← #72266356
Subgroups — #72266356
Order 4096.
At least 9154 conjugacy classes of subgroups; only the 887 normal subgroups are shown.
The subgroup lattice has 269 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72266355 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72266353 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72266352 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #72266310 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72266307 | C22 | 1 | 2 | yes | complemented |
| 6 | #72266133 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #72265766 | C22 | 1 | 2 | yes | complemented |
| 8 | #72265766 | C22 | 1 | 4 | yes | complemented |
| 9 | #72265766 | C22 | 1 | 4 | yes | complemented |
| 10 | #72241126 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #72241125 | C22 | 1 | 1 | yes | characteristic |
| 12 | #72241123 | C22 | 1 | 2 | yes | — |
| 13 | #72241122 | C4 | 1 | 2 | yes | complemented |
| 14 | #72241120 | C4 | 1 | 2 | yes | complemented |
| 15 | #72238447 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #72238446 | C22 | 1 | 2 | yes | complemented |
| 17 | #72236870 | C2 | 1 | 2 | yes | maximal, complemented |
| 18 | #72235937 | C22 | 1 | 2 | yes | complemented |
| 19 | #72235718 | C22 | 1 | 4 | yes | complemented |
| 20 | #72235718 | C22 | 1 | 4 | yes | complemented |
| 21 | #72235718 | C22 | 1 | 2 | yes | complemented |
| 22 | #72233780 | C4 | 1 | 2 | yes | complemented |
| 23 | C22×#35346 | C4 | 1 | 2 | yes | complemented |
| 24 | #72225881 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #72225665 | C22 | 1 | 1 | yes | characteristic |
| 26 | #72219377 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#7631286 | C22 | 1 | 2 | yes | — |
| 28 | #72219254 | C22 | 1 | 1 | yes | characteristic |
| 29 | C24×H(5,𝔽2) | C2×C4 | 1 | 2 | yes | — |
| 30 | C22×#3484 | D4 | 1 | 4 | yes | — |
| 31 | C23×D42 | C23 | 1 | 1 | yes | characteristic |
| 32 | C24×#120 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C2×#35347 | D4 | 1 | 4 | yes | — |
| 34 | C2×#35346 | D4 | 1 | 4 | yes | — |
| 35 | C2×#34980 | C23 | 1 | 2 | yes | — |
| 36 | C2×#34980 | C23 | 1 | 2 | yes | — |
| 37 | C2×#34980 | C23 | 1 | 1 | yes | characteristic |
| 38 | C22×#2403 | C2×C4 | 1 | 2 | yes | — |
| 39 | C22×#2403 | C2×C4 | 1 | 2 | yes | — |
| 40 | C22×#2403 | C2×C4 | 1 | 2 | yes | — |
| 41 | C22×#2403 | C2×C4 | 1 | 2 | yes | — |
| 42 | C22×#2403 | C2×C4 | 1 | 2 | yes | — |
| 43 | C22×#2403 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C2×#34256 | D4 | 1 | 4 | yes | — |
| 45 | C2×#34171 | C2×C4 | 1 | 2 | yes | — |
| 46 | C22×#2308 | C2×C4 | 1 | 2 | yes | — |
| 47 | #6342371 | D4 | 1 | 2 | yes | — |
| 48 | #5024691 | D4 | 1 | 8 | yes | — |
| 49 | #4308128 | D4 | 1 | 4 | yes | — |
| 50 | #4308128 | D4 | 1 | 2 | yes | — |
| 51 | #621871 | D4 | 1 | 8 | yes | — |
| 52 | #618316 | D4 | 1 | 4 | yes | — |
| 53 | #617710 | D4 | 1 | 2 | yes | — |
| 54 | #616969 | D4 | 1 | 8 | yes | — |
| 55 | #616960 | D4 | 1 | 2 | yes | — |
| 56 | #556820 | C2×C4 | 1 | 2 | yes | — |
| 57 | #556752 | C23 | 1 | 1 | yes | characteristic |
| 58 | #517411 | C2×C4 | 1 | 2 | yes | — |
| 59 | #517411 | C2×C4 | 1 | 2 | yes | — |
| 60 | #517411 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | #517411 | C2×C4 | 1 | 2 | yes | — |
| 62 | #513778 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C2×#8547 | C23 | 1 | 4 | yes | — |
| 64 | C2×#8547 | C23 | 1 | 2 | yes | — |
| 65 | C2×#8541 | C23 | 1 | 2 | yes | — |
| 66 | C28 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 67 | C23×H(5,𝔽2) | C22⋊C4 | 1 | 4 | yes | — |
| 68 | C23×H(5,𝔽2) | C22⋊C4 | 1 | 4 | yes | — |
| 69 | C25×D4 | C22×C4 | 1 | 2 | yes | — |
| 70 | C25×D4 | C22×C4 | 1 | 2 | yes | — |
| 71 | C25×D4 | C22×C4 | 1 | 2 | yes | — |
| 72 | C25×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 73 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 74 | C22×#534 | C2×D4 | 1 | 4 | yes | — |
| 75 | C22×#534 | C2×D4 | 1 | 4 | yes | — |
| 76 | C22×#534 | C2×D4 | 1 | 2 | yes | — |
| 77 | C23×#127 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | C23×#121 | C2×D4 | 1 | 2 | yes | — |
| 79 | C23×#121 | C2×D4 | 1 | 2 | yes | — |
| 80 | C23×#120 | C22⋊C4 | 1 | 4 | yes | — |
| 81 | C23×#120 | C22⋊C4 | 1 | 4 | yes | — |
| 82 | C23×#120 | C22⋊C4 | 1 | 4 | yes | complemented |
| 83 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 85 | C23×#120 | C24 | 1 | 1 | yes | characteristic |
| 86 | C22×#518 | C22⋊C4 | 1 | 4 | yes | — |
| 87 | C23×C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 88 | C24×C22⋊C4 | C22⋊C4 | 1 | 2 | yes | complemented |
| 89 | C24×C22⋊C4 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 90 | C2×#2849 | C2×D4 | 1 | 4 | yes | — |
| 91 | C2×#2849 | C2×D4 | 1 | 4 | yes | — |
| 92 | C2×#2849 | C2×D4 | 1 | 2 | yes | — |
| 93 | C2×#2846 | C2×D4 | 1 | 4 | yes | — |
| 94 | C2×#2846 | C2×D4 | 1 | 4 | yes | — |
| 95 | C2×#2846 | C2×D4 | 1 | 2 | yes | — |
| 96 | C2×#2403 | C22⋊C4 | 1 | 4 | yes | — |
| 97 | C2×#2403 | C22⋊C4 | 1 | 4 | yes | — |
| 98 | C2×#2403 | C22⋊C4 | 1 | 8 | yes | complemented |
| 99 | C2×#2403 | C22⋊C4 | 1 | 4 | yes | complemented |
| 100 | C2×#2613 | C2×D4 | 1 | 8 | yes | — |
| 101 | C2×#2613 | C2×D4 | 1 | 8 | yes | — |
| 102 | C2×#2613 | C2×D4 | 1 | 4 | yes | — |
| 103 | C2×#2308 | C22⋊C4 | 1 | 4 | yes | — |
| 104 | C2×#2308 | C22⋊C4 | 1 | 8 | yes | complemented |
| 105 | C2×#2308 | C2×D4 | 1 | 4 | yes | — |
| 106 | C2×#2308 | C2×D4 | 1 | 4 | yes | — |
| 107 | C2×#2308 | C2×D4 | 1 | 2 | yes | — |
| 108 | C22×#386 | C22⋊C4 | 1 | 4 | yes | — |
| 109 | C22×#386 | C22⋊C4 | 1 | 4 | yes | — |
| 110 | C22×#386 | C22⋊C4 | 1 | 4 | yes | complemented |
| 111 | C22×#379 | C22×C4 | 1 | 2 | yes | — |
| 112 | C22×#379 | C22×C4 | 1 | 2 | yes | — |
| 113 | C22×#379 | C22×C4 | 1 | 2 | yes | — |
| 114 | C22×#379 | C22×C4 | 1 | 1 | yes | characteristic |
| 115 | #14681 | C22⋊C4 | 1 | 4 | yes | complemented |
| 116 | #14681 | C22⋊C4 | 1 | 4 | yes | complemented |
| 117 | #14681 | C22⋊C4 | 1 | 2 | yes | complemented |
| 118 | #14679 | C22⋊C4 | 1 | 4 | yes | complemented |
| 119 | #14679 | C22⋊C4 | 1 | 4 | yes | complemented |
| 120 | #14679 | C22⋊C4 | 1 | 2 | yes | complemented |
| 121 | #14341 | C2×D4 | 1 | 2 | yes | — |
| 122 | #14335 | C2×D4 | 1 | 2 | yes | — |
| 123 | #14262 | C22⋊C4 | 1 | 8 | yes | complemented |
| 124 | #14255 | C2×D4 | 1 | 8 | yes | — |
| 125 | #13867 | C22⋊C4 | 1 | 4 | yes | — |
| 126 | #13867 | C22⋊C4 | 1 | 4 | yes | — |
| 127 | #13827 | C22⋊C4 | 1 | 4 | yes | complemented |
| 128 | C27 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 129 | C27 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 130 | C27 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 131 | C27 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 132 | C27 | #120 | 1 | 1 | yes | characteristic |
| 133 | C27 | C23×C4 | 1 | 1 | yes | characteristic |
| 134 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 135 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 136 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 137 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 138 | C24×D4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 139 | C24×D4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 140 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 141 | C24×D4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 142 | C24×D4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 143 | C24×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 144 | C24×D4 | #120 | 1 | 2 | yes | — |
| 145 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 146 | C24×D4 | #120 | 1 | 2 | yes | — |
| 147 | C24×D4 | C22×D4 | 1 | 2 | yes | — |
| 148 | C24×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 149 | C25×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 150 | C25×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 151 | C25×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 152 | C25×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 153 | C25×C4 | #120 | 1 | 2 | yes | — |
| 154 | C22×#123 | #120 | 1 | 8 | yes | — |
| 155 | C22×#123 | #120 | 1 | 8 | yes | — |
| 156 | C22×#123 | #120 | 1 | 4 | yes | — |
| 157 | C22×#120 | #99 | 1 | 16 | yes | — |
| 158 | C22×#120 | #120 | 1 | 8 | yes | — |
| 159 | C22×#120 | #120 | 1 | 8 | yes | — |
| 160 | C22×#120 | #120 | 1 | 4 | yes | — |
| 161 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 162 | C22×#120 | C22×D4 | 1 | 4 | yes | — |
| 163 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 164 | C23×C4⋊C4 | #120 | 1 | 2 | yes | — |
| 165 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 166 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 167 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 168 | C23×C22⋊C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 169 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 170 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 171 | C23×C22⋊C4 | #120 | 1 | 1 | yes | characteristic |
| 172 | C23×C22⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 173 | C23×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 174 | C23×C42 | #120 | 1 | 1 | yes | characteristic |
| 175 | C2×#386 | #99 | 1 | 16 | yes | — |
| 176 | C2×#381 | #120 | 1 | 8 | yes | — |
| 177 | C2×#381 | #120 | 1 | 8 | yes | — |
| 178 | C2×#381 | #120 | 1 | 4 | yes | — |
| 179 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 180 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 181 | C2×#379 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 182 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 183 | C2×#379 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 184 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 185 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 186 | C2×#379 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 187 | C2×#379 | #120 | 1 | 8 | yes | — |
| 188 | C2×#379 | #120 | 1 | 8 | yes | — |
| 189 | C2×#379 | #120 | 1 | 4 | yes | — |
| 190 | #1440 | #120 | 1 | 8 | yes | — |
| 191 | #1438 | #120 | 1 | 8 | yes | — |
| 192 | C26 | #379 | 1 | 4 | yes | — |
| 193 | C26 | #379 | 1 | 2 | yes | — |
| 194 | C26 | #379 | 1 | 2 | yes | — |
| 195 | C26 | #379 | 1 | 4 | yes | — |
| 196 | C26 | #379 | 1 | 2 | yes | — |
| 197 | C26 | C2×#99 | 1 | 8 | yes | — |
| 198 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 199 | C26 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 200 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 201 | C26 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 202 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 203 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 204 | C23×D4 | C2×#99 | 1 | 8 | yes | — |
| 205 | C23×D4 | C2×#99 | 1 | 8 | yes | — |
| 206 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 207 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 208 | C23×D4 | C2×#120 | 1 | 2 | yes | — |
| 209 | C23×D4 | C2×#120 | 1 | 2 | yes | — |
| 210 | C24×C4 | #379 | 1 | 2 | yes | — |
| 211 | C24×C4 | #379 | 1 | 2 | yes | — |
| 212 | C24×C4 | #379 | 1 | 4 | yes | — |
| 213 | C24×C4 | #379 | 1 | 2 | yes | — |
| 214 | C24×C4 | #379 | 1 | 4 | yes | — |
| 215 | C24×C4 | C2×#99 | 1 | 8 | yes | — |
| 216 | C24×C4 | C2×#120 | 1 | 2 | yes | — |
| 217 | C24×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 218 | C22×C22⋊C4 | #379 | 1 | 8 | yes | — |
| 219 | C22×C22⋊C4 | #379 | 1 | 4 | yes | — |
| 220 | C22×C22⋊C4 | #379 | 1 | 8 | yes | — |
| 221 | C22×C22⋊C4 | #379 | 1 | 8 | yes | — |
| 222 | C22×C22⋊C4 | C2×#99 | 1 | 8 | yes | — |
| 223 | C22×C22⋊C4 | C2×#99 | 1 | 8 | yes | — |
| 224 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 225 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 226 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 227 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 228 | C25 | #1781 | 1 | 4 | yes | — |
| 229 | C25 | #1781 | 1 | 4 | yes | — |
| 230 | C25 | #1781 | 1 | 8 | yes | — |
| 231 | C25 | C2×#379 | 1 | 2 | yes | — |
| 232 | C25 | C2×#379 | 1 | 2 | yes | — |
| 233 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 234 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 235 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 236 | C25 | #2846 | 1 | 2 | yes | — |
| 237 | C25 | C22×#99 | 1 | 4 | yes | — |
| 238 | C25 | C22×#99 | 1 | 4 | yes | — |
| 239 | C25 | #2883 | 1 | 2 | yes | — |
| 240 | C25 | #2883 | 1 | 2 | yes | — |
| 241 | C23×C4 | #1781 | 1 | 8 | yes | — |
| 242 | C23×C4 | #1781 | 1 | 4 | yes | — |
| 243 | C23×C4 | #1781 | 1 | 4 | yes | — |
| 244 | C23×C4 | #2846 | 1 | 2 | yes | — |
| 245 | C23×C4 | #2846 | 1 | 4 | yes | — |
| 246 | C2×C22⋊C4 | #1781 | 1 | 16 | yes | — |
| 247 | C24 | #12705 | 1 | 16 | yes | complemented |
| 248 | C24 | #14679 | 1 | 1 | yes | characteristic |
| 249 | C24 | C2×#1781 | 1 | 4 | yes | — |
| 250 | C24 | C2×#1781 | 1 | 4 | yes | — |
| 251 | C24 | C2×#1781 | 1 | 2 | yes | — |
| 252 | C24 | C2×#1781 | 1 | 2 | yes | — |
| 253 | C24 | #20585 | 1 | 2 | yes | — |
| 254 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 255 | C24 | #20585 | 1 | 1 | yes | characteristic |
| 256 | C24 | #20586 | 1 | 2 | yes | — |
| 257 | C23 | #188035 | 1 | 1 | yes | characteristic |
| 258 | C23 | #188035 | 1 | 2 | yes | — |
| 259 | C23 | #188035 | 1 | 1 | yes | characteristic |
| 260 | C23 | #392109 | 1 | 2 | yes | — |
| 261 | C23 | #392111 | 1 | 1 | yes | characteristic |
| 262 | C23 | C2×#12705 | 1 | 8 | yes | — |
| 263 | C22 | #72218306 | 1 | 4 | yes | — |
| 264 | C22 | #72219377 | 1 | 1 | yes | characteristic |
| 265 | C22 | #72258097 | 1 | 2 | yes | — |
| 266 | C2 | #72265785 | 1 | 2 | yes | — |
| 267 | C2 | #72265941 | 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