← #72266719
Subgroups — #72266719
Order 4096.
At least 9225 conjugacy classes of subgroups; only the 777 normal subgroups are shown.
The subgroup lattice has 244 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72266581 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #72266555 | C4 | 1 | 3 | yes | complemented |
| 3 | #72266521 | C4 | 1 | 3 | yes | complemented |
| 4 | #72266446 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #72266355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72266165 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #72266039 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72265766 | C22 | 1 | 3 | yes | complemented |
| 9 | #72259010 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #72259008 | C22 | 1 | 3 | yes | complemented |
| 11 | #72240132 | C22 | 1 | 3 | yes | complemented |
| 12 | #72235740 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #72235718 | C22 | 1 | 3 | yes | complemented |
| 14 | #72235186 | C22 | 1 | 3 | yes | complemented |
| 15 | #72234668 | C22 | 1 | 3 | yes | complemented |
| 16 | #72234636 | C22 | 1 | 3 | yes | — |
| 17 | #72232723 | C22 | 1 | 6 | yes | complemented |
| 18 | C2×#139716 | C22 | 1 | 3 | yes | complemented |
| 19 | #72219264 | C22 | 1 | 3 | yes | — |
| 20 | #72219254 | C22 | 1 | 1 | yes | characteristic |
| 21 | #72219241 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #1202 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #72209699 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | C22×#3532 | D4 | 1 | 3 | yes | — |
| 25 | C24×#120 | D4 | 1 | 1 | yes | characteristic |
| 26 | C2×#46996 | D4 | 1 | 3 | yes | — |
| 27 | C2×#34980 | C23 | 1 | 3 | yes | — |
| 28 | #7626202 | C23 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#21746 | C23 | 1 | 3 | yes | complemented |
| 30 | #6342371 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | #6342371 | D4 | 1 | 1 | yes | characteristic |
| 32 | #5025789 | D4 | 1 | 3 | yes | — |
| 33 | #5025782 | D4 | 1 | 3 | yes | — |
| 34 | #5024691 | D4 | 1 | 3 | yes | — |
| 35 | #5021140 | C2×C4 | 1 | 3 | yes | — |
| 36 | #5021138 | C2×C4 | 1 | 3 | yes | — |
| 37 | #5020751 | C2×C4 | 1 | 3 | yes | — |
| 38 | #4466055 | D4 | 1 | 6 | yes | — |
| 39 | #4430405 | D4 | 1 | 3 | yes | — |
| 40 | #4422949 | D4 | 1 | 3 | yes | — |
| 41 | #4420586 | D4 | 1 | 3 | yes | — |
| 42 | #4335643 | D4 | 1 | 6 | yes | — |
| 43 | #4308128 | C2×C4 | 1 | 3 | yes | — |
| 44 | #4308128 | D4 | 1 | 3 | yes | — |
| 45 | #2039146 | C2×C4 | 1 | 6 | yes | — |
| 46 | #763333 | D4 | 1 | 3 | yes | — |
| 47 | #686187 | C2×C4 | 1 | 3 | yes | — |
| 48 | #648360 | C2×C4 | 1 | 3 | yes | — |
| 49 | #647656 | C2×C4 | 1 | 3 | yes | — |
| 50 | #616961 | C23 | 1 | 3 | yes | — |
| 51 | #616960 | D4 | 1 | 3 | yes | — |
| 52 | C2×#15947 | C23 | 1 | 1 | yes | characteristic |
| 53 | #576160 | D4 | 1 | 3 | yes | — |
| 54 | #552670 | D4 | 1 | 3 | yes | — |
| 55 | #517411 | D4 | 1 | 3 | yes | — |
| 56 | C2×#8547 | C23 | 1 | 3 | yes | complemented |
| 57 | C2×#8541 | C23 | 1 | 1 | yes | characteristic, complemented |
| 58 | C28 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 59 | C25×D4 | C2×D4 | 1 | 3 | yes | — |
| 60 | C22×#551 | C22⋊C4 | 1 | 3 | yes | — |
| 61 | C22×D42 | C22⋊C4 | 1 | 3 | yes | — |
| 62 | C22×H(3,𝔽4) | C22⋊C4 | 1 | 3 | yes | — |
| 63 | C22×#560 | C22⋊C4 | 1 | 3 | yes | — |
| 64 | C22×#535 | C2×D4 | 1 | 3 | yes | — |
| 65 | C22×#534 | C2×D4 | 1 | 3 | yes | — |
| 66 | C22×#534 | C2×D4 | 1 | 3 | yes | — |
| 67 | C23×#120 | C2×D4 | 1 | 3 | yes | — |
| 68 | C23×#120 | C24 | 1 | 1 | yes | characteristic |
| 69 | C24×C22⋊C4 | C22⋊C4 | 1 | 3 | yes | complemented |
| 70 | C2×#2760 | C22⋊C4 | 1 | 6 | yes | complemented |
| 71 | C2×#2840 | C22⋊C4 | 1 | 3 | yes | complemented |
| 72 | C2×#2849 | C22×C4 | 1 | 3 | yes | — |
| 73 | C2×#2849 | C2×D4 | 1 | 3 | yes | — |
| 74 | C2×#2846 | C22×C4 | 1 | 3 | yes | — |
| 75 | C2×#2846 | C2×D4 | 1 | 3 | yes | — |
| 76 | C2×#2404 | C2×D4 | 1 | 6 | yes | — |
| 77 | C2×#2403 | C22⋊C4 | 1 | 3 | yes | complemented |
| 78 | C2×#2613 | C2×D4 | 1 | 3 | yes | — |
| 79 | C2×#2613 | C2×D4 | 1 | 3 | yes | — |
| 80 | C2×#2613 | C2×D4 | 1 | 3 | yes | — |
| 81 | C2×#2613 | C2×D4 | 1 | 3 | yes | — |
| 82 | C2×#2308 | C2×D4 | 1 | 3 | yes | — |
| 83 | C2×#2308 | C2×D4 | 1 | 3 | yes | — |
| 84 | C22×#379 | C2×D4 | 1 | 3 | yes | — |
| 85 | #15948 | C22⋊C4 | 1 | 3 | yes | — |
| 86 | #15948 | C22⋊C4 | 1 | 3 | yes | — |
| 87 | #15947 | C22⋊C4 | 1 | 3 | yes | — |
| 88 | #15947 | C22⋊C4 | 1 | 3 | yes | — |
| 89 | #15947 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | #15947 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | #15947 | C2×D4 | 1 | 3 | yes | — |
| 92 | #15947 | C2×D4 | 1 | 3 | yes | — |
| 93 | #15930 | C22⋊C4 | 1 | 6 | yes | complemented |
| 94 | #15561 | C22⋊C4 | 1 | 6 | yes | complemented |
| 95 | #15467 | C22⋊C4 | 1 | 6 | yes | complemented |
| 96 | #15267 | C22⋊C4 | 1 | 6 | yes | complemented |
| 97 | #15262 | C22⋊C4 | 1 | 3 | yes | — |
| 98 | #15261 | C22⋊C4 | 1 | 3 | yes | — |
| 99 | #15259 | C22⋊C4 | 1 | 3 | yes | — |
| 100 | #15259 | C22×C4 | 1 | 3 | yes | — |
| 101 | #15259 | C2×D4 | 1 | 6 | yes | — |
| 102 | #15259 | C2×D4 | 1 | 3 | yes | — |
| 103 | #15258 | C22⋊C4 | 1 | 3 | yes | — |
| 104 | #15258 | C22×C4 | 1 | 3 | yes | — |
| 105 | #15258 | C2×D4 | 1 | 6 | yes | — |
| 106 | #15258 | C2×D4 | 1 | 3 | yes | — |
| 107 | #14681 | C22⋊C4 | 1 | 6 | yes | complemented |
| 108 | #14679 | C22⋊C4 | 1 | 3 | yes | complemented |
| 109 | #14679 | C22⋊C4 | 1 | 3 | yes | complemented |
| 110 | #14658 | C22⋊C4 | 1 | 3 | yes | — |
| 111 | #14657 | C22⋊C4 | 1 | 3 | yes | — |
| 112 | #14507 | C22⋊C4 | 1 | 6 | yes | complemented |
| 113 | #14335 | C2×D4 | 1 | 3 | yes | — |
| 114 | #14167 | C22⋊C4 | 1 | 3 | yes | — |
| 115 | #14134 | C22⋊C4 | 1 | 3 | yes | — |
| 116 | #13868 | C2×D4 | 1 | 6 | yes | — |
| 117 | C2×#1438 | C2×D4 | 1 | 3 | yes | — |
| 118 | #13827 | C22⋊C4 | 1 | 3 | yes | complemented |
| 119 | C22⋊C42 | C22⋊C4 | 1 | 3 | yes | complemented |
| 120 | C27 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 121 | C27 | #120 | 1 | 1 | yes | characteristic |
| 122 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 123 | C23×#41 | #120 | 1 | 3 | yes | — |
| 124 | C24×D4 | #120 | 1 | 3 | yes | — |
| 125 | C24×D4 | #120 | 1 | 3 | yes | — |
| 126 | C24×D4 | #120 | 1 | 3 | yes | — |
| 127 | C24×D4 | #120 | 1 | 3 | yes | — |
| 128 | C24×D4 | C22×D4 | 1 | 3 | yes | — |
| 129 | C25×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 130 | C22×#127 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 131 | C22×#127 | #120 | 1 | 3 | yes | — |
| 132 | C22×#124 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 133 | C22×#124 | #120 | 1 | 3 | yes | — |
| 134 | C22×#123 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 135 | C22×#123 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 136 | C22×#123 | #120 | 1 | 3 | yes | — |
| 137 | C22×#123 | #120 | 1 | 3 | yes | — |
| 138 | C22×#120 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 139 | C22×#120 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 140 | C22×#120 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 141 | C22×#120 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 142 | C22×#120 | #120 | 1 | 3 | yes | — |
| 143 | C22×#120 | #120 | 1 | 3 | yes | — |
| 144 | C22×#120 | #120 | 1 | 3 | yes | — |
| 145 | C22×#120 | #120 | 1 | 3 | yes | — |
| 146 | C22×#120 | C23×C4 | 1 | 1 | yes | characteristic |
| 147 | C22×#120 | C22×D4 | 1 | 3 | yes | — |
| 148 | C22×#120 | C22×D4 | 1 | 3 | yes | — |
| 149 | C22×#120 | C22×D4 | 1 | 1 | yes | characteristic |
| 150 | C22×#117 | #120 | 1 | 3 | yes | — |
| 151 | C23×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 152 | C23×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 153 | C23×C22⋊C4 | #120 | 1 | 3 | yes | — |
| 154 | C23×C22⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 155 | C2×#393 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 156 | C2×#393 | #120 | 1 | 6 | yes | — |
| 157 | C2×#392 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 158 | C2×#392 | #120 | 1 | 6 | yes | — |
| 159 | C2×#381 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 160 | C2×#381 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 161 | C2×#381 | #120 | 1 | 6 | yes | — |
| 162 | C2×#381 | #120 | 1 | 3 | yes | — |
| 163 | C2×#381 | #120 | 1 | 3 | yes | — |
| 164 | C2×#379 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 165 | C2×#379 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 166 | C2×#379 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 167 | C2×#379 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 168 | C2×#379 | #120 | 1 | 3 | yes | — |
| 169 | C2×#379 | #120 | 1 | 3 | yes | — |
| 170 | C2×#379 | #120 | 1 | 3 | yes | — |
| 171 | C2×#379 | #120 | 1 | 3 | yes | — |
| 172 | #1438 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 173 | #1438 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 174 | #1438 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 175 | #1438 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 176 | #1438 | #120 | 1 | 6 | yes | — |
| 177 | #1438 | #120 | 1 | 6 | yes | — |
| 178 | #1437 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 179 | #1437 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 180 | #1437 | #120 | 1 | 6 | yes | — |
| 181 | #1437 | #120 | 1 | 6 | yes | — |
| 182 | C26 | #379 | 1 | 3 | yes | — |
| 183 | C26 | #379 | 1 | 3 | yes | — |
| 184 | C26 | #379 | 1 | 1 | yes | characteristic |
| 185 | C26 | #379 | 1 | 1 | yes | characteristic |
| 186 | C26 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 187 | C26 | C2×#120 | 1 | 3 | yes | — |
| 188 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 189 | C26 | C2×#120 | 1 | 3 | yes | — |
| 190 | C23×Q8 | #379 | 1 | 3 | yes | — |
| 191 | C23×D4 | #379 | 1 | 3 | yes | — |
| 192 | C23×D4 | B(4,𝔽2) | 1 | 6 | yes | — |
| 193 | C23×D4 | #458 | 1 | 6 | yes | — |
| 194 | C23×D4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 195 | C23×D4 | C2×#120 | 1 | 3 | yes | — |
| 196 | C23×D4 | C2×#120 | 1 | 3 | yes | — |
| 197 | C23×D4 | C2×#120 | 1 | 3 | yes | — |
| 198 | C24×C4 | #379 | 1 | 3 | yes | — |
| 199 | C24×C4 | #379 | 1 | 3 | yes | — |
| 200 | C24×C4 | C2×#120 | 1 | 3 | yes | — |
| 201 | C22×C22⋊C4 | #379 | 1 | 3 | yes | — |
| 202 | C22×C22⋊C4 | #379 | 1 | 3 | yes | — |
| 203 | C22×C22⋊C4 | #379 | 1 | 3 | yes | — |
| 204 | C22×C22⋊C4 | #379 | 1 | 3 | yes | — |
| 205 | C22×C22⋊C4 | #379 | 1 | 3 | yes | — |
| 206 | C22×C22⋊C4 | #379 | 1 | 3 | yes | — |
| 207 | C22×C22⋊C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 208 | C22×C22⋊C4 | C2×#120 | 1 | 3 | yes | — |
| 209 | C22×C22⋊C4 | C2×#120 | 1 | 6 | yes | — |
| 210 | C22×C42 | #379 | 1 | 3 | yes | — |
| 211 | C22×C42 | #379 | 1 | 3 | yes | — |
| 212 | C2×#95 | #379 | 1 | 6 | yes | — |
| 213 | C2×#95 | #379 | 1 | 6 | yes | — |
| 214 | C25 | #1790 | 1 | 6 | yes | — |
| 215 | C25 | C2×#379 | 1 | 3 | yes | — |
| 216 | C25 | C2×#379 | 1 | 1 | yes | characteristic |
| 217 | C25 | #2846 | 1 | 1 | yes | characteristic |
| 218 | C25 | #2846 | 1 | 3 | yes | — |
| 219 | C25 | #2846 | 1 | 1 | yes | characteristic |
| 220 | C25 | C2×B(4,𝔽2) | 1 | 3 | yes | — |
| 221 | C25 | C2×#458 | 1 | 3 | yes | — |
| 222 | C25 | #3026 | 1 | 3 | yes | — |
| 223 | C25 | #3026 | 1 | 3 | yes | — |
| 224 | C23×C4 | #1790 | 1 | 6 | yes | — |
| 225 | C23×C4 | C2×#379 | 1 | 3 | yes | — |
| 226 | C23×C4 | #2846 | 1 | 3 | yes | — |
| 227 | C24 | #12753 | 1 | 12 | yes | complemented |
| 228 | C24 | #14679 | 1 | 1 | yes | characteristic |
| 229 | C24 | C2×#1790 | 1 | 3 | yes | — |
| 230 | C24 | #20609 | 1 | 3 | yes | — |
| 231 | C24 | #32898 | 1 | 3 | yes | — |
| 232 | C24 | #32898 | 1 | 3 | yes | — |
| 233 | C24 | #32900 | 1 | 3 | yes | — |
| 234 | C24 | #32900 | 1 | 3 | yes | — |
| 235 | C23 | #347042 | 1 | 1 | yes | characteristic |
| 236 | C23 | #347048 | 1 | 3 | yes | — |
| 237 | C23 | #392125 | 1 | 3 | yes | — |
| 238 | C23 | C2×#12753 | 1 | 6 | yes | — |
| 239 | C22 | #72218980 | 1 | 3 | yes | — |
| 240 | C22 | #72219045 | 1 | 1 | yes | characteristic |
| 241 | C22 | #72237472 | 1 | 3 | yes | — |
| 242 | C2 | #72265775 | 1 | 3 | yes | — |
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