← #72227279
Subgroups — #72227279
Order 4096.
623 conjugacy classes of subgroups.
The subgroup lattice has 526 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72227241 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #72225536 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72225532 | — | 2 | 1 | no | — |
| 4 | #72225526 | — | 2 | 1 | no | — |
| 5 | #72225376 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72225373 | C4 | 1 | 1 | yes | characteristic |
| 7 | #72225373 | C4 | 1 | 1 | yes | characteristic |
| 8 | #72225362 | C4 | 1 | 1 | yes | characteristic |
| 9 | #72225352 | C4 | 1 | 1 | yes | characteristic |
| 10 | #72225351 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #72225350 | — | 2 | 1 | no | — |
| 12 | #72225349 | — | 2 | 1 | no | — |
| 13 | #72225132 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #72225131 | — | 2 | 1 | no | — |
| 15 | #72225131 | — | 2 | 1 | no | — |
| 16 | #72225126 | C22 | 1 | 1 | yes | characteristic |
| 17 | #72216558 | C2 | 1 | 1 | yes | maximal, characteristic |
| 18 | #72216309 | C2 | 1 | 1 | yes | maximal, characteristic |
| 19 | #72216304 | — | 2 | 1 | no | — |
| 20 | #72216302 | — | 2 | 1 | no | — |
| 21 | #72216247 | C22 | 1 | 1 | yes | characteristic |
| 22 | #72216243 | C22 | 1 | 1 | yes | characteristic |
| 23 | #72216243 | C22 | 1 | 1 | yes | characteristic |
| 24 | C8×#1398 | C22 | 1 | 1 | yes | characteristic |
| 25 | #72216215 | C22 | 1 | 1 | yes | characteristic |
| 26 | #72216168 | C22 | 1 | 1 | yes | characteristic |
| 27 | #151981 | — | 2 | 1 | no | — |
| 28 | #151981 | — | 2 | 1 | no | — |
| 29 | #151981 | — | 2 | 1 | no | — |
| 30 | C4×#1398 | D4 | 1 | 1 | yes | characteristic |
| 31 | C4×#1398 | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×#7459 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C2×#7459 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×#7459 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×#7459 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | #151024 | — | 4 | 1 | no | — |
| 37 | C2×#7457 | — | 4 | 1 | no | — |
| 38 | C2×#7457 | — | 4 | 2 | no | — |
| 39 | C2×#7457 | — | 4 | 1 | no | — |
| 40 | C2×#7457 | — | 4 | 1 | no | — |
| 41 | C2×#7456 | — | 2 | 1 | no | — |
| 42 | #149504 | — | 4 | 1 | no | — |
| 43 | #149495 | Q8 | 1 | 1 | yes | characteristic |
| 44 | #149495 | Q8 | 1 | 1 | yes | characteristic |
| 45 | C8×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C8×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #135718 | — | 2 | 1 | no | — |
| 48 | #135718 | — | 2 | 1 | no | — |
| 49 | #135715 | — | 2 | 1 | no | — |
| 50 | #135715 | — | 2 | 1 | no | — |
| 51 | #135713 | — | 2 | 1 | no | — |
| 52 | #129090 | D4 | 1 | 1 | yes | characteristic |
| 53 | #129088 | D4 | 1 | 1 | yes | characteristic |
| 54 | #129051 | — | 2 | 1 | no | — |
| 55 | C8×#346 | C23 | 1 | 1 | yes | characteristic |
| 56 | #99295 | — | 2 | 1 | no | — |
| 57 | #94031 | — | 4 | 1 | no | — |
| 58 | #94030 | — | 4 | 1 | no | — |
| 59 | #94019 | — | 2 | 1 | no | — |
| 60 | #94019 | — | 2 | 1 | no | — |
| 61 | #94018 | Q8 | 1 | 2 | yes | — |
| 62 | #93995 | — | 4 | 1 | no | — |
| 63 | #93885 | — | 2 | 2 | no | — |
| 64 | #93882 | C8 | 1 | 4 | yes | complemented |
| 65 | #93264 | — | 2 | 1 | no | — |
| 66 | C2×#1422 | — | 2 | 1 | no | — |
| 67 | C2×#1422 | — | 2 | 1 | no | — |
| 68 | C2×#1422 | — | 2 | 1 | no | — |
| 69 | C2×#1422 | — | 2 | 1 | no | — |
| 70 | C2×#1422 | — | 2 | 2 | no | — |
| 71 | C2×#1398 | — | 2 | 1 | no | — |
| 72 | C2×#1398 | — | 2 | 1 | no | — |
| 73 | C2×#1398 | — | 4 | 1 | no | — |
| 74 | C2×#1398 | — | 4 | 1 | no | — |
| 75 | C2×#1398 | — | 4 | 1 | no | — |
| 76 | C2×#1398 | SD16 | 1 | 1 | yes | characteristic |
| 77 | C2×#1398 | SD16 | 1 | 1 | yes | characteristic |
| 78 | C2×#1398 | SD16 | 1 | 1 | yes | characteristic |
| 79 | C2×#1398 | SD16 | 1 | 1 | yes | characteristic |
| 80 | C4×M64 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 81 | C4×M64 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 82 | C4×M64 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 83 | C4×M64 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 84 | #12900 | — | 4 | 1 | no | — |
| 85 | C4×#364 | — | 2 | 1 | no | — |
| 86 | C4×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C4×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×#1369 | — | 2 | 1 | no | — |
| 89 | C2×#1369 | — | 4 | 1 | no | — |
| 90 | C2×#1369 | — | 4 | 1 | no | — |
| 91 | C2×#1369 | — | 4 | 1 | no | — |
| 92 | C2×#1369 | — | 4 | 1 | no | — |
| 93 | #11999 | — | 2 | 1 | no | — |
| 94 | C2×#1368 | — | 4 | 1 | no | — |
| 95 | C2×#1368 | — | 4 | 1 | no | — |
| 96 | C2×#1368 | — | 4 | 1 | no | — |
| 97 | C2×#1368 | — | 4 | 1 | no | — |
| 98 | #11996 | — | 8 | 1 | no | — |
| 99 | #11405 | — | 4 | 1 | no | — |
| 100 | C2×#1311 | C2×Q8 | 1 | 1 | yes | characteristic |
| 101 | C2×#1311 | #41 | 1 | 1 | yes | characteristic |
| 102 | C2×C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 103 | C2×C8×C16 | C2×Q8 | 1 | 1 | yes | characteristic |
| 104 | #8805 | — | 4 | 1 | no | — |
| 105 | #8805 | — | 8 | 1 | no | — |
| 106 | #8266 | — | 2 | 1 | no | — |
| 107 | C4×C82 | #41 | 1 | 1 | yes | characteristic |
| 108 | #7468 | — | 4 | 1 | no | — |
| 109 | #7468 | — | 4 | 1 | no | — |
| 110 | #7468 | — | 4 | 1 | no | — |
| 111 | #7459 | — | 2 | 1 | no | — |
| 112 | #7459 | — | 2 | 1 | no | — |
| 113 | #7459 | — | 2 | 1 | no | — |
| 114 | #7459 | — | 2 | 1 | no | — |
| 115 | #7459 | — | 2 | 1 | no | — |
| 116 | #7459 | — | 2 | 1 | no | — |
| 117 | #7459 | C2×C8 | 1 | 2 | yes | — |
| 118 | #7459 | C2×C8 | 1 | 2 | yes | — |
| 119 | #7457 | — | 8 | 2 | no | — |
| 120 | #7457 | — | 8 | 2 | no | — |
| 121 | #7457 | — | 8 | 4 | no | — |
| 122 | #7457 | — | 8 | 2 | no | — |
| 123 | #7457 | — | 8 | 2 | no | — |
| 124 | #7456 | — | 4 | 1 | no | — |
| 125 | #7456 | — | 4 | 1 | no | — |
| 126 | #7333 | — | 8 | 2 | no | — |
| 127 | #7330 | — | 2 | 2 | no | — |
| 128 | #7330 | — | 4 | 1 | no | — |
| 129 | #7329 | — | 2 | 1 | no | — |
| 130 | #7329 | M16 | 1 | 2 | yes | — |
| 131 | C8×C32 | — | 2 | 1 | no | — |
| 132 | C8×C32 | C2×C8 | 1 | 2 | yes | — |
| 133 | #7161 | — | 2 | 1 | no | — |
| 134 | #7157 | — | 2 | 1 | no | — |
| 135 | #7140 | — | 4 | 1 | no | — |
| 136 | C2×M64 | — | 2 | 1 | no | — |
| 137 | C2×M64 | — | 2 | 1 | no | — |
| 138 | C2×M64 | — | 4 | 1 | no | — |
| 139 | C2×M64 | — | 4 | 1 | no | — |
| 140 | C2×M64 | — | 4 | 1 | no | — |
| 141 | C2×M64 | — | 4 | 1 | no | — |
| 142 | C2×M64 | — | 4 | 2 | no | — |
| 143 | C2×M64 | #106 | 1 | 1 | yes | characteristic |
| 144 | C2×M64 | #106 | 1 | 1 | yes | characteristic |
| 145 | C2×M64 | #106 | 1 | 1 | yes | characteristic |
| 146 | C2×M64 | #106 | 1 | 1 | yes | characteristic |
| 147 | C2×#364 | — | 4 | 1 | no | — |
| 148 | C2×#364 | — | 8 | 1 | no | — |
| 149 | C2×#364 | — | 8 | 1 | no | — |
| 150 | #2150 | — | 8 | 1 | no | — |
| 151 | C4×M32 | — | 4 | 1 | no | — |
| 152 | C2×#346 | C2×SD16 | 1 | 1 | yes | characteristic |
| 153 | C2×#346 | C2×SD16 | 1 | 1 | yes | characteristic |
| 154 | C2×#346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 155 | C2×#346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 156 | C2×#346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 157 | C2×#346 | #137 | 1 | 1 | yes | characteristic |
| 158 | C2×#346 | #137 | 1 | 1 | yes | characteristic |
| 159 | C2×#346 | #137 | 1 | 1 | yes | characteristic |
| 160 | C2×C4×C16 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C16 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C16 | C4⋊Q8 | 1 | 1 | yes | characteristic |
| 164 | #1842 | — | 8 | 1 | no | — |
| 165 | C42×C8 | — | 2 | 1 | no | — |
| 166 | C42×C8 | #121 | 1 | 1 | yes | characteristic |
| 167 | #1564 | — | 4 | 1 | no | — |
| 168 | C2×#334 | — | 8 | 1 | no | — |
| 169 | C2×#334 | — | 8 | 1 | no | — |
| 170 | C2×#334 | — | 16 | 2 | no | — |
| 171 | #1450 | — | 4 | 1 | no | — |
| 172 | C2×C82 | — | 2 | 1 | no | — |
| 173 | C2×C82 | C4×Q8 | 1 | 1 | yes | characteristic |
| 174 | C2×C82 | #125 | 1 | 1 | yes | characteristic |
| 175 | #1422 | — | 2 | 2 | no | — |
| 176 | #1422 | — | 2 | 2 | no | — |
| 177 | #1422 | — | 4 | 2 | no | — |
| 178 | #1422 | — | 4 | 2 | no | — |
| 179 | #1422 | — | 4 | 1 | no | — |
| 180 | #1422 | — | 4 | 1 | no | — |
| 181 | #1422 | — | 4 | 1 | no | — |
| 182 | #1422 | — | 4 | 1 | no | — |
| 183 | #1422 | — | 4 | 1 | no | — |
| 184 | #1422 | — | 4 | 1 | no | — |
| 185 | #1398 | — | 2 | 4 | no | — |
| 186 | #1398 | — | 2 | 2 | no | — |
| 187 | #1398 | — | 2 | 2 | no | — |
| 188 | #1398 | — | 2 | 2 | no | — |
| 189 | #1398 | — | 4 | 1 | no | — |
| 190 | #1398 | — | 4 | 2 | no | — |
| 191 | #1398 | — | 8 | 1 | no | — |
| 192 | #1398 | — | 8 | 1 | no | — |
| 193 | #1398 | — | 8 | 1 | no | — |
| 194 | #1398 | — | 8 | 1 | no | — |
| 195 | #1398 | — | 8 | 1 | no | — |
| 196 | #1398 | — | 8 | 1 | no | — |
| 197 | #1397 | — | 2 | 1 | no | — |
| 198 | #1397 | — | 2 | 1 | no | — |
| 199 | #1397 | — | 2 | 1 | no | — |
| 200 | #1397 | #108 | 1 | 2 | yes | — |
| 201 | C4×C32 | — | 2 | 1 | no | — |
| 202 | C4×C32 | — | 2 | 1 | no | — |
| 203 | C4×C32 | C4⋊C8 | 1 | 2 | yes | — |
| 204 | C4×C32 | C4⋊C8 | 1 | 2 | yes | — |
| 205 | #1376 | — | 4 | 1 | no | — |
| 206 | #1369 | — | 4 | 1 | no | — |
| 207 | #1369 | — | 4 | 1 | no | — |
| 208 | #1369 | — | 8 | 1 | no | — |
| 209 | #1369 | — | 8 | 1 | no | — |
| 210 | #1369 | — | 8 | 1 | no | — |
| 211 | #1369 | — | 8 | 2 | no | — |
| 212 | #1369 | — | 8 | 1 | no | — |
| 213 | #1369 | — | 16 | 1 | no | — |
| 214 | #1368 | — | 4 | 1 | no | — |
| 215 | #1368 | — | 4 | 1 | no | — |
| 216 | #1368 | — | 8 | 1 | no | — |
| 217 | #1368 | — | 8 | 1 | no | — |
| 218 | #1368 | — | 8 | 1 | no | — |
| 219 | #1368 | — | 8 | 2 | no | — |
| 220 | #1368 | — | 8 | 1 | no | — |
| 221 | #1368 | — | 16 | 1 | no | — |
| 222 | #1367 | — | 16 | 2 | no | — |
| 223 | #1313 | — | 8 | 1 | no | — |
| 224 | #1313 | — | 8 | 1 | no | — |
| 225 | #1311 | — | 2 | 1 | no | — |
| 226 | #1311 | — | 2 | 1 | no | — |
| 227 | #1311 | — | 2 | 1 | no | — |
| 228 | #1311 | — | 2 | 1 | no | — |
| 229 | C8×C16 | — | 4 | 1 | no | — |
| 230 | C8×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 231 | C8×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 232 | C8×C16 | #131 | 1 | 1 | yes | characteristic |
| 233 | C8×C16 | #131 | 1 | 1 | yes | characteristic |
| 234 | #1276 | — | 4 | 1 | no | — |
| 235 | C2×M32 | — | 8 | 1 | no | — |
| 236 | C2×M32 | — | 16 | 1 | no | — |
| 237 | C22×C16 | C2×#106 | 1 | 1 | yes | characteristic |
| 238 | C22×C16 | #428 | 1 | 1 | yes | characteristic |
| 239 | C22×C16 | #441 | 1 | 1 | yes | characteristic |
| 240 | C22×C16 | #442 | 1 | 1 | yes | characteristic |
| 241 | C22×C16 | #475 | 1 | 1 | yes | characteristic |
| 242 | C22×C16 | #476 | 1 | 1 | yes | characteristic |
| 243 | C22×C16 | #501 | 1 | 1 | yes | characteristic |
| 244 | C22×C16 | #501 | 1 | 1 | yes | characteristic |
| 245 | #431 | — | 8 | 1 | no | — |
| 246 | C2×C4⋊C8 | — | 16 | 2 | no | — |
| 247 | C2×C4⋊C8 | — | 16 | 1 | no | — |
| 248 | C2×C4×C8 | — | 2 | 1 | no | — |
| 249 | C2×C4×C8 | — | 2 | 1 | no | — |
| 250 | C2×C4×C8 | — | 4 | 2 | no | — |
| 251 | C2×C4×C8 | #389 | 1 | 1 | yes | characteristic |
| 252 | C2×C4×C8 | #460 | 1 | 1 | yes | characteristic |
| 253 | C2×C4×C8 | #461 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C8 | #468 | 1 | 1 | yes | characteristic |
| 255 | C2×C4×C8 | #468 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C8 | #471 | 1 | 1 | yes | characteristic |
| 257 | C43 | #471 | 1 | 1 | yes | characteristic |
| 258 | M64 | — | 2 | 2 | no | — |
| 259 | M64 | — | 2 | 2 | no | — |
| 260 | M64 | — | 2 | 1 | no | — |
| 261 | M64 | — | 2 | 1 | no | — |
| 262 | M64 | — | 2 | 1 | no | — |
| 263 | M64 | — | 2 | 2 | no | — |
| 264 | M64 | — | 2 | 1 | no | — |
| 265 | M64 | — | 2 | 1 | no | — |
| 266 | M64 | — | 4 | 1 | no | — |
| 267 | M64 | — | 4 | 2 | no | — |
| 268 | M64 | — | 4 | 2 | no | — |
| 269 | M64 | — | 8 | 1 | no | — |
| 270 | M64 | — | 8 | 1 | no | — |
| 271 | M64 | — | 8 | 2 | no | — |
| 272 | M64 | — | 8 | 2 | no | — |
| 273 | M64 | — | 8 | 1 | no | — |
| 274 | M64 | — | 8 | 1 | no | — |
| 275 | M64 | — | 8 | 1 | no | — |
| 276 | M64 | — | 8 | 1 | no | — |
| 277 | M64 | #365 | 1 | 2 | yes | — |
| 278 | M64 | #365 | 1 | 2 | yes | — |
| 279 | M64 | #365 | 1 | 2 | yes | — |
| 280 | C2×C32 | — | 2 | 2 | no | — |
| 281 | C2×C32 | — | 2 | 1 | no | — |
| 282 | C2×C32 | — | 2 | 1 | no | — |
| 283 | C2×C32 | — | 4 | 1 | no | — |
| 284 | C2×C32 | — | 8 | 1 | no | — |
| 285 | C2×C32 | — | 8 | 1 | no | — |
| 286 | C2×C32 | — | 8 | 1 | no | — |
| 287 | C2×C32 | — | 8 | 1 | no | — |
| 288 | C2×C32 | — | 8 | 2 | no | — |
| 289 | C2×C32 | #334 | 1 | 2 | yes | — |
| 290 | C2×C32 | #334 | 1 | 2 | yes | — |
| 291 | #364 | — | 8 | 1 | no | — |
| 292 | #364 | — | 8 | 1 | no | — |
| 293 | #364 | — | 16 | 1 | no | — |
| 294 | #364 | — | 16 | 1 | no | — |
| 295 | #364 | — | 16 | 1 | no | — |
| 296 | #364 | — | 16 | 1 | no | — |
| 297 | C4⋊C16 | — | 16 | 2 | no | — |
| 298 | #346 | — | 2 | 1 | no | — |
| 299 | #346 | — | 2 | 1 | no | — |
| 300 | #346 | — | 2 | 1 | no | — |
| 301 | #346 | — | 2 | 1 | no | — |
| 302 | #346 | — | 2 | 1 | no | — |
| 303 | #346 | — | 2 | 1 | no | — |
| 304 | #346 | — | 2 | 1 | no | — |
| 305 | #346 | — | 2 | 1 | no | — |
| 306 | #346 | — | 2 | 2 | no | — |
| 307 | #346 | — | 4 | 1 | no | — |
| 308 | #346 | — | 4 | 1 | no | — |
| 309 | #346 | — | 4 | 1 | no | — |
| 310 | #346 | — | 8 | 1 | no | — |
| 311 | C4×C16 | — | 2 | 1 | no | — |
| 312 | C4×C16 | — | 2 | 1 | no | — |
| 313 | C4×C16 | — | 2 | 1 | no | — |
| 314 | C4×C16 | — | 2 | 1 | no | — |
| 315 | C4×C16 | — | 8 | 1 | no | — |
| 316 | C4×C16 | C2×C4⋊C8 | 1 | 1 | yes | characteristic |
| 317 | C4×C16 | #424 | 1 | 1 | yes | characteristic |
| 318 | C4×C16 | C2×#108 | 1 | 1 | yes | characteristic |
| 319 | C4×C16 | #430 | 1 | 1 | yes | characteristic |
| 320 | C4×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 321 | C4×C16 | #436 | 1 | 1 | yes | characteristic |
| 322 | C4×C16 | #444 | 1 | 1 | yes | characteristic |
| 323 | C4×C16 | #444 | 1 | 1 | yes | characteristic |
| 324 | #335 | — | 8 | 1 | no | — |
| 325 | #334 | — | 8 | 1 | no | — |
| 326 | #334 | — | 16 | 1 | no | — |
| 327 | #334 | — | 16 | 1 | no | — |
| 328 | #334 | — | 16 | 1 | no | — |
| 329 | #334 | — | 16 | 1 | no | — |
| 330 | #334 | — | 32 | 4 | no | — |
| 331 | #322 | — | 8 | 1 | no | — |
| 332 | C82 | — | 2 | 1 | no | — |
| 333 | C82 | — | 2 | 1 | no | — |
| 334 | C82 | — | 2 | 1 | no | — |
| 335 | C82 | — | 4 | 2 | no | — |
| 336 | C82 | — | 8 | 1 | no | — |
| 337 | C82 | C8×Q8 | 1 | 1 | yes | characteristic |
| 338 | C82 | #446 | 1 | 1 | yes | characteristic |
| 339 | C22×C8 | — | 2 | 2 | no | — |
| 340 | C22×C8 | — | 4 | 1 | no | — |
| 341 | C22×C8 | — | 32 | 1 | no | — |
| 342 | C22×C8 | #1686 | 1 | 1 | yes | characteristic |
| 343 | C22×C8 | #1691 | 1 | 1 | yes | characteristic |
| 344 | C22×C8 | #1943 | 1 | 1 | yes | characteristic |
| 345 | C22×C8 | #1948 | 1 | 1 | yes | characteristic |
| 346 | C2×C42 | — | 4 | 1 | no | — |
| 347 | C2×C42 | #1686 | 1 | 1 | yes | characteristic |
| 348 | C2×C42 | #1691 | 1 | 1 | yes | characteristic |
| 349 | C2×C42 | #1951 | 1 | 1 | yes | characteristic |
| 350 | M32 | — | 16 | 1 | no | — |
| 351 | M32 | — | 16 | 1 | no | — |
| 352 | M32 | — | 32 | 1 | no | — |
| 353 | M32 | — | 32 | 1 | no | — |
| 354 | C2×C16 | — | 2 | 1 | no | — |
| 355 | C2×C16 | — | 2 | 1 | no | — |
| 356 | C2×C16 | — | 2 | 1 | no | — |
| 357 | C2×C16 | — | 2 | 1 | no | — |
| 358 | C2×C16 | — | 2 | 1 | no | — |
| 359 | C2×C16 | — | 2 | 1 | no | — |
| 360 | C2×C16 | — | 2 | 1 | no | — |
| 361 | C2×C16 | — | 2 | 1 | no | — |
| 362 | C2×C16 | — | 2 | 1 | no | — |
| 363 | C2×C16 | — | 2 | 1 | no | — |
| 364 | C2×C16 | — | 2 | 1 | no | — |
| 365 | C2×C16 | — | 2 | 1 | no | — |
| 366 | C2×C16 | — | 2 | 1 | no | — |
| 367 | C2×C16 | — | 2 | 1 | no | — |
| 368 | C2×C16 | — | 2 | 1 | no | — |
| 369 | C2×C16 | — | 16 | 1 | no | — |
| 370 | C2×C16 | — | 32 | 1 | no | — |
| 371 | C2×C16 | C2×#334 | 1 | 1 | yes | characteristic |
| 372 | C2×C16 | #1565 | 1 | 1 | yes | characteristic |
| 373 | C2×C16 | #1570 | 1 | 1 | yes | characteristic |
| 374 | C2×C16 | #1574 | 1 | 1 | yes | characteristic |
| 375 | C2×C16 | #1579 | 1 | 1 | yes | characteristic |
| 376 | C2×C16 | #1580 | 1 | 1 | yes | characteristic |
| 377 | C2×C16 | #1593 | 1 | 1 | yes | characteristic |
| 378 | C2×C16 | #1594 | 1 | 1 | yes | characteristic |
| 379 | C2×C16 | C2×#365 | 1 | 1 | yes | characteristic |
| 380 | C2×C16 | C2×#365 | 1 | 1 | yes | characteristic |
| 381 | C2×C16 | C2×#365 | 1 | 1 | yes | characteristic |
| 382 | C2×C16 | #2155 | 1 | 1 | yes | characteristic |
| 383 | C2×C16 | #2180 | 1 | 1 | yes | characteristic |
| 384 | C2×C16 | #2180 | 1 | 1 | yes | characteristic |
| 385 | C2×C16 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 386 | C2×C16 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 387 | C2×C16 | #2230 | 1 | 2 | yes | — |
| 388 | C4⋊C8 | — | 16 | 1 | no | — |
| 389 | C4⋊C8 | — | 32 | 1 | no | — |
| 390 | C4⋊C8 | — | 32 | 1 | no | — |
| 391 | C4⋊C8 | — | 32 | 4 | no | — |
| 392 | C22⋊C8 | — | 16 | 1 | no | — |
| 393 | C4×C8 | — | 2 | 2 | no | — |
| 394 | C4×C8 | — | 2 | 1 | no | — |
| 395 | C4×C8 | — | 2 | 1 | no | — |
| 396 | C4×C8 | — | 2 | 1 | no | — |
| 397 | C4×C8 | — | 2 | 1 | no | — |
| 398 | C4×C8 | — | 2 | 1 | no | — |
| 399 | C4×C8 | — | 2 | 1 | no | — |
| 400 | C4×C8 | — | 2 | 1 | no | — |
| 401 | C4×C8 | — | 2 | 1 | no | — |
| 402 | C4×C8 | — | 2 | 1 | no | — |
| 403 | C4×C8 | — | 2 | 1 | no | — |
| 404 | C4×C8 | — | 4 | 1 | no | — |
| 405 | C4×C8 | — | 4 | 1 | no | — |
| 406 | C4×C8 | — | 4 | 1 | no | — |
| 407 | C4×C8 | — | 8 | 4 | no | — |
| 408 | C4×C8 | — | 16 | 1 | no | — |
| 409 | C4×C8 | #1939 | 1 | 1 | yes | characteristic |
| 410 | C4×C8 | #1946 | 1 | 1 | yes | characteristic |
| 411 | C4×C8 | #1950 | 1 | 1 | yes | characteristic |
| 412 | C4×C8 | #1953 | 1 | 1 | yes | characteristic |
| 413 | C32 | — | 2 | 4 | no | — |
| 414 | C32 | — | 2 | 2 | no | — |
| 415 | C32 | — | 2 | 2 | no | — |
| 416 | C32 | — | 4 | 2 | no | — |
| 417 | C32 | — | 4 | 1 | no | — |
| 418 | C32 | — | 8 | 2 | no | — |
| 419 | C32 | — | 8 | 2 | no | — |
| 420 | C32 | — | 16 | 2 | no | — |
| 421 | C32 | — | 16 | 1 | no | — |
| 422 | C32 | — | 16 | 1 | no | — |
| 423 | C32 | #1368 | 1 | 4 | yes | — |
| 424 | C22×C4 | — | 2 | 1 | no | — |
| 425 | C22×C4 | — | 2 | 1 | no | — |
| 426 | C22×C4 | — | 2 | 1 | no | — |
| 427 | C22×C4 | #9618 | 1 | 1 | yes | characteristic |
| 428 | C2×C8 | — | 2 | 2 | no | — |
| 429 | C2×C8 | — | 2 | 2 | no | — |
| 430 | C2×C8 | — | 2 | 1 | no | — |
| 431 | C2×C8 | — | 2 | 1 | no | — |
| 432 | C2×C8 | — | 2 | 1 | no | — |
| 433 | C2×C8 | — | 2 | 1 | no | — |
| 434 | C2×C8 | — | 2 | 1 | no | — |
| 435 | C2×C8 | — | 2 | 1 | no | — |
| 436 | C2×C8 | — | 4 | 4 | no | — |
| 437 | C2×C8 | — | 8 | 1 | no | — |
| 438 | C2×C8 | — | 8 | 2 | no | — |
| 439 | C2×C8 | — | 32 | 1 | no | — |
| 440 | C2×C8 | — | 64 | 1 | no | — |
| 441 | C2×C8 | — | 64 | 2 | no | — |
| 442 | C2×C8 | #9595 | 1 | 1 | yes | characteristic |
| 443 | C2×C8 | #9602 | 1 | 1 | yes | characteristic |
| 444 | C2×C8 | #9625 | 1 | 1 | yes | characteristic |
| 445 | C2×C8 | #9631 | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | #13174 | 1 | 1 | yes | characteristic |
| 447 | C2×C8 | #13174 | 1 | 1 | yes | characteristic |
| 448 | C2×C8 | #13175 | 1 | 1 | yes | characteristic |
| 449 | C2×C8 | #13175 | 1 | 1 | yes | characteristic |
| 450 | C2×C8 | #13183 | 1 | 1 | yes | characteristic |
| 451 | C2×C8 | #13185 | 1 | 1 | yes | characteristic |
| 452 | C2×C8 | #13186 | 1 | 1 | yes | characteristic |
| 453 | C2×C8 | #13188 | 1 | 1 | yes | characteristic |
| 454 | C42 | — | 2 | 1 | no | — |
| 455 | C42 | — | 2 | 1 | no | — |
| 456 | C42 | — | 2 | 1 | no | — |
| 457 | C42 | — | 2 | 1 | no | — |
| 458 | C42 | — | 2 | 1 | no | — |
| 459 | C42 | — | 8 | 2 | no | — |
| 460 | C42 | #9607 | 1 | 1 | yes | characteristic |
| 461 | C42 | #9635 | 1 | 1 | yes | characteristic |
| 462 | C16 | — | 2 | 1 | no | — |
| 463 | C16 | — | 2 | 1 | no | — |
| 464 | C16 | — | 2 | 1 | no | — |
| 465 | C16 | — | 2 | 1 | no | — |
| 466 | C16 | — | 2 | 2 | no | — |
| 467 | C16 | — | 4 | 1 | no | — |
| 468 | C16 | — | 4 | 1 | no | — |
| 469 | C16 | — | 4 | 1 | no | — |
| 470 | C16 | — | 32 | 1 | no | — |
| 471 | C16 | — | 64 | 1 | no | — |
| 472 | C16 | C2×#1368 | 1 | 1 | yes | characteristic |
| 473 | C16 | #12000 | 1 | 1 | yes | characteristic |
| 474 | C16 | #12029 | 1 | 1 | yes | characteristic |
| 475 | C16 | #12030 | 1 | 1 | yes | characteristic |
| 476 | C16 | #12066 | 1 | 1 | yes | characteristic |
| 477 | C16 | #12067 | 1 | 1 | yes | characteristic |
| 478 | C16 | #12087 | 1 | 1 | yes | characteristic |
| 479 | C16 | #12087 | 1 | 1 | yes | characteristic |
| 480 | C23 | #140467 | 1 | 1 | yes | characteristic |
| 481 | C2×C4 | — | 2 | 1 | no | — |
| 482 | C2×C4 | — | 2 | 1 | no | — |
| 483 | C2×C4 | — | 4 | 2 | no | — |
| 484 | C2×C4 | — | 4 | 1 | no | — |
| 485 | C2×C4 | — | 4 | 1 | no | — |
| 486 | C2×C4 | — | 8 | 1 | no | — |
| 487 | C2×C4 | — | 8 | 1 | no | — |
| 488 | C2×C4 | #101934 | 1 | 1 | yes | characteristic |
| 489 | C2×C4 | #140463 | 1 | 1 | yes | characteristic |
| 490 | C2×C4 | #140465 | 1 | 1 | yes | characteristic |
| 491 | C2×C4 | #140466 | 1 | 1 | yes | characteristic |
| 492 | C2×C4 | #140466 | 1 | 1 | yes | characteristic |
| 493 | C2×C4 | #140467 | 1 | 1 | yes | characteristic |
| 494 | C8 | — | 2 | 4 | no | — |
| 495 | C8 | — | 4 | 2 | no | — |
| 496 | C8 | — | 4 | 1 | no | — |
| 497 | C8 | — | 4 | 1 | no | — |
| 498 | C8 | — | 16 | 1 | no | — |
| 499 | C8 | — | 64 | 1 | no | — |
| 500 | C8 | — | 128 | 1 | no | — |
| 501 | C8 | #140354 | 1 | 1 | yes | characteristic |
| 502 | C8 | #140355 | 1 | 1 | yes | characteristic |
| 503 | C8 | #140388 | 1 | 1 | yes | characteristic |
| 504 | C8 | #140390 | 1 | 1 | yes | characteristic |
| 505 | C8 | #140487 | 1 | 1 | yes | characteristic |
| 506 | C8 | #140487 | 1 | 1 | yes | characteristic |
| 507 | C8 | #140503 | 1 | 1 | yes | characteristic |
| 508 | C8 | #140505 | 1 | 1 | yes | characteristic |
| 509 | C22 | — | 4 | 1 | no | — |
| 510 | C22 | #72216390 | 1 | 1 | yes | characteristic |
| 511 | C22 | #72227276 | 1 | 1 | yes | characteristic |
| 512 | C22 | #72227277 | 1 | 1 | yes | characteristic |
| 513 | C4 | — | 2 | 2 | no | — |
| 514 | C4 | — | 4 | 1 | no | — |
| 515 | C4 | — | 8 | 1 | no | — |
| 516 | C4 | — | 8 | 1 | no | — |
| 517 | C4 | #72216306 | 1 | 1 | yes | characteristic |
| 518 | C4 | #72226984 | 1 | 1 | yes | characteristic |
| 519 | C4 | #72227276 | 1 | 1 | yes | characteristic |
| 520 | C4 | #72227277 | 1 | 1 | yes | characteristic |
| 521 | C2 | — | 2 | 1 | no | — |
| 522 | C2 | — | 2 | 1 | no | — |
| 523 | C2 | — | 2 | 1 | no | — |
| 524 | C2 | #72227278 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta