Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1967 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 1967 conjugacy classes of subgroups — too many to draw. Only its 125 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 | C2×#5914 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D4×S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×#127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85496 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #85495 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #85493 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #85492 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #85287 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #37674 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C23×S4 | C22 | 1 | 2 | yes | — |
| 12 | C2×D4×A4 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×D4×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×D4×A4 | C22 | 1 | 4 | yes | complemented |
| 15 | C2×GL(2,ℤ/4) | C22 | 1 | 2 | yes | — |
| 16 | C2×GL(2,ℤ/4) | C22 | 1 | 2 | yes | — |
| 17 | C2×GL(2,ℤ/4) | C22 | 1 | 4 | yes | complemented |
| 18 | C22×SL(2,ℤ/4) | C22 | 1 | 2 | yes | complemented |
| 19 | #5914 | — | 2 | 4 | no | — |
| 20 | D4×S4 | — | 2 | 4 | no | — |
| 21 | C2×C4⋊S4 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C4×S4 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×A4⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #5715 | — | 4 | 1 | no | maximal |
| 25 | C42×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #5432 | C22 | 1 | 4 | yes | complemented |
| 27 | (C2×S4)⋊C4 | C22 | 1 | 2 | yes | — |
| 28 | (C2×S4)⋊C4 | C22 | 1 | 4 | yes | complemented |
| 29 | SL(2,ℤ/4)⋊C4 | C22 | 1 | 2 | yes | complemented |
| 30 | C4×SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C2×#546 | — | 3 | 1 | no | — |
| 32 | C2×D42 | — | 3 | 1 | no | — |
| 33 | C2×#535 | — | 3 | 1 | no | — |
| 34 | C22×#127 | D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | #2850 | — | 3 | 1 | no | — |
| 36 | #2673 | — | 3 | 4 | no | — |
| 37 | #2669 | — | 3 | 4 | no | — |
| 38 | #2657 | — | 3 | 1 | no | — |
| 39 | #2619 | — | 3 | 1 | no | — |
| 40 | #2544 | — | 3 | 1 | no | — |
| 41 | #2541 | — | 3 | 1 | no | — |
| 42 | #2435 | — | 3 | 1 | no | — |
| 43 | #2433 | — | 3 | 1 | no | — |
| 44 | #2433 | — | 3 | 1 | no | — |
| 45 | #2431 | — | 3 | 1 | no | — |
| 46 | #2410 | — | 3 | 4 | no | — |
| 47 | #2403 | — | 3 | 4 | no | — |
| 48 | #2328 | — | 3 | 1 | no | — |
| 49 | #2290 | — | 3 | 1 | no | — |
| 50 | C23×A4 | C23 | 1 | 2 | yes | — |
| 51 | C23×A4 | C23 | 1 | 2 | yes | — |
| 52 | C22×S4 | — | 2 | 4 | no | — |
| 53 | C22×S4 | — | 4 | 4 | no | — |
| 54 | C22×S4 | C23 | 1 | 2 | yes | — |
| 55 | C22×S4 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#237 | — | 4 | 1 | no | — |
| 57 | C2×D3×D4 | — | 4 | 1 | no | — |
| 58 | D4×A4 | — | 2 | 2 | no | — |
| 59 | D4×A4 | — | 2 | 2 | no | — |
| 60 | D4×A4 | — | 4 | 4 | no | — |
| 61 | C2×C4×A4 | C23 | 1 | 2 | yes | — |
| 62 | C2×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 63 | GL(2,ℤ/4) | — | 2 | 4 | no | — |
| 64 | GL(2,ℤ/4) | — | 2 | 4 | no | — |
| 65 | GL(2,ℤ/4) | — | 4 | 4 | no | — |
| 66 | C2×SL(2,ℤ/4) | — | 2 | 4 | no | — |
| 67 | C2×SL(2,ℤ/4) | C23 | 1 | 2 | yes | — |
| 68 | C2×SL(2,ℤ/4) | C23 | 1 | 2 | yes | — |
| 69 | C2×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 70 | C4⋊S4 | — | 2 | 2 | no | — |
| 71 | C4×S4 | D4 | 1 | 4 | yes | complemented |
| 72 | A4⋊Q8 | — | 2 | 2 | no | — |
| 73 | C3×#127 | — | 4 | 1 | no | — |
| 74 | #940 | — | 4 | 1 | no | — |
| 75 | #939 | — | 4 | 4 | no | — |
| 76 | #937 | — | 4 | 4 | no | — |
| 77 | #936 | — | 4 | 1 | no | — |
| 78 | #875 | — | 4 | 1 | no | — |
| 79 | #872 | — | 4 | 1 | no | — |
| 80 | C22×#41 | — | 3 | 1 | no | — |
| 81 | C23×D4 | — | 3 | 1 | no | — |
| 82 | C23×D4 | — | 3 | 2 | no | — |
| 83 | C23×D4 | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | C23×D4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 85 | C23×D4 | C2×D3 | 1 | 4 | yes | complemented |
| 86 | #546 | — | 6 | 4 | no | — |
| 87 | #546 | — | 6 | 4 | no | — |
| 88 | D42 | — | 6 | 4 | no | — |
| 89 | D42 | — | 6 | 4 | no | — |
| 90 | #535 | — | 6 | 1 | no | — |
| 91 | #535 | — | 6 | 1 | no | — |
| 92 | #535 | — | 6 | 4 | no | — |
| 93 | #535 | — | 6 | 1 | no | — |
| 94 | #535 | — | 6 | 1 | no | — |
| 95 | C2×#127 | — | 3 | 1 | no | — |
| 96 | C2×#127 | — | 3 | 1 | no | — |
| 97 | C2×#127 | — | 3 | 4 | no | — |
| 98 | C2×#127 | — | 3 | 1 | no | — |
| 99 | C2×#127 | — | 3 | 1 | no | — |
| 100 | C2×#127 | — | 3 | 1 | no | — |
| 101 | C2×#127 | — | 3 | 1 | no | — |
| 102 | C2×#127 | — | 3 | 1 | no | — |
| 103 | C2×#124 | — | 3 | 1 | no | — |
| 104 | C2×#124 | — | 3 | 1 | no | — |
| 105 | C2×#124 | — | 3 | 1 | no | — |
| 106 | C2×#124 | — | 3 | 1 | no | — |
| 107 | C2×#123 | — | 3 | 2 | no | — |
| 108 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 109 | C2×#121 | — | 3 | 1 | no | — |
| 110 | C2×#121 | — | 3 | 1 | no | — |
| 111 | C2×#121 | — | 3 | 4 | no | — |
| 112 | C2×#121 | — | 3 | 2 | no | — |
| 113 | C2×#121 | — | 3 | 2 | no | — |
| 114 | C2×#121 | — | 3 | 1 | no | — |
| 115 | C2×#121 | — | 3 | 4 | no | — |
| 116 | C2×#120 | — | 3 | 4 | no | — |
| 117 | C2×#120 | — | 3 | 2 | no | — |
| 118 | C2×#120 | — | 3 | 2 | no | — |
| 119 | C2×#120 | — | 3 | 2 | no | — |
| 120 | C2×#120 | — | 3 | 4 | no | — |
| 121 | C2×#120 | — | 3 | 4 | no | — |
| 122 | C2×C4×D4 | — | 3 | 1 | no | — |
| 123 | C2×C4×D4 | — | 3 | 1 | no | — |
| 124 | C2×C4×D4 | — | 3 | 1 | no | — |
| 125 | C2×#117 | — | 3 | 1 | no | — |
| 126 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 127 | C22×C42 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 128 | #394 | — | 3 | 4 | no | — |
| 129 | #394 | — | 3 | 4 | no | — |
| 130 | #394 | — | 3 | 4 | no | — |
| 131 | #392 | — | 3 | 4 | no | — |
| 132 | #392 | — | 3 | 4 | no | — |
| 133 | #392 | — | 3 | 4 | no | — |
| 134 | #392 | — | 3 | 4 | no | — |
| 135 | #392 | — | 3 | 4 | no | — |
| 136 | #392 | — | 3 | 4 | no | — |
| 137 | #392 | — | 3 | 4 | no | — |
| 138 | #391 | — | 3 | 1 | no | — |
| 139 | #390 | — | 3 | 1 | no | — |
| 140 | #390 | — | 3 | 1 | no | — |
| 141 | #390 | — | 3 | 1 | no | — |
| 142 | #390 | — | 3 | 1 | no | — |
| 143 | #390 | — | 3 | 1 | no | — |
| 144 | #388 | — | 3 | 4 | no | — |
| 145 | #388 | — | 3 | 2 | no | — |
| 146 | #387 | — | 3 | 2 | no | — |
| 147 | #386 | — | 3 | 4 | no | — |
| 148 | #386 | — | 3 | 4 | no | — |
| 149 | #386 | — | 3 | 4 | no | — |
| 150 | #386 | — | 3 | 4 | no | — |
| 151 | #386 | — | 3 | 4 | no | — |
| 152 | #386 | — | 3 | 2 | no | — |
| 153 | #385 | — | 3 | 2 | no | — |
| 154 | #382 | — | 3 | 1 | no | — |
| 155 | #379 | — | 3 | 4 | no | — |
| 156 | C4×C4⋊C4 | — | 3 | 1 | no | — |
| 157 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 158 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 159 | #376 | — | 3 | 1 | no | — |
| 160 | C23×D3 | — | 4 | 2 | no | — |
| 161 | C22×A4 | — | 2 | 2 | no | — |
| 162 | C22×A4 | — | 2 | 2 | no | — |
| 163 | C22×A4 | — | 2 | 4 | no | — |
| 164 | C22×A4 | — | 2 | 4 | no | — |
| 165 | C22×A4 | C24 | 1 | 1 | yes | characteristic |
| 166 | C2×S4 | — | 2 | 2 | no | — |
| 167 | C2×S4 | — | 2 | 2 | no | — |
| 168 | C2×S4 | — | 2 | 4 | no | — |
| 169 | C2×S4 | — | 4 | 8 | no | — |
| 170 | C2×S4 | C2×D4 | 1 | 2 | yes | — |
| 171 | C2×C3×D4 | — | 4 | 1 | no | — |
| 172 | C2×C3×D4 | — | 4 | 1 | no | — |
| 173 | C2×C3×D4 | — | 4 | 4 | no | — |
| 174 | C2×#67 | — | 4 | 2 | no | — |
| 175 | C2×#67 | — | 4 | 2 | no | — |
| 176 | C2×#67 | — | 4 | 4 | no | — |
| 177 | C22×Dic3 | — | 4 | 2 | no | — |
| 178 | #237 | — | 8 | 4 | no | — |
| 179 | D3×D4 | — | 8 | 4 | no | — |
| 180 | C2×D12 | — | 4 | 1 | no | — |
| 181 | C2×C4×D3 | — | 4 | 1 | no | — |
| 182 | C2×Dic6 | — | 4 | 1 | no | — |
| 183 | C4×A4 | — | 2 | 2 | no | — |
| 184 | C4×A4 | C2×D4 | 1 | 2 | yes | — |
| 185 | SL(2,ℤ/4) | — | 2 | 2 | no | — |
| 186 | SL(2,ℤ/4) | — | 2 | 2 | no | — |
| 187 | SL(2,ℤ/4) | C2×D4 | 1 | 2 | yes | — |
| 188 | C3×C42 | — | 4 | 1 | no | — |
| 189 | #217 | — | 4 | 4 | no | — |
| 190 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 191 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 192 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 193 | C4×Dic3 | — | 4 | 1 | no | — |
| 194 | C25 | — | 3 | 2 | no | — |
| 195 | C25 | C22×D3 | 1 | 2 | yes | — |
| 196 | C25 | C22×D3 | 1 | 2 | yes | — |
| 197 | C2×#41 | — | 6 | 4 | no | — |
| 198 | C2×#41 | — | 6 | 2 | no | — |
| 199 | C2×#41 | — | 6 | 1 | no | — |
| 200 | C2×#41 | — | 6 | 1 | no | — |
| 201 | C2×#41 | — | 12 | 2 | no | — |
| 202 | C22×Q8 | — | 3 | 1 | no | — |
| 203 | C22×D4 | — | 2 | 2 | no | — |
| 204 | C22×D4 | — | 2 | 2 | no | — |
| 205 | C22×D4 | — | 3 | 1 | no | — |
| 206 | C22×D4 | — | 3 | 1 | no | — |
| 207 | C22×D4 | — | 3 | 1 | no | — |
| 208 | C22×D4 | — | 3 | 4 | no | — |
| 209 | C22×D4 | — | 3 | 1 | no | — |
| 210 | C22×D4 | — | 3 | 1 | no | — |
| 211 | C22×D4 | — | 3 | 2 | no | — |
| 212 | C22×D4 | — | 3 | 4 | no | — |
| 213 | C22×D4 | — | 3 | 2 | no | — |
| 214 | C22×D4 | — | 3 | 4 | no | — |
| 215 | C22×D4 | — | 3 | 4 | no | — |
| 216 | C22×D4 | — | 3 | 1 | no | — |
| 217 | C22×D4 | — | 3 | 2 | no | — |
| 218 | C22×D4 | — | 3 | 2 | no | — |
| 219 | C22×D4 | — | 3 | 2 | no | — |
| 220 | C22×D4 | — | 3 | 2 | no | — |
| 221 | C22×D4 | — | 3 | 2 | no | — |
| 222 | C22×D4 | — | 3 | 4 | no | — |
| 223 | C22×D4 | — | 3 | 2 | no | — |
| 224 | C22×D4 | — | 3 | 2 | no | — |
| 225 | C22×D4 | — | 3 | 4 | no | — |
| 226 | C22×D4 | — | 4 | 4 | no | — |
| 227 | C22×D4 | — | 6 | 2 | no | — |
| 228 | C22×D4 | — | 6 | 2 | no | — |
| 229 | C22×D4 | — | 6 | 4 | no | — |
| 230 | C22×D4 | — | 6 | 4 | no | — |
| 231 | C22×D4 | — | 6 | 2 | no | — |
| 232 | C22×D4 | — | 6 | 1 | no | — |
| 233 | C22×D4 | — | 6 | 4 | no | — |
| 234 | C22×D4 | — | 6 | 1 | no | — |
| 235 | C22×D4 | — | 12 | 4 | no | — |
| 236 | C22×D4 | — | 12 | 2 | no | — |
| 237 | C22×D4 | — | 12 | 4 | no | — |
| 238 | C22×D4 | — | 12 | 4 | no | — |
| 239 | C23×C4 | — | 3 | 1 | no | — |
| 240 | C23×C4 | — | 3 | 2 | no | — |
| 241 | C23×C4 | — | 3 | 2 | no | — |
| 242 | C23×C4 | — | 3 | 2 | no | — |
| 243 | C23×C4 | C22×D3 | 1 | 2 | yes | — |
| 244 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 245 | #127 | — | 3 | 1 | no | — |
| 246 | #127 | — | 3 | 4 | no | — |
| 247 | #127 | — | 3 | 1 | no | — |
| 248 | #127 | — | 3 | 1 | no | — |
| 249 | #127 | — | 6 | 1 | no | — |
| 250 | #127 | — | 6 | 2 | no | — |
| 251 | #127 | — | 6 | 4 | no | — |
| 252 | #127 | — | 6 | 2 | no | — |
| 253 | #127 | — | 6 | 2 | no | — |
| 254 | #127 | — | 6 | 2 | no | — |
| 255 | #127 | — | 6 | 1 | no | — |
| 256 | #127 | — | 6 | 1 | no | — |
| 257 | #127 | — | 12 | 2 | no | — |
| 258 | #127 | S4 | 1 | 1 | yes | characteristic, complemented |
| 259 | #124 | — | 6 | 1 | no | — |
| 260 | #124 | — | 6 | 2 | no | — |
| 261 | #124 | — | 6 | 4 | no | — |
| 262 | #124 | — | 6 | 2 | no | — |
| 263 | #124 | — | 6 | 1 | no | — |
| 264 | #124 | — | 6 | 1 | no | — |
| 265 | #124 | — | 6 | 1 | no | — |
| 266 | #124 | — | 12 | 2 | no | — |
| 267 | #123 | — | 6 | 8 | no | — |
| 268 | C22⋊Q8 | — | 6 | 2 | no | — |
| 269 | C22⋊Q8 | — | 6 | 2 | no | — |
| 270 | #121 | — | 6 | 8 | no | — |
| 271 | #121 | — | 6 | 8 | no | — |
| 272 | #121 | — | 6 | 2 | no | — |
| 273 | #121 | — | 6 | 4 | no | — |
| 274 | #121 | — | 6 | 4 | no | — |
| 275 | #121 | — | 6 | 4 | no | — |
| 276 | #121 | — | 6 | 4 | no | — |
| 277 | #121 | — | 6 | 4 | no | — |
| 278 | #121 | — | 6 | 4 | no | — |
| 279 | #121 | — | 6 | 2 | no | — |
| 280 | #121 | — | 12 | 8 | no | — |
| 281 | #120 | — | 6 | 4 | no | — |
| 282 | #120 | — | 6 | 4 | no | — |
| 283 | #120 | — | 6 | 8 | no | — |
| 284 | #120 | — | 6 | 4 | no | — |
| 285 | #120 | — | 6 | 4 | no | — |
| 286 | #120 | — | 6 | 4 | no | — |
| 287 | #120 | — | 6 | 4 | no | — |
| 288 | #120 | — | 6 | 4 | no | — |
| 289 | #120 | — | 6 | 4 | no | — |
| 290 | #120 | — | 12 | 8 | no | — |
| 291 | #120 | — | 12 | 4 | no | — |
| 292 | #120 | — | 12 | 4 | no | — |
| 293 | C4×D4 | — | 3 | 4 | no | — |
| 294 | C4×D4 | — | 3 | 4 | no | — |
| 295 | C4×D4 | — | 6 | 4 | no | — |
| 296 | C4×D4 | — | 6 | 4 | no | — |
| 297 | #117 | — | 6 | 2 | no | — |
| 298 | #117 | — | 6 | 1 | no | — |
| 299 | #117 | — | 6 | 1 | no | — |
| 300 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 301 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 302 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 303 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 304 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 305 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 306 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 307 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 308 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 309 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 310 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 311 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 312 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 313 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 314 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 315 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 316 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 317 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 318 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 319 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 320 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 321 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 322 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 323 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 324 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 325 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 326 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 327 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 328 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 329 | C2×C42 | — | 3 | 1 | no | — |
| 330 | C2×C42 | — | 3 | 1 | no | — |
| 331 | C2×C42 | — | 3 | 1 | no | — |
| 332 | C2×C42 | — | 3 | 2 | no | — |
| 333 | C2×C42 | — | 3 | 1 | no | — |
| 334 | C2×C42 | — | 3 | 1 | no | — |
| 335 | #95 | — | 3 | 2 | no | — |
| 336 | #95 | — | 3 | 2 | no | — |
| 337 | #95 | — | 3 | 2 | no | — |
| 338 | #95 | — | 3 | 2 | no | — |
| 339 | #95 | — | 3 | 2 | no | — |
| 340 | #95 | — | 3 | 4 | no | — |
| 341 | #95 | — | 3 | 4 | no | — |
| 342 | C23×C3 | — | 4 | 2 | no | — |
| 343 | C23×C3 | — | 4 | 2 | no | — |
| 344 | C22×D3 | — | 4 | 1 | no | — |
| 345 | C22×D3 | — | 4 | 2 | no | — |
| 346 | C22×D3 | — | 8 | 4 | no | — |
| 347 | C22×D3 | — | 16 | 4 | no | — |
| 348 | C2×A4 | — | 4 | 2 | no | — |
| 349 | C2×A4 | — | 4 | 2 | no | — |
| 350 | C2×A4 | C22×D4 | 1 | 1 | yes | characteristic |
| 351 | C2×A4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 352 | S4 | — | 2 | 2 | no | — |
| 353 | S4 | — | 4 | 2 | no | — |
| 354 | C3×D4 | — | 8 | 2 | no | — |
| 355 | C3×D4 | — | 8 | 2 | no | — |
| 356 | C3×D4 | — | 16 | 4 | no | — |
| 357 | C2×C3×C4 | — | 4 | 1 | no | — |
| 358 | C2×C3×C4 | — | 4 | 2 | no | — |
| 359 | #67 | — | 8 | 4 | no | — |
| 360 | #67 | — | 8 | 4 | no | — |
| 361 | #67 | — | 16 | 4 | no | — |
| 362 | C2×Dic3 | — | 4 | 1 | no | — |
| 363 | C2×Dic3 | — | 4 | 2 | no | — |
| 364 | C2×Dic3 | — | 4 | 2 | no | — |
| 365 | C2×Dic3 | — | 8 | 4 | no | — |
| 366 | D12 | — | 8 | 2 | no | — |
| 367 | C4×D3 | — | 4 | 4 | no | — |
| 368 | Dic6 | — | 8 | 2 | no | — |
| 369 | C24 | — | 2 | 2 | no | — |
| 370 | C24 | — | 2 | 2 | no | — |
| 371 | C24 | — | 2 | 4 | no | — |
| 372 | C24 | — | 2 | 4 | no | — |
| 373 | C24 | — | 3 | 1 | no | — |
| 374 | C24 | — | 3 | 2 | no | — |
| 375 | C24 | — | 3 | 2 | no | — |
| 376 | C24 | — | 3 | 2 | no | — |
| 377 | C24 | — | 3 | 2 | no | — |
| 378 | C24 | — | 3 | 2 | no | — |
| 379 | C24 | — | 6 | 2 | no | — |
| 380 | C24 | — | 6 | 2 | no | — |
| 381 | C24 | — | 6 | 4 | no | — |
| 382 | C24 | — | 6 | 4 | no | — |
| 383 | C24 | — | 6 | 4 | no | — |
| 384 | C24 | — | 6 | 2 | no | — |
| 385 | C24 | — | 6 | 2 | no | — |
| 386 | C24 | — | 12 | 4 | no | — |
| 387 | C24 | — | 12 | 2 | no | — |
| 388 | C24 | — | 12 | 4 | no | — |
| 389 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 390 | #41 | — | 12 | 4 | no | — |
| 391 | #41 | — | 12 | 8 | no | — |
| 392 | #41 | — | 12 | 4 | no | — |
| 393 | C2×Q8 | — | 6 | 2 | no | — |
| 394 | C2×Q8 | — | 6 | 1 | no | — |
| 395 | C2×Q8 | — | 6 | 2 | no | — |
| 396 | C2×Q8 | — | 6 | 1 | no | — |
| 397 | C2×D4 | — | 3 | 2 | no | — |
| 398 | C2×D4 | — | 3 | 2 | no | — |
| 399 | C2×D4 | — | 3 | 2 | no | — |
| 400 | C2×D4 | — | 3 | 2 | no | — |
| 401 | C2×D4 | — | 3 | 4 | no | — |
| 402 | C2×D4 | — | 3 | 4 | no | — |
| 403 | C2×D4 | — | 3 | 1 | no | — |
| 404 | C2×D4 | — | 3 | 1 | no | — |
| 405 | C2×D4 | — | 3 | 4 | no | — |
| 406 | C2×D4 | — | 6 | 2 | no | — |
| 407 | C2×D4 | — | 6 | 2 | no | — |
| 408 | C2×D4 | — | 6 | 2 | no | — |
| 409 | C2×D4 | — | 6 | 2 | no | — |
| 410 | C2×D4 | — | 6 | 4 | no | — |
| 411 | C2×D4 | — | 6 | 4 | no | — |
| 412 | C2×D4 | — | 6 | 2 | no | — |
| 413 | C2×D4 | — | 6 | 2 | no | — |
| 414 | C2×D4 | — | 6 | 2 | no | — |
| 415 | C2×D4 | — | 6 | 2 | no | — |
| 416 | C2×D4 | — | 6 | 1 | no | — |
| 417 | C2×D4 | — | 6 | 1 | no | — |
| 418 | C2×D4 | — | 6 | 4 | no | — |
| 419 | C2×D4 | — | 6 | 4 | no | — |
| 420 | C2×D4 | — | 6 | 8 | no | — |
| 421 | C2×D4 | — | 6 | 2 | no | — |
| 422 | C2×D4 | — | 6 | 4 | no | — |
| 423 | C2×D4 | — | 6 | 8 | no | — |
| 424 | C2×D4 | — | 6 | 1 | no | — |
| 425 | C2×D4 | — | 6 | 2 | no | — |
| 426 | C2×D4 | — | 6 | 4 | no | — |
| 427 | C2×D4 | — | 6 | 2 | no | — |
| 428 | C2×D4 | — | 6 | 2 | no | — |
| 429 | C2×D4 | — | 6 | 2 | no | — |
| 430 | C2×D4 | — | 6 | 2 | no | — |
| 431 | C2×D4 | — | 6 | 4 | no | — |
| 432 | C2×D4 | — | 6 | 4 | no | — |
| 433 | C2×D4 | — | 6 | 4 | no | — |
| 434 | C2×D4 | — | 6 | 2 | no | — |
| 435 | C2×D4 | — | 6 | 2 | no | — |
| 436 | C2×D4 | — | 6 | 4 | no | — |
| 437 | C2×D4 | — | 6 | 2 | no | — |
| 438 | C2×D4 | — | 6 | 2 | no | — |
| 439 | C2×D4 | — | 6 | 4 | no | — |
| 440 | C2×D4 | — | 6 | 4 | no | — |
| 441 | C2×D4 | — | 6 | 4 | no | — |
| 442 | C2×D4 | — | 6 | 1 | no | — |
| 443 | C2×D4 | — | 12 | 4 | no | — |
| 444 | C2×D4 | — | 12 | 4 | no | — |
| 445 | C2×D4 | — | 12 | 4 | no | — |
| 446 | C2×D4 | — | 12 | 2 | no | — |
| 447 | C2×D4 | — | 12 | 2 | no | — |
| 448 | C2×D4 | — | 12 | 8 | no | — |
| 449 | C2×D4 | — | 12 | 4 | no | — |
| 450 | C2×D4 | — | 12 | 2 | no | — |
| 451 | C2×D4 | — | 12 | 4 | no | — |
| 452 | C2×D4 | — | 12 | 4 | no | — |
| 453 | C2×D4 | — | 12 | 2 | no | — |
| 454 | C2×D4 | — | 12 | 4 | no | — |
| 455 | C2×D4 | — | 12 | 4 | no | — |
| 456 | C2×D4 | — | 12 | 4 | no | — |
| 457 | C2×D4 | — | 12 | 4 | no | — |
| 458 | C2×D4 | — | 12 | 4 | no | — |
| 459 | C2×D4 | — | 12 | 4 | no | — |
| 460 | C2×D4 | — | 12 | 4 | no | — |
| 461 | C2×D4 | — | 12 | 4 | no | — |
| 462 | C2×D4 | — | 12 | 4 | no | — |
| 463 | C2×D4 | — | 12 | 4 | no | — |
| 464 | C2×D4 | — | 12 | 4 | no | — |
| 465 | C2×D4 | — | 12 | 8 | no | — |
| 466 | C2×D4 | — | 12 | 8 | no | — |
| 467 | C2×D4 | — | 12 | 16 | no | — |
| 468 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 469 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 470 | C2×D4 | C2×S4 | 1 | 4 | yes | complemented |
| 471 | C22×C4 | — | 2 | 2 | no | — |
| 472 | C22×C4 | — | 3 | 1 | no | — |
| 473 | C22×C4 | — | 3 | 2 | no | — |
| 474 | C22×C4 | — | 3 | 1 | no | — |
| 475 | C22×C4 | — | 3 | 2 | no | — |
| 476 | C22×C4 | — | 3 | 1 | no | — |
| 477 | C22×C4 | — | 3 | 1 | no | — |
| 478 | C22×C4 | — | 3 | 1 | no | — |
| 479 | C22×C4 | — | 3 | 4 | no | — |
| 480 | C22×C4 | — | 3 | 2 | no | — |
| 481 | C22×C4 | — | 3 | 2 | no | — |
| 482 | C22×C4 | — | 3 | 2 | no | — |
| 483 | C22×C4 | — | 3 | 2 | no | — |
| 484 | C22×C4 | — | 3 | 2 | no | — |
| 485 | C22×C4 | — | 3 | 2 | no | — |
| 486 | C22×C4 | — | 6 | 2 | no | — |
| 487 | C22×C4 | — | 6 | 1 | no | — |
| 488 | C22×C4 | — | 6 | 2 | no | — |
| 489 | C22×C4 | — | 6 | 4 | no | — |
| 490 | C22×C4 | — | 6 | 4 | no | — |
| 491 | C22×C4 | — | 6 | 4 | no | — |
| 492 | C22×C4 | — | 6 | 1 | no | — |
| 493 | C22×C4 | — | 6 | 2 | no | — |
| 494 | C22×C4 | — | 6 | 2 | no | — |
| 495 | C22×C4 | — | 12 | 4 | no | — |
| 496 | C22×C4 | — | 12 | 2 | no | — |
| 497 | C22×C4 | — | 12 | 4 | no | — |
| 498 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 499 | C4⋊C4 | — | 3 | 4 | no | — |
| 500 | C4⋊C4 | — | 6 | 2 | no | — |
| 501 | C4⋊C4 | — | 6 | 2 | no | — |
| 502 | C4⋊C4 | — | 6 | 2 | no | — |
| 503 | C4⋊C4 | — | 6 | 4 | no | — |
| 504 | C4⋊C4 | — | 6 | 4 | no | — |
| 505 | C4⋊C4 | — | 6 | 2 | no | — |
| 506 | C22⋊C4 | — | 3 | 2 | no | — |
| 507 | C22⋊C4 | — | 3 | 4 | no | — |
| 508 | C22⋊C4 | — | 3 | 2 | no | — |
| 509 | C22⋊C4 | — | 6 | 4 | no | — |
| 510 | C22⋊C4 | — | 6 | 4 | no | — |
| 511 | C22⋊C4 | — | 6 | 2 | no | — |
| 512 | C22⋊C4 | — | 6 | 4 | no | — |
| 513 | C22⋊C4 | — | 6 | 4 | no | — |
| 514 | C22⋊C4 | — | 6 | 4 | no | — |
| 515 | C22⋊C4 | — | 6 | 4 | no | — |
| 516 | C22⋊C4 | — | 6 | 4 | no | — |
| 517 | C22⋊C4 | — | 6 | 4 | no | — |
| 518 | C22⋊C4 | — | 6 | 4 | no | — |
| 519 | C22⋊C4 | — | 6 | 8 | no | — |
| 520 | C22⋊C4 | — | 6 | 2 | no | — |
| 521 | C22⋊C4 | — | 6 | 4 | no | — |
| 522 | C22⋊C4 | — | 6 | 2 | no | — |
| 523 | C22⋊C4 | — | 6 | 2 | no | — |
| 524 | C22⋊C4 | — | 6 | 2 | no | — |
| 525 | C22⋊C4 | — | 6 | 4 | no | — |
| 526 | C22⋊C4 | — | 6 | 2 | no | — |
| 527 | C22⋊C4 | — | 6 | 4 | no | — |
| 528 | C22⋊C4 | — | 12 | 4 | no | — |
| 529 | C22⋊C4 | — | 12 | 4 | no | — |
| 530 | C22⋊C4 | — | 12 | 4 | no | — |
| 531 | C22⋊C4 | — | 12 | 4 | no | — |
| 532 | C22⋊C4 | — | 12 | 4 | no | — |
| 533 | C42 | — | 3 | 4 | no | — |
| 534 | C42 | — | 3 | 2 | no | — |
| 535 | C42 | — | 3 | 1 | no | — |
| 536 | C42 | — | 6 | 1 | no | — |
| 537 | C42 | — | 6 | 1 | no | — |
| 538 | C42 | — | 6 | 2 | no | — |
| 539 | C42 | — | 6 | 1 | no | — |
| 540 | C42 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 541 | C22×C3 | — | 4 | 1 | no | — |
| 542 | C22×C3 | — | 8 | 2 | no | — |
| 543 | C22×C3 | — | 8 | 2 | no | — |
| 544 | C22×C3 | — | 8 | 4 | no | — |
| 545 | C22×C3 | — | 8 | 4 | no | — |
| 546 | C2×D3 | — | 4 | 2 | no | — |
| 547 | C2×D3 | — | 8 | 2 | no | — |
| 548 | C2×D3 | — | 8 | 2 | no | — |
| 549 | C2×D3 | — | 8 | 4 | no | — |
| 550 | C2×D3 | — | 16 | 8 | no | — |
| 551 | A4 | #535 | 1 | 1 | yes | characteristic, complemented |
| 552 | C3×C4 | — | 4 | 2 | no | — |
| 553 | C3×C4 | — | 8 | 2 | no | — |
| 554 | Dic3 | — | 4 | 2 | no | — |
| 555 | Dic3 | — | 8 | 2 | no | — |
| 556 | Dic3 | — | 8 | 2 | no | — |
| 557 | C23 | — | 3 | 1 | no | — |
| 558 | C23 | — | 3 | 1 | no | — |
| 559 | C23 | — | 3 | 2 | no | — |
| 560 | C23 | — | 3 | 2 | no | — |
| 561 | C23 | — | 3 | 2 | no | — |
| 562 | C23 | — | 3 | 2 | no | — |
| 563 | C23 | — | 4 | 2 | no | — |
| 564 | C23 | — | 4 | 2 | no | — |
| 565 | C23 | — | 6 | 2 | no | — |
| 566 | C23 | — | 6 | 2 | no | — |
| 567 | C23 | — | 6 | 4 | no | — |
| 568 | C23 | — | 6 | 4 | no | — |
| 569 | C23 | — | 6 | 2 | no | — |
| 570 | C23 | — | 6 | 4 | no | — |
| 571 | C23 | — | 6 | 4 | no | — |
| 572 | C23 | — | 6 | 2 | no | — |
| 573 | C23 | — | 6 | 2 | no | — |
| 574 | C23 | — | 6 | 1 | no | — |
| 575 | C23 | — | 6 | 2 | no | — |
| 576 | C23 | — | 6 | 2 | no | — |
| 577 | C23 | — | 6 | 2 | no | — |
| 578 | C23 | — | 6 | 2 | no | — |
| 579 | C23 | — | 6 | 4 | no | — |
| 580 | C23 | — | 6 | 4 | no | — |
| 581 | C23 | — | 6 | 2 | no | — |
| 582 | C23 | — | 6 | 4 | no | — |
| 583 | C23 | — | 6 | 4 | no | — |
| 584 | C23 | — | 6 | 2 | no | — |
| 585 | C23 | — | 6 | 4 | no | — |
| 586 | C23 | — | 6 | 2 | no | — |
| 587 | C23 | — | 6 | 4 | no | — |
| 588 | C23 | — | 6 | 1 | no | — |
| 589 | C23 | — | 6 | 2 | no | — |
| 590 | C23 | — | 12 | 4 | no | — |
| 591 | C23 | — | 12 | 2 | no | — |
| 592 | C23 | — | 12 | 4 | no | — |
| 593 | C23 | — | 12 | 2 | no | — |
| 594 | C23 | — | 12 | 4 | no | — |
| 595 | C23 | — | 12 | 4 | no | — |
| 596 | C23 | — | 12 | 8 | no | — |
| 597 | C23 | — | 24 | 4 | no | — |
| 598 | C23 | — | 24 | 2 | no | — |
| 599 | C23 | — | 24 | 2 | no | — |
| 600 | C23 | — | 24 | 4 | no | — |
| 601 | C23 | — | 24 | 4 | no | — |
| 602 | C23 | — | 24 | 8 | no | — |
| 603 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 604 | C23 | #1004 | 1 | 2 | yes | — |
| 605 | C23 | C22×S4 | 1 | 2 | yes | — |
| 606 | C23 | C22×S4 | 1 | 2 | yes | — |
| 607 | Q8 | — | 12 | 2 | no | — |
| 608 | Q8 | — | 12 | 2 | no | — |
| 609 | D4 | — | 2 | 2 | no | — |
| 610 | D4 | — | 2 | 2 | no | — |
| 611 | D4 | — | 4 | 4 | no | — |
| 612 | D4 | — | 6 | 4 | no | — |
| 613 | D4 | — | 6 | 4 | no | — |
| 614 | D4 | — | 6 | 2 | no | — |
| 615 | D4 | — | 6 | 4 | no | — |
| 616 | D4 | — | 6 | 2 | no | — |
| 617 | D4 | — | 6 | 2 | no | — |
| 618 | D4 | — | 6 | 2 | no | — |
| 619 | D4 | — | 12 | 4 | no | — |
| 620 | D4 | — | 12 | 2 | no | — |
| 621 | D4 | — | 12 | 2 | no | — |
| 622 | D4 | — | 12 | 2 | no | — |
| 623 | D4 | — | 12 | 4 | no | — |
| 624 | D4 | — | 12 | 4 | no | — |
| 625 | D4 | — | 12 | 4 | no | — |
| 626 | D4 | — | 12 | 8 | no | — |
| 627 | D4 | — | 12 | 4 | no | — |
| 628 | D4 | — | 12 | 8 | no | — |
| 629 | D4 | — | 12 | 4 | no | — |
| 630 | D4 | — | 12 | 2 | no | — |
| 631 | D4 | — | 12 | 4 | no | — |
| 632 | D4 | — | 12 | 4 | no | — |
| 633 | D4 | — | 12 | 8 | no | — |
| 634 | D4 | — | 12 | 2 | no | — |
| 635 | D4 | — | 12 | 2 | no | — |
| 636 | D4 | — | 24 | 4 | no | — |
| 637 | D4 | — | 24 | 4 | no | — |
| 638 | D4 | — | 24 | 4 | no | — |
| 639 | D4 | — | 24 | 4 | no | — |
| 640 | D4 | — | 24 | 8 | no | — |
| 641 | C2×C4 | — | 3 | 1 | no | — |
| 642 | C2×C4 | — | 3 | 2 | no | — |
| 643 | C2×C4 | — | 3 | 2 | no | — |
| 644 | C2×C4 | — | 3 | 2 | no | — |
| 645 | C2×C4 | — | 3 | 2 | no | — |
| 646 | C2×C4 | — | 3 | 2 | no | — |
| 647 | C2×C4 | — | 3 | 2 | no | — |
| 648 | C2×C4 | — | 3 | 4 | no | — |
| 649 | C2×C4 | — | 3 | 2 | no | — |
| 650 | C2×C4 | — | 6 | 2 | no | — |
| 651 | C2×C4 | — | 6 | 2 | no | — |
| 652 | C2×C4 | — | 6 | 1 | no | — |
| 653 | C2×C4 | — | 6 | 4 | no | — |
| 654 | C2×C4 | — | 6 | 2 | no | — |
| 655 | C2×C4 | — | 6 | 1 | no | — |
| 656 | C2×C4 | — | 6 | 2 | no | — |
| 657 | C2×C4 | — | 6 | 1 | no | — |
| 658 | C2×C4 | — | 6 | 4 | no | — |
| 659 | C2×C4 | — | 6 | 2 | no | — |
| 660 | C2×C4 | — | 6 | 2 | no | — |
| 661 | C2×C4 | — | 6 | 2 | no | — |
| 662 | C2×C4 | — | 6 | 2 | no | — |
| 663 | C2×C4 | — | 6 | 2 | no | — |
| 664 | C2×C4 | — | 6 | 4 | no | — |
| 665 | C2×C4 | — | 6 | 2 | no | — |
| 666 | C2×C4 | — | 6 | 2 | no | — |
| 667 | C2×C4 | — | 6 | 2 | no | — |
| 668 | C2×C4 | — | 6 | 2 | no | — |
| 669 | C2×C4 | — | 6 | 4 | no | — |
| 670 | C2×C4 | — | 6 | 2 | no | — |
| 671 | C2×C4 | — | 6 | 2 | no | — |
| 672 | C2×C4 | — | 6 | 2 | no | — |
| 673 | C2×C4 | — | 12 | 4 | no | — |
| 674 | C2×C4 | — | 12 | 4 | no | — |
| 675 | C2×C4 | — | 12 | 8 | no | — |
| 676 | C2×C4 | — | 24 | 4 | no | — |
| 677 | C2×C4 | C22×S4 | 1 | 2 | yes | — |
| 678 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 679 | C2×C3 | — | 4 | 1 | no | — |
| 680 | C2×C3 | — | 4 | 2 | no | — |
| 681 | C2×C3 | — | 16 | 2 | no | — |
| 682 | C2×C3 | — | 16 | 2 | no | — |
| 683 | D3 | — | 8 | 2 | no | — |
| 684 | D3 | — | 16 | 2 | no | — |
| 685 | C22 | — | 2 | 2 | no | — |
| 686 | C22 | — | 2 | 2 | no | — |
| 687 | C22 | — | 2 | 4 | no | — |
| 688 | C22 | — | 2 | 4 | no | — |
| 689 | C22 | — | 3 | 1 | no | — |
| 690 | C22 | — | 3 | 2 | no | — |
| 691 | C22 | — | 3 | 1 | no | — |
| 692 | C22 | — | 3 | 1 | no | — |
| 693 | C22 | — | 3 | 2 | no | — |
| 694 | C22 | — | 3 | 2 | no | — |
| 695 | C22 | — | 6 | 1 | no | — |
| 696 | C22 | — | 6 | 2 | no | — |
| 697 | C22 | — | 6 | 2 | no | — |
| 698 | C22 | — | 6 | 2 | no | — |
| 699 | C22 | — | 6 | 2 | no | — |
| 700 | C22 | — | 6 | 2 | no | — |
| 701 | C22 | — | 6 | 4 | no | — |
| 702 | C22 | — | 6 | 4 | no | — |
| 703 | C22 | — | 12 | 2 | no | — |
| 704 | C22 | — | 12 | 2 | no | — |
| 705 | C22 | — | 12 | 2 | no | — |
| 706 | C22 | — | 12 | 4 | no | — |
| 707 | C22 | — | 12 | 2 | no | — |
| 708 | C22 | — | 12 | 4 | no | — |
| 709 | C22 | — | 12 | 2 | no | — |
| 710 | C22 | — | 12 | 2 | no | — |
| 711 | C22 | — | 12 | 2 | no | — |
| 712 | C22 | — | 12 | 4 | no | — |
| 713 | C22 | — | 12 | 2 | no | — |
| 714 | C22 | — | 12 | 4 | no | — |
| 715 | C22 | — | 12 | 2 | no | — |
| 716 | C22 | — | 12 | 2 | no | — |
| 717 | C22 | — | 12 | 2 | no | — |
| 718 | C22 | — | 12 | 4 | no | — |
| 719 | C22 | — | 12 | 2 | no | — |
| 720 | C22 | — | 12 | 2 | no | — |
| 721 | C22 | — | 12 | 4 | no | — |
| 722 | C22 | — | 24 | 8 | no | — |
| 723 | C22 | — | 24 | 8 | no | — |
| 724 | C22 | #5715 | 1 | 1 | yes | characteristic, complemented |
| 725 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 726 | C4 | — | 2 | 2 | no | — |
| 727 | C4 | — | 3 | 2 | no | — |
| 728 | C4 | — | 6 | 2 | no | — |
| 729 | C4 | — | 6 | 2 | no | — |
| 730 | C4 | — | 6 | 2 | no | — |
| 731 | C4 | — | 6 | 2 | no | — |
| 732 | C4 | — | 12 | 2 | no | — |
| 733 | C4 | — | 12 | 2 | no | — |
| 734 | C4 | — | 12 | 2 | no | — |
| 735 | C4 | — | 12 | 2 | no | — |
| 736 | C4 | — | 12 | 2 | no | — |
| 737 | C4 | D4×S4 | 1 | 2 | yes | — |
| 738 | C3 | — | 4 | 1 | no | Sylow |
| 739 | C2 | — | 3 | 1 | no | — |
| 740 | C2 | — | 3 | 1 | no | — |
| 741 | C2 | — | 3 | 2 | no | — |
| 742 | C2 | — | 4 | 2 | no | — |
| 743 | C2 | — | 4 | 2 | no | — |
| 744 | C2 | — | 12 | 2 | no | — |
| 745 | C2 | — | 12 | 2 | no | — |
| 746 | C2 | — | 12 | 2 | no | — |
| 747 | C2 | — | 24 | 2 | no | — |
| 748 | C2 | C2×D4×S4 | 1 | 1 | yes | characteristic |
| 749 | C2 | #87477 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×S4 |
| commutator, cosocle | C22×A4 | C24 |
| Fitting | C22×#127 | D3 |
| socle | C24 | C23×D3 |
| hypercenter | #127 | S4 |
| hypocenter | A4 | #535 |
| LCS | G ▷ C22×A4 ▷ A4 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5914 | C2 | semidirect |
| 2. C2×D4×S4 | C2 | semidirect |
| 3. A4×#127 | C2 | semidirect |
| 4. #85496 | C2 | semidirect |
| 5. #85495 | C2 | semidirect |
| 6. #85493 | C2 | semidirect |
| 7. #85492 | C2 | semidirect |
| 8. #85290 | C2 | semidirect |
| 9. #85287 | C2 | semidirect |
| 13. C2×D4×A4 | C22 | semidirect |
| 14. C2×D4×A4 | C22 | semidirect |
| 17. C2×GL(2,ℤ/4) | C22 | semidirect |
| 18. C22×SL(2,ℤ/4) | C22 | semidirect |
| 23. C2×A4⋊Q8 | C22 | semidirect |
| 25. C42×A4 | C22 | semidirect |
| 26. #5432 | C22 | semidirect |
| 28. (C2×S4)⋊C4 | C22 | semidirect |
| 29. SL(2,ℤ/4)⋊C4 | C22 | semidirect |
| 30. C4×SL(2,ℤ/4) | C22 | semidirect |
| 34. C22×#127 | D3 | semidirect |
| 71. C4×S4 | D4 | semidirect |
| 84. C23×D4 | C2×D3 | semidirect |
| 85. C23×D4 | C2×D3 | semidirect |
| 127. C22×C42 | C2×D3 | semidirect |
| 258. #127 | S4 | semidirect |
| 469. C2×D4 | C2×S4 | semidirect |
| 470. C2×D4 | C2×S4 | semidirect |
| 540. C42 | C2×S4 | semidirect |
| 551. A4 | #535 | semidirect |
| 724. C22 | #5715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5914 | 2 |
| C2×D4×S4 | 2 |
| A4×#127 | 2 |
| #85496 | 2 |
| #85495 | 2 |
| #85493 | 2 |
| #85492 | 2 |
| #85290 | 2 |
| #85287 | 2 |
| #37674 | 3 |
| #5715 | 4 |