Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1212 conjugacy classes of subgroups.
The subgroup lattice has 776 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83395 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #78717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #78716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2134 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70149 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70148 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #69161 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #69160 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #33570 | — | 3 | 1 | no | maximal, Sylow |
| 11 | #5964 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×#535 | C22 | 1 | 1 | yes | characteristic |
| 13 | #5832 | C22 | 1 | 1 | yes | characteristic |
| 14 | #5830 | C22 | 1 | 1 | yes | characteristic |
| 15 | D4×#67 | — | 2 | 1 | no | — |
| 16 | C2×#932 | — | 2 | 1 | no | — |
| 17 | #5748 | — | 2 | 1 | no | — |
| 18 | C2×#908 | — | 2 | 1 | no | — |
| 19 | #5715 | — | 2 | 2 | no | — |
| 20 | #5683 | C22 | 1 | 2 | yes | complemented |
| 21 | #5670 | C22 | 1 | 2 | yes | complemented |
| 22 | #5616 | — | 2 | 1 | no | — |
| 23 | #5609 | — | 2 | 1 | no | — |
| 24 | #5607 | — | 2 | 1 | no | — |
| 25 | #5596 | — | 2 | 1 | no | — |
| 26 | #5594 | — | 2 | 1 | no | — |
| 27 | #5592 | — | 2 | 2 | no | — |
| 28 | #5590 | — | 2 | 1 | no | — |
| 29 | #5532 | — | 2 | 1 | no | — |
| 30 | C3×#413 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C3×#413 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #5237 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #5139 | — | 2 | 1 | no | — |
| 34 | C2×#825 | — | 2 | 1 | no | — |
| 35 | #5077 | — | 2 | 2 | no | — |
| 36 | #5062 | C22 | 1 | 4 | yes | complemented |
| 37 | #5005 | — | 2 | 1 | no | — |
| 38 | #4753 | C22 | 1 | 2 | yes | complemented |
| 39 | #4753 | C22 | 1 | 4 | yes | complemented |
| 40 | #4752 | C22 | 1 | 2 | yes | complemented |
| 41 | #4747 | — | 2 | 1 | no | — |
| 42 | #4747 | — | 2 | 2 | no | — |
| 43 | #4746 | — | 2 | 1 | no | — |
| 44 | C3×#355 | C22 | 1 | 4 | yes | complemented |
| 45 | #4478 | C22 | 1 | 2 | yes | complemented |
| 46 | #4477 | C22 | 1 | 2 | yes | complemented |
| 47 | #4477 | C22 | 1 | 4 | yes | complemented |
| 48 | #3549 | — | 3 | 1 | no | — |
| 49 | #3021 | — | 3 | 1 | no | — |
| 50 | #3021 | — | 3 | 1 | no | — |
| 51 | #3018 | — | 3 | 1 | no | — |
| 52 | #2204 | — | 3 | 4 | no | — |
| 53 | #2202 | — | 3 | 4 | no | — |
| 54 | #2134 | — | 3 | 1 | no | — |
| 55 | #2134 | D3 | 1 | 1 | yes | characteristic, complemented |
| 56 | #2132 | — | 3 | 1 | no | — |
| 57 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C3×D4 | D4 | 1 | 1 | yes | characteristic |
| 59 | C22×#67 | — | 2 | 2 | no | — |
| 60 | #1010 | — | 4 | 1 | no | — |
| 61 | #1009 | — | 4 | 1 | no | — |
| 62 | D3×#41 | — | 4 | 2 | no | — |
| 63 | #1007 | C23 | 1 | 2 | yes | — |
| 64 | #1004 | — | 2 | 1 | no | — |
| 65 | #1004 | — | 2 | 1 | no | — |
| 66 | #1004 | — | 2 | 1 | no | — |
| 67 | C2×#237 | — | 2 | 2 | no | — |
| 68 | C2×D3×D4 | — | 2 | 2 | no | — |
| 69 | C2×D3×D4 | — | 2 | 1 | no | — |
| 70 | C2×#235 | — | 2 | 1 | no | — |
| 71 | C2×#235 | — | 2 | 1 | no | — |
| 72 | C2×#235 | — | 2 | 1 | no | — |
| 73 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 74 | C22×D12 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C3×M16 | — | 2 | 1 | no | — |
| 76 | C2×C3×M16 | — | 2 | 1 | no | — |
| 77 | C3×#127 | D4 | 1 | 2 | yes | — |
| 78 | C3×#124 | C23 | 1 | 2 | yes | — |
| 79 | C3×#121 | — | 2 | 1 | no | — |
| 80 | C3×#121 | — | 2 | 1 | no | — |
| 81 | C3×#120 | — | 2 | 1 | no | — |
| 82 | C3×#120 | — | 2 | 1 | no | — |
| 83 | C3×#117 | D4 | 1 | 1 | yes | characteristic |
| 84 | #953 | — | 2 | 2 | no | — |
| 85 | #947 | C23 | 1 | 2 | yes | — |
| 86 | #947 | C23 | 1 | 1 | yes | characteristic |
| 87 | #944 | C23 | 1 | 1 | yes | characteristic |
| 88 | #940 | — | 2 | 2 | no | — |
| 89 | #940 | — | 2 | 1 | no | — |
| 90 | #940 | D4 | 1 | 2 | yes | — |
| 91 | #940 | D4 | 1 | 1 | yes | characteristic |
| 92 | #939 | — | 2 | 2 | no | — |
| 93 | #939 | — | 2 | 2 | no | — |
| 94 | #939 | — | 2 | 2 | no | — |
| 95 | #939 | — | 2 | 1 | no | — |
| 96 | #939 | — | 2 | 1 | no | — |
| 97 | #938 | — | 2 | 1 | no | — |
| 98 | #937 | — | 2 | 2 | no | — |
| 99 | #937 | — | 2 | 2 | no | — |
| 100 | #937 | — | 2 | 2 | no | — |
| 101 | #937 | — | 2 | 1 | no | — |
| 102 | #937 | — | 2 | 1 | no | — |
| 103 | #936 | — | 2 | 2 | no | — |
| 104 | #936 | D4 | 1 | 1 | yes | characteristic |
| 105 | D4×Dic3 | — | 2 | 1 | no | — |
| 106 | C2×#214 | — | 4 | 1 | no | — |
| 107 | #932 | — | 2 | 4 | no | — |
| 108 | #932 | — | 4 | 2 | no | — |
| 109 | C2×#213 | — | 4 | 1 | no | — |
| 110 | #930 | — | 2 | 1 | no | — |
| 111 | #930 | — | 2 | 1 | no | — |
| 112 | C4×#67 | — | 2 | 1 | no | — |
| 113 | C4×#67 | — | 2 | 1 | no | — |
| 114 | #926 | D4 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 116 | C2×#208 | — | 2 | 1 | no | — |
| 117 | #909 | — | 2 | 2 | no | — |
| 118 | #909 | — | 4 | 1 | no | — |
| 119 | #908 | — | 2 | 4 | no | — |
| 120 | #908 | — | 2 | 2 | no | — |
| 121 | #908 | — | 4 | 1 | no | — |
| 122 | #908 | — | 4 | 2 | no | — |
| 123 | #904 | — | 4 | 2 | no | — |
| 124 | C2×D24 | — | 4 | 1 | no | — |
| 125 | C2×#204 | — | 4 | 1 | no | — |
| 126 | #895 | — | 2 | 1 | no | — |
| 127 | #893 | — | 2 | 1 | no | — |
| 128 | #892 | — | 2 | 1 | no | — |
| 129 | #888 | — | 2 | 1 | no | — |
| 130 | #885 | — | 2 | 2 | no | — |
| 131 | #885 | — | 2 | 2 | no | — |
| 132 | #885 | — | 2 | 2 | no | — |
| 133 | #885 | — | 2 | 2 | no | — |
| 134 | #884 | — | 2 | 2 | no | — |
| 135 | #884 | — | 2 | 2 | no | — |
| 136 | #882 | — | 2 | 2 | no | — |
| 137 | #882 | — | 2 | 2 | no | — |
| 138 | #67⋊C4 | — | 2 | 2 | no | — |
| 139 | #877 | — | 2 | 2 | no | — |
| 140 | #875 | — | 2 | 2 | no | — |
| 141 | #872 | — | 2 | 2 | no | — |
| 142 | C3×#101 | C23 | 1 | 2 | yes | — |
| 143 | C3×#101 | C23 | 1 | 2 | yes | — |
| 144 | C3×#100 | — | 2 | 1 | no | — |
| 145 | C3×#100 | — | 2 | 1 | no | — |
| 146 | #836 | C23 | 1 | 2 | yes | — |
| 147 | #833 | — | 2 | 1 | no | — |
| 148 | #825 | — | 2 | 2 | no | — |
| 149 | #825 | — | 2 | 2 | no | — |
| 150 | #825 | — | 2 | 4 | no | — |
| 151 | #805 | — | 2 | 4 | no | — |
| 152 | #585 | — | 3 | 1 | no | — |
| 153 | #575 | — | 6 | 1 | no | — |
| 154 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 155 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 156 | H(3,𝔽4) | — | 3 | 2 | no | — |
| 157 | H(3,𝔽4) | — | 6 | 1 | no | — |
| 158 | #555 | — | 3 | 2 | no | — |
| 159 | #555 | — | 6 | 1 | no | — |
| 160 | #555 | — | 6 | 1 | no | — |
| 161 | D42 | — | 6 | 1 | no | — |
| 162 | D42 | — | 6 | 1 | no | — |
| 163 | D42 | — | 6 | 1 | no | — |
| 164 | #535 | — | 3 | 1 | no | — |
| 165 | #535 | — | 6 | 2 | no | — |
| 166 | #535 | — | 6 | 1 | no | — |
| 167 | #535 | — | 6 | 2 | no | — |
| 168 | #535 | C2×D3 | 1 | 1 | yes | characteristic |
| 169 | #532 | — | 3 | 1 | no | — |
| 170 | #532 | — | 6 | 1 | no | — |
| 171 | #456 | — | 3 | 2 | no | — |
| 172 | #455 | — | 6 | 1 | no | — |
| 173 | #454 | — | 3 | 4 | no | — |
| 174 | #454 | — | 3 | 2 | no | — |
| 175 | #454 | — | 3 | 4 | no | — |
| 176 | #453 | — | 6 | 1 | no | — |
| 177 | #453 | — | 6 | 2 | no | — |
| 178 | #453 | — | 6 | 2 | no | — |
| 179 | #421 | — | 6 | 1 | no | — |
| 180 | #421 | — | 6 | 1 | no | — |
| 181 | C2×#104 | — | 6 | 1 | no | — |
| 182 | #413 | — | 3 | 1 | no | — |
| 183 | #413 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 184 | #413 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 185 | #356 | — | 3 | 2 | no | — |
| 186 | #355 | — | 3 | 2 | no | — |
| 187 | #355 | — | 3 | 4 | no | — |
| 188 | #355 | C2×D3 | 1 | 4 | yes | complemented |
| 189 | C24×C3 | — | 2 | 1 | no | — |
| 190 | C23×D3 | — | 2 | 2 | no | — |
| 191 | C23×D3 | — | 2 | 1 | no | — |
| 192 | C3×#41 | — | 4 | 1 | no | — |
| 193 | C3×#41 | — | 4 | 1 | no | — |
| 194 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 195 | C2×C3×D4 | — | 2 | 2 | no | — |
| 196 | C2×C3×D4 | — | 2 | 2 | no | — |
| 197 | C2×C3×D4 | — | 2 | 1 | no | — |
| 198 | C2×C3×D4 | — | 4 | 1 | no | — |
| 199 | C2×C3×D4 | — | 4 | 1 | no | — |
| 200 | C2×C3×D4 | C2×D4 | 1 | 2 | yes | — |
| 201 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×#67 | — | 2 | 2 | no | — |
| 208 | C2×#67 | — | 2 | 1 | no | — |
| 209 | C2×#67 | — | 2 | 1 | no | — |
| 210 | C2×#67 | — | 2 | 2 | no | — |
| 211 | C2×#67 | — | 2 | 2 | no | — |
| 212 | C2×#67 | — | 2 | 2 | no | — |
| 213 | C2×#67 | — | 2 | 2 | no | — |
| 214 | C2×#67 | — | 2 | 2 | no | — |
| 215 | C2×#67 | — | 2 | 1 | no | — |
| 216 | C2×#67 | — | 4 | 1 | no | — |
| 217 | C2×#67 | — | 4 | 1 | no | — |
| 218 | C2×#67 | — | 4 | 1 | no | — |
| 219 | C2×#67 | — | 8 | 4 | no | — |
| 220 | C22×Dic3 | — | 2 | 2 | no | — |
| 221 | C22×Dic3 | — | 2 | 1 | no | — |
| 222 | #239 | — | 4 | 2 | no | — |
| 223 | D3×Q8 | — | 4 | 2 | no | — |
| 224 | #237 | — | 4 | 2 | no | — |
| 225 | #237 | — | 4 | 2 | no | — |
| 226 | #237 | — | 4 | 2 | no | — |
| 227 | #237 | — | 8 | 4 | no | — |
| 228 | D3×D4 | — | 4 | 2 | no | — |
| 229 | D3×D4 | — | 4 | 2 | no | — |
| 230 | D3×D4 | — | 4 | 2 | no | — |
| 231 | D3×D4 | — | 8 | 1 | no | — |
| 232 | D3×D4 | — | 8 | 1 | no | — |
| 233 | D3×D4 | — | 8 | 4 | no | — |
| 234 | #235 | — | 2 | 2 | no | — |
| 235 | #235 | — | 2 | 2 | no | — |
| 236 | #235 | — | 2 | 2 | no | — |
| 237 | #235 | — | 2 | 2 | no | — |
| 238 | #235 | — | 2 | 2 | no | — |
| 239 | #235 | — | 2 | 2 | no | — |
| 240 | #235 | — | 4 | 1 | no | — |
| 241 | #235 | — | 4 | 1 | no | — |
| 242 | #235 | — | 4 | 1 | no | — |
| 243 | #235 | — | 4 | 1 | no | — |
| 244 | #235 | — | 4 | 1 | no | — |
| 245 | #235 | — | 4 | 1 | no | — |
| 246 | C2×D12 | — | 2 | 1 | no | — |
| 247 | C2×D12 | — | 2 | 1 | no | — |
| 248 | C2×D12 | — | 2 | 1 | no | — |
| 249 | C2×D12 | — | 2 | 1 | no | — |
| 250 | C2×D12 | — | 2 | 2 | no | — |
| 251 | C2×D12 | — | 4 | 1 | no | — |
| 252 | C2×D12 | — | 4 | 1 | no | — |
| 253 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×D12 | C2×D4 | 1 | 2 | yes | — |
| 255 | C2×C4×D3 | — | 2 | 2 | no | — |
| 256 | C2×C4×D3 | — | 2 | 1 | no | — |
| 257 | C2×C4×D3 | — | 4 | 1 | no | — |
| 258 | C2×C4×D3 | — | 4 | 1 | no | — |
| 259 | C2×C4×D3 | — | 4 | 1 | no | — |
| 260 | C2×Dic6 | — | 2 | 1 | no | — |
| 261 | C2×Dic6 | — | 2 | 1 | no | — |
| 262 | C2×Dic6 | — | 2 | 1 | no | — |
| 263 | C2×Dic6 | — | 2 | 2 | no | — |
| 264 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C3×M16 | — | 2 | 2 | no | — |
| 266 | C3×M16 | — | 2 | 2 | no | — |
| 267 | C3×M16 | — | 4 | 1 | no | — |
| 268 | C3×M16 | — | 4 | 1 | no | — |
| 269 | C2×C3×C8 | — | 4 | 1 | no | — |
| 270 | C2×C3×C8 | — | 4 | 1 | no | — |
| 271 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 272 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 273 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 274 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 275 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 276 | #217 | — | 2 | 2 | no | — |
| 277 | #217 | — | 2 | 2 | no | — |
| 278 | #217 | — | 2 | 1 | no | — |
| 279 | #217 | — | 2 | 1 | no | — |
| 280 | #217 | — | 2 | 1 | no | — |
| 281 | #214 | — | 4 | 4 | no | — |
| 282 | #213 | — | 4 | 4 | no | — |
| 283 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 284 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 285 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 286 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 287 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 288 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 289 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 290 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 291 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 292 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 293 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 294 | C4×Dic3 | — | 2 | 2 | no | — |
| 295 | C4×Dic3 | — | 2 | 1 | no | — |
| 296 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 297 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | #208 | — | 2 | 2 | no | — |
| 300 | #208 | — | 4 | 1 | no | — |
| 301 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 302 | Dic12 | — | 4 | 2 | no | — |
| 303 | D24 | — | 4 | 4 | no | — |
| 304 | D24 | — | 4 | 2 | no | — |
| 305 | #204 | — | 4 | 4 | no | — |
| 306 | #204 | — | 4 | 2 | no | — |
| 307 | #204 | — | 4 | 2 | no | — |
| 308 | 2−1+4 | — | 3 | 2 | no | — |
| 309 | 2−1+4 | — | 12 | 1 | no | — |
| 310 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 311 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 312 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 313 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 314 | C2×#41 | — | 3 | 1 | no | — |
| 315 | C2×#41 | — | 6 | 2 | no | — |
| 316 | C2×#41 | — | 6 | 1 | no | — |
| 317 | C2×#41 | — | 6 | 1 | no | — |
| 318 | C2×#41 | — | 6 | 1 | no | — |
| 319 | C2×#41 | — | 12 | 2 | no | — |
| 320 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 321 | C22×D4 | — | 3 | 1 | no | — |
| 322 | C22×D4 | — | 6 | 2 | no | — |
| 323 | C22×D4 | — | 6 | 1 | no | — |
| 324 | C22×D4 | — | 6 | 2 | no | — |
| 325 | C22×D4 | D12 | 1 | 1 | yes | characteristic |
| 326 | #137 | — | 6 | 2 | no | — |
| 327 | #137 | — | 12 | 1 | no | — |
| 328 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 329 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 330 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 331 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 332 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 333 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 334 | #135 | — | 12 | 2 | no | — |
| 335 | C2×SD16 | — | 12 | 1 | no | — |
| 336 | C2×SD16 | — | 12 | 1 | no | — |
| 337 | C2×D8 | — | 12 | 1 | no | — |
| 338 | C2×D8 | — | 12 | 1 | no | — |
| 339 | C2×M16 | — | 2 | 1 | no | — |
| 340 | C2×M16 | — | 2 | 1 | no | — |
| 341 | C2×M16 | — | 6 | 1 | no | — |
| 342 | C4⋊Q8 | — | 3 | 1 | no | — |
| 343 | C4⋊Q8 | — | 6 | 1 | no | — |
| 344 | #127 | — | 3 | 1 | no | — |
| 345 | #127 | — | 3 | 2 | no | — |
| 346 | #127 | — | 6 | 1 | no | — |
| 347 | #127 | — | 6 | 2 | no | — |
| 348 | #127 | D12 | 1 | 2 | yes | — |
| 349 | #124 | — | 3 | 1 | no | — |
| 350 | #124 | — | 3 | 2 | no | — |
| 351 | #124 | — | 3 | 1 | no | — |
| 352 | #124 | — | 6 | 2 | no | — |
| 353 | #124 | — | 6 | 2 | no | — |
| 354 | #124 | — | 6 | 2 | no | — |
| 355 | #124 | — | 6 | 2 | no | — |
| 356 | #124 | — | 6 | 2 | no | — |
| 357 | #124 | — | 6 | 2 | no | — |
| 358 | #124 | C22×D3 | 1 | 2 | yes | — |
| 359 | #121 | — | 2 | 1 | no | — |
| 360 | #121 | — | 2 | 1 | no | — |
| 361 | #121 | — | 6 | 2 | no | — |
| 362 | #121 | — | 6 | 2 | no | — |
| 363 | #121 | — | 6 | 1 | no | — |
| 364 | #121 | — | 6 | 2 | no | — |
| 365 | #121 | — | 6 | 1 | no | — |
| 366 | #121 | — | 6 | 2 | no | — |
| 367 | #121 | — | 6 | 1 | no | — |
| 368 | #121 | — | 6 | 2 | no | — |
| 369 | #121 | — | 6 | 1 | no | — |
| 370 | #121 | — | 6 | 1 | no | — |
| 371 | #121 | — | 6 | 1 | no | — |
| 372 | #120 | — | 2 | 1 | no | — |
| 373 | #120 | — | 2 | 1 | no | — |
| 374 | #120 | — | 6 | 2 | no | — |
| 375 | #120 | — | 6 | 2 | no | — |
| 376 | #120 | — | 6 | 2 | no | — |
| 377 | #120 | — | 6 | 2 | no | — |
| 378 | #120 | — | 6 | 2 | no | — |
| 379 | #120 | — | 6 | 1 | no | — |
| 380 | #120 | — | 6 | 2 | no | — |
| 381 | #120 | — | 6 | 1 | no | — |
| 382 | C4×D4 | — | 6 | 2 | no | — |
| 383 | C4×D4 | — | 6 | 1 | no | — |
| 384 | C4×D4 | — | 6 | 1 | no | — |
| 385 | C4×D4 | — | 6 | 1 | no | — |
| 386 | C4×D4 | — | 6 | 1 | no | — |
| 387 | #117 | — | 3 | 1 | no | — |
| 388 | #117 | — | 6 | 2 | no | — |
| 389 | #117 | — | 6 | 1 | no | — |
| 390 | #117 | — | 6 | 2 | no | — |
| 391 | #117 | D12 | 1 | 1 | yes | characteristic |
| 392 | C2×C42 | — | 3 | 1 | no | — |
| 393 | #104 | — | 6 | 2 | no | — |
| 394 | #104 | — | 6 | 2 | no | — |
| 395 | #104 | — | 6 | 4 | no | — |
| 396 | #104 | — | 6 | 4 | no | — |
| 397 | #101 | — | 3 | 2 | no | — |
| 398 | #101 | C22×D3 | 1 | 2 | yes | — |
| 399 | #101 | C22×D3 | 1 | 2 | yes | — |
| 400 | #100 | — | 2 | 1 | no | — |
| 401 | #100 | — | 2 | 1 | no | — |
| 402 | #100 | — | 6 | 1 | no | — |
| 403 | C23×C3 | — | 2 | 2 | no | — |
| 404 | C23×C3 | — | 8 | 1 | no | — |
| 405 | C23×C3 | — | 8 | 2 | no | — |
| 406 | C23×C3 | #120 | 1 | 1 | yes | characteristic |
| 407 | C23×C3 | #120 | 1 | 1 | yes | characteristic |
| 408 | C23×C3 | #120 | 1 | 1 | yes | characteristic |
| 409 | C22×D3 | — | 2 | 2 | no | — |
| 410 | C22×D3 | — | 2 | 1 | no | — |
| 411 | C22×D3 | — | 4 | 1 | no | — |
| 412 | C22×D3 | — | 4 | 1 | no | — |
| 413 | C22×D3 | — | 4 | 1 | no | — |
| 414 | C22×D3 | — | 8 | 1 | no | — |
| 415 | C22×D3 | — | 8 | 2 | no | — |
| 416 | C22×D3 | — | 8 | 2 | no | — |
| 417 | C22×D3 | — | 8 | 2 | no | — |
| 418 | C22×D3 | — | 8 | 2 | no | — |
| 419 | C3×Q8 | — | 4 | 1 | no | — |
| 420 | C3×D4 | — | 4 | 1 | no | — |
| 421 | C3×D4 | — | 4 | 1 | no | — |
| 422 | C3×D4 | — | 4 | 1 | no | — |
| 423 | C3×D4 | — | 4 | 2 | no | — |
| 424 | C3×D4 | — | 4 | 1 | no | — |
| 425 | C3×D4 | — | 4 | 1 | no | — |
| 426 | C3×D4 | — | 8 | 2 | no | — |
| 427 | C3×D4 | — | 8 | 2 | no | — |
| 428 | C2×C3×C4 | — | 2 | 1 | no | — |
| 429 | C2×C3×C4 | — | 2 | 1 | no | — |
| 430 | C2×C3×C4 | — | 2 | 1 | no | — |
| 431 | C2×C3×C4 | — | 2 | 1 | no | — |
| 432 | C2×C3×C4 | — | 2 | 1 | no | — |
| 433 | C2×C3×C4 | — | 2 | 1 | no | — |
| 434 | C2×C3×C4 | — | 2 | 2 | no | — |
| 435 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 436 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 437 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 438 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 439 | #67 | — | 4 | 2 | no | — |
| 440 | #67 | — | 4 | 4 | no | — |
| 441 | #67 | — | 4 | 2 | no | — |
| 442 | #67 | — | 4 | 2 | no | — |
| 443 | #67 | — | 4 | 2 | no | — |
| 444 | #67 | — | 4 | 2 | no | — |
| 445 | #67 | — | 4 | 2 | no | — |
| 446 | #67 | — | 8 | 1 | no | — |
| 447 | #67 | — | 8 | 2 | no | — |
| 448 | #67 | — | 8 | 2 | no | — |
| 449 | #67 | — | 8 | 2 | no | — |
| 450 | #67 | — | 8 | 2 | no | — |
| 451 | #67 | — | 8 | 2 | no | — |
| 452 | C2×Dic3 | — | 2 | 1 | no | — |
| 453 | C2×Dic3 | — | 2 | 1 | no | — |
| 454 | C2×Dic3 | — | 2 | 2 | no | — |
| 455 | C2×Dic3 | — | 2 | 1 | no | — |
| 456 | C2×Dic3 | — | 4 | 2 | no | — |
| 457 | C2×Dic3 | — | 4 | 4 | no | — |
| 458 | C2×Dic3 | — | 4 | 1 | no | — |
| 459 | C2×Dic3 | — | 4 | 1 | no | — |
| 460 | C2×Dic3 | — | 4 | 1 | no | — |
| 461 | D12 | — | 2 | 2 | no | — |
| 462 | D12 | — | 2 | 2 | no | — |
| 463 | D12 | — | 2 | 2 | no | — |
| 464 | D12 | — | 4 | 2 | no | — |
| 465 | D12 | — | 4 | 1 | no | — |
| 466 | D12 | — | 4 | 1 | no | — |
| 467 | D12 | — | 4 | 1 | no | — |
| 468 | D12 | — | 4 | 1 | no | — |
| 469 | D12 | — | 8 | 2 | no | — |
| 470 | C4×D3 | — | 4 | 4 | no | — |
| 471 | C4×D3 | — | 4 | 2 | no | — |
| 472 | C4×D3 | — | 4 | 2 | no | — |
| 473 | C4×D3 | — | 4 | 2 | no | — |
| 474 | C4×D3 | — | 4 | 1 | no | — |
| 475 | C4×D3 | — | 4 | 1 | no | — |
| 476 | C4×D3 | — | 4 | 2 | no | — |
| 477 | Dic6 | — | 2 | 2 | no | — |
| 478 | Dic6 | — | 2 | 2 | no | — |
| 479 | Dic6 | — | 2 | 2 | no | — |
| 480 | Dic6 | — | 4 | 1 | no | — |
| 481 | Dic6 | — | 4 | 1 | no | — |
| 482 | Dic6 | — | 8 | 2 | no | — |
| 483 | C3×C8 | — | 4 | 2 | no | — |
| 484 | C3×C8 | — | 4 | 2 | no | — |
| 485 | C3⋊C8 | — | 4 | 2 | no | — |
| 486 | C24 | — | 2 | 1 | no | — |
| 487 | C24 | — | 6 | 2 | no | — |
| 488 | C24 | — | 6 | 1 | no | — |
| 489 | #41 | — | 4 | 1 | no | — |
| 490 | #41 | — | 4 | 1 | no | — |
| 491 | #41 | — | 6 | 2 | no | — |
| 492 | #41 | — | 6 | 2 | no | — |
| 493 | #41 | — | 6 | 2 | no | — |
| 494 | #41 | — | 6 | 2 | no | — |
| 495 | #41 | — | 6 | 2 | no | — |
| 496 | #41 | — | 6 | 2 | no | — |
| 497 | #41 | — | 12 | 1 | no | — |
| 498 | #41 | — | 12 | 1 | no | — |
| 499 | #41 | — | 12 | 1 | no | — |
| 500 | #41 | — | 12 | 1 | no | — |
| 501 | #41 | — | 12 | 1 | no | — |
| 502 | #41 | — | 12 | 2 | no | — |
| 503 | #41 | — | 12 | 2 | no | — |
| 504 | #41 | — | 12 | 2 | no | — |
| 505 | #41 | — | 12 | 2 | no | — |
| 506 | #41 | — | 12 | 1 | no | — |
| 507 | #41 | — | 24 | 4 | no | — |
| 508 | C2×Q8 | — | 3 | 1 | no | — |
| 509 | C2×Q8 | — | 6 | 2 | no | — |
| 510 | C2×Q8 | — | 6 | 1 | no | — |
| 511 | C2×Q8 | — | 6 | 1 | no | — |
| 512 | C2×Q8 | — | 6 | 1 | no | — |
| 513 | C2×Q8 | — | 12 | 2 | no | — |
| 514 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 515 | C2×D4 | — | 2 | 2 | no | — |
| 516 | C2×D4 | — | 2 | 2 | no | — |
| 517 | C2×D4 | — | 2 | 1 | no | — |
| 518 | C2×D4 | — | 3 | 1 | no | — |
| 519 | C2×D4 | — | 3 | 2 | no | — |
| 520 | C2×D4 | — | 4 | 1 | no | — |
| 521 | C2×D4 | — | 4 | 1 | no | — |
| 522 | C2×D4 | — | 6 | 1 | no | — |
| 523 | C2×D4 | — | 6 | 1 | no | — |
| 524 | C2×D4 | — | 6 | 1 | no | — |
| 525 | C2×D4 | — | 6 | 2 | no | — |
| 526 | C2×D4 | — | 6 | 2 | no | — |
| 527 | C2×D4 | — | 6 | 1 | no | — |
| 528 | C2×D4 | — | 6 | 1 | no | — |
| 529 | C2×D4 | — | 6 | 2 | no | — |
| 530 | C2×D4 | — | 6 | 2 | no | — |
| 531 | C2×D4 | — | 6 | 2 | no | — |
| 532 | C2×D4 | — | 6 | 2 | no | — |
| 533 | C2×D4 | — | 6 | 2 | no | — |
| 534 | C2×D4 | — | 6 | 1 | no | — |
| 535 | C2×D4 | — | 6 | 1 | no | — |
| 536 | C2×D4 | — | 12 | 1 | no | — |
| 537 | C2×D4 | — | 12 | 1 | no | — |
| 538 | C2×D4 | — | 12 | 2 | no | — |
| 539 | C2×D4 | — | 12 | 2 | no | — |
| 540 | C2×D4 | — | 12 | 2 | no | — |
| 541 | C2×D4 | — | 12 | 1 | no | — |
| 542 | C2×D4 | — | 12 | 1 | no | — |
| 543 | C2×D4 | — | 12 | 1 | no | — |
| 544 | C2×D4 | — | 24 | 1 | no | — |
| 545 | C2×D4 | — | 24 | 1 | no | — |
| 546 | C2×D4 | — | 24 | 4 | no | — |
| 547 | C2×D4 | — | 24 | 4 | no | — |
| 548 | C2×D4 | C2×D12 | 1 | 2 | yes | — |
| 549 | C2×D4 | C2×D12 | 1 | 1 | yes | characteristic |
| 550 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 551 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 552 | C22×C4 | — | 6 | 2 | no | — |
| 553 | C22×C4 | — | 6 | 2 | no | — |
| 554 | C22×C4 | — | 6 | 1 | no | — |
| 555 | C22×C4 | — | 6 | 1 | no | — |
| 556 | C22×C4 | — | 12 | 1 | no | — |
| 557 | C22×C4 | — | 12 | 1 | no | — |
| 558 | C22×C4 | — | 12 | 1 | no | — |
| 559 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 560 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 561 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 562 | Q16 | — | 12 | 2 | no | — |
| 563 | SD16 | — | 12 | 2 | no | — |
| 564 | SD16 | — | 12 | 4 | no | — |
| 565 | SD16 | — | 12 | 2 | no | — |
| 566 | SD16 | — | 12 | 4 | no | — |
| 567 | D8 | — | 12 | 4 | no | — |
| 568 | D8 | — | 12 | 2 | no | — |
| 569 | D8 | — | 12 | 4 | no | — |
| 570 | M16 | — | 2 | 2 | no | — |
| 571 | M16 | — | 2 | 2 | no | — |
| 572 | M16 | — | 4 | 1 | no | — |
| 573 | M16 | — | 4 | 1 | no | — |
| 574 | M16 | — | 6 | 2 | no | — |
| 575 | M16 | — | 12 | 1 | no | — |
| 576 | C2×C8 | — | 4 | 1 | no | — |
| 577 | C2×C8 | — | 4 | 1 | no | — |
| 578 | C2×C8 | — | 12 | 1 | no | — |
| 579 | C4⋊C4 | — | 2 | 1 | no | — |
| 580 | C4⋊C4 | — | 6 | 2 | no | — |
| 581 | C4⋊C4 | — | 6 | 1 | no | — |
| 582 | C4⋊C4 | — | 6 | 1 | no | — |
| 583 | C4⋊C4 | — | 6 | 1 | no | — |
| 584 | C22⋊C4 | — | 2 | 1 | no | — |
| 585 | C22⋊C4 | — | 2 | 2 | no | — |
| 586 | C22⋊C4 | — | 2 | 2 | no | — |
| 587 | C22⋊C4 | — | 6 | 2 | no | — |
| 588 | C22⋊C4 | — | 6 | 2 | no | — |
| 589 | C22⋊C4 | — | 6 | 2 | no | — |
| 590 | C22⋊C4 | — | 6 | 2 | no | — |
| 591 | C22⋊C4 | — | 6 | 2 | no | — |
| 592 | C22⋊C4 | — | 6 | 1 | no | — |
| 593 | C22⋊C4 | — | 6 | 1 | no | — |
| 594 | C22⋊C4 | — | 6 | 1 | no | — |
| 595 | C22⋊C4 | — | 6 | 2 | no | — |
| 596 | C22⋊C4 | — | 6 | 1 | no | — |
| 597 | C22⋊C4 | — | 6 | 1 | no | — |
| 598 | C22⋊C4 | — | 6 | 2 | no | — |
| 599 | C42 | — | 3 | 1 | no | — |
| 600 | C42 | — | 3 | 1 | no | — |
| 601 | C42 | — | 3 | 2 | no | — |
| 602 | C42 | — | 6 | 2 | no | — |
| 603 | C42 | — | 6 | 1 | no | — |
| 604 | C42 | C2×D12 | 1 | 2 | yes | — |
| 605 | C22×C3 | — | 2 | 1 | no | — |
| 606 | C22×C3 | — | 2 | 1 | no | — |
| 607 | C22×C3 | — | 2 | 1 | no | — |
| 608 | C22×C3 | — | 4 | 1 | no | — |
| 609 | C22×C3 | — | 4 | 1 | no | — |
| 610 | C22×C3 | — | 4 | 1 | no | — |
| 611 | C22×C3 | — | 4 | 2 | no | — |
| 612 | C22×C3 | — | 4 | 2 | no | — |
| 613 | C22×C3 | — | 4 | 2 | no | — |
| 614 | C22×C3 | — | 16 | 2 | no | — |
| 615 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 616 | C2×D3 | — | 4 | 2 | no | — |
| 617 | C2×D3 | — | 4 | 1 | no | — |
| 618 | C2×D3 | — | 4 | 2 | no | — |
| 619 | C2×D3 | — | 4 | 1 | no | — |
| 620 | C2×D3 | — | 4 | 2 | no | — |
| 621 | C2×D3 | — | 4 | 1 | no | — |
| 622 | C2×D3 | — | 4 | 2 | no | — |
| 623 | C2×D3 | — | 16 | 1 | no | — |
| 624 | C2×D3 | — | 16 | 1 | no | — |
| 625 | C2×D3 | — | 16 | 1 | no | — |
| 626 | C2×D3 | — | 16 | 2 | no | — |
| 627 | C2×D3 | — | 16 | 4 | no | — |
| 628 | C3×C4 | — | 2 | 1 | no | — |
| 629 | C3×C4 | — | 2 | 1 | no | — |
| 630 | C3×C4 | — | 2 | 1 | no | — |
| 631 | C3×C4 | — | 4 | 2 | no | — |
| 632 | C3×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 633 | C3×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 634 | Dic3 | — | 2 | 2 | no | — |
| 635 | Dic3 | — | 4 | 1 | no | — |
| 636 | Dic3 | — | 4 | 2 | no | — |
| 637 | Dic3 | — | 4 | 2 | no | — |
| 638 | Dic3 | — | 4 | 1 | no | — |
| 639 | C23 | — | 2 | 2 | no | — |
| 640 | C23 | — | 6 | 2 | no | — |
| 641 | C23 | — | 6 | 1 | no | — |
| 642 | C23 | — | 8 | 1 | no | — |
| 643 | C23 | — | 8 | 2 | no | — |
| 644 | C23 | — | 12 | 1 | no | — |
| 645 | C23 | — | 12 | 1 | no | — |
| 646 | C23 | — | 12 | 1 | no | — |
| 647 | C23 | — | 24 | 1 | no | — |
| 648 | C23 | — | 24 | 2 | no | — |
| 649 | C23 | — | 24 | 2 | no | — |
| 650 | C23 | — | 24 | 2 | no | — |
| 651 | C23 | — | 24 | 2 | no | — |
| 652 | C23 | #882 | 1 | 1 | yes | characteristic |
| 653 | C23 | #882 | 1 | 1 | yes | characteristic |
| 654 | C23 | #882 | 1 | 1 | yes | characteristic |
| 655 | Q8 | — | 4 | 1 | no | — |
| 656 | Q8 | — | 6 | 2 | no | — |
| 657 | Q8 | — | 6 | 2 | no | — |
| 658 | Q8 | — | 6 | 2 | no | — |
| 659 | Q8 | — | 12 | 1 | no | — |
| 660 | Q8 | — | 12 | 1 | no | — |
| 661 | Q8 | — | 24 | 2 | no | — |
| 662 | D4 | — | 4 | 1 | no | — |
| 663 | D4 | — | 4 | 1 | no | — |
| 664 | D4 | — | 4 | 1 | no | — |
| 665 | D4 | — | 4 | 2 | no | — |
| 666 | D4 | — | 4 | 1 | no | — |
| 667 | D4 | — | 4 | 1 | no | — |
| 668 | D4 | — | 6 | 2 | no | — |
| 669 | D4 | — | 6 | 2 | no | — |
| 670 | D4 | — | 6 | 2 | no | — |
| 671 | D4 | — | 8 | 2 | no | — |
| 672 | D4 | — | 8 | 2 | no | — |
| 673 | D4 | — | 12 | 2 | no | — |
| 674 | D4 | — | 12 | 1 | no | — |
| 675 | D4 | — | 12 | 2 | no | — |
| 676 | D4 | — | 12 | 2 | no | — |
| 677 | D4 | — | 12 | 4 | no | — |
| 678 | D4 | — | 12 | 2 | no | — |
| 679 | D4 | — | 12 | 2 | no | — |
| 680 | D4 | — | 12 | 2 | no | — |
| 681 | D4 | — | 12 | 2 | no | — |
| 682 | D4 | — | 12 | 1 | no | — |
| 683 | D4 | — | 12 | 1 | no | — |
| 684 | D4 | — | 12 | 1 | no | — |
| 685 | D4 | — | 24 | 2 | no | — |
| 686 | D4 | — | 24 | 1 | no | — |
| 687 | D4 | — | 24 | 2 | no | — |
| 688 | D4 | — | 24 | 2 | no | — |
| 689 | D4 | — | 24 | 2 | no | — |
| 690 | D4 | — | 24 | 2 | no | — |
| 691 | D4 | — | 24 | 2 | no | — |
| 692 | C2×C4 | — | 2 | 1 | no | — |
| 693 | C2×C4 | — | 2 | 1 | no | — |
| 694 | C2×C4 | — | 2 | 1 | no | — |
| 695 | C2×C4 | — | 2 | 1 | no | — |
| 696 | C2×C4 | — | 2 | 1 | no | — |
| 697 | C2×C4 | — | 2 | 1 | no | — |
| 698 | C2×C4 | — | 2 | 2 | no | — |
| 699 | C2×C4 | — | 6 | 1 | no | — |
| 700 | C2×C4 | — | 6 | 1 | no | — |
| 701 | C2×C4 | — | 6 | 2 | no | — |
| 702 | C2×C4 | — | 6 | 1 | no | — |
| 703 | C2×C4 | — | 12 | 2 | no | — |
| 704 | C2×C4 | — | 12 | 2 | no | — |
| 705 | C2×C4 | — | 12 | 2 | no | — |
| 706 | C2×C4 | — | 12 | 4 | no | — |
| 707 | C2×C4 | — | 12 | 4 | no | — |
| 708 | C2×C4 | — | 12 | 2 | no | — |
| 709 | C2×C4 | — | 12 | 1 | no | — |
| 710 | C2×C4 | — | 12 | 1 | no | — |
| 711 | C2×C4 | — | 12 | 1 | no | — |
| 712 | C2×C4 | — | 12 | 1 | no | — |
| 713 | C2×C4 | — | 12 | 1 | no | — |
| 714 | C2×C4 | — | 12 | 2 | no | — |
| 715 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 716 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 717 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 718 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 719 | C8 | — | 4 | 2 | no | — |
| 720 | C8 | — | 4 | 2 | no | — |
| 721 | C8 | — | 12 | 2 | no | — |
| 722 | C2×C3 | — | 2 | 1 | no | — |
| 723 | C2×C3 | — | 4 | 1 | no | — |
| 724 | C2×C3 | — | 4 | 1 | no | — |
| 725 | C2×C3 | — | 4 | 1 | no | — |
| 726 | C2×C3 | — | 8 | 2 | no | — |
| 727 | C2×C3 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 728 | D3 | — | 8 | 2 | no | — |
| 729 | D3 | — | 8 | 1 | no | — |
| 730 | D3 | — | 8 | 2 | no | — |
| 731 | C22 | — | 2 | 1 | no | — |
| 732 | C22 | — | 2 | 1 | no | — |
| 733 | C22 | — | 2 | 1 | no | — |
| 734 | C22 | — | 4 | 1 | no | — |
| 735 | C22 | — | 4 | 1 | no | — |
| 736 | C22 | — | 4 | 1 | no | — |
| 737 | C22 | — | 4 | 2 | no | — |
| 738 | C22 | — | 4 | 2 | no | — |
| 739 | C22 | — | 4 | 2 | no | — |
| 740 | C22 | — | 12 | 2 | no | — |
| 741 | C22 | — | 12 | 1 | no | — |
| 742 | C22 | — | 12 | 2 | no | — |
| 743 | C22 | — | 12 | 1 | no | — |
| 744 | C22 | — | 12 | 2 | no | — |
| 745 | C22 | — | 12 | 1 | no | — |
| 746 | C22 | — | 12 | 2 | no | — |
| 747 | C22 | — | 16 | 2 | no | — |
| 748 | C22 | — | 48 | 1 | no | — |
| 749 | C22 | — | 48 | 1 | no | — |
| 750 | C22 | — | 48 | 1 | no | — |
| 751 | C22 | — | 48 | 2 | no | — |
| 752 | C22 | — | 48 | 4 | no | — |
| 753 | C22 | C2×#882 | 1 | 1 | yes | characteristic |
| 754 | C4 | — | 2 | 1 | no | — |
| 755 | C4 | — | 2 | 1 | no | — |
| 756 | C4 | — | 2 | 1 | no | — |
| 757 | C4 | — | 4 | 2 | no | — |
| 758 | C4 | — | 6 | 2 | no | — |
| 759 | C4 | — | 12 | 2 | no | — |
| 760 | C4 | — | 12 | 1 | no | — |
| 761 | C4 | — | 12 | 1 | no | — |
| 762 | C4 | — | 12 | 2 | no | — |
| 763 | C4 | #4741 | 1 | 1 | yes | characteristic |
| 764 | C4 | #4741 | 1 | 1 | yes | characteristic |
| 765 | C3 | #33570 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 766 | C2 | — | 2 | 1 | no | — |
| 767 | C2 | — | 4 | 1 | no | — |
| 768 | C2 | — | 4 | 1 | no | — |
| 769 | C2 | — | 4 | 1 | no | — |
| 770 | C2 | — | 8 | 2 | no | — |
| 771 | C2 | — | 24 | 2 | no | — |
| 772 | C2 | — | 24 | 1 | no | — |
| 773 | C2 | — | 24 | 2 | no | — |
| 774 | C2 | C2×#4741 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86326 | C2 | semidirect |
| 2. #83395 | C2 | semidirect |
| 3. #78717 | C2 | semidirect |
| 4. #78716 | C2 | semidirect |
| 5. C3×#2134 | C2 | semidirect |
| 6. #70149 | C2 | semidirect |
| 7. #70148 | C2 | semidirect |
| 8. #69161 | C2 | semidirect |
| 9. #69160 | C2 | semidirect |
| 11. #5964 | C22 | semidirect |
| 20. #5683 | C22 | semidirect |
| 21. #5670 | C22 | semidirect |
| 30. C3×#413 | C22 | semidirect |
| 31. C3×#413 | C22 | semidirect |
| 32. #5237 | C22 | semidirect |
| 36. #5062 | C22 | semidirect |
| 38. #4753 | C22 | semidirect |
| 39. #4753 | C22 | semidirect |
| 40. #4752 | C22 | semidirect |
| 44. C3×#355 | C22 | semidirect |
| 45. #4478 | C22 | semidirect |
| 46. #4477 | C22 | semidirect |
| 47. #4477 | C22 | semidirect |
| 55. #2134 | D3 | semidirect |
| 183. #413 | C2×D3 | semidirect |
| 184. #413 | C2×D3 | semidirect |
| 188. #355 | C2×D3 | semidirect |
| 765. C3 | #33570 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86326 | 2 |
| #83395 | 2 |
| #78717 | 2 |
| #78716 | 2 |
| C3×#2134 | 2 |
| #70149 | 2 |
| #70148 | 2 |
| #69161 | 2 |
| #69160 | 2 |
| #33570 | 3 |