← #72266312
Subgroups — #72266312
Order 4096.
At least 12517 conjugacy classes of subgroups; only the 755 normal subgroups are shown.
The subgroup lattice has 293 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72266310 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72266308 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72266307 | C22 | 1 | 2 | yes | complemented |
| 4 | #72266267 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72266265 | C22 | 1 | 2 | yes | — |
| 6 | #72266264 | C4 | 1 | 4 | yes | complemented |
| 7 | #72266167 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72266165 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #72266163 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #72266044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #72266041 | C22 | 1 | 2 | yes | complemented |
| 12 | #72265766 | C22 | 1 | 2 | yes | complemented |
| 13 | #72259008 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #72240132 | C22 | 1 | 4 | yes | complemented |
| 15 | #72240132 | C22 | 1 | 4 | yes | complemented |
| 16 | #72236034 | C2 | 1 | 2 | yes | maximal, complemented |
| 17 | #72235930 | C22 | 1 | 2 | yes | — |
| 18 | #72235922 | C4 | 1 | 4 | yes | complemented |
| 19 | #72235847 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #72234636 | C22 | 1 | 2 | yes | — |
| 21 | #72232723 | C22 | 1 | 4 | yes | complemented |
| 22 | #72232723 | C22 | 1 | 4 | yes | complemented |
| 23 | #72225881 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #72225665 | C22 | 1 | 1 | yes | characteristic |
| 25 | #72219377 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #72219307 | C22 | 1 | 2 | yes | complemented |
| 27 | C22×#3484 | D4 | 1 | 2 | yes | — |
| 28 | C23×D42 | C23 | 1 | 1 | yes | characteristic |
| 29 | C2×#46996 | C2×C4 | 1 | 2 | yes | — |
| 30 | C2×#35347 | C2×C4 | 1 | 2 | yes | — |
| 31 | C2×#35346 | D4 | 1 | 2 | yes | — |
| 32 | C2×#34980 | C23 | 1 | 1 | yes | characteristic |
| 33 | C22×#2403 | D4 | 1 | 2 | yes | — |
| 34 | C2×#21746 | C23 | 1 | 2 | yes | — |
| 35 | C2×#21746 | C23 | 1 | 2 | yes | — |
| 36 | #5123779 | D4 | 1 | 4 | yes | — |
| 37 | #5119613 | D4 | 1 | 4 | yes | — |
| 38 | #5024691 | D4 | 1 | 2 | yes | — |
| 39 | #5020751 | D4 | 1 | 2 | yes | — |
| 40 | #4893962 | C2×C4 | 1 | 2 | yes | — |
| 41 | #4866548 | C2×C4 | 1 | 2 | yes | — |
| 42 | #4466055 | D4 | 1 | 4 | yes | — |
| 43 | #4430405 | D4 | 1 | 2 | yes | — |
| 44 | #4335643 | C2×C4 | 1 | 4 | yes | — |
| 45 | #2435299 | D4 | 1 | 4 | yes | — |
| 46 | #2108865 | D4 | 1 | 4 | yes | — |
| 47 | #2039146 | D4 | 1 | 4 | yes | — |
| 48 | #648360 | D4 | 1 | 2 | yes | — |
| 49 | #635987 | C2×C4 | 1 | 4 | yes | — |
| 50 | #618316 | C2×C4 | 1 | 4 | yes | — |
| 51 | #617710 | D4 | 1 | 2 | yes | — |
| 52 | #617709 | D4 | 1 | 4 | yes | — |
| 53 | #616961 | C23 | 1 | 4 | yes | — |
| 54 | #616960 | D4 | 1 | 2 | yes | — |
| 55 | #612429 | D4 | 1 | 4 | yes | — |
| 56 | #587363 | C2×C4 | 1 | 4 | yes | — |
| 57 | #576160 | C2×C4 | 1 | 2 | yes | — |
| 58 | #556752 | C23 | 1 | 1 | yes | characteristic |
| 59 | #517411 | D4 | 1 | 2 | yes | — |
| 60 | #517411 | D4 | 1 | 2 | yes | — |
| 61 | #515362 | C2×C4 | 1 | 2 | yes | — |
| 62 | #515285 | D4 | 1 | 2 | yes | — |
| 63 | C2×#8547 | C23 | 1 | 2 | yes | — |
| 64 | C2×#8541 | C23 | 1 | 2 | yes | — |
| 65 | C23×H(5,𝔽2) | C22⋊C4 | 1 | 2 | yes | complemented |
| 66 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 67 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 68 | C25×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C22×#535 | C2×D4 | 1 | 4 | yes | — |
| 70 | C22×#534 | C2×D4 | 1 | 2 | yes | — |
| 71 | C23×#127 | C2×D4 | 1 | 1 | yes | characteristic |
| 72 | C22×#525 | C22⋊C4 | 1 | 4 | yes | complemented |
| 73 | C23×#121 | C22×C4 | 1 | 2 | yes | — |
| 74 | C23×#121 | C2×D4 | 1 | 2 | yes | — |
| 75 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 77 | C23×#120 | C24 | 1 | 1 | yes | characteristic |
| 78 | C22×#518 | C22⋊C4 | 1 | 2 | yes | complemented |
| 79 | C23×C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 80 | C2×#2760 | C22⋊C4 | 1 | 4 | yes | complemented |
| 81 | C2×#2840 | C22⋊C4 | 1 | 2 | yes | complemented |
| 82 | C2×#2849 | C2×D4 | 1 | 2 | yes | — |
| 83 | C2×#2846 | C2×D4 | 1 | 2 | yes | — |
| 84 | C2×#2406 | C22⋊C4 | 1 | 4 | yes | complemented |
| 85 | C2×#2404 | C22⋊C4 | 1 | 4 | yes | complemented |
| 86 | C2×#2404 | C22×C4 | 1 | 4 | yes | — |
| 87 | C2×#2404 | C2×D4 | 1 | 4 | yes | — |
| 88 | C2×#2403 | C22⋊C4 | 1 | 4 | yes | — |
| 89 | C2×#2403 | C22⋊C4 | 1 | 4 | yes | — |
| 90 | C2×#2403 | C22⋊C4 | 1 | 2 | yes | complemented |
| 91 | C2×#2613 | C2×D4 | 1 | 2 | yes | — |
| 92 | C2×#2613 | C2×D4 | 1 | 2 | yes | — |
| 93 | C2×#2308 | C22⋊C4 | 1 | 2 | yes | complemented |
| 94 | C2×#2308 | C22⋊C4 | 1 | 2 | yes | complemented |
| 95 | C2×#2308 | C22×C4 | 1 | 2 | yes | — |
| 96 | C22×#379 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C22×#379 | C2×D4 | 1 | 2 | yes | — |
| 98 | #17198 | C22⋊C4 | 1 | 2 | yes | complemented |
| 99 | #17105 | C22⋊C4 | 1 | 4 | yes | complemented |
| 100 | #17102 | C22⋊C4 | 1 | 2 | yes | complemented |
| 101 | #16247 | C22⋊C4 | 1 | 2 | yes | complemented |
| 102 | #16211 | C22⋊C4 | 1 | 2 | yes | complemented |
| 103 | #15930 | C22⋊C4 | 1 | 4 | yes | complemented |
| 104 | #15636 | C22⋊C4 | 1 | 4 | yes | complemented |
| 105 | #15561 | C22⋊C4 | 1 | 4 | yes | complemented |
| 106 | #15467 | C22⋊C4 | 1 | 4 | yes | complemented |
| 107 | #15267 | C22⋊C4 | 1 | 4 | yes | complemented |
| 108 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 109 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 110 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 111 | #15259 | C2×D4 | 1 | 4 | yes | — |
| 112 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 113 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 114 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 115 | #15258 | C2×D4 | 1 | 4 | yes | — |
| 116 | #14681 | C22⋊C4 | 1 | 4 | yes | complemented |
| 117 | #14649 | C22⋊C4 | 1 | 4 | yes | complemented |
| 118 | #14609 | C22⋊C4 | 1 | 4 | yes | complemented |
| 119 | #14533 | C22⋊C4 | 1 | 4 | yes | complemented |
| 120 | #14507 | C22⋊C4 | 1 | 4 | yes | complemented |
| 121 | #14341 | C22×C4 | 1 | 2 | yes | — |
| 122 | #14335 | C2×D4 | 1 | 4 | yes | — |
| 123 | #14335 | C2×D4 | 1 | 2 | yes | — |
| 124 | #14255 | C2×D4 | 1 | 4 | yes | — |
| 125 | #14255 | C2×D4 | 1 | 4 | yes | — |
| 126 | #14207 | C22⋊C4 | 1 | 4 | yes | complemented |
| 127 | #13870 | C22⋊C4 | 1 | 4 | yes | complemented |
| 128 | #13868 | C22⋊C4 | 1 | 4 | yes | complemented |
| 129 | #13868 | C22×C4 | 1 | 4 | yes | — |
| 130 | #13868 | C2×D4 | 1 | 4 | yes | — |
| 131 | #13867 | C22⋊C4 | 1 | 4 | yes | — |
| 132 | #13867 | C22⋊C4 | 1 | 4 | yes | — |
| 133 | #13827 | C22⋊C4 | 1 | 2 | yes | complemented |
| 134 | C22⋊C42 | C22⋊C4 | 1 | 2 | yes | complemented |
| 135 | C27 | #120 | 1 | 1 | yes | characteristic |
| 136 | C27 | #120 | 1 | 2 | yes | — |
| 137 | C27 | #120 | 1 | 1 | yes | characteristic |
| 138 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 139 | C23×#41 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 140 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 141 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 142 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 143 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 144 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 145 | C24×D4 | #120 | 1 | 2 | yes | — |
| 146 | C24×D4 | #120 | 1 | 2 | yes | — |
| 147 | C24×D4 | #120 | 1 | 2 | yes | — |
| 148 | C24×D4 | #120 | 1 | 2 | yes | — |
| 149 | C24×D4 | C22×D4 | 1 | 2 | yes | — |
| 150 | C24×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 151 | C25×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 152 | C25×C4 | #120 | 1 | 2 | yes | — |
| 153 | C25×C4 | #120 | 1 | 1 | yes | characteristic |
| 154 | C22×#127 | #120 | 1 | 4 | yes | — |
| 155 | C22×#127 | #120 | 1 | 4 | yes | — |
| 156 | C22×#124 | #120 | 1 | 4 | yes | — |
| 157 | C22×#124 | #120 | 1 | 4 | yes | — |
| 158 | C22×#123 | #120 | 1 | 2 | yes | — |
| 159 | C22×#123 | #120 | 1 | 2 | yes | — |
| 160 | C22×#120 | #120 | 1 | 2 | yes | — |
| 161 | C22×#120 | #120 | 1 | 2 | yes | — |
| 162 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 163 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 164 | C22×#120 | C22×D4 | 1 | 4 | yes | — |
| 165 | C22×#117 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 166 | C23×C4⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 167 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 168 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 169 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 170 | C23×C22⋊C4 | #120 | 1 | 1 | yes | characteristic |
| 171 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 172 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 173 | C23×C22⋊C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 174 | C23×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 175 | C23×C42 | #120 | 1 | 1 | yes | characteristic |
| 176 | C2×#393 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 177 | C2×#393 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 178 | C2×#393 | #120 | 1 | 4 | yes | — |
| 179 | C2×#393 | #120 | 1 | 4 | yes | — |
| 180 | C2×#392 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 181 | C2×#392 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 182 | C2×#392 | #120 | 1 | 4 | yes | — |
| 183 | C2×#392 | #120 | 1 | 4 | yes | — |
| 184 | C2×#381 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 185 | C2×#381 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 186 | C2×#381 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 187 | C2×#381 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 188 | C2×#379 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 189 | C2×#379 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 190 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 191 | C2×#379 | #120 | 1 | 2 | yes | — |
| 192 | C2×#379 | #120 | 1 | 4 | yes | — |
| 193 | C2×#379 | #120 | 1 | 1 | yes | characteristic |
| 194 | C2×#379 | #120 | 1 | 1 | yes | characteristic |
| 195 | #1440 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 196 | #1440 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 197 | #1440 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 198 | #1438 | #120 | 1 | 4 | yes | — |
| 199 | #1438 | #120 | 1 | 4 | yes | — |
| 200 | #1438 | #120 | 1 | 4 | yes | — |
| 201 | #1438 | #120 | 1 | 4 | yes | — |
| 202 | #1438 | #120 | 1 | 4 | yes | — |
| 203 | #1438 | #120 | 1 | 2 | yes | — |
| 204 | #1438 | #120 | 1 | 2 | yes | — |
| 205 | #1437 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 206 | #1437 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 207 | #1437 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 208 | #1437 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 209 | #1437 | #120 | 1 | 4 | yes | — |
| 210 | #1437 | #120 | 1 | 4 | yes | — |
| 211 | #1437 | #120 | 1 | 4 | yes | — |
| 212 | #1437 | #120 | 1 | 4 | yes | — |
| 213 | C26 | #379 | 1 | 2 | yes | — |
| 214 | C26 | #379 | 1 | 2 | yes | — |
| 215 | C26 | #379 | 1 | 2 | yes | — |
| 216 | C26 | B(4,𝔽2) | 1 | 4 | yes | — |
| 217 | C26 | #458 | 1 | 4 | yes | — |
| 218 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 219 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 220 | C26 | C2×#120 | 1 | 2 | yes | — |
| 221 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 222 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 223 | C26 | C2×#120 | 1 | 2 | yes | — |
| 224 | C23×Q8 | #379 | 1 | 4 | yes | — |
| 225 | C23×D4 | #379 | 1 | 4 | yes | — |
| 226 | C23×D4 | C2×#120 | 1 | 2 | yes | — |
| 227 | C23×D4 | C2×#120 | 1 | 2 | yes | — |
| 228 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 229 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 230 | C24×C4 | #379 | 1 | 2 | yes | — |
| 231 | C24×C4 | #379 | 1 | 2 | yes | — |
| 232 | C24×C4 | #379 | 1 | 2 | yes | — |
| 233 | C24×C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 234 | C24×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 235 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 236 | C22×C22⋊C4 | #379 | 1 | 2 | yes | — |
| 237 | C22×C22⋊C4 | #379 | 1 | 4 | yes | — |
| 238 | C22×C22⋊C4 | #379 | 1 | 4 | yes | — |
| 239 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 240 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 241 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 242 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 243 | C22×C42 | #379 | 1 | 4 | yes | — |
| 244 | C22×C42 | #379 | 1 | 4 | yes | — |
| 245 | C2×#95 | #379 | 1 | 4 | yes | — |
| 246 | C2×#95 | #379 | 1 | 4 | yes | — |
| 247 | C2×#95 | #379 | 1 | 4 | yes | — |
| 248 | C2×#95 | #379 | 1 | 4 | yes | — |
| 249 | C25 | #1790 | 1 | 4 | yes | — |
| 250 | C25 | #1790 | 1 | 4 | yes | — |
| 251 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 252 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 253 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 254 | C25 | #2846 | 1 | 2 | yes | — |
| 255 | C25 | #2846 | 1 | 2 | yes | — |
| 256 | C25 | #2846 | 1 | 2 | yes | — |
| 257 | C25 | #2883 | 1 | 1 | yes | characteristic |
| 258 | C25 | #2883 | 1 | 1 | yes | characteristic |
| 259 | C25 | #2883 | 1 | 1 | yes | characteristic |
| 260 | C25 | #2883 | 1 | 1 | yes | characteristic |
| 261 | C25 | C2×B(4,𝔽2) | 1 | 2 | yes | — |
| 262 | C25 | C2×#458 | 1 | 2 | yes | — |
| 263 | C25 | #3026 | 1 | 2 | yes | — |
| 264 | C25 | #3026 | 1 | 2 | yes | — |
| 265 | C23×C4 | C2×#379 | 1 | 4 | yes | — |
| 266 | C23×C4 | #2846 | 1 | 2 | yes | — |
| 267 | C24 | #14679 | 1 | 1 | yes | characteristic |
| 268 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 269 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 270 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 271 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 272 | C24 | #20586 | 1 | 1 | yes | characteristic |
| 273 | C24 | #20586 | 1 | 1 | yes | characteristic |
| 274 | C24 | C2×#1790 | 1 | 2 | yes | — |
| 275 | C24 | #20609 | 1 | 2 | yes | — |
| 276 | C24 | #32898 | 1 | 2 | yes | — |
| 277 | C24 | #32898 | 1 | 2 | yes | — |
| 278 | C24 | #32900 | 1 | 2 | yes | — |
| 279 | C24 | #32900 | 1 | 2 | yes | — |
| 280 | C23 | #187934 | 1 | 2 | yes | — |
| 281 | C23 | #187940 | 1 | 1 | yes | characteristic |
| 282 | C23 | #187949 | 1 | 1 | yes | characteristic |
| 283 | C23 | #392111 | 1 | 1 | yes | characteristic |
| 284 | C23 | #392125 | 1 | 2 | yes | — |
| 285 | C23 | #511790 | 1 | 4 | yes | — |
| 286 | C22 | #72218475 | 1 | 2 | yes | — |
| 287 | C22 | #72225624 | 1 | 1 | yes | characteristic |
| 288 | C22 | #72237472 | 1 | 2 | yes | — |
| 289 | C22 | #72258094 | 1 | 2 | yes | — |
| 290 | C2 | #72265776 | 1 | 2 | yes | — |
| 291 | C2 | #72265934 | 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