← #72268216
Subgroups — #72268216
Order 2048.
Only the 2332 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 288 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72268215 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72268214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72268213 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72268212 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #72268072 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #72268070 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72268068 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72268067 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | #72268062 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10586407 | C22 | 1 | 8 | yes | — |
| 11 | #10586405 | C22 | 1 | 4 | yes | — |
| 12 | C2×#62844 | C22 | 1 | 2 | yes | — |
| 13 | C2×#62843 | C22 | 1 | 1 | yes | characteristic |
| 14 | #6499839 | C22 | 1 | 8 | yes | complemented |
| 15 | #6499774 | C22 | 1 | 4 | yes | complemented |
| 16 | C2×#25947 | C22 | 1 | 4 | yes | complemented |
| 17 | #6346730 | C22 | 1 | 8 | yes | complemented |
| 18 | C2×#18162 | C22 | 1 | 4 | yes | complemented |
| 19 | C2×#18135 | C22 | 1 | 4 | yes | complemented |
| 20 | #4928940 | C22 | 1 | 1 | yes | characteristic |
| 21 | #764240 | C22 | 1 | 2 | yes | complemented |
| 22 | #362741 | C22 | 1 | 4 | yes | complemented |
| 23 | #362714 | C22 | 1 | 2 | yes | complemented |
| 24 | #354795 | C22 | 1 | 1 | yes | characteristic |
| 25 | #188123 | C22 | 1 | 4 | yes | complemented |
| 26 | #187978 | C22 | 1 | 8 | yes | complemented |
| 27 | #187171 | C22 | 1 | 16 | yes | complemented |
| 28 | #186979 | C22 | 1 | 16 | yes | complemented |
| 29 | #186831 | C22 | 1 | 8 | yes | complemented |
| 30 | #186006 | C22 | 1 | 4 | yes | complemented |
| 31 | #185993 | C22 | 1 | 4 | yes | complemented |
| 32 | #185854 | C22 | 1 | 8 | yes | complemented |
| 33 | #185463 | C22 | 1 | 8 | yes | complemented |
| 34 | #185277 | C22 | 1 | 8 | yes | complemented |
| 35 | #185249 | C22 | 1 | 8 | yes | complemented |
| 36 | #185095 | C22 | 1 | 4 | yes | complemented |
| 37 | #184786 | C22 | 1 | 2 | yes | — |
| 38 | #62904 | D4 | 1 | 16 | yes | complemented |
| 39 | #62902 | D4 | 1 | 16 | yes | complemented |
| 40 | #62894 | D4 | 1 | 16 | yes | complemented |
| 41 | #62893 | D4 | 1 | 16 | yes | complemented |
| 42 | #62819 | D4 | 1 | 16 | yes | complemented |
| 43 | #62819 | D4 | 1 | 16 | yes | complemented |
| 44 | #62819 | C23 | 1 | 8 | yes | — |
| 45 | #62819 | C23 | 1 | 8 | yes | — |
| 46 | C2×#3491 | D4 | 1 | 4 | yes | — |
| 47 | C2×#3505 | D4 | 1 | 4 | yes | — |
| 48 | C2×#3505 | C23 | 1 | 4 | yes | — |
| 49 | C2×#3490 | C23 | 1 | 4 | yes | — |
| 50 | C2×#3501 | D4 | 1 | 4 | yes | — |
| 51 | C2×#3501 | C23 | 1 | 4 | yes | — |
| 52 | C2×#3459 | D4 | 1 | 4 | yes | — |
| 53 | C2×#3459 | C23 | 1 | 4 | yes | — |
| 54 | C22×#543 | D4 | 1 | 2 | yes | — |
| 55 | C22×#543 | D4 | 1 | 2 | yes | — |
| 56 | C22×#543 | C23 | 1 | 2 | yes | — |
| 57 | C22×#534 | D4 | 1 | 2 | yes | — |
| 58 | C22×#518 | D4 | 1 | 2 | yes | — |
| 59 | C22×#518 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#3003 | C23 | 1 | 8 | yes | complemented |
| 61 | C2×#2435 | C23 | 1 | 4 | yes | complemented |
| 62 | C2×#2408 | C23 | 1 | 2 | yes | — |
| 63 | C22×#392 | C23 | 1 | 1 | yes | characteristic |
| 64 | #21773 | C23 | 1 | 16 | yes | complemented |
| 65 | #21769 | C23 | 1 | 8 | yes | complemented |
| 66 | #21753 | C23 | 1 | 8 | yes | complemented |
| 67 | #21742 | C23 | 1 | 4 | yes | — |
| 68 | C2×#1996 | C23 | 1 | 8 | yes | complemented |
| 69 | C2×C4×#99 | C23 | 1 | 4 | yes | — |
| 70 | C2×#1513 | C23 | 1 | 8 | yes | complemented |
| 71 | #17542 | C23 | 1 | 16 | yes | complemented |
| 72 | C2×#1504 | C23 | 1 | 8 | yes | complemented |
| 73 | #17397 | C23 | 1 | 8 | yes | complemented |
| 74 | C2×#1465 | C23 | 1 | 4 | yes | — |
| 75 | C2×#1462 | C23 | 1 | 4 | yes | — |
| 76 | #14338 | C23 | 1 | 1 | yes | characteristic |
| 77 | #14159 | C23 | 1 | 4 | yes | complemented |
| 78 | #13960 | C23 | 1 | 2 | yes | — |
| 79 | #13775 | C23 | 1 | 2 | yes | — |
| 80 | C24×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C24×D4 | C24 | 1 | 1 | yes | characteristic |
| 82 | #3538 | C2×D4 | 1 | 32 | yes | — |
| 83 | #3536 | C2×D4 | 1 | 32 | yes | — |
| 84 | #3501 | C2×D4 | 1 | 16 | yes | — |
| 85 | #3501 | C2×D4 | 1 | 16 | yes | — |
| 86 | #3495 | C2×D4 | 1 | 32 | yes | — |
| 87 | #3492 | C2×D4 | 1 | 16 | yes | — |
| 88 | #3492 | C2×D4 | 1 | 32 | yes | — |
| 89 | #3490 | C2×D4 | 1 | 32 | yes | — |
| 90 | #3489 | C2×D4 | 1 | 32 | yes | — |
| 91 | #3486 | C2×D4 | 1 | 16 | yes | — |
| 92 | C2×#553 | C2×D4 | 1 | 8 | yes | — |
| 93 | C2×#552 | C2×D4 | 1 | 8 | yes | — |
| 94 | C2×#548 | C2×D4 | 1 | 8 | yes | — |
| 95 | C2×#546 | C2×D4 | 1 | 8 | yes | — |
| 96 | #3459 | C2×D4 | 1 | 16 | yes | — |
| 97 | #3459 | C2×D4 | 1 | 16 | yes | — |
| 98 | C2×#543 | C2×D4 | 1 | 8 | yes | — |
| 99 | C2×#543 | C2×D4 | 1 | 4 | yes | — |
| 100 | C2×#543 | C2×D4 | 1 | 4 | yes | — |
| 101 | C2×#539 | C2×D4 | 1 | 8 | yes | — |
| 102 | C2×#538 | C2×D4 | 1 | 8 | yes | — |
| 103 | C2×#534 | C2×D4 | 1 | 4 | yes | — |
| 104 | C2×#534 | C2×D4 | 1 | 4 | yes | — |
| 105 | C2×#529 | C2×D4 | 1 | 8 | yes | — |
| 106 | C2×#525 | C24 | 1 | 8 | yes | — |
| 107 | C22×C22⋊Q8 | C2×D4 | 1 | 8 | yes | — |
| 108 | C22×C22⋊Q8 | C2×D4 | 1 | 8 | yes | — |
| 109 | C22×C22⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 110 | C22×C22⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 111 | C22×C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 112 | C22×#121 | C2×D4 | 1 | 4 | yes | — |
| 113 | C2×#518 | C2×D4 | 1 | 8 | yes | — |
| 114 | C22×C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 115 | C22×C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 116 | C22×C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 117 | C22×C4×D4 | C24 | 1 | 2 | yes | — |
| 118 | C22×#117 | C2×D4 | 1 | 2 | yes | — |
| 119 | C23×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 120 | C23×C22⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C23×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 122 | C23×C22⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 123 | C2×#407 | C24 | 1 | 8 | yes | — |
| 124 | C2×#380 | C24 | 1 | 2 | yes | — |
| 125 | C2×C4×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 126 | C22×#95 | C24 | 1 | 1 | yes | characteristic |
| 127 | C26 | #120 | 1 | 1 | yes | characteristic |
| 128 | C26 | C22×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×2−1+4 | #120 | 1 | 16 | yes | complemented |
| 130 | C22×#41 | C22×D4 | 1 | 8 | yes | — |
| 131 | C23×Q8 | #120 | 1 | 4 | yes | — |
| 132 | C23×Q8 | #120 | 1 | 4 | yes | — |
| 133 | C23×Q8 | C22×D4 | 1 | 4 | yes | — |
| 134 | C23×D4 | #120 | 1 | 4 | yes | — |
| 135 | C23×D4 | #120 | 1 | 2 | yes | — |
| 136 | C23×D4 | C22×D4 | 1 | 2 | yes | — |
| 137 | C24×C4 | #120 | 1 | 1 | yes | characteristic |
| 138 | C24×C4 | #120 | 1 | 1 | yes | characteristic |
| 139 | C24×C4 | #120 | 1 | 1 | yes | characteristic |
| 140 | C24×C4 | #120 | 1 | 2 | yes | — |
| 141 | C24×C4 | #120 | 1 | 4 | yes | — |
| 142 | C24×C4 | #120 | 1 | 4 | yes | — |
| 143 | C24×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 144 | C24×C4 | C22×D4 | 1 | 2 | yes | — |
| 145 | C24×C4 | C25 | 1 | 1 | yes | characteristic |
| 146 | #544 | #120 | 1 | 16 | yes | complemented |
| 147 | #544 | #120 | 1 | 32 | yes | complemented |
| 148 | #543 | #120 | 1 | 32 | yes | — |
| 149 | #543 | #120 | 1 | 8 | yes | — |
| 150 | #543 | #120 | 1 | 8 | yes | — |
| 151 | #543 | #120 | 1 | 16 | yes | — |
| 152 | #539 | #120 | 1 | 32 | yes | — |
| 153 | #539 | #120 | 1 | 64 | yes | complemented |
| 154 | #538 | #120 | 1 | 32 | yes | — |
| 155 | #537 | #120 | 1 | 32 | yes | complemented |
| 156 | #537 | #120 | 1 | 16 | yes | complemented |
| 157 | #536 | #120 | 1 | 32 | yes | complemented |
| 158 | #534 | #120 | 1 | 8 | yes | — |
| 159 | #534 | #120 | 1 | 8 | yes | — |
| 160 | #534 | #120 | 1 | 16 | yes | — |
| 161 | C2×#125 | #120 | 1 | 8 | yes | — |
| 162 | C2×#124 | #120 | 1 | 8 | yes | — |
| 163 | #525 | C22×D4 | 1 | 32 | yes | — |
| 164 | #525 | C22×D4 | 1 | 32 | yes | — |
| 165 | C2×C22⋊Q8 | #120 | 1 | 8 | yes | — |
| 166 | C2×C22⋊Q8 | C22×D4 | 1 | 32 | yes | — |
| 167 | C2×C22⋊Q8 | C22×D4 | 1 | 8 | yes | — |
| 168 | C2×C22⋊Q8 | C22×D4 | 1 | 8 | yes | — |
| 169 | C2×#121 | #120 | 1 | 8 | yes | — |
| 170 | C2×#121 | C22×D4 | 1 | 8 | yes | — |
| 171 | C2×#121 | C22×D4 | 1 | 8 | yes | — |
| 172 | #520 | #120 | 1 | 32 | yes | complemented |
| 173 | #519 | #120 | 1 | 16 | yes | complemented |
| 174 | #518 | #120 | 1 | 16 | yes | — |
| 175 | #518 | #120 | 1 | 16 | yes | — |
| 176 | C2×C4×Q8 | #120 | 1 | 8 | yes | — |
| 177 | C2×C4×D4 | #120 | 1 | 8 | yes | — |
| 178 | C2×C4×D4 | C22×D4 | 1 | 8 | yes | — |
| 179 | C2×C4×D4 | C22×D4 | 1 | 8 | yes | — |
| 180 | C2×#117 | C22×D4 | 1 | 8 | yes | — |
| 181 | C22×C4⋊C4 | #120 | 1 | 4 | yes | — |
| 182 | C22×C4⋊C4 | #120 | 1 | 4 | yes | — |
| 183 | C22×C4⋊C4 | #120 | 1 | 2 | yes | — |
| 184 | C22×C4⋊C4 | #120 | 1 | 4 | yes | — |
| 185 | C22×C4⋊C4 | #120 | 1 | 8 | yes | — |
| 186 | C22×C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 187 | C22×C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 188 | C22×C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 189 | C22×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 190 | C22×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 191 | C22×C22⋊C4 | #120 | 1 | 8 | yes | — |
| 192 | C22×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 193 | C22×C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 194 | C22×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 195 | C22×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 196 | C22×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 197 | C22×C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 198 | C22×C42 | #120 | 1 | 2 | yes | — |
| 199 | C22×C42 | C22×D4 | 1 | 2 | yes | — |
| 200 | C25 | #454 | 1 | 4 | yes | complemented |
| 201 | C25 | C2×#120 | 1 | 4 | yes | — |
| 202 | C25 | C2×#120 | 1 | 1 | yes | characteristic |
| 203 | C25 | C2×#120 | 1 | 1 | yes | characteristic |
| 204 | C25 | C2×#120 | 1 | 2 | yes | — |
| 205 | C25 | C23×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×#41 | C2×#120 | 1 | 32 | yes | — |
| 207 | C22×Q8 | C2×#120 | 1 | 16 | yes | — |
| 208 | C22×Q8 | C2×#120 | 1 | 8 | yes | — |
| 209 | C22×D4 | C2×#120 | 1 | 4 | yes | — |
| 210 | C22×D4 | C2×#120 | 1 | 4 | yes | — |
| 211 | C22×D4 | C2×#120 | 1 | 8 | yes | — |
| 212 | C23×C4 | C2×#120 | 1 | 2 | yes | — |
| 213 | C23×C4 | C2×#120 | 1 | 2 | yes | — |
| 214 | C23×C4 | C2×#120 | 1 | 2 | yes | — |
| 215 | C23×C4 | C2×#120 | 1 | 8 | yes | — |
| 216 | C23×C4 | C2×#120 | 1 | 8 | yes | — |
| 217 | C23×C4 | C2×#120 | 1 | 4 | yes | — |
| 218 | C23×C4 | C2×#120 | 1 | 2 | yes | — |
| 219 | C23×C4 | C2×#120 | 1 | 4 | yes | — |
| 220 | C23×C4 | C2×#120 | 1 | 4 | yes | — |
| 221 | C23×C4 | C23×D4 | 1 | 2 | yes | — |
| 222 | C23×C4 | C23×D4 | 1 | 4 | yes | — |
| 223 | C23×C4 | C23×D4 | 1 | 8 | yes | — |
| 224 | C22⋊Q8 | C2×#120 | 1 | 16 | yes | — |
| 225 | C22⋊Q8 | C2×#120 | 1 | 16 | yes | — |
| 226 | C22⋊Q8 | C2×#120 | 1 | 32 | yes | — |
| 227 | #121 | C2×#120 | 1 | 16 | yes | — |
| 228 | #121 | C2×#120 | 1 | 16 | yes | — |
| 229 | #121 | C2×#120 | 1 | 32 | yes | — |
| 230 | #117 | C2×#120 | 1 | 32 | yes | — |
| 231 | C2×C4⋊C4 | C2×#120 | 1 | 8 | yes | — |
| 232 | C2×C4⋊C4 | C2×#120 | 1 | 8 | yes | — |
| 233 | C2×C4⋊C4 | C2×#120 | 1 | 8 | yes | — |
| 234 | C2×C4⋊C4 | C2×#120 | 1 | 16 | yes | — |
| 235 | C2×C4⋊C4 | C2×#120 | 1 | 32 | yes | — |
| 236 | C2×C22⋊C4 | C2×#120 | 1 | 8 | yes | — |
| 237 | C2×C22⋊C4 | C2×#120 | 1 | 32 | yes | — |
| 238 | C2×C22⋊C4 | C2×#120 | 1 | 8 | yes | — |
| 239 | C2×C22⋊C4 | C2×#120 | 1 | 8 | yes | — |
| 240 | C2×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 241 | C2×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 242 | C2×C42 | C2×#120 | 1 | 8 | yes | — |
| 243 | C24 | #2846 | 1 | 2 | yes | — |
| 244 | C24 | #2846 | 1 | 2 | yes | — |
| 245 | C24 | #2846 | 1 | 2 | yes | — |
| 246 | C24 | #2846 | 1 | 2 | yes | — |
| 247 | C24 | C2×#454 | 1 | 2 | yes | — |
| 248 | C24 | C2×#454 | 1 | 4 | yes | — |
| 249 | C24 | #3020 | 1 | 2 | yes | — |
| 250 | C24 | #3020 | 1 | 4 | yes | — |
| 251 | C24 | C22×#120 | 1 | 4 | yes | — |
| 252 | C24 | C22×#120 | 1 | 2 | yes | — |
| 253 | C24 | C22×#120 | 1 | 1 | yes | characteristic |
| 254 | C2×Q8 | #2846 | 1 | 16 | yes | — |
| 255 | C2×D4 | #2846 | 1 | 16 | yes | — |
| 256 | C22×C4 | #2846 | 1 | 4 | yes | — |
| 257 | C22×C4 | #2846 | 1 | 4 | yes | — |
| 258 | C22×C4 | #2846 | 1 | 4 | yes | — |
| 259 | C22×C4 | #2846 | 1 | 16 | yes | — |
| 260 | C22×C4 | #2846 | 1 | 4 | yes | — |
| 261 | C22×C4 | #2846 | 1 | 16 | yes | — |
| 262 | C22×C4 | C22×#120 | 1 | 4 | yes | — |
| 263 | C22×C4 | C22×#120 | 1 | 4 | yes | — |
| 264 | C22×C4 | C22×#120 | 1 | 4 | yes | — |
| 265 | C22×C4 | C22×#120 | 1 | 8 | yes | — |
| 266 | C22×C4 | C22×#120 | 1 | 8 | yes | — |
| 267 | C4⋊C4 | #2846 | 1 | 16 | yes | — |
| 268 | C4⋊C4 | #2846 | 1 | 16 | yes | — |
| 269 | C23 | #32889 | 1 | 4 | yes | — |
| 270 | C23 | #32889 | 1 | 4 | yes | — |
| 271 | C23 | #32889 | 1 | 4 | yes | — |
| 272 | C23 | C2×#2846 | 1 | 2 | yes | — |
| 273 | C23 | C2×#2846 | 1 | 1 | yes | characteristic |
| 274 | C23 | C2×#2846 | 1 | 4 | yes | — |
| 275 | C23 | C22×#454 | 1 | 1 | yes | characteristic |
| 276 | C23 | C2×#3020 | 1 | 1 | yes | characteristic |
| 277 | C23 | C2×#3020 | 1 | 2 | yes | — |
| 278 | C2×C4 | C2×#2846 | 1 | 8 | yes | — |
| 279 | C22 | #6342371 | 1 | 1 | yes | characteristic |
| 280 | C22 | C2×#32889 | 1 | 2 | yes | — |
| 281 | C22 | C2×#32889 | 1 | 1 | yes | characteristic |
| 282 | C22 | #6628868 | 1 | 2 | yes | — |
| 283 | C22 | #6628868 | 1 | 1 | yes | characteristic |
| 284 | C2 | #72210025 | 1 | 1 | yes | characteristic |
| 285 | C2 | #72210333 | 1 | 1 | yes | characteristic |
| 286 | C2 | #72227588 | 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