Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1448 conjugacy classes of subgroups.
The subgroup lattice has 754 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86319 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #83185 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #78921 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2002 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72094 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71763 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #70385 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | Dic3×#104 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #70323 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #70070 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #70064 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68760 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #25588 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×C3×AGL(1,ℤ/8) | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#535 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C3×#127 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5830 | C22 | 1 | 1 | yes | characteristic |
| 21 | Dic3×#41 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#949 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#940 | — | 2 | 4 | no | — |
| 24 | C2×#940 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#940 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#940 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#940 | C22 | 1 | 1 | yes | characteristic |
| 28 | #5798 | C22 | 1 | 1 | yes | characteristic |
| 29 | #5718 | — | 2 | 2 | no | — |
| 30 | #5681 | — | 2 | 2 | no | — |
| 31 | #5619 | — | 2 | 2 | no | — |
| 32 | #5596 | — | 2 | 2 | no | — |
| 33 | #5591 | — | 2 | 4 | no | — |
| 34 | #5521 | C22 | 1 | 1 | yes | characteristic |
| 35 | #5517 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×C3×#104 | C22 | 1 | 1 | yes | characteristic |
| 38 | C3×#418 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×C3×#100 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#837 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#833 | C22 | 1 | 1 | yes | characteristic |
| 42 | #5215 | C22 | 1 | 1 | yes | characteristic |
| 43 | #5215 | C22 | 1 | 1 | yes | characteristic |
| 44 | #5163 | — | 2 | 2 | no | — |
| 45 | #5150 | — | 2 | 2 | no | — |
| 46 | #5131 | C22 | 1 | 1 | yes | characteristic |
| 47 | #5131 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#823 | C22 | 1 | 1 | yes | characteristic |
| 49 | C2×#823 | C22 | 1 | 1 | yes | characteristic |
| 50 | #5118 | C22 | 1 | 1 | yes | characteristic |
| 51 | Dic3×M16 | C22 | 1 | 1 | yes | characteristic |
| 52 | #5001 | C22 | 1 | 1 | yes | characteristic |
| 53 | C42×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 54 | #4764 | — | 2 | 2 | no | — |
| 55 | #4760 | — | 2 | 2 | no | — |
| 56 | C3×#339 | C22 | 1 | 1 | yes | characteristic |
| 57 | #4555 | C22 | 1 | 1 | yes | characteristic |
| 58 | #4555 | C22 | 1 | 1 | yes | characteristic |
| 59 | #4532 | C22 | 1 | 1 | yes | characteristic |
| 60 | #4523 | C22 | 1 | 1 | yes | characteristic |
| 61 | #4523 | C22 | 1 | 1 | yes | characteristic |
| 62 | #3508 | — | 3 | 1 | no | — |
| 63 | #3138 | — | 3 | 1 | no | — |
| 64 | #3038 | — | 3 | 1 | no | — |
| 65 | #2867 | — | 3 | 1 | no | — |
| 66 | #2002 | — | 3 | 1 | no | — |
| 67 | #2002 | — | 3 | 1 | no | — |
| 68 | #2002 | — | 3 | 1 | no | — |
| 69 | #2002 | D3 | 1 | 1 | yes | characteristic, complemented |
| 70 | #1994 | — | 3 | 1 | no | — |
| 71 | #1965 | — | 3 | 1 | no | — |
| 72 | #1887 | — | 3 | 1 | no | — |
| 73 | #1887 | — | 3 | 1 | no | — |
| 74 | #1887 | — | 3 | 1 | no | — |
| 75 | #1887 | — | 3 | 1 | no | — |
| 76 | C4×#104 | — | 3 | 1 | no | — |
| 77 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C3×D4 | — | 2 | 2 | no | — |
| 79 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×#67 | — | 2 | 2 | no | — |
| 82 | C22×#67 | — | 2 | 2 | no | — |
| 83 | C22×#67 | — | 2 | 2 | no | — |
| 84 | C22×#67 | D4 | 1 | 4 | yes | — |
| 85 | C2×#237 | — | 2 | 4 | no | — |
| 86 | C22×D12 | — | 2 | 2 | no | — |
| 87 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 88 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 89 | C3×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 90 | C3×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 91 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 92 | C2×C3×D8 | — | 2 | 1 | no | — |
| 93 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 95 | C3×#127 | — | 2 | 1 | no | — |
| 96 | C3×#127 | — | 2 | 2 | no | — |
| 97 | C3×#127 | — | 4 | 1 | no | — |
| 98 | C3×#124 | — | 2 | 1 | no | — |
| 99 | C3×#121 | — | 2 | 2 | no | — |
| 100 | C3×#120 | — | 2 | 2 | no | — |
| 101 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×#217 | — | 2 | 2 | no | — |
| 104 | #949 | — | 4 | 1 | no | — |
| 105 | #949 | — | 4 | 1 | no | — |
| 106 | #947 | — | 2 | 1 | no | — |
| 107 | Q8×Dic3 | D4 | 1 | 2 | yes | complemented |
| 108 | C2×#215 | — | 2 | 1 | no | — |
| 109 | #940 | — | 2 | 1 | no | — |
| 110 | #940 | — | 2 | 2 | no | — |
| 111 | #940 | — | 2 | 1 | no | — |
| 112 | #940 | — | 2 | 1 | no | — |
| 113 | #940 | — | 2 | 2 | no | — |
| 114 | #940 | — | 2 | 1 | no | — |
| 115 | #940 | — | 2 | 1 | no | — |
| 116 | #940 | — | 2 | 2 | no | — |
| 117 | #940 | — | 2 | 2 | no | — |
| 118 | #940 | — | 4 | 1 | no | — |
| 119 | #940 | — | 4 | 1 | no | — |
| 120 | #940 | — | 4 | 16 | no | — |
| 121 | #939 | — | 2 | 4 | no | — |
| 122 | #939 | — | 2 | 4 | no | — |
| 123 | #938 | — | 2 | 4 | no | — |
| 124 | #937 | — | 2 | 2 | no | — |
| 125 | D4×Dic3 | — | 2 | 2 | no | — |
| 126 | D4×Dic3 | — | 2 | 2 | no | — |
| 127 | D4×Dic3 | — | 2 | 2 | no | — |
| 128 | D4×Dic3 | D4 | 1 | 2 | yes | complemented |
| 129 | C2×#213 | — | 2 | 1 | no | — |
| 130 | #930 | — | 2 | 2 | no | — |
| 131 | #926 | — | 2 | 1 | no | — |
| 132 | #926 | C23 | 1 | 1 | yes | characteristic |
| 133 | #926 | C23 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 135 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 136 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 138 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 139 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 140 | #893 | — | 2 | 2 | no | — |
| 141 | #890 | D4 | 1 | 2 | yes | complemented |
| 142 | #888 | D4 | 1 | 2 | yes | complemented |
| 143 | #886 | — | 2 | 4 | no | — |
| 144 | #885 | — | 2 | 4 | no | — |
| 145 | #883 | — | 2 | 4 | no | — |
| 146 | #67⋊C4 | — | 2 | 4 | no | — |
| 147 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 148 | #878 | — | 2 | 2 | no | — |
| 149 | #874 | — | 2 | 2 | no | — |
| 150 | #874 | — | 4 | 1 | no | — |
| 151 | C4×D12 | — | 2 | 2 | no | — |
| 152 | C4×Dic6 | — | 2 | 2 | no | — |
| 153 | C3×#104 | — | 2 | 2 | no | — |
| 154 | C3×#102 | — | 2 | 2 | no | — |
| 155 | C3×#100 | — | 4 | 1 | no | — |
| 156 | #837 | — | 2 | 2 | no | — |
| 157 | #833 | — | 4 | 1 | no | — |
| 158 | #832 | — | 2 | 2 | no | — |
| 159 | #832 | — | 2 | 2 | no | — |
| 160 | #823 | — | 4 | 1 | no | — |
| 161 | #823 | — | 4 | 1 | no | — |
| 162 | #821 | — | 2 | 2 | no | — |
| 163 | #821 | — | 2 | 2 | no | — |
| 164 | #815 | — | 2 | 1 | no | — |
| 165 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 166 | C8×Dic3 | — | 2 | 1 | no | — |
| 167 | #809 | — | 2 | 2 | no | — |
| 168 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 169 | C2×AGL(1,ℤ/8) | C2×D3 | 1 | 1 | yes | characteristic |
| 170 | #559 | — | 6 | 2 | no | — |
| 171 | #550 | — | 6 | 2 | no | — |
| 172 | #546 | — | 6 | 4 | no | — |
| 173 | #540 | — | 6 | 2 | no | — |
| 174 | #535 | — | 3 | 1 | no | — |
| 175 | #535 | C2×D3 | 1 | 1 | yes | characteristic |
| 176 | #533 | — | 3 | 1 | no | — |
| 177 | #532 | — | 6 | 2 | no | — |
| 178 | C2×#127 | — | 3 | 1 | no | — |
| 179 | C2×#127 | — | 3 | 1 | no | — |
| 180 | C2×#127 | — | 3 | 1 | no | — |
| 181 | C2×#127 | — | 3 | 1 | no | — |
| 182 | C2×#127 | — | 3 | 1 | no | — |
| 183 | C2×#127 | — | 6 | 4 | no | — |
| 184 | C2×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 185 | #518 | — | 3 | 1 | no | — |
| 186 | #518 | — | 3 | 1 | no | — |
| 187 | C4×#41 | — | 3 | 1 | no | — |
| 188 | #490 | — | 6 | 2 | no | — |
| 189 | #486 | — | 6 | 2 | no | — |
| 190 | #460 | — | 6 | 2 | no | — |
| 191 | #459 | — | 6 | 2 | no | — |
| 192 | #423 | — | 3 | 1 | no | — |
| 193 | C2×#104 | — | 3 | 1 | no | — |
| 194 | C2×#104 | C2×D3 | 1 | 1 | yes | characteristic |
| 195 | #418 | — | 3 | 1 | no | — |
| 196 | #418 | — | 3 | 1 | no | — |
| 197 | #418 | — | 3 | 1 | no | — |
| 198 | #418 | — | 3 | 1 | no | — |
| 199 | #418 | — | 3 | 1 | no | — |
| 200 | #418 | C2×D3 | 1 | 1 | yes | characteristic |
| 201 | C2×#100 | — | 3 | 1 | no | — |
| 202 | C2×#100 | — | 3 | 1 | no | — |
| 203 | C2×#100 | — | 3 | 1 | no | — |
| 204 | C2×#100 | C2×D3 | 1 | 1 | yes | characteristic |
| 205 | C4×M16 | — | 3 | 1 | no | — |
| 206 | C43 | — | 3 | 1 | no | — |
| 207 | #339 | — | 3 | 1 | no | — |
| 208 | #339 | — | 3 | 1 | no | — |
| 209 | #339 | — | 3 | 1 | no | — |
| 210 | #339 | — | 3 | 1 | no | — |
| 211 | #339 | — | 3 | 1 | no | — |
| 212 | #339 | C2×D3 | 1 | 1 | yes | characteristic |
| 213 | C24×C3 | — | 2 | 1 | no | — |
| 214 | C24×C3 | C2×D4 | 1 | 2 | yes | — |
| 215 | C23×D3 | — | 2 | 1 | no | — |
| 216 | C23×D3 | C2×D4 | 1 | 2 | yes | — |
| 217 | C3×#41 | — | 2 | 1 | no | — |
| 218 | C3×#41 | — | 2 | 1 | no | — |
| 219 | C3×#41 | — | 2 | 1 | no | — |
| 220 | C3×#41 | — | 2 | 1 | no | — |
| 221 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C2×C3×D4 | — | 2 | 1 | no | — |
| 223 | C2×C3×D4 | — | 2 | 4 | no | — |
| 224 | C2×C3×D4 | — | 2 | 1 | no | — |
| 225 | C2×C3×D4 | — | 2 | 1 | no | — |
| 226 | C2×C3×D4 | — | 2 | 1 | no | — |
| 227 | C2×C3×D4 | — | 2 | 1 | no | — |
| 228 | C2×C3×D4 | — | 2 | 1 | no | — |
| 229 | C2×C3×D4 | — | 2 | 1 | no | — |
| 230 | C2×C3×D4 | — | 2 | 1 | no | — |
| 231 | C2×C3×D4 | — | 2 | 1 | no | — |
| 232 | C2×C3×D4 | — | 2 | 1 | no | — |
| 233 | C2×C3×D4 | — | 2 | 1 | no | — |
| 234 | C2×C3×D4 | — | 2 | 1 | no | — |
| 235 | C2×C3×D4 | — | 2 | 1 | no | — |
| 236 | C2×C3×D4 | — | 4 | 4 | no | — |
| 237 | C2×C3×D4 | — | 4 | 8 | no | — |
| 238 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C22×C3×C4 | — | 2 | 1 | no | — |
| 240 | C22×C3×C4 | — | 2 | 1 | no | — |
| 241 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 242 | C2×#67 | — | 2 | 4 | no | — |
| 243 | C2×#67 | — | 2 | 4 | no | — |
| 244 | C2×#67 | — | 2 | 4 | no | — |
| 245 | C2×#67 | — | 4 | 8 | no | — |
| 246 | C2×#67 | — | 4 | 4 | no | — |
| 247 | C2×#67 | — | 4 | 4 | no | — |
| 248 | C2×#67 | — | 4 | 8 | no | — |
| 249 | C2×#67 | — | 4 | 8 | no | — |
| 250 | C2×#67 | — | 4 | 8 | no | — |
| 251 | C2×#67 | — | 4 | 2 | no | — |
| 252 | C2×#67 | — | 4 | 2 | no | — |
| 253 | C22×Dic3 | — | 2 | 1 | no | — |
| 254 | C22×Dic3 | — | 2 | 4 | no | — |
| 255 | C22×Dic3 | — | 2 | 2 | no | — |
| 256 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 257 | #237 | — | 8 | 8 | no | — |
| 258 | C2×D12 | — | 2 | 1 | no | — |
| 259 | C2×D12 | — | 2 | 1 | no | — |
| 260 | C2×D12 | — | 2 | 1 | no | — |
| 261 | C2×D12 | — | 2 | 1 | no | — |
| 262 | C2×D12 | — | 2 | 1 | no | — |
| 263 | C2×D12 | — | 2 | 1 | no | — |
| 264 | C2×D12 | — | 2 | 1 | no | — |
| 265 | C2×D12 | — | 2 | 1 | no | — |
| 266 | C2×D12 | — | 2 | 1 | no | — |
| 267 | C2×D12 | — | 2 | 1 | no | — |
| 268 | C2×D12 | — | 2 | 1 | no | — |
| 269 | C2×D12 | — | 2 | 1 | no | — |
| 270 | C2×D12 | — | 4 | 4 | no | — |
| 271 | C2×D12 | — | 4 | 8 | no | — |
| 272 | C2×C4×D3 | — | 2 | 4 | no | — |
| 273 | C2×Dic6 | — | 2 | 2 | no | — |
| 274 | C3×SD16 | — | 4 | 2 | no | — |
| 275 | C3×D8 | — | 4 | 2 | no | — |
| 276 | C3×M16 | — | 2 | 1 | no | — |
| 277 | C3×M16 | — | 2 | 1 | no | — |
| 278 | C3×M16 | — | 2 | 1 | no | — |
| 279 | C3×M16 | — | 2 | 1 | no | — |
| 280 | C2×C3×C8 | — | 2 | 1 | no | — |
| 281 | C2×C3×C8 | — | 2 | 1 | no | — |
| 282 | C3×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 283 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 284 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 285 | C3×C42 | — | 2 | 1 | no | — |
| 286 | C3×C42 | — | 2 | 1 | no | — |
| 287 | C3×C42 | #41 | 1 | 2 | yes | complemented |
| 288 | #217 | — | 2 | 4 | no | — |
| 289 | #217 | — | 2 | 1 | no | — |
| 290 | #217 | — | 2 | 1 | no | — |
| 291 | #217 | — | 2 | 2 | no | — |
| 292 | #215 | — | 4 | 2 | no | — |
| 293 | #213 | — | 4 | 2 | no | — |
| 294 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 295 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 296 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 297 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 298 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 299 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 300 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 301 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 302 | C4×Dic3 | — | 2 | 8 | no | — |
| 303 | C4×Dic3 | — | 2 | 1 | no | — |
| 304 | C4×Dic3 | — | 2 | 1 | no | — |
| 305 | C4×Dic3 | — | 2 | 1 | no | — |
| 306 | C4×Dic3 | — | 2 | 2 | no | — |
| 307 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 308 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 309 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 310 | C4×Dic3 | #41 | 1 | 2 | yes | complemented |
| 311 | #208 | — | 2 | 1 | no | — |
| 312 | #208 | — | 2 | 1 | no | — |
| 313 | #208 | — | 2 | 1 | no | — |
| 314 | #208 | — | 2 | 1 | no | — |
| 315 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 316 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 317 | C2×#41 | — | 6 | 4 | no | — |
| 318 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 319 | C22×D4 | — | 2 | 2 | no | — |
| 320 | C22×D4 | — | 3 | 4 | no | — |
| 321 | C22×D4 | — | 3 | 1 | no | — |
| 322 | C22×D4 | — | 3 | 1 | no | — |
| 323 | C22×D4 | — | 6 | 2 | no | — |
| 324 | C22×D4 | — | 6 | 2 | no | — |
| 325 | C22×D4 | — | 6 | 2 | no | — |
| 326 | C22×D4 | — | 6 | 2 | no | — |
| 327 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 328 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 329 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 330 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 331 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 332 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 333 | C2×SD16 | — | 2 | 1 | no | — |
| 334 | C2×SD16 | — | 6 | 1 | no | — |
| 335 | C2×D8 | — | 2 | 1 | no | — |
| 336 | C2×D8 | — | 6 | 1 | no | — |
| 337 | C2×M16 | — | 3 | 1 | no | — |
| 338 | C2×M16 | — | 3 | 1 | no | — |
| 339 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 340 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 341 | C4⋊Q8 | — | 3 | 2 | no | — |
| 342 | #127 | — | 2 | 1 | no | — |
| 343 | #127 | — | 2 | 2 | no | — |
| 344 | #127 | — | 4 | 1 | no | — |
| 345 | #127 | — | 6 | 1 | no | — |
| 346 | #127 | — | 6 | 1 | no | — |
| 347 | #127 | — | 6 | 2 | no | — |
| 348 | #127 | — | 6 | 2 | no | — |
| 349 | #127 | — | 6 | 2 | no | — |
| 350 | #127 | — | 6 | 2 | no | — |
| 351 | #127 | — | 6 | 1 | no | — |
| 352 | #127 | — | 6 | 1 | no | — |
| 353 | #127 | — | 6 | 1 | no | — |
| 354 | #127 | — | 6 | 2 | no | — |
| 355 | #127 | — | 12 | 1 | no | — |
| 356 | #127 | — | 12 | 1 | no | — |
| 357 | #127 | — | 12 | 1 | no | — |
| 358 | #127 | — | 12 | 16 | no | — |
| 359 | #125 | — | 3 | 2 | no | — |
| 360 | #124 | — | 2 | 1 | no | — |
| 361 | #124 | — | 6 | 4 | no | — |
| 362 | #124 | — | 6 | 1 | no | — |
| 363 | #123 | — | 6 | 4 | no | — |
| 364 | #123 | — | 6 | 4 | no | — |
| 365 | C22⋊Q8 | — | 6 | 2 | no | — |
| 366 | #121 | — | 2 | 2 | no | — |
| 367 | #121 | — | 6 | 2 | no | — |
| 368 | #121 | — | 6 | 4 | no | — |
| 369 | #121 | — | 6 | 4 | no | — |
| 370 | #121 | — | 6 | 4 | no | — |
| 371 | #120 | — | 2 | 2 | no | — |
| 372 | #120 | — | 6 | 2 | no | — |
| 373 | C4×Q8 | — | 3 | 2 | no | — |
| 374 | C4×Q8 | — | 6 | 2 | no | — |
| 375 | C4×D4 | — | 3 | 2 | no | — |
| 376 | C4×D4 | — | 6 | 2 | no | — |
| 377 | C4×D4 | — | 6 | 4 | no | — |
| 378 | C4×D4 | — | 6 | 2 | no | — |
| 379 | C4×D4 | — | 6 | 2 | no | — |
| 380 | C4×D4 | — | 6 | 2 | no | — |
| 381 | C4×D4 | — | 6 | 2 | no | — |
| 382 | #117 | — | 3 | 1 | no | — |
| 383 | #117 | — | 3 | 1 | no | — |
| 384 | #117 | — | 6 | 1 | no | — |
| 385 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 386 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 387 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 388 | C2×C42 | — | 3 | 1 | no | — |
| 389 | C2×C42 | — | 3 | 1 | no | — |
| 390 | C2×C42 | — | 6 | 1 | no | — |
| 391 | C2×C42 | — | 6 | 2 | no | — |
| 392 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 393 | C4⋊C8 | — | 6 | 2 | no | — |
| 394 | #104 | — | 2 | 2 | no | — |
| 395 | #104 | — | 6 | 2 | no | — |
| 396 | #102 | — | 2 | 2 | no | — |
| 397 | #102 | — | 6 | 2 | no | — |
| 398 | #102 | — | 6 | 2 | no | — |
| 399 | #102 | — | 6 | 2 | no | — |
| 400 | #102 | — | 6 | 2 | no | — |
| 401 | #102 | — | 6 | 2 | no | — |
| 402 | #100 | — | 4 | 1 | no | — |
| 403 | #100 | — | 12 | 1 | no | — |
| 404 | #100 | — | 12 | 1 | no | — |
| 405 | #100 | — | 12 | 1 | no | — |
| 406 | #97 | — | 6 | 1 | no | — |
| 407 | C4×C8 | — | 6 | 1 | no | — |
| 408 | C23×C3 | — | 2 | 2 | no | — |
| 409 | C23×C3 | — | 2 | 1 | no | — |
| 410 | C23×C3 | — | 2 | 2 | no | — |
| 411 | C23×C3 | — | 2 | 2 | no | — |
| 412 | C23×C3 | — | 4 | 4 | no | — |
| 413 | C23×C3 | — | 4 | 4 | no | — |
| 414 | C23×C3 | — | 4 | 1 | no | — |
| 415 | C23×C3 | — | 4 | 1 | no | — |
| 416 | C23×C3 | — | 4 | 1 | no | — |
| 417 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 418 | C22×D3 | — | 2 | 2 | no | — |
| 419 | C22×D3 | — | 2 | 2 | no | — |
| 420 | C22×D3 | — | 2 | 2 | no | — |
| 421 | C22×D3 | — | 4 | 4 | no | — |
| 422 | C22×D3 | — | 4 | 4 | no | — |
| 423 | C22×D3 | — | 4 | 1 | no | — |
| 424 | C22×D3 | — | 4 | 1 | no | — |
| 425 | C22×D3 | — | 4 | 1 | no | — |
| 426 | C3×Q8 | — | 2 | 1 | no | — |
| 427 | C3×Q8 | — | 2 | 1 | no | — |
| 428 | C3×D4 | — | 2 | 1 | no | — |
| 429 | C3×D4 | — | 2 | 1 | no | — |
| 430 | C3×D4 | — | 4 | 1 | no | — |
| 431 | C3×D4 | — | 4 | 1 | no | — |
| 432 | C3×D4 | — | 4 | 1 | no | — |
| 433 | C3×D4 | — | 4 | 1 | no | — |
| 434 | C3×D4 | — | 4 | 1 | no | — |
| 435 | C3×D4 | — | 4 | 1 | no | — |
| 436 | C3×D4 | — | 4 | 1 | no | — |
| 437 | C3×D4 | — | 4 | 1 | no | — |
| 438 | C3×D4 | — | 4 | 1 | no | — |
| 439 | C3×D4 | — | 4 | 1 | no | — |
| 440 | C3×D4 | — | 8 | 8 | no | — |
| 441 | C3×D4 | — | 8 | 4 | no | — |
| 442 | C2×C3×C4 | — | 2 | 4 | no | — |
| 443 | C2×C3×C4 | — | 2 | 2 | no | — |
| 444 | C2×C3×C4 | — | 2 | 1 | no | — |
| 445 | C2×C3×C4 | — | 2 | 2 | no | — |
| 446 | C2×C3×C4 | — | 4 | 1 | no | — |
| 447 | C2×C3×C4 | — | 4 | 1 | no | — |
| 448 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 449 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 450 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 451 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 452 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 453 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 454 | #67 | — | 4 | 8 | no | — |
| 455 | #67 | — | 8 | 4 | no | — |
| 456 | #67 | — | 8 | 8 | no | — |
| 457 | #67 | — | 8 | 8 | no | — |
| 458 | #67 | — | 8 | 4 | no | — |
| 459 | #67 | — | 8 | 4 | no | — |
| 460 | #67 | — | 8 | 4 | no | — |
| 461 | C2×Dic3 | — | 2 | 4 | no | — |
| 462 | C2×Dic3 | — | 2 | 2 | no | — |
| 463 | C2×Dic3 | — | 2 | 4 | no | — |
| 464 | C2×Dic3 | — | 2 | 2 | no | — |
| 465 | C2×Dic3 | — | 2 | 2 | no | — |
| 466 | C2×Dic3 | — | 4 | 4 | no | — |
| 467 | C2×Dic3 | — | 8 | 4 | no | — |
| 468 | C2×Dic3 | #120 | 1 | 2 | yes | — |
| 469 | C2×Dic3 | #120 | 1 | 2 | yes | — |
| 470 | D12 | — | 4 | 1 | no | — |
| 471 | D12 | — | 4 | 1 | no | — |
| 472 | D12 | — | 4 | 1 | no | — |
| 473 | D12 | — | 4 | 1 | no | — |
| 474 | D12 | — | 4 | 1 | no | — |
| 475 | D12 | — | 4 | 1 | no | — |
| 476 | D12 | — | 4 | 1 | no | — |
| 477 | D12 | — | 4 | 1 | no | — |
| 478 | D12 | — | 8 | 8 | no | — |
| 479 | C4×D3 | — | 8 | 4 | no | — |
| 480 | Dic6 | — | 4 | 4 | no | — |
| 481 | C3×C8 | — | 4 | 1 | no | — |
| 482 | C3×C8 | — | 4 | 1 | no | — |
| 483 | C3⋊C8 | — | 4 | 1 | no | — |
| 484 | C3⋊C8 | — | 4 | 1 | no | — |
| 485 | C24 | — | 2 | 1 | no | — |
| 486 | C24 | — | 3 | 2 | no | — |
| 487 | C24 | — | 6 | 1 | no | — |
| 488 | C24 | D3×D4 | 1 | 2 | yes | — |
| 489 | #41 | — | 2 | 1 | no | — |
| 490 | #41 | — | 2 | 1 | no | — |
| 491 | #41 | — | 2 | 1 | no | — |
| 492 | #41 | — | 2 | 1 | no | — |
| 493 | #41 | — | 24 | 8 | no | — |
| 494 | C2×Q8 | — | 6 | 2 | no | — |
| 495 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 496 | C2×D4 | — | 2 | 1 | no | — |
| 497 | C2×D4 | — | 2 | 4 | no | — |
| 498 | C2×D4 | — | 2 | 1 | no | — |
| 499 | C2×D4 | — | 2 | 1 | no | — |
| 500 | C2×D4 | — | 2 | 1 | no | — |
| 501 | C2×D4 | — | 2 | 1 | no | — |
| 502 | C2×D4 | — | 2 | 1 | no | — |
| 503 | C2×D4 | — | 2 | 1 | no | — |
| 504 | C2×D4 | — | 2 | 1 | no | — |
| 505 | C2×D4 | — | 2 | 1 | no | — |
| 506 | C2×D4 | — | 2 | 1 | no | — |
| 507 | C2×D4 | — | 2 | 1 | no | — |
| 508 | C2×D4 | — | 2 | 1 | no | — |
| 509 | C2×D4 | — | 2 | 1 | no | — |
| 510 | C2×D4 | — | 4 | 4 | no | — |
| 511 | C2×D4 | — | 4 | 8 | no | — |
| 512 | C2×D4 | — | 6 | 4 | no | — |
| 513 | C2×D4 | — | 6 | 4 | no | — |
| 514 | C2×D4 | — | 6 | 4 | no | — |
| 515 | C2×D4 | — | 6 | 1 | no | — |
| 516 | C2×D4 | — | 6 | 1 | no | — |
| 517 | C2×D4 | — | 6 | 1 | no | — |
| 518 | C2×D4 | — | 6 | 1 | no | — |
| 519 | C2×D4 | — | 6 | 1 | no | — |
| 520 | C2×D4 | — | 6 | 1 | no | — |
| 521 | C2×D4 | — | 6 | 1 | no | — |
| 522 | C2×D4 | — | 6 | 1 | no | — |
| 523 | C2×D4 | — | 6 | 1 | no | — |
| 524 | C2×D4 | — | 6 | 1 | no | — |
| 525 | C2×D4 | — | 6 | 1 | no | — |
| 526 | C2×D4 | — | 6 | 1 | no | — |
| 527 | C2×D4 | — | 12 | 4 | no | — |
| 528 | C2×D4 | — | 12 | 8 | no | — |
| 529 | C2×D4 | — | 12 | 2 | no | — |
| 530 | C2×D4 | — | 12 | 2 | no | — |
| 531 | C2×D4 | — | 12 | 8 | no | — |
| 532 | C2×D4 | — | 12 | 4 | no | — |
| 533 | C2×D4 | — | 12 | 4 | no | — |
| 534 | C2×D4 | — | 12 | 8 | no | — |
| 535 | C2×D4 | — | 12 | 8 | no | — |
| 536 | C2×D4 | — | 12 | 8 | no | — |
| 537 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 538 | C22×C4 | — | 2 | 1 | no | — |
| 539 | C22×C4 | — | 2 | 1 | no | — |
| 540 | C22×C4 | — | 3 | 2 | no | — |
| 541 | C22×C4 | — | 6 | 4 | no | — |
| 542 | C22×C4 | — | 6 | 2 | no | — |
| 543 | C22×C4 | — | 6 | 1 | no | — |
| 544 | C22×C4 | — | 6 | 4 | no | — |
| 545 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 546 | SD16 | — | 4 | 2 | no | — |
| 547 | SD16 | — | 12 | 2 | no | — |
| 548 | D8 | — | 4 | 2 | no | — |
| 549 | D8 | — | 12 | 2 | no | — |
| 550 | M16 | — | 2 | 1 | no | — |
| 551 | M16 | — | 2 | 1 | no | — |
| 552 | M16 | — | 2 | 1 | no | — |
| 553 | M16 | — | 2 | 1 | no | — |
| 554 | M16 | — | 6 | 1 | no | — |
| 555 | M16 | — | 6 | 1 | no | — |
| 556 | M16 | — | 6 | 1 | no | — |
| 557 | M16 | — | 6 | 1 | no | — |
| 558 | C2×C8 | — | 2 | 1 | no | — |
| 559 | C2×C8 | — | 2 | 1 | no | — |
| 560 | C2×C8 | — | 6 | 1 | no | — |
| 561 | C2×C8 | — | 6 | 1 | no | — |
| 562 | C4⋊C4 | — | 3 | 2 | no | — |
| 563 | C4⋊C4 | — | 3 | 2 | no | — |
| 564 | C4⋊C4 | — | 6 | 2 | no | — |
| 565 | C4⋊C4 | — | 6 | 2 | no | — |
| 566 | C4⋊C4 | — | 6 | 2 | no | — |
| 567 | C4⋊C4 | — | 6 | 2 | no | — |
| 568 | C4⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 569 | C22⋊C4 | — | 2 | 4 | no | — |
| 570 | C22⋊C4 | — | 2 | 1 | no | — |
| 571 | C22⋊C4 | — | 6 | 4 | no | — |
| 572 | C22⋊C4 | — | 6 | 4 | no | — |
| 573 | C22⋊C4 | — | 6 | 2 | no | — |
| 574 | C22⋊C4 | — | 6 | 4 | no | — |
| 575 | C22⋊C4 | — | 6 | 1 | no | — |
| 576 | C22⋊C4 | — | 6 | 1 | no | — |
| 577 | C42 | — | 2 | 1 | no | — |
| 578 | C42 | — | 2 | 1 | no | — |
| 579 | C42 | — | 3 | 1 | no | — |
| 580 | C42 | — | 3 | 1 | no | — |
| 581 | C42 | — | 3 | 2 | no | — |
| 582 | C42 | — | 3 | 2 | no | — |
| 583 | C42 | — | 6 | 2 | no | — |
| 584 | C42 | — | 6 | 8 | no | — |
| 585 | C42 | — | 6 | 1 | no | — |
| 586 | C42 | — | 6 | 1 | no | — |
| 587 | C42 | — | 6 | 1 | no | — |
| 588 | C42 | #237 | 1 | 2 | yes | complemented |
| 589 | C22×C3 | — | 2 | 2 | no | — |
| 590 | C22×C3 | — | 4 | 1 | no | — |
| 591 | C22×C3 | — | 4 | 2 | no | — |
| 592 | C22×C3 | — | 4 | 2 | no | — |
| 593 | C22×C3 | — | 4 | 4 | no | — |
| 594 | C22×C3 | — | 8 | 2 | no | — |
| 595 | C22×C3 | — | 8 | 2 | no | — |
| 596 | C22×C3 | — | 8 | 2 | no | — |
| 597 | C22×C3 | — | 8 | 2 | no | — |
| 598 | C22×C3 | — | 8 | 1 | no | — |
| 599 | C22×C3 | — | 8 | 2 | no | — |
| 600 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 601 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 602 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 603 | C2×D3 | — | 4 | 2 | no | — |
| 604 | C2×D3 | — | 4 | 4 | no | — |
| 605 | C2×D3 | — | 8 | 2 | no | — |
| 606 | C2×D3 | — | 8 | 2 | no | — |
| 607 | C2×D3 | — | 8 | 2 | no | — |
| 608 | C2×D3 | — | 8 | 2 | no | — |
| 609 | C2×D3 | — | 8 | 1 | no | — |
| 610 | C2×D3 | — | 8 | 2 | no | — |
| 611 | C3×C4 | — | 2 | 4 | no | — |
| 612 | C3×C4 | — | 4 | 1 | no | — |
| 613 | C3×C4 | — | 4 | 2 | no | — |
| 614 | C3×C4 | #532 | 1 | 1 | yes | characteristic |
| 615 | C3×C4 | #535 | 1 | 1 | yes | characteristic |
| 616 | C3×C4 | #550 | 1 | 1 | yes | characteristic |
| 617 | C3×C4 | #550 | 1 | 1 | yes | characteristic |
| 618 | Dic3 | — | 2 | 4 | no | — |
| 619 | Dic3 | — | 2 | 2 | no | — |
| 620 | Dic3 | — | 4 | 2 | no | — |
| 621 | Dic3 | — | 4 | 2 | no | — |
| 622 | Dic3 | #453 | 1 | 4 | yes | — |
| 623 | C23 | — | 2 | 2 | no | — |
| 624 | C23 | — | 2 | 1 | no | — |
| 625 | C23 | — | 2 | 2 | no | — |
| 626 | C23 | — | 2 | 2 | no | — |
| 627 | C23 | — | 4 | 4 | no | — |
| 628 | C23 | — | 4 | 4 | no | — |
| 629 | C23 | — | 4 | 1 | no | — |
| 630 | C23 | — | 4 | 1 | no | — |
| 631 | C23 | — | 4 | 1 | no | — |
| 632 | C23 | — | 6 | 2 | no | — |
| 633 | C23 | — | 6 | 2 | no | — |
| 634 | C23 | — | 6 | 2 | no | — |
| 635 | C23 | — | 12 | 4 | no | — |
| 636 | C23 | — | 12 | 4 | no | — |
| 637 | C23 | — | 12 | 1 | no | — |
| 638 | C23 | — | 12 | 1 | no | — |
| 639 | C23 | — | 12 | 1 | no | — |
| 640 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 641 | Q8 | — | 2 | 1 | no | — |
| 642 | Q8 | — | 2 | 1 | no | — |
| 643 | Q8 | — | 12 | 4 | no | — |
| 644 | D4 | — | 2 | 1 | no | — |
| 645 | D4 | — | 2 | 1 | no | — |
| 646 | D4 | — | 4 | 1 | no | — |
| 647 | D4 | — | 4 | 1 | no | — |
| 648 | D4 | — | 4 | 1 | no | — |
| 649 | D4 | — | 4 | 1 | no | — |
| 650 | D4 | — | 4 | 1 | no | — |
| 651 | D4 | — | 4 | 1 | no | — |
| 652 | D4 | — | 4 | 1 | no | — |
| 653 | D4 | — | 4 | 1 | no | — |
| 654 | D4 | — | 4 | 1 | no | — |
| 655 | D4 | — | 4 | 1 | no | — |
| 656 | D4 | — | 8 | 8 | no | — |
| 657 | D4 | — | 8 | 4 | no | — |
| 658 | D4 | — | 12 | 8 | no | — |
| 659 | D4 | — | 12 | 1 | no | — |
| 660 | D4 | — | 12 | 1 | no | — |
| 661 | D4 | — | 12 | 1 | no | — |
| 662 | D4 | — | 12 | 1 | no | — |
| 663 | D4 | — | 12 | 1 | no | — |
| 664 | D4 | — | 12 | 1 | no | — |
| 665 | D4 | — | 12 | 1 | no | — |
| 666 | D4 | — | 12 | 1 | no | — |
| 667 | D4 | — | 24 | 8 | no | — |
| 668 | D4 | — | 24 | 4 | no | — |
| 669 | D4 | — | 24 | 4 | no | — |
| 670 | D4 | — | 24 | 8 | no | — |
| 671 | D4 | — | 24 | 8 | no | — |
| 672 | D4 | — | 24 | 4 | no | — |
| 673 | D4 | — | 24 | 4 | no | — |
| 674 | C2×C4 | — | 2 | 4 | no | — |
| 675 | C2×C4 | — | 2 | 2 | no | — |
| 676 | C2×C4 | — | 2 | 2 | no | — |
| 677 | C2×C4 | — | 2 | 1 | no | — |
| 678 | C2×C4 | — | 3 | 2 | no | — |
| 679 | C2×C4 | — | 3 | 2 | no | — |
| 680 | C2×C4 | — | 4 | 1 | no | — |
| 681 | C2×C4 | — | 4 | 1 | no | — |
| 682 | C2×C4 | — | 6 | 4 | no | — |
| 683 | C2×C4 | — | 6 | 4 | no | — |
| 684 | C2×C4 | — | 6 | 2 | no | — |
| 685 | C2×C4 | — | 6 | 2 | no | — |
| 686 | C2×C4 | — | 6 | 2 | no | — |
| 687 | C2×C4 | — | 12 | 4 | no | — |
| 688 | C2×C4 | — | 24 | 4 | no | — |
| 689 | C2×C4 | — | 24 | 4 | no | — |
| 690 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 691 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 692 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 693 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 694 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 695 | C2×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 696 | C8 | — | 4 | 1 | no | — |
| 697 | C8 | — | 4 | 1 | no | — |
| 698 | C8 | — | 12 | 1 | no | — |
| 699 | C8 | — | 12 | 1 | no | — |
| 700 | C2×C3 | — | 2 | 1 | no | — |
| 701 | C2×C3 | — | 2 | 1 | no | — |
| 702 | C2×C3 | — | 8 | 1 | no | — |
| 703 | C2×C3 | — | 8 | 2 | no | — |
| 704 | C2×C3 | — | 16 | 1 | no | — |
| 705 | C2×C3 | #2431 | 1 | 1 | yes | characteristic |
| 706 | C2×C3 | C2×#453 | 1 | 2 | yes | — |
| 707 | D3 | — | 8 | 2 | no | — |
| 708 | D3 | — | 16 | 1 | no | — |
| 709 | C22 | — | 2 | 2 | no | — |
| 710 | C22 | — | 4 | 1 | no | — |
| 711 | C22 | — | 4 | 2 | no | — |
| 712 | C22 | — | 4 | 2 | no | — |
| 713 | C22 | — | 4 | 4 | no | — |
| 714 | C22 | — | 8 | 2 | no | — |
| 715 | C22 | — | 8 | 2 | no | — |
| 716 | C22 | — | 8 | 2 | no | — |
| 717 | C22 | — | 8 | 2 | no | — |
| 718 | C22 | — | 8 | 1 | no | — |
| 719 | C22 | — | 8 | 2 | no | — |
| 720 | C22 | — | 12 | 2 | no | — |
| 721 | C22 | — | 12 | 4 | no | — |
| 722 | C22 | — | 24 | 2 | no | — |
| 723 | C22 | — | 24 | 2 | no | — |
| 724 | C22 | — | 24 | 2 | no | — |
| 725 | C22 | — | 24 | 2 | no | — |
| 726 | C22 | — | 24 | 1 | no | — |
| 727 | C22 | — | 24 | 2 | no | — |
| 728 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 729 | C22 | #5591 | 1 | 1 | yes | characteristic |
| 730 | C22 | #5610 | 1 | 1 | yes | characteristic |
| 731 | C4 | — | 2 | 4 | no | — |
| 732 | C4 | — | 3 | 4 | no | — |
| 733 | C4 | — | 4 | 1 | no | — |
| 734 | C4 | — | 4 | 2 | no | — |
| 735 | C4 | — | 6 | 4 | no | — |
| 736 | C4 | — | 6 | 2 | no | — |
| 737 | C4 | — | 12 | 2 | no | — |
| 738 | C4 | — | 12 | 2 | no | — |
| 739 | C4 | #5592 | 1 | 1 | yes | characteristic |
| 740 | C4 | #5596 | 1 | 1 | yes | characteristic |
| 741 | C4 | #5599 | 1 | 1 | yes | characteristic |
| 742 | C4 | #5718 | 1 | 1 | yes | characteristic |
| 743 | C3 | #25588 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 744 | C2 | — | 2 | 1 | no | — |
| 745 | C2 | — | 2 | 1 | no | — |
| 746 | C2 | — | 8 | 2 | no | — |
| 747 | C2 | — | 8 | 1 | no | — |
| 748 | C2 | — | 16 | 1 | no | — |
| 749 | C2 | — | 24 | 2 | no | — |
| 750 | C2 | — | 48 | 1 | no | — |
| 751 | C2 | #76672 | 1 | 1 | yes | characteristic |
| 752 | C2 | D3×#453 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86319 | C2 | semidirect |
| 2. #83932 | C2 | semidirect |
| 3. #83185 | C2 | semidirect |
| 4. #78921 | C2 | semidirect |
| 5. C3×#2002 | C2 | semidirect |
| 6. #72094 | C2 | semidirect |
| 7. #71856 | C2 | semidirect |
| 8. #71763 | C2 | semidirect |
| 9. #70385 | C2 | semidirect |
| 10. Dic3×#104 | C2 | semidirect |
| 11. #70323 | C2 | semidirect |
| 12. #70070 | C2 | semidirect |
| 13. #70064 | C2 | semidirect |
| 14. #68760 | C2 | semidirect |
| 15. #68731 | C2 | semidirect |
| 69. #2002 | D3 | semidirect |
| 107. Q8×Dic3 | D4 | semidirect |
| 128. D4×Dic3 | D4 | semidirect |
| 141. #890 | D4 | semidirect |
| 142. #888 | D4 | semidirect |
| 287. C3×C42 | #41 | semidirect |
| 310. C4×Dic3 | #41 | semidirect |
| 588. C42 | #237 | semidirect |
| 743. C3 | #25588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86319 | 2 |
| #83932 | 2 |
| #83185 | 2 |
| #78921 | 2 |
| C3×#2002 | 2 |
| #72094 | 2 |
| #71856 | 2 |
| #71763 | 2 |
| #70385 | 2 |
| Dic3×#104 | 2 |
| #70323 | 2 |
| #70070 | 2 |
| #70064 | 2 |
| #68760 | 2 |
| #68731 | 2 |
| #25588 | 3 |