← #72312305
Subgroups — #72312305
Order 2048.
At least 7463 conjugacy classes of subgroups; only the 1166 normal subgroups are shown.
The subgroup lattice has 489 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#6437585 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #72312292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72312288 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72303721 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72303717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72303110 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72280695 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72280532 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #72267961 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#7622467 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #72255896 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C22×#3585 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#62852 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#60398 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#60387 | C22 | 1 | 1 | yes | characteristic |
| 16 | C22×#2883 | C22 | 1 | 2 | yes | — |
| 17 | C2×#33358 | C22 | 1 | 2 | yes | — |
| 18 | C2×#33358 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#33358 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#23874 | C4 | 1 | 4 | yes | complemented |
| 21 | C2×#23872 | C4 | 1 | 4 | yes | complemented |
| 22 | #6374181 | C22 | 1 | 2 | yes | — |
| 23 | #6374140 | C22 | 1 | 1 | yes | characteristic |
| 24 | #6374127 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#21017 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#20947 | C22 | 1 | 1 | yes | characteristic |
| 27 | C22×#1795 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#20620 | C22 | 1 | 2 | yes | complemented |
| 29 | #6370734 | C22 | 1 | 2 | yes | complemented |
| 30 | #6370719 | C22 | 1 | 2 | yes | — |
| 31 | C2×#12589 | C22 | 1 | 2 | yes | complemented |
| 32 | #492899 | C22 | 1 | 2 | yes | complemented |
| 33 | C2×#12577 | C22 | 1 | 2 | yes | complemented |
| 34 | #492886 | C22 | 1 | 2 | yes | complemented |
| 35 | #353434 | C22 | 1 | 2 | yes | complemented |
| 36 | #353422 | C22 | 1 | 2 | yes | complemented |
| 37 | C22×#585 | D4 | 1 | 1 | yes | characteristic |
| 38 | C22×#585 | C23 | 1 | 1 | yes | characteristic |
| 39 | C23×H(5,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×#3585 | C2×C4 | 1 | 4 | yes | — |
| 41 | C2×#3585 | D4 | 1 | 8 | yes | — |
| 42 | C22×#568 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×#3500 | C2×C4 | 1 | 2 | yes | — |
| 44 | C2×#3500 | D4 | 1 | 2 | yes | — |
| 45 | C2×#3498 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×#3498 | D4 | 1 | 2 | yes | — |
| 47 | C2×#3449 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×#3449 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×#535 | D4 | 1 | 1 | yes | characteristic |
| 50 | C22×#535 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×#3428 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×#3028 | C2×C4 | 1 | 2 | yes | complemented |
| 53 | C2×#3027 | C2×C4 | 1 | 2 | yes | complemented |
| 54 | C2×#3018 | C2×C4 | 1 | 4 | yes | complemented |
| 55 | C2×#2896 | D4 | 1 | 2 | yes | complemented |
| 56 | C2×#2896 | D4 | 1 | 2 | yes | complemented |
| 57 | C22×#418 | D4 | 1 | 2 | yes | complemented |
| 58 | C22×#418 | D4 | 1 | 2 | yes | complemented |
| 59 | C22×#413 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#2883 | D4 | 1 | 8 | yes | complemented |
| 61 | C22×#410 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×#410 | C23 | 1 | 2 | yes | — |
| 63 | C22×#410 | C23 | 1 | 2 | yes | — |
| 64 | C2×#2879 | C23 | 1 | 2 | yes | — |
| 65 | #34044 | C23 | 1 | 2 | yes | — |
| 66 | #33358 | D4 | 1 | 8 | yes | — |
| 67 | C2×#2129 | D4 | 1 | 2 | yes | complemented |
| 68 | C2×#2128 | D4 | 1 | 2 | yes | complemented |
| 69 | C2×#2127 | D4 | 1 | 4 | yes | complemented |
| 70 | C2×#1915 | C2×C4 | 1 | 2 | yes | complemented |
| 71 | C2×#1914 | C2×C4 | 1 | 2 | yes | complemented |
| 72 | C2×#1884 | C2×C4 | 1 | 4 | yes | complemented |
| 73 | C2×#1795 | C2×C4 | 1 | 4 | yes | — |
| 74 | C2×#1795 | D4 | 1 | 8 | yes | — |
| 75 | C2×#585 | C22×C4 | 1 | 2 | yes | — |
| 76 | C2×#585 | C2×D4 | 1 | 4 | yes | — |
| 77 | C22×2−1+4 | C22⋊C4 | 1 | 2 | yes | complemented |
| 78 | C22×H(5,𝔽2) | C22⋊C4 | 1 | 2 | yes | complemented |
| 79 | C22×H(5,𝔽2) | C22×C4 | 1 | 2 | yes | — |
| 80 | C22×H(5,𝔽2) | C2×D4 | 1 | 2 | yes | — |
| 81 | C22×H(5,𝔽2) | C2×D4 | 1 | 4 | yes | — |
| 82 | C22×H(5,𝔽2) | C2×D4 | 1 | 4 | yes | — |
| 83 | C22×H(5,𝔽2) | C2×D4 | 1 | 4 | yes | — |
| 84 | C22×H(5,𝔽2) | #41 | 1 | 4 | yes | — |
| 85 | C22×H(5,𝔽2) | #41 | 1 | 4 | yes | — |
| 86 | C23×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C23×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C23×#41 | C2×D4 | 1 | 2 | yes | — |
| 89 | C23×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C23×#41 | C24 | 1 | 1 | yes | characteristic |
| 91 | C24×D4 | C2×D4 | 1 | 2 | yes | — |
| 92 | C24×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | #3585 | C22⋊C4 | 1 | 16 | yes | — |
| 94 | C2×#568 | C22×C4 | 1 | 2 | yes | — |
| 95 | C2×#568 | C2×D4 | 1 | 4 | yes | — |
| 96 | C23×M16 | C2×D4 | 1 | 2 | yes | — |
| 97 | C23×M16 | C2×D4 | 1 | 2 | yes | — |
| 98 | #3449 | C2×D4 | 1 | 4 | yes | — |
| 99 | #3449 | #41 | 1 | 4 | yes | — |
| 100 | C2×#536 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | C2×#536 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×#536 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×#536 | #41 | 1 | 1 | yes | characteristic |
| 104 | C2×#536 | #41 | 1 | 2 | yes | — |
| 105 | C2×#535 | C22⋊C4 | 1 | 2 | yes | complemented |
| 106 | C2×#535 | C22⋊C4 | 1 | 2 | yes | complemented |
| 107 | C2×#535 | C22×C4 | 1 | 1 | yes | characteristic |
| 108 | C2×#535 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×#535 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×#535 | C2×D4 | 1 | 2 | yes | — |
| 111 | C2×#535 | #41 | 1 | 1 | yes | characteristic |
| 112 | C2×#532 | C22×C4 | 1 | 2 | yes | — |
| 113 | C2×#532 | C2×D4 | 1 | 2 | yes | — |
| 114 | C22×#127 | C22⋊C4 | 1 | 2 | yes | complemented |
| 115 | C22×#124 | C22⋊C4 | 1 | 2 | yes | complemented |
| 116 | C2×C4×#41 | C22⋊C4 | 1 | 2 | yes | complemented |
| 117 | C2×C4×#41 | C22⋊C4 | 1 | 2 | yes | complemented |
| 118 | C22×#117 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C22×#117 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C22×#117 | C2×D4 | 1 | 2 | yes | — |
| 121 | C22×#117 | C2×D4 | 1 | 2 | yes | — |
| 122 | C2×#413 | C22×C4 | 1 | 2 | yes | — |
| 123 | C2×#413 | C2×D4 | 1 | 4 | yes | — |
| 124 | C2×#410 | C22×C4 | 1 | 2 | yes | — |
| 125 | C2×#410 | C2×D4 | 1 | 4 | yes | — |
| 126 | C2×#410 | C2×D4 | 1 | 4 | yes | — |
| 127 | C2×#410 | C2×D4 | 1 | 4 | yes | — |
| 128 | C2×#410 | C2×D4 | 1 | 4 | yes | — |
| 129 | C2×#410 | C2×D4 | 1 | 4 | yes | — |
| 130 | C2×#410 | C2×D4 | 1 | 4 | yes | — |
| 131 | C22×#99 | C2×D4 | 1 | 4 | yes | — |
| 132 | #1795 | C22⋊C4 | 1 | 16 | yes | complemented |
| 133 | #585 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 134 | C2×H(5,𝔽2) | C2×C22⋊C4 | 1 | 4 | yes | — |
| 135 | C2×H(5,𝔽2) | C2×C22⋊C4 | 1 | 4 | yes | — |
| 136 | C2×H(5,𝔽2) | C4×D4 | 1 | 8 | yes | — |
| 137 | C2×H(5,𝔽2) | #120 | 1 | 8 | yes | — |
| 138 | C2×H(5,𝔽2) | #120 | 1 | 4 | yes | — |
| 139 | C2×H(5,𝔽2) | #121 | 1 | 8 | yes | — |
| 140 | C2×H(5,𝔽2) | #121 | 1 | 8 | yes | — |
| 141 | C2×H(5,𝔽2) | #123 | 1 | 8 | yes | — |
| 142 | C2×H(5,𝔽2) | #123 | 1 | 4 | yes | — |
| 143 | C2×H(5,𝔽2) | #124 | 1 | 8 | yes | — |
| 144 | C22×#41 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 145 | C22×#41 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 146 | C22×#41 | C4×D4 | 1 | 4 | yes | — |
| 147 | C22×#41 | #120 | 1 | 4 | yes | — |
| 148 | C22×#41 | #120 | 1 | 4 | yes | — |
| 149 | C22×#41 | #121 | 1 | 2 | yes | — |
| 150 | C22×#41 | #121 | 1 | 4 | yes | — |
| 151 | C22×#41 | #121 | 1 | 4 | yes | — |
| 152 | C22×#41 | #121 | 1 | 4 | yes | — |
| 153 | C22×#41 | #121 | 1 | 4 | yes | — |
| 154 | C22×#41 | #121 | 1 | 4 | yes | — |
| 155 | C22×#41 | #123 | 1 | 2 | yes | — |
| 156 | C22×#41 | #127 | 1 | 4 | yes | — |
| 157 | C22×#41 | C23×C4 | 1 | 1 | yes | characteristic |
| 158 | C22×#41 | C22×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×#41 | C22×D4 | 1 | 2 | yes | — |
| 160 | C22×#41 | C22×D4 | 1 | 2 | yes | — |
| 161 | C22×#41 | C22×D4 | 1 | 2 | yes | — |
| 162 | C22×#41 | C22×D4 | 1 | 2 | yes | — |
| 163 | C22×#41 | C22×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×#41 | C2×#41 | 1 | 2 | yes | — |
| 165 | C22×#41 | C2×#41 | 1 | 2 | yes | — |
| 166 | C22×#41 | C2×#41 | 1 | 1 | yes | characteristic |
| 167 | C22×#41 | C2×#41 | 1 | 2 | yes | — |
| 168 | C22×#41 | H(5,𝔽2) | 1 | 2 | yes | — |
| 169 | C22×#41 | H(5,𝔽2) | 1 | 2 | yes | — |
| 170 | C22×#41 | H(5,𝔽2) | 1 | 2 | yes | — |
| 171 | C23×Q8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | C23×Q8 | #120 | 1 | 1 | yes | characteristic |
| 173 | C23×Q8 | #121 | 1 | 1 | yes | characteristic |
| 174 | C23×Q8 | C2×#41 | 1 | 1 | yes | characteristic |
| 175 | C23×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 176 | C23×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 177 | C23×D4 | C4×D4 | 1 | 4 | yes | — |
| 178 | C23×D4 | #120 | 1 | 4 | yes | — |
| 179 | C23×D4 | #120 | 1 | 4 | yes | — |
| 180 | C23×D4 | #120 | 1 | 2 | yes | — |
| 181 | C23×D4 | #120 | 1 | 1 | yes | characteristic |
| 182 | C23×D4 | #121 | 1 | 4 | yes | — |
| 183 | C23×D4 | #121 | 1 | 4 | yes | — |
| 184 | C23×D4 | #121 | 1 | 4 | yes | — |
| 185 | C23×D4 | #121 | 1 | 1 | yes | characteristic |
| 186 | C23×D4 | #121 | 1 | 4 | yes | — |
| 187 | C23×D4 | #123 | 1 | 2 | yes | — |
| 188 | C23×D4 | #127 | 1 | 4 | yes | — |
| 189 | C23×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 190 | C23×D4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 191 | C24×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 192 | C24×C4 | C22×D4 | 1 | 2 | yes | — |
| 193 | #568 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 194 | #536 | C4×D4 | 1 | 4 | yes | — |
| 195 | #536 | #120 | 1 | 2 | yes | — |
| 196 | #536 | #123 | 1 | 2 | yes | — |
| 197 | #535 | C4×D4 | 1 | 4 | yes | — |
| 198 | #535 | #120 | 1 | 2 | yes | — |
| 199 | #535 | #123 | 1 | 2 | yes | — |
| 200 | C2×C4⋊Q8 | C4×D4 | 1 | 2 | yes | — |
| 201 | C2×C4⋊Q8 | #123 | 1 | 2 | yes | — |
| 202 | C2×#127 | C4×D4 | 1 | 2 | yes | — |
| 203 | C2×#127 | #120 | 1 | 2 | yes | — |
| 204 | C2×#124 | C4×D4 | 1 | 2 | yes | — |
| 205 | C2×#124 | C4×D4 | 1 | 2 | yes | — |
| 206 | C2×#124 | #120 | 1 | 2 | yes | — |
| 207 | C2×#124 | #123 | 1 | 2 | yes | — |
| 208 | C2×#117 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 209 | C2×#117 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 210 | C2×#117 | #121 | 1 | 4 | yes | — |
| 211 | C2×#117 | #121 | 1 | 2 | yes | — |
| 212 | C2×#117 | #121 | 1 | 1 | yes | characteristic |
| 213 | C2×#117 | #121 | 1 | 1 | yes | characteristic |
| 214 | C22×C42 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 215 | #413 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 216 | #410 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 217 | #410 | #120 | 1 | 8 | yes | — |
| 218 | C2×#99 | #120 | 1 | 8 | yes | — |
| 219 | C25 | #534 | 1 | 1 | yes | characteristic |
| 220 | C25 | D42 | 1 | 2 | yes | — |
| 221 | C2×#41 | #379 | 1 | 4 | yes | — |
| 222 | C2×#41 | #386 | 1 | 4 | yes | — |
| 223 | C2×#41 | #386 | 1 | 8 | yes | — |
| 224 | C2×#41 | #390 | 1 | 8 | yes | — |
| 225 | C2×#41 | #392 | 1 | 8 | yes | — |
| 226 | C2×#41 | #394 | 1 | 8 | yes | — |
| 227 | C2×#41 | #394 | 1 | 8 | yes | — |
| 228 | C2×#41 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 229 | C2×#41 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 230 | C2×#41 | C2×C4×D4 | 1 | 2 | yes | — |
| 231 | C2×#41 | C2×C4×D4 | 1 | 2 | yes | — |
| 232 | C2×#41 | #518 | 1 | 1 | yes | characteristic |
| 233 | C2×#41 | #518 | 1 | 1 | yes | characteristic |
| 234 | C2×#41 | C2×#120 | 1 | 2 | yes | — |
| 235 | C2×#41 | C2×#120 | 1 | 1 | yes | characteristic |
| 236 | C2×#41 | C2×#120 | 1 | 2 | yes | — |
| 237 | C2×#41 | C2×#120 | 1 | 1 | yes | characteristic |
| 238 | C2×#41 | C2×#121 | 1 | 2 | yes | — |
| 239 | C2×#41 | C2×#121 | 1 | 2 | yes | — |
| 240 | C2×#41 | C2×#123 | 1 | 1 | yes | characteristic |
| 241 | C2×#41 | C2×#123 | 1 | 2 | yes | — |
| 242 | C2×#41 | C2×#123 | 1 | 1 | yes | characteristic |
| 243 | C2×#41 | #525 | 1 | 2 | yes | — |
| 244 | C2×#41 | #525 | 1 | 2 | yes | — |
| 245 | C2×#41 | #525 | 1 | 2 | yes | — |
| 246 | C2×#41 | C2×#124 | 1 | 2 | yes | — |
| 247 | C2×#41 | #534 | 1 | 2 | yes | — |
| 248 | C2×#41 | #534 | 1 | 2 | yes | — |
| 249 | C2×#41 | #535 | 1 | 2 | yes | — |
| 250 | C2×#41 | #538 | 1 | 2 | yes | — |
| 251 | C2×#41 | #538 | 1 | 2 | yes | — |
| 252 | C2×#41 | D42 | 1 | 2 | yes | — |
| 253 | C2×#41 | D42 | 1 | 2 | yes | — |
| 254 | C2×#41 | D42 | 1 | 2 | yes | — |
| 255 | C2×#41 | D42 | 1 | 2 | yes | — |
| 256 | C2×#41 | #546 | 1 | 2 | yes | — |
| 257 | C2×#41 | #546 | 1 | 2 | yes | — |
| 258 | C2×#41 | #546 | 1 | 2 | yes | — |
| 259 | C2×#41 | #546 | 1 | 2 | yes | — |
| 260 | C2×#41 | #546 | 1 | 2 | yes | — |
| 261 | C2×#41 | #546 | 1 | 2 | yes | — |
| 262 | C2×#41 | #551 | 1 | 2 | yes | — |
| 263 | C2×#41 | #551 | 1 | 2 | yes | — |
| 264 | C22×Q8 | #386 | 1 | 2 | yes | — |
| 265 | C22×Q8 | #386 | 1 | 2 | yes | — |
| 266 | C22×Q8 | #386 | 1 | 2 | yes | — |
| 267 | C22×Q8 | #392 | 1 | 4 | yes | — |
| 268 | C22×Q8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 269 | C22×Q8 | C2×#123 | 1 | 1 | yes | characteristic |
| 270 | C22×Q8 | #525 | 1 | 2 | yes | — |
| 271 | C22×Q8 | #525 | 1 | 2 | yes | — |
| 272 | C22×Q8 | #546 | 1 | 2 | yes | — |
| 273 | C22×Q8 | #546 | 1 | 2 | yes | — |
| 274 | C22×Q8 | #551 | 1 | 2 | yes | — |
| 275 | C22×D4 | #379 | 1 | 4 | yes | — |
| 276 | C22×D4 | #386 | 1 | 4 | yes | — |
| 277 | C22×D4 | #386 | 1 | 8 | yes | — |
| 278 | C22×D4 | #386 | 1 | 2 | yes | — |
| 279 | C22×D4 | #386 | 1 | 2 | yes | — |
| 280 | C22×D4 | #386 | 1 | 2 | yes | — |
| 281 | C22×D4 | #386 | 1 | 4 | yes | — |
| 282 | C22×D4 | #390 | 1 | 8 | yes | — |
| 283 | C22×D4 | #392 | 1 | 4 | yes | — |
| 284 | C22×D4 | #392 | 1 | 4 | yes | — |
| 285 | C22×D4 | #392 | 1 | 8 | yes | — |
| 286 | C22×D4 | #392 | 1 | 4 | yes | — |
| 287 | C22×D4 | #394 | 1 | 8 | yes | — |
| 288 | C22×D4 | #394 | 1 | 8 | yes | — |
| 289 | C22×D4 | B(4,𝔽2) | 1 | 2 | yes | — |
| 290 | C22×D4 | B(4,𝔽2) | 1 | 2 | yes | — |
| 291 | C22×D4 | B(4,𝔽2) | 1 | 4 | yes | — |
| 292 | C22×D4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 293 | C22×D4 | #518 | 1 | 2 | yes | — |
| 294 | C22×D4 | C2×#120 | 1 | 2 | yes | — |
| 295 | C22×D4 | C2×#120 | 1 | 1 | yes | characteristic |
| 296 | C22×D4 | #525 | 1 | 2 | yes | — |
| 297 | C22×D4 | #534 | 1 | 2 | yes | — |
| 298 | C22×D4 | #534 | 1 | 2 | yes | — |
| 299 | C22×D4 | #535 | 1 | 2 | yes | — |
| 300 | C22×D4 | #538 | 1 | 2 | yes | — |
| 301 | C22×D4 | #538 | 1 | 2 | yes | — |
| 302 | C22×D4 | D42 | 1 | 2 | yes | — |
| 303 | C22×D4 | D42 | 1 | 2 | yes | — |
| 304 | C22×D4 | D42 | 1 | 2 | yes | — |
| 305 | C22×D4 | D42 | 1 | 2 | yes | — |
| 306 | C22×D4 | #546 | 1 | 2 | yes | — |
| 307 | C22×D4 | #546 | 1 | 2 | yes | — |
| 308 | C22×D4 | #546 | 1 | 2 | yes | — |
| 309 | C22×D4 | #546 | 1 | 2 | yes | — |
| 310 | C22×D4 | #551 | 1 | 2 | yes | — |
| 311 | C23×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 312 | C23×C4 | C2×C4×D4 | 1 | 2 | yes | — |
| 313 | C23×C4 | C2×#120 | 1 | 2 | yes | — |
| 314 | C23×C4 | C2×#120 | 1 | 2 | yes | — |
| 315 | C23×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 316 | C23×C4 | C2×#121 | 1 | 2 | yes | — |
| 317 | C23×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 318 | C23×C4 | C2×#121 | 1 | 2 | yes | — |
| 319 | C23×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 320 | C23×C4 | C2×#121 | 1 | 2 | yes | — |
| 321 | C23×C4 | C2×#121 | 1 | 2 | yes | — |
| 322 | C23×C4 | C2×#121 | 1 | 2 | yes | — |
| 323 | C23×C4 | C2×#123 | 1 | 1 | yes | characteristic |
| 324 | C23×C4 | C2×#127 | 1 | 2 | yes | — |
| 325 | C23×C4 | #534 | 1 | 2 | yes | — |
| 326 | C23×C4 | #534 | 1 | 1 | yes | characteristic |
| 327 | C23×C4 | D42 | 1 | 2 | yes | — |
| 328 | C23×C4 | D42 | 1 | 2 | yes | — |
| 329 | C23×C4 | D42 | 1 | 2 | yes | — |
| 330 | C23×C4 | #546 | 1 | 2 | yes | — |
| 331 | C23×C4 | #546 | 1 | 2 | yes | — |
| 332 | C23×C4 | #546 | 1 | 2 | yes | — |
| 333 | C23×C4 | #546 | 1 | 2 | yes | — |
| 334 | #117 | #386 | 1 | 2 | yes | — |
| 335 | #117 | #386 | 1 | 2 | yes | — |
| 336 | C2×C42 | #386 | 1 | 2 | yes | — |
| 337 | C2×C42 | #386 | 1 | 2 | yes | — |
| 338 | C24 | #2308 | 1 | 1 | yes | characteristic |
| 339 | C24 | #2358 | 1 | 2 | yes | — |
| 340 | C24 | #2403 | 1 | 2 | yes | — |
| 341 | C24 | #2410 | 1 | 2 | yes | — |
| 342 | C24 | #2410 | 1 | 2 | yes | — |
| 343 | C24 | #2410 | 1 | 1 | yes | characteristic |
| 344 | C24 | #2412 | 1 | 1 | yes | characteristic |
| 345 | C24 | #2424 | 1 | 2 | yes | — |
| 346 | C24 | #2424 | 1 | 2 | yes | — |
| 347 | C24 | #2433 | 1 | 2 | yes | — |
| 348 | C24 | #2617 | 1 | 2 | yes | — |
| 349 | C2×Q8 | #1438 | 1 | 4 | yes | — |
| 350 | C2×Q8 | C4×#120 | 1 | 2 | yes | — |
| 351 | C2×Q8 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 352 | C2×Q8 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 353 | C2×Q8 | #2405 | 1 | 2 | yes | — |
| 354 | C2×Q8 | #2411 | 1 | 2 | yes | — |
| 355 | C2×Q8 | #2418 | 1 | 2 | yes | — |
| 356 | C2×Q8 | #2472 | 1 | 2 | yes | — |
| 357 | C2×Q8 | #2534 | 1 | 2 | yes | — |
| 358 | C2×Q8 | #2849 | 1 | 1 | yes | characteristic |
| 359 | C2×Q8 | #2849 | 1 | 1 | yes | characteristic |
| 360 | C2×D4 | #1438 | 1 | 8 | yes | — |
| 361 | C2×D4 | #1438 | 1 | 4 | yes | — |
| 362 | C2×D4 | #1889 | 1 | 4 | yes | — |
| 363 | C2×D4 | #1889 | 1 | 4 | yes | — |
| 364 | C2×D4 | #2021 | 1 | 8 | yes | — |
| 365 | C2×D4 | #2021 | 1 | 8 | yes | — |
| 366 | C2×D4 | C4×#120 | 1 | 2 | yes | — |
| 367 | C2×D4 | #2321 | 1 | 2 | yes | — |
| 368 | C2×D4 | #2321 | 1 | 2 | yes | — |
| 369 | C2×D4 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 370 | C2×D4 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 371 | C2×D4 | D4×C22⋊C4 | 1 | 2 | yes | — |
| 372 | C2×D4 | D4×C22⋊C4 | 1 | 2 | yes | — |
| 373 | C2×D4 | #2403 | 1 | 2 | yes | — |
| 374 | C2×D4 | #2403 | 1 | 2 | yes | — |
| 375 | C2×D4 | #2405 | 1 | 2 | yes | — |
| 376 | C2×D4 | #2408 | 1 | 2 | yes | — |
| 377 | C2×D4 | #2408 | 1 | 2 | yes | — |
| 378 | C2×D4 | #2410 | 1 | 2 | yes | — |
| 379 | C2×D4 | #2410 | 1 | 2 | yes | — |
| 380 | C2×D4 | #2411 | 1 | 2 | yes | — |
| 381 | C2×D4 | #2418 | 1 | 2 | yes | — |
| 382 | C2×D4 | #2418 | 1 | 2 | yes | — |
| 383 | C2×D4 | #2418 | 1 | 2 | yes | — |
| 384 | C2×D4 | #2472 | 1 | 2 | yes | — |
| 385 | C2×D4 | #2472 | 1 | 2 | yes | — |
| 386 | C2×D4 | #2472 | 1 | 2 | yes | — |
| 387 | C2×D4 | #2534 | 1 | 2 | yes | — |
| 388 | C2×D4 | #2613 | 1 | 2 | yes | — |
| 389 | C2×D4 | #2622 | 1 | 2 | yes | — |
| 390 | C2×D4 | #2846 | 1 | 1 | yes | characteristic |
| 391 | C2×D4 | #2849 | 1 | 1 | yes | characteristic |
| 392 | C22×C4 | C2×#379 | 1 | 1 | yes | characteristic |
| 393 | C22×C4 | C2×#386 | 1 | 1 | yes | characteristic |
| 394 | C22×C4 | C2×#386 | 1 | 2 | yes | — |
| 395 | C22×C4 | C2×#386 | 1 | 1 | yes | characteristic |
| 396 | C22×C4 | C2×#386 | 1 | 1 | yes | characteristic |
| 397 | C22×C4 | C2×#386 | 1 | 1 | yes | characteristic |
| 398 | C22×C4 | C2×#390 | 1 | 2 | yes | — |
| 399 | C22×C4 | #2308 | 1 | 1 | yes | characteristic |
| 400 | C22×C4 | #2358 | 1 | 2 | yes | — |
| 401 | C22×C4 | #2358 | 1 | 2 | yes | — |
| 402 | C22×C4 | #2358 | 1 | 2 | yes | — |
| 403 | C22×C4 | C2×#392 | 1 | 2 | yes | — |
| 404 | C22×C4 | C2×#392 | 1 | 2 | yes | — |
| 405 | C22×C4 | C2×#394 | 1 | 2 | yes | — |
| 406 | C22×C4 | C2×#394 | 1 | 2 | yes | — |
| 407 | C22×C4 | #2403 | 1 | 2 | yes | — |
| 408 | C22×C4 | #2404 | 1 | 2 | yes | — |
| 409 | C22×C4 | #2404 | 1 | 2 | yes | — |
| 410 | C22×C4 | #2410 | 1 | 2 | yes | — |
| 411 | C22×C4 | #2410 | 1 | 2 | yes | — |
| 412 | C22×C4 | #2410 | 1 | 2 | yes | — |
| 413 | C22×C4 | #2410 | 1 | 2 | yes | — |
| 414 | C22×C4 | #2410 | 1 | 2 | yes | — |
| 415 | C22×C4 | #2410 | 1 | 1 | yes | characteristic |
| 416 | C22×C4 | #2412 | 1 | 2 | yes | — |
| 417 | C22×C4 | #2412 | 1 | 2 | yes | — |
| 418 | C22×C4 | #2412 | 1 | 2 | yes | — |
| 419 | C22×C4 | #2412 | 1 | 1 | yes | characteristic |
| 420 | C22×C4 | #2424 | 1 | 2 | yes | — |
| 421 | C22×C4 | #2424 | 1 | 2 | yes | — |
| 422 | C22×C4 | #2424 | 1 | 2 | yes | — |
| 423 | C22×C4 | #2424 | 1 | 2 | yes | — |
| 424 | C22×C4 | #2424 | 1 | 2 | yes | — |
| 425 | C22×C4 | #2424 | 1 | 2 | yes | — |
| 426 | C22×C4 | #2433 | 1 | 2 | yes | — |
| 427 | C22×C4 | #2539 | 1 | 2 | yes | — |
| 428 | C22×C4 | #2539 | 1 | 2 | yes | — |
| 429 | C22×C4 | #2617 | 1 | 2 | yes | — |
| 430 | C22×C4 | #2847 | 1 | 2 | yes | — |
| 431 | C22×C4 | #2847 | 1 | 2 | yes | — |
| 432 | C22×C4 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 433 | C22×C4 | C2×B(4,𝔽2) | 1 | 2 | yes | — |
| 434 | C22×C4 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 435 | C22×C4 | #3026 | 1 | 1 | yes | characteristic |
| 436 | C22×C4 | #3026 | 1 | 2 | yes | — |
| 437 | C22×C4 | #3026 | 1 | 1 | yes | characteristic |
| 438 | C23 | #13867 | 1 | 1 | yes | characteristic |
| 439 | C23 | #13967 | 1 | 2 | yes | — |
| 440 | C23 | #13995 | 1 | 2 | yes | — |
| 441 | C23 | #14134 | 1 | 1 | yes | characteristic |
| 442 | C23 | #14255 | 1 | 1 | yes | characteristic |
| 443 | C23 | #14715 | 1 | 2 | yes | — |
| 444 | C23 | #14716 | 1 | 2 | yes | — |
| 445 | C23 | #14718 | 1 | 2 | yes | — |
| 446 | C23 | #14725 | 1 | 2 | yes | — |
| 447 | C23 | #24404 | 1 | 1 | yes | characteristic |
| 448 | C23 | #24404 | 1 | 2 | yes | — |
| 449 | C23 | #24404 | 1 | 1 | yes | characteristic |
| 450 | D4 | #10991 | 1 | 8 | yes | — |
| 451 | C2×C4 | C2×#1438 | 1 | 1 | yes | characteristic |
| 452 | C2×C4 | #13867 | 1 | 1 | yes | characteristic |
| 453 | C2×C4 | #13967 | 1 | 2 | yes | — |
| 454 | C2×C4 | #13995 | 1 | 2 | yes | — |
| 455 | C2×C4 | #14134 | 1 | 1 | yes | characteristic |
| 456 | C2×C4 | #14694 | 1 | 1 | yes | characteristic |
| 457 | C2×C4 | #14716 | 1 | 2 | yes | — |
| 458 | C2×C4 | #14718 | 1 | 2 | yes | — |
| 459 | C2×C4 | #14725 | 1 | 2 | yes | — |
| 460 | C2×C4 | #14911 | 1 | 2 | yes | — |
| 461 | C2×C4 | C2×#1889 | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | C2×#1889 | 1 | 1 | yes | characteristic |
| 463 | C2×C4 | #20960 | 1 | 1 | yes | characteristic |
| 464 | C2×C4 | #20960 | 1 | 1 | yes | characteristic |
| 465 | C2×C4 | C2×#2021 | 1 | 2 | yes | — |
| 466 | C2×C4 | C2×#2021 | 1 | 2 | yes | — |
| 467 | C2×C4 | #23444 | 1 | 2 | yes | — |
| 468 | C2×C4 | #23444 | 1 | 2 | yes | — |
| 469 | C2×C4 | #24404 | 1 | 2 | yes | — |
| 470 | C2×C4 | #24404 | 1 | 2 | yes | — |
| 471 | C2×C4 | #24404 | 1 | 2 | yes | — |
| 472 | C2×C4 | #24404 | 1 | 2 | yes | — |
| 473 | C2×C4 | #24404 | 1 | 1 | yes | characteristic |
| 474 | C2×C4 | #24404 | 1 | 1 | yes | characteristic |
| 475 | C2×C4 | #24404 | 1 | 2 | yes | — |
| 476 | C22 | #154195 | 1 | 1 | yes | characteristic |
| 477 | C22 | #374038 | 1 | 1 | yes | characteristic |
| 478 | C22 | #374038 | 1 | 1 | yes | characteristic |
| 479 | C22 | #394267 | 1 | 2 | yes | — |
| 480 | C22 | #394267 | 1 | 2 | yes | — |
| 481 | C4 | C2×#10991 | 1 | 1 | yes | characteristic |
| 482 | C4 | #357530 | 1 | 1 | yes | characteristic |
| 483 | C4 | #374038 | 1 | 1 | yes | characteristic |
| 484 | C4 | #374038 | 1 | 1 | yes | characteristic |
| 485 | C4 | #394267 | 1 | 2 | yes | — |
| 486 | C4 | #394267 | 1 | 2 | yes | — |
| 487 | C2 | #72260770 | 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