Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
2008 conjugacy classes of subgroups.
The subgroup lattice has 631 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72225586 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72225585 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72225584 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72225579 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225394 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72225339 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#93751 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72216236 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72214187 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #7623661 | — | 2 | 2 | no | — |
| 11 | #512928 | — | 2 | 2 | no | — |
| 12 | #492533 | C22 | 1 | 2 | yes | — |
| 13 | #492532 | C22 | 1 | 2 | yes | — |
| 14 | #492531 | — | 2 | 2 | no | — |
| 15 | #492530 | — | 2 | 4 | no | — |
| 16 | #491485 | — | 2 | 2 | no | — |
| 17 | #491465 | C22 | 1 | 1 | yes | characteristic |
| 18 | #491465 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #490484 | — | 2 | 2 | no | — |
| 20 | #488869 | — | 2 | 2 | no | — |
| 21 | C2×#12046 | C22 | 1 | 2 | yes | — |
| 22 | #151636 | — | 2 | 4 | no | — |
| 23 | #151635 | C22 | 1 | 4 | yes | complemented |
| 24 | #151634 | C22 | 1 | 4 | yes | complemented |
| 25 | C2×#7459 | C22 | 1 | 2 | yes | complemented |
| 26 | #150950 | — | 2 | 2 | no | — |
| 27 | #123406 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #123406 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #123405 | — | 2 | 2 | no | — |
| 30 | #123404 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #123403 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C2×C162 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #93867 | C22 | 1 | 2 | yes | complemented |
| 34 | #93866 | C22 | 1 | 2 | yes | complemented |
| 35 | #93751 | C22 | 1 | 4 | yes | complemented |
| 36 | #93751 | C22 | 1 | 4 | yes | complemented |
| 37 | #62635 | — | 4 | 2 | no | — |
| 38 | #61105 | — | 2 | 2 | no | — |
| 39 | #33981 | — | 4 | 2 | no | — |
| 40 | #33860 | — | 2 | 4 | no | — |
| 41 | #33859 | — | 4 | 4 | no | — |
| 42 | #33858 | — | 2 | 4 | no | — |
| 43 | #33857 | — | 4 | 4 | no | — |
| 44 | #33856 | — | 2 | 8 | no | — |
| 45 | #33733 | — | 4 | 4 | no | — |
| 46 | #33713 | — | 2 | 2 | no | — |
| 47 | #33713 | — | 2 | 2 | no | — |
| 48 | #33617 | — | 4 | 2 | no | — |
| 49 | #33594 | — | 2 | 4 | no | — |
| 50 | #33538 | — | 4 | 4 | no | — |
| 51 | C2×#2178 | D4 | 1 | 2 | yes | — |
| 52 | C2×#2170 | — | 2 | 2 | no | — |
| 53 | #19603 | — | 2 | 1 | no | — |
| 54 | #19603 | D4 | 1 | 2 | yes | — |
| 55 | #13693 | — | 2 | 4 | no | — |
| 56 | #13692 | — | 2 | 4 | no | — |
| 57 | #13691 | — | 4 | 4 | no | — |
| 58 | C2×#1422 | — | 2 | 2 | no | — |
| 59 | #13625 | — | 4 | 2 | no | — |
| 60 | #12521 | — | 2 | 2 | no | — |
| 61 | #12518 | — | 2 | 2 | no | — |
| 62 | #12518 | — | 2 | 2 | no | — |
| 63 | #12517 | — | 2 | 1 | no | — |
| 64 | #12517 | D4 | 1 | 2 | yes | — |
| 65 | #12516 | C23 | 1 | 1 | yes | characteristic |
| 66 | #12516 | C23 | 1 | 1 | yes | characteristic |
| 67 | #12515 | — | 2 | 2 | no | — |
| 68 | #12515 | C23 | 1 | 1 | yes | characteristic |
| 69 | #12515 | C23 | 1 | 1 | yes | characteristic |
| 70 | #12509 | — | 2 | 2 | no | — |
| 71 | #12509 | — | 2 | 2 | no | — |
| 72 | #12503 | — | 4 | 4 | no | — |
| 73 | #12438 | — | 2 | 8 | no | — |
| 74 | #12437 | — | 2 | 4 | no | — |
| 75 | #12436 | — | 2 | 4 | no | — |
| 76 | #12313 | — | 2 | 4 | no | — |
| 77 | #12312 | — | 2 | 4 | no | — |
| 78 | #12311 | — | 2 | 4 | no | — |
| 79 | #12310 | — | 2 | 4 | no | — |
| 80 | #12046 | — | 2 | 2 | no | — |
| 81 | #12046 | — | 2 | 2 | no | — |
| 82 | #12046 | D4 | 1 | 4 | yes | — |
| 83 | #12046 | C23 | 1 | 4 | yes | — |
| 84 | C2×#1373 | D4 | 1 | 2 | yes | — |
| 85 | #11920 | — | 2 | 2 | no | — |
| 86 | C2×#1335 | — | 2 | 2 | no | — |
| 87 | C2×C8×C16 | — | 2 | 1 | no | — |
| 88 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 89 | #7459 | — | 2 | 2 | no | — |
| 90 | #7459 | C23 | 1 | 4 | yes | — |
| 91 | #7449 | — | 2 | 4 | no | — |
| 92 | #7448 | — | 2 | 4 | no | — |
| 93 | C162 | — | 2 | 1 | no | — |
| 94 | C162 | C23 | 1 | 1 | yes | characteristic |
| 95 | C162 | C23 | 1 | 1 | yes | characteristic |
| 96 | #3584 | — | 4 | 4 | no | — |
| 97 | #3417 | — | 4 | 4 | no | — |
| 98 | #3417 | — | 8 | 2 | no | — |
| 99 | #3416 | — | 4 | 8 | no | — |
| 100 | #3416 | — | 8 | 4 | no | — |
| 101 | #3415 | — | 4 | 4 | no | — |
| 102 | #3415 | — | 8 | 2 | no | — |
| 103 | #3414 | — | 4 | 4 | no | — |
| 104 | #3414 | — | 8 | 4 | no | — |
| 105 | C2×#508 | — | 4 | 2 | no | — |
| 106 | C2×#508 | — | 4 | 2 | no | — |
| 107 | C2×#508 | — | 4 | 2 | no | — |
| 108 | C2×#508 | — | 4 | 2 | no | — |
| 109 | C2×#508 | — | 8 | 4 | no | — |
| 110 | C2×#508 | D8 | 1 | 2 | yes | — |
| 111 | C2×#504 | — | 4 | 2 | no | — |
| 112 | #3293 | — | 2 | 4 | no | — |
| 113 | #3292 | — | 2 | 4 | no | — |
| 114 | #3291 | — | 8 | 2 | no | — |
| 115 | #3290 | — | 4 | 8 | no | — |
| 116 | #3169 | — | 4 | 2 | no | — |
| 117 | #3169 | — | 4 | 2 | no | — |
| 118 | #3147 | — | 2 | 2 | no | — |
| 119 | #3147 | — | 4 | 1 | no | — |
| 120 | #3067 | — | 4 | 4 | no | — |
| 121 | #3018 | — | 8 | 2 | no | — |
| 122 | C2×#443 | — | 2 | 2 | no | — |
| 123 | #2264 | — | 4 | 4 | no | — |
| 124 | #2264 | — | 8 | 2 | no | — |
| 125 | #2263 | — | 4 | 4 | no | — |
| 126 | #2263 | — | 8 | 2 | no | — |
| 127 | #2262 | — | 8 | 4 | no | — |
| 128 | C2×M64 | — | 4 | 2 | no | — |
| 129 | #2252 | — | 4 | 4 | no | — |
| 130 | #2249 | — | 4 | 2 | no | — |
| 131 | #2249 | — | 4 | 2 | no | — |
| 132 | #2249 | — | 4 | 2 | no | — |
| 133 | #2249 | — | 4 | 2 | no | — |
| 134 | #2248 | — | 2 | 4 | no | — |
| 135 | #2248 | — | 4 | 2 | no | — |
| 136 | #2247 | — | 2 | 2 | no | — |
| 137 | #2247 | — | 2 | 2 | no | — |
| 138 | #2246 | — | 2 | 2 | no | — |
| 139 | #2246 | — | 2 | 2 | no | — |
| 140 | #2246 | — | 4 | 4 | no | — |
| 141 | #2240 | — | 4 | 4 | no | — |
| 142 | #2240 | — | 4 | 4 | no | — |
| 143 | #2223 | — | 4 | 8 | no | — |
| 144 | #2222 | — | 4 | 4 | no | — |
| 145 | #2221 | — | 4 | 4 | no | — |
| 146 | #2215 | — | 8 | 8 | no | — |
| 147 | #2214 | — | 2 | 8 | no | — |
| 148 | #2213 | — | 2 | 8 | no | — |
| 149 | #2212 | — | 4 | 8 | no | — |
| 150 | #2195 | — | 4 | 8 | no | — |
| 151 | #2194 | — | 4 | 8 | no | — |
| 152 | #2193 | — | 4 | 8 | no | — |
| 153 | #2192 | — | 4 | 8 | no | — |
| 154 | #2178 | — | 2 | 2 | no | — |
| 155 | #2178 | — | 2 | 2 | no | — |
| 156 | #2178 | D8 | 1 | 4 | yes | — |
| 157 | #2178 | C2×D4 | 1 | 4 | yes | — |
| 158 | C4×D16 | — | 8 | 8 | no | — |
| 159 | #2170 | — | 2 | 4 | no | — |
| 160 | #2170 | — | 2 | 4 | no | — |
| 161 | #2170 | — | 4 | 2 | no | — |
| 162 | #2170 | — | 4 | 2 | no | — |
| 163 | C2×#368 | D8 | 1 | 2 | yes | — |
| 164 | C2×#364 | — | 2 | 2 | no | — |
| 165 | #2148 | — | 4 | 4 | no | — |
| 166 | C2×#359 | — | 2 | 2 | no | — |
| 167 | C2×#350 | — | 4 | 2 | no | — |
| 168 | C2×C4×C16 | — | 2 | 2 | no | — |
| 169 | C2×C4×C16 | C2×D4 | 1 | 2 | yes | — |
| 170 | #1713 | — | 2 | 1 | no | — |
| 171 | #1713 | C2×D4 | 1 | 2 | yes | — |
| 172 | #1712 | — | 2 | 1 | no | — |
| 173 | #1712 | C2×D4 | 1 | 2 | yes | — |
| 174 | #1709 | — | 2 | 2 | no | — |
| 175 | #1709 | — | 4 | 1 | no | — |
| 176 | #1706 | — | 4 | 2 | no | — |
| 177 | #1706 | — | 4 | 2 | no | — |
| 178 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | #1422 | — | 2 | 4 | no | — |
| 180 | #1422 | — | 4 | 2 | no | — |
| 181 | #1420 | — | 4 | 4 | no | — |
| 182 | #1419 | — | 4 | 4 | no | — |
| 183 | #1373 | — | 2 | 2 | no | — |
| 184 | #1373 | C2×D4 | 1 | 4 | yes | — |
| 185 | #1358 | — | 2 | 4 | no | — |
| 186 | #1357 | — | 2 | 4 | no | — |
| 187 | #1335 | — | 2 | 4 | no | — |
| 188 | #1335 | — | 2 | 4 | no | — |
| 189 | C8×C16 | — | 2 | 2 | no | — |
| 190 | C8×C16 | — | 2 | 1 | no | — |
| 191 | C8×C16 | — | 2 | 1 | no | — |
| 192 | C8×C16 | C2×D4 | 1 | 2 | yes | — |
| 193 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C8×C16 | C24 | 1 | 1 | yes | characteristic |
| 195 | #585 | — | 8 | 2 | no | — |
| 196 | #578 | — | 4 | 8 | no | — |
| 197 | #578 | — | 8 | 4 | no | — |
| 198 | #577 | — | 8 | 8 | no | — |
| 199 | #577 | — | 16 | 4 | no | — |
| 200 | #576 | — | 4 | 8 | no | — |
| 201 | #576 | — | 8 | 4 | no | — |
| 202 | #575 | — | 8 | 4 | no | — |
| 203 | #575 | — | 16 | 4 | no | — |
| 204 | C2×#135 | — | 2 | 2 | no | — |
| 205 | C2×#135 | — | 4 | 4 | no | — |
| 206 | C2×#135 | — | 8 | 8 | no | — |
| 207 | C2×#135 | — | 8 | 2 | no | — |
| 208 | C2×#131 | — | 4 | 2 | no | — |
| 209 | #532 | — | 4 | 2 | no | — |
| 210 | #532 | — | 8 | 1 | no | — |
| 211 | #510 | — | 4 | 8 | no | — |
| 212 | #510 | — | 8 | 8 | no | — |
| 213 | #510 | — | 8 | 8 | no | — |
| 214 | #510 | — | 8 | 4 | no | — |
| 215 | #509 | — | 4 | 8 | no | — |
| 216 | #509 | — | 8 | 8 | no | — |
| 217 | #509 | — | 8 | 8 | no | — |
| 218 | #509 | — | 8 | 4 | no | — |
| 219 | #508 | — | 2 | 2 | no | — |
| 220 | #508 | — | 2 | 2 | no | — |
| 221 | #508 | — | 8 | 8 | no | — |
| 222 | #508 | — | 8 | 8 | no | — |
| 223 | #508 | — | 8 | 4 | no | — |
| 224 | #508 | — | 8 | 4 | no | — |
| 225 | #508 | — | 8 | 2 | no | — |
| 226 | #508 | — | 8 | 2 | no | — |
| 227 | #508 | — | 8 | 2 | no | — |
| 228 | #508 | — | 8 | 2 | no | — |
| 229 | #508 | — | 8 | 2 | no | — |
| 230 | #508 | — | 8 | 2 | no | — |
| 231 | #508 | — | 8 | 2 | no | — |
| 232 | #508 | — | 8 | 2 | no | — |
| 233 | #508 | — | 16 | 2 | no | — |
| 234 | #508 | — | 16 | 2 | no | — |
| 235 | #508 | — | 16 | 2 | no | — |
| 236 | #508 | — | 16 | 2 | no | — |
| 237 | #508 | D16 | 1 | 4 | yes | complemented |
| 238 | #508 | C2×D8 | 1 | 4 | yes | — |
| 239 | C2×Q32 | — | 4 | 2 | no | — |
| 240 | C2×Q32 | — | 4 | 2 | no | — |
| 241 | C2×Q32 | — | 4 | 2 | no | — |
| 242 | C2×Q32 | — | 4 | 2 | no | — |
| 243 | C2×Q32 | — | 8 | 4 | no | — |
| 244 | C2×Q32 | D16 | 1 | 2 | yes | complemented |
| 245 | C2×SD32 | — | 2 | 2 | no | — |
| 246 | C2×SD32 | — | 4 | 4 | no | — |
| 247 | C2×SD32 | — | 4 | 4 | no | — |
| 248 | C2×SD32 | — | 8 | 8 | no | — |
| 249 | C2×SD32 | — | 8 | 2 | no | — |
| 250 | C2×SD32 | — | 8 | 2 | no | — |
| 251 | C2×D16 | — | 4 | 2 | no | — |
| 252 | C2×D16 | — | 4 | 2 | no | — |
| 253 | C2×D16 | — | 4 | 2 | no | — |
| 254 | C2×D16 | — | 4 | 2 | no | — |
| 255 | C2×D16 | — | 8 | 8 | no | — |
| 256 | C2×D16 | — | 8 | 4 | no | — |
| 257 | C2×D16 | D16 | 1 | 2 | yes | complemented |
| 258 | #504 | — | 4 | 4 | no | — |
| 259 | #504 | — | 4 | 4 | no | — |
| 260 | #504 | — | 8 | 2 | no | — |
| 261 | #504 | — | 8 | 2 | no | — |
| 262 | C2×M32 | — | 4 | 2 | no | — |
| 263 | C2×M32 | — | 8 | 2 | no | — |
| 264 | C22×C16 | — | 2 | 4 | no | — |
| 265 | C22×C16 | — | 8 | 2 | no | — |
| 266 | C22×C16 | C2×D8 | 1 | 2 | yes | — |
| 267 | C22×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 268 | #500 | — | 4 | 2 | no | — |
| 269 | #500 | — | 4 | 2 | no | — |
| 270 | #495 | — | 4 | 4 | no | — |
| 271 | #495 | — | 8 | 2 | no | — |
| 272 | #494 | — | 2 | 2 | no | — |
| 273 | #494 | — | 4 | 1 | no | — |
| 274 | #493 | — | 2 | 2 | no | — |
| 275 | #493 | — | 4 | 2 | no | — |
| 276 | #493 | — | 4 | 2 | no | — |
| 277 | #493 | — | 4 | 1 | no | — |
| 278 | #492 | — | 4 | 2 | no | — |
| 279 | #492 | — | 8 | 1 | no | — |
| 280 | #486 | — | 8 | 2 | no | — |
| 281 | #486 | — | 8 | 2 | no | — |
| 282 | #473 | — | 4 | 8 | no | — |
| 283 | #472 | — | 4 | 8 | no | — |
| 284 | #471 | — | 8 | 8 | no | — |
| 285 | #466 | — | 8 | 4 | no | — |
| 286 | #466 | — | 8 | 4 | no | — |
| 287 | #456 | — | 8 | 4 | no | — |
| 288 | #455 | — | 8 | 4 | no | — |
| 289 | #454 | — | 8 | 4 | no | — |
| 290 | #453 | — | 8 | 4 | no | — |
| 291 | #443 | — | 2 | 4 | no | — |
| 292 | #443 | — | 2 | 4 | no | — |
| 293 | #443 | — | 4 | 2 | no | — |
| 294 | #443 | — | 4 | 2 | no | — |
| 295 | C4×D8 | — | 8 | 4 | no | — |
| 296 | C4×D8 | — | 8 | 4 | no | — |
| 297 | C2×#108 | — | 2 | 2 | no | — |
| 298 | C2×#104 | — | 4 | 2 | no | — |
| 299 | #413 | — | 8 | 2 | no | — |
| 300 | C2×C4×C8 | — | 2 | 1 | no | — |
| 301 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 302 | Q64 | — | 8 | 4 | no | — |
| 303 | SD64 | — | 8 | 4 | no | — |
| 304 | SD64 | — | 8 | 4 | no | — |
| 305 | D32 | — | 8 | 4 | no | — |
| 306 | M64 | — | 4 | 4 | no | — |
| 307 | M64 | — | 8 | 2 | no | — |
| 308 | C2×C32 | — | 8 | 2 | no | — |
| 309 | #368 | — | 2 | 2 | no | — |
| 310 | #368 | C2×D8 | 1 | 4 | yes | — |
| 311 | #366 | — | 8 | 8 | no | — |
| 312 | #364 | — | 2 | 4 | no | — |
| 313 | #364 | — | 4 | 2 | no | — |
| 314 | #362 | — | 4 | 8 | no | — |
| 315 | #361 | — | 4 | 8 | no | — |
| 316 | #359 | — | 2 | 4 | no | — |
| 317 | #359 | — | 2 | 4 | no | — |
| 318 | #357 | — | 8 | 8 | no | — |
| 319 | #357 | — | 8 | 8 | no | — |
| 320 | #350 | — | 4 | 4 | no | — |
| 321 | #350 | — | 4 | 4 | no | — |
| 322 | C4×C16 | — | 2 | 2 | no | — |
| 323 | C4×C16 | — | 2 | 2 | no | — |
| 324 | C4×C16 | — | 2 | 4 | no | — |
| 325 | C4×C16 | #120 | 1 | 2 | yes | — |
| 326 | C4×C16 | C2×D8 | 1 | 2 | yes | — |
| 327 | C4×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 328 | C4×C16 | C22×D4 | 1 | 2 | yes | — |
| 329 | C82 | — | 2 | 1 | no | — |
| 330 | C82 | #120 | 1 | 1 | yes | characteristic |
| 331 | C82 | C22×D4 | 1 | 1 | yes | characteristic |
| 332 | 2−1+4 | — | 8 | 4 | no | — |
| 333 | 2−1+4 | — | 16 | 4 | no | — |
| 334 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 335 | H(5,𝔽2) | — | 16 | 4 | no | — |
| 336 | H(5,𝔽2) | — | 32 | 2 | no | — |
| 337 | C2×#41 | — | 4 | 2 | no | — |
| 338 | C2×#41 | — | 8 | 2 | no | — |
| 339 | C2×#41 | — | 16 | 8 | no | — |
| 340 | C2×#41 | — | 16 | 1 | no | — |
| 341 | C2×#41 | — | 32 | 2 | no | — |
| 342 | #137 | — | 8 | 8 | no | — |
| 343 | #137 | — | 16 | 8 | no | — |
| 344 | #137 | — | 16 | 8 | no | — |
| 345 | #137 | — | 16 | 4 | no | — |
| 346 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 347 | AGL(1,ℤ/8) | — | 16 | 8 | no | — |
| 348 | AGL(1,ℤ/8) | — | 16 | 8 | no | — |
| 349 | AGL(1,ℤ/8) | — | 16 | 4 | no | — |
| 350 | #135 | — | 2 | 4 | no | — |
| 351 | #135 | — | 2 | 4 | no | — |
| 352 | #135 | — | 4 | 2 | no | — |
| 353 | #135 | — | 4 | 2 | no | — |
| 354 | #135 | — | 8 | 8 | no | — |
| 355 | #135 | — | 8 | 8 | no | — |
| 356 | #135 | — | 8 | 4 | no | — |
| 357 | #135 | — | 8 | 4 | no | — |
| 358 | #135 | — | 8 | 4 | no | — |
| 359 | #135 | — | 8 | 4 | no | — |
| 360 | #135 | — | 16 | 8 | no | — |
| 361 | #135 | — | 16 | 8 | no | — |
| 362 | #135 | — | 16 | 2 | no | — |
| 363 | #135 | — | 16 | 2 | no | — |
| 364 | #135 | — | 16 | 2 | no | — |
| 365 | #135 | — | 16 | 2 | no | — |
| 366 | C2×Q16 | — | 2 | 2 | no | — |
| 367 | C2×Q16 | — | 4 | 4 | no | — |
| 368 | C2×Q16 | — | 8 | 8 | no | — |
| 369 | C2×Q16 | — | 8 | 2 | no | — |
| 370 | C2×SD16 | — | 4 | 2 | no | — |
| 371 | C2×SD16 | — | 8 | 4 | no | — |
| 372 | C2×SD16 | — | 16 | 8 | no | — |
| 373 | C2×SD16 | — | 16 | 2 | no | — |
| 374 | C2×D8 | — | 2 | 2 | no | — |
| 375 | C2×D8 | — | 4 | 4 | no | — |
| 376 | C2×D8 | — | 8 | 4 | no | — |
| 377 | C2×D8 | — | 8 | 4 | no | — |
| 378 | C2×D8 | — | 8 | 8 | no | — |
| 379 | C2×D8 | — | 8 | 2 | no | — |
| 380 | #131 | — | 4 | 4 | no | — |
| 381 | #131 | — | 4 | 4 | no | — |
| 382 | #131 | — | 8 | 2 | no | — |
| 383 | #131 | — | 8 | 2 | no | — |
| 384 | C2×M16 | — | 4 | 2 | no | — |
| 385 | C2×M16 | — | 8 | 2 | no | — |
| 386 | C22×C8 | — | 2 | 2 | no | — |
| 387 | C22×C8 | — | 8 | 2 | no | — |
| 388 | C22×C8 | #447 | 1 | 2 | yes | — |
| 389 | C4⋊Q8 | — | 4 | 2 | no | — |
| 390 | C4⋊Q8 | — | 8 | 1 | no | — |
| 391 | #127 | — | 4 | 2 | no | — |
| 392 | #127 | — | 8 | 1 | no | — |
| 393 | #124 | — | 8 | 2 | no | — |
| 394 | #124 | — | 16 | 1 | no | — |
| 395 | #121 | — | 16 | 2 | no | — |
| 396 | #121 | — | 16 | 2 | no | — |
| 397 | C4×D4 | — | 16 | 2 | no | — |
| 398 | C4×D4 | — | 16 | 2 | no | — |
| 399 | C2×C42 | #453 | 1 | 1 | yes | characteristic |
| 400 | Q32 | — | 2 | 2 | no | — |
| 401 | Q32 | — | 8 | 8 | no | — |
| 402 | Q32 | — | 8 | 2 | no | — |
| 403 | Q32 | — | 8 | 2 | no | — |
| 404 | Q32 | — | 8 | 2 | no | — |
| 405 | Q32 | — | 8 | 2 | no | — |
| 406 | Q32 | — | 16 | 2 | no | — |
| 407 | Q32 | — | 16 | 2 | no | — |
| 408 | Q32 | C2×D16 | 1 | 4 | yes | — |
| 409 | SD32 | — | 2 | 4 | no | — |
| 410 | SD32 | — | 2 | 4 | no | — |
| 411 | SD32 | — | 8 | 8 | no | — |
| 412 | SD32 | — | 8 | 8 | no | — |
| 413 | SD32 | — | 8 | 4 | no | — |
| 414 | SD32 | — | 8 | 4 | no | — |
| 415 | SD32 | — | 16 | 4 | no | — |
| 416 | SD32 | — | 16 | 4 | no | — |
| 417 | SD32 | — | 16 | 2 | no | — |
| 418 | SD32 | — | 16 | 2 | no | — |
| 419 | D16 | — | 2 | 2 | no | — |
| 420 | D16 | — | 8 | 8 | no | — |
| 421 | D16 | — | 8 | 2 | no | — |
| 422 | D16 | — | 8 | 2 | no | — |
| 423 | D16 | — | 8 | 2 | no | — |
| 424 | D16 | — | 8 | 2 | no | — |
| 425 | D16 | — | 16 | 2 | no | — |
| 426 | D16 | — | 16 | 2 | no | — |
| 427 | D16 | — | 16 | 16 | no | — |
| 428 | D16 | C2×D16 | 1 | 4 | yes | — |
| 429 | M32 | — | 4 | 4 | no | — |
| 430 | M32 | — | 8 | 2 | no | — |
| 431 | M32 | — | 8 | 4 | no | — |
| 432 | M32 | — | 8 | 4 | no | — |
| 433 | C2×C16 | — | 2 | 4 | no | — |
| 434 | C2×C16 | — | 2 | 2 | no | — |
| 435 | C2×C16 | — | 2 | 2 | no | — |
| 436 | C2×C16 | — | 2 | 4 | no | — |
| 437 | C2×C16 | — | 4 | 8 | no | — |
| 438 | C2×C16 | — | 8 | 2 | no | — |
| 439 | C2×C16 | — | 8 | 4 | no | — |
| 440 | C2×C16 | — | 8 | 4 | no | — |
| 441 | C2×C16 | #447 | 1 | 2 | yes | — |
| 442 | C2×C16 | #447 | 1 | 2 | yes | — |
| 443 | C2×C16 | C2×D16 | 1 | 2 | yes | — |
| 444 | C2×C16 | C2×D16 | 1 | 2 | yes | — |
| 445 | C2×C16 | #509 | 1 | 2 | yes | — |
| 446 | C2×C16 | #509 | 1 | 2 | yes | — |
| 447 | C2×C16 | C22×D8 | 1 | 2 | yes | — |
| 448 | C2×C16 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 449 | #108 | — | 2 | 4 | no | — |
| 450 | #108 | — | 4 | 2 | no | — |
| 451 | #107 | — | 8 | 4 | no | — |
| 452 | #107 | — | 8 | 4 | no | — |
| 453 | #104 | — | 4 | 4 | no | — |
| 454 | #104 | — | 4 | 4 | no | — |
| 455 | #102 | — | 16 | 4 | no | — |
| 456 | #102 | — | 16 | 4 | no | — |
| 457 | #101 | — | 8 | 4 | no | — |
| 458 | #100 | — | 8 | 4 | no | — |
| 459 | C4×C8 | — | 2 | 2 | no | — |
| 460 | C4×C8 | — | 2 | 1 | no | — |
| 461 | C4×C8 | — | 2 | 1 | no | — |
| 462 | C4×C8 | #447 | 1 | 2 | yes | — |
| 463 | C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 464 | C4×C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 465 | C32 | — | 8 | 4 | no | — |
| 466 | #41 | — | 4 | 4 | no | — |
| 467 | #41 | — | 4 | 4 | no | — |
| 468 | #41 | — | 8 | 2 | no | — |
| 469 | #41 | — | 8 | 2 | no | — |
| 470 | #41 | — | 16 | 8 | no | — |
| 471 | #41 | — | 16 | 8 | no | — |
| 472 | #41 | — | 16 | 4 | no | — |
| 473 | #41 | — | 16 | 4 | no | — |
| 474 | #41 | — | 32 | 4 | no | — |
| 475 | #41 | — | 32 | 8 | no | — |
| 476 | #41 | — | 32 | 4 | no | — |
| 477 | #41 | — | 32 | 4 | no | — |
| 478 | #41 | — | 32 | 2 | no | — |
| 479 | #41 | — | 32 | 2 | no | — |
| 480 | C2×Q8 | — | 4 | 2 | no | — |
| 481 | C2×Q8 | — | 8 | 2 | no | — |
| 482 | C2×Q8 | — | 16 | 8 | no | — |
| 483 | C2×Q8 | — | 16 | 1 | no | — |
| 484 | C2×Q8 | — | 32 | 2 | no | — |
| 485 | C2×D4 | — | 4 | 2 | no | — |
| 486 | C2×D4 | — | 8 | 2 | no | — |
| 487 | C2×D4 | — | 8 | 2 | no | — |
| 488 | C2×D4 | — | 16 | 2 | no | — |
| 489 | C2×D4 | — | 16 | 2 | no | — |
| 490 | C2×D4 | — | 16 | 8 | no | — |
| 491 | C2×D4 | — | 16 | 2 | no | — |
| 492 | C2×D4 | — | 16 | 1 | no | — |
| 493 | C2×D4 | — | 32 | 4 | no | — |
| 494 | C2×D4 | — | 32 | 2 | no | — |
| 495 | C2×D4 | — | 32 | 8 | no | — |
| 496 | C2×D4 | — | 32 | 1 | no | — |
| 497 | C22×C4 | — | 2 | 1 | no | — |
| 498 | C22×C4 | — | 8 | 2 | no | — |
| 499 | C22×C4 | — | 16 | 2 | no | — |
| 500 | C22×C4 | — | 32 | 4 | no | — |
| 501 | C22×C4 | — | 32 | 1 | no | — |
| 502 | C22×C4 | #1619 | 1 | 1 | yes | characteristic |
| 503 | Q16 | — | 2 | 4 | no | — |
| 504 | Q16 | — | 4 | 2 | no | — |
| 505 | Q16 | — | 8 | 4 | no | — |
| 506 | Q16 | — | 8 | 4 | no | — |
| 507 | Q16 | — | 16 | 8 | no | — |
| 508 | Q16 | — | 16 | 2 | no | — |
| 509 | Q16 | — | 16 | 2 | no | — |
| 510 | SD16 | — | 4 | 4 | no | — |
| 511 | SD16 | — | 4 | 4 | no | — |
| 512 | SD16 | — | 16 | 8 | no | — |
| 513 | SD16 | — | 16 | 8 | no | — |
| 514 | SD16 | — | 16 | 4 | no | — |
| 515 | SD16 | — | 16 | 4 | no | — |
| 516 | SD16 | — | 32 | 2 | no | — |
| 517 | SD16 | — | 32 | 2 | no | — |
| 518 | D8 | — | 2 | 4 | no | — |
| 519 | D8 | — | 4 | 2 | no | — |
| 520 | D8 | — | 8 | 4 | no | — |
| 521 | D8 | — | 8 | 4 | no | — |
| 522 | D8 | — | 16 | 8 | no | — |
| 523 | D8 | — | 16 | 8 | no | — |
| 524 | D8 | — | 16 | 8 | no | — |
| 525 | D8 | — | 16 | 2 | no | — |
| 526 | D8 | — | 16 | 2 | no | — |
| 527 | M16 | — | 4 | 4 | no | — |
| 528 | M16 | — | 8 | 2 | no | — |
| 529 | M16 | — | 8 | 4 | no | — |
| 530 | M16 | — | 8 | 4 | no | — |
| 531 | C2×C8 | — | 2 | 2 | no | — |
| 532 | C2×C8 | — | 2 | 2 | no | — |
| 533 | C2×C8 | — | 4 | 4 | no | — |
| 534 | C2×C8 | — | 8 | 2 | no | — |
| 535 | C2×C8 | — | 8 | 4 | no | — |
| 536 | C2×C8 | — | 8 | 4 | no | — |
| 537 | C2×C8 | #1619 | 1 | 2 | yes | — |
| 538 | C2×C8 | #2184 | 1 | 2 | yes | — |
| 539 | C2×C8 | #2184 | 1 | 2 | yes | — |
| 540 | C2×C8 | #2192 | 1 | 2 | yes | — |
| 541 | C2×C8 | #2192 | 1 | 2 | yes | — |
| 542 | C2×C8 | C2×#447 | 1 | 2 | yes | — |
| 543 | C4⋊C4 | — | 16 | 2 | no | — |
| 544 | C4⋊C4 | — | 16 | 2 | no | — |
| 545 | C22⋊C4 | — | 32 | 2 | no | — |
| 546 | C22⋊C4 | — | 32 | 2 | no | — |
| 547 | C42 | — | 2 | 1 | no | — |
| 548 | C42 | #1619 | 1 | 1 | yes | characteristic |
| 549 | C42 | C2×#453 | 1 | 1 | yes | characteristic |
| 550 | C16 | — | 2 | 8 | no | — |
| 551 | C16 | — | 2 | 2 | no | — |
| 552 | C16 | — | 2 | 2 | no | — |
| 553 | C16 | — | 4 | 4 | no | — |
| 554 | C16 | — | 8 | 4 | no | — |
| 555 | C16 | #2184 | 1 | 2 | yes | — |
| 556 | C16 | #2184 | 1 | 2 | yes | — |
| 557 | C16 | C22×D16 | 1 | 2 | yes | — |
| 558 | C16 | C2×#509 | 1 | 2 | yes | — |
| 559 | C23 | — | 8 | 2 | no | — |
| 560 | C23 | — | 16 | 2 | no | — |
| 561 | C23 | — | 32 | 4 | no | — |
| 562 | C23 | — | 32 | 1 | no | — |
| 563 | C23 | #12310 | 1 | 1 | yes | characteristic |
| 564 | Q8 | — | 4 | 4 | no | — |
| 565 | Q8 | — | 8 | 2 | no | — |
| 566 | Q8 | — | 16 | 4 | no | — |
| 567 | Q8 | — | 32 | 4 | no | — |
| 568 | Q8 | — | 32 | 2 | no | — |
| 569 | D4 | — | 4 | 4 | no | — |
| 570 | D4 | — | 8 | 4 | no | — |
| 571 | D4 | — | 8 | 4 | no | — |
| 572 | D4 | — | 8 | 2 | no | — |
| 573 | D4 | — | 16 | 4 | no | — |
| 574 | D4 | — | 32 | 4 | no | — |
| 575 | D4 | — | 32 | 4 | no | — |
| 576 | D4 | — | 32 | 8 | no | — |
| 577 | D4 | — | 32 | 4 | no | — |
| 578 | D4 | — | 32 | 4 | no | — |
| 579 | D4 | — | 32 | 2 | no | — |
| 580 | D4 | — | 64 | 2 | no | — |
| 581 | C2×C4 | — | 2 | 1 | no | — |
| 582 | C2×C4 | — | 2 | 1 | no | — |
| 583 | C2×C4 | — | 4 | 2 | no | — |
| 584 | C2×C4 | — | 8 | 2 | no | — |
| 585 | C2×C4 | — | 8 | 4 | no | — |
| 586 | C2×C4 | — | 8 | 4 | no | — |
| 587 | C2×C4 | — | 16 | 2 | no | — |
| 588 | C2×C4 | — | 32 | 4 | no | — |
| 589 | C2×C4 | — | 32 | 8 | no | — |
| 590 | C2×C4 | — | 32 | 2 | no | — |
| 591 | C2×C4 | — | 32 | 2 | no | — |
| 592 | C2×C4 | — | 32 | 1 | no | — |
| 593 | C2×C4 | — | 64 | 1 | no | — |
| 594 | C2×C4 | — | 64 | 1 | no | — |
| 595 | C2×C4 | #12310 | 1 | 1 | yes | characteristic |
| 596 | C2×C4 | #12316 | 1 | 2 | yes | — |
| 597 | C2×C4 | #12316 | 1 | 2 | yes | — |
| 598 | C2×C4 | C2×#1619 | 1 | 1 | yes | characteristic |
| 599 | C8 | — | 2 | 4 | no | — |
| 600 | C8 | — | 4 | 2 | no | — |
| 601 | C8 | — | 8 | 4 | no | — |
| 602 | C8 | #12316 | 1 | 2 | yes | — |
| 603 | C8 | #12316 | 1 | 2 | yes | — |
| 604 | C8 | C2×#2184 | 1 | 2 | yes | — |
| 605 | C8 | C2×#2192 | 1 | 2 | yes | — |
| 606 | C22 | — | 4 | 1 | no | — |
| 607 | C22 | — | 8 | 4 | no | — |
| 608 | C22 | — | 32 | 2 | no | — |
| 609 | C22 | — | 32 | 2 | no | — |
| 610 | C22 | — | 64 | 2 | no | — |
| 611 | C22 | — | 64 | 2 | no | — |
| 612 | C22 | — | 64 | 1 | no | — |
| 613 | C22 | — | 128 | 4 | no | — |
| 614 | C22 | #123275 | 1 | 2 | yes | — |
| 615 | C22 | C2×#12310 | 1 | 1 | yes | characteristic |
| 616 | C4 | — | 2 | 2 | no | — |
| 617 | C4 | — | 4 | 1 | no | — |
| 618 | C4 | — | 8 | 4 | no | — |
| 619 | C4 | — | 32 | 2 | no | — |
| 620 | C4 | — | 64 | 1 | no | — |
| 621 | C4 | #123275 | 1 | 1 | yes | characteristic |
| 622 | C4 | #123275 | 1 | 1 | yes | characteristic |
| 623 | C4 | C2×#12316 | 1 | 2 | yes | — |
| 624 | C2 | — | 2 | 1 | no | — |
| 625 | C2 | — | 2 | 2 | no | — |
| 626 | C2 | — | 16 | 4 | no | — |
| 627 | C2 | — | 64 | 2 | no | — |
| 628 | C2 | — | 128 | 1 | no | — |
| 629 | C2 | C2×#123275 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #123275 |
| commutator, Frattini, cosocle | C8×C16 | C24 |
| socle | C2 | C2×#123275 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ G | |
| LECS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225586 | C2 | semidirect |
| 2. #72225585 | C2 | semidirect |
| 3. #72225584 | C2 | semidirect |
| 4. #72225579 | C2 | semidirect |
| 5. #72225394 | C2 | semidirect |
| 6. #72225339 | C2 | semidirect |
| 7. C2×#93751 | C2 | semidirect |
| 8. #72216236 | C2 | semidirect |
| 9. #72214187 | C2 | semidirect |
| 18. #491465 | C22 | semidirect |
| 23. #151635 | C22 | semidirect |
| 24. #151634 | C22 | semidirect |
| 25. C2×#7459 | C22 | semidirect |
| 27. #123406 | C22 | semidirect |
| 28. #123406 | C22 | semidirect |
| 30. #123404 | C22 | semidirect |
| 31. #123403 | C22 | semidirect |
| 32. C2×C162 | C22 | semidirect |
| 33. #93867 | C22 | semidirect |
| 34. #93866 | C22 | semidirect |
| 35. #93751 | C22 | semidirect |
| 36. #93751 | C22 | semidirect |
| 237. #508 | D16 | semidirect |
| 244. C2×Q32 | D16 | semidirect |
| 257. C2×D16 | D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225586 | 2 |
| #72225585 | 2 |
| #72225584 | 2 |
| #72225579 | 2 |
| #72225394 | 2 |
| #72225339 | 2 |
| C2×#93751 | 2 |
| #72216236 | 2 |
| #72214187 | 2 |