Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
832 conjugacy classes of subgroups.
The subgroup lattice has 610 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72225490 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225475 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225473 | — | 2 | 2 | no | — |
| 4 | #72225455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225453 | — | 2 | 1 | no | — |
| 6 | #72225452 | — | 2 | 1 | no | — |
| 7 | #72225430 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #72225427 | — | 2 | 1 | no | — |
| 9 | #72225425 | — | 2 | 2 | no | — |
| 10 | #72225424 | — | 2 | 1 | no | — |
| 11 | #72225423 | C4 | 1 | 2 | yes | — |
| 12 | #72225422 | C4 | 1 | 2 | yes | — |
| 13 | #72225410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #72225395 | C22 | 1 | 1 | yes | characteristic |
| 15 | #72225395 | C22 | 1 | 1 | yes | characteristic |
| 16 | #72225372 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #72225369 | — | 2 | 2 | no | — |
| 18 | #72225369 | — | 2 | 2 | no | — |
| 19 | #72225362 | C22 | 1 | 1 | yes | characteristic |
| 20 | #72225353 | — | 2 | 1 | no | — |
| 21 | #72225308 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#93752 | — | 2 | 1 | no | — |
| 23 | #72216326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 24 | #72216296 | C22 | 1 | 1 | yes | characteristic |
| 25 | #72216283 | — | 2 | 1 | no | — |
| 26 | #72216261 | C22 | 1 | 1 | yes | characteristic |
| 27 | #72216244 | — | 2 | 1 | no | — |
| 28 | #72216226 | C22 | 1 | 1 | yes | characteristic |
| 29 | #513082 | — | 2 | 1 | no | — |
| 30 | #513082 | — | 2 | 1 | no | — |
| 31 | #512773 | D4 | 1 | 1 | yes | characteristic |
| 32 | #512751 | — | 4 | 1 | no | — |
| 33 | #491485 | — | 2 | 1 | no | — |
| 34 | C2×#12046 | — | 2 | 1 | no | — |
| 35 | #153681 | — | 4 | 1 | no | — |
| 36 | #153674 | — | 2 | 2 | no | — |
| 37 | #153656 | — | 2 | 2 | no | — |
| 38 | #153607 | — | 4 | 1 | no | — |
| 39 | #153598 | — | 4 | 2 | no | — |
| 40 | #153582 | — | 2 | 1 | no | — |
| 41 | #153582 | — | 2 | 1 | no | — |
| 42 | #151732 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | #151724 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | #151718 | — | 2 | 1 | no | — |
| 45 | #151715 | — | 2 | 1 | no | — |
| 46 | #151715 | — | 2 | 1 | no | — |
| 47 | #151082 | — | 2 | 1 | no | — |
| 48 | #151082 | D4 | 1 | 2 | yes | — |
| 49 | #151081 | — | 2 | 1 | no | — |
| 50 | #151081 | C2×C4 | 1 | 2 | yes | — |
| 51 | #151073 | — | 2 | 4 | no | — |
| 52 | #151072 | — | 4 | 2 | no | — |
| 53 | #151055 | — | 2 | 1 | no | — |
| 54 | #151055 | — | 2 | 1 | no | — |
| 55 | #151035 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×#7459 | — | 2 | 1 | no | — |
| 57 | #150160 | — | 4 | 1 | no | — |
| 58 | #150160 | — | 4 | 1 | no | — |
| 59 | #150067 | — | 2 | 1 | no | — |
| 60 | #150051 | — | 4 | 1 | no | — |
| 61 | C8×M64 | D4 | 1 | 1 | yes | characteristic |
| 62 | C8×M64 | C23 | 1 | 1 | yes | characteristic |
| 63 | #141812 | — | 4 | 1 | no | — |
| 64 | #141671 | — | 4 | 1 | no | — |
| 65 | #135796 | — | 2 | 1 | no | — |
| 66 | C2×#7052 | D4 | 1 | 1 | yes | characteristic |
| 67 | #94748 | — | 2 | 1 | no | — |
| 68 | #94748 | C2×C4 | 1 | 2 | yes | — |
| 69 | #94746 | — | 2 | 1 | no | — |
| 70 | #94746 | — | 2 | 1 | no | — |
| 71 | #94743 | — | 2 | 2 | no | — |
| 72 | #94738 | — | 2 | 2 | no | — |
| 73 | #94613 | — | 4 | 2 | no | — |
| 74 | #93885 | — | 2 | 1 | no | — |
| 75 | #93885 | D4 | 1 | 2 | yes | — |
| 76 | #93752 | — | 2 | 4 | no | — |
| 77 | #93666 | — | 2 | 1 | no | — |
| 78 | #93666 | — | 2 | 1 | no | — |
| 79 | #33981 | SD16 | 1 | 1 | yes | characteristic |
| 80 | #33974 | — | 8 | 1 | no | — |
| 81 | #33733 | — | 4 | 1 | no | — |
| 82 | #33733 | — | 4 | 1 | no | — |
| 83 | C2×#2178 | — | 2 | 1 | no | — |
| 84 | C2×#2170 | — | 4 | 1 | no | — |
| 85 | #19603 | — | 4 | 1 | no | — |
| 86 | #13742 | — | 4 | 2 | no | — |
| 87 | #13733 | — | 2 | 1 | no | — |
| 88 | #13733 | — | 2 | 1 | no | — |
| 89 | #13725 | — | 2 | 1 | no | — |
| 90 | #13725 | — | 2 | 1 | no | — |
| 91 | #13719 | — | 4 | 1 | no | — |
| 92 | #13719 | — | 4 | 1 | no | — |
| 93 | #13697 | — | 4 | 1 | no | — |
| 94 | #13697 | — | 4 | 1 | no | — |
| 95 | #13697 | — | 8 | 1 | no | — |
| 96 | #13656 | — | 2 | 1 | no | — |
| 97 | #13656 | D8 | 1 | 2 | yes | — |
| 98 | #13655 | — | 2 | 1 | no | — |
| 99 | #13655 | C22⋊C4 | 1 | 2 | yes | — |
| 100 | #13654 | — | 4 | 1 | no | — |
| 101 | #13654 | — | 4 | 1 | no | — |
| 102 | #13654 | — | 8 | 1 | no | — |
| 103 | #13648 | — | 8 | 2 | no | — |
| 104 | #13647 | — | 4 | 4 | no | — |
| 105 | #13636 | SD16 | 1 | 1 | yes | characteristic |
| 106 | C2×#1422 | — | 4 | 1 | no | — |
| 107 | #13620 | — | 2 | 1 | no | — |
| 108 | #13558 | — | 8 | 1 | no | — |
| 109 | C4×M64 | D8 | 1 | 1 | yes | characteristic |
| 110 | C4×M64 | D8 | 1 | 1 | yes | characteristic |
| 111 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C4×M64 | #41 | 1 | 1 | yes | characteristic |
| 113 | #13208 | — | 8 | 2 | no | — |
| 114 | #12521 | — | 2 | 1 | no | — |
| 115 | #12515 | — | 2 | 1 | no | — |
| 116 | #12509 | — | 4 | 1 | no | — |
| 117 | #12503 | — | 4 | 1 | no | — |
| 118 | #12503 | — | 4 | 1 | no | — |
| 119 | #12046 | — | 2 | 2 | no | — |
| 120 | #12046 | — | 2 | 2 | no | — |
| 121 | #12046 | — | 4 | 1 | no | — |
| 122 | #12046 | — | 4 | 1 | no | — |
| 123 | #12023 | — | 4 | 1 | no | — |
| 124 | #12023 | — | 4 | 1 | no | — |
| 125 | C2×#1373 | — | 2 | 1 | no | — |
| 126 | #11671 | — | 8 | 2 | no | — |
| 127 | C2×#1335 | — | 4 | 1 | no | — |
| 128 | C2×C8×C16 | — | 2 | 1 | no | — |
| 129 | C2×C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | #8823 | — | 4 | 1 | no | — |
| 131 | #7548 | — | 4 | 2 | no | — |
| 132 | #7544 | — | 2 | 2 | no | — |
| 133 | #7544 | — | 4 | 1 | no | — |
| 134 | #7541 | — | 4 | 2 | no | — |
| 135 | #7540 | — | 4 | 2 | no | — |
| 136 | #7513 | — | 4 | 1 | no | — |
| 137 | #7513 | — | 4 | 1 | no | — |
| 138 | #7511 | — | 4 | 1 | no | — |
| 139 | #7511 | — | 4 | 1 | no | — |
| 140 | #7463 | — | 4 | 1 | no | — |
| 141 | #7463 | — | 4 | 1 | no | — |
| 142 | #7463 | — | 8 | 1 | no | — |
| 143 | #7462 | — | 2 | 1 | no | — |
| 144 | #7462 | C22⋊C4 | 1 | 2 | yes | — |
| 145 | #7459 | — | 2 | 2 | no | — |
| 146 | #7459 | — | 4 | 1 | no | — |
| 147 | #7387 | — | 2 | 2 | no | — |
| 148 | #7387 | — | 2 | 2 | no | — |
| 149 | #7385 | — | 8 | 2 | no | — |
| 150 | #7385 | — | 8 | 2 | no | — |
| 151 | #7381 | — | 4 | 4 | no | — |
| 152 | #7329 | — | 2 | 1 | no | — |
| 153 | #7329 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | #7329 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C8×C32 | — | 2 | 1 | no | — |
| 156 | C8×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 157 | C8×C32 | #41 | 1 | 1 | yes | characteristic |
| 158 | #7052 | — | 2 | 1 | no | — |
| 159 | #7052 | — | 2 | 1 | no | — |
| 160 | C2×#508 | — | 2 | 1 | no | — |
| 161 | C2×#504 | — | 8 | 1 | no | — |
| 162 | #3169 | — | 8 | 1 | no | — |
| 163 | #3169 | — | 8 | 1 | no | — |
| 164 | #3147 | — | 8 | 1 | no | — |
| 165 | C2×#443 | — | 4 | 1 | no | — |
| 166 | #2264 | — | 2 | 2 | no | — |
| 167 | #2263 | — | 2 | 2 | no | — |
| 168 | #2262 | — | 2 | 1 | no | — |
| 169 | #2262 | #102 | 1 | 2 | yes | — |
| 170 | C2×D32 | — | 4 | 1 | no | — |
| 171 | C2×D32 | — | 4 | 1 | no | — |
| 172 | C2×D32 | — | 8 | 1 | no | — |
| 173 | #2258 | — | 8 | 4 | no | — |
| 174 | #2258 | — | 16 | 2 | no | — |
| 175 | C2×M64 | — | 2 | 1 | no | — |
| 176 | C2×M64 | — | 2 | 1 | no | — |
| 177 | C2×M64 | — | 2 | 1 | no | — |
| 178 | C2×M64 | — | 8 | 1 | no | — |
| 179 | C2×M64 | — | 16 | 2 | no | — |
| 180 | C2×M64 | C2×SD16 | 1 | 1 | yes | characteristic |
| 181 | C2×M64 | #135 | 1 | 1 | yes | characteristic |
| 182 | #2252 | — | 4 | 1 | no | — |
| 183 | #2252 | — | 4 | 1 | no | — |
| 184 | #2246 | — | 4 | 1 | no | — |
| 185 | #2246 | — | 4 | 1 | no | — |
| 186 | #2240 | — | 8 | 1 | no | — |
| 187 | #2240 | — | 8 | 1 | no | — |
| 188 | #2215 | — | 8 | 1 | no | — |
| 189 | #2215 | — | 8 | 1 | no | — |
| 190 | #2215 | — | 8 | 1 | no | — |
| 191 | #2215 | — | 8 | 1 | no | — |
| 192 | #2178 | — | 2 | 2 | no | — |
| 193 | #2178 | — | 2 | 2 | no | — |
| 194 | #2178 | — | 4 | 1 | no | — |
| 195 | #2178 | — | 4 | 1 | no | — |
| 196 | C4×D16 | — | 8 | 1 | no | — |
| 197 | C4×D16 | — | 8 | 1 | no | — |
| 198 | C4×D16 | — | 8 | 1 | no | — |
| 199 | C4×D16 | — | 8 | 1 | no | — |
| 200 | #2170 | — | 4 | 2 | no | — |
| 201 | #2170 | — | 4 | 2 | no | — |
| 202 | #2170 | — | 8 | 1 | no | — |
| 203 | #2170 | — | 8 | 1 | no | — |
| 204 | C2×#368 | — | 2 | 1 | no | — |
| 205 | C2×#364 | — | 4 | 1 | no | — |
| 206 | C2×#359 | — | 4 | 1 | no | — |
| 207 | C2×#359 | — | 16 | 4 | no | — |
| 208 | C2×#350 | — | 8 | 1 | no | — |
| 209 | C2×C4×C16 | — | 2 | 2 | no | — |
| 210 | C2×C4×C16 | #121 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 212 | #1848 | — | 8 | 1 | no | — |
| 213 | #1713 | — | 4 | 1 | no | — |
| 214 | #1712 | — | 4 | 1 | no | — |
| 215 | #1709 | — | 8 | 1 | no | — |
| 216 | #1706 | — | 8 | 1 | no | — |
| 217 | #1706 | — | 8 | 1 | no | — |
| 218 | #1567 | — | 8 | 1 | no | — |
| 219 | #1567 | — | 8 | 1 | no | — |
| 220 | C2×C82 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 221 | SD128 | — | 8 | 2 | no | — |
| 222 | D64 | — | 8 | 2 | no | — |
| 223 | M128 | — | 4 | 2 | no | — |
| 224 | M128 | — | 8 | 1 | no | — |
| 225 | #1425 | — | 2 | 1 | no | — |
| 226 | #1425 | #102 | 1 | 2 | yes | — |
| 227 | #1424 | — | 4 | 1 | no | — |
| 228 | #1424 | — | 4 | 1 | no | — |
| 229 | #1424 | — | 8 | 1 | no | — |
| 230 | #1422 | — | 4 | 2 | no | — |
| 231 | #1422 | — | 8 | 1 | no | — |
| 232 | #1417 | — | 2 | 2 | no | — |
| 233 | #1417 | — | 2 | 2 | no | — |
| 234 | #1415 | — | 8 | 2 | no | — |
| 235 | #1415 | — | 8 | 1 | no | — |
| 236 | #1415 | — | 8 | 1 | no | — |
| 237 | #1401 | — | 8 | 4 | no | — |
| 238 | #1397 | — | 2 | 1 | no | — |
| 239 | #1397 | — | 2 | 1 | no | — |
| 240 | #1397 | D16 | 1 | 2 | yes | — |
| 241 | #1397 | C2×D8 | 1 | 1 | yes | characteristic |
| 242 | #1397 | #135 | 1 | 1 | yes | characteristic |
| 243 | C4×C32 | — | 2 | 1 | no | — |
| 244 | C4×C32 | — | 2 | 1 | no | — |
| 245 | C4×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 246 | C4×C32 | C4×D4 | 1 | 1 | yes | characteristic |
| 247 | C4×C32 | #121 | 1 | 1 | yes | characteristic |
| 248 | C4×C32 | #123 | 1 | 1 | yes | characteristic |
| 249 | #1373 | — | 2 | 2 | no | — |
| 250 | #1373 | — | 4 | 1 | no | — |
| 251 | #1372 | — | 8 | 1 | no | — |
| 252 | #1372 | — | 8 | 1 | no | — |
| 253 | #1372 | — | 8 | 1 | no | — |
| 254 | #1372 | — | 8 | 1 | no | — |
| 255 | #1335 | — | 4 | 2 | no | — |
| 256 | #1335 | — | 4 | 2 | no | — |
| 257 | #1331 | — | 16 | 4 | no | — |
| 258 | C8×C16 | — | 4 | 1 | no | — |
| 259 | C8×C16 | — | 4 | 1 | no | — |
| 260 | C8×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 261 | C8×C16 | #120 | 1 | 1 | yes | characteristic |
| 262 | C8×C16 | #135 | 1 | 1 | yes | characteristic |
| 263 | C8×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 264 | C2×#135 | — | 4 | 1 | no | — |
| 265 | C2×#135 | — | 16 | 2 | no | — |
| 266 | C2×#131 | — | 8 | 1 | no | — |
| 267 | #532 | — | 16 | 1 | no | — |
| 268 | #508 | — | 2 | 2 | no | — |
| 269 | #508 | — | 2 | 2 | no | — |
| 270 | #508 | — | 4 | 1 | no | — |
| 271 | #508 | — | 4 | 1 | no | — |
| 272 | C2×Q32 | — | 2 | 1 | no | — |
| 273 | C2×SD32 | — | 4 | 1 | no | — |
| 274 | C2×D16 | — | 2 | 1 | no | — |
| 275 | C2×D16 | — | 8 | 1 | no | — |
| 276 | C2×D16 | — | 8 | 1 | no | — |
| 277 | C2×D16 | — | 8 | 1 | no | — |
| 278 | C2×D16 | — | 8 | 1 | no | — |
| 279 | #504 | — | 8 | 2 | no | — |
| 280 | #504 | — | 8 | 2 | no | — |
| 281 | #504 | — | 16 | 1 | no | — |
| 282 | #504 | — | 16 | 1 | no | — |
| 283 | C2×M32 | — | 8 | 1 | no | — |
| 284 | C2×M32 | — | 16 | 1 | no | — |
| 285 | C22×C16 | — | 4 | 2 | no | — |
| 286 | C22×C16 | — | 16 | 1 | no | — |
| 287 | C22×C16 | #465 | 1 | 1 | yes | characteristic |
| 288 | C22×C16 | #471 | 1 | 1 | yes | characteristic |
| 289 | C22×C16 | #508 | 1 | 1 | yes | characteristic |
| 290 | C22×C16 | #509 | 1 | 1 | yes | characteristic |
| 291 | #500 | — | 8 | 1 | no | — |
| 292 | #500 | — | 8 | 1 | no | — |
| 293 | #495 | — | 16 | 2 | no | — |
| 294 | #494 | — | 8 | 1 | no | — |
| 295 | #493 | — | 8 | 1 | no | — |
| 296 | #493 | — | 8 | 1 | no | — |
| 297 | #493 | — | 8 | 1 | no | — |
| 298 | #492 | — | 16 | 1 | no | — |
| 299 | #486 | — | 16 | 1 | no | — |
| 300 | #486 | — | 16 | 1 | no | — |
| 301 | #466 | — | 16 | 2 | no | — |
| 302 | #466 | — | 16 | 1 | no | — |
| 303 | #466 | — | 16 | 1 | no | — |
| 304 | #443 | — | 4 | 2 | no | — |
| 305 | #443 | — | 4 | 2 | no | — |
| 306 | #443 | — | 8 | 1 | no | — |
| 307 | #443 | — | 8 | 1 | no | — |
| 308 | C4×D8 | — | 16 | 2 | no | — |
| 309 | C4×D8 | — | 16 | 1 | no | — |
| 310 | C4×D8 | — | 16 | 1 | no | — |
| 311 | C2×#108 | — | 4 | 1 | no | — |
| 312 | C2×#108 | — | 16 | 2 | no | — |
| 313 | #423 | — | 16 | 1 | no | — |
| 314 | C2×#104 | — | 8 | 1 | no | — |
| 315 | C2×C4×C8 | — | 2 | 1 | no | — |
| 316 | C2×C4×C8 | #459 | 1 | 1 | yes | characteristic |
| 317 | Q64 | — | 2 | 1 | no | — |
| 318 | Q64 | #359 | 1 | 2 | yes | complemented |
| 319 | SD64 | — | 2 | 2 | no | — |
| 320 | SD64 | — | 2 | 2 | no | — |
| 321 | D32 | — | 2 | 1 | no | — |
| 322 | D32 | — | 8 | 2 | no | — |
| 323 | D32 | — | 16 | 1 | no | — |
| 324 | D32 | — | 16 | 2 | no | — |
| 325 | D32 | #359 | 1 | 2 | yes | complemented |
| 326 | M64 | — | 2 | 2 | no | — |
| 327 | M64 | — | 4 | 1 | no | — |
| 328 | M64 | — | 4 | 2 | no | — |
| 329 | M64 | — | 4 | 1 | no | — |
| 330 | M64 | — | 4 | 1 | no | — |
| 331 | M64 | — | 8 | 1 | no | — |
| 332 | M64 | — | 8 | 2 | no | — |
| 333 | M64 | — | 16 | 4 | no | — |
| 334 | M64 | — | 16 | 1 | no | — |
| 335 | C2×C32 | — | 2 | 1 | no | — |
| 336 | C2×C32 | — | 2 | 1 | no | — |
| 337 | C2×C32 | — | 2 | 2 | no | — |
| 338 | C2×C32 | — | 4 | 1 | no | — |
| 339 | C2×C32 | — | 16 | 4 | no | — |
| 340 | C2×C32 | — | 16 | 1 | no | — |
| 341 | C2×C32 | C2×#102 | 1 | 1 | yes | characteristic |
| 342 | C2×C32 | #416 | 1 | 1 | yes | characteristic |
| 343 | C2×C32 | #465 | 1 | 1 | yes | characteristic |
| 344 | C2×C32 | #466 | 1 | 1 | yes | characteristic |
| 345 | #368 | — | 2 | 2 | no | — |
| 346 | #368 | — | 4 | 1 | no | — |
| 347 | #366 | — | 8 | 1 | no | — |
| 348 | #366 | — | 8 | 1 | no | — |
| 349 | #366 | — | 8 | 1 | no | — |
| 350 | #366 | — | 8 | 1 | no | — |
| 351 | #364 | — | 4 | 2 | no | — |
| 352 | #364 | — | 8 | 1 | no | — |
| 353 | #359 | — | 4 | 2 | no | — |
| 354 | #359 | — | 4 | 2 | no | — |
| 355 | #359 | — | 32 | 8 | no | — |
| 356 | #357 | — | 16 | 1 | no | — |
| 357 | #357 | — | 16 | 1 | no | — |
| 358 | #357 | — | 16 | 1 | no | — |
| 359 | #357 | — | 16 | 1 | no | — |
| 360 | #350 | — | 8 | 2 | no | — |
| 361 | #350 | — | 8 | 2 | no | — |
| 362 | C4×C16 | — | 4 | 2 | no | — |
| 363 | C4×C16 | — | 4 | 2 | no | — |
| 364 | C4×C16 | #386 | 1 | 1 | yes | characteristic |
| 365 | C4×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 366 | C4×C16 | #447 | 1 | 1 | yes | characteristic |
| 367 | C4×C16 | #463 | 1 | 1 | yes | characteristic |
| 368 | C4×C16 | #466 | 1 | 1 | yes | characteristic |
| 369 | C4×C16 | #472 | 1 | 1 | yes | characteristic |
| 370 | C4×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 371 | C4×C16 | #509 | 1 | 1 | yes | characteristic |
| 372 | #335 | — | 16 | 2 | no | — |
| 373 | #335 | — | 16 | 1 | no | — |
| 374 | #335 | — | 16 | 1 | no | — |
| 375 | C82 | — | 2 | 1 | no | — |
| 376 | C82 | #442 | 1 | 1 | yes | characteristic |
| 377 | C82 | #449 | 1 | 1 | yes | characteristic |
| 378 | C64 | — | 8 | 2 | no | — |
| 379 | C64 | — | 16 | 1 | no | — |
| 380 | C2×#41 | — | 8 | 1 | no | — |
| 381 | C2×#41 | — | 32 | 1 | no | — |
| 382 | #135 | — | 4 | 2 | no | — |
| 383 | #135 | — | 4 | 2 | no | — |
| 384 | #135 | — | 8 | 1 | no | — |
| 385 | #135 | — | 8 | 1 | no | — |
| 386 | #135 | — | 32 | 4 | no | — |
| 387 | #135 | — | 32 | 4 | no | — |
| 388 | C2×Q16 | — | 4 | 1 | no | — |
| 389 | C2×Q16 | — | 16 | 2 | no | — |
| 390 | C2×SD16 | — | 8 | 1 | no | — |
| 391 | C2×SD16 | — | 32 | 2 | no | — |
| 392 | C2×D8 | — | 4 | 1 | no | — |
| 393 | C2×D8 | — | 16 | 2 | no | — |
| 394 | C2×D8 | — | 16 | 2 | no | — |
| 395 | C2×D8 | — | 16 | 1 | no | — |
| 396 | C2×D8 | — | 16 | 1 | no | — |
| 397 | #131 | — | 8 | 2 | no | — |
| 398 | #131 | — | 8 | 2 | no | — |
| 399 | #131 | — | 16 | 1 | no | — |
| 400 | #131 | — | 16 | 1 | no | — |
| 401 | C2×M16 | — | 8 | 1 | no | — |
| 402 | C2×M16 | — | 16 | 1 | no | — |
| 403 | C2×M16 | — | 32 | 1 | no | — |
| 404 | C22×C8 | — | 2 | 2 | no | — |
| 405 | C22×C8 | — | 16 | 1 | no | — |
| 406 | C22×C8 | #1665 | 1 | 1 | yes | characteristic |
| 407 | C22×C8 | #2210 | 1 | 1 | yes | characteristic |
| 408 | C4⋊Q8 | — | 16 | 1 | no | — |
| 409 | #127 | — | 16 | 1 | no | — |
| 410 | #124 | — | 32 | 1 | no | — |
| 411 | #121 | — | 32 | 1 | no | — |
| 412 | #121 | — | 32 | 1 | no | — |
| 413 | C4×D4 | — | 32 | 1 | no | — |
| 414 | C4×D4 | — | 32 | 1 | no | — |
| 415 | C2×C42 | #2213 | 1 | 1 | yes | characteristic |
| 416 | Q32 | — | 2 | 2 | no | — |
| 417 | Q32 | — | 4 | 1 | no | — |
| 418 | SD32 | — | 4 | 2 | no | — |
| 419 | SD32 | — | 4 | 2 | no | — |
| 420 | D16 | — | 2 | 2 | no | — |
| 421 | D16 | — | 4 | 1 | no | — |
| 422 | D16 | — | 16 | 2 | no | — |
| 423 | D16 | — | 16 | 2 | no | — |
| 424 | D16 | — | 16 | 1 | no | — |
| 425 | D16 | — | 16 | 1 | no | — |
| 426 | D16 | — | 16 | 1 | no | — |
| 427 | D16 | — | 16 | 1 | no | — |
| 428 | M32 | — | 8 | 2 | no | — |
| 429 | M32 | — | 16 | 2 | no | — |
| 430 | M32 | — | 16 | 1 | no | — |
| 431 | M32 | — | 16 | 2 | no | — |
| 432 | C2×C16 | — | 2 | 1 | no | — |
| 433 | C2×C16 | — | 2 | 1 | no | — |
| 434 | C2×C16 | — | 2 | 1 | no | — |
| 435 | C2×C16 | — | 2 | 1 | no | — |
| 436 | C2×C16 | — | 4 | 1 | no | — |
| 437 | C2×C16 | — | 4 | 1 | no | — |
| 438 | C2×C16 | — | 8 | 2 | no | — |
| 439 | C2×C16 | — | 8 | 4 | no | — |
| 440 | C2×C16 | — | 16 | 2 | no | — |
| 441 | C2×C16 | — | 16 | 1 | no | — |
| 442 | C2×C16 | — | 16 | 2 | no | — |
| 443 | C2×C16 | #1677 | 1 | 1 | yes | characteristic |
| 444 | C2×C16 | #1681 | 1 | 1 | yes | characteristic |
| 445 | C2×C16 | #1893 | 1 | 1 | yes | characteristic |
| 446 | C2×C16 | #1907 | 1 | 1 | yes | characteristic |
| 447 | C2×C16 | C4×D16 | 1 | 1 | yes | characteristic |
| 448 | C2×C16 | #2177 | 1 | 1 | yes | characteristic |
| 449 | C2×C16 | #2184 | 1 | 1 | yes | characteristic |
| 450 | C2×C16 | #2186 | 1 | 1 | yes | characteristic |
| 451 | #108 | — | 4 | 2 | no | — |
| 452 | #108 | — | 8 | 1 | no | — |
| 453 | #108 | — | 32 | 4 | no | — |
| 454 | #107 | — | 16 | 2 | no | — |
| 455 | #107 | — | 16 | 1 | no | — |
| 456 | #107 | — | 16 | 1 | no | — |
| 457 | C4⋊C8 | — | 32 | 1 | no | — |
| 458 | C4⋊C8 | — | 32 | 1 | no | — |
| 459 | #104 | — | 8 | 2 | no | — |
| 460 | #104 | — | 8 | 2 | no | — |
| 461 | #102 | — | 32 | 2 | no | — |
| 462 | #102 | — | 32 | 1 | no | — |
| 463 | #102 | — | 32 | 1 | no | — |
| 464 | C4×C8 | — | 2 | 2 | no | — |
| 465 | C4×C8 | — | 2 | 1 | no | — |
| 466 | C4×C8 | — | 2 | 1 | no | — |
| 467 | C4×C8 | #1667 | 1 | 1 | yes | characteristic |
| 468 | C4×C8 | #1879 | 1 | 1 | yes | characteristic |
| 469 | C4×C8 | #2206 | 1 | 1 | yes | characteristic |
| 470 | C4×C8 | #2212 | 1 | 1 | yes | characteristic |
| 471 | C32 | — | 2 | 2 | no | — |
| 472 | C32 | — | 2 | 1 | no | — |
| 473 | C32 | — | 2 | 1 | no | — |
| 474 | C32 | — | 2 | 1 | no | — |
| 475 | C32 | — | 4 | 2 | no | — |
| 476 | C32 | — | 4 | 1 | no | — |
| 477 | C32 | — | 8 | 1 | no | — |
| 478 | C32 | — | 16 | 2 | no | — |
| 479 | C32 | C2×#359 | 1 | 2 | yes | — |
| 480 | #41 | — | 8 | 2 | no | — |
| 481 | #41 | — | 8 | 2 | no | — |
| 482 | #41 | — | 16 | 1 | no | — |
| 483 | #41 | — | 16 | 1 | no | — |
| 484 | #41 | — | 64 | 2 | no | — |
| 485 | #41 | — | 64 | 2 | no | — |
| 486 | C2×Q8 | — | 8 | 1 | no | — |
| 487 | C2×Q8 | — | 32 | 1 | no | — |
| 488 | C2×D4 | — | 8 | 1 | no | — |
| 489 | C2×D4 | — | 16 | 1 | no | — |
| 490 | C2×D4 | — | 32 | 1 | no | — |
| 491 | C2×D4 | — | 32 | 1 | no | — |
| 492 | C2×D4 | — | 32 | 1 | no | — |
| 493 | C2×D4 | — | 64 | 1 | no | — |
| 494 | C22×C4 | — | 2 | 1 | no | — |
| 495 | C22×C4 | — | 16 | 1 | no | — |
| 496 | C22×C4 | — | 64 | 1 | no | — |
| 497 | C22×C4 | #12418 | 1 | 1 | yes | characteristic |
| 498 | Q16 | — | 4 | 2 | no | — |
| 499 | Q16 | — | 8 | 1 | no | — |
| 500 | Q16 | — | 32 | 4 | no | — |
| 501 | SD16 | — | 8 | 2 | no | — |
| 502 | SD16 | — | 8 | 2 | no | — |
| 503 | SD16 | — | 64 | 4 | no | — |
| 504 | D8 | — | 4 | 2 | no | — |
| 505 | D8 | — | 8 | 1 | no | — |
| 506 | D8 | — | 32 | 4 | no | — |
| 507 | D8 | — | 32 | 4 | no | — |
| 508 | D8 | — | 32 | 1 | no | — |
| 509 | D8 | — | 32 | 1 | no | — |
| 510 | D8 | — | 32 | 1 | no | — |
| 511 | D8 | — | 32 | 1 | no | — |
| 512 | M16 | — | 8 | 2 | no | — |
| 513 | M16 | — | 16 | 2 | no | — |
| 514 | M16 | — | 16 | 1 | no | — |
| 515 | M16 | — | 16 | 2 | no | — |
| 516 | M16 | — | 64 | 2 | no | — |
| 517 | C2×C8 | — | 2 | 2 | no | — |
| 518 | C2×C8 | — | 2 | 1 | no | — |
| 519 | C2×C8 | — | 2 | 1 | no | — |
| 520 | C2×C8 | — | 2 | 1 | no | — |
| 521 | C2×C8 | — | 2 | 1 | no | — |
| 522 | C2×C8 | — | 2 | 2 | no | — |
| 523 | C2×C8 | — | 4 | 4 | no | — |
| 524 | C2×C8 | — | 16 | 2 | no | — |
| 525 | C2×C8 | — | 16 | 1 | no | — |
| 526 | C2×C8 | — | 16 | 2 | no | — |
| 527 | C2×C8 | — | 64 | 1 | no | — |
| 528 | C2×C8 | #9221 | 1 | 1 | yes | characteristic |
| 529 | C2×C8 | #12416 | 1 | 1 | yes | characteristic |
| 530 | C2×C8 | #12428 | 1 | 1 | yes | characteristic |
| 531 | C2×C8 | #13012 | 1 | 1 | yes | characteristic |
| 532 | C4⋊C4 | — | 32 | 1 | no | — |
| 533 | C4⋊C4 | — | 32 | 1 | no | — |
| 534 | C22⋊C4 | — | 64 | 1 | no | — |
| 535 | C22⋊C4 | — | 64 | 1 | no | — |
| 536 | C42 | — | 2 | 1 | no | — |
| 537 | C42 | #12424 | 1 | 1 | yes | characteristic |
| 538 | C42 | #13029 | 1 | 1 | yes | characteristic |
| 539 | C16 | — | 2 | 1 | no | — |
| 540 | C16 | — | 2 | 1 | no | — |
| 541 | C16 | — | 2 | 1 | no | — |
| 542 | C16 | — | 2 | 1 | no | — |
| 543 | C16 | — | 2 | 1 | no | — |
| 544 | C16 | — | 2 | 1 | no | — |
| 545 | C16 | — | 16 | 2 | no | — |
| 546 | C16 | — | 16 | 2 | no | — |
| 547 | C16 | #13063 | 1 | 1 | yes | characteristic |
| 548 | C16 | #13071 | 1 | 1 | yes | characteristic |
| 549 | C16 | #13658 | 1 | 1 | yes | characteristic |
| 550 | C16 | #13658 | 1 | 1 | yes | characteristic |
| 551 | C23 | — | 16 | 1 | no | — |
| 552 | C23 | — | 64 | 1 | no | — |
| 553 | C23 | #151626 | 1 | 1 | yes | characteristic |
| 554 | Q8 | — | 8 | 2 | no | — |
| 555 | Q8 | — | 16 | 1 | no | — |
| 556 | Q8 | — | 64 | 2 | no | — |
| 557 | D4 | — | 8 | 2 | no | — |
| 558 | D4 | — | 16 | 1 | no | — |
| 559 | D4 | — | 16 | 2 | no | — |
| 560 | D4 | — | 16 | 2 | no | — |
| 561 | D4 | — | 64 | 2 | no | — |
| 562 | D4 | — | 64 | 2 | no | — |
| 563 | D4 | — | 64 | 1 | no | — |
| 564 | D4 | — | 64 | 1 | no | — |
| 565 | D4 | — | 128 | 2 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 1 | no | — |
| 568 | C2×C4 | — | 2 | 1 | no | — |
| 569 | C2×C4 | — | 2 | 1 | no | — |
| 570 | C2×C4 | — | 4 | 2 | no | — |
| 571 | C2×C4 | — | 16 | 2 | no | — |
| 572 | C2×C4 | — | 16 | 1 | no | — |
| 573 | C2×C4 | — | 16 | 2 | no | — |
| 574 | C2×C4 | — | 64 | 1 | no | — |
| 575 | C2×C4 | — | 128 | 1 | no | — |
| 576 | C2×C4 | — | 128 | 1 | no | — |
| 577 | C2×C4 | #138625 | 1 | 1 | yes | characteristic |
| 578 | C2×C4 | #151626 | 1 | 1 | yes | characteristic |
| 579 | C8 | — | 2 | 4 | no | — |
| 580 | C8 | — | 2 | 1 | no | — |
| 581 | C8 | — | 2 | 1 | no | — |
| 582 | C8 | — | 4 | 2 | no | — |
| 583 | C8 | — | 16 | 2 | no | — |
| 584 | C8 | — | 128 | 1 | no | — |
| 585 | C8 | #138646 | 1 | 1 | yes | characteristic |
| 586 | C8 | #138657 | 1 | 1 | yes | characteristic |
| 587 | C8 | #152536 | 1 | 1 | yes | characteristic |
| 588 | C8 | #152549 | 1 | 1 | yes | characteristic |
| 589 | C22 | — | 2 | 1 | no | — |
| 590 | C22 | — | 4 | 1 | no | — |
| 591 | C22 | — | 16 | 2 | no | — |
| 592 | C22 | — | 64 | 1 | no | — |
| 593 | C22 | — | 128 | 1 | no | — |
| 594 | C22 | — | 128 | 1 | no | — |
| 595 | C22 | — | 128 | 1 | no | — |
| 596 | C22 | #72216264 | 1 | 1 | yes | characteristic |
| 597 | C4 | — | 2 | 2 | no | — |
| 598 | C4 | — | 2 | 1 | no | — |
| 599 | C4 | — | 4 | 1 | no | — |
| 600 | C4 | — | 16 | 2 | no | — |
| 601 | C4 | — | 128 | 1 | no | — |
| 602 | C4 | #72225511 | 1 | 1 | yes | characteristic |
| 603 | C4 | #72225513 | 1 | 1 | yes | characteristic |
| 604 | C2 | — | 256 | 1 | no | — |
| 605 | C2 | — | 2 | 1 | no | — |
| 606 | C2 | — | 4 | 1 | no | — |
| 607 | C2 | — | 32 | 2 | no | — |
| 608 | C2 | #72225514 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72225514 |
| commutator | C8×C32 | C22×C4 |
| Frattini, cosocle | C8×M64 | C23 |
| prime radical | #72225430 | C2 |
| LCS | G ▷ C8×C32 ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ #72216226 ◁ G | |
| LECS | G ▷ C8×M64 ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225490 | C2 | semidirect |
| 2. #72225475 | C2 | semidirect |
| 4. #72225455 | C2 | semidirect |
| 13. #72225410 | C2 | semidirect |
| 16. #72225372 | C2 | semidirect |
| 23. #72216326 | C2 | semidirect |
| 318. Q64 | #359 | semidirect |
| 325. D32 | #359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225490 | 2 |
| #72225475 | 2 |
| #72225455 | 2 |
| #72225430 | 2 |
| #72225410 | 2 |
| #72225372 | 2 |
| #72216326 | 2 |