Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
4836 conjugacy classes of subgroups.
The subgroup lattice has 808 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D3×#585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #86035 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#3025 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #84125 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #82936 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #80311 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #80309 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #80307 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #80305 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | D3×#410 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #78690 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #60398 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C3×#585 | C22 | 1 | 1 | yes | characteristic |
| 14 | #5968 | — | 2 | 3 | no | — |
| 15 | D3×2−1+4 | — | 2 | 3 | no | — |
| 16 | #5966 | — | 2 | 3 | no | — |
| 17 | #5966 | C22 | 1 | 4 | yes | — |
| 18 | D3×H(5,𝔽2) | — | 2 | 3 | no | — |
| 19 | D3×H(5,𝔽2) | C22 | 1 | 4 | yes | — |
| 20 | #5964 | — | 2 | 6 | no | — |
| 21 | #5964 | C22 | 1 | 3 | yes | — |
| 22 | C2×D3×#41 | — | 2 | 6 | no | — |
| 23 | C2×D3×#41 | C22 | 1 | 3 | yes | — |
| 24 | C22×#235 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×#525 | C22 | 1 | 3 | yes | complemented |
| 26 | #5828 | C22 | 1 | 3 | yes | complemented |
| 27 | #5791 | C22 | 1 | 3 | yes | complemented |
| 28 | #5653 | C22 | 1 | 6 | yes | complemented |
| 29 | #5648 | C22 | 1 | 6 | yes | complemented |
| 30 | #5629 | — | 2 | 3 | no | — |
| 31 | #5628 | — | 2 | 3 | no | — |
| 32 | #5608 | — | 2 | 3 | no | — |
| 33 | #5607 | — | 2 | 3 | no | — |
| 34 | #5592 | C22 | 1 | 6 | yes | complemented |
| 35 | #5589 | C22 | 1 | 6 | yes | complemented |
| 36 | #5548 | — | 2 | 6 | no | — |
| 37 | #5547 | — | 2 | 6 | no | — |
| 38 | #5524 | C22 | 1 | 3 | yes | complemented |
| 39 | D3×#117 | C22 | 1 | 3 | yes | complemented |
| 40 | C3×#458 | C22 | 1 | 4 | yes | complemented |
| 41 | C3×B(4,𝔽2) | C22 | 1 | 4 | yes | complemented |
| 42 | C3×#410 | C22 | 1 | 3 | yes | complemented |
| 43 | #5244 | C22 | 1 | 4 | yes | complemented |
| 44 | #5243 | C22 | 1 | 4 | yes | complemented |
| 45 | #5240 | C22 | 1 | 3 | yes | complemented |
| 46 | #5053 | C22 | 1 | 12 | yes | complemented |
| 47 | #5032 | C22 | 1 | 12 | yes | complemented |
| 48 | #5006 | C22 | 1 | 6 | yes | complemented |
| 49 | D3×#99 | C22 | 1 | 12 | yes | complemented |
| 50 | #4742 | C22 | 1 | 12 | yes | complemented |
| 51 | #4741 | C22 | 1 | 12 | yes | complemented |
| 52 | #4740 | C22 | 1 | 12 | yes | complemented |
| 53 | C2×#585 | — | 3 | 1 | no | — |
| 54 | #3449 | — | 3 | 3 | no | — |
| 55 | #3028 | — | 3 | 4 | no | — |
| 56 | #3027 | — | 3 | 4 | no | — |
| 57 | #3026 | — | 3 | 4 | no | — |
| 58 | #3026 | — | 3 | 4 | no | — |
| 59 | #3025 | — | 3 | 3 | no | — |
| 60 | #3025 | — | 3 | 1 | no | — |
| 61 | #3025 | — | 3 | 3 | no | — |
| 62 | #3025 | D3 | 1 | 1 | yes | characteristic, complemented |
| 63 | C2×#410 | — | 3 | 3 | no | — |
| 64 | C3×2−1+4 | — | 2 | 3 | no | — |
| 65 | C3×H(5,𝔽2) | — | 2 | 3 | no | — |
| 66 | C3×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 67 | C2×C3×#41 | — | 2 | 6 | no | — |
| 68 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 69 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic, complemented |
| 70 | C22×#67 | C23 | 1 | 1 | yes | characteristic |
| 71 | C22×#67 | C23 | 1 | 1 | yes | characteristic, complemented |
| 72 | #1010 | — | 2 | 12 | no | — |
| 73 | #1010 | — | 2 | 12 | no | — |
| 74 | #1010 | — | 2 | 6 | no | — |
| 75 | #1009 | — | 2 | 12 | no | — |
| 76 | #1009 | — | 2 | 12 | no | — |
| 77 | #1009 | — | 2 | 6 | no | — |
| 78 | D3×#41 | — | 2 | 4 | no | — |
| 79 | D3×#41 | — | 2 | 12 | no | — |
| 80 | D3×#41 | — | 2 | 12 | no | — |
| 81 | D3×#41 | — | 2 | 12 | no | — |
| 82 | D3×#41 | — | 2 | 6 | no | — |
| 83 | D3×#41 | — | 2 | 12 | no | — |
| 84 | D3×#41 | — | 2 | 12 | no | — |
| 85 | D3×#41 | — | 2 | 12 | no | — |
| 86 | D3×#41 | — | 2 | 6 | no | — |
| 87 | D3×#41 | — | 2 | 6 | no | — |
| 88 | D3×#41 | — | 2 | 6 | no | — |
| 89 | #1007 | — | 2 | 12 | no | — |
| 90 | #1007 | — | 2 | 3 | no | — |
| 91 | C2×#239 | — | 2 | 6 | no | — |
| 92 | C2×#239 | D4 | 1 | 3 | yes | complemented |
| 93 | C2×D3×Q8 | — | 2 | 6 | no | — |
| 94 | C2×D3×Q8 | D4 | 1 | 3 | yes | complemented |
| 95 | #1004 | — | 2 | 12 | no | — |
| 96 | #1004 | — | 2 | 3 | no | — |
| 97 | #1004 | — | 2 | 12 | no | — |
| 98 | #1004 | — | 2 | 12 | no | — |
| 99 | #1004 | C23 | 1 | 12 | yes | — |
| 100 | C2×#237 | — | 2 | 6 | no | — |
| 101 | C2×#237 | — | 2 | 12 | no | — |
| 102 | C2×#237 | D4 | 1 | 3 | yes | complemented |
| 103 | C2×#237 | C23 | 1 | 6 | yes | — |
| 104 | C2×D3×D4 | — | 2 | 6 | no | — |
| 105 | C2×D3×D4 | — | 2 | 12 | no | — |
| 106 | C2×D3×D4 | D4 | 1 | 3 | yes | complemented |
| 107 | C2×D3×D4 | C23 | 1 | 6 | yes | — |
| 108 | C2×#235 | — | 2 | 12 | no | — |
| 109 | C2×#235 | — | 2 | 6 | no | — |
| 110 | C2×#235 | — | 2 | 3 | no | — |
| 111 | C2×#235 | — | 2 | 3 | no | — |
| 112 | C2×#235 | — | 2 | 3 | no | — |
| 113 | C2×#235 | — | 2 | 3 | no | — |
| 114 | C2×#235 | D4 | 1 | 6 | yes | complemented |
| 115 | C2×#235 | C23 | 1 | 3 | yes | — |
| 116 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 117 | C22×C4×D3 | — | 2 | 4 | no | — |
| 118 | C22×C4×D3 | D4 | 1 | 6 | yes | complemented |
| 119 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 120 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 121 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic, complemented |
| 122 | C3×#123 | C23 | 1 | 6 | yes | complemented |
| 123 | C3×C22⋊Q8 | — | 2 | 3 | no | — |
| 124 | C3×#121 | — | 2 | 3 | no | — |
| 125 | C3×#120 | C23 | 1 | 6 | yes | complemented |
| 126 | C3×C4×D4 | — | 2 | 6 | no | — |
| 127 | C3×#117 | C23 | 1 | 3 | yes | complemented |
| 128 | #953 | C23 | 1 | 6 | yes | complemented |
| 129 | #946 | — | 2 | 3 | no | — |
| 130 | #940 | — | 2 | 6 | no | — |
| 131 | #939 | — | 2 | 6 | no | — |
| 132 | #938 | — | 2 | 3 | no | — |
| 133 | #938 | — | 2 | 6 | no | — |
| 134 | #937 | — | 2 | 6 | no | — |
| 135 | #937 | C23 | 1 | 6 | yes | complemented |
| 136 | #935 | C23 | 1 | 6 | yes | complemented |
| 137 | #930 | — | 2 | 3 | no | — |
| 138 | #929 | C23 | 1 | 6 | yes | complemented |
| 139 | C4×#67 | — | 2 | 6 | no | — |
| 140 | C4×#67 | — | 2 | 6 | no | — |
| 141 | #926 | C23 | 1 | 3 | yes | complemented |
| 142 | #924 | — | 2 | 3 | no | — |
| 143 | #897 | — | 2 | 3 | no | — |
| 144 | #896 | — | 2 | 6 | no | — |
| 145 | #895 | — | 2 | 6 | no | — |
| 146 | #895 | — | 2 | 3 | no | — |
| 147 | #894 | — | 2 | 6 | no | — |
| 148 | #892 | — | 2 | 3 | no | — |
| 149 | D3×C4⋊C4 | — | 2 | 3 | no | — |
| 150 | #888 | — | 2 | 6 | no | — |
| 151 | #886 | C23 | 1 | 6 | yes | complemented |
| 152 | #885 | — | 2 | 6 | no | — |
| 153 | #885 | — | 2 | 6 | no | — |
| 154 | #884 | — | 2 | 6 | no | — |
| 155 | #884 | — | 2 | 6 | no | — |
| 156 | #884 | — | 2 | 6 | no | — |
| 157 | #883 | — | 2 | 6 | no | — |
| 158 | #882 | — | 2 | 6 | no | — |
| 159 | #882 | C23 | 1 | 6 | yes | complemented |
| 160 | D3×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 161 | #878 | — | 2 | 6 | no | — |
| 162 | #877 | C23 | 1 | 6 | yes | complemented |
| 163 | C4×D12 | — | 2 | 6 | no | — |
| 164 | #872 | — | 2 | 3 | no | — |
| 165 | C42×D3 | — | 2 | 3 | no | — |
| 166 | C3×#99 | C23 | 1 | 12 | yes | complemented |
| 167 | #834 | C23 | 1 | 12 | yes | complemented |
| 168 | #806 | C23 | 1 | 24 | yes | complemented |
| 169 | #585 | — | 3 | 4 | no | — |
| 170 | #585 | — | 3 | 3 | no | — |
| 171 | #585 | — | 6 | 6 | no | — |
| 172 | #585 | — | 6 | 3 | no | — |
| 173 | #585 | — | 6 | 3 | no | — |
| 174 | #585 | C2×D3 | 1 | 1 | yes | characteristic |
| 175 | C2×2−1+4 | — | 6 | 3 | no | — |
| 176 | C2×H(5,𝔽2) | — | 3 | 4 | no | — |
| 177 | C2×H(5,𝔽2) | — | 6 | 3 | no | — |
| 178 | C22×#41 | — | 3 | 3 | no | — |
| 179 | C22×#41 | — | 3 | 1 | no | — |
| 180 | C22×#41 | — | 6 | 6 | no | — |
| 181 | #537 | — | 6 | 3 | no | — |
| 182 | #537 | — | 6 | 3 | no | — |
| 183 | #536 | — | 3 | 6 | no | — |
| 184 | #536 | — | 6 | 3 | no | — |
| 185 | #535 | — | 3 | 6 | no | — |
| 186 | #535 | — | 6 | 3 | no | — |
| 187 | #534 | — | 3 | 6 | no | — |
| 188 | #534 | — | 3 | 6 | no | — |
| 189 | #532 | — | 6 | 6 | no | — |
| 190 | #525 | — | 3 | 3 | no | — |
| 191 | #525 | — | 3 | 3 | no | — |
| 192 | #525 | — | 3 | 3 | no | — |
| 193 | #525 | — | 6 | 6 | no | — |
| 194 | #525 | C2×D3 | 1 | 3 | yes | complemented |
| 195 | C2×#117 | — | 3 | 3 | no | — |
| 196 | #458 | — | 3 | 4 | no | — |
| 197 | #458 | — | 3 | 12 | no | — |
| 198 | #458 | — | 3 | 12 | no | — |
| 199 | #458 | C2×D3 | 1 | 4 | yes | complemented |
| 200 | B(4,𝔽2) | — | 3 | 4 | no | — |
| 201 | B(4,𝔽2) | — | 3 | 12 | no | — |
| 202 | B(4,𝔽2) | — | 3 | 12 | no | — |
| 203 | B(4,𝔽2) | C2×D3 | 1 | 4 | yes | complemented |
| 204 | #410 | — | 3 | 3 | no | — |
| 205 | #410 | — | 3 | 6 | no | — |
| 206 | #410 | — | 3 | 12 | no | — |
| 207 | #410 | C2×D3 | 1 | 3 | yes | complemented |
| 208 | C2×#99 | — | 3 | 12 | no | — |
| 209 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 210 | C23×D3 | — | 2 | 4 | no | — |
| 211 | C23×D3 | C2×D4 | 1 | 6 | yes | — |
| 212 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 213 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 214 | C3×#41 | — | 2 | 4 | no | — |
| 215 | C3×#41 | — | 2 | 12 | no | — |
| 216 | C3×#41 | — | 2 | 6 | no | — |
| 217 | C3×#41 | — | 2 | 12 | no | — |
| 218 | C3×#41 | — | 2 | 6 | no | — |
| 219 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 220 | C2×C3×Q8 | C2×D4 | 1 | 3 | yes | — |
| 221 | C2×C3×D4 | — | 2 | 6 | no | — |
| 222 | C2×C3×D4 | — | 2 | 12 | no | — |
| 223 | C2×C3×D4 | — | 2 | 6 | no | — |
| 224 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 225 | C2×C3×D4 | C24 | 1 | 6 | yes | — |
| 226 | C22×C3×C4 | — | 2 | 4 | no | — |
| 227 | C22×C3×C4 | — | 2 | 3 | no | — |
| 228 | C22×C3×C4 | — | 2 | 3 | no | — |
| 229 | C22×C3×C4 | C2×D4 | 1 | 6 | yes | — |
| 230 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 231 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 232 | C2×#67 | — | 2 | 12 | no | — |
| 233 | C2×#67 | — | 2 | 12 | no | — |
| 234 | C2×#67 | — | 2 | 12 | no | — |
| 235 | C2×#67 | — | 2 | 3 | no | — |
| 236 | C2×#67 | — | 2 | 3 | no | — |
| 237 | C2×#67 | — | 2 | 6 | no | — |
| 238 | C2×#67 | — | 2 | 6 | no | — |
| 239 | C2×#67 | — | 2 | 3 | no | — |
| 240 | C2×#67 | — | 2 | 3 | no | — |
| 241 | C2×#67 | C2×D4 | 1 | 6 | yes | — |
| 242 | C2×#67 | C2×D4 | 1 | 6 | yes | — |
| 243 | C2×#67 | C24 | 1 | 6 | yes | — |
| 244 | C22×Dic3 | — | 2 | 4 | no | — |
| 245 | C22×Dic3 | C2×D4 | 1 | 6 | yes | — |
| 246 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 247 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 248 | #239 | — | 2 | 4 | no | — |
| 249 | #239 | — | 2 | 12 | no | — |
| 250 | #239 | — | 2 | 12 | no | — |
| 251 | #239 | — | 2 | 6 | no | — |
| 252 | #239 | — | 2 | 6 | no | — |
| 253 | D3×Q8 | — | 2 | 4 | no | — |
| 254 | D3×Q8 | — | 2 | 12 | no | — |
| 255 | D3×Q8 | — | 2 | 12 | no | — |
| 256 | D3×Q8 | — | 2 | 6 | no | — |
| 257 | D3×Q8 | — | 2 | 6 | no | — |
| 258 | #237 | — | 2 | 12 | no | — |
| 259 | #237 | — | 2 | 12 | no | — |
| 260 | #237 | — | 2 | 12 | no | — |
| 261 | #237 | — | 2 | 24 | no | — |
| 262 | #237 | — | 2 | 12 | no | — |
| 263 | #237 | — | 2 | 24 | no | — |
| 264 | #237 | — | 2 | 12 | no | — |
| 265 | #237 | — | 2 | 6 | no | — |
| 266 | #237 | — | 2 | 6 | no | — |
| 267 | D3×D4 | — | 2 | 12 | no | — |
| 268 | D3×D4 | — | 2 | 24 | no | — |
| 269 | D3×D4 | — | 2 | 12 | no | — |
| 270 | D3×D4 | — | 2 | 12 | no | — |
| 271 | D3×D4 | — | 2 | 12 | no | — |
| 272 | D3×D4 | — | 2 | 24 | no | — |
| 273 | D3×D4 | — | 2 | 12 | no | — |
| 274 | D3×D4 | — | 2 | 6 | no | — |
| 275 | D3×D4 | — | 2 | 6 | no | — |
| 276 | #235 | — | 2 | 12 | no | — |
| 277 | #235 | — | 2 | 24 | no | — |
| 278 | #235 | — | 2 | 12 | no | — |
| 279 | #235 | — | 2 | 24 | no | — |
| 280 | #235 | — | 2 | 6 | no | — |
| 281 | #235 | — | 2 | 12 | no | — |
| 282 | #235 | — | 2 | 6 | no | — |
| 283 | #235 | — | 2 | 12 | no | — |
| 284 | #235 | — | 2 | 12 | no | — |
| 285 | #235 | — | 4 | 1 | no | — |
| 286 | #235 | — | 4 | 3 | no | — |
| 287 | #235 | — | 4 | 3 | no | — |
| 288 | #235 | — | 4 | 3 | no | — |
| 289 | #235 | — | 4 | 6 | no | — |
| 290 | C2×D12 | — | 2 | 12 | no | — |
| 291 | C2×D12 | — | 2 | 6 | no | — |
| 292 | C2×D12 | — | 2 | 3 | no | — |
| 293 | C2×D12 | — | 2 | 3 | no | — |
| 294 | C2×D12 | — | 2 | 6 | no | — |
| 295 | C2×D12 | C2×D4 | 1 | 6 | yes | — |
| 296 | C2×D12 | C2×D4 | 1 | 3 | yes | — |
| 297 | C2×C4×D3 | — | 2 | 12 | no | — |
| 298 | C2×C4×D3 | — | 2 | 12 | no | — |
| 299 | C2×C4×D3 | — | 2 | 12 | no | — |
| 300 | C2×C4×D3 | — | 2 | 6 | no | — |
| 301 | C2×C4×D3 | — | 2 | 6 | no | — |
| 302 | C2×C4×D3 | — | 2 | 6 | no | — |
| 303 | C2×C4×D3 | — | 2 | 6 | no | — |
| 304 | C2×C4×D3 | — | 2 | 3 | no | — |
| 305 | C2×C4×D3 | — | 2 | 3 | no | — |
| 306 | C2×C4×D3 | — | 2 | 6 | no | — |
| 307 | C2×C4×D3 | C2×D4 | 1 | 6 | yes | — |
| 308 | C2×C4×D3 | C2×D4 | 1 | 6 | yes | — |
| 309 | C2×C4×D3 | C2×D4 | 1 | 6 | yes | — |
| 310 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 311 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 312 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 313 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 314 | C2×Dic6 | — | 2 | 6 | no | — |
| 315 | C2×Dic6 | — | 2 | 12 | no | — |
| 316 | C2×Dic6 | — | 2 | 3 | no | — |
| 317 | C2×Dic6 | — | 2 | 3 | no | — |
| 318 | C2×Dic6 | C2×D4 | 1 | 6 | yes | — |
| 319 | C2×Dic6 | C2×D4 | 1 | 3 | yes | — |
| 320 | C3×C4⋊C4 | — | 2 | 6 | no | — |
| 321 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 322 | C3×C22⋊C4 | — | 2 | 6 | no | — |
| 323 | C3×C22⋊C4 | — | 2 | 6 | no | — |
| 324 | C3×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 325 | C3×C42 | — | 2 | 3 | no | — |
| 326 | #217 | — | 2 | 6 | no | — |
| 327 | #217 | — | 2 | 6 | no | — |
| 328 | #217 | C24 | 1 | 6 | yes | — |
| 329 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 330 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 331 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 332 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 333 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 334 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 335 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 336 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 337 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 338 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 339 | C4×Dic3 | — | 2 | 3 | no | — |
| 340 | C4×Dic3 | — | 2 | 6 | no | — |
| 341 | 2−1+4 | — | 2 | 3 | no | — |
| 342 | 2−1+4 | — | 6 | 12 | no | — |
| 343 | 2−1+4 | — | 6 | 6 | no | — |
| 344 | 2−1+4 | — | 6 | 12 | no | — |
| 345 | 2−1+4 | — | 6 | 12 | no | — |
| 346 | 2−1+4 | — | 6 | 3 | no | — |
| 347 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 348 | H(5,𝔽2) | — | 3 | 12 | no | — |
| 349 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 350 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 351 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 352 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 353 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 354 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 355 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 356 | H(5,𝔽2) | C22×D3 | 1 | 4 | yes | — |
| 357 | C2×#41 | — | 2 | 6 | no | — |
| 358 | C2×#41 | — | 3 | 3 | no | — |
| 359 | C2×#41 | — | 3 | 3 | no | — |
| 360 | C2×#41 | — | 3 | 6 | no | — |
| 361 | C2×#41 | — | 3 | 6 | no | — |
| 362 | C2×#41 | — | 3 | 3 | no | — |
| 363 | C2×#41 | — | 6 | 3 | no | — |
| 364 | C2×#41 | — | 6 | 3 | no | — |
| 365 | C2×#41 | — | 6 | 3 | no | — |
| 366 | C2×#41 | — | 6 | 3 | no | — |
| 367 | C2×#41 | — | 6 | 12 | no | — |
| 368 | C2×#41 | — | 6 | 12 | no | — |
| 369 | C2×#41 | — | 6 | 6 | no | — |
| 370 | C2×#41 | — | 6 | 6 | no | — |
| 371 | C2×#41 | — | 6 | 6 | no | — |
| 372 | C2×#41 | — | 6 | 6 | no | — |
| 373 | C2×#41 | — | 6 | 12 | no | — |
| 374 | C2×#41 | — | 6 | 12 | no | — |
| 375 | C2×#41 | — | 6 | 12 | no | — |
| 376 | C2×#41 | — | 6 | 6 | no | — |
| 377 | C2×#41 | — | 6 | 6 | no | — |
| 378 | C2×#41 | — | 6 | 4 | no | — |
| 379 | C2×#41 | — | 6 | 12 | no | — |
| 380 | C2×#41 | — | 6 | 12 | no | — |
| 381 | C2×#41 | — | 6 | 12 | no | — |
| 382 | C2×#41 | — | 6 | 6 | no | — |
| 383 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 384 | C22×Q8 | — | 3 | 3 | no | — |
| 385 | C22×Q8 | — | 3 | 1 | no | — |
| 386 | C22×Q8 | — | 6 | 6 | no | — |
| 387 | C22×D4 | — | 3 | 3 | no | — |
| 388 | C22×D4 | — | 3 | 6 | no | — |
| 389 | C22×D4 | — | 3 | 1 | no | — |
| 390 | C22×D4 | — | 3 | 1 | no | — |
| 391 | C22×D4 | — | 3 | 1 | no | — |
| 392 | C22×D4 | — | 6 | 12 | no | — |
| 393 | C22×D4 | — | 6 | 6 | no | — |
| 394 | C23×C4 | — | 3 | 1 | no | — |
| 395 | C23×C4 | — | 3 | 6 | no | — |
| 396 | C23×C4 | — | 3 | 1 | no | — |
| 397 | C23×C4 | — | 6 | 4 | no | — |
| 398 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 399 | C4⋊Q8 | — | 6 | 6 | no | — |
| 400 | #127 | — | 6 | 6 | no | — |
| 401 | #124 | — | 6 | 6 | no | — |
| 402 | #124 | — | 6 | 6 | no | — |
| 403 | #123 | — | 3 | 6 | no | — |
| 404 | #123 | — | 3 | 6 | no | — |
| 405 | #123 | — | 3 | 6 | no | — |
| 406 | #123 | — | 6 | 6 | no | — |
| 407 | #123 | — | 6 | 6 | no | — |
| 408 | #123 | C22×D3 | 1 | 6 | yes | complemented |
| 409 | C22⋊Q8 | — | 2 | 3 | no | — |
| 410 | C22⋊Q8 | — | 6 | 6 | no | — |
| 411 | C22⋊Q8 | — | 6 | 6 | no | — |
| 412 | C22⋊Q8 | — | 6 | 3 | no | — |
| 413 | C22⋊Q8 | — | 6 | 3 | no | — |
| 414 | C22⋊Q8 | — | 6 | 3 | no | — |
| 415 | #121 | — | 2 | 3 | no | — |
| 416 | #121 | — | 6 | 6 | no | — |
| 417 | #121 | — | 6 | 6 | no | — |
| 418 | #121 | — | 6 | 6 | no | — |
| 419 | #121 | — | 6 | 3 | no | — |
| 420 | #121 | — | 6 | 6 | no | — |
| 421 | #121 | — | 6 | 3 | no | — |
| 422 | #121 | — | 6 | 6 | no | — |
| 423 | #121 | — | 6 | 6 | no | — |
| 424 | #121 | — | 6 | 3 | no | — |
| 425 | #120 | — | 3 | 6 | no | — |
| 426 | #120 | — | 3 | 6 | no | — |
| 427 | #120 | — | 3 | 6 | no | — |
| 428 | #120 | — | 6 | 6 | no | — |
| 429 | #120 | — | 6 | 6 | no | — |
| 430 | #120 | C22×D3 | 1 | 6 | yes | complemented |
| 431 | C4×D4 | — | 2 | 6 | no | — |
| 432 | C4×D4 | — | 6 | 6 | no | — |
| 433 | C4×D4 | — | 6 | 6 | no | — |
| 434 | C4×D4 | — | 6 | 6 | no | — |
| 435 | #117 | — | 3 | 3 | no | — |
| 436 | #117 | — | 3 | 6 | no | — |
| 437 | #117 | — | 6 | 3 | no | — |
| 438 | #117 | — | 6 | 3 | no | — |
| 439 | #117 | C22×D3 | 1 | 3 | yes | complemented |
| 440 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 441 | C2×C22⋊C4 | — | 3 | 6 | no | — |
| 442 | C2×C42 | — | 6 | 3 | no | — |
| 443 | #99 | — | 3 | 12 | no | — |
| 444 | #99 | — | 3 | 24 | no | — |
| 445 | #99 | C22×D3 | 1 | 12 | yes | complemented |
| 446 | C23×C3 | — | 2 | 4 | no | — |
| 447 | C23×C3 | — | 2 | 3 | no | — |
| 448 | C23×C3 | — | 8 | 1 | no | — |
| 449 | C23×C3 | C22×D4 | 1 | 6 | yes | — |
| 450 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 451 | C22×D3 | — | 2 | 12 | no | — |
| 452 | C22×D3 | — | 2 | 6 | no | — |
| 453 | C22×D3 | — | 2 | 6 | no | — |
| 454 | C22×D3 | — | 2 | 3 | no | — |
| 455 | C22×D3 | — | 8 | 1 | no | — |
| 456 | C22×D3 | — | 8 | 1 | no | — |
| 457 | C22×D3 | — | 8 | 6 | no | — |
| 458 | C22×D3 | — | 8 | 8 | no | — |
| 459 | C22×D3 | C22×D4 | 1 | 6 | yes | — |
| 460 | C22×D3 | C22×D4 | 1 | 3 | yes | — |
| 461 | C22×D3 | C22×D4 | 1 | 3 | yes | — |
| 462 | C3×Q8 | — | 2 | 4 | no | — |
| 463 | C3×Q8 | — | 2 | 6 | no | — |
| 464 | C3×D4 | — | 2 | 12 | no | — |
| 465 | C3×D4 | — | 2 | 12 | no | — |
| 466 | C3×D4 | — | 2 | 6 | no | — |
| 467 | C3×D4 | — | 8 | 6 | no | — |
| 468 | C2×C3×C4 | — | 2 | 12 | no | — |
| 469 | C2×C3×C4 | — | 2 | 6 | no | — |
| 470 | C2×C3×C4 | — | 2 | 6 | no | — |
| 471 | C2×C3×C4 | — | 2 | 6 | no | — |
| 472 | C2×C3×C4 | — | 2 | 3 | no | — |
| 473 | C2×C3×C4 | — | 4 | 3 | no | — |
| 474 | C2×C3×C4 | — | 4 | 1 | no | — |
| 475 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 476 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 477 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 478 | #67 | — | 2 | 24 | no | — |
| 479 | #67 | — | 2 | 12 | no | — |
| 480 | #67 | — | 2 | 12 | no | — |
| 481 | #67 | — | 2 | 12 | no | — |
| 482 | #67 | — | 4 | 1 | no | — |
| 483 | #67 | — | 4 | 3 | no | — |
| 484 | #67 | — | 4 | 3 | no | — |
| 485 | #67 | — | 4 | 1 | no | — |
| 486 | #67 | — | 8 | 6 | no | — |
| 487 | #67 | — | 8 | 6 | no | — |
| 488 | C2×Dic3 | — | 2 | 12 | no | — |
| 489 | C2×Dic3 | — | 2 | 6 | no | — |
| 490 | C2×Dic3 | — | 2 | 6 | no | — |
| 491 | C2×Dic3 | — | 2 | 6 | no | — |
| 492 | C2×Dic3 | — | 2 | 3 | no | — |
| 493 | C2×Dic3 | C22×D4 | 1 | 6 | yes | — |
| 494 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 495 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 496 | D12 | — | 2 | 12 | no | — |
| 497 | D12 | — | 2 | 12 | no | — |
| 498 | D12 | — | 2 | 6 | no | — |
| 499 | D12 | — | 4 | 1 | no | — |
| 500 | D12 | — | 4 | 3 | no | — |
| 501 | D12 | — | 8 | 6 | no | — |
| 502 | C4×D3 | — | 2 | 24 | no | — |
| 503 | C4×D3 | — | 2 | 6 | no | — |
| 504 | C4×D3 | — | 2 | 6 | no | — |
| 505 | C4×D3 | — | 2 | 6 | no | — |
| 506 | C4×D3 | — | 2 | 6 | no | — |
| 507 | C4×D3 | — | 2 | 6 | no | — |
| 508 | C4×D3 | — | 2 | 6 | no | — |
| 509 | C4×D3 | — | 4 | 3 | no | — |
| 510 | C4×D3 | — | 4 | 1 | no | — |
| 511 | C4×D3 | — | 8 | 6 | no | — |
| 512 | C4×D3 | #120 | 1 | 1 | yes | characteristic |
| 513 | C4×D3 | #120 | 1 | 3 | yes | — |
| 514 | C4×D3 | #120 | 1 | 3 | yes | — |
| 515 | C4×D3 | #120 | 1 | 3 | yes | — |
| 516 | C4×D3 | #120 | 1 | 6 | yes | — |
| 517 | Dic6 | — | 2 | 12 | no | — |
| 518 | Dic6 | — | 2 | 6 | no | — |
| 519 | Dic6 | — | 2 | 12 | no | — |
| 520 | Dic6 | — | 4 | 3 | no | — |
| 521 | Dic6 | — | 4 | 1 | no | — |
| 522 | C24 | — | 3 | 1 | no | — |
| 523 | C24 | — | 3 | 6 | no | — |
| 524 | C24 | — | 3 | 1 | no | — |
| 525 | C24 | — | 6 | 4 | no | — |
| 526 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 527 | #41 | — | 2 | 4 | no | — |
| 528 | #41 | — | 2 | 12 | no | — |
| 529 | #41 | — | 2 | 6 | no | — |
| 530 | #41 | — | 2 | 12 | no | — |
| 531 | #41 | — | 2 | 6 | no | — |
| 532 | #41 | — | 6 | 12 | no | — |
| 533 | #41 | — | 6 | 12 | no | — |
| 534 | #41 | — | 6 | 12 | no | — |
| 535 | #41 | — | 6 | 24 | no | — |
| 536 | #41 | — | 6 | 24 | no | — |
| 537 | #41 | — | 6 | 12 | no | — |
| 538 | #41 | — | 6 | 12 | no | — |
| 539 | #41 | — | 6 | 6 | no | — |
| 540 | #41 | — | 6 | 12 | no | — |
| 541 | #41 | — | 6 | 6 | no | — |
| 542 | #41 | — | 6 | 24 | no | — |
| 543 | #41 | — | 6 | 6 | no | — |
| 544 | #41 | — | 6 | 6 | no | — |
| 545 | #41 | — | 6 | 12 | no | — |
| 546 | #41 | — | 6 | 12 | no | — |
| 547 | #41 | — | 6 | 24 | no | — |
| 548 | #41 | — | 6 | 12 | no | — |
| 549 | #41 | — | 6 | 4 | no | — |
| 550 | #41 | — | 6 | 12 | no | — |
| 551 | #41 | — | 6 | 12 | no | — |
| 552 | #41 | — | 6 | 6 | no | — |
| 553 | #41 | — | 6 | 6 | no | — |
| 554 | #41 | — | 6 | 12 | no | — |
| 555 | #41 | — | 12 | 3 | no | — |
| 556 | #41 | — | 12 | 3 | no | — |
| 557 | #41 | — | 12 | 6 | no | — |
| 558 | #41 | — | 12 | 1 | no | — |
| 559 | #41 | — | 12 | 3 | no | — |
| 560 | C2×Q8 | — | 2 | 6 | no | — |
| 561 | C2×Q8 | — | 3 | 3 | no | — |
| 562 | C2×Q8 | — | 3 | 6 | no | — |
| 563 | C2×Q8 | — | 6 | 3 | no | — |
| 564 | C2×Q8 | — | 6 | 3 | no | — |
| 565 | C2×Q8 | — | 6 | 12 | no | — |
| 566 | C2×Q8 | — | 6 | 6 | no | — |
| 567 | C2×Q8 | — | 6 | 6 | no | — |
| 568 | C2×Q8 | — | 6 | 6 | no | — |
| 569 | C2×Q8 | — | 6 | 4 | no | — |
| 570 | C2×Q8 | — | 6 | 12 | no | — |
| 571 | C2×Q8 | — | 6 | 12 | no | — |
| 572 | C2×Q8 | D3×D4 | 1 | 3 | yes | — |
| 573 | C2×D4 | — | 2 | 6 | no | — |
| 574 | C2×D4 | — | 2 | 12 | no | — |
| 575 | C2×D4 | — | 2 | 6 | no | — |
| 576 | C2×D4 | — | 3 | 6 | no | — |
| 577 | C2×D4 | — | 3 | 6 | no | — |
| 578 | C2×D4 | — | 3 | 6 | no | — |
| 579 | C2×D4 | — | 3 | 6 | no | — |
| 580 | C2×D4 | — | 3 | 3 | no | — |
| 581 | C2×D4 | — | 6 | 12 | no | — |
| 582 | C2×D4 | — | 6 | 6 | no | — |
| 583 | C2×D4 | — | 6 | 3 | no | — |
| 584 | C2×D4 | — | 6 | 3 | no | — |
| 585 | C2×D4 | — | 6 | 6 | no | — |
| 586 | C2×D4 | — | 6 | 6 | no | — |
| 587 | C2×D4 | — | 6 | 6 | no | — |
| 588 | C2×D4 | — | 6 | 3 | no | — |
| 589 | C2×D4 | — | 6 | 3 | no | — |
| 590 | C2×D4 | — | 6 | 12 | no | — |
| 591 | C2×D4 | — | 6 | 12 | no | — |
| 592 | C2×D4 | — | 6 | 24 | no | — |
| 593 | C2×D4 | — | 6 | 12 | no | — |
| 594 | C2×D4 | — | 6 | 12 | no | — |
| 595 | C2×D4 | — | 6 | 24 | no | — |
| 596 | C2×D4 | — | 6 | 12 | no | — |
| 597 | C2×D4 | — | 6 | 12 | no | — |
| 598 | C2×D4 | — | 6 | 12 | no | — |
| 599 | C2×D4 | — | 6 | 12 | no | — |
| 600 | C2×D4 | — | 6 | 3 | no | — |
| 601 | C2×D4 | — | 6 | 3 | no | — |
| 602 | C2×D4 | — | 6 | 6 | no | — |
| 603 | C2×D4 | — | 6 | 6 | no | — |
| 604 | C2×D4 | D3×D4 | 1 | 3 | yes | — |
| 605 | C2×D4 | C23×D3 | 1 | 6 | yes | — |
| 606 | C22×C4 | — | 2 | 4 | no | — |
| 607 | C22×C4 | — | 2 | 3 | no | — |
| 608 | C22×C4 | — | 2 | 3 | no | — |
| 609 | C22×C4 | — | 3 | 1 | no | — |
| 610 | C22×C4 | — | 3 | 3 | no | — |
| 611 | C22×C4 | — | 3 | 3 | no | — |
| 612 | C22×C4 | — | 3 | 3 | no | — |
| 613 | C22×C4 | — | 3 | 3 | no | — |
| 614 | C22×C4 | — | 3 | 6 | no | — |
| 615 | C22×C4 | — | 3 | 6 | no | — |
| 616 | C22×C4 | — | 3 | 6 | no | — |
| 617 | C22×C4 | — | 3 | 6 | no | — |
| 618 | C22×C4 | — | 3 | 1 | no | — |
| 619 | C22×C4 | — | 6 | 6 | no | — |
| 620 | C22×C4 | — | 6 | 6 | no | — |
| 621 | C22×C4 | — | 6 | 6 | no | — |
| 622 | C22×C4 | — | 6 | 6 | no | — |
| 623 | C22×C4 | — | 6 | 12 | no | — |
| 624 | C22×C4 | — | 6 | 12 | no | — |
| 625 | C22×C4 | — | 6 | 12 | no | — |
| 626 | C22×C4 | — | 6 | 6 | no | — |
| 627 | C22×C4 | — | 6 | 4 | no | — |
| 628 | C22×C4 | — | 6 | 3 | no | — |
| 629 | C22×C4 | — | 6 | 3 | no | — |
| 630 | C22×C4 | D3×D4 | 1 | 6 | yes | — |
| 631 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 632 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 633 | C4⋊C4 | — | 2 | 3 | no | — |
| 634 | C4⋊C4 | — | 2 | 6 | no | — |
| 635 | C4⋊C4 | — | 6 | 6 | no | — |
| 636 | C4⋊C4 | — | 6 | 6 | no | — |
| 637 | C4⋊C4 | — | 6 | 6 | no | — |
| 638 | C4⋊C4 | — | 6 | 3 | no | — |
| 639 | C4⋊C4 | — | 6 | 6 | no | — |
| 640 | C22⋊C4 | — | 2 | 6 | no | — |
| 641 | C22⋊C4 | — | 2 | 6 | no | — |
| 642 | C22⋊C4 | — | 3 | 6 | no | — |
| 643 | C22⋊C4 | — | 6 | 6 | no | — |
| 644 | C22⋊C4 | — | 6 | 6 | no | — |
| 645 | C22⋊C4 | — | 6 | 6 | no | — |
| 646 | C22⋊C4 | — | 6 | 6 | no | — |
| 647 | C22⋊C4 | — | 6 | 6 | no | — |
| 648 | C22⋊C4 | — | 6 | 6 | no | — |
| 649 | C22⋊C4 | — | 6 | 6 | no | — |
| 650 | C22⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 651 | C42 | — | 2 | 3 | no | — |
| 652 | C42 | — | 6 | 6 | no | — |
| 653 | C42 | — | 6 | 3 | no | — |
| 654 | C22×C3 | — | 2 | 6 | no | — |
| 655 | C22×C3 | — | 4 | 1 | no | — |
| 656 | C22×C3 | — | 4 | 6 | no | — |
| 657 | C22×C3 | — | 4 | 3 | no | — |
| 658 | C22×C3 | — | 4 | 3 | no | — |
| 659 | C22×C3 | — | 4 | 1 | no | — |
| 660 | C22×C3 | — | 8 | 4 | no | — |
| 661 | C22×C3 | C23×D4 | 1 | 3 | yes | — |
| 662 | C2×D3 | — | 2 | 6 | no | — |
| 663 | C2×D3 | — | 4 | 3 | no | — |
| 664 | C2×D3 | — | 4 | 3 | no | — |
| 665 | C2×D3 | — | 4 | 12 | no | — |
| 666 | C2×D3 | — | 4 | 6 | no | — |
| 667 | C2×D3 | — | 4 | 3 | no | — |
| 668 | C2×D3 | — | 4 | 3 | no | — |
| 669 | C2×D3 | — | 4 | 1 | no | — |
| 670 | C2×D3 | — | 8 | 6 | no | — |
| 671 | C2×D3 | — | 8 | 12 | no | — |
| 672 | C2×D3 | C2×#120 | 1 | 1 | yes | characteristic |
| 673 | C2×D3 | C2×#120 | 1 | 3 | yes | — |
| 674 | C3×C4 | — | 2 | 6 | no | — |
| 675 | C3×C4 | — | 4 | 6 | no | — |
| 676 | C3×C4 | — | 4 | 1 | no | — |
| 677 | C3×C4 | C2×#120 | 1 | 3 | yes | — |
| 678 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 679 | Dic3 | — | 2 | 6 | no | — |
| 680 | Dic3 | — | 4 | 6 | no | — |
| 681 | Dic3 | — | 4 | 1 | no | — |
| 682 | Dic3 | C2×#120 | 1 | 3 | yes | — |
| 683 | Dic3 | C2×#120 | 1 | 1 | yes | characteristic |
| 684 | C23 | — | 2 | 4 | no | — |
| 685 | C23 | — | 2 | 3 | no | — |
| 686 | C23 | — | 3 | 3 | no | — |
| 687 | C23 | — | 3 | 3 | no | — |
| 688 | C23 | — | 3 | 6 | no | — |
| 689 | C23 | — | 6 | 6 | no | — |
| 690 | C23 | — | 6 | 6 | no | — |
| 691 | C23 | — | 6 | 12 | no | — |
| 692 | C23 | — | 6 | 3 | no | — |
| 693 | C23 | — | 8 | 1 | no | — |
| 694 | C23 | — | 24 | 1 | no | — |
| 695 | C23 | — | 24 | 1 | no | — |
| 696 | C23 | — | 24 | 6 | no | — |
| 697 | C23 | — | 24 | 8 | no | — |
| 698 | C23 | C2×D3×D4 | 1 | 6 | yes | — |
| 699 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 700 | Q8 | — | 2 | 4 | no | — |
| 701 | Q8 | — | 2 | 6 | no | — |
| 702 | Q8 | — | 6 | 12 | no | — |
| 703 | Q8 | — | 6 | 12 | no | — |
| 704 | Q8 | — | 6 | 6 | no | — |
| 705 | Q8 | — | 12 | 1 | no | — |
| 706 | Q8 | — | 12 | 3 | no | — |
| 707 | D4 | — | 2 | 12 | no | — |
| 708 | D4 | — | 2 | 12 | no | — |
| 709 | D4 | — | 2 | 6 | no | — |
| 710 | D4 | — | 6 | 12 | no | — |
| 711 | D4 | — | 6 | 12 | no | — |
| 712 | D4 | — | 6 | 12 | no | — |
| 713 | D4 | — | 6 | 12 | no | — |
| 714 | D4 | — | 6 | 24 | no | — |
| 715 | D4 | — | 6 | 12 | no | — |
| 716 | D4 | — | 6 | 6 | no | — |
| 717 | D4 | — | 8 | 6 | no | — |
| 718 | D4 | — | 12 | 1 | no | — |
| 719 | D4 | — | 12 | 3 | no | — |
| 720 | D4 | — | 12 | 1 | no | — |
| 721 | D4 | — | 12 | 3 | no | — |
| 722 | D4 | — | 12 | 1 | no | — |
| 723 | D4 | — | 12 | 3 | no | — |
| 724 | D4 | — | 24 | 6 | no | — |
| 725 | D4 | — | 24 | 6 | no | — |
| 726 | D4 | — | 24 | 6 | no | — |
| 727 | C2×C4 | — | 2 | 12 | no | — |
| 728 | C2×C4 | — | 2 | 6 | no | — |
| 729 | C2×C4 | — | 2 | 6 | no | — |
| 730 | C2×C4 | — | 2 | 6 | no | — |
| 731 | C2×C4 | — | 2 | 3 | no | — |
| 732 | C2×C4 | — | 3 | 3 | no | — |
| 733 | C2×C4 | — | 3 | 3 | no | — |
| 734 | C2×C4 | — | 3 | 3 | no | — |
| 735 | C2×C4 | — | 3 | 3 | no | — |
| 736 | C2×C4 | — | 3 | 6 | no | — |
| 737 | C2×C4 | — | 3 | 1 | no | — |
| 738 | C2×C4 | — | 3 | 3 | no | — |
| 739 | C2×C4 | — | 3 | 6 | no | — |
| 740 | C2×C4 | — | 4 | 3 | no | — |
| 741 | C2×C4 | — | 4 | 1 | no | — |
| 742 | C2×C4 | — | 6 | 6 | no | — |
| 743 | C2×C4 | — | 6 | 6 | no | — |
| 744 | C2×C4 | — | 6 | 6 | no | — |
| 745 | C2×C4 | — | 6 | 6 | no | — |
| 746 | C2×C4 | — | 6 | 24 | no | — |
| 747 | C2×C4 | — | 6 | 6 | no | — |
| 748 | C2×C4 | — | 6 | 6 | no | — |
| 749 | C2×C4 | — | 6 | 12 | no | — |
| 750 | C2×C4 | — | 6 | 6 | no | — |
| 751 | C2×C4 | — | 6 | 6 | no | — |
| 752 | C2×C4 | — | 6 | 6 | no | — |
| 753 | C2×C4 | — | 6 | 3 | no | — |
| 754 | C2×C4 | — | 12 | 3 | no | — |
| 755 | C2×C4 | — | 12 | 1 | no | — |
| 756 | C2×C4 | — | 24 | 6 | no | — |
| 757 | C2×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 758 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 759 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 760 | C2×C3 | — | 2 | 3 | no | — |
| 761 | C2×C3 | — | 4 | 6 | no | — |
| 762 | C2×C3 | — | 8 | 1 | no | — |
| 763 | C2×C3 | C22×#120 | 1 | 1 | yes | characteristic |
| 764 | D3 | — | 2 | 1 | no | — |
| 765 | D3 | — | 2 | 3 | no | — |
| 766 | D3 | — | 4 | 6 | no | — |
| 767 | D3 | — | 8 | 1 | no | — |
| 768 | C22 | — | 2 | 6 | no | — |
| 769 | C22 | — | 3 | 1 | no | — |
| 770 | C22 | — | 3 | 3 | no | — |
| 771 | C22 | — | 4 | 1 | no | — |
| 772 | C22 | — | 4 | 6 | no | — |
| 773 | C22 | — | 4 | 3 | no | — |
| 774 | C22 | — | 4 | 3 | no | — |
| 775 | C22 | — | 4 | 1 | no | — |
| 776 | C22 | — | 6 | 6 | no | — |
| 777 | C22 | — | 8 | 4 | no | — |
| 778 | C22 | — | 12 | 3 | no | — |
| 779 | C22 | — | 12 | 3 | no | — |
| 780 | C22 | — | 12 | 6 | no | — |
| 781 | C22 | — | 12 | 3 | no | — |
| 782 | C22 | — | 12 | 3 | no | — |
| 783 | C22 | — | 12 | 12 | no | — |
| 784 | C22 | — | 12 | 1 | no | — |
| 785 | C22 | — | 24 | 6 | no | — |
| 786 | C22 | — | 24 | 12 | no | — |
| 787 | C22 | C22×D3×D4 | 1 | 3 | yes | — |
| 788 | C4 | — | 2 | 6 | no | — |
| 789 | C4 | — | 3 | 1 | no | — |
| 790 | C4 | — | 3 | 3 | no | — |
| 791 | C4 | — | 4 | 6 | no | — |
| 792 | C4 | — | 4 | 1 | no | — |
| 793 | C4 | — | 6 | 6 | no | — |
| 794 | C4 | — | 12 | 6 | no | — |
| 795 | C4 | — | 12 | 1 | no | — |
| 796 | C4 | D3×#120 | 1 | 3 | yes | — |
| 797 | C4 | D3×#120 | 1 | 1 | yes | characteristic |
| 798 | C3 | #60398 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 799 | C2 | — | 2 | 3 | no | — |
| 800 | C2 | — | 4 | 6 | no | — |
| 801 | C2 | — | 6 | 1 | no | — |
| 802 | C2 | — | 6 | 3 | no | — |
| 803 | C2 | — | 8 | 1 | no | — |
| 804 | C2 | — | 12 | 6 | no | — |
| 805 | C2 | — | 24 | 1 | no | — |
| 806 | C2 | C2×D3×#120 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D3×#120 |
| commutator, cosocle | C23×C3 | C25 |
| Frattini | C23 | C24×D3 |
| Fitting | C3×#3025 | C2 |
| socle | C2×C3 | C22×#120 |
| hypercenter | #3025 | D3 |
| hypocenter | C3 | #60398 |
| LCS | G ▷ C23×C3 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #3025 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×#585 | C2 | semidirect |
| 2. #86035 | C2 | semidirect |
| 3. C3×#3025 | C2 | semidirect |
| 4. #84125 | C2 | semidirect |
| 5. #82936 | C2 | semidirect |
| 6. #80311 | C2 | semidirect |
| 7. #80309 | C2 | semidirect |
| 8. #80307 | C2 | semidirect |
| 9. #80305 | C2 | semidirect |
| 10. D3×#410 | C2 | semidirect |
| 11. #78690 | C2 | semidirect |
| 24. C22×#235 | C22 | semidirect |
| 25. C3×#525 | C22 | semidirect |
| 26. #5828 | C22 | semidirect |
| 27. #5791 | C22 | semidirect |
| 28. #5653 | C22 | semidirect |
| 29. #5648 | C22 | semidirect |
| 34. #5592 | C22 | semidirect |
| 35. #5589 | C22 | semidirect |
| 38. #5524 | C22 | semidirect |
| 39. D3×#117 | C22 | semidirect |
| 40. C3×#458 | C22 | semidirect |
| 41. C3×B(4,𝔽2) | C22 | semidirect |
| 42. C3×#410 | C22 | semidirect |
| 43. #5244 | C22 | semidirect |
| 44. #5243 | C22 | semidirect |
| 45. #5240 | C22 | semidirect |
| 46. #5053 | C22 | semidirect |
| 47. #5032 | C22 | semidirect |
| 48. #5006 | C22 | semidirect |
| 49. D3×#99 | C22 | semidirect |
| 50. #4742 | C22 | semidirect |
| 51. #4741 | C22 | semidirect |
| 52. #4740 | C22 | semidirect |
| 62. #3025 | D3 | semidirect |
| 69. C23×C3×C4 | C23 | semidirect |
| 71. C22×#67 | C23 | semidirect |
| 92. C2×#239 | D4 | semidirect |
| 94. C2×D3×Q8 | D4 | semidirect |
| 102. C2×#237 | D4 | semidirect |
| 106. C2×D3×D4 | D4 | semidirect |
| 114. C2×#235 | D4 | semidirect |
| 118. C22×C4×D3 | D4 | semidirect |
| 120. C22×C4×D3 | C23 | semidirect |
| 121. C22×Dic6 | C23 | semidirect |
| 122. C3×#123 | C23 | semidirect |
| 125. C3×#120 | C23 | semidirect |
| 127. C3×#117 | C23 | semidirect |
| 128. #953 | C23 | semidirect |
| 135. #937 | C23 | semidirect |
| 136. #935 | C23 | semidirect |
| 138. #929 | C23 | semidirect |
| 141. #926 | C23 | semidirect |
| 151. #886 | C23 | semidirect |
| 159. #882 | C23 | semidirect |
| 162. #877 | C23 | semidirect |
| 166. C3×#99 | C23 | semidirect |
| 167. #834 | C23 | semidirect |
| 168. #806 | C23 | semidirect |
| 194. #525 | C2×D3 | semidirect |
| 199. #458 | C2×D3 | semidirect |
| 203. B(4,𝔽2) | C2×D3 | semidirect |
| 207. #410 | C2×D3 | semidirect |
| 398. C23×C4 | C22×D3 | semidirect |
| 408. #123 | C22×D3 | semidirect |
| 430. #120 | C22×D3 | semidirect |
| 439. #117 | C22×D3 | semidirect |
| 445. #99 | C22×D3 | semidirect |
| 798. C3 | #60398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#585 | 2 |
| #86035 | 2 |
| C3×#3025 | 2 |
| #84125 | 2 |
| #82936 | 2 |
| #80311 | 2 |
| #80309 | 2 |
| #80307 | 2 |
| #80305 | 2 |
| D3×#410 | 2 |
| #78690 | 2 |
| #60398 | 3 |