Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
634 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #83310 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83297 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #79055 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#1492 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #69787 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #67711 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10254 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C3×#532 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#949 | — | 2 | 1 | no | — |
| 11 | C2×#908 | — | 2 | 1 | no | — |
| 12 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C4×D12 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#423 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 16 | #5232 | — | 2 | 1 | no | — |
| 17 | #5133 | — | 2 | 1 | no | — |
| 18 | C2×(C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 19 | #5087 | — | 2 | 1 | no | — |
| 20 | #5083 | — | 2 | 1 | no | — |
| 21 | #5072 | — | 2 | 1 | no | — |
| 22 | #5072 | — | 2 | 1 | no | — |
| 23 | #5057 | — | 2 | 2 | no | — |
| 24 | #5038 | — | 2 | 2 | no | — |
| 25 | #5015 | — | 2 | 1 | no | — |
| 26 | #5007 | — | 2 | 1 | no | — |
| 27 | #4924 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C4⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 29 | #4844 | — | 2 | 2 | no | — |
| 30 | #4843 | — | 2 | 1 | no | — |
| 31 | #4841 | — | 2 | 1 | no | — |
| 32 | C3×D4⋊C8 | — | 2 | 2 | no | — |
| 33 | #4459 | — | 2 | 2 | no | — |
| 34 | #3245 | — | 3 | 1 | no | — |
| 35 | #3036 | — | 3 | 1 | no | — |
| 36 | #3036 | — | 3 | 1 | no | — |
| 37 | #1954 | — | 3 | 1 | no | — |
| 38 | #1492 | — | 3 | 1 | no | — |
| 39 | #1492 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #1292 | — | 3 | 1 | no | — |
| 41 | C2×C3×#41 | — | 2 | 1 | no | — |
| 42 | C2×#235 | — | 2 | 1 | no | — |
| 43 | C22×D12 | D4 | 1 | 1 | yes | characteristic |
| 44 | C22×C4×D3 | — | 2 | 1 | no | — |
| 45 | C2×C3×M16 | — | 2 | 1 | no | — |
| 46 | C22×C3×C8 | — | 2 | 1 | no | — |
| 47 | C3×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 48 | C3×#127 | D4 | 1 | 1 | yes | characteristic |
| 49 | C3×#124 | — | 2 | 1 | no | — |
| 50 | C3×#121 | — | 2 | 1 | no | — |
| 51 | C3×#121 | — | 2 | 1 | no | — |
| 52 | C3×C4×D4 | — | 2 | 1 | no | — |
| 53 | C3×C4×D4 | — | 2 | 1 | no | — |
| 54 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 55 | #949 | — | 4 | 2 | no | — |
| 56 | #949 | — | 4 | 2 | no | — |
| 57 | C2×#215 | — | 2 | 2 | no | — |
| 58 | C2×#213 | — | 2 | 2 | no | — |
| 59 | C2×#213 | — | 2 | 2 | no | — |
| 60 | #930 | — | 2 | 1 | no | — |
| 61 | #930 | — | 2 | 1 | no | — |
| 62 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 63 | C2×C4⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×#208 | — | 2 | 1 | no | — |
| 65 | C22×C3⋊C8 | D4 | 1 | 2 | yes | — |
| 66 | #908 | — | 4 | 2 | no | — |
| 67 | #908 | — | 4 | 2 | no | — |
| 68 | C2×D24 | — | 2 | 2 | no | — |
| 69 | C2×#204 | — | 2 | 2 | no | — |
| 70 | #875 | — | 2 | 1 | no | — |
| 71 | #874 | D4 | 1 | 1 | yes | characteristic |
| 72 | C4×D12 | — | 2 | 1 | no | — |
| 73 | C4×D12 | — | 2 | 1 | no | — |
| 74 | C4×D12 | — | 2 | 1 | no | — |
| 75 | C4×D12 | — | 2 | 1 | no | — |
| 76 | C4×D12 | — | 2 | 1 | no | — |
| 77 | C4×D12 | — | 2 | 1 | no | — |
| 78 | #869 | D4 | 1 | 1 | yes | characteristic |
| 79 | C3×C4⋊C8 | — | 2 | 1 | no | — |
| 80 | C3×C4⋊C8 | D4 | 1 | 2 | yes | — |
| 81 | C3×C4×C8 | — | 2 | 1 | no | — |
| 82 | C3×C4×C8 | — | 2 | 1 | no | — |
| 83 | #835 | — | 2 | 2 | no | — |
| 84 | #832 | — | 2 | 2 | no | — |
| 85 | #832 | — | 2 | 2 | no | — |
| 86 | #821 | — | 2 | 2 | no | — |
| 87 | (C2×D3)⋊C8 | — | 4 | 4 | no | — |
| 88 | #816 | — | 2 | 2 | no | — |
| 89 | #809 | — | 2 | 2 | no | — |
| 90 | #807 | — | 2 | 2 | no | — |
| 91 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 92 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 93 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 94 | C4⋊(C3⋊C8) | D4 | 1 | 2 | yes | — |
| 95 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 96 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 97 | #532 | — | 3 | 1 | no | — |
| 98 | #532 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | C2×C4×D4 | — | 3 | 1 | no | — |
| 100 | #474 | — | 6 | 1 | no | — |
| 101 | #474 | — | 6 | 1 | no | — |
| 102 | #466 | — | 6 | 2 | no | — |
| 103 | #463 | — | 6 | 2 | no | — |
| 104 | #463 | — | 6 | 2 | no | — |
| 105 | #461 | — | 6 | 1 | no | — |
| 106 | #461 | — | 6 | 1 | no | — |
| 107 | #459 | — | 6 | 1 | no | — |
| 108 | #459 | — | 6 | 1 | no | — |
| 109 | #459 | — | 6 | 1 | no | — |
| 110 | #459 | — | 6 | 1 | no | — |
| 111 | #423 | — | 3 | 1 | no | — |
| 112 | #423 | C2×D3 | 1 | 1 | yes | characteristic |
| 113 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 114 | #417 | — | 6 | 1 | no | — |
| 115 | #417 | — | 6 | 1 | no | — |
| 116 | C2×C22⋊C8 | — | 6 | 2 | no | — |
| 117 | C2×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 118 | D4⋊C8 | — | 2 | 2 | no | — |
| 119 | D4⋊C8 | — | 6 | 2 | no | — |
| 120 | C23×D3 | — | 2 | 1 | no | — |
| 121 | C3×#41 | — | 4 | 1 | no | — |
| 122 | C3×#41 | — | 4 | 1 | no | — |
| 123 | C3×#41 | — | 4 | 1 | no | — |
| 124 | C3×#41 | — | 4 | 1 | no | — |
| 125 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 126 | C2×C3×D4 | — | 2 | 1 | no | — |
| 127 | C2×C3×D4 | — | 2 | 1 | no | — |
| 128 | C2×C3×D4 | — | 2 | 1 | no | — |
| 129 | C2×C3×D4 | — | 4 | 1 | no | — |
| 130 | C22×C3×C4 | — | 4 | 1 | no | — |
| 131 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic |
| 134 | C2×#67 | — | 4 | 1 | no | — |
| 135 | C22×Dic3 | — | 2 | 1 | no | — |
| 136 | #235 | — | 4 | 1 | no | — |
| 137 | #235 | — | 4 | 1 | no | — |
| 138 | #235 | — | 4 | 1 | no | — |
| 139 | #235 | — | 4 | 1 | no | — |
| 140 | C2×D12 | — | 2 | 1 | no | — |
| 141 | C2×D12 | — | 2 | 1 | no | — |
| 142 | C2×D12 | — | 2 | 1 | no | — |
| 143 | C2×D12 | — | 2 | 1 | no | — |
| 144 | C2×D12 | — | 2 | 1 | no | — |
| 145 | C2×D12 | — | 2 | 1 | no | — |
| 146 | C2×D12 | — | 2 | 1 | no | — |
| 147 | C2×D12 | — | 2 | 1 | no | — |
| 148 | C2×D12 | D8 | 1 | 2 | yes | complemented |
| 149 | C2×C4×D3 | — | 4 | 2 | no | — |
| 150 | C2×C4×D3 | — | 4 | 2 | no | — |
| 151 | C2×C4×D3 | — | 4 | 1 | no | — |
| 152 | C2×C4×D3 | — | 4 | 1 | no | — |
| 153 | C2×C4×D3 | — | 4 | 1 | no | — |
| 154 | C2×Dic6 | — | 2 | 1 | no | — |
| 155 | C3×M16 | — | 4 | 1 | no | — |
| 156 | C3×M16 | — | 4 | 1 | no | — |
| 157 | C2×C3×C8 | — | 2 | 2 | no | — |
| 158 | C2×C3×C8 | — | 2 | 2 | no | — |
| 159 | C2×C3×C8 | — | 4 | 1 | no | — |
| 160 | C2×C3×C8 | — | 4 | 1 | no | — |
| 161 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 162 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 163 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 164 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 165 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | #215 | — | 4 | 4 | no | — |
| 170 | #213 | — | 4 | 4 | no | — |
| 171 | #213 | — | 8 | 2 | no | — |
| 172 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 173 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 174 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 175 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 176 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 177 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 178 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 179 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 180 | #208 | — | 4 | 1 | no | — |
| 181 | #208 | — | 4 | 1 | no | — |
| 182 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 183 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 184 | C2×C3⋊C8 | — | 4 | 2 | no | — |
| 185 | D24 | — | 4 | 4 | no | — |
| 186 | #204 | — | 4 | 4 | no | — |
| 187 | C2×#41 | — | 2 | 1 | no | — |
| 188 | C2×#41 | — | 6 | 1 | no | — |
| 189 | C22×D4 | — | 3 | 1 | no | — |
| 190 | C23×C4 | — | 6 | 1 | no | — |
| 191 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 192 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 193 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 194 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 195 | C2×SD16 | — | 6 | 2 | no | — |
| 196 | C2×SD16 | — | 6 | 2 | no | — |
| 197 | C2×D8 | — | 6 | 2 | no | — |
| 198 | C2×D8 | — | 6 | 2 | no | — |
| 199 | C2×D8 | — | 6 | 2 | no | — |
| 200 | C2×M16 | — | 2 | 1 | no | — |
| 201 | C2×M16 | — | 6 | 1 | no | — |
| 202 | C22×C8 | — | 2 | 1 | no | — |
| 203 | C22×C8 | — | 3 | 2 | no | — |
| 204 | C4⋊Q8 | — | 3 | 1 | no | — |
| 205 | C4⋊Q8 | D12 | 1 | 1 | yes | characteristic |
| 206 | #127 | — | 3 | 1 | no | — |
| 207 | #127 | D12 | 1 | 1 | yes | characteristic |
| 208 | #124 | — | 2 | 1 | no | — |
| 209 | #124 | — | 6 | 1 | no | — |
| 210 | #121 | — | 2 | 1 | no | — |
| 211 | #121 | — | 2 | 1 | no | — |
| 212 | #121 | — | 6 | 1 | no | — |
| 213 | #121 | — | 6 | 1 | no | — |
| 214 | C4×D4 | — | 2 | 1 | no | — |
| 215 | C4×D4 | — | 2 | 1 | no | — |
| 216 | C4×D4 | — | 6 | 1 | no | — |
| 217 | C4×D4 | — | 6 | 1 | no | — |
| 218 | C4×D4 | — | 6 | 1 | no | — |
| 219 | C4×D4 | — | 6 | 1 | no | — |
| 220 | C4×D4 | — | 6 | 1 | no | — |
| 221 | C4×D4 | — | 6 | 1 | no | — |
| 222 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 223 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 224 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 225 | #107 | — | 6 | 2 | no | — |
| 226 | C4⋊C8 | — | 2 | 1 | no | — |
| 227 | C4⋊C8 | — | 3 | 2 | no | — |
| 228 | C4⋊C8 | — | 6 | 1 | no | — |
| 229 | C4⋊C8 | — | 6 | 1 | no | — |
| 230 | C4⋊C8 | — | 6 | 1 | no | — |
| 231 | C4⋊C8 | #67 | 1 | 2 | yes | — |
| 232 | #103 | — | 6 | 2 | no | — |
| 233 | #103 | — | 6 | 2 | no | — |
| 234 | #102 | — | 6 | 2 | no | — |
| 235 | #102 | — | 6 | 2 | no | — |
| 236 | #102 | — | 6 | 2 | no | — |
| 237 | #102 | — | 6 | 2 | no | — |
| 238 | C22⋊C8 | — | 12 | 4 | no | — |
| 239 | C4×C8 | — | 2 | 1 | no | — |
| 240 | C4×C8 | — | 2 | 1 | no | — |
| 241 | C23×C3 | — | 4 | 1 | no | — |
| 242 | C23×C3 | #121 | 1 | 1 | yes | characteristic |
| 243 | C22×D3 | — | 2 | 2 | no | — |
| 244 | C22×D3 | — | 4 | 2 | no | — |
| 245 | C22×D3 | — | 4 | 2 | no | — |
| 246 | C22×D3 | — | 4 | 1 | no | — |
| 247 | C22×D3 | — | 4 | 1 | no | — |
| 248 | C22×D3 | — | 4 | 1 | no | — |
| 249 | C3×Q8 | — | 4 | 1 | no | — |
| 250 | C3×Q8 | — | 4 | 1 | no | — |
| 251 | C3×D4 | — | 4 | 2 | no | — |
| 252 | C3×D4 | — | 4 | 1 | no | — |
| 253 | C3×D4 | — | 4 | 1 | no | — |
| 254 | C3×D4 | — | 4 | 1 | no | — |
| 255 | C3×D4 | — | 4 | 1 | no | — |
| 256 | C3×D4 | — | 8 | 1 | no | — |
| 257 | C3×D4 | — | 8 | 1 | no | — |
| 258 | C2×C3×C4 | — | 2 | 1 | no | — |
| 259 | C2×C3×C4 | — | 2 | 1 | no | — |
| 260 | C2×C3×C4 | — | 4 | 1 | no | — |
| 261 | C2×C3×C4 | — | 4 | 1 | no | — |
| 262 | C2×C3×C4 | — | 8 | 1 | no | — |
| 263 | C2×C3×C4 | — | 8 | 1 | no | — |
| 264 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 265 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 266 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 267 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 268 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 269 | C2×C3×C4 | #127 | 1 | 1 | yes | characteristic |
| 270 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 271 | C2×C3×C4 | #135 | 1 | 1 | yes | characteristic |
| 272 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 273 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 274 | #67 | — | 8 | 1 | no | — |
| 275 | #67 | — | 8 | 1 | no | — |
| 276 | C2×Dic3 | — | 4 | 2 | no | — |
| 277 | C2×Dic3 | — | 4 | 1 | no | — |
| 278 | C2×Dic3 | — | 4 | 1 | no | — |
| 279 | D12 | — | 2 | 2 | no | — |
| 280 | D12 | — | 2 | 2 | no | — |
| 281 | D12 | — | 4 | 2 | no | — |
| 282 | D12 | — | 4 | 1 | no | — |
| 283 | D12 | — | 4 | 1 | no | — |
| 284 | D12 | — | 4 | 1 | no | — |
| 285 | D12 | — | 4 | 1 | no | — |
| 286 | D12 | — | 4 | 1 | no | — |
| 287 | D12 | — | 4 | 1 | no | — |
| 288 | C4×D3 | — | 8 | 2 | no | — |
| 289 | C4×D3 | — | 8 | 1 | no | — |
| 290 | C4×D3 | — | 8 | 1 | no | — |
| 291 | C4×D3 | — | 8 | 1 | no | — |
| 292 | C4×D3 | — | 8 | 1 | no | — |
| 293 | Dic6 | — | 4 | 1 | no | — |
| 294 | Dic6 | — | 4 | 1 | no | — |
| 295 | C3×C8 | — | 4 | 2 | no | — |
| 296 | C3×C8 | — | 4 | 2 | no | — |
| 297 | C3⋊C8 | — | 4 | 2 | no | — |
| 298 | C3⋊C8 | — | 4 | 2 | no | — |
| 299 | C24 | — | 6 | 1 | no | — |
| 300 | #41 | — | 4 | 1 | no | — |
| 301 | #41 | — | 4 | 1 | no | — |
| 302 | #41 | — | 4 | 1 | no | — |
| 303 | #41 | — | 4 | 1 | no | — |
| 304 | #41 | — | 12 | 1 | no | — |
| 305 | #41 | — | 12 | 1 | no | — |
| 306 | #41 | — | 12 | 1 | no | — |
| 307 | #41 | — | 12 | 1 | no | — |
| 308 | C2×Q8 | — | 2 | 1 | no | — |
| 309 | C2×Q8 | — | 6 | 1 | no | — |
| 310 | C2×D4 | — | 2 | 1 | no | — |
| 311 | C2×D4 | — | 2 | 1 | no | — |
| 312 | C2×D4 | — | 2 | 1 | no | — |
| 313 | C2×D4 | — | 3 | 2 | no | — |
| 314 | C2×D4 | — | 4 | 1 | no | — |
| 315 | C2×D4 | — | 6 | 1 | no | — |
| 316 | C2×D4 | — | 6 | 1 | no | — |
| 317 | C2×D4 | — | 6 | 1 | no | — |
| 318 | C2×D4 | — | 6 | 1 | no | — |
| 319 | C2×D4 | — | 6 | 1 | no | — |
| 320 | C2×D4 | — | 6 | 1 | no | — |
| 321 | C2×D4 | — | 6 | 1 | no | — |
| 322 | C2×D4 | — | 6 | 1 | no | — |
| 323 | C2×D4 | — | 12 | 1 | no | — |
| 324 | C22×C4 | — | 4 | 1 | no | — |
| 325 | C22×C4 | — | 6 | 1 | no | — |
| 326 | C22×C4 | — | 12 | 2 | no | — |
| 327 | C22×C4 | — | 12 | 2 | no | — |
| 328 | C22×C4 | — | 12 | 1 | no | — |
| 329 | C22×C4 | — | 12 | 1 | no | — |
| 330 | C22×C4 | — | 12 | 1 | no | — |
| 331 | C22×C4 | #235 | 1 | 1 | yes | characteristic |
| 332 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 333 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 334 | SD16 | — | 12 | 4 | no | — |
| 335 | SD16 | — | 12 | 4 | no | — |
| 336 | D8 | — | 12 | 4 | no | — |
| 337 | D8 | — | 12 | 4 | no | — |
| 338 | D8 | — | 24 | 2 | no | — |
| 339 | M16 | — | 4 | 1 | no | — |
| 340 | M16 | — | 4 | 1 | no | — |
| 341 | M16 | — | 12 | 1 | no | — |
| 342 | M16 | — | 12 | 1 | no | — |
| 343 | C2×C8 | — | 2 | 2 | no | — |
| 344 | C2×C8 | — | 2 | 2 | no | — |
| 345 | C2×C8 | — | 4 | 1 | no | — |
| 346 | C2×C8 | — | 4 | 1 | no | — |
| 347 | C2×C8 | — | 6 | 2 | no | — |
| 348 | C2×C8 | — | 6 | 2 | no | — |
| 349 | C2×C8 | — | 12 | 2 | no | — |
| 350 | C4⋊C4 | — | 2 | 1 | no | — |
| 351 | C4⋊C4 | — | 2 | 1 | no | — |
| 352 | C4⋊C4 | — | 6 | 1 | no | — |
| 353 | C4⋊C4 | — | 6 | 1 | no | — |
| 354 | C4⋊C4 | — | 6 | 1 | no | — |
| 355 | C4⋊C4 | — | 6 | 1 | no | — |
| 356 | C22⋊C4 | — | 4 | 1 | no | — |
| 357 | C22⋊C4 | — | 4 | 1 | no | — |
| 358 | C22⋊C4 | — | 12 | 1 | no | — |
| 359 | C22⋊C4 | — | 12 | 1 | no | — |
| 360 | C22⋊C4 | — | 12 | 1 | no | — |
| 361 | C22⋊C4 | — | 12 | 1 | no | — |
| 362 | C42 | C2×D12 | 1 | 1 | yes | characteristic |
| 363 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 364 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 365 | C42 | C2×#67 | 1 | 1 | yes | characteristic |
| 366 | C22×C3 | — | 2 | 1 | no | — |
| 367 | C22×C3 | — | 2 | 1 | no | — |
| 368 | C22×C3 | — | 8 | 1 | no | — |
| 369 | C22×C3 | — | 8 | 1 | no | — |
| 370 | C22×C3 | — | 8 | 1 | no | — |
| 371 | C22×C3 | #392 | 1 | 1 | yes | characteristic |
| 372 | C22×C3 | #466 | 1 | 1 | yes | characteristic |
| 373 | C22×C3 | #469 | 1 | 1 | yes | characteristic |
| 374 | C2×D3 | — | 4 | 4 | no | — |
| 375 | C2×D3 | — | 4 | 2 | no | — |
| 376 | C2×D3 | — | 8 | 2 | no | — |
| 377 | C2×D3 | — | 8 | 1 | no | — |
| 378 | C2×D3 | — | 8 | 1 | no | — |
| 379 | C2×D3 | — | 8 | 1 | no | — |
| 380 | C2×D3 | — | 8 | 1 | no | — |
| 381 | C2×D3 | — | 8 | 1 | no | — |
| 382 | C3×C4 | — | 2 | 1 | no | — |
| 383 | C3×C4 | — | 2 | 1 | no | — |
| 384 | C3×C4 | — | 2 | 1 | no | — |
| 385 | C3×C4 | — | 8 | 1 | no | — |
| 386 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 387 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 388 | C3×C4 | #449 | 1 | 1 | yes | characteristic |
| 389 | C3×C4 | #449 | 1 | 1 | yes | characteristic |
| 390 | C3×C4 | #453 | 1 | 1 | yes | characteristic |
| 391 | C3×C4 | #454 | 1 | 1 | yes | characteristic |
| 392 | Dic3 | — | 8 | 1 | no | — |
| 393 | Dic3 | — | 8 | 1 | no | — |
| 394 | C23 | — | 4 | 1 | no | — |
| 395 | C23 | — | 6 | 2 | no | — |
| 396 | C23 | — | 12 | 2 | no | — |
| 397 | C23 | — | 12 | 2 | no | — |
| 398 | C23 | — | 12 | 1 | no | — |
| 399 | C23 | — | 12 | 1 | no | — |
| 400 | C23 | — | 12 | 1 | no | — |
| 401 | C23 | #884 | 1 | 1 | yes | characteristic |
| 402 | Q8 | — | 4 | 1 | no | — |
| 403 | Q8 | — | 4 | 1 | no | — |
| 404 | Q8 | — | 12 | 1 | no | — |
| 405 | Q8 | — | 12 | 1 | no | — |
| 406 | D4 | — | 4 | 2 | no | — |
| 407 | D4 | — | 4 | 1 | no | — |
| 408 | D4 | — | 4 | 1 | no | — |
| 409 | D4 | — | 4 | 1 | no | — |
| 410 | D4 | — | 4 | 1 | no | — |
| 411 | D4 | — | 6 | 2 | no | — |
| 412 | D4 | — | 6 | 2 | no | — |
| 413 | D4 | — | 8 | 1 | no | — |
| 414 | D4 | — | 8 | 1 | no | — |
| 415 | D4 | — | 12 | 2 | no | — |
| 416 | D4 | — | 12 | 1 | no | — |
| 417 | D4 | — | 12 | 1 | no | — |
| 418 | D4 | — | 12 | 1 | no | — |
| 419 | D4 | — | 12 | 1 | no | — |
| 420 | D4 | — | 12 | 1 | no | — |
| 421 | D4 | — | 12 | 1 | no | — |
| 422 | D4 | — | 24 | 1 | no | — |
| 423 | D4 | — | 24 | 1 | no | — |
| 424 | C2×C4 | — | 2 | 1 | no | — |
| 425 | C2×C4 | — | 2 | 1 | no | — |
| 426 | C2×C4 | — | 4 | 1 | no | — |
| 427 | C2×C4 | — | 4 | 1 | no | — |
| 428 | C2×C4 | — | 8 | 1 | no | — |
| 429 | C2×C4 | — | 8 | 1 | no | — |
| 430 | C2×C4 | — | 12 | 2 | no | — |
| 431 | C2×C4 | — | 12 | 1 | no | — |
| 432 | C2×C4 | — | 12 | 1 | no | — |
| 433 | C2×C4 | — | 24 | 2 | no | — |
| 434 | C2×C4 | — | 24 | 1 | no | — |
| 435 | C2×C4 | — | 24 | 1 | no | — |
| 436 | C2×C4 | — | 24 | 1 | no | — |
| 437 | C2×C4 | — | 24 | 1 | no | — |
| 438 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 439 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 440 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 441 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 442 | C2×C4 | #911 | 1 | 1 | yes | characteristic |
| 443 | C2×C4 | #914 | 1 | 1 | yes | characteristic |
| 444 | C2×C4 | #916 | 1 | 1 | yes | characteristic |
| 445 | C2×C4 | #930 | 1 | 1 | yes | characteristic |
| 446 | C2×C4 | #937 | 1 | 1 | yes | characteristic |
| 447 | C2×C4 | #940 | 1 | 1 | yes | characteristic |
| 448 | C8 | — | 4 | 2 | no | — |
| 449 | C8 | — | 4 | 2 | no | — |
| 450 | C8 | — | 12 | 2 | no | — |
| 451 | C8 | — | 12 | 2 | no | — |
| 452 | C2×C3 | — | 2 | 1 | no | — |
| 453 | C2×C3 | — | 2 | 1 | no | — |
| 454 | C2×C3 | — | 16 | 1 | no | — |
| 455 | C2×C3 | #1999 | 1 | 1 | yes | characteristic |
| 456 | C2×C3 | #2006 | 1 | 1 | yes | characteristic |
| 457 | C2×C3 | #2017 | 1 | 1 | yes | characteristic |
| 458 | D3 | — | 8 | 2 | no | — |
| 459 | D3 | — | 16 | 1 | no | — |
| 460 | C22 | — | 2 | 1 | no | — |
| 461 | C22 | — | 2 | 1 | no | — |
| 462 | C22 | — | 8 | 1 | no | — |
| 463 | C22 | — | 8 | 1 | no | — |
| 464 | C22 | — | 8 | 1 | no | — |
| 465 | C22 | — | 12 | 4 | no | — |
| 466 | C22 | — | 12 | 2 | no | — |
| 467 | C22 | — | 24 | 2 | no | — |
| 468 | C22 | — | 24 | 1 | no | — |
| 469 | C22 | — | 24 | 1 | no | — |
| 470 | C22 | — | 24 | 1 | no | — |
| 471 | C22 | — | 24 | 1 | no | — |
| 472 | C22 | — | 24 | 1 | no | — |
| 473 | C22 | #4775 | 1 | 1 | yes | characteristic |
| 474 | C22 | #4782 | 1 | 1 | yes | characteristic |
| 475 | C22 | #4960 | 1 | 1 | yes | characteristic |
| 476 | C4 | — | 2 | 1 | no | — |
| 477 | C4 | — | 2 | 1 | no | — |
| 478 | C4 | — | 2 | 1 | no | — |
| 479 | C4 | — | 8 | 1 | no | — |
| 480 | C4 | — | 24 | 1 | no | — |
| 481 | C4 | — | 24 | 1 | no | — |
| 482 | C4 | #4773 | 1 | 1 | yes | characteristic |
| 483 | C4 | #4781 | 1 | 1 | yes | characteristic |
| 484 | C4 | #4822 | 1 | 1 | yes | characteristic |
| 485 | C4 | #4827 | 1 | 1 | yes | characteristic |
| 486 | C4 | #5156 | 1 | 1 | yes | characteristic |
| 487 | C4 | #5172 | 1 | 1 | yes | characteristic |
| 488 | C3 | #10254 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 489 | C2 | — | 2 | 1 | no | — |
| 490 | C2 | — | 2 | 1 | no | — |
| 491 | C2 | — | 16 | 1 | no | — |
| 492 | C2 | — | 24 | 2 | no | — |
| 493 | C2 | — | 48 | 1 | no | — |
| 494 | C2 | #70013 | 1 | 1 | yes | characteristic |
| 495 | C2 | #70204 | 1 | 1 | yes | characteristic |
| 496 | C2 | #70392 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #83310 | C2 | semidirect |
| 2. #83297 | C2 | semidirect |
| 3. #79055 | C2 | semidirect |
| 4. C3×#1492 | C2 | semidirect |
| 5. #69787 | C2 | semidirect |
| 6. #69735 | C2 | semidirect |
| 7. #67711 | C2 | semidirect |
| 39. #1492 | D3 | semidirect |
| 148. C2×D12 | D8 | semidirect |
| 488. C3 | #10254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83310 | 2 |
| #83297 | 2 |
| #79055 | 2 |
| C3×#1492 | 2 |
| #69787 | 2 |
| #69735 | 2 |
| #67711 | 2 |
| #10254 | 3 |