Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2750 conjugacy classes of subgroups.
The subgroup lattice has 858 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87268 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5822 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#5748 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#5504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C3×#417 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #83750 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#4966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #78913 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #78912 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #78911 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #78910 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #78815 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #78767 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | #60425 | — | 3 | 1 | no | maximal, Sylow |
| 15 | C22×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 16 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×C3×M16 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C3×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5833 | — | 2 | 1 | no | — |
| 21 | #5833 | — | 2 | 1 | no | — |
| 22 | #5832 | C22 | 1 | 4 | yes | — |
| 23 | #5830 | C22 | 1 | 2 | yes | complemented |
| 24 | #5828 | — | 2 | 2 | no | — |
| 25 | #5825 | C22 | 1 | 2 | yes | complemented |
| 26 | C2×#951 | C22 | 1 | 2 | yes | complemented |
| 27 | #5822 | — | 2 | 8 | no | — |
| 28 | C2×#950 | C22 | 1 | 4 | yes | — |
| 29 | C2×#949 | C22 | 1 | 2 | yes | complemented |
| 30 | #5816 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×#942 | C22 | 1 | 2 | yes | complemented |
| 32 | #5805 | C22 | 1 | 2 | yes | complemented |
| 33 | #5804 | — | 2 | 2 | no | — |
| 34 | C2×#932 | C22 | 1 | 2 | yes | complemented |
| 35 | #5791 | — | 2 | 2 | no | — |
| 36 | C2×C4×#67 | — | 2 | 2 | no | — |
| 37 | C2×#926 | C22 | 1 | 1 | yes | characteristic |
| 38 | C22×#208 | C22 | 1 | 1 | yes | characteristic |
| 39 | #5748 | — | 2 | 8 | no | — |
| 40 | C2×#909 | C22 | 1 | 2 | yes | complemented |
| 41 | C2×#909 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×#908 | C22 | 1 | 2 | yes | complemented |
| 43 | C2×#908 | C22 | 1 | 2 | yes | complemented |
| 44 | C2×#904 | C22 | 1 | 4 | yes | — |
| 45 | #5504 | — | 2 | 2 | no | — |
| 46 | #5504 | — | 2 | 2 | no | — |
| 47 | #5504 | C22 | 1 | 4 | yes | complemented |
| 48 | #5504 | C22 | 1 | 4 | yes | complemented |
| 49 | C2×#893 | C22 | 1 | 2 | yes | complemented |
| 50 | C2×#892 | — | 2 | 1 | no | — |
| 51 | C2×D3×C4⋊C4 | — | 2 | 1 | no | — |
| 52 | C2×#887 | C22 | 1 | 2 | yes | complemented |
| 53 | C3×#417 | C22 | 1 | 4 | yes | complemented |
| 54 | C3×#417 | C22 | 1 | 4 | yes | complemented |
| 55 | C2×C3×#103 | C22 | 1 | 2 | yes | complemented |
| 56 | C2×C3×#102 | C22 | 1 | 2 | yes | complemented |
| 57 | #5119 | C22 | 1 | 4 | yes | complemented |
| 58 | #5118 | C22 | 1 | 4 | yes | complemented |
| 59 | #5102 | C22 | 1 | 4 | yes | complemented |
| 60 | C2×#810 | C22 | 1 | 2 | yes | complemented |
| 61 | #4966 | C22 | 1 | 4 | yes | complemented |
| 62 | #4966 | C22 | 1 | 4 | yes | complemented |
| 63 | C2×#809 | C22 | 1 | 2 | yes | complemented |
| 64 | #4819 | C22 | 1 | 8 | yes | complemented |
| 65 | #4818 | C22 | 1 | 8 | yes | complemented |
| 66 | #4798 | C22 | 1 | 8 | yes | complemented |
| 67 | #4795 | C22 | 1 | 8 | yes | complemented |
| 68 | #4787 | C22 | 1 | 8 | yes | complemented |
| 69 | #4786 | C22 | 1 | 8 | yes | complemented |
| 70 | #4767 | C22 | 1 | 8 | yes | complemented |
| 71 | #4762 | C22 | 1 | 8 | yes | complemented |
| 72 | C2×#575 | — | 3 | 1 | no | — |
| 73 | C2×#575 | — | 3 | 1 | no | — |
| 74 | #3449 | — | 3 | 1 | no | — |
| 75 | C2×#520 | — | 3 | 1 | no | — |
| 76 | #3046 | — | 3 | 4 | no | — |
| 77 | #3046 | — | 3 | 4 | no | — |
| 78 | #3045 | — | 3 | 4 | no | — |
| 79 | #3045 | — | 3 | 4 | no | — |
| 80 | #3037 | — | 3 | 4 | no | — |
| 81 | #3036 | — | 3 | 4 | no | — |
| 82 | #2905 | — | 3 | 1 | no | — |
| 83 | C2×#417 | — | 3 | 1 | no | — |
| 84 | C2×#417 | D3 | 1 | 1 | yes | characteristic, complemented |
| 85 | C2×C3×#41 | — | 2 | 1 | no | — |
| 86 | C2×C3×#41 | — | 2 | 1 | no | — |
| 87 | C2×C3×#41 | — | 2 | 4 | no | — |
| 88 | C2×C3×#41 | — | 2 | 4 | no | — |
| 89 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 90 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 91 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 92 | C22×C3×D4 | — | 2 | 1 | no | — |
| 93 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 94 | C23×C3×C4 | — | 2 | 1 | no | — |
| 95 | C23×C3×C4 | — | 2 | 1 | no | — |
| 96 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 97 | C22×#67 | — | 2 | 1 | no | — |
| 98 | C22×#67 | — | 2 | 1 | no | — |
| 99 | C2×#235 | — | 2 | 1 | no | — |
| 100 | C2×#235 | — | 2 | 1 | no | — |
| 101 | C2×#235 | — | 2 | 4 | no | — |
| 102 | C2×#235 | — | 2 | 1 | no | — |
| 103 | C2×#235 | — | 2 | 1 | no | — |
| 104 | C2×#235 | — | 2 | 4 | no | — |
| 105 | C2×#235 | — | 2 | 4 | no | — |
| 106 | C2×#235 | D4 | 1 | 8 | yes | complemented |
| 107 | C2×#235 | C23 | 1 | 2 | yes | — |
| 108 | C2×#235 | C23 | 1 | 2 | yes | — |
| 109 | C2×#235 | C23 | 1 | 2 | yes | — |
| 110 | C2×#235 | C23 | 1 | 2 | yes | — |
| 111 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 112 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 113 | C22×C4×D3 | — | 2 | 1 | no | — |
| 114 | C22×C4×D3 | — | 2 | 1 | no | — |
| 115 | C22×C4×D3 | — | 2 | 2 | no | — |
| 116 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 117 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 118 | C2×C3×M16 | — | 2 | 4 | no | — |
| 119 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 120 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 121 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 122 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 123 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 124 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 125 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 126 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 127 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 128 | #953 | — | 2 | 4 | no | — |
| 129 | C2×#217 | D4 | 1 | 2 | yes | — |
| 130 | #951 | — | 2 | 8 | no | — |
| 131 | #950 | — | 2 | 16 | no | — |
| 132 | #949 | — | 2 | 8 | no | — |
| 133 | #947 | C23 | 1 | 4 | yes | — |
| 134 | #946 | — | 2 | 2 | no | — |
| 135 | #946 | — | 2 | 2 | no | — |
| 136 | #944 | C23 | 1 | 4 | yes | — |
| 137 | C2×#216 | C23 | 1 | 4 | yes | — |
| 138 | #942 | — | 2 | 8 | no | — |
| 139 | C2×#215 | C23 | 1 | 4 | yes | — |
| 140 | #940 | C23 | 1 | 4 | yes | — |
| 141 | #939 | — | 2 | 4 | no | — |
| 142 | #939 | — | 2 | 4 | no | — |
| 143 | #938 | — | 2 | 2 | no | — |
| 144 | #938 | — | 2 | 2 | no | — |
| 145 | #937 | — | 2 | 4 | no | — |
| 146 | #936 | C23 | 1 | 4 | yes | — |
| 147 | #935 | — | 2 | 4 | no | — |
| 148 | C2×#214 | C23 | 1 | 4 | yes | — |
| 149 | #932 | — | 2 | 8 | no | — |
| 150 | C2×#213 | C23 | 1 | 4 | yes | — |
| 151 | #930 | — | 2 | 2 | no | — |
| 152 | #930 | — | 2 | 2 | no | — |
| 153 | #929 | — | 2 | 4 | no | — |
| 154 | C4×#67 | — | 2 | 8 | no | — |
| 155 | C4×#67 | — | 2 | 8 | no | — |
| 156 | C4×#67 | — | 2 | 4 | no | — |
| 157 | C4×#67 | — | 2 | 4 | no | — |
| 158 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 159 | #926 | D4 | 1 | 2 | yes | — |
| 160 | #926 | D4 | 1 | 2 | yes | — |
| 161 | #926 | C23 | 1 | 2 | yes | — |
| 162 | #926 | C23 | 1 | 2 | yes | — |
| 163 | C2×C4⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C4⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 165 | #924 | — | 2 | 2 | no | — |
| 166 | #924 | — | 2 | 2 | no | — |
| 167 | C2×Dic3⋊C4 | — | 2 | 2 | no | — |
| 168 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 169 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 170 | C2×#208 | — | 2 | 4 | no | — |
| 171 | C2×#208 | C23 | 1 | 2 | yes | — |
| 172 | C2×#208 | C23 | 1 | 2 | yes | — |
| 173 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 174 | #909 | — | 2 | 8 | no | — |
| 175 | #909 | — | 2 | 8 | no | — |
| 176 | #908 | — | 2 | 8 | no | — |
| 177 | #908 | — | 2 | 8 | no | — |
| 178 | C2×Dic12 | C23 | 1 | 4 | yes | — |
| 179 | #904 | — | 2 | 16 | no | — |
| 180 | C2×D24 | C23 | 1 | 4 | yes | — |
| 181 | C2×#204 | C23 | 1 | 4 | yes | — |
| 182 | C2×#204 | C23 | 1 | 4 | yes | — |
| 183 | #893 | — | 2 | 4 | no | — |
| 184 | #893 | C23 | 1 | 8 | yes | — |
| 185 | #892 | — | 2 | 4 | no | — |
| 186 | #892 | — | 2 | 4 | no | — |
| 187 | D3×C4⋊C4 | — | 2 | 4 | no | — |
| 188 | D3×C4⋊C4 | — | 2 | 4 | no | — |
| 189 | #887 | — | 2 | 4 | no | — |
| 190 | #887 | C23 | 1 | 8 | yes | — |
| 191 | C3×#103 | C23 | 1 | 8 | yes | — |
| 192 | C3×#102 | C23 | 1 | 8 | yes | — |
| 193 | Dic3⋊C8 | C23 | 1 | 8 | yes | — |
| 194 | Dic3⋊C8 | C23 | 1 | 8 | yes | — |
| 195 | #810 | C23 | 1 | 8 | yes | — |
| 196 | #809 | C23 | 1 | 8 | yes | — |
| 197 | C22×#41 | — | 3 | 1 | no | — |
| 198 | C22×#41 | — | 3 | 1 | no | — |
| 199 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 200 | #575 | — | 6 | 8 | no | — |
| 201 | #575 | — | 6 | 8 | no | — |
| 202 | C2×#137 | — | 3 | 2 | no | — |
| 203 | C2×#137 | — | 3 | 2 | no | — |
| 204 | C2×#137 | — | 3 | 2 | no | — |
| 205 | C2×#137 | — | 3 | 2 | no | — |
| 206 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 207 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 208 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 209 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 210 | C2×#135 | — | 3 | 4 | no | — |
| 211 | C2×#135 | — | 3 | 4 | no | — |
| 212 | C22×M16 | — | 3 | 1 | no | — |
| 213 | C22×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 214 | #537 | — | 6 | 1 | no | — |
| 215 | #537 | — | 6 | 1 | no | — |
| 216 | #536 | — | 3 | 2 | no | — |
| 217 | #536 | — | 3 | 2 | no | — |
| 218 | #535 | — | 3 | 2 | no | — |
| 219 | #535 | — | 3 | 2 | no | — |
| 220 | #534 | — | 6 | 2 | no | — |
| 221 | #532 | — | 3 | 4 | no | — |
| 222 | #525 | — | 6 | 2 | no | — |
| 223 | #525 | — | 6 | 2 | no | — |
| 224 | #520 | — | 3 | 4 | no | — |
| 225 | #520 | — | 3 | 4 | no | — |
| 226 | #520 | — | 6 | 2 | no | — |
| 227 | #520 | — | 6 | 2 | no | — |
| 228 | C2×C4×Q8 | — | 3 | 2 | no | — |
| 229 | C2×C4×D4 | — | 3 | 2 | no | — |
| 230 | C2×C4×D4 | — | 6 | 2 | no | — |
| 231 | C2×#117 | — | 3 | 1 | no | — |
| 232 | C2×#117 | — | 6 | 1 | no | — |
| 233 | C22×C4⋊C4 | — | 6 | 1 | no | — |
| 234 | C22×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 235 | #464 | — | 3 | 8 | no | — |
| 236 | #464 | — | 3 | 8 | no | — |
| 237 | #463 | — | 3 | 8 | no | — |
| 238 | #463 | — | 3 | 8 | no | — |
| 239 | #462 | — | 3 | 8 | no | — |
| 240 | #461 | — | 3 | 8 | no | — |
| 241 | #460 | — | 3 | 8 | no | — |
| 242 | #459 | — | 3 | 8 | no | — |
| 243 | #424 | — | 3 | 4 | no | — |
| 244 | #424 | — | 3 | 4 | no | — |
| 245 | #423 | — | 3 | 4 | no | — |
| 246 | #417 | — | 3 | 4 | no | — |
| 247 | #417 | — | 3 | 4 | no | — |
| 248 | #417 | C2×D3 | 1 | 4 | yes | complemented |
| 249 | #417 | C2×D3 | 1 | 4 | yes | complemented |
| 250 | C2×#103 | — | 3 | 2 | no | — |
| 251 | C2×#103 | C2×D3 | 1 | 2 | yes | complemented |
| 252 | C2×#102 | — | 3 | 2 | no | — |
| 253 | C2×#102 | C2×D3 | 1 | 2 | yes | complemented |
| 254 | C24×C3 | — | 2 | 1 | no | — |
| 255 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | C23×D3 | — | 2 | 1 | no | — |
| 257 | C23×D3 | — | 2 | 1 | no | — |
| 258 | C3×#41 | — | 2 | 4 | no | — |
| 259 | C3×#41 | — | 2 | 4 | no | — |
| 260 | C3×#41 | — | 2 | 4 | no | — |
| 261 | C3×#41 | — | 2 | 4 | no | — |
| 262 | C3×#41 | — | 4 | 4 | no | — |
| 263 | C3×#41 | — | 4 | 4 | no | — |
| 264 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 265 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 266 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 267 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 268 | C2×C3×D4 | — | 2 | 2 | no | — |
| 269 | C2×C3×D4 | — | 2 | 2 | no | — |
| 270 | C2×C3×D4 | — | 2 | 2 | no | — |
| 271 | C2×C3×D4 | — | 2 | 1 | no | — |
| 272 | C2×C3×D4 | — | 2 | 2 | no | — |
| 273 | C2×C3×D4 | — | 4 | 4 | no | — |
| 274 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 275 | C22×C3×C4 | — | 2 | 2 | no | — |
| 276 | C22×C3×C4 | — | 2 | 1 | no | — |
| 277 | C22×C3×C4 | — | 2 | 2 | no | — |
| 278 | C22×C3×C4 | — | 2 | 2 | no | — |
| 279 | C22×C3×C4 | — | 2 | 2 | no | — |
| 280 | C22×C3×C4 | — | 2 | 2 | no | — |
| 281 | C22×C3×C4 | — | 4 | 4 | no | — |
| 282 | C22×C3×C4 | — | 8 | 2 | no | — |
| 283 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 284 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 285 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 286 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 287 | C22×C3×C4 | #41 | 1 | 4 | yes | — |
| 288 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 289 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 290 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 291 | C2×#67 | — | 2 | 8 | no | — |
| 292 | C2×#67 | — | 2 | 2 | no | — |
| 293 | C2×#67 | — | 2 | 2 | no | — |
| 294 | C2×#67 | — | 2 | 2 | no | — |
| 295 | C2×#67 | — | 2 | 2 | no | — |
| 296 | C2×#67 | — | 2 | 4 | no | — |
| 297 | C2×#67 | — | 2 | 4 | no | — |
| 298 | C2×#67 | — | 4 | 4 | no | — |
| 299 | C22×Dic3 | — | 2 | 1 | no | — |
| 300 | C22×Dic3 | — | 2 | 1 | no | — |
| 301 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 302 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 303 | #235 | — | 2 | 8 | no | — |
| 304 | #235 | — | 2 | 8 | no | — |
| 305 | #235 | — | 2 | 4 | no | — |
| 306 | #235 | — | 2 | 4 | no | — |
| 307 | #235 | — | 2 | 4 | no | — |
| 308 | #235 | — | 2 | 4 | no | — |
| 309 | #235 | — | 2 | 4 | no | — |
| 310 | #235 | — | 2 | 4 | no | — |
| 311 | #235 | — | 4 | 4 | no | — |
| 312 | #235 | — | 4 | 4 | no | — |
| 313 | #235 | C2×D4 | 1 | 8 | yes | — |
| 314 | #235 | C2×D4 | 1 | 8 | yes | — |
| 315 | C2×D12 | — | 2 | 1 | no | — |
| 316 | C2×D12 | — | 2 | 2 | no | — |
| 317 | C2×D12 | — | 2 | 2 | no | — |
| 318 | C2×D12 | — | 2 | 2 | no | — |
| 319 | C2×D12 | — | 2 | 1 | no | — |
| 320 | C2×D12 | C2×D4 | 1 | 4 | yes | — |
| 321 | C2×D12 | C24 | 1 | 2 | yes | — |
| 322 | C2×D12 | C24 | 1 | 2 | yes | — |
| 323 | C2×C4×D3 | — | 2 | 8 | no | — |
| 324 | C2×C4×D3 | — | 2 | 2 | no | — |
| 325 | C2×C4×D3 | — | 2 | 2 | no | — |
| 326 | C2×C4×D3 | — | 2 | 2 | no | — |
| 327 | C2×C4×D3 | — | 2 | 2 | no | — |
| 328 | C2×C4×D3 | — | 2 | 8 | no | — |
| 329 | C2×C4×D3 | — | 4 | 4 | no | — |
| 330 | C2×C4×D3 | — | 8 | 4 | no | — |
| 331 | C2×Dic6 | — | 2 | 1 | no | — |
| 332 | C2×Dic6 | — | 2 | 2 | no | — |
| 333 | C2×Dic6 | — | 2 | 2 | no | — |
| 334 | C2×Dic6 | — | 2 | 2 | no | — |
| 335 | C2×Dic6 | — | 2 | 1 | no | — |
| 336 | C2×Dic6 | C2×D4 | 1 | 4 | yes | — |
| 337 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 338 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 339 | C3×M16 | — | 2 | 4 | no | — |
| 340 | C3×M16 | — | 2 | 4 | no | — |
| 341 | C2×C3×C8 | — | 2 | 4 | no | — |
| 342 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 343 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 344 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 345 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 346 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 347 | #217 | — | 2 | 4 | no | — |
| 348 | #217 | — | 2 | 4 | no | — |
| 349 | #217 | C2×D4 | 1 | 4 | yes | — |
| 350 | #217 | C2×D4 | 1 | 4 | yes | — |
| 351 | #216 | — | 2 | 8 | no | — |
| 352 | #215 | — | 2 | 8 | no | — |
| 353 | #214 | — | 2 | 8 | no | — |
| 354 | #213 | — | 2 | 8 | no | — |
| 355 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 356 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 357 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 358 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 359 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 360 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 361 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 362 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 363 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 364 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 365 | C4×Dic3 | — | 2 | 8 | no | — |
| 366 | C4×Dic3 | C2×D4 | 1 | 4 | yes | — |
| 367 | C4×Dic3 | C24 | 1 | 4 | yes | — |
| 368 | #208 | — | 2 | 4 | no | — |
| 369 | #208 | — | 2 | 4 | no | — |
| 370 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 371 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 372 | Dic12 | — | 2 | 8 | no | — |
| 373 | D24 | — | 2 | 8 | no | — |
| 374 | #204 | — | 2 | 8 | no | — |
| 375 | #204 | — | 2 | 8 | no | — |
| 376 | C2×#41 | — | 2 | 1 | no | — |
| 377 | C2×#41 | — | 2 | 1 | no | — |
| 378 | C2×#41 | — | 2 | 4 | no | — |
| 379 | C2×#41 | — | 2 | 4 | no | — |
| 380 | C2×#41 | — | 3 | 8 | no | — |
| 381 | C2×#41 | — | 3 | 2 | no | — |
| 382 | C2×#41 | — | 3 | 2 | no | — |
| 383 | C2×#41 | — | 3 | 2 | no | — |
| 384 | C2×#41 | — | 3 | 2 | no | — |
| 385 | C2×#41 | — | 6 | 4 | no | — |
| 386 | C2×#41 | — | 6 | 1 | no | — |
| 387 | C2×#41 | — | 6 | 1 | no | — |
| 388 | C2×#41 | — | 6 | 1 | no | — |
| 389 | C2×#41 | — | 6 | 1 | no | — |
| 390 | C2×#41 | — | 6 | 4 | no | — |
| 391 | C2×#41 | — | 6 | 4 | no | — |
| 392 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 393 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 394 | C22×Q8 | — | 3 | 1 | no | — |
| 395 | C22×Q8 | — | 3 | 1 | no | — |
| 396 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 397 | C22×D4 | — | 2 | 1 | no | — |
| 398 | C22×D4 | — | 3 | 1 | no | — |
| 399 | C22×D4 | — | 3 | 1 | no | — |
| 400 | C22×D4 | — | 6 | 1 | no | — |
| 401 | C22×D4 | — | 6 | 1 | no | — |
| 402 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 403 | C23×C4 | — | 2 | 1 | no | — |
| 404 | C23×C4 | — | 2 | 1 | no | — |
| 405 | C23×C4 | — | 6 | 2 | no | — |
| 406 | C23×C4 | — | 6 | 1 | no | — |
| 407 | C23×C4 | — | 6 | 1 | no | — |
| 408 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 409 | #137 | — | 6 | 8 | no | — |
| 410 | #137 | — | 6 | 8 | no | — |
| 411 | #137 | — | 6 | 8 | no | — |
| 412 | #137 | — | 6 | 8 | no | — |
| 413 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 414 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 415 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 416 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 417 | #135 | — | 6 | 16 | no | — |
| 418 | #135 | — | 6 | 16 | no | — |
| 419 | C2×Q16 | — | 3 | 4 | no | — |
| 420 | C2×Q16 | — | 3 | 4 | no | — |
| 421 | C2×SD16 | — | 3 | 4 | no | — |
| 422 | C2×SD16 | — | 3 | 4 | no | — |
| 423 | C2×SD16 | — | 3 | 4 | no | — |
| 424 | C2×SD16 | — | 3 | 4 | no | — |
| 425 | C2×D8 | — | 3 | 4 | no | — |
| 426 | C2×D8 | — | 3 | 4 | no | — |
| 427 | C2×M16 | — | 2 | 4 | no | — |
| 428 | C2×M16 | — | 3 | 2 | no | — |
| 429 | C2×M16 | — | 3 | 2 | no | — |
| 430 | C2×M16 | — | 6 | 4 | no | — |
| 431 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 432 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 433 | C22×C8 | — | 3 | 2 | no | — |
| 434 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 435 | C4⋊Q8 | — | 3 | 4 | no | — |
| 436 | #127 | — | 3 | 4 | no | — |
| 437 | #124 | — | 3 | 4 | no | — |
| 438 | #124 | — | 3 | 4 | no | — |
| 439 | #123 | — | 6 | 4 | no | — |
| 440 | #123 | — | 6 | 4 | no | — |
| 441 | C22⋊Q8 | — | 6 | 2 | no | — |
| 442 | C22⋊Q8 | — | 6 | 2 | no | — |
| 443 | C22⋊Q8 | — | 6 | 2 | no | — |
| 444 | C22⋊Q8 | — | 6 | 2 | no | — |
| 445 | #121 | — | 6 | 2 | no | — |
| 446 | #121 | — | 6 | 2 | no | — |
| 447 | #121 | — | 6 | 2 | no | — |
| 448 | #121 | — | 6 | 2 | no | — |
| 449 | #121 | — | 6 | 4 | no | — |
| 450 | #121 | — | 6 | 4 | no | — |
| 451 | #120 | — | 6 | 4 | no | — |
| 452 | #120 | — | 6 | 4 | no | — |
| 453 | C4×Q8 | — | 3 | 8 | no | — |
| 454 | C4×Q8 | — | 6 | 4 | no | — |
| 455 | C4×D4 | — | 3 | 8 | no | — |
| 456 | C4×D4 | — | 6 | 4 | no | — |
| 457 | C4×D4 | — | 6 | 4 | no | — |
| 458 | C4×D4 | — | 6 | 4 | no | — |
| 459 | C4×D4 | — | 6 | 8 | no | — |
| 460 | C4×D4 | — | 6 | 8 | no | — |
| 461 | #117 | — | 3 | 2 | no | — |
| 462 | #117 | — | 3 | 2 | no | — |
| 463 | #117 | — | 3 | 2 | no | — |
| 464 | #117 | — | 3 | 2 | no | — |
| 465 | #117 | — | 6 | 4 | no | — |
| 466 | #117 | — | 6 | 4 | no | — |
| 467 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 468 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 469 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 470 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 471 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 472 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 473 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 474 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 475 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 476 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 477 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 478 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 479 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 480 | C2×C42 | — | 3 | 2 | no | — |
| 481 | C2×C42 | — | 6 | 2 | no | — |
| 482 | C4⋊C8 | — | 3 | 8 | no | — |
| 483 | C4⋊C8 | — | 3 | 8 | no | — |
| 484 | #103 | — | 3 | 8 | no | — |
| 485 | #103 | C22×D3 | 1 | 8 | yes | — |
| 486 | #102 | — | 3 | 8 | no | — |
| 487 | #102 | C22×D3 | 1 | 8 | yes | — |
| 488 | C23×C3 | — | 2 | 2 | no | — |
| 489 | C23×C3 | — | 4 | 1 | no | — |
| 490 | C23×C3 | — | 4 | 1 | no | — |
| 491 | C23×C3 | — | 4 | 2 | no | — |
| 492 | C23×C3 | — | 8 | 1 | no | — |
| 493 | C23×C3 | — | 8 | 1 | no | — |
| 494 | C23×C3 | #121 | 1 | 4 | yes | — |
| 495 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 496 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 497 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 498 | C22×D3 | — | 2 | 4 | no | — |
| 499 | C22×D3 | — | 2 | 2 | no | — |
| 500 | C22×D3 | — | 2 | 2 | no | — |
| 501 | C22×D3 | — | 4 | 2 | no | — |
| 502 | C22×D3 | — | 4 | 2 | no | — |
| 503 | C22×D3 | — | 4 | 2 | no | — |
| 504 | C22×D3 | — | 8 | 1 | no | — |
| 505 | C22×D3 | — | 8 | 1 | no | — |
| 506 | C3×Q8 | — | 2 | 2 | no | — |
| 507 | C3×Q8 | — | 2 | 2 | no | — |
| 508 | C3×Q8 | — | 4 | 2 | no | — |
| 509 | C3×D4 | — | 2 | 2 | no | — |
| 510 | C3×D4 | — | 2 | 2 | no | — |
| 511 | C3×D4 | — | 4 | 4 | no | — |
| 512 | C3×D4 | — | 4 | 4 | no | — |
| 513 | C3×D4 | — | 4 | 2 | no | — |
| 514 | C2×C3×C4 | — | 2 | 4 | no | — |
| 515 | C2×C3×C4 | — | 2 | 2 | no | — |
| 516 | C2×C3×C4 | — | 4 | 4 | no | — |
| 517 | C2×C3×C4 | — | 4 | 2 | no | — |
| 518 | C2×C3×C4 | — | 4 | 4 | no | — |
| 519 | C2×C3×C4 | — | 4 | 4 | no | — |
| 520 | C2×C3×C4 | — | 8 | 2 | no | — |
| 521 | C2×C3×C4 | — | 8 | 2 | no | — |
| 522 | C2×C3×C4 | #121 | 1 | 4 | yes | — |
| 523 | C2×C3×C4 | #121 | 1 | 4 | yes | — |
| 524 | C2×C3×C4 | #121 | 1 | 4 | yes | — |
| 525 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 526 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 527 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 528 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 529 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 530 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 531 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 532 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 533 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 534 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 535 | #67 | — | 2 | 8 | no | — |
| 536 | #67 | — | 2 | 8 | no | — |
| 537 | #67 | — | 4 | 4 | no | — |
| 538 | #67 | — | 4 | 4 | no | — |
| 539 | #67 | — | 8 | 4 | no | — |
| 540 | #67 | — | 8 | 4 | no | — |
| 541 | C2×Dic3 | — | 2 | 4 | no | — |
| 542 | C2×Dic3 | — | 2 | 2 | no | — |
| 543 | C2×Dic3 | — | 2 | 2 | no | — |
| 544 | C2×Dic3 | — | 4 | 2 | no | — |
| 545 | C2×Dic3 | — | 4 | 2 | no | — |
| 546 | C2×Dic3 | — | 4 | 2 | no | — |
| 547 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 548 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 549 | D12 | — | 2 | 4 | no | — |
| 550 | D12 | — | 2 | 2 | no | — |
| 551 | D12 | — | 2 | 2 | no | — |
| 552 | D12 | — | 2 | 2 | no | — |
| 553 | D12 | — | 4 | 2 | no | — |
| 554 | D12 | C22×D4 | 1 | 4 | yes | — |
| 555 | C4×D3 | — | 2 | 8 | no | — |
| 556 | C4×D3 | — | 2 | 8 | no | — |
| 557 | C4×D3 | — | 4 | 4 | no | — |
| 558 | C4×D3 | — | 4 | 4 | no | — |
| 559 | C4×D3 | — | 8 | 8 | no | — |
| 560 | Dic6 | — | 2 | 4 | no | — |
| 561 | Dic6 | — | 2 | 2 | no | — |
| 562 | Dic6 | — | 2 | 2 | no | — |
| 563 | Dic6 | — | 2 | 2 | no | — |
| 564 | Dic6 | — | 4 | 2 | no | — |
| 565 | Dic6 | C22×D4 | 1 | 4 | yes | — |
| 566 | C3×C8 | — | 2 | 4 | no | — |
| 567 | C3⋊C8 | — | 2 | 4 | no | — |
| 568 | C24 | — | 2 | 1 | no | — |
| 569 | C24 | — | 6 | 1 | no | — |
| 570 | C24 | — | 6 | 1 | no | — |
| 571 | C24 | D3×D4 | 1 | 1 | yes | characteristic |
| 572 | #41 | — | 2 | 4 | no | — |
| 573 | #41 | — | 2 | 4 | no | — |
| 574 | #41 | — | 2 | 4 | no | — |
| 575 | #41 | — | 2 | 4 | no | — |
| 576 | #41 | — | 3 | 8 | no | — |
| 577 | #41 | — | 3 | 8 | no | — |
| 578 | #41 | — | 4 | 4 | no | — |
| 579 | #41 | — | 4 | 4 | no | — |
| 580 | #41 | — | 6 | 8 | no | — |
| 581 | #41 | — | 6 | 8 | no | — |
| 582 | #41 | — | 6 | 4 | no | — |
| 583 | #41 | — | 6 | 4 | no | — |
| 584 | #41 | — | 6 | 4 | no | — |
| 585 | #41 | — | 6 | 4 | no | — |
| 586 | #41 | — | 6 | 4 | no | — |
| 587 | #41 | — | 6 | 4 | no | — |
| 588 | #41 | — | 12 | 4 | no | — |
| 589 | #41 | — | 12 | 4 | no | — |
| 590 | C2×Q8 | — | 2 | 1 | no | — |
| 591 | C2×Q8 | — | 2 | 2 | no | — |
| 592 | C2×Q8 | — | 2 | 2 | no | — |
| 593 | C2×Q8 | — | 3 | 4 | no | — |
| 594 | C2×Q8 | — | 3 | 2 | no | — |
| 595 | C2×Q8 | — | 3 | 2 | no | — |
| 596 | C2×Q8 | — | 6 | 2 | no | — |
| 597 | C2×Q8 | — | 6 | 1 | no | — |
| 598 | C2×Q8 | — | 6 | 1 | no | — |
| 599 | C2×Q8 | — | 6 | 2 | no | — |
| 600 | C2×Q8 | — | 6 | 2 | no | — |
| 601 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 602 | C2×D4 | — | 2 | 2 | no | — |
| 603 | C2×D4 | — | 2 | 2 | no | — |
| 604 | C2×D4 | — | 2 | 2 | no | — |
| 605 | C2×D4 | — | 2 | 2 | no | — |
| 606 | C2×D4 | — | 2 | 1 | no | — |
| 607 | C2×D4 | — | 3 | 4 | no | — |
| 608 | C2×D4 | — | 3 | 2 | no | — |
| 609 | C2×D4 | — | 3 | 2 | no | — |
| 610 | C2×D4 | — | 4 | 4 | no | — |
| 611 | C2×D4 | — | 6 | 4 | no | — |
| 612 | C2×D4 | — | 6 | 4 | no | — |
| 613 | C2×D4 | — | 6 | 8 | no | — |
| 614 | C2×D4 | — | 6 | 2 | no | — |
| 615 | C2×D4 | — | 6 | 2 | no | — |
| 616 | C2×D4 | — | 6 | 2 | no | — |
| 617 | C2×D4 | — | 6 | 2 | no | — |
| 618 | C2×D4 | — | 6 | 2 | no | — |
| 619 | C2×D4 | — | 6 | 2 | no | — |
| 620 | C2×D4 | — | 6 | 1 | no | — |
| 621 | C2×D4 | — | 6 | 2 | no | — |
| 622 | C2×D4 | — | 6 | 1 | no | — |
| 623 | C2×D4 | — | 12 | 4 | no | — |
| 624 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 625 | C22×C4 | — | 2 | 2 | no | — |
| 626 | C22×C4 | — | 2 | 1 | no | — |
| 627 | C22×C4 | — | 2 | 2 | no | — |
| 628 | C22×C4 | — | 2 | 2 | no | — |
| 629 | C22×C4 | — | 2 | 2 | no | — |
| 630 | C22×C4 | — | 2 | 2 | no | — |
| 631 | C22×C4 | — | 3 | 2 | no | — |
| 632 | C22×C4 | — | 3 | 2 | no | — |
| 633 | C22×C4 | — | 4 | 4 | no | — |
| 634 | C22×C4 | — | 6 | 8 | no | — |
| 635 | C22×C4 | — | 6 | 1 | no | — |
| 636 | C22×C4 | — | 6 | 8 | no | — |
| 637 | C22×C4 | — | 6 | 2 | no | — |
| 638 | C22×C4 | — | 6 | 2 | no | — |
| 639 | C22×C4 | — | 6 | 1 | no | — |
| 640 | C22×C4 | — | 6 | 2 | no | — |
| 641 | C22×C4 | — | 6 | 2 | no | — |
| 642 | C22×C4 | — | 8 | 2 | no | — |
| 643 | C22×C4 | — | 12 | 4 | no | — |
| 644 | C22×C4 | — | 24 | 4 | no | — |
| 645 | C22×C4 | #235 | 1 | 4 | yes | — |
| 646 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 647 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 648 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 649 | C22×C4 | D3×D4 | 1 | 4 | yes | — |
| 650 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 651 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 652 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 653 | Q16 | — | 6 | 8 | no | — |
| 654 | Q16 | — | 6 | 8 | no | — |
| 655 | SD16 | — | 6 | 8 | no | — |
| 656 | SD16 | — | 6 | 8 | no | — |
| 657 | SD16 | — | 6 | 8 | no | — |
| 658 | SD16 | — | 6 | 8 | no | — |
| 659 | D8 | — | 6 | 8 | no | — |
| 660 | D8 | — | 6 | 8 | no | — |
| 661 | M16 | — | 2 | 4 | no | — |
| 662 | M16 | — | 2 | 4 | no | — |
| 663 | M16 | — | 6 | 4 | no | — |
| 664 | M16 | — | 6 | 4 | no | — |
| 665 | C2×C8 | — | 2 | 4 | no | — |
| 666 | C2×C8 | — | 3 | 4 | no | — |
| 667 | C2×C8 | — | 6 | 4 | no | — |
| 668 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 669 | C4⋊C4 | — | 2 | 2 | no | — |
| 670 | C4⋊C4 | — | 2 | 2 | no | — |
| 671 | C4⋊C4 | — | 2 | 2 | no | — |
| 672 | C4⋊C4 | — | 3 | 2 | no | — |
| 673 | C4⋊C4 | — | 3 | 2 | no | — |
| 674 | C4⋊C4 | — | 3 | 2 | no | — |
| 675 | C4⋊C4 | — | 3 | 2 | no | — |
| 676 | C4⋊C4 | — | 6 | 8 | no | — |
| 677 | C4⋊C4 | — | 6 | 4 | no | — |
| 678 | C4⋊C4 | — | 6 | 4 | no | — |
| 679 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 680 | C22⋊C4 | — | 3 | 4 | no | — |
| 681 | C22⋊C4 | — | 3 | 4 | no | — |
| 682 | C22⋊C4 | — | 6 | 8 | no | — |
| 683 | C22⋊C4 | — | 6 | 4 | no | — |
| 684 | C22⋊C4 | — | 6 | 4 | no | — |
| 685 | C22⋊C4 | — | 6 | 4 | no | — |
| 686 | C22⋊C4 | — | 6 | 4 | no | — |
| 687 | C42 | — | 3 | 4 | no | — |
| 688 | C42 | — | 3 | 4 | no | — |
| 689 | C42 | — | 6 | 8 | no | — |
| 690 | C22×C3 | — | 2 | 1 | no | — |
| 691 | C22×C3 | — | 2 | 1 | no | — |
| 692 | C22×C3 | — | 2 | 1 | no | — |
| 693 | C22×C3 | — | 2 | 1 | no | — |
| 694 | C22×C3 | — | 2 | 1 | no | — |
| 695 | C22×C3 | — | 2 | 1 | no | — |
| 696 | C22×C3 | — | 4 | 4 | no | — |
| 697 | C22×C3 | — | 4 | 2 | no | — |
| 698 | C22×C3 | — | 4 | 2 | no | — |
| 699 | C22×C3 | — | 4 | 2 | no | — |
| 700 | C22×C3 | — | 8 | 4 | no | — |
| 701 | C22×C3 | C2×#121 | 1 | 2 | yes | — |
| 702 | C22×C3 | C2×#121 | 1 | 2 | yes | — |
| 703 | C22×C3 | C2×#121 | 1 | 2 | yes | — |
| 704 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 705 | C2×D3 | — | 2 | 4 | no | — |
| 706 | C2×D3 | — | 4 | 8 | no | — |
| 707 | C2×D3 | — | 4 | 2 | no | — |
| 708 | C2×D3 | — | 4 | 2 | no | — |
| 709 | C2×D3 | — | 4 | 2 | no | — |
| 710 | C2×D3 | — | 4 | 2 | no | — |
| 711 | C2×D3 | — | 4 | 2 | no | — |
| 712 | C2×D3 | — | 8 | 4 | no | — |
| 713 | C3×C4 | — | 4 | 4 | no | — |
| 714 | C3×C4 | — | 4 | 2 | no | — |
| 715 | C3×C4 | C2×#121 | 1 | 2 | yes | — |
| 716 | C3×C4 | C2×#121 | 1 | 2 | yes | — |
| 717 | C3×C4 | C2×#121 | 1 | 2 | yes | — |
| 718 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 719 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 720 | Dic3 | — | 2 | 4 | no | — |
| 721 | Dic3 | — | 2 | 4 | no | — |
| 722 | Dic3 | — | 2 | 4 | no | — |
| 723 | Dic3 | — | 4 | 2 | no | — |
| 724 | C23 | — | 2 | 2 | no | — |
| 725 | C23 | — | 4 | 1 | no | — |
| 726 | C23 | — | 4 | 1 | no | — |
| 727 | C23 | — | 4 | 2 | no | — |
| 728 | C23 | — | 6 | 2 | no | — |
| 729 | C23 | — | 6 | 4 | no | — |
| 730 | C23 | — | 6 | 2 | no | — |
| 731 | C23 | — | 8 | 1 | no | — |
| 732 | C23 | — | 8 | 1 | no | — |
| 733 | C23 | — | 12 | 2 | no | — |
| 734 | C23 | — | 12 | 2 | no | — |
| 735 | C23 | — | 12 | 2 | no | — |
| 736 | C23 | — | 24 | 1 | no | — |
| 737 | C23 | — | 24 | 1 | no | — |
| 738 | C23 | #884 | 1 | 4 | yes | — |
| 739 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 740 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 741 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 742 | Q8 | — | 2 | 2 | no | — |
| 743 | Q8 | — | 2 | 2 | no | — |
| 744 | Q8 | — | 3 | 4 | no | — |
| 745 | Q8 | — | 4 | 2 | no | — |
| 746 | Q8 | — | 6 | 2 | no | — |
| 747 | Q8 | — | 6 | 4 | no | — |
| 748 | Q8 | — | 6 | 2 | no | — |
| 749 | Q8 | — | 6 | 2 | no | — |
| 750 | Q8 | — | 12 | 2 | no | — |
| 751 | D4 | — | 2 | 2 | no | — |
| 752 | D4 | — | 2 | 2 | no | — |
| 753 | D4 | — | 3 | 4 | no | — |
| 754 | D4 | — | 4 | 4 | no | — |
| 755 | D4 | — | 4 | 4 | no | — |
| 756 | D4 | — | 4 | 2 | no | — |
| 757 | D4 | — | 6 | 8 | no | — |
| 758 | D4 | — | 6 | 8 | no | — |
| 759 | D4 | — | 6 | 2 | no | — |
| 760 | D4 | — | 6 | 2 | no | — |
| 761 | D4 | — | 6 | 2 | no | — |
| 762 | D4 | — | 6 | 4 | no | — |
| 763 | D4 | — | 12 | 4 | no | — |
| 764 | D4 | — | 12 | 4 | no | — |
| 765 | D4 | — | 12 | 2 | no | — |
| 766 | D4 | — | 24 | 4 | no | — |
| 767 | D4 | — | 24 | 4 | no | — |
| 768 | C2×C4 | — | 2 | 4 | no | — |
| 769 | C2×C4 | — | 2 | 2 | no | — |
| 770 | C2×C4 | — | 3 | 4 | no | — |
| 771 | C2×C4 | — | 3 | 4 | no | — |
| 772 | C2×C4 | — | 4 | 4 | no | — |
| 773 | C2×C4 | — | 4 | 2 | no | — |
| 774 | C2×C4 | — | 4 | 4 | no | — |
| 775 | C2×C4 | — | 4 | 4 | no | — |
| 776 | C2×C4 | — | 6 | 2 | no | — |
| 777 | C2×C4 | — | 6 | 4 | no | — |
| 778 | C2×C4 | — | 6 | 8 | no | — |
| 779 | C2×C4 | — | 6 | 8 | no | — |
| 780 | C2×C4 | — | 6 | 2 | no | — |
| 781 | C2×C4 | — | 8 | 2 | no | — |
| 782 | C2×C4 | — | 8 | 2 | no | — |
| 783 | C2×C4 | — | 12 | 2 | no | — |
| 784 | C2×C4 | — | 12 | 2 | no | — |
| 785 | C2×C4 | — | 12 | 2 | no | — |
| 786 | C2×C4 | — | 12 | 4 | no | — |
| 787 | C2×C4 | — | 12 | 4 | no | — |
| 788 | C2×C4 | — | 24 | 8 | no | — |
| 789 | C2×C4 | #884 | 1 | 4 | yes | — |
| 790 | C2×C4 | #884 | 1 | 4 | yes | — |
| 791 | C2×C4 | #884 | 1 | 4 | yes | — |
| 792 | C2×C4 | C2×#235 | 1 | 2 | yes | — |
| 793 | C2×C4 | C2×#235 | 1 | 2 | yes | — |
| 794 | C2×C4 | C2×#235 | 1 | 2 | yes | — |
| 795 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 796 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 797 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 798 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 799 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 800 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 801 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 802 | C8 | — | 2 | 4 | no | — |
| 803 | C8 | — | 6 | 4 | no | — |
| 804 | C2×C3 | — | 2 | 2 | no | — |
| 805 | C2×C3 | — | 2 | 2 | no | — |
| 806 | C2×C3 | — | 2 | 2 | no | — |
| 807 | C2×C3 | — | 8 | 2 | no | — |
| 808 | C2×C3 | C22×#121 | 1 | 1 | yes | characteristic |
| 809 | C2×C3 | #3585 | 1 | 1 | yes | characteristic |
| 810 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 811 | D3 | — | 4 | 4 | no | — |
| 812 | D3 | — | 8 | 2 | no | — |
| 813 | C22 | — | 2 | 1 | no | — |
| 814 | C22 | — | 2 | 1 | no | — |
| 815 | C22 | — | 2 | 1 | no | — |
| 816 | C22 | — | 2 | 1 | no | — |
| 817 | C22 | — | 2 | 1 | no | — |
| 818 | C22 | — | 2 | 1 | no | — |
| 819 | C22 | — | 4 | 4 | no | — |
| 820 | C22 | — | 4 | 2 | no | — |
| 821 | C22 | — | 4 | 2 | no | — |
| 822 | C22 | — | 4 | 2 | no | — |
| 823 | C22 | — | 6 | 4 | no | — |
| 824 | C22 | — | 8 | 4 | no | — |
| 825 | C22 | — | 12 | 8 | no | — |
| 826 | C22 | — | 12 | 2 | no | — |
| 827 | C22 | — | 12 | 2 | no | — |
| 828 | C22 | — | 12 | 2 | no | — |
| 829 | C22 | — | 12 | 2 | no | — |
| 830 | C22 | — | 12 | 2 | no | — |
| 831 | C22 | — | 24 | 4 | no | — |
| 832 | C22 | C2×#884 | 1 | 2 | yes | — |
| 833 | C22 | C2×#884 | 1 | 2 | yes | — |
| 834 | C22 | C2×#884 | 1 | 2 | yes | — |
| 835 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 836 | C4 | — | 4 | 4 | no | — |
| 837 | C4 | — | 4 | 2 | no | — |
| 838 | C4 | — | 6 | 4 | no | — |
| 839 | C4 | — | 6 | 4 | no | — |
| 840 | C4 | — | 6 | 4 | no | — |
| 841 | C4 | — | 12 | 2 | no | — |
| 842 | C4 | C2×#884 | 1 | 2 | yes | — |
| 843 | C4 | C2×#884 | 1 | 2 | yes | — |
| 844 | C4 | C2×#884 | 1 | 2 | yes | — |
| 845 | C4 | C22×#235 | 1 | 1 | yes | characteristic |
| 846 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 847 | C3 | #60425 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 848 | C2 | — | 2 | 2 | no | — |
| 849 | C2 | — | 2 | 2 | no | — |
| 850 | C2 | — | 2 | 2 | no | — |
| 851 | C2 | — | 8 | 2 | no | — |
| 852 | C2 | — | 12 | 4 | no | — |
| 853 | C2 | — | 24 | 2 | no | — |
| 854 | C2 | C22×#884 | 1 | 1 | yes | characteristic |
| 855 | C2 | #87192 | 1 | 1 | yes | characteristic |
| 856 | C2 | #87197 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87268 | C2 | semidirect |
| 2. C2×#5822 | C2 | semidirect |
| 3. C2×#5748 | C2 | semidirect |
| 4. C2×#5504 | C2 | semidirect |
| 5. C2×C3×#417 | C2 | semidirect |
| 6. #83750 | C2 | semidirect |
| 7. C2×#4966 | C2 | semidirect |
| 8. #78913 | C2 | semidirect |
| 9. #78912 | C2 | semidirect |
| 10. #78911 | C2 | semidirect |
| 11. #78910 | C2 | semidirect |
| 12. #78815 | C2 | semidirect |
| 13. #78767 | C2 | semidirect |
| 23. #5830 | C22 | semidirect |
| 25. #5825 | C22 | semidirect |
| 26. C2×#951 | C22 | semidirect |
| 29. C2×#949 | C22 | semidirect |
| 30. #5816 | C22 | semidirect |
| 31. C2×#942 | C22 | semidirect |
| 32. #5805 | C22 | semidirect |
| 34. C2×#932 | C22 | semidirect |
| 40. C2×#909 | C22 | semidirect |
| 41. C2×#909 | C22 | semidirect |
| 42. C2×#908 | C22 | semidirect |
| 43. C2×#908 | C22 | semidirect |
| 47. #5504 | C22 | semidirect |
| 48. #5504 | C22 | semidirect |
| 49. C2×#893 | C22 | semidirect |
| 52. C2×#887 | C22 | semidirect |
| 53. C3×#417 | C22 | semidirect |
| 54. C3×#417 | C22 | semidirect |
| 55. C2×C3×#103 | C22 | semidirect |
| 56. C2×C3×#102 | C22 | semidirect |
| 57. #5119 | C22 | semidirect |
| 58. #5118 | C22 | semidirect |
| 59. #5102 | C22 | semidirect |
| 60. C2×#810 | C22 | semidirect |
| 61. #4966 | C22 | semidirect |
| 62. #4966 | C22 | semidirect |
| 63. C2×#809 | C22 | semidirect |
| 64. #4819 | C22 | semidirect |
| 65. #4818 | C22 | semidirect |
| 66. #4798 | C22 | semidirect |
| 67. #4795 | C22 | semidirect |
| 68. #4787 | C22 | semidirect |
| 69. #4786 | C22 | semidirect |
| 70. #4767 | C22 | semidirect |
| 71. #4762 | C22 | semidirect |
| 84. C2×#417 | D3 | semidirect |
| 106. C2×#235 | D4 | semidirect |
| 248. #417 | C2×D3 | semidirect |
| 249. #417 | C2×D3 | semidirect |
| 251. C2×#103 | C2×D3 | semidirect |
| 253. C2×#102 | C2×D3 | semidirect |
| 847. C3 | #60425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87268 | 2 |
| C2×#5822 | 2 |
| C2×#5748 | 2 |
| C2×#5504 | 2 |
| C2×C3×#417 | 2 |
| #83750 | 2 |
| C2×#4966 | 2 |
| #78913 | 2 |
| #78912 | 2 |
| #78911 | 2 |
| #78910 | 2 |
| #78815 | 2 |
| #78767 | 2 |
| #60425 | 3 |