Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1060 conjugacy classes of subgroups.
The subgroup lattice has 844 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #85869 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #79216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #79208 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #76453 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#1856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71647 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70681 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70667 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #70081 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #70066 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #69665 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #68771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #68755 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68754 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #24084 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C3×#518 | C22 | 1 | 1 | yes | characteristic |
| 18 | #5805 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#938 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×D3×M16 | C22 | 1 | 1 | yes | characteristic |
| 21 | #5563 | — | 2 | 1 | no | — |
| 22 | #5562 | — | 2 | 1 | no | — |
| 23 | #5561 | — | 2 | 1 | no | — |
| 24 | #5558 | — | 2 | 1 | no | — |
| 25 | #5558 | — | 2 | 1 | no | — |
| 26 | #5557 | — | 2 | 1 | no | — |
| 27 | #5551 | — | 2 | 1 | no | — |
| 28 | #5548 | — | 2 | 1 | no | — |
| 29 | #5524 | C22 | 1 | 1 | yes | characteristic |
| 30 | #5523 | C22 | 1 | 1 | yes | characteristic |
| 31 | D3×#117 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5519 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#892 | C22 | 1 | 1 | yes | characteristic |
| 34 | #5495 | — | 2 | 2 | no | — |
| 35 | #5490 | — | 2 | 2 | no | — |
| 36 | C3×#428 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×#428 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C3×#100 | C22 | 1 | 1 | yes | characteristic |
| 39 | C3×#390 | C22 | 1 | 1 | yes | characteristic |
| 40 | #5221 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#833 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#825 | C22 | 1 | 1 | yes | characteristic |
| 43 | #5133 | C22 | 1 | 1 | yes | characteristic |
| 44 | #5126 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5121 | C22 | 1 | 1 | yes | characteristic |
| 46 | #4995 | C22 | 1 | 1 | yes | characteristic |
| 47 | #4995 | C22 | 1 | 1 | yes | characteristic |
| 48 | #4977 | C22 | 1 | 1 | yes | characteristic |
| 49 | #4966 | C22 | 1 | 1 | yes | characteristic |
| 50 | #4964 | C22 | 1 | 1 | yes | characteristic |
| 51 | #4961 | — | 2 | 2 | no | — |
| 52 | #4951 | — | 2 | 2 | no | — |
| 53 | C4×(C2×D3)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 54 | #4935 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#805 | C22 | 1 | 1 | yes | characteristic |
| 56 | #4888 | — | 2 | 1 | no | — |
| 57 | #4885 | — | 2 | 1 | no | — |
| 58 | #4881 | — | 2 | 1 | no | — |
| 59 | #4880 | — | 2 | 1 | no | — |
| 60 | #4868 | — | 2 | 1 | no | — |
| 61 | #4866 | — | 2 | 1 | no | — |
| 62 | #4861 | — | 2 | 1 | no | — |
| 63 | #4860 | — | 2 | 1 | no | — |
| 64 | C3×#339 | C22 | 1 | 1 | yes | characteristic |
| 65 | C3×#339 | C22 | 1 | 1 | yes | characteristic |
| 66 | #4555 | C22 | 1 | 1 | yes | characteristic |
| 67 | #4554 | C22 | 1 | 1 | yes | characteristic |
| 68 | #4554 | C22 | 1 | 1 | yes | characteristic |
| 69 | #4532 | C22 | 1 | 1 | yes | characteristic |
| 70 | #4532 | C22 | 1 | 1 | yes | characteristic |
| 71 | #4523 | C22 | 1 | 1 | yes | characteristic |
| 72 | #3494 | — | 3 | 1 | no | — |
| 73 | #3093 | — | 3 | 1 | no | — |
| 74 | #2911 | — | 3 | 1 | no | — |
| 75 | #2500 | — | 3 | 1 | no | — |
| 76 | #2061 | — | 3 | 1 | no | — |
| 77 | #2060 | — | 3 | 1 | no | — |
| 78 | #2037 | — | 3 | 1 | no | — |
| 79 | #2037 | — | 3 | 1 | no | — |
| 80 | #1900 | — | 3 | 1 | no | — |
| 81 | #1871 | — | 3 | 1 | no | — |
| 82 | #1860 | — | 3 | 1 | no | — |
| 83 | #1859 | — | 3 | 1 | no | — |
| 84 | #1856 | — | 3 | 1 | no | — |
| 85 | #1856 | D3 | 1 | 1 | yes | characteristic, complemented |
| 86 | #1826 | — | 3 | 1 | no | — |
| 87 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 88 | C22×#67 | D4 | 1 | 2 | yes | — |
| 89 | C2×#235 | — | 2 | 2 | no | — |
| 90 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 94 | C3×C4×D4 | — | 2 | 1 | no | — |
| 95 | C3×C4×D4 | — | 2 | 1 | no | — |
| 96 | C3×C4×D4 | — | 2 | 1 | no | — |
| 97 | C3×C4×D4 | — | 2 | 1 | no | — |
| 98 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 99 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×C3×C22⋊C4 | — | 2 | 2 | no | — |
| 102 | C2×C3×C22⋊C4 | — | 2 | 2 | no | — |
| 103 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 104 | #953 | — | 2 | 2 | no | — |
| 105 | C2×#217 | — | 2 | 2 | no | — |
| 106 | C2×#217 | D4 | 1 | 2 | yes | — |
| 107 | #940 | — | 2 | 1 | no | — |
| 108 | #938 | — | 2 | 1 | no | — |
| 109 | #938 | — | 2 | 1 | no | — |
| 110 | #938 | — | 2 | 1 | no | — |
| 111 | #938 | — | 2 | 1 | no | — |
| 112 | #938 | — | 2 | 1 | no | — |
| 113 | #938 | — | 2 | 1 | no | — |
| 114 | #936 | — | 2 | 1 | no | — |
| 115 | #930 | — | 2 | 2 | no | — |
| 116 | #929 | — | 2 | 2 | no | — |
| 117 | #929 | — | 2 | 2 | no | — |
| 118 | C4×#67 | — | 2 | 2 | no | — |
| 119 | C4×#67 | — | 2 | 2 | no | — |
| 120 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 121 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 122 | #926 | — | 2 | 2 | no | — |
| 123 | #926 | C23 | 1 | 1 | yes | characteristic |
| 124 | C2×C4⋊Dic3 | — | 2 | 2 | no | — |
| 125 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 127 | #924 | — | 2 | 2 | no | — |
| 128 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 129 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 130 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 131 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 132 | D3×M16 | — | 2 | 2 | no | — |
| 133 | D3×M16 | — | 2 | 2 | no | — |
| 134 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 135 | C2×D3×C8 | — | 2 | 1 | no | — |
| 136 | #897 | D4 | 1 | 1 | yes | characteristic |
| 137 | #897 | D4 | 1 | 1 | yes | characteristic |
| 138 | #895 | D4 | 1 | 1 | yes | characteristic |
| 139 | #895 | D4 | 1 | 1 | yes | characteristic |
| 140 | #892 | — | 2 | 1 | no | — |
| 141 | #892 | — | 2 | 1 | no | — |
| 142 | #892 | — | 2 | 1 | no | — |
| 143 | #892 | — | 2 | 1 | no | — |
| 144 | #892 | — | 2 | 1 | no | — |
| 145 | #892 | D4 | 1 | 1 | yes | characteristic |
| 146 | #892 | D4 | 1 | 1 | yes | characteristic |
| 147 | D3×C4⋊C4 | — | 2 | 1 | no | — |
| 148 | D3×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 149 | D3×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 150 | #890 | — | 2 | 1 | no | — |
| 151 | #888 | — | 2 | 1 | no | — |
| 152 | #886 | — | 2 | 1 | no | — |
| 153 | #885 | — | 2 | 2 | no | — |
| 154 | #885 | — | 2 | 2 | no | — |
| 155 | #884 | — | 2 | 2 | no | — |
| 156 | #884 | — | 2 | 2 | no | — |
| 157 | #883 | — | 2 | 2 | no | — |
| 158 | #883 | — | 2 | 2 | no | — |
| 159 | #882 | — | 2 | 1 | no | — |
| 160 | #67⋊C4 | — | 2 | 2 | no | — |
| 161 | D3×C22⋊C4 | — | 2 | 1 | no | — |
| 162 | #879 | — | 2 | 2 | no | — |
| 163 | #879 | — | 2 | 2 | no | — |
| 164 | #878 | — | 2 | 2 | no | — |
| 165 | #877 | — | 2 | 1 | no | — |
| 166 | C4×D12 | — | 2 | 1 | no | — |
| 167 | C4×D12 | — | 2 | 1 | no | — |
| 168 | C4×D12 | — | 2 | 1 | no | — |
| 169 | #872 | — | 2 | 1 | no | — |
| 170 | C42×D3 | — | 2 | 1 | no | — |
| 171 | #870 | — | 2 | 1 | no | — |
| 172 | #869 | — | 2 | 1 | no | — |
| 173 | C4×Dic6 | — | 2 | 1 | no | — |
| 174 | C3×#107 | — | 2 | 1 | no | — |
| 175 | C3×#107 | — | 2 | 1 | no | — |
| 176 | C3×#106 | — | 2 | 1 | no | — |
| 177 | C3×#106 | — | 2 | 1 | no | — |
| 178 | C3×#100 | — | 2 | 2 | no | — |
| 179 | #833 | — | 2 | 2 | no | — |
| 180 | C3⋊#95 | — | 2 | 1 | no | — |
| 181 | C3⋊#95 | — | 2 | 2 | no | — |
| 182 | #825 | — | 2 | 2 | no | — |
| 183 | #821 | — | 2 | 1 | no | — |
| 184 | (C2×D3)⋊C8 | — | 2 | 1 | no | — |
| 185 | (C2×D3)⋊C8 | — | 2 | 1 | no | — |
| 186 | #818 | — | 2 | 1 | no | — |
| 187 | #817 | — | 2 | 1 | no | — |
| 188 | #816 | — | 2 | 1 | no | — |
| 189 | #810 | — | 2 | 1 | no | — |
| 190 | #809 | — | 2 | 1 | no | — |
| 191 | #808 | — | 2 | 1 | no | — |
| 192 | #808 | — | 2 | 1 | no | — |
| 193 | #808 | — | 2 | 1 | no | — |
| 194 | #807 | — | 2 | 1 | no | — |
| 195 | #807 | — | 2 | 1 | no | — |
| 196 | #807 | — | 2 | 1 | no | — |
| 197 | #805 | — | 2 | 2 | no | — |
| 198 | C22×M16 | — | 3 | 1 | no | — |
| 199 | #555 | — | 6 | 1 | no | — |
| 200 | #553 | — | 6 | 1 | no | — |
| 201 | #553 | — | 6 | 1 | no | — |
| 202 | #551 | — | 6 | 2 | no | — |
| 203 | #547 | — | 6 | 1 | no | — |
| 204 | #546 | — | 6 | 2 | no | — |
| 205 | #544 | — | 3 | 1 | no | — |
| 206 | #542 | — | 6 | 1 | no | — |
| 207 | #540 | — | 6 | 1 | no | — |
| 208 | #535 | — | 3 | 1 | no | — |
| 209 | #532 | — | 6 | 1 | no | — |
| 210 | #529 | — | 6 | 1 | no | — |
| 211 | #525 | — | 3 | 1 | no | — |
| 212 | C2×#121 | — | 3 | 1 | no | — |
| 213 | #520 | — | 3 | 1 | no | — |
| 214 | #518 | C2×D3 | 1 | 1 | yes | characteristic |
| 215 | C2×#117 | — | 3 | 1 | no | — |
| 216 | C2×#117 | — | 3 | 1 | no | — |
| 217 | #485 | — | 6 | 1 | no | — |
| 218 | #485 | — | 6 | 1 | no | — |
| 219 | #482 | — | 6 | 1 | no | — |
| 220 | #482 | — | 6 | 1 | no | — |
| 221 | #428 | — | 3 | 1 | no | — |
| 222 | #428 | — | 3 | 1 | no | — |
| 223 | #428 | — | 3 | 1 | no | — |
| 224 | #428 | — | 3 | 1 | no | — |
| 225 | #428 | — | 6 | 1 | no | — |
| 226 | #428 | — | 6 | 1 | no | — |
| 227 | #428 | C2×D3 | 1 | 1 | yes | characteristic |
| 228 | #428 | C2×D3 | 1 | 1 | yes | characteristic |
| 229 | #427 | — | 6 | 1 | no | — |
| 230 | #427 | — | 6 | 1 | no | — |
| 231 | C2×#104 | — | 3 | 1 | no | — |
| 232 | C2×#104 | — | 3 | 1 | no | — |
| 233 | #417 | — | 3 | 1 | no | — |
| 234 | #417 | — | 3 | 1 | no | — |
| 235 | C2×#100 | — | 3 | 1 | no | — |
| 236 | C2×#100 | C2×D3 | 1 | 1 | yes | characteristic |
| 237 | #407 | — | 3 | 1 | no | — |
| 238 | #394 | — | 6 | 2 | no | — |
| 239 | #390 | — | 3 | 1 | no | — |
| 240 | #390 | C2×D3 | 1 | 1 | yes | characteristic |
| 241 | #388 | — | 6 | 2 | no | — |
| 242 | #384 | — | 3 | 1 | no | — |
| 243 | #382 | — | 3 | 1 | no | — |
| 244 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 245 | #343 | — | 3 | 1 | no | — |
| 246 | #343 | — | 3 | 1 | no | — |
| 247 | #339 | — | 3 | 1 | no | — |
| 248 | #339 | — | 3 | 1 | no | — |
| 249 | #339 | — | 3 | 1 | no | — |
| 250 | #339 | — | 3 | 1 | no | — |
| 251 | #339 | C2×D3 | 1 | 1 | yes | characteristic |
| 252 | #339 | C2×D3 | 1 | 1 | yes | characteristic |
| 253 | C24×C3 | C2×D4 | 1 | 2 | yes | — |
| 254 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×C3×D4 | — | 2 | 1 | no | — |
| 256 | C2×C3×D4 | — | 2 | 1 | no | — |
| 257 | C2×C3×D4 | — | 2 | 1 | no | — |
| 258 | C2×C3×D4 | — | 2 | 1 | no | — |
| 259 | C2×C3×D4 | — | 2 | 1 | no | — |
| 260 | C2×C3×D4 | — | 2 | 1 | no | — |
| 261 | C22×C3×C4 | — | 2 | 1 | no | — |
| 262 | C22×C3×C4 | — | 2 | 2 | no | — |
| 263 | C22×C3×C4 | — | 2 | 2 | no | — |
| 264 | C22×C3×C4 | — | 2 | 1 | no | — |
| 265 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 266 | C2×#67 | — | 2 | 1 | no | — |
| 267 | C2×#67 | — | 2 | 2 | no | — |
| 268 | C2×#67 | — | 2 | 2 | no | — |
| 269 | C2×#67 | — | 2 | 2 | no | — |
| 270 | C2×#67 | — | 2 | 2 | no | — |
| 271 | C2×#67 | — | 8 | 2 | no | — |
| 272 | C22×Dic3 | — | 2 | 1 | no | — |
| 273 | C22×Dic3 | — | 2 | 1 | no | — |
| 274 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 276 | #235 | — | 2 | 1 | no | — |
| 277 | #235 | — | 2 | 1 | no | — |
| 278 | #235 | — | 2 | 1 | no | — |
| 279 | #235 | — | 2 | 1 | no | — |
| 280 | #235 | — | 8 | 4 | no | — |
| 281 | C2×D12 | — | 2 | 1 | no | — |
| 282 | C2×D12 | — | 2 | 1 | no | — |
| 283 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 284 | C2×C4×D3 | — | 2 | 1 | no | — |
| 285 | C2×C4×D3 | — | 2 | 1 | no | — |
| 286 | C2×C4×D3 | — | 2 | 1 | no | — |
| 287 | C2×C4×D3 | — | 2 | 1 | no | — |
| 288 | C2×C4×D3 | — | 2 | 1 | no | — |
| 289 | C2×C4×D3 | — | 2 | 1 | no | — |
| 290 | C2×C4×D3 | — | 2 | 2 | no | — |
| 291 | C2×C4×D3 | — | 2 | 1 | no | — |
| 292 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 295 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 296 | C2×Dic6 | — | 2 | 2 | no | — |
| 297 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C3×M16 | — | 2 | 1 | no | — |
| 299 | C3×M16 | — | 2 | 1 | no | — |
| 300 | C3×M16 | — | 2 | 1 | no | — |
| 301 | C3×M16 | #41 | 1 | 2 | yes | complemented |
| 302 | C2×C3×C8 | — | 2 | 1 | no | — |
| 303 | C2×C3×C8 | — | 2 | 1 | no | — |
| 304 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 305 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 306 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 308 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 309 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 310 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 311 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 312 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 313 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 314 | C3×C22⋊C4 | — | 4 | 4 | no | — |
| 315 | C3×C42 | — | 2 | 1 | no | — |
| 316 | C3×C42 | — | 2 | 1 | no | — |
| 317 | C3×C42 | — | 2 | 1 | no | — |
| 318 | C3×C42 | — | 2 | 1 | no | — |
| 319 | #217 | — | 2 | 2 | no | — |
| 320 | #217 | — | 2 | 2 | no | — |
| 321 | #217 | — | 2 | 1 | no | — |
| 322 | #217 | — | 2 | 2 | no | — |
| 323 | #217 | — | 2 | 2 | no | — |
| 324 | #217 | — | 8 | 2 | no | — |
| 325 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 326 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 327 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 328 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 329 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 330 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 331 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 332 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 333 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 334 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 335 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 336 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 337 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 338 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 339 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 340 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 341 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 342 | C4⋊Dic3 | — | 8 | 2 | no | — |
| 343 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 344 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 345 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 346 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 347 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 348 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 349 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 350 | C4×Dic3 | — | 2 | 2 | no | — |
| 351 | C4×Dic3 | — | 2 | 1 | no | — |
| 352 | C4×Dic3 | — | 2 | 1 | no | — |
| 353 | C4×Dic3 | — | 2 | 1 | no | — |
| 354 | C4×Dic3 | — | 2 | 1 | no | — |
| 355 | C4×Dic3 | — | 2 | 1 | no | — |
| 356 | C4×Dic3 | — | 4 | 1 | no | — |
| 357 | C4×Dic3 | — | 4 | 1 | no | — |
| 358 | #208 | — | 2 | 1 | no | — |
| 359 | #208 | — | 2 | 1 | no | — |
| 360 | #208 | — | 2 | 1 | no | — |
| 361 | #208 | #41 | 1 | 2 | yes | complemented |
| 362 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 363 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 364 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 365 | D3×C8 | — | 2 | 4 | no | — |
| 366 | C2×#41 | — | 3 | 1 | no | — |
| 367 | C2×#41 | — | 6 | 2 | no | — |
| 368 | C22×D4 | — | 3 | 2 | no | — |
| 369 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 370 | C23×C4 | — | 3 | 1 | no | — |
| 371 | C2×M16 | — | 3 | 1 | no | — |
| 372 | C2×M16 | — | 3 | 1 | no | — |
| 373 | C2×M16 | — | 6 | 1 | no | — |
| 374 | C2×M16 | — | 6 | 2 | no | — |
| 375 | C2×M16 | — | 6 | 2 | no | — |
| 376 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 377 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 378 | C22×C8 | — | 6 | 1 | no | — |
| 379 | C4⋊Q8 | — | 6 | 1 | no | — |
| 380 | C4⋊Q8 | — | 6 | 1 | no | — |
| 381 | #127 | — | 6 | 1 | no | — |
| 382 | #126 | — | 6 | 2 | no | — |
| 383 | #126 | — | 6 | 2 | no | — |
| 384 | #125 | — | 6 | 1 | no | — |
| 385 | #125 | — | 6 | 1 | no | — |
| 386 | #124 | — | 6 | 2 | no | — |
| 387 | #124 | — | 6 | 2 | no | — |
| 388 | #124 | — | 6 | 1 | no | — |
| 389 | #123 | — | 6 | 1 | no | — |
| 390 | #123 | — | 6 | 2 | no | — |
| 391 | #123 | — | 6 | 2 | no | — |
| 392 | #123 | — | 6 | 2 | no | — |
| 393 | #123 | — | 6 | 2 | no | — |
| 394 | C22⋊Q8 | — | 3 | 1 | no | — |
| 395 | C22⋊Q8 | — | 3 | 1 | no | — |
| 396 | C22⋊Q8 | — | 6 | 2 | no | — |
| 397 | C22⋊Q8 | — | 6 | 2 | no | — |
| 398 | #121 | — | 3 | 1 | no | — |
| 399 | #121 | — | 3 | 1 | no | — |
| 400 | #121 | — | 6 | 2 | no | — |
| 401 | #121 | — | 6 | 2 | no | — |
| 402 | #121 | — | 6 | 1 | no | — |
| 403 | #121 | — | 6 | 1 | no | — |
| 404 | #121 | — | 6 | 2 | no | — |
| 405 | #121 | — | 6 | 1 | no | — |
| 406 | #121 | — | 6 | 1 | no | — |
| 407 | #121 | — | 6 | 1 | no | — |
| 408 | #121 | — | 6 | 1 | no | — |
| 409 | #120 | — | 6 | 1 | no | — |
| 410 | #120 | — | 6 | 2 | no | — |
| 411 | C4×Q8 | — | 6 | 1 | no | — |
| 412 | C4×D4 | — | 2 | 1 | no | — |
| 413 | C4×D4 | — | 2 | 1 | no | — |
| 414 | C4×D4 | — | 2 | 1 | no | — |
| 415 | C4×D4 | — | 2 | 1 | no | — |
| 416 | C4×D4 | — | 6 | 1 | no | — |
| 417 | C4×D4 | — | 6 | 1 | no | — |
| 418 | C4×D4 | — | 6 | 1 | no | — |
| 419 | C4×D4 | — | 6 | 2 | no | — |
| 420 | C4×D4 | — | 6 | 2 | no | — |
| 421 | C4×D4 | — | 6 | 2 | no | — |
| 422 | #117 | — | 3 | 1 | no | — |
| 423 | #117 | — | 3 | 1 | no | — |
| 424 | #117 | — | 3 | 1 | no | — |
| 425 | #117 | — | 6 | 1 | no | — |
| 426 | #117 | — | 6 | 1 | no | — |
| 427 | #117 | — | 6 | 2 | no | — |
| 428 | #117 | — | 6 | 1 | no | — |
| 429 | #117 | — | 6 | 1 | no | — |
| 430 | #117 | — | 6 | 1 | no | — |
| 431 | #117 | — | 6 | 1 | no | — |
| 432 | #117 | — | 6 | 1 | no | — |
| 433 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 434 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 435 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 436 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 437 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 438 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 439 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 440 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 441 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 442 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 443 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 444 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 445 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 446 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 447 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 448 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 449 | C2×C42 | — | 3 | 1 | no | — |
| 450 | C2×C42 | — | 6 | 1 | no | — |
| 451 | C2×C42 | — | 6 | 1 | no | — |
| 452 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 453 | #107 | — | 2 | 1 | no | — |
| 454 | #107 | — | 2 | 1 | no | — |
| 455 | #107 | — | 6 | 1 | no | — |
| 456 | #107 | — | 6 | 1 | no | — |
| 457 | #107 | — | 6 | 1 | no | — |
| 458 | #107 | — | 6 | 1 | no | — |
| 459 | #106 | — | 2 | 1 | no | — |
| 460 | #106 | — | 2 | 1 | no | — |
| 461 | #106 | — | 6 | 1 | no | — |
| 462 | #106 | — | 6 | 1 | no | — |
| 463 | #106 | — | 6 | 1 | no | — |
| 464 | #106 | — | 6 | 1 | no | — |
| 465 | #104 | — | 6 | 2 | no | — |
| 466 | #104 | — | 6 | 2 | no | — |
| 467 | #103 | — | 6 | 1 | no | — |
| 468 | #103 | — | 6 | 1 | no | — |
| 469 | #102 | — | 6 | 1 | no | — |
| 470 | #102 | — | 6 | 1 | no | — |
| 471 | #100 | — | 2 | 2 | no | — |
| 472 | #100 | — | 6 | 2 | no | — |
| 473 | C22⋊C8 | — | 6 | 1 | no | — |
| 474 | C22⋊C8 | — | 6 | 1 | no | — |
| 475 | #95 | — | 6 | 1 | no | — |
| 476 | #95 | — | 6 | 2 | no | — |
| 477 | C23×C3 | — | 2 | 2 | no | — |
| 478 | C23×C3 | — | 2 | 2 | no | — |
| 479 | C23×C3 | — | 2 | 2 | no | — |
| 480 | C23×C3 | — | 4 | 2 | no | — |
| 481 | C23×C3 | — | 4 | 2 | no | — |
| 482 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 483 | C22×D3 | — | 2 | 1 | no | — |
| 484 | C22×D3 | — | 2 | 1 | no | — |
| 485 | C22×D3 | — | 2 | 1 | no | — |
| 486 | C22×D3 | — | 4 | 1 | no | — |
| 487 | C22×D3 | — | 4 | 1 | no | — |
| 488 | C22×D3 | #120 | 1 | 1 | yes | characteristic |
| 489 | C22×D3 | #120 | 1 | 1 | yes | characteristic |
| 490 | C3×D4 | — | 4 | 1 | no | — |
| 491 | C3×D4 | — | 4 | 1 | no | — |
| 492 | C3×D4 | — | 4 | 1 | no | — |
| 493 | C3×D4 | — | 4 | 1 | no | — |
| 494 | C2×C3×C4 | — | 2 | 2 | no | — |
| 495 | C2×C3×C4 | — | 2 | 1 | no | — |
| 496 | C2×C3×C4 | — | 2 | 1 | no | — |
| 497 | C2×C3×C4 | — | 2 | 1 | no | — |
| 498 | C2×C3×C4 | — | 2 | 1 | no | — |
| 499 | C2×C3×C4 | — | 4 | 1 | no | — |
| 500 | C2×C3×C4 | — | 4 | 1 | no | — |
| 501 | C2×C3×C4 | — | 4 | 2 | no | — |
| 502 | C2×C3×C4 | — | 4 | 1 | no | — |
| 503 | C2×C3×C4 | — | 8 | 2 | no | — |
| 504 | C2×C3×C4 | — | 8 | 2 | no | — |
| 505 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 506 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 507 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 508 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 509 | C2×C3×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 510 | C2×C3×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 511 | #67 | — | 4 | 4 | no | — |
| 512 | #67 | — | 4 | 1 | no | — |
| 513 | #67 | — | 4 | 1 | no | — |
| 514 | #67 | — | 8 | 2 | no | — |
| 515 | #67 | — | 8 | 2 | no | — |
| 516 | #67 | — | 8 | 2 | no | — |
| 517 | C2×Dic3 | — | 2 | 1 | no | — |
| 518 | C2×Dic3 | — | 2 | 1 | no | — |
| 519 | C2×Dic3 | — | 2 | 1 | no | — |
| 520 | C2×Dic3 | — | 2 | 1 | no | — |
| 521 | C2×Dic3 | — | 2 | 1 | no | — |
| 522 | C2×Dic3 | — | 2 | 2 | no | — |
| 523 | C2×Dic3 | — | 4 | 2 | no | — |
| 524 | C2×Dic3 | — | 4 | 2 | no | — |
| 525 | C2×Dic3 | — | 4 | 1 | no | — |
| 526 | C2×Dic3 | — | 4 | 1 | no | — |
| 527 | C2×Dic3 | — | 4 | 1 | no | — |
| 528 | C2×Dic3 | — | 4 | 1 | no | — |
| 529 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 530 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 531 | D12 | — | 2 | 1 | no | — |
| 532 | D12 | — | 2 | 1 | no | — |
| 533 | D12 | — | 4 | 2 | no | — |
| 534 | D12 | — | 8 | 1 | no | — |
| 535 | C4×D3 | — | 2 | 1 | no | — |
| 536 | C4×D3 | — | 2 | 1 | no | — |
| 537 | C4×D3 | — | 2 | 1 | no | — |
| 538 | C4×D3 | — | 2 | 1 | no | — |
| 539 | C4×D3 | — | 2 | 1 | no | — |
| 540 | C4×D3 | — | 2 | 1 | no | — |
| 541 | C4×D3 | — | 2 | 1 | no | — |
| 542 | C4×D3 | — | 2 | 1 | no | — |
| 543 | C4×D3 | — | 4 | 2 | no | — |
| 544 | C4×D3 | — | 4 | 1 | no | — |
| 545 | C4×D3 | — | 4 | 1 | no | — |
| 546 | C4×D3 | — | 8 | 1 | no | — |
| 547 | C4×D3 | — | 8 | 2 | no | — |
| 548 | Dic6 | — | 2 | 1 | no | — |
| 549 | Dic6 | — | 2 | 1 | no | — |
| 550 | Dic6 | — | 8 | 2 | no | — |
| 551 | C3×C8 | — | 2 | 2 | no | — |
| 552 | C3×C8 | — | 4 | 1 | no | — |
| 553 | C3⋊C8 | — | 2 | 2 | no | — |
| 554 | C3⋊C8 | — | 4 | 1 | no | — |
| 555 | C24 | — | 3 | 1 | no | — |
| 556 | C24 | D3×D4 | 1 | 2 | yes | — |
| 557 | #41 | — | 6 | 1 | no | — |
| 558 | #41 | — | 6 | 1 | no | — |
| 559 | #41 | — | 6 | 1 | no | — |
| 560 | #41 | — | 6 | 1 | no | — |
| 561 | #41 | — | 24 | 4 | no | — |
| 562 | C2×Q8 | — | 3 | 1 | no | — |
| 563 | C2×Q8 | — | 6 | 2 | no | — |
| 564 | C2×D4 | — | 2 | 1 | no | — |
| 565 | C2×D4 | — | 2 | 1 | no | — |
| 566 | C2×D4 | — | 2 | 1 | no | — |
| 567 | C2×D4 | — | 2 | 1 | no | — |
| 568 | C2×D4 | — | 2 | 1 | no | — |
| 569 | C2×D4 | — | 2 | 1 | no | — |
| 570 | C2×D4 | — | 3 | 1 | no | — |
| 571 | C2×D4 | — | 6 | 1 | no | — |
| 572 | C2×D4 | — | 6 | 1 | no | — |
| 573 | C2×D4 | — | 6 | 2 | no | — |
| 574 | C2×D4 | — | 6 | 1 | no | — |
| 575 | C2×D4 | — | 6 | 2 | no | — |
| 576 | C2×D4 | — | 6 | 2 | no | — |
| 577 | C2×D4 | — | 6 | 2 | no | — |
| 578 | C2×D4 | — | 24 | 2 | no | — |
| 579 | C22×C4 | — | 2 | 1 | no | — |
| 580 | C22×C4 | — | 2 | 2 | no | — |
| 581 | C22×C4 | — | 2 | 2 | no | — |
| 582 | C22×C4 | — | 2 | 1 | no | — |
| 583 | C22×C4 | — | 3 | 1 | no | — |
| 584 | C22×C4 | — | 3 | 1 | no | — |
| 585 | C22×C4 | — | 3 | 1 | no | — |
| 586 | C22×C4 | — | 3 | 1 | no | — |
| 587 | C22×C4 | — | 3 | 1 | no | — |
| 588 | C22×C4 | — | 3 | 2 | no | — |
| 589 | C22×C4 | — | 6 | 1 | no | — |
| 590 | C22×C4 | — | 6 | 1 | 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 | 1 | no | — |
| 596 | C22×C4 | — | 6 | 1 | no | — |
| 597 | C22×C4 | — | 6 | 1 | no | — |
| 598 | C22×C4 | — | 6 | 1 | no | — |
| 599 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 600 | M16 | — | 2 | 1 | no | — |
| 601 | M16 | — | 2 | 1 | no | — |
| 602 | M16 | — | 2 | 1 | no | — |
| 603 | M16 | — | 3 | 2 | no | — |
| 604 | M16 | — | 6 | 4 | no | — |
| 605 | M16 | — | 6 | 1 | no | — |
| 606 | M16 | — | 6 | 1 | no | — |
| 607 | M16 | — | 6 | 1 | no | — |
| 608 | M16 | #235 | 1 | 2 | yes | complemented |
| 609 | C2×C8 | — | 2 | 1 | no | — |
| 610 | C2×C8 | — | 2 | 1 | no | — |
| 611 | C2×C8 | — | 6 | 4 | no | — |
| 612 | C2×C8 | — | 6 | 1 | no | — |
| 613 | C2×C8 | — | 6 | 1 | no | — |
| 614 | C4⋊C4 | — | 2 | 1 | no | — |
| 615 | C4⋊C4 | — | 2 | 1 | no | — |
| 616 | C4⋊C4 | — | 3 | 1 | no | — |
| 617 | C4⋊C4 | — | 3 | 1 | no | — |
| 618 | C4⋊C4 | — | 6 | 1 | no | — |
| 619 | C4⋊C4 | — | 6 | 1 | no | — |
| 620 | C4⋊C4 | — | 6 | 1 | no | — |
| 621 | C4⋊C4 | — | 6 | 1 | no | — |
| 622 | C4⋊C4 | — | 6 | 2 | no | — |
| 623 | C4⋊C4 | — | 6 | 2 | no | — |
| 624 | C4⋊C4 | — | 6 | 2 | no | — |
| 625 | C4⋊C4 | — | 6 | 2 | no | — |
| 626 | C4⋊C4 | — | 6 | 1 | no | — |
| 627 | C4⋊C4 | — | 6 | 1 | no | — |
| 628 | C4⋊C4 | — | 6 | 1 | no | — |
| 629 | C4⋊C4 | — | 6 | 1 | no | — |
| 630 | C4⋊C4 | — | 24 | 2 | no | — |
| 631 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 632 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 633 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 634 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 635 | C22⋊C4 | — | 2 | 2 | no | — |
| 636 | C22⋊C4 | — | 2 | 2 | no | — |
| 637 | C22⋊C4 | — | 2 | 1 | no | — |
| 638 | C22⋊C4 | — | 2 | 1 | no | — |
| 639 | C22⋊C4 | — | 4 | 4 | no | — |
| 640 | C22⋊C4 | — | 6 | 1 | no | — |
| 641 | C22⋊C4 | — | 6 | 1 | no | — |
| 642 | C22⋊C4 | — | 6 | 1 | no | — |
| 643 | C22⋊C4 | — | 6 | 1 | no | — |
| 644 | C22⋊C4 | — | 6 | 1 | no | — |
| 645 | C22⋊C4 | — | 6 | 1 | no | — |
| 646 | C22⋊C4 | — | 6 | 2 | no | — |
| 647 | C22⋊C4 | — | 6 | 2 | no | — |
| 648 | C22⋊C4 | — | 6 | 2 | no | — |
| 649 | C22⋊C4 | — | 6 | 2 | no | — |
| 650 | C22⋊C4 | — | 6 | 2 | no | — |
| 651 | C22⋊C4 | — | 6 | 1 | no | — |
| 652 | C22⋊C4 | — | 12 | 2 | no | — |
| 653 | C22⋊C4 | — | 12 | 1 | no | — |
| 654 | C22⋊C4 | — | 12 | 1 | no | — |
| 655 | C22⋊C4 | — | 24 | 2 | no | — |
| 656 | C42 | — | 2 | 1 | no | — |
| 657 | C42 | — | 2 | 1 | no | — |
| 658 | C42 | — | 2 | 1 | no | — |
| 659 | C42 | — | 2 | 1 | no | — |
| 660 | C42 | — | 6 | 1 | no | — |
| 661 | C42 | — | 6 | 1 | no | — |
| 662 | C42 | — | 6 | 2 | no | — |
| 663 | C42 | — | 6 | 1 | no | — |
| 664 | C42 | — | 6 | 1 | no | — |
| 665 | C42 | — | 6 | 1 | no | — |
| 666 | C42 | — | 12 | 1 | no | — |
| 667 | C42 | — | 12 | 1 | no | — |
| 668 | C22×C3 | — | 2 | 1 | no | — |
| 669 | C22×C3 | — | 2 | 1 | no | — |
| 670 | C22×C3 | — | 4 | 2 | no | — |
| 671 | C22×C3 | — | 4 | 2 | no | — |
| 672 | C22×C3 | — | 4 | 2 | no | — |
| 673 | C22×C3 | — | 8 | 2 | no | — |
| 674 | C22×C3 | — | 8 | 2 | no | — |
| 675 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 676 | C22×C3 | #547 | 1 | 1 | yes | characteristic |
| 677 | C22×C3 | #547 | 1 | 1 | yes | characteristic |
| 678 | C2×D3 | — | 2 | 1 | no | — |
| 679 | C2×D3 | — | 2 | 1 | no | — |
| 680 | C2×D3 | — | 2 | 1 | no | — |
| 681 | C2×D3 | — | 2 | 1 | no | — |
| 682 | C2×D3 | — | 2 | 1 | no | — |
| 683 | C2×D3 | — | 2 | 1 | no | — |
| 684 | C2×D3 | — | 4 | 1 | no | — |
| 685 | C2×D3 | — | 4 | 1 | no | — |
| 686 | C2×D3 | — | 4 | 1 | no | — |
| 687 | C2×D3 | — | 8 | 1 | no | — |
| 688 | C2×D3 | — | 8 | 1 | no | — |
| 689 | C3×C4 | — | 4 | 2 | no | — |
| 690 | C3×C4 | — | 4 | 1 | no | — |
| 691 | C3×C4 | — | 4 | 1 | no | — |
| 692 | C3×C4 | — | 4 | 1 | no | — |
| 693 | C3×C4 | — | 4 | 1 | no | — |
| 694 | C3×C4 | — | 8 | 1 | no | — |
| 695 | C3×C4 | #525 | 1 | 1 | yes | characteristic |
| 696 | C3×C4 | #536 | 1 | 1 | yes | characteristic |
| 697 | C3×C4 | #547 | 1 | 1 | yes | characteristic |
| 698 | C3×C4 | #547 | 1 | 1 | yes | characteristic |
| 699 | Dic3 | — | 2 | 1 | no | — |
| 700 | Dic3 | — | 2 | 1 | no | — |
| 701 | Dic3 | — | 4 | 1 | no | — |
| 702 | Dic3 | — | 4 | 1 | no | — |
| 703 | Dic3 | — | 4 | 1 | no | — |
| 704 | Dic3 | — | 4 | 2 | no | — |
| 705 | Dic3 | — | 8 | 1 | no | — |
| 706 | Dic3 | — | 8 | 1 | no | — |
| 707 | C23 | — | 2 | 2 | no | — |
| 708 | C23 | — | 2 | 2 | no | — |
| 709 | C23 | — | 2 | 2 | no | — |
| 710 | C23 | — | 3 | 1 | no | — |
| 711 | C23 | — | 3 | 1 | no | — |
| 712 | C23 | — | 4 | 2 | no | — |
| 713 | C23 | — | 4 | 2 | no | — |
| 714 | C23 | — | 6 | 1 | no | — |
| 715 | C23 | — | 6 | 1 | no | — |
| 716 | C23 | — | 6 | 1 | no | — |
| 717 | C23 | — | 12 | 1 | no | — |
| 718 | C23 | — | 12 | 1 | no | — |
| 719 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 720 | Q8 | — | 6 | 1 | no | — |
| 721 | Q8 | — | 6 | 1 | no | — |
| 722 | Q8 | — | 24 | 2 | no | — |
| 723 | D4 | — | 4 | 1 | no | — |
| 724 | D4 | — | 4 | 1 | no | — |
| 725 | D4 | — | 4 | 1 | no | — |
| 726 | D4 | — | 4 | 1 | no | — |
| 727 | D4 | — | 6 | 1 | no | — |
| 728 | D4 | — | 6 | 1 | no | — |
| 729 | D4 | — | 12 | 2 | no | — |
| 730 | D4 | — | 12 | 4 | no | — |
| 731 | D4 | — | 12 | 1 | no | — |
| 732 | D4 | — | 12 | 1 | no | — |
| 733 | D4 | — | 24 | 1 | no | — |
| 734 | D4 | — | 24 | 2 | no | — |
| 735 | D4 | — | 24 | 2 | no | — |
| 736 | D4 | — | 24 | 2 | no | — |
| 737 | C2×C4 | — | 2 | 2 | no | — |
| 738 | C2×C4 | — | 2 | 1 | no | — |
| 739 | C2×C4 | — | 2 | 1 | no | — |
| 740 | C2×C4 | — | 2 | 1 | no | — |
| 741 | C2×C4 | — | 2 | 1 | no | — |
| 742 | C2×C4 | — | 3 | 1 | no | — |
| 743 | C2×C4 | — | 3 | 1 | no | — |
| 744 | C2×C4 | — | 4 | 1 | no | — |
| 745 | C2×C4 | — | 4 | 1 | no | — |
| 746 | C2×C4 | — | 4 | 2 | no | — |
| 747 | C2×C4 | — | 4 | 1 | no | — |
| 748 | C2×C4 | — | 6 | 1 | no | — |
| 749 | C2×C4 | — | 6 | 1 | no | — |
| 750 | C2×C4 | — | 6 | 1 | no | — |
| 751 | C2×C4 | — | 6 | 1 | no | — |
| 752 | C2×C4 | — | 6 | 1 | no | — |
| 753 | C2×C4 | — | 6 | 1 | no | — |
| 754 | C2×C4 | — | 6 | 1 | no | — |
| 755 | C2×C4 | — | 6 | 1 | no | — |
| 756 | C2×C4 | — | 6 | 1 | no | — |
| 757 | C2×C4 | — | 6 | 1 | no | — |
| 758 | C2×C4 | — | 6 | 1 | no | — |
| 759 | C2×C4 | — | 6 | 1 | no | — |
| 760 | C2×C4 | — | 6 | 1 | no | — |
| 761 | C2×C4 | — | 6 | 2 | no | — |
| 762 | C2×C4 | — | 8 | 2 | no | — |
| 763 | C2×C4 | — | 8 | 2 | no | — |
| 764 | C2×C4 | — | 12 | 2 | no | — |
| 765 | C2×C4 | — | 12 | 1 | no | — |
| 766 | C2×C4 | — | 12 | 1 | no | — |
| 767 | C2×C4 | — | 12 | 2 | no | — |
| 768 | C2×C4 | — | 12 | 1 | no | — |
| 769 | C2×C4 | — | 12 | 1 | no | — |
| 770 | C2×C4 | — | 12 | 2 | no | — |
| 771 | C2×C4 | — | 12 | 1 | no | — |
| 772 | C2×C4 | — | 12 | 1 | no | — |
| 773 | C2×C4 | — | 24 | 1 | no | — |
| 774 | C2×C4 | — | 24 | 2 | no | — |
| 775 | C2×C4 | C2×#235 | 1 | 1 | yes | characteristic |
| 776 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 777 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 778 | C2×C4 | #1007 | 1 | 1 | yes | characteristic |
| 779 | C2×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 780 | C2×C4 | #1010 | 1 | 1 | yes | characteristic |
| 781 | C8 | — | 2 | 2 | no | — |
| 782 | C8 | — | 4 | 1 | no | — |
| 783 | C8 | — | 6 | 2 | no | — |
| 784 | C8 | — | 12 | 1 | no | — |
| 785 | C2×C3 | — | 2 | 1 | no | — |
| 786 | C2×C3 | — | 2 | 1 | no | — |
| 787 | C2×C3 | — | 8 | 2 | no | — |
| 788 | C2×C3 | #2406 | 1 | 1 | yes | characteristic |
| 789 | C2×C3 | #3018 | 1 | 1 | yes | characteristic |
| 790 | C2×C3 | #3019 | 1 | 1 | yes | characteristic |
| 791 | D3 | — | 4 | 1 | no | — |
| 792 | D3 | — | 4 | 1 | no | — |
| 793 | D3 | — | 8 | 1 | no | — |
| 794 | C22 | — | 2 | 1 | no | — |
| 795 | C22 | — | 2 | 1 | no | — |
| 796 | C22 | — | 4 | 2 | no | — |
| 797 | C22 | — | 4 | 2 | no | — |
| 798 | C22 | — | 4 | 2 | no | — |
| 799 | C22 | — | 6 | 1 | no | — |
| 800 | C22 | — | 6 | 1 | no | — |
| 801 | C22 | — | 6 | 1 | no | — |
| 802 | C22 | — | 6 | 1 | no | — |
| 803 | C22 | — | 6 | 1 | no | — |
| 804 | C22 | — | 6 | 1 | no | — |
| 805 | C22 | — | 8 | 2 | no | — |
| 806 | C22 | — | 8 | 2 | no | — |
| 807 | C22 | — | 12 | 1 | no | — |
| 808 | C22 | — | 12 | 1 | no | — |
| 809 | C22 | — | 12 | 1 | no | — |
| 810 | C22 | — | 24 | 1 | no | — |
| 811 | C22 | — | 24 | 1 | no | — |
| 812 | C22 | #5507 | 1 | 1 | yes | characteristic |
| 813 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 814 | C22 | #5655 | 1 | 1 | yes | characteristic |
| 815 | C4 | — | 4 | 2 | no | — |
| 816 | C4 | — | 4 | 1 | no | — |
| 817 | C4 | — | 4 | 1 | no | — |
| 818 | C4 | — | 4 | 1 | no | — |
| 819 | C4 | — | 4 | 1 | no | — |
| 820 | C4 | — | 6 | 1 | no | — |
| 821 | C4 | — | 6 | 1 | no | — |
| 822 | C4 | — | 8 | 1 | no | — |
| 823 | C4 | — | 12 | 1 | no | — |
| 824 | C4 | — | 12 | 1 | no | — |
| 825 | C4 | — | 12 | 1 | no | — |
| 826 | C4 | — | 12 | 2 | no | — |
| 827 | C4 | — | 24 | 1 | no | — |
| 828 | C4 | — | 24 | 1 | no | — |
| 829 | C4 | #5547 | 1 | 1 | yes | characteristic |
| 830 | C4 | #5551 | 1 | 1 | yes | characteristic |
| 831 | C4 | #5628 | 1 | 1 | yes | characteristic |
| 832 | C4 | #5631 | 1 | 1 | yes | characteristic |
| 833 | C3 | #24084 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 834 | C2 | — | 2 | 1 | no | — |
| 835 | C2 | — | 2 | 1 | no | — |
| 836 | C2 | — | 8 | 2 | no | — |
| 837 | C2 | — | 12 | 1 | no | — |
| 838 | C2 | — | 12 | 1 | no | — |
| 839 | C2 | — | 24 | 1 | no | — |
| 840 | C2 | #74600 | 1 | 1 | yes | characteristic |
| 841 | C2 | #80277 | 1 | 1 | yes | characteristic |
| 842 | C2 | #80292 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #79216 | C2 | semidirect |
| 3. #79208 | C2 | semidirect |
| 4. #76453 | C2 | semidirect |
| 5. C3×#1856 | C2 | semidirect |
| 6. #71647 | C2 | semidirect |
| 7. #70681 | C2 | semidirect |
| 8. #70667 | C2 | semidirect |
| 9. #70081 | C2 | semidirect |
| 10. #70066 | C2 | semidirect |
| 11. #69665 | C2 | semidirect |
| 12. #68771 | C2 | semidirect |
| 13. #68755 | C2 | semidirect |
| 14. #68754 | C2 | semidirect |
| 15. #68735 | C2 | semidirect |
| 85. #1856 | D3 | semidirect |
| 301. C3×M16 | #41 | semidirect |
| 361. #208 | #41 | semidirect |
| 608. M16 | #235 | semidirect |
| 833. C3 | #24084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #85869 | 2 |
| #79216 | 2 |
| #79208 | 2 |
| #76453 | 2 |
| C3×#1856 | 2 |
| #71647 | 2 |
| #70681 | 2 |
| #70667 | 2 |
| #70081 | 2 |
| #70066 | 2 |
| #69665 | 2 |
| #68771 | 2 |
| #68755 | 2 |
| #68754 | 2 |
| #68735 | 2 |
| #24084 | 3 |