes | characteristic |
| 13 | #152996 | — | 2 | 1 | no | — |
| 14 | #151636 | — | 2 | 2 | no | — |
| 15 | #151635 | C4 | 1 | 2 | yes | complemented |
| 16 | #151634 | C4 | 1 | 2 | yes | complemented |
| 17 | C2×#7459 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#7459 | C22 | 1 | 1 | yes | characteristic |
| 19 | #150950 | — | 2 | 1 | no | — |
| 20 | #150947 | — | 2 | 1 | no | — |
| 21 | #141812 | — | 2 | 2 | no | — |
| 22 | #140438 | — | 2 | 1 | no | — |
| 23 | #136326 | — | 2 | 2 | no | — |
| 24 | #135781 | C22 | 1 | 1 | yes | characteristic |
| 25 | #134971 | — | 2 | 1 | no | — |
| 26 | #129142 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#7052 | C22 | 1 | 1 | yes | characteristic |
| 28 | #93752 | — | 2 | 2 | no | — |
| 29 | #33981 | — | 4 | 1 | no | — |
| 30 | #33713 | — | 2 | 1 | no | — |
| 31 | #33713 | — | 2 | 1 | no | — |
| 32 | #33465 | — | 4 | 1 | no | — |
| 33 | C2×#2178 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×#2170 | — | 2 | 1 | no | — |
| 35 | #33414 | — | 4 | 1 | no | — |
| 36 | #22694 | — | 2 | 2 | no | — |
| 37 | #19603 | — | 2 | 1 | no | — |
| 38 | #13693 | — | 2 | 2 | no | — |
| 39 | #13692 | — | 2 | 2 | no | — |
| 40 | #13691 | — | 4 | 2 | no | — |
| 41 | C2×#1422 | — | 2 | 1 | no | — |
| 42 | C2×#1422 | — | 2 | 1 | no | — |
| 43 | #13625 | — | 4 | 1 | no | — |
| 44 | #13622 | — | 4 | 1 | no | — |
| 45 | #13620 | — | 4 | 1 | no | — |
| 46 | #13182 | — | 2 | 2 | no | — |
| 47 | #13173 | — | 4 | 1 | no | — |
| 48 | #12947 | — | 4 | 2 | no | — |
| 49 | #12927 | — | 4 | 2 | no | — |
| 50 | #12909 | — | 2 | 1 | no | — |
| 51 | #12909 | — | 2 | 1 | no | — |
| 52 | #12841 | — | 4 | 1 | no | — |
| 53 | #12822 | — | 2 | 2 | no | — |
| 54 | #12670 | D4 | 1 | 1 | yes | characteristic |
| 55 | #12664 | — | 2 | 1 | no | — |
| 56 | #12518 | — | 2 | 1 | no | — |
| 57 | #12518 | — | 2 | 1 | no | — |
| 58 | #12517 | — | 2 | 1 | no | — |
| 59 | #12516 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | #12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | #12046 | — | 2 | 1 | no | — |
| 62 | #12046 | — | 2 | 1 | no | — |
| 63 | #12046 | C2×C4 | 1 | 2 | yes | — |
| 64 | #12046 | D4 | 1 | 2 | yes | — |
| 65 | C2×#1373 | D4 | 1 | 1 | yes | characteristic |
| 66 | C2×#1373 | D4 | 1 | 1 | yes | characteristic |
| 67 | #11671 | — | 4 | 4 | no | — |
| 68 | C2×#1335 | — | 2 | 1 | no | — |
| 69 | C2×C8×C16 | — | 2 | 1 | no | — |
| 70 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 71 | #8823 | D4 | 1 | 2 | yes | — |
| 72 | #7459 | — | 2 | 1 | no | — |
| 73 | #7459 | — | 2 | 1 | no | — |
| 74 | #7459 | — | 2 | 1 | no | — |
| 75 | #7459 | C2×C4 | 1 | 2 | yes | — |
| 76 | #7449 | — | 2 | 2 | no | — |
| 77 | #7448 | — | 2 | 2 | no | — |
| 78 | #7447 | — | 4 | 2 | no | — |
| 79 | #7270 | — | 2 | 2 | no | — |
| 80 | #7179 | — | 2 | 1 | no | — |
| 81 | #7052 | — | 2 | 1 | no | — |
| 82 | #7052 | — | 2 | 1 | no | — |
| 83 | C2×#508 | — | 4 | 1 | no | — |
| 84 | C2×#508 | — | 4 | 1 | no | — |
| 85 | C2×#508 | — | 4 | 1 | no | — |
| 86 | C2×#508 | — | 4 | 1 | no | — |
| 87 | C2×#508 | D8 | 1 | 1 | yes | characteristic |
| 88 | C2×#504 | — | 4 | 1 | no | — |
| 89 | #3169 | — | 4 | 2 | no | — |
| 90 | #3147 | — | 4 | 1 | no | — |
| 91 | #2957 | — | 4 | 2 | no | — |
| 92 | C2×#443 | — | 2 | 1 | no | — |
| 93 | #2916 | — | 4 | 2 | no | — |
| 94 | #2264 | — | 4 | 2 | no | — |
| 95 | #2264 | — | 8 | 1 | no | — |
| 96 | #2263 | — | 4 | 2 | no | — |
| 97 | #2263 | — | 8 | 1 | no | — |
| 98 | #2262 | — | 8 | 2 | no | — |
| 99 | C2×M64 | — | 4 | 1 | no | — |
| 100 | C2×M64 | — | 4 | 1 | no | — |
| 101 | #2249 | — | 4 | 1 | no | — |
| 102 | #2249 | — | 4 | 1 | no | — |
| 103 | #2249 | — | 4 | 1 | no | — |
| 104 | #2249 | — | 4 | 1 | no | — |
| 105 | #2248 | — | 4 | 1 | no | — |
| 106 | #2248 | — | 4 | 1 | no | — |
| 107 | #2247 | — | 2 | 1 | no | — |
| 108 | #2247 | — | 2 | 1 | no | — |
| 109 | #2246 | — | 2 | 1 | no | — |
| 110 | #2246 | — | 2 | 1 | no | — |
| 111 | #2179 | — | 8 | 2 | no | — |
| 112 | #2178 | — | 2 | 1 | no | — |
| 113 | #2178 | — | 2 | 1 | no | — |
| 114 | #2178 | — | 8 | 2 | no | — |
| 115 | #2178 | C22⋊C4 | 1 | 2 | yes | — |
| 116 | #2178 | SD16 | 1 | 2 | yes | — |
| 117 | #2170 | — | 2 | 2 | no | — |
| 118 | #2170 | — | 2 | 2 | no | — |
| 119 | #2170 | — | 4 | 1 | no | — |
| 120 | #2170 | — | 4 | 1 | no | — |
| 121 | #2161 | — | 4 | 2 | no | — |
| 122 | #2161 | — | 8 | 2 | no | — |
| 123 | C2×#368 | — | 4 | 1 | no | — |
| 124 | C2×#368 | — | 4 | 1 | no | — |
| 125 | C2×#368 | — | 4 | 1 | no | — |
| 126 | C2×#368 | — | 4 | 1 | no | — |
| 127 | C2×#368 | — | 8 | 2 | no | — |
| 128 | C2×#368 | D8 | 1 | 1 | yes | characteristic |
| 129 | C2×#368 | D8 | 1 | 1 | yes | characteristic |
| 130 | #2158 | D8 | 1 | 1 | yes | characteristic |
| 131 | C2×#364 | — | 2 | 1 | no | — |
| 132 | C2×#364 | — | 2 | 1 | no | — |
| 133 | #2143 | — | 4 | 2 | no | — |
| 134 | C2×#359 | — | 2 | 1 | no | — |
| 135 | C2×#350 | — | 4 | 1 | no | — |
| 136 | #2108 | — | 4 | 1 | no | — |
| 137 | C2×C4×C16 | — | 2 | 2 | no | — |
| 138 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | #1953 | — | 4 | 2 | no | — |
| 141 | #1861 | — | 8 | 2 | no | — |
| 142 | #1848 | — | 2 | 2 | no | — |
| 143 | #1814 | — | 4 | 2 | no | — |
| 144 | #1772 | — | 2 | 1 | no | — |
| 145 | #1713 | — | 2 | 1 | no | — |
| 146 | #1712 | — | 2 | 1 | no | — |
| 147 | #1709 | — | 4 | 1 | no | — |
| 148 | #1706 | — | 4 | 2 | no | — |
| 149 | #1567 | — | 4 | 2 | no | — |
| 150 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | #1422 | — | 2 | 2 | no | — |
| 152 | #1422 | — | 4 | 1 | no | — |
| 153 | #1422 | — | 4 | 1 | no | — |
| 154 | #1422 | — | 4 | 1 | no | — |
| 155 | #1420 | — | 4 | 2 | no | — |
| 156 | #1419 | — | 4 | 2 | no | — |
| 157 | #1418 | — | 8 | 2 | no | — |
| 158 | #1417 | — | 8 | 2 | no | — |
| 159 | #1389 | — | 4 | 2 | no | — |
| 160 | #1388 | — | 4 | 2 | no | — |
| 161 | #1382 | — | 2 | 1 | no | — |
| 162 | #1379 | — | 4 | 1 | no | — |
| 163 | #1373 | — | 2 | 1 | no | — |
| 164 | #1373 | — | 2 | 1 | no | — |
| 165 | #1373 | — | 2 | 1 | no | — |
| 166 | #1373 | C22⋊C4 | 1 | 2 | yes | — |
| 167 | #1335 | — | 2 | 2 | no | — |
| 168 | #1335 | — | 2 | 2 | no | — |
| 169 | #1331 | — | 8 | 8 | no | — |
| 170 | C8×C16 | — | 4 | 1 | no | — |
| 171 | C8×C16 | — | 4 | 1 | no | — |
| 172 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 173 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 175 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 176 | C2×#135 | — | 2 | 1 | no | — |
| 177 | C2×#135 | — | 8 | 1 | no | — |
| 178 | C2×#135 | — | 8 | 1 | no | — |
| 179 | #568 | — | 8 | 2 | no | — |
| 180 | C2×#131 | — | 4 | 1 | no | — |
| 181 | #532 | — | 8 | 1 | no | — |
| 182 | #508 | — | 2 | 1 | no | — |
| 183 | #508 | — | 2 | 1 | no | — |
| 184 | #508 | — | 8 | 1 | no | — |
| 185 | #508 | — | 8 | 1 | no | — |
| 186 | #508 | — | 8 | 1 | no | — |
| 187 | #508 | — | 8 | 1 | no | — |
| 188 | #508 | — | 8 | 1 | no | — |
| 189 | #508 | — | 8 | 1 | no | — |
| 190 | #508 | — | 8 | 1 | no | — |
| 191 | #508 | — | 8 | 1 | no | — |
| 192 | #508 | — | 16 | 1 | no | — |
| 193 | #508 | — | 16 | 1 | no | — |
| 194 | #508 | — | 16 | 1 | no | — |
| 195 | #508 | — | 16 | 1 | no | — |
| 196 | #508 | #102 | 1 | 2 | yes | — |
| 197 | #508 | D16 | 1 | 2 | yes | — |
| 198 | C2×Q32 | — | 4 | 1 | no | — |
| 199 | C2×Q32 | — | 4 | 1 | no | — |
| 200 | C2×Q32 | — | 4 | 1 | no | — |
| 201 | C2×Q32 | — | 4 | 1 | no | — |
| 202 | C2×Q32 | SD32 | 1 | 1 | yes | characteristic |
| 203 | C2×SD32 | — | 2 | 1 | no | — |
| 204 | C2×SD32 | — | 8 | 1 | no | — |
| 205 | C2×SD32 | — | 8 | 1 | no | — |
| 206 | C2×SD32 | — | 8 | 1 | no | — |
| 207 | C2×SD32 | — | 8 | 1 | no | — |
| 208 | C2×D16 | — | 4 | 1 | no | — |
| 209 | C2×D16 | — | 4 | 1 | no | — |
| 210 | C2×D16 | — | 4 | 1 | no | — |
| 211 | C2×D16 | — | 4 | 1 | no | — |
| 212 | C2×D16 | SD32 | 1 | 1 | yes | characteristic |
| 213 | #504 | — | 4 | 2 | no | — |
| 214 | #504 | — | 4 | 2 | no | — |
| 215 | #504 | — | 8 | 1 | no | — |
| 216 | #504 | — | 8 | 1 | no | — |
| 217 | C2×M32 | — | 4 | 1 | no | — |
| 218 | C2×M32 | — | 4 | 1 | no | — |
| 219 | C2×M32 | — | 8 | 1 | no | — |
| 220 | C22×C16 | — | 4 | 2 | no | — |
| 221 | C22×C16 | — | 8 | 1 | no | — |
| 222 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 223 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 224 | C22×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 225 | C22×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 226 | #500 | — | 4 | 2 | no | — |
| 227 | #495 | — | 8 | 1 | no | — |
| 228 | #495 | — | 8 | 1 | no | — |
| 229 | #494 | — | 4 | 1 | no | — |
| 230 | #493 | — | 4 | 2 | no | — |
| 231 | #493 | — | 4 | 1 | no | — |
| 232 | #492 | — | 8 | 1 | no | — |
| 233 | #486 | — | 8 | 2 | no | — |
| 234 | #466 | — | 8 | 4 | no | — |
| 235 | #444 | — | 16 | 2 | no | — |
| 236 | #443 | — | 2 | 2 | no | — |
| 237 | #443 | — | 2 | 2 | no | — |
| 238 | #443 | — | 4 | 1 | no | — |
| 239 | #443 | — | 4 | 1 | no | — |
| 240 | #443 | — | 8 | 4 | no | — |
| 241 | C4×D8 | — | 8 | 4 | no | — |
| 242 | #430 | — | 8 | 2 | no | — |
| 243 | #430 | — | 16 | 2 | no | — |
| 244 | C2×#108 | — | 2 | 1 | no | — |
| 245 | C2×#108 | — | 2 | 1 | no | — |
| 246 | C2×#108 | — | 4 | 2 | no | — |
| 247 | C2×#108 | — | 4 | 2 | no | — |
| 248 | C2×#108 | — | 8 | 4 | no | — |
| 249 | #427 | — | 2 | 1 | no | — |
| 250 | #423 | — | 4 | 2 | no | — |
| 251 | #421 | — | 8 | 2 | no | — |
| 252 | C2×#104 | — | 4 | 1 | no | — |
| 253 | #405 | — | 4 | 1 | no | — |
| 254 | C2×C4×C8 | — | 2 | 1 | no | — |
| 255 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 256 | Q64 | — | 8 | 2 | no | — |
| 257 | SD64 | — | 8 | 2 | no | — |
| 258 | SD64 | — | 8 | 2 | no | — |
| 259 | D32 | — | 8 | 2 | no | — |
| 260 | M64 | — | 4 | 2 | no | — |
| 261 | M64 | — | 8 | 1 | no | — |
| 262 | M64 | — | 8 | 1 | no | — |
| 263 | M64 | — | 8 | 1 | no | — |
| 264 | C2×C32 | — | 8 | 1 | no | — |
| 265 | C2×C32 | — | 8 | 1 | no | — |
| 266 | #368 | — | 2 | 1 | no | — |
| 267 | #368 | — | 2 | 1 | no | — |
| 268 | #368 | — | 8 | 4 | no | — |
| 269 | #368 | — | 8 | 1 | no | — |
| 270 | #368 | — | 8 | 1 | no | — |
| 271 | #368 | — | 8 | 1 | no | — |
| 272 | #368 | — | 8 | 1 | no | — |
| 273 | #368 | — | 16 | 1 | no | — |
| 274 | #368 | — | 16 | 1 | no | — |
| 275 | #368 | #102 | 1 | 2 | yes | — |
| 276 | #368 | D16 | 1 | 2 | yes | — |
| 277 | #367 | — | 2 | 1 | no | — |
| 278 | #366 | — | 2 | 1 | no | — |
| 279 | #364 | — | 2 | 2 | no | — |
| 280 | #364 | — | 4 | 1 | no | — |
| 281 | #364 | — | 4 | 1 | no | — |
| 282 | #364 | — | 4 | 1 | no | — |
| 283 | #359 | — | 2 | 2 | no | — |
| 284 | #359 | — | 2 | 2 | no | — |
| 285 | #359 | — | 8 | 4 | no | — |
| 286 | #350 | — | 4 | 2 | no | — |
| 287 | #350 | — | 4 | 2 | no | — |
| 288 | #346 | — | 8 | 1 | no | — |
| 289 | C4×C16 | — | 2 | 4 | no | — |
| 290 | C4×C16 | — | 4 | 2 | no | — |
| 291 | C4×C16 | — | 8 | 1 | no | — |
| 292 | C4×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 293 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 294 | C4×C16 | #121 | 1 | 1 | yes | characteristic |
| 295 | C4×C16 | #123 | 1 | 1 | yes | characteristic |
| 296 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 297 | C4×C16 | #135 | 1 | 1 | yes | characteristic |
| 298 | C4×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 299 | C4×C16 | #137 | 1 | 1 | yes | characteristic |
| 300 | #344 | — | 8 | 2 | no | — |
| 301 | #339 | — | 4 | 1 | no | — |
| 302 | #335 | — | 8 | 4 | no | — |
| 303 | C82 | — | 2 | 1 | no | — |
| 304 | C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 305 | C82 | #121 | 1 | 1 | yes | characteristic |
| 306 | C2×#41 | — | 4 | 1 | no | — |
| 307 | C2×#41 | — | 16 | 1 | no | — |
| 308 | #135 | — | 2 | 2 | no | — |
| 309 | #135 | — | 2 | 2 | no | — |
| 310 | #135 | — | 4 | 1 | no | — |
| 311 | #135 | — | 4 | 1 | no | — |
| 312 | #135 | — | 16 | 1 | no | — |
| 313 | #135 | — | 16 | 1 | no | — |
| 314 | #135 | — | 16 | 1 | no | — |
| 315 | #135 | — | 16 | 1 | no | — |
| 316 | #135 | — | 16 | 1 | no | — |
| 317 | #135 | — | 16 | 1 | no | — |
| 318 | #135 | — | 16 | 1 | no | — |
| 319 | #135 | — | 16 | 1 | no | — |
| 320 | C2×Q16 | — | 2 | 1 | no | — |
| 321 | C2×Q16 | — | 8 | 1 | no | — |
| 322 | C2×Q16 | — | 8 | 1 | no | — |
| 323 | C2×SD16 | — | 4 | 1 | no | — |
| 324 | C2×SD16 | — | 16 | 1 | no | — |
| 325 | C2×SD16 | — | 16 | 1 | no | — |
| 326 | C2×D8 | — | 2 | 1 | no | — |
| 327 | C2×D8 | — | 8 | 4 | no | — |
| 328 | C2×D8 | — | 8 | 1 | no | — |
| 329 | C2×D8 | — | 8 | 1 | no | — |
| 330 | #131 | — | 4 | 2 | no | — |
| 331 | #131 | — | 4 | 2 | no | — |
| 332 | #131 | — | 8 | 1 | no | — |
| 333 | #131 | — | 8 | 1 | no | — |
| 334 | #131 | — | 16 | 4 | no | — |
| 335 | #131 | — | 32 | 2 | no | — |
| 336 | C2×M16 | — | 4 | 1 | no | — |
| 337 | C2×M16 | — | 4 | 1 | no | — |
| 338 | C2×M16 | — | 8 | 1 | no | — |
| 339 | C2×M16 | — | 8 | 2 | no | — |
| 340 | C2×M16 | — | 16 | 4 | no | — |
| 341 | C22×C8 | — | 2 | 2 | no | — |
| 342 | C22×C8 | — | 8 | 1 | no | — |
| 343 | C22×C8 | #447 | 1 | 1 | yes | characteristic |
| 344 | C22×C8 | #447 | 1 | 1 | yes | characteristic |
| 345 | C4⋊Q8 | — | 8 | 1 | no | — |
| 346 | #127 | — | 8 | 1 | no | — |
| 347 | #124 | — | 16 | 1 | no | — |
| 348 | #121 | — | 16 | 2 | no | — |
| 349 | C4×D4 | — | 16 | 2 | no | — |
| 350 | #117 | — | 4 | 1 | no | — |
| 351 | C2×C42 | #453 | 1 | 1 | yes | characteristic |
| 352 | Q32 | — | 2 | 1 | no | — |
| 353 | Q32 | — | 8 | 1 | no | — |
| 354 | Q32 | — | 8 | 1 | no | — |
| 355 | Q32 | — | 8 | 1 | no | — |
| 356 | Q32 | — | 8 | 1 | no | — |
| 357 | Q32 | — | 16 | 1 | no | — |
| 358 | Q32 | — | 16 | 1 | no | — |
| 359 | Q32 | #357 | 1 | 2 | yes | — |
| 360 | SD32 | — | 2 | 2 | no | — |
| 361 | SD32 | — | 2 | 2 | no | — |
| 362 | SD32 | — | 16 | 2 | no | — |
| 363 | SD32 | — | 16 | 2 | no | — |
| 364 | SD32 | — | 16 | 1 | no | — |
| 365 | SD32 | — | 16 | 1 | no | — |
| 366 | SD32 | — | 16 | 1 | no | — |
| 367 | SD32 | — | 16 | 1 | no | — |
| 368 | D16 | — | 2 | 1 | no | — |
| 369 | D16 | — | 8 | 1 | no | — |
| 370 | D16 | — | 8 | 1 | no | — |
| 371 | D16 | — | 8 | 1 | no | — |
| 372 | D16 | — | 8 | 1 | no | — |
| 373 | D16 | — | 16 | 1 | no | — |
| 374 | D16 | — | 16 | 1 | no | — |
| 375 | D16 | #357 | 1 | 2 | yes | — |
| 376 | M32 | — | 4 | 2 | no | — |
| 377 | M32 | — | 8 | 1 | no | — |
| 378 | M32 | — | 8 | 2 | no | — |
| 379 | M32 | — | 8 | 2 | no | — |
| 380 | M32 | — | 8 | 1 | no | — |
| 381 | M32 | — | 8 | 1 | no | — |
| 382 | C2×C16 | — | 2 | 1 | no | — |
| 383 | C2×C16 | — | 2 | 1 | no | — |
| 384 | C2×C16 | — | 2 | 1 | no | — |
| 385 | C2×C16 | — | 2 | 1 | no | — |
| 386 | C2×C16 | — | 4 | 4 | no | — |
| 387 | C2×C16 | — | 8 | 4 | no | — |
| 388 | C2×C16 | — | 8 | 1 | no | — |
| 389 | C2×C16 | — | 8 | 2 | no | — |
| 390 | C2×C16 | — | 8 | 2 | no | — |
| 391 | C2×C16 | — | 8 | 1 | no | — |
| 392 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 393 | C2×C16 | #417 | 1 | 1 | yes | characteristic |
| 394 | C2×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 395 | C2×C16 | #442 | 1 | 1 | yes | characteristic |
| 396 | C2×C16 | #459 | 1 | 1 | yes | characteristic |
| 397 | C2×C16 | #463 | 1 | 1 | yes | characteristic |
| 398 | C2×C16 | #480 | 1 | 1 | yes | characteristic |
| 399 | C2×C16 | #481 | 1 | 1 | yes | characteristic |
| 400 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 401 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 402 | C2×C16 | C2×SD32 | 1 | 1 | yes | characteristic |
| 403 | C2×C16 | #508 | 1 | 1 | yes | characteristic |
| 404 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 405 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 406 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 407 | C2×C16 | #510 | 1 | 1 | yes | characteristic |
| 408 | #108 | — | 2 | 2 | no | — |
| 409 | #108 | — | 2 | 2 | no | — |
| 410 | #108 | — | 4 | 1 | no | — |
| 411 | #108 | — | 4 | 1 | no | — |
| 412 | #108 | — | 8 | 2 | no | — |
| 413 | #108 | — | 8 | 2 | no | — |
| 414 | #108 | — | 8 | 2 | no | — |
| 415 | #108 | — | 8 | 2 | no | — |
| 416 | #108 | — | 16 | 4 | no | — |
| 417 | #107 | — | 4 | 1 | no | — |
| 418 | #107 | — | 8 | 4 | no | — |
| 419 | #106 | — | 4 | 1 | no | — |
| 420 | C4⋊C8 | — | 16 | 2 | no | — |
| 421 | #104 | — | 4 | 2 | no | — |
| 422 | #104 | — | 4 | 2 | no | — |
| 423 | #104 | — | 16 | 4 | no | — |
| 424 | #102 | — | 16 | 4 | no | — |
| 425 | #97 | — | 8 | 1 | no | — |
| 426 | C4×C8 | — | 2 | 2 | no | — |
| 427 | C4×C8 | — | 2 | 1 | no | — |
| 428 | C4×C8 | — | 2 | 1 | no | — |
| 429 | C4×C8 | — | 8 | 1 | no | — |
| 430 | C4×C8 | #386 | 1 | 1 | yes | characteristic |
| 431 | C4×C8 | #448 | 1 | 1 | yes | characteristic |
| 432 | C4×C8 | #449 | 1 | 1 | yes | characteristic |
| 433 | C4×C8 | #454 | 1 | 1 | yes | characteristic |
| 434 | C32 | — | 8 | 2 | no | — |
| 435 | C32 | — | 16 | 1 | no | — |
| 436 | #41 | — | 4 | 2 | no | — |
| 437 | #41 | — | 4 | 2 | no | — |
| 438 | #41 | — | 8 | 1 | no | — |
| 439 | #41 | — | 8 | 1 | no | — |
| 440 | #41 | — | 32 | 1 | no | — |
| 441 | #41 | — | 32 | 1 | no | — |
| 442 | #41 | — | 32 | 1 | no | — |
| 443 | #41 | — | 32 | 1 | no | — |
| 444 | C2×Q8 | — | 4 | 1 | no | — |
| 445 | C2×Q8 | — | 16 | 1 | no | — |
| 446 | C2×D4 | — | 4 | 1 | no | — |
| 447 | C2×D4 | — | 8 | 1 | no | — |
| 448 | C2×D4 | — | 16 | 2 | no | — |
| 449 | C2×D4 | — | 16 | 1 | no | — |
| 450 | C2×D4 | — | 32 | 1 | no | — |
| 451 | C22×C4 | — | 2 | 1 | no | — |
| 452 | C22×C4 | — | 8 | 1 | no | — |
| 453 | C22×C4 | — | 32 | 1 | no | — |
| 454 | C22×C4 | #1619 | 1 | 1 | yes | characteristic |
| 455 | Q16 | — | 2 | 2 | no | — |
| 456 | Q16 | — | 4 | 1 | no | — |
| 457 | Q16 | — | 16 | 1 | no | — |
| 458 | Q16 | — | 16 | 1 | no | — |
| 459 | Q16 | — | 16 | 1 | no | — |
| 460 | Q16 | — | 16 | 1 | no | — |
| 461 | SD16 | — | 4 | 2 | no | — |
| 462 | SD16 | — | 4 | 2 | no | — |
| 463 | SD16 | — | 32 | 1 | no | — |
| 464 | SD16 | — | 32 | 1 | no | — |
| 465 | SD16 | — | 32 | 1 | no | — |
| 466 | SD16 | — | 32 | 1 | no | — |
| 467 | D8 | — | 2 | 2 | no | — |
| 468 | D8 | — | 4 | 1 | no | — |
| 469 | D8 | — | 16 | 8 | no | — |
| 470 | D8 | — | 16 | 1 | no | — |
| 471 | D8 | — | 16 | 1 | no | — |
| 472 | D8 | — | 16 | 1 | no | — |
| 473 | D8 | — | 16 | 1 | no | — |
| 474 | M16 | — | 4 | 2 | no | — |
| 475 | M16 | — | 4 | 2 | no | — |
| 476 | M16 | — | 8 | 1 | no | — |
| 477 | M16 | — | 8 | 1 | no | — |
| 478 | M16 | — | 8 | 2 | no | — |
| 479 | M16 | — | 8 | 2 | no | — |
| 480 | M16 | — | 16 | 2 | no | — |
| 481 | M16 | — | 16 | 2 | no | — |
| 482 | M16 | — | 32 | 4 | no | — |
| 483 | C2×C8 | — | 2 | 2 | no | — |
| 484 | C2×C8 | — | 2 | 2 | no | — |
| 485 | C2×C8 | — | 4 | 4 | no | — |
| 486 | C2×C8 | — | 8 | 1 | no | — |
| 487 | C2×C8 | — | 8 | 1 | no | — |
| 488 | C2×C8 | — | 8 | 2 | no | — |
| 489 | C2×C8 | — | 8 | 2 | no | — |
| 490 | C2×C8 | — | 16 | 2 | no | — |
| 491 | C2×C8 | — | 32 | 4 | no | — |
| 492 | C2×C8 | #1625 | 1 | 1 | yes | characteristic |
| 493 | C2×C8 | #1627 | 1 | 1 | yes | characteristic |
| 494 | C2×C8 | #1874 | 1 | 1 | yes | characteristic |
| 495 | C2×C8 | #1879 | 1 | 1 | yes | characteristic |
| 496 | C2×C8 | #2184 | 1 | 1 | yes | characteristic |
| 497 | C2×C8 | #2184 | 1 | 1 | yes | characteristic |
| 498 | C2×C8 | #2185 | 1 | 1 | yes | characteristic |
| 499 | C2×C8 | #2186 | 1 | 1 | yes | characteristic |
| 500 | C2×C8 | #2192 | 1 | 1 | yes | characteristic |
| 501 | C2×C8 | #2192 | 1 | 1 | yes | characteristic |
| 502 | C2×C8 | #2193 | 1 | 1 | yes | characteristic |
| 503 | C2×C8 | #2193 | 1 | 1 | yes | characteristic |
| 504 | C4⋊C4 | — | 8 | 1 | no | — |
| 505 | C4⋊C4 | — | 16 | 2 | no | — |
| 506 | C22⋊C4 | — | 8 | 1 | no | — |
| 507 | C22⋊C4 | — | 32 | 2 | no | — |
| 508 | C42 | — | 2 | 1 | no | — |
| 509 | C42 | — | 8 | 1 | no | — |
| 510 | C42 | #1622 | 1 | 1 | yes | characteristic |
| 511 | C42 | #1883 | 1 | 1 | yes | characteristic |
| 512 | C16 | — | 2 | 1 | no | — |
| 513 | C16 | — | 2 | 1 | no | — |
| 514 | C16 | — | 2 | 1 | no | — |
| 515 | C16 | — | 2 | 1 | no | — |
| 516 | C16 | — | 8 | 4 | no | — |
| 517 | C16 | — | 8 | 2 | no | — |
| 518 | C16 | — | 16 | 1 | no | — |
| 519 | C16 | C2×#357 | 1 | 1 | yes | characteristic |
| 520 | C16 | #2139 | 1 | 1 | yes | characteristic |
| 521 | C16 | C4×D16 | 1 | 1 | yes | characteristic |
| 522 | C16 | #2177 | 1 | 1 | yes | characteristic |
| 523 | C16 | #2206 | 1 | 1 | yes | characteristic |
| 524 | C16 | #2210 | 1 | 1 | yes | characteristic |
| 525 | C16 | #2232 | 1 | 1 | yes | characteristic |
| 526 | C16 | #2233 | 1 | 1 | yes | characteristic |
| 527 | C23 | — | 8 | 1 | no | — |
| 528 | C23 | — | 32 | 1 | no | — |
| 529 | C23 | #12311 | 1 | 1 | yes | characteristic |
| 530 | Q8 | — | 4 | 2 | no | — |
| 531 | Q8 | — | 8 | 1 | no | — |
| 532 | Q8 | — | 32 | 1 | no | — |
| 533 | Q8 | — | 32 | 1 | no | — |
| 534 | D4 | — | 4 | 2 | no | — |
| 535 | D4 | — | 8 | 2 | no | — |
| 536 | D4 | — | 8 | 2 | no | — |
| 537 | D4 | — | 8 | 1 | no | — |
| 538 | D4 | — | 32 | 4 | no | — |
| 539 | D4 | — | 32 | 1 | no | — |
| 540 | D4 | — | 32 | 1 | no | — |
| 541 | D4 | — | 64 | 1 | no | — |
| 542 | D4 | — | 64 | 1 | no | — |
| 543 | C2×C4 | — | 2 | 1 | no | — |
| 544 | C2×C4 | — | 2 | 1 | no | — |
| 545 | C2×C4 | — | 4 | 2 | no | — |
| 546 | C2×C4 | — | 8 | 1 | no | — |
| 547 | C2×C4 | — | 8 | 2 | no | — |
| 548 | C2×C4 | — | 8 | 2 | no | — |
| 549 | C2×C4 | — | 16 | 1 | no | — |
| 550 | C2×C4 | — | 32 | 1 | no | — |
| 551 | C2×C4 | — | 64 | 1 | no | — |
| 552 | C2×C4 | — | 64 | 1 | no | — |
| 553 | C2×C4 | #8977 | 1 | 1 | yes | characteristic |
| 554 | C2×C4 | #12310 | 1 | 1 | yes | characteristic |
| 555 | C2×C4 | #12316 | 1 | 1 | yes | characteristic |
| 556 | C2×C4 | #12316 | 1 | 1 | yes | characteristic |
| 557 | C2×C4 | #12318 | 1 | 1 | yes | characteristic |
| 558 | C2×C4 | #12319 | 1 | 1 | yes | characteristic |
| 559 | C8 | — | 2 | 4 | no | — |
| 560 | C8 | — | 4 | 2 | no | — |
| 561 | C8 | — | 8 | 2 | no | — |
| 562 | C8 | — | 8 | 2 | no | — |
| 563 | C8 | — | 32 | 2 | no | — |
| 564 | C8 | #12340 | 1 | 1 | yes | characteristic |
| 565 | C8 | #12342 | 1 | 1 | yes | characteristic |
| 566 | C8 | #12352 | 1 | 1 | yes | characteristic |
| 567 | C8 | #12355 | 1 | 1 | yes | characteristic |
| 568 | C8 | #12991 | 1 | 1 | yes | characteristic |
| 569 | C8 | #12996 | 1 | 1 | yes | characteristic |
| 570 | C8 | #13012 | 1 | 1 | yes | characteristic |
| 571 | C8 | #13022 | 1 | 1 | yes | characteristic |
| 572 | C22 | — | 4 | 1 | no | — |
| 573 | C22 | — | 8 | 2 | no | — |
| 574 | C22 | — | 32 | 1 | no | — |
| 575 | C22 | — | 64 | 2 | no | — |
| 576 | C22 | — | 64 | 1 | no | — |
| 577 | C22 | #123281 | 1 | 1 | yes | characteristic |
| 578 | C22 | #123283 | 1 | 1 | yes | characteristic |
| 579 | C22 | #136865 | 1 | 1 | yes | characteristic |
| 580 | C4 | — | 2 | 2 | no | — |
| 581 | C4 | — | 4 | 1 | no | — |
| 582 | C4 | — | 8 | 2 | no | — |
| 583 | C4 | — | 32 | 1 | no | — |
| 584 | C4 | — | 64 | 1 | no | — |
| 585 | C4 | #123275 | 1 | 1 | yes | characteristic |
| 586 | C4 | #123278 | 1 | 1 | yes | characteristic |
| 587 | C4 | #136878 | 1 | 1 | yes | characteristic |
| 588 | C4 | #136893 | 1 | 1 | yes | characteristic |
| 589 | C2 | — | 2 | 1 | no | — |
| 590 | C2 | — | 2 | 1 | no | — |
| 591 | C2 | — | 2 | 1 | no | — |
| 592 | C2 | — | 16 | 2 | no | — |
| 593 | C2 | — | 128 | 1 | no | — |
| 594 | C2 | #72225188 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #123275 |
| commutator | C8×C16 | C22×C4 |
| Frattini, cosocle | C2×C8×C16 | C23 |
| socle | C2 | #72225188 |
| prime radical | #72225339 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225599 | C2 | semidirect |
| 2. #72225401 | C2 | semidirect |
| 3. #72225344 | C2 | semidirect |
| 5. #72216535 | C2 | semidirect |
| 6. C2×#93752 | C2 | semidirect |
| 7. #72216251 | C2 | semidirect |
| 15. #151635 | C4 | semidirect |
| 16. #151634 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225599 | 2 |
| #72225401 | 2 |
| #72225344 | 2 |
| #72225339 | 2 |
| #72216535 | 2 |
| C2×#93752 | 2 |
| #72216251 | 2 |