← #72262404
Subgroups — #72262404
Order 2048.
At least 6402 conjugacy classes of subgroups; only the 1314 normal subgroups are shown.
The subgroup lattice has 307 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72262400 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | #72262399 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #72262397 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72262355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72240616 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #72234164 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72234155 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #72234150 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #72234135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #72233348 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #72232787 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C23×#585 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×D4×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 14 | #7631287 | C22 | 1 | 3 | yes | complemented |
| 15 | #7631286 | C22 | 1 | 3 | yes | — |
| 16 | #7631286 | C22 | 1 | 3 | yes | complemented |
| 17 | #7631032 | C22 | 1 | 3 | yes | complemented |
| 18 | C2×#36212 | C22 | 1 | 3 | yes | — |
| 19 | C22⋊C4×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×#32898 | C22 | 1 | 2 | yes | — |
| 21 | C2×#32898 | C22 | 1 | 3 | yes | complemented |
| 22 | C2×#32898 | C22 | 1 | 6 | yes | complemented |
| 23 | #6470225 | C22 | 1 | 6 | yes | complemented |
| 24 | #6385971 | C22 | 1 | 3 | yes | complemented |
| 25 | C22×#1790 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #613188 | C22 | 1 | 6 | yes | complemented |
| 27 | #405090 | C22 | 1 | 6 | yes | complemented |
| 28 | #394267 | C22 | 1 | 6 | yes | complemented |
| 29 | #392125 | C22 | 1 | 2 | yes | complemented |
| 30 | #392125 | C22 | 1 | 6 | yes | complemented |
| 31 | #392110 | C22 | 1 | 6 | yes | complemented |
| 32 | #374038 | C22 | 1 | 3 | yes | complemented |
| 33 | #364471 | C22 | 1 | 6 | yes | complemented |
| 34 | #359863 | C22 | 1 | 3 | yes | complemented |
| 35 | #359579 | C22 | 1 | 3 | yes | complemented |
| 36 | #233541 | C22 | 1 | 12 | yes | complemented |
| 37 | #201664 | C22 | 1 | 6 | yes | complemented |
| 38 | #201664 | C22 | 1 | 6 | yes | complemented |
| 39 | #188035 | C22 | 1 | 3 | yes | complemented |
| 40 | #187928 | C22 | 1 | 6 | yes | complemented |
| 41 | #115691 | C22 | 1 | 6 | yes | complemented |
| 42 | #115204 | C22 | 1 | 12 | yes | complemented |
| 43 | #115163 | C22 | 1 | 6 | yes | complemented |
| 44 | #106766 | C22 | 1 | 6 | yes | complemented |
| 45 | #106654 | C22 | 1 | 6 | yes | complemented |
| 46 | C23×H(5,𝔽2) | D4 | 1 | 1 | yes | characteristic, complemented |
| 47 | C23×H(5,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 48 | C23×H(5,𝔽2) | C23 | 1 | 3 | yes | — |
| 49 | C23×H(5,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 50 | C24×#41 | C23 | 1 | 3 | yes | — |
| 51 | C2×#3496 | D4 | 1 | 3 | yes | complemented |
| 52 | C2×#3484 | D4 | 1 | 3 | yes | complemented |
| 53 | C2×#3484 | C23 | 1 | 3 | yes | — |
| 54 | C22×D42 | C23 | 1 | 3 | yes | — |
| 55 | C2×C4×H(5,𝔽2) | D4 | 1 | 1 | yes | characteristic, complemented |
| 56 | C22×B(4,𝔽2) | D4 | 1 | 8 | yes | complemented |
| 57 | C23×#99 | C23 | 1 | 1 | yes | characteristic |
| 58 | C23×#99 | C23 | 1 | 2 | yes | complemented |
| 59 | C2×#2849 | D4 | 1 | 3 | yes | complemented |
| 60 | C2×#2849 | C23 | 1 | 3 | yes | — |
| 61 | C2×#2847 | D4 | 1 | 3 | yes | complemented |
| 62 | #35527 | D4 | 1 | 6 | yes | complemented |
| 63 | #35512 | D4 | 1 | 6 | yes | complemented |
| 64 | #35347 | D4 | 1 | 6 | yes | complemented |
| 65 | #35346 | D4 | 1 | 6 | yes | complemented |
| 66 | #34980 | C23 | 1 | 6 | yes | — |
| 67 | #34980 | C23 | 1 | 6 | yes | — |
| 68 | C2×#2436 | D4 | 1 | 3 | yes | complemented |
| 69 | C2×#2409 | D4 | 1 | 3 | yes | complemented |
| 70 | C2×#2410 | D4 | 1 | 3 | yes | complemented |
| 71 | C2×#2410 | C23 | 1 | 3 | yes | — |
| 72 | C2×#2403 | D4 | 1 | 3 | yes | complemented |
| 73 | C2×#2403 | C23 | 1 | 6 | yes | — |
| 74 | C2×#2403 | C23 | 1 | 3 | yes | — |
| 75 | C2×#2403 | C23 | 1 | 6 | yes | complemented |
| 76 | #34171 | C23 | 1 | 3 | yes | — |
| 77 | #34171 | C23 | 1 | 3 | yes | — |
| 78 | C2×D4×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 79 | C2×C4×#120 | D4 | 1 | 3 | yes | complemented |
| 80 | C22×#386 | D4 | 1 | 3 | yes | complemented |
| 81 | C22×#386 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×#386 | C23 | 1 | 2 | yes | complemented |
| 83 | #21746 | C23 | 1 | 6 | yes | — |
| 84 | #21746 | C23 | 1 | 6 | yes | — |
| 85 | C2×#1898 | C23 | 1 | 6 | yes | — |
| 86 | C2×#1790 | D4 | 1 | 8 | yes | complemented |
| 87 | C2×#1781 | C23 | 1 | 6 | yes | — |
| 88 | C2×#1781 | C23 | 1 | 3 | yes | — |
| 89 | C2×#1781 | C23 | 1 | 6 | yes | — |
| 90 | C2×#1781 | C23 | 1 | 6 | yes | complemented |
| 91 | C2×#1781 | C23 | 1 | 12 | yes | complemented |
| 92 | #14681 | C23 | 1 | 6 | yes | complemented |
| 93 | #13867 | C23 | 1 | 6 | yes | — |
| 94 | #13867 | C23 | 1 | 6 | yes | complemented |
| 95 | #10735 | C23 | 1 | 6 | yes | complemented |
| 96 | #10735 | C23 | 1 | 6 | yes | complemented |
| 97 | #8101 | C23 | 1 | 12 | yes | complemented |
| 98 | C22×H(5,𝔽2) | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C22×H(5,𝔽2) | C2×D4 | 1 | 8 | yes | — |
| 100 | C22×H(5,𝔽2) | C2×D4 | 1 | 3 | yes | — |
| 101 | C22×H(5,𝔽2) | C2×D4 | 1 | 3 | yes | — |
| 102 | C22×H(5,𝔽2) | C2×D4 | 1 | 6 | yes | complemented |
| 103 | C22×H(5,𝔽2) | C2×D4 | 1 | 6 | yes | complemented |
| 104 | C24×Q8 | C2×D4 | 1 | 3 | yes | complemented |
| 105 | C24×D4 | C2×D4 | 1 | 3 | yes | — |
| 106 | C24×D4 | C2×D4 | 1 | 3 | yes | — |
| 107 | C24×D4 | C2×D4 | 1 | 3 | yes | complemented |
| 108 | C24×D4 | C24 | 1 | 2 | yes | — |
| 109 | C24×D4 | C24 | 1 | 3 | yes | — |
| 110 | C24×D4 | C24 | 1 | 3 | yes | — |
| 111 | C24×D4 | C24 | 1 | 1 | yes | characteristic |
| 112 | C25×C4 | C2×D4 | 1 | 3 | yes | complemented |
| 113 | C25×C4 | C2×D4 | 1 | 3 | yes | complemented |
| 114 | C25×C4 | C24 | 1 | 1 | yes | characteristic |
| 115 | C2×#534 | C2×D4 | 1 | 6 | yes | — |
| 116 | C22×#127 | C2×D4 | 1 | 3 | yes | — |
| 117 | C22×#121 | C2×D4 | 1 | 3 | yes | — |
| 118 | C22×#121 | C2×D4 | 1 | 3 | yes | — |
| 119 | C22×#121 | C2×D4 | 1 | 3 | yes | — |
| 120 | C22×#121 | C2×D4 | 1 | 3 | yes | — |
| 121 | C22×#120 | C2×D4 | 1 | 3 | yes | — |
| 122 | C22×#120 | C2×D4 | 1 | 3 | yes | — |
| 123 | C22×#120 | C2×D4 | 1 | 3 | yes | — |
| 124 | C22×#120 | C2×D4 | 1 | 3 | yes | — |
| 125 | C22×#120 | C2×D4 | 1 | 3 | yes | — |
| 126 | C22×#120 | C2×D4 | 1 | 12 | yes | complemented |
| 127 | C22×#120 | C2×D4 | 1 | 3 | yes | complemented |
| 128 | C22×#120 | C24 | 1 | 3 | yes | — |
| 129 | C2×#518 | C2×D4 | 1 | 3 | yes | — |
| 130 | C22×C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 131 | C22×C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 132 | C23×C22⋊C4 | C2×D4 | 1 | 3 | yes | complemented |
| 133 | C23×C22⋊C4 | C24 | 1 | 2 | yes | — |
| 134 | C23×C22⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 135 | C22×#99 | C2×D4 | 1 | 24 | yes | complemented |
| 136 | #2405 | C2×D4 | 1 | 12 | yes | complemented |
| 137 | #2403 | C2×D4 | 1 | 12 | yes | — |
| 138 | #2403 | C2×D4 | 1 | 12 | yes | — |
| 139 | #2403 | C2×D4 | 1 | 12 | yes | complemented |
| 140 | #2309 | C2×D4 | 1 | 6 | yes | complemented |
| 141 | #2308 | C2×D4 | 1 | 6 | yes | complemented |
| 142 | C2×#386 | C2×D4 | 1 | 3 | yes | — |
| 143 | C2×#386 | C2×D4 | 1 | 3 | yes | — |
| 144 | C2×#386 | C2×D4 | 1 | 3 | yes | — |
| 145 | C2×#386 | C2×D4 | 1 | 3 | yes | — |
| 146 | C2×#386 | C2×D4 | 1 | 3 | yes | — |
| 147 | C2×#386 | C2×D4 | 1 | 3 | yes | — |
| 148 | C2×#386 | C2×D4 | 1 | 3 | yes | complemented |
| 149 | C2×#386 | C2×D4 | 1 | 3 | yes | complemented |
| 150 | C2×#386 | C2×D4 | 1 | 12 | yes | complemented |
| 151 | C2×#386 | C2×D4 | 1 | 3 | yes | complemented |
| 152 | C2×#385 | C2×D4 | 1 | 3 | yes | complemented |
| 153 | C2×#385 | C2×D4 | 1 | 3 | yes | complemented |
| 154 | C2×#385 | C2×D4 | 1 | 3 | yes | complemented |
| 155 | C2×#380 | C2×D4 | 1 | 3 | yes | complemented |
| 156 | C2×#379 | C2×D4 | 1 | 3 | yes | complemented |
| 157 | C2×#379 | C2×D4 | 1 | 3 | yes | complemented |
| 158 | C2×#379 | C24 | 1 | 6 | yes | — |
| 159 | C2×#379 | C24 | 1 | 6 | yes | — |
| 160 | C2×#379 | C24 | 1 | 3 | yes | — |
| 161 | C2×C4×C22⋊C4 | C2×D4 | 1 | 3 | yes | complemented |
| 162 | C26 | #120 | 1 | 3 | yes | — |
| 163 | C26 | C22×D4 | 1 | 2 | yes | — |
| 164 | C26 | C22×D4 | 1 | 3 | yes | — |
| 165 | C26 | C22×D4 | 1 | 3 | yes | — |
| 166 | C26 | C22×D4 | 1 | 1 | yes | characteristic |
| 167 | C26 | C25 | 1 | 1 | yes | characteristic |
| 168 | C2×H(5,𝔽2) | #120 | 1 | 4 | yes | — |
| 169 | C2×H(5,𝔽2) | #120 | 1 | 12 | yes | — |
| 170 | C23×D4 | #120 | 1 | 3 | yes | — |
| 171 | C23×D4 | #120 | 1 | 3 | yes | — |
| 172 | C23×D4 | #120 | 1 | 3 | yes | — |
| 173 | C23×D4 | #120 | 1 | 3 | yes | — |
| 174 | C23×D4 | #120 | 1 | 3 | yes | — |
| 175 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 176 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 177 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 178 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 179 | C23×D4 | C22×D4 | 1 | 12 | yes | — |
| 180 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 181 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 182 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 183 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 184 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 185 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 186 | C23×D4 | C22×D4 | 1 | 3 | yes | — |
| 187 | C23×D4 | C22×D4 | 1 | 12 | yes | — |
| 188 | C23×D4 | H(5,𝔽2) | 1 | 12 | yes | — |
| 189 | C24×C4 | #120 | 1 | 3 | yes | — |
| 190 | C24×C4 | #120 | 1 | 3 | yes | — |
| 191 | C24×C4 | C22×D4 | 1 | 2 | yes | — |
| 192 | C24×C4 | C22×D4 | 1 | 3 | yes | — |
| 193 | C24×C4 | C22×D4 | 1 | 3 | yes | — |
| 194 | C24×C4 | C22×D4 | 1 | 3 | yes | — |
| 195 | C24×C4 | C22×D4 | 1 | 3 | yes | — |
| 196 | C24×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×#120 | #120 | 1 | 6 | yes | — |
| 198 | C2×#120 | #120 | 1 | 6 | yes | — |
| 199 | C2×#120 | #120 | 1 | 12 | yes | — |
| 200 | C22×C4⋊C4 | #120 | 1 | 3 | yes | — |
| 201 | C22×C4⋊C4 | #120 | 1 | 3 | yes | — |
| 202 | C22×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 203 | C22×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 204 | C22×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 205 | C22×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 206 | C22×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 207 | C22×C22⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 208 | C22×C22⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 209 | C22×C22⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 210 | C22×C22⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 211 | C22×C22⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 212 | C22×C22⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 213 | C22×C22⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 214 | C22×C22⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 215 | C22×C42 | #120 | 1 | 3 | yes | — |
| 216 | #386 | #120 | 1 | 3 | yes | — |
| 217 | #386 | #120 | 1 | 6 | yes | — |
| 218 | #386 | #120 | 1 | 12 | yes | — |
| 219 | #386 | #120 | 1 | 3 | yes | — |
| 220 | #386 | #120 | 1 | 6 | yes | — |
| 221 | #386 | #120 | 1 | 6 | yes | — |
| 222 | #386 | #120 | 1 | 3 | yes | — |
| 223 | #386 | #120 | 1 | 1 | yes | characteristic |
| 224 | #379 | C22×D4 | 1 | 12 | yes | — |
| 225 | C25 | C2×#120 | 1 | 3 | yes | — |
| 226 | C25 | C2×#120 | 1 | 3 | yes | — |
| 227 | C25 | C2×#120 | 1 | 3 | yes | — |
| 228 | C25 | C2×#120 | 1 | 6 | yes | — |
| 229 | C25 | C2×#120 | 1 | 3 | yes | — |
| 230 | C25 | C2×#120 | 1 | 3 | yes | — |
| 231 | C25 | D42 | 1 | 12 | yes | — |
| 232 | C25 | C23×D4 | 1 | 1 | yes | characteristic |
| 233 | C25 | C23×D4 | 1 | 3 | yes | — |
| 234 | C25 | C23×D4 | 1 | 2 | yes | — |
| 235 | C25 | C23×D4 | 1 | 3 | yes | — |
| 236 | C25 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 237 | H(5,𝔽2) | B(4,𝔽2) | 1 | 16 | yes | complemented |
| 238 | C22×D4 | C2×#120 | 1 | 3 | yes | — |
| 239 | C22×D4 | C2×#120 | 1 | 3 | yes | — |
| 240 | C22×D4 | C2×#120 | 1 | 3 | yes | — |
| 241 | C22×D4 | C2×#120 | 1 | 1 | yes | characteristic |
| 242 | C22×D4 | C2×#120 | 1 | 6 | yes | — |
| 243 | C22×D4 | C2×#120 | 1 | 6 | yes | — |
| 244 | C22×D4 | C2×#120 | 1 | 6 | yes | — |
| 245 | C22×D4 | #534 | 1 | 6 | yes | — |
| 246 | C22×D4 | #534 | 1 | 6 | yes | — |
| 247 | C22×D4 | D42 | 1 | 12 | yes | — |
| 248 | C22×D4 | D42 | 1 | 12 | yes | — |
| 249 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 250 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 251 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 252 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 253 | C23×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 254 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 255 | C23×C4 | C2×#120 | 1 | 6 | yes | — |
| 256 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 257 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 258 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 259 | C23×C4 | D42 | 1 | 12 | yes | — |
| 260 | C2×C22⋊C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 261 | C2×C22⋊C4 | C2×#120 | 1 | 3 | yes | — |
| 262 | C2×C22⋊C4 | C2×#120 | 1 | 6 | yes | — |
| 263 | C2×C22⋊C4 | C2×#120 | 1 | 6 | yes | — |
| 264 | C24 | #2403 | 1 | 6 | yes | — |
| 265 | C24 | #2403 | 1 | 6 | yes | — |
| 266 | C24 | #2846 | 1 | 3 | yes | — |
| 267 | C24 | #2846 | 1 | 1 | yes | characteristic |
| 268 | C24 | C22×#120 | 1 | 3 | yes | — |
| 269 | C24 | C22×#120 | 1 | 3 | yes | — |
| 270 | C24 | C22×#120 | 1 | 1 | yes | characteristic |
| 271 | C24 | C22×#120 | 1 | 1 | yes | characteristic |
| 272 | C24 | C2×#534 | 1 | 3 | yes | — |
| 273 | C24 | C2×D42 | 1 | 6 | yes | — |
| 274 | C24 | C2×D42 | 1 | 6 | yes | — |
| 275 | C24 | #3484 | 1 | 6 | yes | — |
| 276 | C24 | #3484 | 1 | 6 | yes | — |
| 277 | C2×D4 | C2×B(4,𝔽2) | 1 | 24 | yes | — |
| 278 | C2×D4 | #3025 | 1 | 2 | yes | — |
| 279 | C2×D4 | #3027 | 1 | 2 | yes | — |
| 280 | C22×C4 | #2403 | 1 | 6 | yes | — |
| 281 | C22×C4 | #2403 | 1 | 6 | yes | — |
| 282 | C22×C4 | #2846 | 1 | 3 | yes | — |
| 283 | C22×C4 | #2846 | 1 | 1 | yes | characteristic |
| 284 | C23 | #23900 | 1 | 12 | yes | — |
| 285 | C23 | #32899 | 1 | 2 | yes | complemented |
| 286 | C23 | C2×#2403 | 1 | 3 | yes | — |
| 287 | C23 | #34980 | 1 | 3 | yes | — |
| 288 | C23 | D4×#120 | 1 | 6 | yes | — |
| 289 | C23 | D4×#120 | 1 | 2 | yes | — |
| 290 | C23 | C2×#2846 | 1 | 1 | yes | characteristic |
| 291 | C23 | C22×B(4,𝔽2) | 1 | 4 | yes | — |
| 292 | C23 | C2×#3025 | 1 | 1 | yes | characteristic |
| 293 | C23 | C2×#3027 | 1 | 1 | yes | characteristic |
| 294 | C23 | #60399 | 1 | 2 | yes | — |
| 295 | C2×C4 | #23900 | 1 | 12 | yes | — |
| 296 | C2×C4 | #32899 | 1 | 2 | yes | complemented |
| 297 | C22 | #612424 | 1 | 1 | yes | characteristic |
| 298 | C22 | C2×#23900 | 1 | 6 | yes | — |
| 299 | C22 | #6573710 | 1 | 2 | yes | — |
| 300 | C22 | #6573716 | 1 | 2 | yes | — |
| 301 | C22 | C2×#32899 | 1 | 1 | yes | characteristic |
| 302 | C22 | #6628896 | 1 | 1 | yes | characteristic |
| 303 | C2 | #72215858 | 1 | 1 | yes | characteristic |
| 304 | C2 | #72240574 | 1 | 1 | yes | characteristic |
| 305 | C2 | #72260725 | 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