Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1050 conjugacy classes of subgroups.
The subgroup lattice has 848 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83931 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #82953 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #78917 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2003 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72088 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71730 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #70363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #70357 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #70328 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #70100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #70097 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68732 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #24181 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×C3×AGL(1,ℤ/8) | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#536 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C3×#124 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5832 | C22 | 1 | 1 | yes | characteristic |
| 21 | #5827 | C22 | 1 | 1 | yes | characteristic |
| 22 | #5816 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×Q8×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×D4×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#932 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5732 | — | 2 | 1 | no | — |
| 27 | #5721 | — | 2 | 1 | no | — |
| 28 | #5681 | — | 2 | 1 | no | — |
| 29 | #5671 | — | 2 | 1 | no | — |
| 30 | #5665 | — | 2 | 2 | no | — |
| 31 | #5649 | — | 2 | 2 | no | — |
| 32 | #5642 | — | 2 | 1 | no | — |
| 33 | #5641 | — | 2 | 1 | no | — |
| 34 | #5639 | — | 2 | 1 | no | — |
| 35 | #5635 | — | 2 | 1 | no | — |
| 36 | #5523 | C22 | 1 | 1 | yes | characteristic |
| 37 | #5517 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C3×#104 | C22 | 1 | 1 | yes | characteristic |
| 39 | C3×#418 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×C3×#101 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#837 | C22 | 1 | 1 | yes | characteristic |
| 42 | #5232 | C22 | 1 | 1 | yes | characteristic |
| 43 | #5229 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#836 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5221 | C22 | 1 | 1 | yes | characteristic |
| 46 | #5215 | C22 | 1 | 1 | yes | characteristic |
| 47 | #5165 | — | 2 | 1 | no | — |
| 48 | #5162 | — | 2 | 1 | no | — |
| 49 | #5153 | — | 2 | 1 | no | — |
| 50 | #5150 | — | 2 | 1 | no | — |
| 51 | C2×#825 | C22 | 1 | 1 | yes | characteristic |
| 52 | #5133 | C22 | 1 | 1 | yes | characteristic |
| 53 | #5121 | C22 | 1 | 1 | yes | characteristic |
| 54 | #5118 | C22 | 1 | 1 | yes | characteristic |
| 55 | #5118 | C22 | 1 | 1 | yes | characteristic |
| 56 | #4995 | C22 | 1 | 1 | yes | characteristic |
| 57 | #4951 | — | 2 | 2 | no | — |
| 58 | #4950 | — | 2 | 2 | no | — |
| 59 | #4935 | C22 | 1 | 1 | yes | characteristic |
| 60 | #4932 | C22 | 1 | 1 | yes | characteristic |
| 61 | C2×#805 | C22 | 1 | 1 | yes | characteristic |
| 62 | #4766 | — | 2 | 1 | no | — |
| 63 | #4763 | — | 2 | 1 | no | — |
| 64 | #4761 | — | 2 | 1 | no | — |
| 65 | #4759 | — | 2 | 1 | no | — |
| 66 | C3×#339 | C22 | 1 | 1 | yes | characteristic |
| 67 | #4555 | C22 | 1 | 1 | yes | characteristic |
| 68 | #4554 | C22 | 1 | 1 | yes | characteristic |
| 69 | #4554 | C22 | 1 | 1 | yes | characteristic |
| 70 | #4532 | C22 | 1 | 1 | yes | characteristic |
| 71 | #4523 | C22 | 1 | 1 | yes | characteristic |
| 72 | #3507 | — | 3 | 1 | no | — |
| 73 | #3077 | — | 3 | 1 | no | — |
| 74 | #3036 | — | 3 | 1 | no | — |
| 75 | #2326 | — | 3 | 1 | no | — |
| 76 | #2038 | — | 3 | 1 | no | — |
| 77 | #2038 | — | 3 | 1 | no | — |
| 78 | #2003 | — | 3 | 1 | no | — |
| 79 | #2003 | D3 | 1 | 1 | yes | characteristic, complemented |
| 80 | #1995 | — | 3 | 1 | no | — |
| 81 | #1963 | — | 3 | 1 | no | — |
| 82 | #1883 | — | 3 | 1 | no | — |
| 83 | #1883 | — | 3 | 1 | no | — |
| 84 | #1859 | — | 3 | 1 | no | — |
| 85 | #1859 | — | 3 | 1 | no | — |
| 86 | #1801 | — | 3 | 1 | no | — |
| 87 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 88 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 89 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 90 | C23×Dic3 | — | 2 | 1 | no | — |
| 91 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 92 | C3×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 93 | C3×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 94 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 95 | C2×C3×D8 | — | 2 | 1 | no | — |
| 96 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 98 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 99 | C3×#124 | — | 2 | 1 | no | — |
| 100 | C3×#124 | — | 2 | 2 | no | — |
| 101 | C3×#124 | — | 2 | 2 | no | — |
| 102 | C3×#123 | — | 2 | 2 | no | — |
| 103 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 104 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 105 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×C3×C22⋊C4 | — | 2 | 2 | no | — |
| 107 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×#217 | — | 2 | 1 | no | — |
| 109 | C2×#217 | — | 2 | 2 | no | — |
| 110 | #947 | — | 2 | 1 | no | — |
| 111 | #947 | D4 | 1 | 1 | yes | characteristic |
| 112 | #946 | — | 2 | 1 | no | — |
| 113 | #946 | — | 2 | 1 | no | — |
| 114 | Q8×Dic3 | — | 2 | 1 | no | — |
| 115 | Q8×Dic3 | — | 2 | 1 | no | — |
| 116 | Q8×Dic3 | — | 2 | 1 | no | — |
| 117 | Q8×Dic3 | — | 2 | 1 | no | — |
| 118 | Q8×Dic3 | — | 2 | 1 | no | — |
| 119 | #944 | — | 2 | 1 | no | — |
| 120 | #944 | D4 | 1 | 1 | yes | characteristic |
| 121 | #940 | D4 | 1 | 1 | yes | characteristic |
| 122 | #939 | — | 2 | 1 | no | — |
| 123 | #939 | — | 2 | 1 | no | — |
| 124 | #936 | D4 | 1 | 1 | yes | characteristic |
| 125 | D4×Dic3 | — | 2 | 1 | no | — |
| 126 | D4×Dic3 | — | 2 | 2 | no | — |
| 127 | D4×Dic3 | — | 2 | 1 | no | — |
| 128 | D4×Dic3 | — | 2 | 1 | no | — |
| 129 | D4×Dic3 | — | 2 | 1 | no | — |
| 130 | D4×Dic3 | — | 2 | 1 | no | — |
| 131 | C2×#214 | — | 2 | 1 | no | — |
| 132 | #932 | — | 2 | 2 | no | — |
| 133 | #932 | — | 4 | 1 | no | — |
| 134 | C2×#213 | — | 2 | 1 | no | — |
| 135 | #929 | — | 2 | 2 | no | — |
| 136 | C4×#67 | — | 2 | 1 | no | — |
| 137 | C4×#67 | — | 2 | 1 | no | — |
| 138 | #926 | — | 2 | 1 | no | — |
| 139 | #926 | C23 | 1 | 1 | yes | characteristic |
| 140 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 141 | C2×C4⋊Dic3 | — | 2 | 2 | no | — |
| 142 | C2×C4⋊Dic3 | D4 | 1 | 2 | yes | — |
| 143 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×Dic3 | D4 | 1 | 2 | yes | — |
| 146 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 147 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 148 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 149 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 150 | #898 | — | 2 | 2 | no | — |
| 151 | #898 | — | 2 | 2 | no | — |
| 152 | #897 | — | 2 | 2 | no | — |
| 153 | #892 | — | 2 | 2 | no | — |
| 154 | #892 | — | 2 | 1 | no | — |
| 155 | D3×C4⋊C4 | — | 2 | 1 | no | — |
| 156 | #890 | — | 2 | 2 | no | — |
| 157 | #890 | D4 | 1 | 1 | yes | characteristic |
| 158 | #890 | D4 | 1 | 1 | yes | characteristic |
| 159 | #889 | — | 2 | 2 | no | — |
| 160 | #889 | — | 2 | 2 | no | — |
| 161 | #888 | D4 | 1 | 1 | yes | characteristic |
| 162 | #888 | D4 | 1 | 1 | yes | characteristic |
| 163 | #887 | — | 2 | 2 | no | — |
| 164 | #886 | — | 2 | 2 | no | — |
| 165 | #885 | — | 2 | 2 | no | — |
| 166 | #883 | — | 2 | 2 | no | — |
| 167 | #67⋊C4 | — | 2 | 2 | no | — |
| 168 | #67⋊C4 | — | 2 | 2 | no | — |
| 169 | #879 | — | 2 | 2 | no | — |
| 170 | #879 | — | 2 | 2 | no | — |
| 171 | #878 | — | 2 | 2 | no | — |
| 172 | #878 | — | 2 | 1 | no | — |
| 173 | #878 | — | 2 | 1 | no | — |
| 174 | #877 | — | 2 | 2 | no | — |
| 175 | C4×D12 | — | 2 | 1 | no | — |
| 176 | C4×Dic6 | — | 2 | 1 | no | — |
| 177 | C4×Dic6 | — | 2 | 1 | no | — |
| 178 | C4×Dic6 | — | 2 | 1 | no | — |
| 179 | C3×#104 | — | 2 | 2 | no | — |
| 180 | C3×#102 | — | 2 | 1 | no | — |
| 181 | C3×#102 | — | 2 | 1 | no | — |
| 182 | C3×#101 | — | 4 | 1 | no | — |
| 183 | #837 | — | 4 | 1 | no | — |
| 184 | #836 | — | 4 | 1 | no | — |
| 185 | #835 | — | 2 | 1 | no | — |
| 186 | #832 | — | 2 | 1 | no | — |
| 187 | #832 | — | 2 | 1 | no | — |
| 188 | #832 | — | 2 | 1 | no | — |
| 189 | C3⋊#95 | — | 2 | 2 | no | — |
| 190 | C3⋊#95 | — | 2 | 1 | no | — |
| 191 | C3⋊#95 | — | 2 | 1 | no | — |
| 192 | #825 | — | 4 | 1 | no | — |
| 193 | #821 | — | 2 | 1 | no | — |
| 194 | #818 | — | 2 | 1 | no | — |
| 195 | #817 | — | 2 | 1 | no | — |
| 196 | #816 | — | 2 | 1 | no | — |
| 197 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 198 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 199 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 200 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 201 | #808 | — | 2 | 1 | no | — |
| 202 | #807 | — | 2 | 1 | no | — |
| 203 | #805 | — | 2 | 2 | no | — |
| 204 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 205 | C2×AGL(1,ℤ/8) | C2×D3 | 1 | 1 | yes | characteristic |
| 206 | #559 | — | 6 | 1 | no | — |
| 207 | #557 | — | 6 | 1 | no | — |
| 208 | #556 | — | 6 | 1 | no | — |
| 209 | #556 | — | 6 | 1 | no | — |
| 210 | #556 | — | 6 | 1 | no | — |
| 211 | #554 | — | 6 | 1 | no | — |
| 212 | #552 | — | 6 | 1 | no | — |
| 213 | #552 | — | 6 | 1 | no | — |
| 214 | #539 | — | 6 | 2 | no | — |
| 215 | #536 | — | 3 | 1 | no | — |
| 216 | #536 | C2×D3 | 1 | 1 | yes | characteristic |
| 217 | #533 | — | 3 | 1 | no | — |
| 218 | #532 | — | 3 | 1 | no | — |
| 219 | #529 | — | 6 | 2 | no | — |
| 220 | C2×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 221 | #520 | — | 3 | 1 | no | — |
| 222 | #520 | — | 3 | 1 | no | — |
| 223 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 224 | C2×C4×D4 | — | 3 | 1 | no | — |
| 225 | #478 | — | 6 | 1 | no | — |
| 226 | #478 | — | 6 | 1 | no | — |
| 227 | #476 | — | 6 | 1 | no | — |
| 228 | #474 | — | 6 | 1 | no | — |
| 229 | #463 | — | 6 | 1 | no | — |
| 230 | #463 | — | 6 | 1 | no | — |
| 231 | #461 | — | 6 | 1 | no | — |
| 232 | #459 | — | 6 | 1 | no | — |
| 233 | #428 | — | 3 | 1 | no | — |
| 234 | #428 | — | 3 | 1 | no | — |
| 235 | #423 | — | 3 | 1 | no | — |
| 236 | #423 | — | 3 | 1 | no | — |
| 237 | C2×#104 | — | 3 | 1 | no | — |
| 238 | C2×#104 | — | 3 | 1 | no | — |
| 239 | C2×#104 | — | 3 | 1 | no | — |
| 240 | C2×#104 | C2×D3 | 1 | 1 | yes | characteristic |
| 241 | #418 | — | 3 | 1 | no | — |
| 242 | #418 | C2×D3 | 1 | 1 | yes | characteristic |
| 243 | #417 | — | 3 | 1 | no | — |
| 244 | #417 | — | 3 | 1 | no | — |
| 245 | C2×#101 | — | 3 | 1 | no | — |
| 246 | C2×#101 | C2×D3 | 1 | 1 | yes | characteristic |
| 247 | #391 | — | 3 | 1 | no | — |
| 248 | #390 | — | 3 | 1 | no | — |
| 249 | #388 | — | 6 | 2 | no | — |
| 250 | #385 | — | 6 | 2 | no | — |
| 251 | #384 | — | 3 | 1 | no | — |
| 252 | #376 | — | 3 | 1 | no | — |
| 253 | #343 | — | 3 | 1 | no | — |
| 254 | #343 | — | 3 | 1 | no | — |
| 255 | #339 | — | 3 | 1 | no | — |
| 256 | #339 | — | 3 | 1 | no | — |
| 257 | #339 | — | 3 | 1 | no | — |
| 258 | #339 | C2×D3 | 1 | 1 | yes | characteristic |
| 259 | C24×C3 | — | 2 | 1 | no | — |
| 260 | C3×#41 | — | 2 | 1 | no | — |
| 261 | C3×#41 | — | 2 | 1 | no | — |
| 262 | C3×#41 | — | 2 | 1 | no | — |
| 263 | C3×#41 | — | 2 | 1 | no | — |
| 264 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 265 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 266 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 267 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 268 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 269 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 270 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | C2×C3×D4 | — | 2 | 1 | no | — |
| 272 | C2×C3×D4 | — | 2 | 1 | no | — |
| 273 | C2×C3×D4 | — | 2 | 1 | no | — |
| 274 | C2×C3×D4 | — | 2 | 1 | no | — |
| 275 | C2×C3×D4 | — | 2 | 1 | no | — |
| 276 | C2×C3×D4 | — | 2 | 1 | no | — |
| 277 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 278 | C2×C3×D4 | #41 | 1 | 2 | yes | — |
| 279 | C22×C3×C4 | — | 2 | 1 | no | — |
| 280 | C22×C3×C4 | — | 2 | 1 | no | — |
| 281 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 282 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 283 | C2×#67 | — | 2 | 1 | no | — |
| 284 | C2×#67 | — | 2 | 1 | no | — |
| 285 | C2×#67 | — | 2 | 1 | no | — |
| 286 | C22×Dic3 | — | 2 | 2 | no | — |
| 287 | C22×Dic3 | — | 2 | 1 | no | — |
| 288 | C22×Dic3 | — | 2 | 1 | no | — |
| 289 | C22×Dic3 | — | 4 | 1 | no | — |
| 290 | C22×Dic3 | — | 4 | 1 | no | — |
| 291 | C22×Dic3 | — | 8 | 2 | no | — |
| 292 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 293 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 295 | #235 | — | 2 | 1 | no | — |
| 296 | #235 | — | 2 | 1 | no | — |
| 297 | #235 | — | 2 | 1 | no | — |
| 298 | #235 | — | 2 | 1 | no | — |
| 299 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | C2×C4×D3 | — | 2 | 1 | no | — |
| 301 | C2×C4×D3 | — | 2 | 2 | no | — |
| 302 | C2×Dic6 | — | 2 | 1 | no | — |
| 303 | C2×Dic6 | — | 2 | 1 | no | — |
| 304 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 305 | C3×SD16 | — | 4 | 2 | no | — |
| 306 | C3×D8 | — | 4 | 2 | no | — |
| 307 | C3×M16 | — | 2 | 1 | no | — |
| 308 | C3×M16 | — | 2 | 1 | no | — |
| 309 | C3×M16 | — | 2 | 1 | no | — |
| 310 | C3×M16 | — | 2 | 1 | no | — |
| 311 | C2×C3×C8 | — | 2 | 1 | no | — |
| 312 | C2×C3×C8 | — | 2 | 1 | no | — |
| 313 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 314 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 315 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 316 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 317 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 318 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 319 | C3×C22⋊C4 | — | 2 | 8 | no | — |
| 320 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 321 | C3×C42 | — | 2 | 1 | no | — |
| 322 | C3×C42 | — | 2 | 1 | no | — |
| 323 | C3×C42 | #41 | 1 | 2 | yes | — |
| 324 | #217 | — | 2 | 2 | no | — |
| 325 | #217 | — | 2 | 1 | no | — |
| 326 | #217 | — | 2 | 1 | no | — |
| 327 | #217 | — | 2 | 1 | no | — |
| 328 | #217 | — | 4 | 1 | no | — |
| 329 | #217 | — | 4 | 1 | no | — |
| 330 | #217 | — | 8 | 2 | no | — |
| 331 | #214 | — | 4 | 2 | no | — |
| 332 | #213 | — | 4 | 2 | no | — |
| 333 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 334 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 335 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 336 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 337 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 338 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 339 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 340 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 341 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 342 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 343 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 344 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 345 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 346 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 347 | C4⋊Dic3 | — | 8 | 2 | no | — |
| 348 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 349 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 350 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 351 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 352 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 353 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 354 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 355 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 356 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 357 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 358 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 359 | C4×Dic3 | — | 2 | 2 | no | — |
| 360 | C4×Dic3 | — | 2 | 2 | no | — |
| 361 | C4×Dic3 | — | 2 | 1 | no | — |
| 362 | C4×Dic3 | — | 2 | 2 | no | — |
| 363 | C4×Dic3 | — | 2 | 2 | no | — |
| 364 | C4×Dic3 | — | 2 | 1 | no | — |
| 365 | C4×Dic3 | — | 2 | 1 | no | — |
| 366 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 367 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 368 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 369 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 370 | #208 | — | 2 | 1 | no | — |
| 371 | #208 | — | 2 | 1 | no | — |
| 372 | #208 | — | 2 | 1 | no | — |
| 373 | #208 | — | 2 | 1 | no | — |
| 374 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 375 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 376 | C2×#41 | — | 3 | 1 | no | — |
| 377 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 378 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 379 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 380 | C23×C4 | — | 6 | 1 | no | — |
| 381 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 382 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 383 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 384 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 385 | C2×SD16 | — | 2 | 1 | no | — |
| 386 | C2×SD16 | — | 6 | 1 | no | — |
| 387 | C2×D8 | — | 2 | 1 | no | — |
| 388 | C2×D8 | — | 6 | 1 | no | — |
| 389 | C2×M16 | — | 3 | 1 | no | — |
| 390 | C2×M16 | — | 3 | 1 | no | — |
| 391 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 392 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 393 | C4⋊Q8 | — | 2 | 1 | no | — |
| 394 | C4⋊Q8 | — | 3 | 1 | no | — |
| 395 | C4⋊Q8 | — | 3 | 1 | no | — |
| 396 | C4⋊Q8 | — | 3 | 1 | no | — |
| 397 | C4⋊Q8 | — | 6 | 1 | no | — |
| 398 | #127 | — | 3 | 1 | no | — |
| 399 | #126 | — | 6 | 2 | no | — |
| 400 | #126 | — | 6 | 2 | no | — |
| 401 | #126 | — | 6 | 2 | no | — |
| 402 | #126 | — | 6 | 2 | no | — |
| 403 | #125 | — | 3 | 1 | no | — |
| 404 | #125 | — | 3 | 1 | no | — |
| 405 | #125 | — | 6 | 2 | no | — |
| 406 | #125 | — | 6 | 2 | no | — |
| 407 | #125 | — | 6 | 2 | no | — |
| 408 | #124 | — | 2 | 1 | no | — |
| 409 | #124 | — | 2 | 2 | no | — |
| 410 | #124 | — | 2 | 2 | no | — |
| 411 | #124 | — | 3 | 1 | no | — |
| 412 | #124 | — | 3 | 1 | no | — |
| 413 | #124 | — | 6 | 2 | no | — |
| 414 | #124 | — | 6 | 1 | no | — |
| 415 | #123 | — | 2 | 2 | no | — |
| 416 | #123 | — | 6 | 2 | no | — |
| 417 | #123 | — | 6 | 2 | no | — |
| 418 | #123 | — | 6 | 2 | no | — |
| 419 | C22⋊Q8 | — | 2 | 1 | no | — |
| 420 | C22⋊Q8 | — | 2 | 1 | no | — |
| 421 | C22⋊Q8 | — | 6 | 1 | no | — |
| 422 | C22⋊Q8 | — | 6 | 1 | no | — |
| 423 | C22⋊Q8 | — | 6 | 2 | no | — |
| 424 | C22⋊Q8 | — | 6 | 2 | no | — |
| 425 | C22⋊Q8 | — | 6 | 1 | no | — |
| 426 | C22⋊Q8 | — | 6 | 1 | no | — |
| 427 | #121 | — | 6 | 1 | no | — |
| 428 | #121 | — | 6 | 1 | no | — |
| 429 | C4×Q8 | — | 6 | 1 | no | — |
| 430 | C4×Q8 | — | 6 | 1 | no | — |
| 431 | C4×Q8 | — | 6 | 1 | no | — |
| 432 | C4×Q8 | — | 6 | 1 | no | — |
| 433 | C4×Q8 | — | 6 | 1 | no | — |
| 434 | C4×Q8 | — | 6 | 1 | no | — |
| 435 | C4×Q8 | — | 6 | 1 | no | — |
| 436 | C4×Q8 | — | 6 | 2 | no | — |
| 437 | C4×Q8 | — | 6 | 1 | no | — |
| 438 | C4×D4 | — | 6 | 1 | no | — |
| 439 | C4×D4 | — | 6 | 1 | no | — |
| 440 | C4×D4 | — | 6 | 1 | no | — |
| 441 | C4×D4 | — | 6 | 1 | no | — |
| 442 | C4×D4 | — | 6 | 1 | no | — |
| 443 | C4×D4 | — | 6 | 1 | no | — |
| 444 | C4×D4 | — | 6 | 1 | no | — |
| 445 | C4×D4 | — | 6 | 2 | no | — |
| 446 | C4×D4 | — | 6 | 2 | no | — |
| 447 | C4×D4 | — | 6 | 2 | no | — |
| 448 | C4×D4 | — | 6 | 1 | no | — |
| 449 | #117 | — | 3 | 1 | no | — |
| 450 | #117 | — | 6 | 2 | no | — |
| 451 | #117 | — | 6 | 2 | no | — |
| 452 | #117 | — | 6 | 1 | no | — |
| 453 | #117 | — | 6 | 1 | no | — |
| 454 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 455 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 456 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 457 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 458 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 459 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 460 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 461 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 462 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 463 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 464 | C2×C42 | — | 3 | 1 | no | — |
| 465 | C2×C42 | — | 3 | 2 | no | — |
| 466 | C2×C42 | — | 3 | 1 | no | — |
| 467 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 468 | #107 | — | 6 | 1 | no | — |
| 469 | #107 | — | 6 | 1 | no | — |
| 470 | #106 | — | 6 | 1 | no | — |
| 471 | #106 | — | 6 | 1 | no | — |
| 472 | C4⋊C8 | — | 6 | 1 | no | — |
| 473 | C4⋊C8 | — | 6 | 1 | no | — |
| 474 | C4⋊C8 | — | 6 | 1 | no | — |
| 475 | C4⋊C8 | — | 6 | 1 | no | — |
| 476 | #104 | — | 2 | 2 | no | — |
| 477 | #104 | — | 6 | 2 | no | — |
| 478 | #104 | — | 12 | 1 | no | — |
| 479 | #104 | — | 12 | 1 | no | — |
| 480 | #103 | — | 6 | 1 | no | — |
| 481 | #103 | — | 6 | 1 | no | — |
| 482 | #102 | — | 2 | 1 | no | — |
| 483 | #102 | — | 2 | 1 | no | — |
| 484 | #102 | — | 6 | 1 | no | — |
| 485 | #102 | — | 6 | 1 | no | — |
| 486 | #102 | — | 6 | 1 | no | — |
| 487 | #102 | — | 6 | 1 | no | — |
| 488 | #101 | — | 4 | 1 | no | — |
| 489 | #101 | — | 12 | 1 | no | — |
| 490 | #95 | — | 6 | 1 | no | — |
| 491 | #95 | — | 6 | 1 | no | — |
| 492 | #95 | — | 6 | 2 | no | — |
| 493 | C23×C3 | — | 2 | 1 | no | — |
| 494 | C23×C3 | — | 2 | 2 | no | — |
| 495 | C23×C3 | — | 4 | 2 | no | — |
| 496 | C23×C3 | — | 4 | 2 | no | — |
| 497 | C23×C3 | — | 4 | 1 | no | — |
| 498 | C23×C3 | — | 4 | 1 | no | — |
| 499 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 500 | C22×D3 | — | 2 | 1 | no | — |
| 501 | C3×Q8 | — | 2 | 1 | no | — |
| 502 | C3×Q8 | — | 2 | 1 | no | — |
| 503 | C3×Q8 | — | 4 | 1 | no | — |
| 504 | C3×Q8 | — | 4 | 1 | no | — |
| 505 | C3×Q8 | — | 4 | 1 | no | — |
| 506 | C3×Q8 | — | 4 | 1 | no | — |
| 507 | C3×D4 | — | 2 | 2 | no | — |
| 508 | C3×D4 | — | 2 | 1 | no | — |
| 509 | C3×D4 | — | 2 | 1 | no | — |
| 510 | C3×D4 | — | 2 | 2 | no | — |
| 511 | C3×D4 | — | 4 | 1 | no | — |
| 512 | C3×D4 | — | 4 | 1 | no | — |
| 513 | C3×D4 | — | 4 | 1 | no | — |
| 514 | C3×D4 | — | 4 | 1 | no | — |
| 515 | C2×C3×C4 | — | 2 | 2 | no | — |
| 516 | C2×C3×C4 | — | 2 | 1 | no | — |
| 517 | C2×C3×C4 | — | 2 | 1 | no | — |
| 518 | C2×C3×C4 | — | 2 | 1 | no | — |
| 519 | C2×C3×C4 | — | 2 | 2 | no | — |
| 520 | C2×C3×C4 | — | 2 | 2 | no | — |
| 521 | C2×C3×C4 | — | 2 | 2 | no | — |
| 522 | C2×C3×C4 | — | 4 | 1 | no | — |
| 523 | C2×C3×C4 | — | 4 | 1 | no | — |
| 524 | C2×C3×C4 | — | 4 | 1 | no | — |
| 525 | C2×C3×C4 | — | 4 | 1 | no | — |
| 526 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 527 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 528 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 529 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 530 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 531 | C2×C3×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 532 | #67 | — | 4 | 2 | no | — |
| 533 | #67 | — | 4 | 1 | no | — |
| 534 | #67 | — | 4 | 1 | no | — |
| 535 | #67 | — | 8 | 1 | no | — |
| 536 | C2×Dic3 | — | 2 | 2 | no | — |
| 537 | C2×Dic3 | — | 2 | 1 | no | — |
| 538 | C2×Dic3 | — | 2 | 1 | no | — |
| 539 | C2×Dic3 | — | 2 | 1 | no | — |
| 540 | C2×Dic3 | — | 4 | 1 | no | — |
| 541 | C2×Dic3 | — | 4 | 1 | no | — |
| 542 | C2×Dic3 | — | 4 | 2 | no | — |
| 543 | C2×Dic3 | — | 4 | 2 | no | — |
| 544 | C2×Dic3 | — | 4 | 1 | no | — |
| 545 | C2×Dic3 | — | 4 | 1 | no | — |
| 546 | C2×Dic3 | — | 4 | 1 | no | — |
| 547 | C2×Dic3 | — | 4 | 1 | no | — |
| 548 | C2×Dic3 | — | 8 | 2 | no | — |
| 549 | C2×Dic3 | — | 8 | 2 | no | — |
| 550 | C2×Dic3 | — | 8 | 2 | no | — |
| 551 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 552 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 553 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 554 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 555 | D12 | — | 2 | 1 | no | — |
| 556 | D12 | — | 2 | 1 | no | — |
| 557 | C4×D3 | — | 4 | 1 | no | — |
| 558 | C4×D3 | — | 4 | 1 | no | — |
| 559 | C4×D3 | — | 8 | 2 | no | — |
| 560 | Dic6 | — | 2 | 1 | no | — |
| 561 | Dic6 | — | 2 | 1 | no | — |
| 562 | Dic6 | — | 4 | 2 | no | — |
| 563 | Dic6 | — | 8 | 1 | no | — |
| 564 | C3×C8 | — | 4 | 1 | no | — |
| 565 | C3×C8 | — | 4 | 1 | no | — |
| 566 | C3⋊C8 | — | 4 | 1 | no | — |
| 567 | C3⋊C8 | — | 4 | 1 | no | — |
| 568 | C24 | — | 2 | 1 | no | — |
| 569 | #41 | — | 2 | 1 | no | — |
| 570 | #41 | — | 2 | 1 | no | — |
| 571 | #41 | — | 2 | 1 | no | — |
| 572 | #41 | — | 2 | 1 | no | — |
| 573 | #41 | — | 6 | 1 | no | — |
| 574 | #41 | — | 6 | 1 | no | — |
| 575 | #41 | — | 6 | 1 | no | — |
| 576 | #41 | — | 6 | 1 | no | — |
| 577 | C2×Q8 | — | 2 | 1 | no | — |
| 578 | C2×Q8 | — | 2 | 1 | no | — |
| 579 | C2×Q8 | — | 2 | 1 | no | — |
| 580 | C2×Q8 | — | 2 | 1 | no | — |
| 581 | C2×Q8 | — | 2 | 1 | no | — |
| 582 | C2×Q8 | — | 2 | 1 | no | — |
| 583 | C2×Q8 | — | 3 | 1 | no | — |
| 584 | C2×Q8 | — | 6 | 1 | no | — |
| 585 | C2×Q8 | — | 6 | 1 | no | — |
| 586 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 587 | C2×D4 | — | 2 | 1 | no | — |
| 588 | C2×D4 | — | 2 | 1 | no | — |
| 589 | C2×D4 | — | 2 | 1 | no | — |
| 590 | C2×D4 | — | 2 | 1 | no | — |
| 591 | C2×D4 | — | 2 | 1 | no | — |
| 592 | C2×D4 | — | 2 | 1 | no | — |
| 593 | C2×D4 | — | 3 | 1 | no | — |
| 594 | C2×D4 | — | 6 | 1 | no | — |
| 595 | C2×D4 | — | 6 | 1 | no | — |
| 596 | C2×D4 | — | 6 | 1 | no | — |
| 597 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 598 | C2×D4 | #237 | 1 | 2 | yes | — |
| 599 | C22×C4 | — | 2 | 1 | no | — |
| 600 | C22×C4 | — | 2 | 1 | no | — |
| 601 | C22×C4 | — | 3 | 1 | no | — |
| 602 | C22×C4 | — | 3 | 1 | no | — |
| 603 | C22×C4 | — | 3 | 2 | no | — |
| 604 | C22×C4 | — | 6 | 2 | no | — |
| 605 | C22×C4 | — | 6 | 2 | no | — |
| 606 | C22×C4 | — | 6 | 1 | no | — |
| 607 | C22×C4 | — | 6 | 1 | no | — |
| 608 | C22×C4 | — | 6 | 1 | no | — |
| 609 | C22×C4 | — | 12 | 1 | no | — |
| 610 | C22×C4 | — | 12 | 1 | no | — |
| 611 | C22×C4 | — | 24 | 2 | no | — |
| 612 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 613 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 614 | SD16 | — | 4 | 2 | no | — |
| 615 | SD16 | — | 12 | 2 | no | — |
| 616 | D8 | — | 4 | 2 | no | — |
| 617 | D8 | — | 12 | 2 | no | — |
| 618 | M16 | — | 2 | 1 | no | — |
| 619 | M16 | — | 2 | 1 | no | — |
| 620 | M16 | — | 2 | 1 | no | — |
| 621 | M16 | — | 2 | 1 | no | — |
| 622 | M16 | — | 6 | 1 | no | — |
| 623 | M16 | — | 6 | 1 | no | — |
| 624 | M16 | — | 6 | 1 | no | — |
| 625 | M16 | — | 6 | 1 | no | — |
| 626 | C2×C8 | — | 2 | 1 | no | — |
| 627 | C2×C8 | — | 2 | 1 | no | — |
| 628 | C2×C8 | — | 6 | 1 | no | — |
| 629 | C2×C8 | — | 6 | 1 | no | — |
| 630 | C4⋊C4 | — | 2 | 2 | no | — |
| 631 | C4⋊C4 | — | 2 | 2 | no | — |
| 632 | C4⋊C4 | — | 3 | 1 | no | — |
| 633 | C4⋊C4 | — | 3 | 1 | no | — |
| 634 | C4⋊C4 | — | 6 | 2 | no | — |
| 635 | C4⋊C4 | — | 6 | 2 | no | — |
| 636 | C4⋊C4 | — | 6 | 1 | no | — |
| 637 | C4⋊C4 | — | 6 | 1 | no | — |
| 638 | C4⋊C4 | — | 6 | 1 | no | — |
| 639 | C4⋊C4 | — | 6 | 1 | no | — |
| 640 | C4⋊C4 | — | 6 | 1 | no | — |
| 641 | C4⋊C4 | — | 6 | 1 | no | — |
| 642 | C4⋊C4 | — | 6 | 1 | no | — |
| 643 | C4⋊C4 | — | 6 | 1 | no | — |
| 644 | C4⋊C4 | — | 6 | 2 | no | — |
| 645 | C4⋊C4 | — | 6 | 2 | no | — |
| 646 | C4⋊C4 | — | 6 | 2 | no | — |
| 647 | C4⋊C4 | — | 6 | 2 | no | — |
| 648 | C4⋊C4 | — | 6 | 1 | no | — |
| 649 | C4⋊C4 | — | 6 | 1 | no | — |
| 650 | C4⋊C4 | — | 6 | 1 | no | — |
| 651 | C4⋊C4 | — | 6 | 1 | no | — |
| 652 | C4⋊C4 | — | 24 | 2 | no | — |
| 653 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 654 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 655 | C22⋊C4 | — | 2 | 8 | no | — |
| 656 | C22⋊C4 | — | 2 | 2 | no | — |
| 657 | C22⋊C4 | — | 2 | 2 | no | — |
| 658 | C22⋊C4 | — | 2 | 1 | no | — |
| 659 | C22⋊C4 | — | 6 | 1 | no | — |
| 660 | C22⋊C4 | — | 6 | 1 | no | — |
| 661 | C22⋊C4 | — | 6 | 2 | no | — |
| 662 | C22⋊C4 | — | 6 | 2 | no | — |
| 663 | C22⋊C4 | — | 6 | 2 | no | — |
| 664 | C22⋊C4 | — | 6 | 1 | no | — |
| 665 | C22⋊C4 | — | 6 | 1 | no | — |
| 666 | C22⋊C4 | — | 6 | 2 | no | — |
| 667 | C22⋊C4 | — | 6 | 1 | no | — |
| 668 | C22⋊C4 | — | 12 | 1 | no | — |
| 669 | C22⋊C4 | — | 12 | 1 | no | — |
| 670 | C22⋊C4 | — | 24 | 2 | no | — |
| 671 | C42 | — | 2 | 1 | no | — |
| 672 | C42 | — | 2 | 1 | no | — |
| 673 | C42 | — | 3 | 1 | no | — |
| 674 | C42 | — | 3 | 1 | no | — |
| 675 | C42 | — | 3 | 1 | no | — |
| 676 | C42 | — | 3 | 1 | no | — |
| 677 | C42 | — | 6 | 2 | no | — |
| 678 | C42 | — | 6 | 2 | no | — |
| 679 | C42 | — | 6 | 2 | no | — |
| 680 | C42 | — | 6 | 2 | no | — |
| 681 | C42 | — | 6 | 1 | no | — |
| 682 | C42 | — | 6 | 1 | no | — |
| 683 | C42 | — | 6 | 1 | no | — |
| 684 | C42 | #237 | 1 | 2 | yes | — |
| 685 | C22×C3 | — | 2 | 1 | no | — |
| 686 | C22×C3 | — | 2 | 1 | no | — |
| 687 | C22×C3 | — | 4 | 4 | no | — |
| 688 | C22×C3 | — | 4 | 1 | no | — |
| 689 | C22×C3 | — | 4 | 2 | no | — |
| 690 | C22×C3 | — | 4 | 1 | no | — |
| 691 | C22×C3 | — | 4 | 1 | no | — |
| 692 | C22×C3 | — | 8 | 2 | no | — |
| 693 | C22×C3 | — | 8 | 1 | no | — |
| 694 | C22×C3 | — | 8 | 1 | no | — |
| 695 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 696 | C22×C3 | #525 | 1 | 1 | yes | characteristic |
| 697 | C22×C3 | #537 | 1 | 1 | yes | characteristic |
| 698 | C2×D3 | — | 4 | 1 | no | — |
| 699 | C2×D3 | — | 4 | 1 | no | — |
| 700 | C2×D3 | — | 4 | 1 | no | — |
| 701 | C3×C4 | — | 4 | 2 | no | — |
| 702 | C3×C4 | — | 4 | 2 | no | — |
| 703 | C3×C4 | — | 4 | 1 | no | — |
| 704 | C3×C4 | — | 4 | 1 | no | — |
| 705 | C3×C4 | — | 4 | 1 | no | — |
| 706 | C3×C4 | #546 | 1 | 1 | yes | characteristic |
| 707 | C3×C4 | #547 | 1 | 1 | yes | characteristic |
| 708 | C3×C4 | #548 | 1 | 1 | yes | characteristic |
| 709 | C3×C4 | #550 | 1 | 1 | yes | characteristic |
| 710 | Dic3 | — | 2 | 1 | no | — |
| 711 | Dic3 | — | 2 | 1 | no | — |
| 712 | Dic3 | — | 2 | 1 | no | — |
| 713 | Dic3 | — | 2 | 1 | no | — |
| 714 | Dic3 | — | 4 | 1 | no | — |
| 715 | Dic3 | — | 4 | 1 | no | — |
| 716 | Dic3 | — | 4 | 1 | no | — |
| 717 | Dic3 | — | 4 | 2 | no | — |
| 718 | Dic3 | — | 8 | 1 | no | — |
| 719 | Dic3 | — | 8 | 1 | no | — |
| 720 | C23 | — | 2 | 2 | no | — |
| 721 | C23 | — | 2 | 1 | no | — |
| 722 | C23 | — | 4 | 2 | no | — |
| 723 | C23 | — | 4 | 2 | no | — |
| 724 | C23 | — | 4 | 1 | no | — |
| 725 | C23 | — | 4 | 1 | no | — |
| 726 | C23 | — | 6 | 1 | no | — |
| 727 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 728 | Q8 | — | 2 | 1 | no | — |
| 729 | Q8 | — | 2 | 1 | no | — |
| 730 | Q8 | — | 4 | 1 | no | — |
| 731 | Q8 | — | 4 | 1 | no | — |
| 732 | Q8 | — | 4 | 1 | no | — |
| 733 | Q8 | — | 4 | 1 | no | — |
| 734 | Q8 | — | 6 | 1 | no | — |
| 735 | Q8 | — | 6 | 1 | no | — |
| 736 | Q8 | — | 12 | 2 | no | — |
| 737 | Q8 | — | 24 | 1 | no | — |
| 738 | D4 | — | 2 | 1 | no | — |
| 739 | D4 | — | 2 | 2 | no | — |
| 740 | D4 | — | 2 | 2 | no | — |
| 741 | D4 | — | 2 | 1 | no | — |
| 742 | D4 | — | 4 | 1 | no | — |
| 743 | D4 | — | 4 | 1 | no | — |
| 744 | D4 | — | 4 | 1 | no | — |
| 745 | D4 | — | 4 | 1 | no | — |
| 746 | D4 | — | 6 | 1 | no | — |
| 747 | D4 | — | 6 | 1 | no | — |
| 748 | D4 | — | 12 | 2 | no | — |
| 749 | D4 | — | 12 | 1 | no | — |
| 750 | D4 | — | 12 | 1 | no | — |
| 751 | D4 | — | 24 | 1 | no | — |
| 752 | C2×C4 | — | 2 | 2 | no | — |
| 753 | C2×C4 | — | 2 | 2 | no | — |
| 754 | C2×C4 | — | 2 | 1 | no | — |
| 755 | C2×C4 | — | 2 | 1 | no | — |
| 756 | C2×C4 | — | 2 | 2 | no | — |
| 757 | C2×C4 | — | 2 | 1 | no | — |
| 758 | C2×C4 | — | 2 | 2 | no | — |
| 759 | C2×C4 | — | 3 | 1 | no | — |
| 760 | C2×C4 | — | 3 | 1 | no | — |
| 761 | C2×C4 | — | 3 | 1 | no | — |
| 762 | C2×C4 | — | 3 | 1 | no | — |
| 763 | C2×C4 | — | 4 | 1 | no | — |
| 764 | C2×C4 | — | 4 | 1 | no | — |
| 765 | C2×C4 | — | 4 | 1 | no | — |
| 766 | C2×C4 | — | 4 | 1 | no | — |
| 767 | C2×C4 | — | 6 | 2 | no | — |
| 768 | C2×C4 | — | 6 | 1 | no | — |
| 769 | C2×C4 | — | 6 | 1 | no | — |
| 770 | C2×C4 | — | 6 | 1 | no | — |
| 771 | C2×C4 | — | 12 | 1 | no | — |
| 772 | C2×C4 | — | 12 | 1 | no | — |
| 773 | C2×C4 | — | 12 | 1 | no | — |
| 774 | C2×C4 | — | 12 | 1 | no | — |
| 775 | C2×C4 | — | 12 | 2 | no | — |
| 776 | C2×C4 | — | 12 | 1 | no | — |
| 777 | C2×C4 | — | 12 | 2 | no | — |
| 778 | C2×C4 | — | 12 | 1 | no | — |
| 779 | C2×C4 | — | 12 | 1 | no | — |
| 780 | C2×C4 | — | 12 | 1 | no | — |
| 781 | C2×C4 | — | 24 | 2 | no | — |
| 782 | C2×C4 | — | 24 | 2 | no | — |
| 783 | C2×C4 | — | 24 | 2 | no | — |
| 784 | C2×C4 | — | 24 | 2 | no | — |
| 785 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 786 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 787 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 788 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 789 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 790 | C2×C4 | #1010 | 1 | 1 | yes | characteristic |
| 791 | C8 | — | 4 | 1 | no | — |
| 792 | C8 | — | 4 | 1 | no | — |
| 793 | C8 | — | 12 | 1 | no | — |
| 794 | C8 | — | 12 | 1 | no | — |
| 795 | C2×C3 | — | 2 | 1 | no | — |
| 796 | C2×C3 | — | 2 | 1 | no | — |
| 797 | C2×C3 | — | 8 | 1 | no | — |
| 798 | C2×C3 | — | 8 | 2 | no | — |
| 799 | C2×C3 | #2407 | 1 | 1 | yes | characteristic |
| 800 | C2×C3 | #3020 | 1 | 1 | yes | characteristic |
| 801 | C2×C3 | #3021 | 1 | 1 | yes | characteristic |
| 802 | D3 | — | 8 | 1 | no | — |
| 803 | C22 | — | 2 | 1 | no | — |
| 804 | C22 | — | 2 | 1 | no | — |
| 805 | C22 | — | 4 | 4 | no | — |
| 806 | C22 | — | 4 | 1 | no | — |
| 807 | C22 | — | 4 | 2 | no | — |
| 808 | C22 | — | 4 | 1 | no | — |
| 809 | C22 | — | 4 | 1 | no | — |
| 810 | C22 | — | 8 | 2 | no | — |
| 811 | C22 | — | 8 | 1 | no | — |
| 812 | C22 | — | 8 | 1 | no | — |
| 813 | C22 | — | 12 | 1 | no | — |
| 814 | C22 | — | 12 | 1 | no | — |
| 815 | C22 | — | 12 | 1 | no | — |
| 816 | C22 | #5586 | 1 | 1 | yes | characteristic |
| 817 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 818 | C22 | #5597 | 1 | 1 | yes | characteristic |
| 819 | C4 | — | 4 | 2 | no | — |
| 820 | C4 | — | 4 | 2 | no | — |
| 821 | C4 | — | 4 | 1 | no | — |
| 822 | C4 | — | 4 | 1 | no | — |
| 823 | C4 | — | 4 | 1 | no | — |
| 824 | C4 | — | 6 | 1 | no | — |
| 825 | C4 | — | 6 | 1 | no | — |
| 826 | C4 | — | 6 | 1 | no | — |
| 827 | C4 | — | 6 | 1 | no | — |
| 828 | C4 | — | 12 | 1 | no | — |
| 829 | C4 | — | 12 | 1 | no | — |
| 830 | C4 | — | 12 | 2 | no | — |
| 831 | C4 | — | 12 | 1 | no | — |
| 832 | C4 | — | 24 | 1 | no | — |
| 833 | C4 | — | 24 | 1 | no | — |
| 834 | C4 | #5591 | 1 | 1 | yes | characteristic |
| 835 | C4 | #5598 | 1 | 1 | yes | characteristic |
| 836 | C4 | #5611 | 1 | 1 | yes | characteristic |
| 837 | C4 | #5718 | 1 | 1 | yes | characteristic |
| 838 | C3 | #24181 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 839 | C2 | — | 2 | 1 | no | — |
| 840 | C2 | — | 2 | 1 | no | — |
| 841 | C2 | — | 8 | 2 | no | — |
| 842 | C2 | — | 8 | 1 | no | — |
| 843 | C2 | — | 24 | 1 | no | — |
| 844 | C2 | #76668 | 1 | 1 | yes | characteristic |
| 845 | C2 | #80285 | 1 | 1 | yes | characteristic |
| 846 | C2 | #80286 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86342 | C2 | semidirect |
| 3. #82953 | C2 | semidirect |
| 4. #78917 | C2 | semidirect |
| 5. C3×#2003 | C2 | semidirect |
| 6. #72088 | C2 | semidirect |
| 7. #71863 | C2 | semidirect |
| 8. #71730 | C2 | semidirect |
| 9. #70363 | C2 | semidirect |
| 10. #70357 | C2 | semidirect |
| 11. #70328 | C2 | semidirect |
| 12. #70100 | C2 | semidirect |
| 13. #70097 | C2 | semidirect |
| 14. #68771 | C2 | semidirect |
| 15. #68732 | C2 | semidirect |
| 79. #2003 | D3 | semidirect |
| 838. C3 | #24181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86342 | 2 |
| #83931 | 2 |
| #82953 | 2 |
| #78917 | 2 |
| C3×#2003 | 2 |
| #72088 | 2 |
| #71863 | 2 |
| #71730 | 2 |
| #70363 | 2 |
| #70357 | 2 |
| #70328 | 2 |
| #70100 | 2 |
| #70097 | 2 |
| #68771 | 2 |
| #68732 | 2 |
| #24181 | 3 |