Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
2067 conjugacy classes of subgroups.
The subgroup lattice has 639 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72216569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72216565 | — | 2 | 2 | no | — |
| 3 | #72216544 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72216431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72216426 | — | 2 | 2 | no | — |
| 6 | #72216424 | — | 2 | 2 | no | — |
| 7 | #72216421 | — | 2 | 2 | no | — |
| 8 | #72216300 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #72216297 | — | 2 | 2 | no | — |
| 10 | #72216293 | — | 2 | 2 | no | — |
| 11 | #72216247 | C22 | 1 | 2 | yes | — |
| 12 | #72216215 | C22 | 1 | 2 | yes | — |
| 13 | #72216199 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #72216197 | C4 | 1 | 1 | yes | characteristic |
| 15 | #72216196 | — | 2 | 2 | no | — |
| 16 | #72216196 | C4 | 1 | 1 | yes | characteristic |
| 17 | #72216196 | C4 | 1 | 1 | yes | characteristic |
| 18 | C2×#123403 | C4 | 1 | 1 | yes | characteristic |
| 19 | #72216182 | C22 | 1 | 1 | yes | characteristic |
| 20 | #72216165 | — | 2 | 2 | no | — |
| 21 | #72216165 | C22 | 1 | 1 | yes | characteristic |
| 22 | #72216165 | C22 | 1 | 1 | yes | characteristic |
| 23 | #496104 | — | 2 | 2 | no | — |
| 24 | #496104 | — | 2 | 2 | no | — |
| 25 | #496104 | — | 4 | 4 | no | — |
| 26 | C2×#12515 | — | 2 | 2 | no | — |
| 27 | C2×#12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C2×#12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | #483596 | — | 4 | 2 | no | — |
| 30 | #231469 | — | 2 | 2 | no | — |
| 31 | C4×#1712 | — | 2 | 1 | no | — |
| 32 | C4×#1712 | D4 | 1 | 2 | yes | — |
| 33 | #151981 | — | 2 | 2 | no | — |
| 34 | C2×#7456 | — | 2 | 2 | no | — |
| 35 | C2×#7390 | — | 4 | 4 | no | — |
| 36 | #141681 | — | 2 | 2 | no | — |
| 37 | #141681 | — | 2 | 2 | no | — |
| 38 | #141681 | — | 4 | 4 | no | — |
| 39 | #141665 | — | 2 | 2 | no | — |
| 40 | #141665 | — | 2 | 1 | no | — |
| 41 | #141665 | — | 2 | 2 | no | — |
| 42 | #141665 | D4 | 1 | 2 | yes | — |
| 43 | #140849 | — | 2 | 4 | no | — |
| 44 | #140747 | — | 4 | 2 | no | — |
| 45 | #136703 | — | 4 | 4 | no | — |
| 46 | #135778 | — | 2 | 2 | no | — |
| 47 | #135778 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #135778 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #129090 | D4 | 1 | 2 | yes | — |
| 50 | #129088 | D4 | 1 | 2 | yes | — |
| 51 | #129051 | — | 2 | 2 | no | — |
| 52 | C8×#346 | — | 2 | 1 | no | — |
| 53 | C8×#346 | C23 | 1 | 1 | yes | characteristic |
| 54 | #124215 | — | 2 | 2 | no | — |
| 55 | #123403 | — | 2 | 2 | no | — |
| 56 | #123403 | C8 | 1 | 4 | yes | complemented |
| 57 | C2×#7052 | — | 2 | 1 | no | — |
| 58 | C2×#7052 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C2×C162 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | #94018 | — | 2 | 2 | no | — |
| 61 | #93924 | — | 4 | 4 | no | — |
| 62 | #93264 | — | 2 | 2 | no | — |
| 63 | C2×#2246 | — | 2 | 2 | no | — |
| 64 | C2×#2246 | — | 2 | 2 | no | — |
| 65 | C2×#2246 | — | 4 | 4 | no | — |
| 66 | C2×#2177 | — | 4 | 2 | no | — |
| 67 | C2×#2177 | — | 4 | 2 | no | — |
| 68 | C2×#2177 | — | 4 | 2 | no | — |
| 69 | C2×#2177 | — | 4 | 2 | no | — |
| 70 | C2×#2177 | — | 8 | 8 | no | — |
| 71 | C4×#493 | — | 2 | 2 | no | — |
| 72 | C4×#493 | — | 4 | 2 | no | — |
| 73 | C4×#493 | — | 4 | 2 | no | — |
| 74 | C4×#493 | — | 4 | 1 | no | — |
| 75 | C2×#1712 | — | 2 | 1 | no | — |
| 76 | C2×#1712 | C22⋊C4 | 1 | 2 | yes | — |
| 77 | #17854 | — | 4 | 4 | no | — |
| 78 | C2×#1422 | — | 4 | 2 | no | — |
| 79 | C2×#1398 | — | 4 | 2 | no | — |
| 80 | #13239 | — | 4 | 2 | no | — |
| 81 | #13239 | — | 4 | 2 | no | — |
| 82 | #13239 | — | 4 | 2 | no | — |
| 83 | #13239 | — | 4 | 2 | no | — |
| 84 | #13239 | — | 8 | 8 | no | — |
| 85 | #13202 | — | 2 | 4 | no | — |
| 86 | #13202 | — | 4 | 4 | no | — |
| 87 | #13202 | — | 4 | 4 | no | — |
| 88 | #13202 | — | 4 | 2 | no | — |
| 89 | #12906 | — | 2 | 2 | no | — |
| 90 | #12906 | — | 2 | 2 | no | — |
| 91 | #12906 | — | 4 | 4 | no | — |
| 92 | C4×#364 | — | 2 | 2 | no | — |
| 93 | C4×#346 | — | 2 | 2 | no | — |
| 94 | C4×#346 | C2×D4 | 1 | 2 | yes | — |
| 95 | #12515 | — | 2 | 8 | no | — |
| 96 | #12515 | — | 2 | 1 | no | — |
| 97 | #12515 | — | 2 | 2 | no | — |
| 98 | #12515 | — | 2 | 2 | no | — |
| 99 | #12515 | — | 4 | 4 | no | — |
| 100 | #12515 | C2×C8 | 1 | 2 | yes | — |
| 101 | #12515 | C2×C8 | 1 | 2 | yes | complemented |
| 102 | #12515 | M16 | 1 | 2 | yes | — |
| 103 | #12067 | — | 8 | 8 | no | — |
| 104 | C2×#1369 | — | 2 | 2 | no | — |
| 105 | #11999 | — | 2 | 2 | no | — |
| 106 | #11599 | — | 4 | 4 | no | — |
| 107 | #11593 | — | 4 | 4 | no | — |
| 108 | #11405 | — | 4 | 2 | no | — |
| 109 | C2×#1311 | — | 2 | 2 | no | — |
| 110 | C2×#1311 | #41 | 1 | 2 | yes | — |
| 111 | C2×C8×C16 | — | 2 | 1 | no | — |
| 112 | C2×C8×C16 | — | 2 | 1 | no | — |
| 113 | C2×C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | #9824 | — | 2 | 2 | no | — |
| 116 | #9824 | — | 4 | 2 | no | — |
| 117 | #9824 | — | 4 | 2 | no | — |
| 118 | #9824 | — | 4 | 1 | no | — |
| 119 | #9668 | — | 4 | 4 | no | — |
| 120 | #8959 | — | 8 | 2 | no | — |
| 121 | #8818 | — | 2 | 1 | no | — |
| 122 | #8818 | C22⋊C4 | 1 | 2 | yes | — |
| 123 | #8266 | — | 2 | 2 | no | — |
| 124 | C4×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | #7468 | — | 4 | 2 | no | — |
| 126 | #7456 | — | 2 | 4 | no | — |
| 127 | #7456 | — | 4 | 2 | no | — |
| 128 | #7390 | — | 8 | 8 | no | — |
| 129 | #7161 | — | 2 | 2 | no | — |
| 130 | #7157 | D8 | 1 | 4 | yes | — |
| 131 | #7140 | — | 4 | 2 | no | — |
| 132 | #7107 | — | 8 | 2 | no | — |
| 133 | #7052 | — | 2 | 2 | no | — |
| 134 | #7052 | — | 4 | 2 | no | — |
| 135 | C162 | — | 2 | 1 | no | — |
| 136 | C162 | C2×C8 | 1 | 2 | yes | complemented |
| 137 | C22×D16 | — | 4 | 2 | no | — |
| 138 | C22×D16 | — | 4 | 2 | no | — |
| 139 | C22×D16 | — | 4 | 2 | no | — |
| 140 | C22×D16 | — | 4 | 2 | no | — |
| 141 | C22×D16 | — | 8 | 8 | no | — |
| 142 | C2×#493 | — | 2 | 2 | no | — |
| 143 | C2×#493 | — | 4 | 2 | no | — |
| 144 | C2×#493 | — | 4 | 2 | no | — |
| 145 | C2×#493 | — | 4 | 1 | no | — |
| 146 | #2972 | — | 8 | 2 | no | — |
| 147 | C2×C4×D8 | — | 4 | 4 | no | — |
| 148 | C2×C4×D8 | — | 8 | 4 | no | — |
| 149 | C2×C4×D8 | — | 8 | 4 | no | — |
| 150 | C2×C4×D8 | — | 8 | 2 | no | — |
| 151 | C4×#127 | — | 4 | 2 | no | — |
| 152 | C4×#127 | — | 8 | 1 | no | — |
| 153 | C2×M64 | — | 8 | 2 | no | — |
| 154 | #2246 | — | 2 | 4 | no | — |
| 155 | #2246 | — | 2 | 4 | no | — |
| 156 | #2246 | — | 2 | 4 | no | — |
| 157 | #2246 | — | 4 | 16 | no | — |
| 158 | #2246 | — | 4 | 2 | no | — |
| 159 | #2246 | — | 4 | 2 | no | — |
| 160 | #2246 | — | 4 | 2 | no | — |
| 161 | #2246 | — | 4 | 2 | no | — |
| 162 | #2246 | — | 4 | 2 | no | — |
| 163 | #2246 | — | 8 | 8 | no | — |
| 164 | #2177 | — | 8 | 4 | no | — |
| 165 | #2177 | — | 8 | 4 | no | — |
| 166 | #2177 | — | 8 | 4 | no | — |
| 167 | #2177 | — | 8 | 4 | no | — |
| 168 | #2177 | — | 16 | 2 | no | — |
| 169 | #2177 | — | 16 | 2 | no | — |
| 170 | #2177 | — | 16 | 32 | no | — |
| 171 | #2177 | — | 16 | 4 | no | — |
| 172 | C2×#367 | — | 4 | 2 | no | — |
| 173 | C2×#367 | — | 4 | 2 | no | — |
| 174 | C2×#367 | — | 4 | 2 | no | — |
| 175 | C2×#367 | — | 4 | 2 | no | — |
| 176 | C2×#367 | — | 8 | 8 | no | — |
| 177 | C2×#364 | — | 4 | 2 | no | — |
| 178 | C2×#357 | — | 4 | 4 | no | — |
| 179 | C2×#357 | — | 4 | 4 | no | — |
| 180 | C2×#357 | — | 8 | 8 | no | — |
| 181 | C2×#357 | — | 8 | 8 | no | — |
| 182 | C2×#357 | — | 8 | 2 | no | — |
| 183 | C2×#357 | — | 8 | 2 | no | — |
| 184 | C4×M32 | — | 4 | 2 | no | — |
| 185 | C2×#346 | — | 2 | 8 | no | — |
| 186 | C2×#346 | C2×D8 | 1 | 2 | yes | — |
| 187 | C2×#346 | #135 | 1 | 2 | yes | — |
| 188 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 189 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 190 | C2×C4×C16 | — | 2 | 2 | no | — |
| 191 | C2×C4×C16 | — | 2 | 2 | no | — |
| 192 | C2×C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 193 | C2×C4×C16 | #121 | 1 | 2 | yes | — |
| 194 | #1970 | — | 4 | 4 | no | — |
| 195 | #1970 | — | 8 | 4 | no | — |
| 196 | #1970 | — | 8 | 4 | no | — |
| 197 | #1970 | — | 8 | 2 | no | — |
| 198 | #1957 | — | 4 | 2 | no | — |
| 199 | #1957 | — | 8 | 2 | no | — |
| 200 | #1957 | — | 8 | 2 | no | — |
| 201 | #1957 | — | 8 | 1 | no | — |
| 202 | #1845 | — | 2 | 2 | no | — |
| 203 | #1845 | — | 4 | 2 | no | — |
| 204 | #1845 | — | 4 | 2 | no | — |
| 205 | #1845 | — | 4 | 1 | no | — |
| 206 | C42×C8 | — | 2 | 1 | no | — |
| 207 | C42×C8 | #120 | 1 | 1 | yes | characteristic |
| 208 | #1712 | — | 2 | 2 | no | — |
| 209 | #1712 | — | 2 | 2 | no | — |
| 210 | #1712 | — | 4 | 2 | no | — |
| 211 | #1712 | — | 4 | 2 | no | — |
| 212 | #1712 | — | 4 | 1 | no | — |
| 213 | #1712 | C22⋊C8 | 1 | 4 | yes | — |
| 214 | #1580 | — | 8 | 8 | no | — |
| 215 | C8×D8 | — | 16 | 4 | no | — |
| 216 | #1564 | — | 2 | 4 | no | — |
| 217 | #1478 | — | 8 | 4 | no | — |
| 218 | #1460 | — | 8 | 2 | no | — |
| 219 | #1450 | — | 4 | 2 | no | — |
| 220 | C2×C82 | — | 2 | 1 | no | — |
| 221 | C2×C82 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 222 | C2×C82 | #123 | 1 | 1 | yes | characteristic |
| 223 | #1422 | — | 4 | 4 | no | — |
| 224 | #1422 | — | 8 | 2 | no | — |
| 225 | #1398 | — | 8 | 4 | no | — |
| 226 | #1376 | — | 4 | 2 | no | — |
| 227 | #1369 | — | 4 | 4 | no | — |
| 228 | #1368 | — | 4 | 4 | no | — |
| 229 | #1333 | — | 8 | 8 | no | — |
| 230 | #1331 | — | 16 | 4 | no | — |
| 231 | #1313 | — | 8 | 4 | no | — |
| 232 | #1311 | — | 2 | 2 | no | — |
| 233 | #1311 | — | 2 | 2 | no | — |
| 234 | #1311 | — | 4 | 4 | no | — |
| 235 | C8×C16 | — | 2 | 2 | no | — |
| 236 | C8×C16 | — | 2 | 2 | no | — |
| 237 | C8×C16 | — | 4 | 1 | no | — |
| 238 | C8×C16 | — | 4 | 1 | no | — |
| 239 | C8×C16 | — | 4 | 1 | no | — |
| 240 | C8×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 241 | C8×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 242 | C8×C16 | #131 | 1 | 2 | yes | — |
| 243 | #1276 | — | 4 | 2 | no | — |
| 244 | C22×D8 | — | 4 | 4 | no | — |
| 245 | C22×D8 | — | 8 | 4 | no | — |
| 246 | C22×D8 | — | 8 | 4 | no | — |
| 247 | C22×D8 | — | 8 | 2 | no | — |
| 248 | C2×#127 | — | 4 | 2 | no | — |
| 249 | C2×#127 | — | 8 | 1 | no | — |
| 250 | C2×C4×D4 | — | 8 | 2 | no | — |
| 251 | C2×C4×D4 | — | 16 | 2 | no | — |
| 252 | C2×C4×D4 | — | 16 | 2 | no | — |
| 253 | C2×C4×D4 | — | 16 | 1 | no | — |
| 254 | C2×D16 | — | 4 | 4 | no | — |
| 255 | C2×D16 | — | 4 | 4 | no | — |
| 256 | C2×D16 | — | 4 | 4 | no | — |
| 257 | C2×D16 | — | 4 | 4 | no | — |
| 258 | C2×D16 | — | 4 | 4 | no | — |
| 259 | C2×D16 | — | 4 | 4 | no | — |
| 260 | C2×D16 | — | 8 | 32 | no | — |
| 261 | C2×D16 | — | 8 | 2 | no | — |
| 262 | C2×D16 | — | 8 | 2 | no | — |
| 263 | C2×D16 | — | 8 | 4 | no | — |
| 264 | C2×D16 | — | 8 | 4 | no | — |
| 265 | C2×D16 | — | 8 | 4 | no | — |
| 266 | C2×D16 | — | 8 | 4 | no | — |
| 267 | C2×D16 | — | 16 | 2 | no | — |
| 268 | C2×D16 | — | 16 | 2 | no | — |
| 269 | C2×D16 | — | 16 | 2 | no | — |
| 270 | C2×D16 | — | 16 | 2 | no | — |
| 271 | C2×D16 | — | 16 | 16 | no | — |
| 272 | C2×D16 | — | 16 | 16 | no | — |
| 273 | C2×M32 | — | 8 | 2 | no | — |
| 274 | C22×C16 | — | 2 | 4 | no | — |
| 275 | C22×C16 | — | 2 | 4 | no | — |
| 276 | C22×C16 | C4×D8 | 1 | 2 | yes | — |
| 277 | C22×C16 | #442 | 1 | 2 | yes | — |
| 278 | C22×C16 | #459 | 1 | 2 | yes | — |
| 279 | C22×C16 | #463 | 1 | 2 | yes | — |
| 280 | #493 | — | 2 | 4 | no | — |
| 281 | #493 | — | 4 | 4 | no | — |
| 282 | #493 | — | 4 | 4 | no | — |
| 283 | #493 | — | 4 | 2 | no | — |
| 284 | #493 | — | 4 | 4 | no | — |
| 285 | #493 | — | 4 | 2 | no | — |
| 286 | #493 | — | 8 | 2 | no | — |
| 287 | #493 | — | 8 | 2 | no | — |
| 288 | #493 | — | 8 | 4 | no | — |
| 289 | #493 | — | 8 | 4 | no | — |
| 290 | #493 | — | 8 | 2 | no | — |
| 291 | #493 | — | 8 | 1 | no | — |
| 292 | C4×D8 | — | 8 | 4 | no | — |
| 293 | C4×D8 | — | 8 | 4 | no | — |
| 294 | C4×D8 | — | 8 | 4 | no | — |
| 295 | C4×D8 | — | 8 | 4 | no | — |
| 296 | C4×D8 | — | 16 | 4 | no | — |
| 297 | C4×D8 | — | 16 | 4 | no | — |
| 298 | C4×D8 | — | 16 | 16 | no | — |
| 299 | C4×D8 | — | 16 | 16 | no | — |
| 300 | C8×D4 | — | 16 | 8 | no | — |
| 301 | #431 | — | 4 | 4 | no | — |
| 302 | C2×#107 | — | 4 | 4 | no | — |
| 303 | C2×#107 | — | 8 | 4 | no | — |
| 304 | C2×#107 | — | 8 | 4 | no | — |
| 305 | C2×#107 | — | 8 | 2 | no | — |
| 306 | C2×#102 | — | 8 | 4 | no | — |
| 307 | C2×#102 | — | 16 | 4 | no | — |
| 308 | C2×#102 | — | 16 | 4 | no | — |
| 309 | C2×#102 | — | 16 | 2 | no | — |
| 310 | C2×C22⋊C8 | — | 32 | 2 | no | — |
| 311 | C2×C4×C8 | — | 2 | 1 | no | — |
| 312 | C2×C4×C8 | — | 2 | 4 | no | — |
| 313 | C2×C4×C8 | — | 2 | 1 | no | — |
| 314 | C2×C4×C8 | #386 | 1 | 1 | yes | characteristic |
| 315 | C2×C4×C8 | #447 | 1 | 2 | yes | — |
| 316 | C2×C4×C8 | #449 | 1 | 2 | yes | — |
| 317 | C2×C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 318 | #390 | — | 8 | 2 | no | — |
| 319 | #390 | — | 16 | 2 | no | — |
| 320 | #390 | — | 16 | 2 | no | — |
| 321 | #390 | — | 16 | 1 | no | — |
| 322 | #384 | — | 4 | 2 | no | — |
| 323 | #384 | — | 8 | 1 | no | — |
| 324 | C43 | #453 | 1 | 1 | yes | characteristic |
| 325 | M64 | — | 8 | 4 | no | — |
| 326 | M64 | — | 16 | 2 | no | — |
| 327 | C2×C32 | — | 16 | 2 | no | — |
| 328 | #367 | — | 8 | 4 | no | — |
| 329 | #367 | — | 8 | 4 | no | — |
| 330 | #367 | — | 16 | 2 | no | — |
| 331 | #367 | — | 16 | 16 | no | — |
| 332 | #367 | — | 16 | 2 | no | — |
| 333 | #364 | — | 8 | 2 | no | — |
| 334 | #364 | — | 8 | 2 | no | — |
| 335 | #357 | — | 8 | 8 | no | — |
| 336 | #357 | — | 16 | 4 | no | — |
| 337 | #357 | — | 16 | 2 | no | — |
| 338 | #357 | — | 16 | 2 | no | — |
| 339 | #357 | — | 16 | 4 | no | — |
| 340 | #357 | — | 16 | 16 | no | — |
| 341 | #357 | — | 16 | 16 | no | — |
| 342 | #346 | — | 2 | 4 | no | — |
| 343 | #346 | — | 2 | 4 | no | — |
| 344 | #346 | — | 4 | 2 | no | — |
| 345 | #346 | — | 4 | 2 | no | — |
| 346 | #346 | — | 4 | 16 | no | — |
| 347 | #346 | — | 8 | 2 | no | — |
| 348 | C4×C16 | — | 2 | 4 | no | — |
| 349 | C4×C16 | — | 2 | 4 | no | — |
| 350 | C4×C16 | — | 2 | 2 | no | — |
| 351 | C4×C16 | — | 2 | 2 | no | — |
| 352 | C4×C16 | — | 4 | 2 | no | — |
| 353 | C4×C16 | — | 4 | 2 | no | — |
| 354 | C4×C16 | — | 8 | 2 | no | — |
| 355 | C4×C16 | C8×D4 | 1 | 2 | yes | — |
| 356 | C4×C16 | #435 | 1 | 2 | yes | — |
| 357 | C4×C16 | #443 | 1 | 2 | yes | — |
| 358 | C4×C16 | #444 | 1 | 2 | yes | — |
| 359 | #335 | — | 4 | 4 | no | — |
| 360 | #334 | — | 4 | 4 | no | — |
| 361 | D4⋊C8 | — | 16 | 8 | no | — |
| 362 | #323 | — | 32 | 2 | no | — |
| 363 | #322 | — | 8 | 2 | no | — |
| 364 | C82 | — | 2 | 1 | no | — |
| 365 | C82 | — | 2 | 2 | no | — |
| 366 | C82 | — | 4 | 2 | no | — |
| 367 | C82 | — | 8 | 2 | no | — |
| 368 | C82 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 369 | C82 | #408 | 1 | 1 | yes | characteristic |
| 370 | C22×D4 | — | 8 | 2 | no | — |
| 371 | C22×D4 | — | 16 | 2 | no | — |
| 372 | C22×D4 | — | 16 | 2 | no | — |
| 373 | C22×D4 | — | 16 | 1 | no | — |
| 374 | C23×C4 | — | 16 | 2 | no | — |
| 375 | C23×C4 | — | 32 | 1 | no | — |
| 376 | C2×D8 | — | 4 | 8 | no | — |
| 377 | C2×D8 | — | 8 | 8 | no | — |
| 378 | C2×D8 | — | 8 | 8 | no | — |
| 379 | C2×D8 | — | 8 | 4 | no | — |
| 380 | C2×D8 | — | 8 | 4 | no | — |
| 381 | C2×D8 | — | 8 | 4 | no | — |
| 382 | C2×D8 | — | 8 | 4 | no | — |
| 383 | C2×D8 | — | 8 | 4 | no | — |
| 384 | C2×D8 | — | 8 | 4 | no | — |
| 385 | C2×D8 | — | 16 | 8 | no | — |
| 386 | C2×D8 | — | 16 | 8 | no | — |
| 387 | C2×D8 | — | 16 | 8 | no | — |
| 388 | C2×D8 | — | 16 | 8 | no | — |
| 389 | C2×D8 | — | 16 | 4 | no | — |
| 390 | C2×D8 | — | 16 | 4 | no | — |
| 391 | C2×D8 | — | 16 | 2 | no | — |
| 392 | C2×D8 | — | 16 | 2 | no | — |
| 393 | C2×D8 | — | 16 | 2 | no | — |
| 394 | C2×D8 | — | 16 | 2 | no | — |
| 395 | C2×D8 | — | 16 | 2 | no | — |
| 396 | C22×C8 | — | 2 | 2 | no | — |
| 397 | C22×C8 | — | 2 | 2 | no | — |
| 398 | C22×C8 | — | 32 | 4 | no | — |
| 399 | C22×C8 | #1621 | 1 | 2 | yes | — |
| 400 | C22×C8 | #1879 | 1 | 2 | yes | — |
| 401 | #127 | — | 4 | 4 | no | — |
| 402 | #127 | — | 8 | 2 | no | — |
| 403 | #127 | — | 8 | 2 | no | — |
| 404 | #127 | — | 16 | 2 | no | — |
| 405 | #127 | — | 16 | 2 | no | — |
| 406 | #127 | — | 16 | 1 | no | — |
| 407 | C4×D4 | — | 16 | 4 | no | — |
| 408 | C4×D4 | — | 16 | 4 | no | — |
| 409 | C4×D4 | — | 32 | 4 | no | — |
| 410 | C4×D4 | — | 32 | 8 | no | — |
| 411 | C4×D4 | — | 32 | 8 | no | — |
| 412 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 413 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 414 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 415 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 416 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 417 | C2×C22⋊C4 | — | 32 | 2 | no | — |
| 418 | C2×C22⋊C4 | — | 32 | 1 | no | — |
| 419 | C2×C22⋊C4 | — | 32 | 2 | no | — |
| 420 | C2×C42 | — | 2 | 2 | no | — |
| 421 | C2×C42 | #1619 | 1 | 1 | yes | characteristic |
| 422 | C2×C42 | #1620 | 1 | 1 | yes | characteristic |
| 423 | C2×C42 | #1887 | 1 | 1 | yes | characteristic |
| 424 | D16 | — | 8 | 8 | no | — |
| 425 | D16 | — | 8 | 8 | no | — |
| 426 | D16 | — | 8 | 8 | no | — |
| 427 | D16 | — | 16 | 4 | no | — |
| 428 | D16 | — | 16 | 4 | no | — |
| 429 | D16 | — | 16 | 4 | no | — |
| 430 | D16 | — | 16 | 64 | no | — |
| 431 | D16 | — | 16 | 4 | no | — |
| 432 | D16 | — | 16 | 4 | no | — |
| 433 | M32 | — | 16 | 2 | no | — |
| 434 | M32 | — | 16 | 2 | no | — |
| 435 | C2×C16 | — | 2 | 8 | no | — |
| 436 | C2×C16 | — | 2 | 16 | no | — |
| 437 | C2×C16 | — | 2 | 2 | no | — |
| 438 | C2×C16 | — | 2 | 2 | no | — |
| 439 | C2×C16 | — | 2 | 2 | no | — |
| 440 | C2×C16 | — | 2 | 2 | no | — |
| 441 | C2×C16 | — | 2 | 2 | no | — |
| 442 | C2×C16 | — | 2 | 2 | no | — |
| 443 | C2×C16 | — | 2 | 2 | no | — |
| 444 | C2×C16 | — | 2 | 2 | no | — |
| 445 | C2×C16 | — | 4 | 4 | no | — |
| 446 | C2×C16 | — | 4 | 8 | no | — |
| 447 | C2×C16 | — | 16 | 2 | no | — |
| 448 | C2×C16 | C8×D8 | 1 | 2 | yes | — |
| 449 | C2×C16 | #1580 | 1 | 2 | yes | — |
| 450 | C2×C16 | #1581 | 1 | 2 | yes | — |
| 451 | C2×C16 | #1586 | 1 | 2 | yes | — |
| 452 | C2×C16 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 453 | C2×C16 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 454 | #107 | — | 8 | 4 | no | — |
| 455 | #107 | — | 8 | 4 | no | — |
| 456 | #107 | — | 16 | 8 | no | — |
| 457 | #107 | — | 16 | 8 | no | — |
| 458 | #107 | — | 16 | 2 | no | — |
| 459 | #107 | — | 16 | 2 | no | — |
| 460 | C4⋊C8 | — | 8 | 4 | no | — |
| 461 | #102 | — | 16 | 4 | no | — |
| 462 | #102 | — | 16 | 4 | no | — |
| 463 | #102 | — | 32 | 4 | no | — |
| 464 | #102 | — | 32 | 8 | no | — |
| 465 | #102 | — | 32 | 8 | no | — |
| 466 | C22⋊C8 | — | 8 | 4 | no | — |
| 467 | C22⋊C8 | — | 32 | 4 | no | — |
| 468 | C4×C8 | — | 2 | 2 | no | — |
| 469 | C4×C8 | — | 2 | 2 | no | — |
| 470 | C4×C8 | — | 2 | 2 | no | — |
| 471 | C4×C8 | — | 2 | 2 | no | — |
| 472 | C4×C8 | — | 2 | 2 | no | — |
| 473 | C4×C8 | — | 2 | 1 | no | — |
| 474 | C4×C8 | — | 2 | 1 | no | — |
| 475 | C4×C8 | — | 4 | 1 | no | — |
| 476 | C4×C8 | — | 4 | 1 | no | — |
| 477 | C4×C8 | — | 4 | 8 | no | — |
| 478 | C4×C8 | — | 4 | 1 | no | — |
| 479 | C4×C8 | — | 8 | 4 | no | — |
| 480 | C4×C8 | #1869 | 1 | 1 | yes | characteristic |
| 481 | C4×C8 | #1876 | 1 | 2 | yes | — |
| 482 | C4×C8 | #1884 | 1 | 1 | yes | characteristic |
| 483 | C32 | — | 16 | 4 | no | — |
| 484 | C24 | — | 16 | 2 | no | — |
| 485 | C24 | — | 32 | 1 | no | — |
| 486 | C2×D4 | — | 8 | 4 | no | — |
| 487 | C2×D4 | — | 16 | 4 | no | — |
| 488 | C2×D4 | — | 16 | 4 | no | — |
| 489 | C2×D4 | — | 16 | 2 | no | — |
| 490 | C2×D4 | — | 16 | 4 | no | — |
| 491 | C2×D4 | — | 16 | 4 | no | — |
| 492 | C2×D4 | — | 16 | 2 | no | — |
| 493 | C2×D4 | — | 32 | 4 | no | — |
| 494 | C2×D4 | — | 32 | 4 | no | — |
| 495 | C2×D4 | — | 32 | 4 | no | — |
| 496 | C2×D4 | — | 32 | 4 | no | — |
| 497 | C2×D4 | — | 32 | 2 | no | — |
| 498 | C2×D4 | — | 32 | 2 | no | — |
| 499 | C2×D4 | — | 32 | 2 | no | — |
| 500 | C2×D4 | — | 32 | 2 | no | — |
| 501 | C2×D4 | — | 32 | 1 | no | — |
| 502 | C22×C4 | — | 2 | 1 | no | — |
| 503 | C22×C4 | — | 2 | 1 | no | — |
| 504 | C22×C4 | — | 16 | 2 | no | — |
| 505 | C22×C4 | — | 32 | 2 | no | — |
| 506 | C22×C4 | — | 32 | 2 | no | — |
| 507 | C22×C4 | — | 32 | 1 | no | — |
| 508 | C22×C4 | — | 64 | 4 | no | — |
| 509 | C22×C4 | — | 64 | 4 | no | — |
| 510 | C22×C4 | — | 64 | 2 | no | — |
| 511 | C22×C4 | #9061 | 1 | 1 | yes | characteristic |
| 512 | C22×C4 | #12310 | 1 | 2 | yes | — |
| 513 | D8 | — | 8 | 8 | no | — |
| 514 | D8 | — | 8 | 8 | no | — |
| 515 | D8 | — | 16 | 16 | no | — |
| 516 | D8 | — | 16 | 16 | no | — |
| 517 | D8 | — | 16 | 4 | no | — |
| 518 | D8 | — | 16 | 4 | no | — |
| 519 | D8 | — | 16 | 4 | no | — |
| 520 | D8 | — | 16 | 4 | no | — |
| 521 | D8 | — | 32 | 8 | no | — |
| 522 | D8 | — | 32 | 8 | no | — |
| 523 | D8 | — | 32 | 2 | no | — |
| 524 | D8 | — | 32 | 2 | no | — |
| 525 | C2×C8 | — | 2 | 2 | no | — |
| 526 | C2×C8 | — | 2 | 2 | no | — |
| 527 | C2×C8 | — | 2 | 8 | no | — |
| 528 | C2×C8 | — | 2 | 2 | no | — |
| 529 | C2×C8 | — | 2 | 2 | no | — |
| 530 | C2×C8 | — | 2 | 2 | no | — |
| 531 | C2×C8 | — | 4 | 4 | no | — |
| 532 | C2×C8 | — | 4 | 2 | no | — |
| 533 | C2×C8 | — | 16 | 4 | no | — |
| 534 | C2×C8 | — | 128 | 4 | no | — |
| 535 | C2×C8 | #8947 | 1 | 2 | yes | — |
| 536 | C2×C8 | #9053 | 1 | 2 | yes | — |
| 537 | C2×C8 | #13033 | 1 | 2 | yes | — |
| 538 | C2×C8 | #13036 | 1 | 2 | yes | — |
| 539 | C2×C8 | #13037 | 1 | 2 | yes | — |
| 540 | C2×C8 | #13040 | 1 | 2 | yes | — |
| 541 | C4⋊C4 | — | 16 | 4 | no | — |
| 542 | C4⋊C4 | — | 32 | 4 | no | — |
| 543 | C4⋊C4 | — | 32 | 4 | no | — |
| 544 | C4⋊C4 | — | 32 | 2 | no | — |
| 545 | C22⋊C4 | — | 32 | 4 | no | — |
| 546 | C22⋊C4 | — | 64 | 4 | no | — |
| 547 | C22⋊C4 | — | 64 | 4 | no | — |
| 548 | C22⋊C4 | — | 64 | 2 | no | — |
| 549 | C42 | — | 2 | 2 | no | — |
| 550 | C42 | — | 2 | 1 | no | — |
| 551 | C42 | — | 2 | 2 | no | — |
| 552 | C42 | — | 4 | 4 | no | — |
| 553 | C42 | #8959 | 1 | 1 | yes | characteristic |
| 554 | C42 | #9069 | 1 | 1 | yes | characteristic |
| 555 | C16 | — | 2 | 16 | no | — |
| 556 | C16 | — | 2 | 2 | no | — |
| 557 | C16 | — | 2 | 2 | no | — |
| 558 | C16 | — | 4 | 2 | no | — |
| 559 | C16 | — | 4 | 2 | no | — |
| 560 | C16 | — | 8 | 4 | no | — |
| 561 | C16 | — | 32 | 2 | no | — |
| 562 | C16 | #12067 | 1 | 4 | yes | — |
| 563 | C16 | #12078 | 1 | 4 | yes | — |
| 564 | C23 | — | 16 | 4 | no | — |
| 565 | C23 | — | 32 | 2 | no | — |
| 566 | C23 | — | 32 | 2 | no | — |
| 567 | C23 | — | 32 | 2 | no | — |
| 568 | C23 | — | 64 | 2 | no | — |
| 569 | C23 | — | 64 | 2 | no | — |
| 570 | C23 | — | 64 | 2 | no | — |
| 571 | C23 | — | 64 | 2 | no | — |
| 572 | C23 | — | 64 | 1 | no | — |
| 573 | C23 | — | 64 | 1 | no | — |
| 574 | C23 | #137551 | 1 | 1 | yes | characteristic |
| 575 | D4 | — | 16 | 8 | no | — |
| 576 | D4 | — | 32 | 8 | no | — |
| 577 | D4 | — | 32 | 8 | no | — |
| 578 | D4 | — | 32 | 4 | no | — |
| 579 | D4 | — | 32 | 4 | no | — |
| 580 | D4 | — | 64 | 4 | no | — |
| 581 | D4 | — | 64 | 4 | no | — |
| 582 | D4 | — | 64 | 2 | no | — |
| 583 | C2×C4 | — | 2 | 4 | no | — |
| 584 | C2×C4 | — | 2 | 1 | no | — |
| 585 | C2×C4 | — | 2 | 1 | no | — |
| 586 | C2×C4 | — | 2 | 2 | no | — |
| 587 | C2×C4 | — | 4 | 2 | no | — |
| 588 | C2×C4 | — | 4 | 2 | no | — |
| 589 | C2×C4 | — | 4 | 1 | no | — |
| 590 | C2×C4 | — | 32 | 2 | no | — |
| 591 | C2×C4 | — | 64 | 4 | no | — |
| 592 | C2×C4 | — | 64 | 2 | no | — |
| 593 | C2×C4 | — | 64 | 2 | no | — |
| 594 | C2×C4 | — | 64 | 1 | no | — |
| 595 | C2×C4 | — | 128 | 2 | no | — |
| 596 | C2×C4 | — | 128 | 4 | no | — |
| 597 | C2×C4 | #99599 | 1 | 1 | yes | characteristic |
| 598 | C2×C4 | #137546 | 1 | 2 | yes | — |
| 599 | C2×C4 | #137549 | 1 | 2 | yes | — |
| 600 | C2×C4 | #137550 | 1 | 1 | yes | characteristic |
| 601 | C8 | — | 2 | 4 | no | — |
| 602 | C8 | — | 2 | 4 | no | — |
| 603 | C8 | — | 4 | 2 | no | — |
| 604 | C8 | — | 8 | 2 | no | — |
| 605 | C8 | — | 32 | 4 | no | — |
| 606 | C8 | #136703 | 1 | 2 | yes | — |
| 607 | C8 | #136707 | 1 | 2 | yes | — |
| 608 | C8 | #137499 | 1 | 2 | yes | — |
| 609 | C8 | #137501 | 1 | 2 | yes | — |
| 610 | C22 | — | 2 | 2 | no | — |
| 611 | C22 | — | 32 | 4 | no | — |
| 612 | C22 | — | 64 | 4 | no | — |
| 613 | C22 | — | 64 | 4 | no | — |
| 614 | C22 | — | 64 | 2 | no | — |
| 615 | C22 | — | 64 | 2 | no | — |
| 616 | C22 | — | 64 | 2 | no | — |
| 617 | C22 | — | 128 | 2 | no | — |
| 618 | C22 | — | 128 | 1 | no | — |
| 619 | C22 | — | 128 | 1 | no | — |
| 620 | C22 | — | 128 | 2 | no | — |
| 621 | C22 | #72214397 | 1 | 1 | yes | characteristic |
| 622 | C22 | #72216426 | 1 | 1 | yes | characteristic |
| 623 | C22 | #72225246 | 1 | 1 | yes | characteristic |
| 624 | C4 | — | 2 | 2 | no | — |
| 625 | C4 | — | 2 | 2 | no | — |
| 626 | C4 | — | 4 | 2 | no | — |
| 627 | C4 | — | 8 | 1 | no | — |
| 628 | C4 | — | 64 | 2 | no | — |
| 629 | C4 | — | 128 | 1 | no | — |
| 630 | C4 | #72225244 | 1 | 2 | yes | — |
| 631 | C4 | #72225245 | 1 | 2 | yes | — |
| 632 | C2 | — | 2 | 1 | no | — |
| 633 | C2 | — | 2 | 1 | no | — |
| 634 | C2 | — | 64 | 4 | no | — |
| 635 | C2 | — | 128 | 2 | no | — |
| 636 | C2 | #72214406 | 1 | 2 | yes | — |
| 637 | C2 | #72225250 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72214397 |
| commutator | C8×C16 | C22×C8 |
| Frattini, cosocle | C8×#346 | C23 |
| prime radical | C2×#123403 | C4 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C42×C8 ◁ C8×#346 ◁ G | |
| LECS | G ▷ C8×#346 ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72216569 | C2 | semidirect |
| 3. #72216544 | C2 | semidirect |
| 4. #72216431 | C2 | semidirect |
| 8. #72216300 | C2 | semidirect |
| 56. #123403 | C8 | semidirect |
| 101. #12515 | C2×C8 | semidirect |
| 136. C162 | C2×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72216569 | 2 |
| #72216544 | 2 |
| #72216431 | 2 |
| #72216300 | 2 |
| #72216199 | 2 |