Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
4836 conjugacy classes of subgroups.
The subgroup lattice has 830 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #86294 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#3026 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #84110 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83375 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #80309 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #80308 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #80305 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #80304 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #78686 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×#4740 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #60398 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×C3×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 14 | #5966 | — | 2 | 6 | no | — |
| 15 | #5966 | — | 2 | 6 | no | — |
| 16 | #5966 | C22 | 1 | 4 | yes | — |
| 17 | #5966 | C22 | 1 | 4 | yes | — |
| 18 | C2×#1010 | — | 2 | 3 | no | — |
| 19 | C2×D3×#41 | — | 2 | 3 | no | — |
| 20 | C2×#1004 | — | 2 | 3 | no | — |
| 21 | C2×#1004 | C22 | 1 | 3 | yes | — |
| 22 | C22×#237 | — | 2 | 3 | no | — |
| 23 | C22×#237 | C22 | 1 | 3 | yes | — |
| 24 | C22×#237 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×#534 | C22 | 1 | 3 | yes | complemented |
| 26 | #5804 | C22 | 1 | 3 | yes | complemented |
| 27 | #5804 | C22 | 1 | 3 | yes | complemented |
| 28 | #5656 | — | 2 | 3 | no | — |
| 29 | #5656 | C22 | 1 | 6 | yes | complemented |
| 30 | #5648 | — | 2 | 3 | no | — |
| 31 | #5648 | C22 | 1 | 6 | yes | complemented |
| 32 | #5597 | — | 2 | 6 | no | — |
| 33 | #5596 | — | 2 | 6 | no | — |
| 34 | #5592 | — | 2 | 3 | no | — |
| 35 | #5592 | C22 | 1 | 6 | yes | complemented |
| 36 | #5586 | — | 2 | 3 | no | — |
| 37 | #5586 | C22 | 1 | 6 | yes | complemented |
| 38 | #5493 | C22 | 1 | 3 | yes | complemented |
| 39 | C2×#877 | C22 | 1 | 3 | yes | complemented |
| 40 | C3×#458 | C22 | 1 | 4 | yes | complemented |
| 41 | C3×B(4,𝔽2) | C22 | 1 | 4 | yes | complemented |
| 42 | C2×C3×#99 | C22 | 1 | 3 | yes | complemented |
| 43 | #5244 | C22 | 1 | 4 | yes | complemented |
| 44 | #5243 | C22 | 1 | 4 | yes | complemented |
| 45 | C2×#834 | C22 | 1 | 3 | yes | complemented |
| 46 | #5053 | C22 | 1 | 12 | yes | complemented |
| 47 | #5032 | C22 | 1 | 12 | yes | complemented |
| 48 | C2×#806 | C22 | 1 | 6 | yes | complemented |
| 49 | #4742 | C22 | 1 | 12 | yes | complemented |
| 50 | #4741 | C22 | 1 | 12 | yes | complemented |
| 51 | #4740 | 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 | 3 | no | — |
| 58 | #3026 | — | 3 | 1 | no | — |
| 59 | #3026 | — | 3 | 3 | no | — |
| 60 | #3026 | D3 | 1 | 1 | yes | characteristic, complemented |
| 61 | #3025 | — | 3 | 4 | no | — |
| 62 | #3025 | — | 3 | 4 | no | — |
| 63 | C2×#410 | — | 3 | 3 | no | — |
| 64 | C3×H(5,𝔽2) | — | 2 | 6 | no | — |
| 65 | C3×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 66 | C2×C3×#41 | — | 2 | 3 | no | — |
| 67 | C22×C3×D4 | — | 2 | 3 | no | — |
| 68 | C22×C3×D4 | C23 | 1 | 3 | yes | — |
| 69 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×#67 | — | 2 | 3 | no | — |
| 71 | C22×#67 | — | 2 | 3 | no | — |
| 72 | C22×#67 | D4 | 1 | 3 | yes | complemented |
| 73 | C22×#67 | C23 | 1 | 3 | yes | — |
| 74 | C22×#67 | C23 | 1 | 1 | yes | characteristic |
| 75 | C22×#67 | C23 | 1 | 1 | yes | characteristic, complemented |
| 76 | C23×Dic3 | — | 2 | 1 | no | — |
| 77 | C23×Dic3 | D4 | 1 | 3 | yes | complemented |
| 78 | C23×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 79 | C23×Dic3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 80 | #1010 | — | 2 | 24 | no | — |
| 81 | #1010 | — | 2 | 12 | no | — |
| 82 | #1010 | — | 2 | 12 | no | — |
| 83 | D3×#41 | — | 2 | 12 | no | — |
| 84 | D3×#41 | — | 2 | 12 | no | — |
| 85 | D3×#41 | — | 2 | 12 | no | — |
| 86 | D3×#41 | — | 2 | 12 | no | — |
| 87 | C2×#239 | — | 2 | 1 | no | — |
| 88 | C2×D3×Q8 | — | 2 | 3 | no | — |
| 89 | #1004 | — | 2 | 24 | no | — |
| 90 | #1004 | — | 2 | 6 | no | — |
| 91 | #1004 | — | 2 | 12 | no | — |
| 92 | #1004 | — | 2 | 12 | no | — |
| 93 | #1004 | — | 2 | 12 | no | — |
| 94 | #1004 | C23 | 1 | 12 | yes | — |
| 95 | C2×#237 | — | 2 | 3 | no | — |
| 96 | C2×#237 | — | 2 | 6 | no | — |
| 97 | C2×#237 | — | 2 | 12 | no | — |
| 98 | C2×#237 | — | 2 | 12 | no | — |
| 99 | C2×#237 | — | 2 | 6 | no | — |
| 100 | C2×#237 | — | 2 | 6 | no | — |
| 101 | C2×#237 | — | 2 | 12 | no | — |
| 102 | C2×#237 | — | 2 | 12 | no | — |
| 103 | C2×#237 | — | 2 | 6 | no | — |
| 104 | C2×#237 | — | 2 | 6 | no | — |
| 105 | C2×#237 | — | 2 | 6 | no | — |
| 106 | C2×#237 | — | 2 | 3 | no | — |
| 107 | C2×#237 | — | 2 | 3 | no | — |
| 108 | C2×#237 | — | 2 | 3 | no | — |
| 109 | C2×#237 | — | 2 | 3 | no | — |
| 110 | C2×#237 | D4 | 1 | 6 | yes | complemented |
| 111 | C2×#237 | D4 | 1 | 6 | yes | complemented |
| 112 | C2×#237 | C23 | 1 | 6 | yes | — |
| 113 | C2×#237 | C23 | 1 | 6 | yes | — |
| 114 | C2×D3×D4 | — | 2 | 3 | no | — |
| 115 | C2×D3×D4 | — | 2 | 6 | no | — |
| 116 | C2×#235 | — | 2 | 6 | no | — |
| 117 | C2×#235 | — | 2 | 3 | no | — |
| 118 | C22×C4×D3 | — | 2 | 3 | no | — |
| 119 | C22×C4×D3 | D4 | 1 | 3 | yes | complemented |
| 120 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 121 | C22×Dic6 | — | 2 | 3 | no | — |
| 122 | C22×Dic6 | D4 | 1 | 3 | yes | complemented |
| 123 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic, complemented |
| 124 | C3×#123 | — | 2 | 3 | no | — |
| 125 | C3×#123 | C23 | 1 | 6 | yes | complemented |
| 126 | C3×#121 | — | 2 | 6 | no | — |
| 127 | C3×#120 | — | 2 | 3 | no | — |
| 128 | C3×#120 | C23 | 1 | 6 | yes | complemented |
| 129 | C2×C3×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 130 | #953 | — | 2 | 3 | no | — |
| 131 | #953 | C23 | 1 | 6 | yes | complemented |
| 132 | C2×#217 | C23 | 1 | 3 | yes | — |
| 133 | #940 | — | 2 | 6 | no | — |
| 134 | #939 | — | 2 | 6 | no | — |
| 135 | #939 | — | 2 | 6 | no | — |
| 136 | #939 | — | 2 | 6 | no | — |
| 137 | #939 | — | 2 | 6 | no | — |
| 138 | #937 | — | 2 | 3 | no | — |
| 139 | #937 | C23 | 1 | 6 | yes | complemented |
| 140 | #935 | — | 2 | 3 | no | — |
| 141 | #935 | C23 | 1 | 6 | yes | complemented |
| 142 | D4×Dic3 | — | 2 | 6 | no | — |
| 143 | #930 | — | 2 | 6 | no | — |
| 144 | #929 | — | 2 | 3 | no | — |
| 145 | #929 | C23 | 1 | 6 | yes | complemented |
| 146 | C2×Dic3⋊C4 | — | 2 | 3 | no | — |
| 147 | C2×C4×Dic3 | — | 2 | 3 | no | — |
| 148 | #896 | — | 2 | 6 | no | — |
| 149 | #896 | — | 2 | 6 | no | — |
| 150 | #893 | — | 2 | 6 | no | — |
| 151 | #888 | — | 2 | 6 | no | — |
| 152 | #886 | — | 2 | 3 | no | — |
| 153 | #886 | C23 | 1 | 6 | yes | complemented |
| 154 | #885 | — | 2 | 6 | no | — |
| 155 | #885 | — | 2 | 6 | no | — |
| 156 | #884 | — | 2 | 6 | no | — |
| 157 | #884 | — | 2 | 6 | no | — |
| 158 | #882 | — | 2 | 3 | no | — |
| 159 | #882 | C23 | 1 | 6 | yes | complemented |
| 160 | #67⋊C4 | — | 2 | 6 | no | — |
| 161 | #67⋊C4 | — | 2 | 6 | no | — |
| 162 | #878 | — | 2 | 6 | no | — |
| 163 | #878 | — | 2 | 6 | no | — |
| 164 | #877 | — | 2 | 3 | no | — |
| 165 | #877 | — | 2 | 3 | no | — |
| 166 | #877 | C23 | 1 | 6 | yes | complemented |
| 167 | #877 | C23 | 1 | 6 | yes | complemented |
| 168 | C3×#99 | C23 | 1 | 12 | yes | complemented |
| 169 | #834 | C23 | 1 | 12 | yes | complemented |
| 170 | #806 | C23 | 1 | 24 | yes | complemented |
| 171 | #585 | — | 3 | 4 | no | — |
| 172 | #585 | — | 3 | 4 | no | — |
| 173 | #585 | — | 6 | 6 | no | — |
| 174 | #585 | — | 6 | 6 | no | — |
| 175 | C2×2−1+4 | — | 6 | 3 | no | — |
| 176 | C2×H(5,𝔽2) | — | 3 | 3 | no | — |
| 177 | C2×H(5,𝔽2) | — | 6 | 3 | no | — |
| 178 | C2×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 179 | C22×#41 | — | 3 | 3 | no | — |
| 180 | C22×#41 | — | 3 | 1 | no | — |
| 181 | C22×#41 | — | 6 | 3 | no | — |
| 182 | C22×#41 | — | 6 | 3 | no | — |
| 183 | #537 | — | 6 | 6 | no | — |
| 184 | #536 | — | 3 | 6 | no | — |
| 185 | #536 | — | 6 | 3 | no | — |
| 186 | #535 | — | 3 | 6 | no | — |
| 187 | #535 | — | 6 | 3 | no | — |
| 188 | #534 | — | 3 | 3 | no | — |
| 189 | #534 | — | 3 | 3 | no | — |
| 190 | #534 | — | 3 | 3 | no | — |
| 191 | #534 | C2×D3 | 1 | 3 | yes | complemented |
| 192 | #532 | — | 6 | 6 | no | — |
| 193 | #525 | — | 3 | 6 | no | — |
| 194 | #525 | — | 3 | 6 | no | — |
| 195 | #525 | — | 6 | 3 | no | — |
| 196 | #525 | — | 6 | 3 | no | — |
| 197 | C2×#117 | — | 3 | 3 | no | — |
| 198 | #458 | — | 3 | 4 | no | — |
| 199 | #458 | — | 3 | 12 | no | — |
| 200 | #458 | — | 3 | 12 | no | — |
| 201 | #458 | C2×D3 | 1 | 4 | yes | complemented |
| 202 | B(4,𝔽2) | — | 3 | 4 | no | — |
| 203 | B(4,𝔽2) | — | 3 | 12 | no | — |
| 204 | B(4,𝔽2) | — | 3 | 12 | no | — |
| 205 | B(4,𝔽2) | C2×D3 | 1 | 4 | yes | complemented |
| 206 | #410 | — | 3 | 12 | no | — |
| 207 | #410 | — | 3 | 12 | no | — |
| 208 | C2×#99 | — | 3 | 3 | no | — |
| 209 | C2×#99 | — | 3 | 6 | no | — |
| 210 | C2×#99 | C2×D3 | 1 | 3 | yes | complemented |
| 211 | C24×C3 | — | 2 | 1 | no | — |
| 212 | C24×C3 | C2×D4 | 1 | 3 | yes | — |
| 213 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 214 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 215 | C23×D3 | — | 2 | 3 | no | — |
| 216 | C23×D3 | C2×D4 | 1 | 3 | yes | — |
| 217 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 218 | C3×#41 | — | 2 | 12 | no | — |
| 219 | C3×#41 | — | 2 | 12 | no | — |
| 220 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 221 | C2×C3×D4 | — | 2 | 3 | no | — |
| 222 | C2×C3×D4 | — | 2 | 12 | no | — |
| 223 | C2×C3×D4 | — | 2 | 6 | no | — |
| 224 | C2×C3×D4 | — | 2 | 12 | no | — |
| 225 | C2×C3×D4 | — | 2 | 6 | no | — |
| 226 | C2×C3×D4 | — | 2 | 3 | no | — |
| 227 | C2×C3×D4 | — | 2 | 3 | no | — |
| 228 | C2×C3×D4 | — | 2 | 6 | no | — |
| 229 | C2×C3×D4 | C2×D4 | 1 | 6 | yes | — |
| 230 | C2×C3×D4 | C24 | 1 | 6 | yes | — |
| 231 | C22×C3×C4 | — | 2 | 3 | no | — |
| 232 | C22×C3×C4 | — | 2 | 3 | no | — |
| 233 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 234 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 235 | C2×#67 | — | 2 | 6 | no | — |
| 236 | C2×#67 | — | 2 | 12 | no | — |
| 237 | C2×#67 | — | 2 | 12 | no | — |
| 238 | C2×#67 | — | 2 | 12 | no | — |
| 239 | C2×#67 | — | 2 | 6 | no | — |
| 240 | C2×#67 | — | 2 | 6 | no | — |
| 241 | C2×#67 | — | 2 | 12 | no | — |
| 242 | C2×#67 | — | 2 | 3 | no | — |
| 243 | C2×#67 | — | 2 | 3 | no | — |
| 244 | C2×#67 | — | 2 | 6 | no | — |
| 245 | C2×#67 | — | 2 | 6 | no | — |
| 246 | C2×#67 | — | 2 | 6 | no | — |
| 247 | C2×#67 | — | 2 | 6 | no | — |
| 248 | C2×#67 | — | 2 | 3 | no | — |
| 249 | C2×#67 | — | 2 | 3 | no | — |
| 250 | C2×#67 | C2×D4 | 1 | 6 | yes | — |
| 251 | C2×#67 | C2×D4 | 1 | 6 | yes | — |
| 252 | C2×#67 | C2×D4 | 1 | 6 | yes | — |
| 253 | C2×#67 | C24 | 1 | 6 | yes | — |
| 254 | C22×Dic3 | — | 2 | 3 | no | — |
| 255 | C22×Dic3 | — | 2 | 4 | no | — |
| 256 | C22×Dic3 | — | 2 | 4 | no | — |
| 257 | C22×Dic3 | — | 2 | 3 | no | — |
| 258 | C22×Dic3 | — | 2 | 3 | no | — |
| 259 | C22×Dic3 | — | 2 | 3 | no | — |
| 260 | C22×Dic3 | — | 2 | 3 | no | — |
| 261 | C22×Dic3 | — | 2 | 3 | no | — |
| 262 | C22×Dic3 | — | 2 | 3 | no | — |
| 263 | C22×Dic3 | — | 2 | 3 | no | — |
| 264 | C22×Dic3 | C2×D4 | 1 | 6 | yes | — |
| 265 | C22×Dic3 | C2×D4 | 1 | 6 | yes | — |
| 266 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 267 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 268 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 269 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 270 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 271 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 272 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 273 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 274 | #239 | — | 2 | 4 | no | — |
| 275 | #239 | — | 2 | 4 | no | — |
| 276 | D3×Q8 | — | 2 | 12 | no | — |
| 277 | D3×Q8 | — | 2 | 12 | no | — |
| 278 | #237 | — | 2 | 12 | no | — |
| 279 | #237 | — | 2 | 12 | no | — |
| 280 | #237 | — | 2 | 24 | no | — |
| 281 | #237 | — | 2 | 24 | no | — |
| 282 | #237 | — | 2 | 24 | no | — |
| 283 | #237 | — | 2 | 12 | no | — |
| 284 | #237 | — | 2 | 12 | no | — |
| 285 | #237 | — | 2 | 12 | no | — |
| 286 | #237 | — | 2 | 12 | no | — |
| 287 | #237 | — | 2 | 12 | no | — |
| 288 | #237 | — | 2 | 12 | no | — |
| 289 | #237 | — | 2 | 24 | no | — |
| 290 | #237 | — | 2 | 12 | no | — |
| 291 | #237 | — | 2 | 12 | no | — |
| 292 | #237 | — | 4 | 3 | no | — |
| 293 | #237 | — | 4 | 6 | no | — |
| 294 | #237 | — | 4 | 1 | no | — |
| 295 | #237 | — | 4 | 3 | no | — |
| 296 | #237 | — | 4 | 3 | no | — |
| 297 | D3×D4 | — | 2 | 24 | no | — |
| 298 | D3×D4 | — | 2 | 12 | no | — |
| 299 | D3×D4 | — | 2 | 12 | no | — |
| 300 | D3×D4 | — | 2 | 24 | no | — |
| 301 | #235 | — | 2 | 12 | no | — |
| 302 | #235 | — | 2 | 24 | no | — |
| 303 | #235 | — | 2 | 24 | no | — |
| 304 | #235 | — | 2 | 12 | no | — |
| 305 | C2×D12 | — | 2 | 3 | no | — |
| 306 | C2×D12 | — | 2 | 6 | no | — |
| 307 | C2×C4×D3 | — | 2 | 6 | no | — |
| 308 | C2×C4×D3 | — | 2 | 12 | no | — |
| 309 | C2×C4×D3 | — | 2 | 12 | no | — |
| 310 | C2×C4×D3 | — | 2 | 3 | no | — |
| 311 | C2×C4×D3 | — | 2 | 3 | no | — |
| 312 | C2×C4×D3 | — | 2 | 3 | no | — |
| 313 | C2×C4×D3 | — | 2 | 3 | no | — |
| 314 | C2×C4×D3 | — | 2 | 3 | no | — |
| 315 | C2×C4×D3 | — | 2 | 3 | no | — |
| 316 | C2×C4×D3 | C2×D4 | 1 | 6 | yes | — |
| 317 | C2×C4×D3 | C2×D4 | 1 | 6 | yes | — |
| 318 | C2×Dic6 | — | 2 | 3 | no | — |
| 319 | C2×Dic6 | — | 2 | 12 | no | — |
| 320 | C2×Dic6 | — | 2 | 12 | no | — |
| 321 | C2×Dic6 | — | 2 | 6 | no | — |
| 322 | C2×Dic6 | — | 2 | 6 | no | — |
| 323 | C2×Dic6 | — | 2 | 3 | no | — |
| 324 | C2×Dic6 | — | 2 | 3 | no | — |
| 325 | C2×Dic6 | C2×D4 | 1 | 6 | yes | — |
| 326 | C2×Dic6 | C2×D4 | 1 | 6 | yes | — |
| 327 | C3×C4⋊C4 | — | 2 | 6 | no | — |
| 328 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 329 | C3×C22⋊C4 | — | 2 | 6 | no | — |
| 330 | C3×C22⋊C4 | — | 2 | 6 | no | — |
| 331 | C3×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 332 | #217 | — | 2 | 3 | no | — |
| 333 | #217 | — | 2 | 6 | no | — |
| 334 | #217 | — | 2 | 6 | no | — |
| 335 | #217 | C24 | 1 | 6 | yes | — |
| 336 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 337 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 338 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 339 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 340 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 341 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 342 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 343 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 344 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 345 | C4×Dic3 | — | 2 | 6 | no | — |
| 346 | C4×Dic3 | — | 2 | 6 | no | — |
| 347 | 2−1+4 | — | 6 | 12 | no | — |
| 348 | 2−1+4 | — | 6 | 12 | no | — |
| 349 | 2−1+4 | — | 6 | 24 | no | — |
| 350 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 351 | H(5,𝔽2) | — | 3 | 12 | no | — |
| 352 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 353 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 354 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 355 | H(5,𝔽2) | — | 6 | 24 | no | — |
| 356 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 357 | H(5,𝔽2) | C22×D3 | 1 | 4 | yes | — |
| 358 | C2×#41 | — | 2 | 3 | no | — |
| 359 | C2×#41 | — | 3 | 6 | no | — |
| 360 | C2×#41 | — | 3 | 6 | no | — |
| 361 | C2×#41 | — | 3 | 6 | no | — |
| 362 | C2×#41 | — | 3 | 6 | no | — |
| 363 | C2×#41 | — | 6 | 6 | no | — |
| 364 | C2×#41 | — | 6 | 6 | no | — |
| 365 | C2×#41 | — | 6 | 6 | no | — |
| 366 | C2×#41 | — | 6 | 6 | no | — |
| 367 | C2×#41 | — | 6 | 6 | no | — |
| 368 | C2×#41 | — | 6 | 6 | no | — |
| 369 | C2×#41 | — | 6 | 12 | no | — |
| 370 | C2×#41 | — | 6 | 12 | no | — |
| 371 | C2×#41 | — | 6 | 3 | no | — |
| 372 | C2×#41 | — | 6 | 3 | no | — |
| 373 | C2×#41 | — | 6 | 3 | no | — |
| 374 | C2×#41 | — | 6 | 3 | no | — |
| 375 | C2×#41 | — | 6 | 12 | no | — |
| 376 | C2×#41 | — | 6 | 12 | no | — |
| 377 | C2×#41 | — | 6 | 3 | no | — |
| 378 | C2×#41 | — | 6 | 6 | no | — |
| 379 | C2×#41 | — | 6 | 12 | no | — |
| 380 | C2×#41 | — | 6 | 12 | no | — |
| 381 | C2×#41 | — | 6 | 1 | no | — |
| 382 | C2×#41 | — | 6 | 12 | no | — |
| 383 | C2×#41 | — | 6 | 12 | no | — |
| 384 | C2×#41 | — | 6 | 3 | no | — |
| 385 | C22×Q8 | — | 3 | 3 | no | — |
| 386 | C22×Q8 | — | 3 | 1 | no | — |
| 387 | C22×Q8 | — | 6 | 3 | no | — |
| 388 | C22×Q8 | — | 6 | 3 | no | — |
| 389 | C22×D4 | — | 2 | 3 | no | — |
| 390 | C22×D4 | — | 3 | 3 | no | — |
| 391 | C22×D4 | — | 3 | 3 | no | — |
| 392 | C22×D4 | — | 3 | 1 | no | — |
| 393 | C22×D4 | — | 3 | 1 | no | — |
| 394 | C22×D4 | — | 6 | 6 | no | — |
| 395 | C22×D4 | — | 6 | 3 | no | — |
| 396 | C22×D4 | — | 6 | 3 | no | — |
| 397 | C22×D4 | — | 6 | 3 | no | — |
| 398 | C22×D4 | C22×D3 | 1 | 3 | yes | — |
| 399 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 400 | C23×C4 | — | 3 | 1 | no | — |
| 401 | C23×C4 | — | 3 | 3 | no | — |
| 402 | C23×C4 | — | 3 | 3 | no | — |
| 403 | C23×C4 | — | 3 | 1 | no | — |
| 404 | C23×C4 | — | 3 | 1 | no | — |
| 405 | C23×C4 | — | 6 | 3 | no | — |
| 406 | C23×C4 | — | 6 | 1 | no | — |
| 407 | C4⋊Q8 | — | 6 | 6 | no | — |
| 408 | #127 | — | 6 | 6 | no | — |
| 409 | #124 | — | 6 | 6 | no | — |
| 410 | #124 | — | 6 | 6 | no | — |
| 411 | #123 | — | 2 | 3 | no | — |
| 412 | #123 | — | 3 | 6 | no | — |
| 413 | #123 | — | 3 | 6 | no | — |
| 414 | #123 | — | 3 | 6 | no | — |
| 415 | #123 | — | 6 | 3 | no | — |
| 416 | #123 | — | 6 | 3 | no | — |
| 417 | #123 | — | 6 | 3 | no | — |
| 418 | #123 | C22×D3 | 1 | 6 | yes | complemented |
| 419 | C22⋊Q8 | — | 6 | 6 | no | — |
| 420 | C22⋊Q8 | — | 6 | 6 | no | — |
| 421 | C22⋊Q8 | — | 6 | 6 | no | — |
| 422 | C22⋊Q8 | — | 6 | 6 | no | — |
| 423 | #121 | — | 2 | 6 | no | — |
| 424 | #121 | — | 6 | 6 | no | — |
| 425 | #121 | — | 6 | 6 | no | — |
| 426 | #121 | — | 6 | 6 | no | — |
| 427 | #121 | — | 6 | 6 | no | — |
| 428 | #121 | — | 6 | 6 | no | — |
| 429 | #121 | — | 6 | 6 | no | — |
| 430 | #121 | — | 6 | 6 | no | — |
| 431 | #120 | — | 2 | 3 | no | — |
| 432 | #120 | — | 3 | 6 | no | — |
| 433 | #120 | — | 3 | 6 | no | — |
| 434 | #120 | — | 3 | 6 | no | — |
| 435 | #120 | — | 6 | 3 | no | — |
| 436 | #120 | — | 6 | 3 | no | — |
| 437 | #120 | — | 6 | 3 | no | — |
| 438 | #120 | C22×D3 | 1 | 6 | yes | complemented |
| 439 | C4×D4 | — | 6 | 6 | no | — |
| 440 | C4×D4 | — | 6 | 6 | no | — |
| 441 | C4×D4 | — | 6 | 6 | no | — |
| 442 | C4×D4 | — | 6 | 6 | no | — |
| 443 | #117 | — | 3 | 6 | no | — |
| 444 | #117 | — | 3 | 6 | no | — |
| 445 | #117 | — | 6 | 3 | no | — |
| 446 | #117 | — | 6 | 3 | no | — |
| 447 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 448 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 449 | C2×C22⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 450 | C2×C42 | — | 6 | 3 | no | — |
| 451 | #99 | — | 3 | 12 | no | — |
| 452 | #99 | — | 3 | 24 | no | — |
| 453 | #99 | C22×D3 | 1 | 12 | yes | complemented |
| 454 | C23×C3 | — | 2 | 4 | no | — |
| 455 | C23×C3 | — | 2 | 3 | no | — |
| 456 | C23×C3 | — | 2 | 3 | no | — |
| 457 | C23×C3 | — | 2 | 3 | no | — |
| 458 | C23×C3 | — | 8 | 1 | no | — |
| 459 | C23×C3 | — | 8 | 1 | no | — |
| 460 | C23×C3 | — | 8 | 3 | no | — |
| 461 | C23×C3 | — | 8 | 2 | no | — |
| 462 | C23×C3 | C22×D4 | 1 | 6 | yes | — |
| 463 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 464 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 465 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 466 | C22×D3 | — | 2 | 3 | no | — |
| 467 | C22×D3 | — | 2 | 12 | no | — |
| 468 | C22×D3 | — | 2 | 3 | no | — |
| 469 | C22×D3 | — | 2 | 3 | no | — |
| 470 | C22×D3 | — | 8 | 1 | no | — |
| 471 | C22×D3 | — | 8 | 3 | no | — |
| 472 | C22×D3 | — | 8 | 6 | no | — |
| 473 | C22×D3 | C22×D4 | 1 | 6 | yes | — |
| 474 | C3×Q8 | — | 2 | 4 | no | — |
| 475 | C3×D4 | — | 2 | 12 | no | — |
| 476 | C3×D4 | — | 2 | 12 | no | — |
| 477 | C3×D4 | — | 2 | 12 | no | — |
| 478 | C3×D4 | — | 4 | 1 | no | — |
| 479 | C3×D4 | — | 4 | 3 | no | — |
| 480 | C3×D4 | — | 8 | 6 | no | — |
| 481 | C2×C3×C4 | — | 2 | 12 | no | — |
| 482 | C2×C3×C4 | — | 2 | 3 | no | — |
| 483 | C2×C3×C4 | — | 2 | 3 | no | — |
| 484 | C2×C3×C4 | — | 2 | 6 | no | — |
| 485 | C2×C3×C4 | — | 2 | 3 | no | — |
| 486 | C2×C3×C4 | — | 8 | 3 | no | — |
| 487 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 488 | #67 | — | 2 | 24 | no | — |
| 489 | #67 | — | 2 | 12 | no | — |
| 490 | #67 | — | 2 | 12 | no | — |
| 491 | #67 | — | 2 | 12 | no | — |
| 492 | #67 | — | 2 | 12 | no | — |
| 493 | #67 | — | 4 | 1 | no | — |
| 494 | #67 | — | 4 | 3 | no | — |
| 495 | #67 | — | 4 | 3 | no | — |
| 496 | #67 | — | 4 | 1 | no | — |
| 497 | #67 | — | 8 | 6 | no | — |
| 498 | #67 | — | 8 | 6 | no | — |
| 499 | C2×Dic3 | — | 2 | 12 | no | — |
| 500 | C2×Dic3 | — | 2 | 3 | no | — |
| 501 | C2×Dic3 | — | 2 | 3 | no | — |
| 502 | C2×Dic3 | — | 2 | 6 | no | — |
| 503 | C2×Dic3 | — | 2 | 6 | no | — |
| 504 | C2×Dic3 | — | 2 | 6 | no | — |
| 505 | C2×Dic3 | — | 2 | 6 | no | — |
| 506 | C2×Dic3 | — | 2 | 6 | no | — |
| 507 | C2×Dic3 | — | 2 | 3 | no | — |
| 508 | C2×Dic3 | — | 4 | 3 | no | — |
| 509 | C2×Dic3 | — | 4 | 1 | no | — |
| 510 | C2×Dic3 | — | 8 | 3 | no | — |
| 511 | C2×Dic3 | #120 | 1 | 3 | yes | — |
| 512 | C2×Dic3 | #120 | 1 | 6 | yes | — |
| 513 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 514 | C2×Dic3 | #120 | 1 | 3 | yes | — |
| 515 | C2×Dic3 | #120 | 1 | 3 | yes | — |
| 516 | C2×Dic3 | C22×D4 | 1 | 6 | yes | — |
| 517 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 518 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 519 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 520 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 521 | D12 | — | 2 | 12 | no | — |
| 522 | D12 | — | 8 | 6 | no | — |
| 523 | C4×D3 | — | 2 | 24 | no | — |
| 524 | C4×D3 | — | 2 | 6 | no | — |
| 525 | C4×D3 | — | 2 | 6 | no | — |
| 526 | C4×D3 | — | 2 | 6 | no | — |
| 527 | C4×D3 | — | 2 | 6 | no | — |
| 528 | C4×D3 | — | 4 | 3 | no | — |
| 529 | C4×D3 | — | 4 | 1 | no | — |
| 530 | Dic6 | — | 2 | 12 | no | — |
| 531 | Dic6 | — | 2 | 12 | no | — |
| 532 | Dic6 | — | 2 | 12 | no | — |
| 533 | Dic6 | — | 4 | 3 | no | — |
| 534 | Dic6 | — | 4 | 1 | no | — |
| 535 | C24 | — | 2 | 1 | no | — |
| 536 | C24 | — | 3 | 3 | no | — |
| 537 | C24 | — | 3 | 1 | no | — |
| 538 | C24 | — | 6 | 3 | no | — |
| 539 | C24 | D3×D4 | 1 | 3 | yes | — |
| 540 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 541 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 542 | #41 | — | 2 | 12 | no | — |
| 543 | #41 | — | 2 | 12 | no | — |
| 544 | #41 | — | 6 | 24 | no | — |
| 545 | #41 | — | 6 | 24 | no | — |
| 546 | #41 | — | 6 | 12 | no | — |
| 547 | #41 | — | 6 | 12 | no | — |
| 548 | #41 | — | 6 | 12 | no | — |
| 549 | #41 | — | 6 | 12 | no | — |
| 550 | #41 | — | 6 | 12 | no | — |
| 551 | #41 | — | 6 | 12 | no | — |
| 552 | #41 | — | 6 | 12 | no | — |
| 553 | #41 | — | 6 | 12 | no | — |
| 554 | #41 | — | 6 | 12 | no | — |
| 555 | #41 | — | 6 | 24 | no | — |
| 556 | #41 | — | 6 | 12 | no | — |
| 557 | #41 | — | 6 | 12 | no | — |
| 558 | #41 | — | 6 | 24 | no | — |
| 559 | #41 | — | 6 | 24 | no | — |
| 560 | #41 | — | 6 | 24 | no | — |
| 561 | #41 | — | 6 | 4 | no | — |
| 562 | #41 | — | 6 | 4 | no | — |
| 563 | #41 | — | 6 | 12 | no | — |
| 564 | #41 | — | 12 | 1 | no | — |
| 565 | #41 | — | 12 | 3 | no | — |
| 566 | #41 | — | 12 | 3 | no | — |
| 567 | #41 | — | 12 | 3 | no | — |
| 568 | #41 | — | 12 | 6 | no | — |
| 569 | C2×Q8 | — | 2 | 1 | no | — |
| 570 | C2×Q8 | — | 3 | 6 | no | — |
| 571 | C2×Q8 | — | 3 | 6 | no | — |
| 572 | C2×Q8 | — | 6 | 6 | no | — |
| 573 | C2×Q8 | — | 6 | 6 | no | — |
| 574 | C2×Q8 | — | 6 | 3 | no | — |
| 575 | C2×Q8 | — | 6 | 3 | no | — |
| 576 | C2×Q8 | — | 6 | 3 | no | — |
| 577 | C2×Q8 | — | 6 | 12 | no | — |
| 578 | C2×Q8 | — | 6 | 12 | no | — |
| 579 | C2×Q8 | — | 6 | 12 | no | — |
| 580 | C2×Q8 | — | 6 | 12 | no | — |
| 581 | C2×D4 | — | 2 | 3 | no | — |
| 582 | C2×D4 | — | 2 | 12 | no | — |
| 583 | C2×D4 | — | 2 | 6 | no | — |
| 584 | C2×D4 | — | 2 | 12 | no | — |
| 585 | C2×D4 | — | 2 | 6 | no | — |
| 586 | C2×D4 | — | 2 | 3 | no | — |
| 587 | C2×D4 | — | 2 | 3 | no | — |
| 588 | C2×D4 | — | 2 | 6 | no | — |
| 589 | C2×D4 | — | 3 | 6 | no | — |
| 590 | C2×D4 | — | 3 | 6 | no | — |
| 591 | C2×D4 | — | 3 | 6 | no | — |
| 592 | C2×D4 | — | 3 | 6 | no | — |
| 593 | C2×D4 | — | 6 | 3 | no | — |
| 594 | C2×D4 | — | 6 | 6 | no | — |
| 595 | C2×D4 | — | 6 | 6 | no | — |
| 596 | C2×D4 | — | 6 | 6 | no | — |
| 597 | C2×D4 | — | 6 | 3 | no | — |
| 598 | C2×D4 | — | 6 | 3 | no | — |
| 599 | C2×D4 | — | 6 | 24 | no | — |
| 600 | C2×D4 | — | 6 | 12 | no | — |
| 601 | C2×D4 | — | 6 | 12 | no | — |
| 602 | C2×D4 | — | 6 | 24 | no | — |
| 603 | C2×D4 | — | 6 | 6 | no | — |
| 604 | C2×D4 | — | 6 | 12 | no | — |
| 605 | C2×D4 | — | 6 | 12 | no | — |
| 606 | C2×D4 | — | 6 | 12 | no | — |
| 607 | C2×D4 | — | 6 | 6 | no | — |
| 608 | C2×D4 | — | 6 | 6 | no | — |
| 609 | C2×D4 | — | 6 | 12 | no | — |
| 610 | C2×D4 | — | 6 | 3 | no | — |
| 611 | C2×D4 | — | 6 | 3 | no | — |
| 612 | C2×D4 | — | 6 | 6 | no | — |
| 613 | C2×D4 | — | 6 | 6 | no | — |
| 614 | C2×D4 | D3×D4 | 1 | 6 | yes | — |
| 615 | C2×D4 | C23×D3 | 1 | 6 | yes | — |
| 616 | C22×C4 | — | 2 | 3 | no | — |
| 617 | C22×C4 | — | 2 | 3 | no | — |
| 618 | C22×C4 | — | 3 | 3 | no | — |
| 619 | C22×C4 | — | 3 | 3 | no | — |
| 620 | C22×C4 | — | 3 | 3 | no | — |
| 621 | C22×C4 | — | 3 | 3 | no | — |
| 622 | C22×C4 | — | 3 | 1 | no | — |
| 623 | C22×C4 | — | 3 | 1 | no | — |
| 624 | C22×C4 | — | 3 | 6 | no | — |
| 625 | C22×C4 | — | 3 | 6 | no | — |
| 626 | C22×C4 | — | 3 | 3 | no | — |
| 627 | C22×C4 | — | 3 | 6 | no | — |
| 628 | C22×C4 | — | 3 | 6 | no | — |
| 629 | C22×C4 | — | 3 | 1 | no | — |
| 630 | C22×C4 | — | 6 | 3 | no | — |
| 631 | C22×C4 | — | 6 | 3 | no | — |
| 632 | C22×C4 | — | 6 | 3 | no | — |
| 633 | C22×C4 | — | 6 | 3 | no | — |
| 634 | C22×C4 | — | 6 | 3 | no | — |
| 635 | C22×C4 | — | 6 | 3 | no | — |
| 636 | C22×C4 | — | 6 | 6 | no | — |
| 637 | C22×C4 | — | 6 | 12 | no | — |
| 638 | C22×C4 | — | 6 | 12 | no | — |
| 639 | C22×C4 | — | 6 | 3 | no | — |
| 640 | C22×C4 | — | 6 | 3 | no | — |
| 641 | C22×C4 | — | 6 | 3 | no | — |
| 642 | C22×C4 | — | 6 | 3 | no | — |
| 643 | C22×C4 | — | 6 | 3 | no | — |
| 644 | C22×C4 | — | 6 | 3 | no | — |
| 645 | C22×C4 | — | 6 | 3 | no | — |
| 646 | C22×C4 | — | 6 | 4 | no | — |
| 647 | C22×C4 | — | 6 | 4 | no | — |
| 648 | C22×C4 | — | 6 | 3 | no | — |
| 649 | C22×C4 | D3×D4 | 1 | 3 | yes | — |
| 650 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 651 | C4⋊C4 | — | 2 | 6 | no | — |
| 652 | C4⋊C4 | — | 6 | 6 | no | — |
| 653 | C4⋊C4 | — | 6 | 6 | no | — |
| 654 | C4⋊C4 | — | 6 | 6 | no | — |
| 655 | C4⋊C4 | — | 6 | 6 | no | — |
| 656 | C4⋊C4 | — | 6 | 6 | no | — |
| 657 | C22⋊C4 | — | 2 | 3 | no | — |
| 658 | C22⋊C4 | — | 2 | 6 | no | — |
| 659 | C22⋊C4 | — | 2 | 6 | no | — |
| 660 | C22⋊C4 | — | 3 | 6 | no | — |
| 661 | C22⋊C4 | — | 6 | 6 | no | — |
| 662 | C22⋊C4 | — | 6 | 6 | no | — |
| 663 | C22⋊C4 | — | 6 | 6 | no | — |
| 664 | C22⋊C4 | — | 6 | 6 | no | — |
| 665 | C22⋊C4 | — | 6 | 3 | no | — |
| 666 | C22⋊C4 | — | 6 | 6 | no | — |
| 667 | C22⋊C4 | — | 6 | 6 | no | — |
| 668 | C22⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 669 | C42 | — | 6 | 6 | no | — |
| 670 | C42 | — | 6 | 6 | no | — |
| 671 | C22×C3 | — | 2 | 6 | no | — |
| 672 | C22×C3 | — | 4 | 3 | no | — |
| 673 | C22×C3 | — | 4 | 3 | no | — |
| 674 | C22×C3 | — | 4 | 1 | no | — |
| 675 | C22×C3 | — | 4 | 6 | no | — |
| 676 | C22×C3 | — | 4 | 6 | no | — |
| 677 | C22×C3 | — | 4 | 6 | no | — |
| 678 | C22×C3 | — | 4 | 1 | no | — |
| 679 | C22×C3 | — | 8 | 3 | no | — |
| 680 | C22×C3 | — | 8 | 4 | no | — |
| 681 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 682 | C22×C3 | C2×#120 | 1 | 3 | yes | — |
| 683 | C22×C3 | C23×D4 | 1 | 3 | yes | — |
| 684 | C2×D3 | — | 2 | 6 | no | — |
| 685 | C2×D3 | — | 4 | 6 | no | — |
| 686 | C2×D3 | — | 4 | 6 | no | — |
| 687 | C2×D3 | — | 4 | 6 | no | — |
| 688 | C2×D3 | — | 4 | 1 | no | — |
| 689 | C2×D3 | — | 8 | 3 | no | — |
| 690 | C2×D3 | — | 8 | 12 | no | — |
| 691 | C3×C4 | — | 2 | 6 | no | — |
| 692 | C3×C4 | — | 4 | 6 | no | — |
| 693 | C3×C4 | — | 4 | 1 | no | — |
| 694 | Dic3 | — | 2 | 6 | no | — |
| 695 | Dic3 | — | 4 | 6 | no | — |
| 696 | Dic3 | — | 4 | 1 | no | — |
| 697 | Dic3 | C2×#120 | 1 | 3 | yes | — |
| 698 | Dic3 | C2×#120 | 1 | 3 | yes | — |
| 699 | Dic3 | C2×#120 | 1 | 1 | yes | characteristic |
| 700 | Dic3 | C2×#120 | 1 | 1 | yes | characteristic |
| 701 | C23 | — | 2 | 4 | no | — |
| 702 | C23 | — | 2 | 3 | no | — |
| 703 | C23 | — | 2 | 3 | no | — |
| 704 | C23 | — | 2 | 3 | no | — |
| 705 | C23 | — | 3 | 6 | no | — |
| 706 | C23 | — | 6 | 12 | no | — |
| 707 | C23 | — | 6 | 3 | no | — |
| 708 | C23 | — | 6 | 3 | no | — |
| 709 | C23 | — | 6 | 3 | no | — |
| 710 | C23 | — | 8 | 1 | no | — |
| 711 | C23 | — | 8 | 1 | no | — |
| 712 | C23 | — | 8 | 3 | no | — |
| 713 | C23 | — | 8 | 2 | no | — |
| 714 | C23 | — | 24 | 1 | no | — |
| 715 | C23 | — | 24 | 3 | no | — |
| 716 | C23 | — | 24 | 6 | no | — |
| 717 | C23 | C2×D3×D4 | 1 | 6 | yes | — |
| 718 | C23 | C2×D3×D4 | 1 | 3 | yes | — |
| 719 | C23 | C2×D3×D4 | 1 | 3 | yes | — |
| 720 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 721 | Q8 | — | 2 | 4 | no | — |
| 722 | Q8 | — | 6 | 12 | no | — |
| 723 | Q8 | — | 6 | 12 | no | — |
| 724 | Q8 | — | 6 | 12 | no | — |
| 725 | Q8 | — | 12 | 1 | no | — |
| 726 | Q8 | — | 12 | 3 | no | — |
| 727 | D4 | — | 2 | 12 | no | — |
| 728 | D4 | — | 2 | 12 | no | — |
| 729 | D4 | — | 2 | 12 | no | — |
| 730 | D4 | — | 4 | 1 | no | — |
| 731 | D4 | — | 4 | 3 | no | — |
| 732 | D4 | — | 6 | 12 | no | — |
| 733 | D4 | — | 6 | 12 | no | — |
| 734 | D4 | — | 6 | 12 | no | — |
| 735 | D4 | — | 6 | 24 | no | — |
| 736 | D4 | — | 6 | 12 | no | — |
| 737 | D4 | — | 6 | 12 | no | — |
| 738 | D4 | — | 8 | 6 | no | — |
| 739 | D4 | — | 12 | 1 | no | — |
| 740 | D4 | — | 12 | 3 | no | — |
| 741 | D4 | — | 12 | 1 | no | — |
| 742 | D4 | — | 12 | 3 | no | — |
| 743 | D4 | — | 24 | 6 | no | — |
| 744 | D4 | — | 24 | 6 | no | — |
| 745 | D4 | — | 24 | 6 | no | — |
| 746 | C2×C4 | — | 2 | 12 | no | — |
| 747 | C2×C4 | — | 2 | 3 | no | — |
| 748 | C2×C4 | — | 2 | 3 | no | — |
| 749 | C2×C4 | — | 2 | 6 | no | — |
| 750 | C2×C4 | — | 2 | 3 | no | — |
| 751 | C2×C4 | — | 3 | 3 | no | — |
| 752 | C2×C4 | — | 3 | 3 | no | — |
| 753 | C2×C4 | — | 3 | 3 | no | — |
| 754 | C2×C4 | — | 3 | 3 | no | — |
| 755 | C2×C4 | — | 3 | 1 | no | — |
| 756 | C2×C4 | — | 3 | 3 | no | — |
| 757 | C2×C4 | — | 3 | 3 | no | — |
| 758 | C2×C4 | — | 3 | 3 | no | — |
| 759 | C2×C4 | — | 3 | 6 | no | — |
| 760 | C2×C4 | — | 3 | 6 | no | — |
| 761 | C2×C4 | — | 6 | 6 | no | — |
| 762 | C2×C4 | — | 6 | 6 | no | — |
| 763 | C2×C4 | — | 6 | 6 | no | — |
| 764 | C2×C4 | — | 6 | 6 | no | — |
| 765 | C2×C4 | — | 6 | 24 | no | — |
| 766 | C2×C4 | — | 6 | 6 | no | — |
| 767 | C2×C4 | — | 6 | 6 | no | — |
| 768 | C2×C4 | — | 6 | 6 | no | — |
| 769 | C2×C4 | — | 6 | 6 | no | — |
| 770 | C2×C4 | — | 6 | 12 | no | — |
| 771 | C2×C4 | — | 6 | 3 | no | — |
| 772 | C2×C4 | — | 6 | 3 | no | — |
| 773 | C2×C4 | — | 6 | 6 | no | — |
| 774 | C2×C4 | — | 6 | 3 | no | — |
| 775 | C2×C4 | — | 8 | 3 | no | — |
| 776 | C2×C4 | — | 12 | 1 | no | — |
| 777 | C2×C4 | — | 12 | 3 | no | — |
| 778 | C2×C4 | — | 12 | 1 | no | — |
| 779 | C2×C4 | — | 12 | 3 | no | — |
| 780 | C2×C4 | — | 24 | 3 | no | — |
| 781 | C2×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 782 | C2×C3 | — | 2 | 3 | no | — |
| 783 | C2×C3 | — | 2 | 1 | no | — |
| 784 | C2×C3 | — | 2 | 3 | no | — |
| 785 | C2×C3 | — | 4 | 6 | no | — |
| 786 | C2×C3 | — | 8 | 1 | no | — |
| 787 | C2×C3 | C22×#120 | 1 | 1 | yes | characteristic |
| 788 | D3 | — | 4 | 6 | no | — |
| 789 | D3 | — | 8 | 1 | no | — |
| 790 | C22 | — | 2 | 6 | no | — |
| 791 | C22 | — | 4 | 3 | no | — |
| 792 | C22 | — | 4 | 3 | no | — |
| 793 | C22 | — | 4 | 1 | no | — |
| 794 | C22 | — | 4 | 6 | no | — |
| 795 | C22 | — | 4 | 6 | no | — |
| 796 | C22 | — | 4 | 6 | no | — |
| 797 | C22 | — | 4 | 1 | no | — |
| 798 | C22 | — | 6 | 6 | no | — |
| 799 | C22 | — | 8 | 3 | no | — |
| 800 | C22 | — | 8 | 4 | no | — |
| 801 | C22 | — | 12 | 6 | no | — |
| 802 | C22 | — | 12 | 6 | no | — |
| 803 | C22 | — | 12 | 6 | no | — |
| 804 | C22 | — | 12 | 1 | no | — |
| 805 | C22 | — | 24 | 3 | no | — |
| 806 | C22 | — | 24 | 12 | no | — |
| 807 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 808 | C22 | D3×#120 | 1 | 3 | yes | — |
| 809 | C22 | C22×D3×D4 | 1 | 3 | yes | — |
| 810 | C4 | — | 2 | 6 | no | — |
| 811 | C4 | — | 3 | 1 | no | — |
| 812 | C4 | — | 3 | 1 | no | — |
| 813 | C4 | — | 3 | 3 | no | — |
| 814 | C4 | — | 3 | 3 | no | — |
| 815 | C4 | — | 4 | 6 | no | — |
| 816 | C4 | — | 4 | 1 | no | — |
| 817 | C4 | — | 6 | 6 | no | — |
| 818 | C4 | — | 12 | 6 | no | — |
| 819 | C4 | — | 12 | 1 | no | — |
| 820 | C3 | #60398 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 821 | C2 | — | 2 | 3 | no | — |
| 822 | C2 | — | 2 | 1 | no | — |
| 823 | C2 | — | 2 | 3 | no | — |
| 824 | C2 | — | 4 | 6 | no | — |
| 825 | C2 | — | 8 | 1 | no | — |
| 826 | C2 | — | 12 | 6 | no | — |
| 827 | C2 | — | 24 | 1 | no | — |
| 828 | C2 | C2×D3×#120 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D3×#120 |
| commutator, cosocle | C23×C3 | C25 |
| Frattini | C23 | C24×D3 |
| Fitting | C3×#3026 | C2 |
| socle | C2×C3 | C22×#120 |
| hypercenter | #3026 | D3 |
| hypocenter | C3 | #60398 |
| LCS | G ▷ C23×C3 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ #3026 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5966 | C2 | semidirect |
| 2. #86294 | C2 | semidirect |
| 3. C3×#3026 | C2 | semidirect |
| 4. #84110 | C2 | semidirect |
| 5. #83375 | C2 | semidirect |
| 6. #80309 | C2 | semidirect |
| 7. #80308 | C2 | semidirect |
| 8. #80305 | C2 | semidirect |
| 9. #80304 | C2 | semidirect |
| 10. #78686 | C2 | semidirect |
| 11. C2×#4740 | C2 | semidirect |
| 24. C22×#237 | C22 | semidirect |
| 25. C3×#534 | C22 | semidirect |
| 26. #5804 | C22 | semidirect |
| 27. #5804 | C22 | semidirect |
| 29. #5656 | C22 | semidirect |
| 31. #5648 | C22 | semidirect |
| 35. #5592 | C22 | semidirect |
| 37. #5586 | C22 | semidirect |
| 38. #5493 | C22 | semidirect |
| 39. C2×#877 | C22 | semidirect |
| 40. C3×#458 | C22 | semidirect |
| 41. C3×B(4,𝔽2) | C22 | semidirect |
| 42. C2×C3×#99 | C22 | semidirect |
| 43. #5244 | C22 | semidirect |
| 44. #5243 | C22 | semidirect |
| 45. C2×#834 | C22 | semidirect |
| 46. #5053 | C22 | semidirect |
| 47. #5032 | C22 | semidirect |
| 48. C2×#806 | C22 | semidirect |
| 49. #4742 | C22 | semidirect |
| 50. #4741 | C22 | semidirect |
| 51. #4740 | C22 | semidirect |
| 52. #4740 | C22 | semidirect |
| 60. #3026 | D3 | semidirect |
| 72. C22×#67 | D4 | semidirect |
| 75. C22×#67 | C23 | semidirect |
| 77. C23×Dic3 | D4 | semidirect |
| 79. C23×Dic3 | C23 | semidirect |
| 110. C2×#237 | D4 | semidirect |
| 111. C2×#237 | D4 | semidirect |
| 119. C22×C4×D3 | D4 | semidirect |
| 120. C22×C4×D3 | C23 | semidirect |
| 122. C22×Dic6 | D4 | semidirect |
| 123. C22×Dic6 | C23 | semidirect |
| 125. C3×#123 | C23 | semidirect |
| 128. C3×#120 | C23 | semidirect |
| 131. #953 | C23 | semidirect |
| 139. #937 | C23 | semidirect |
| 141. #935 | C23 | semidirect |
| 145. #929 | C23 | semidirect |
| 153. #886 | C23 | semidirect |
| 159. #882 | C23 | semidirect |
| 166. #877 | C23 | semidirect |
| 167. #877 | C23 | semidirect |
| 168. C3×#99 | C23 | semidirect |
| 169. #834 | C23 | semidirect |
| 170. #806 | C23 | semidirect |
| 191. #534 | C2×D3 | semidirect |
| 201. #458 | C2×D3 | semidirect |
| 205. B(4,𝔽2) | C2×D3 | semidirect |
| 210. C2×#99 | C2×D3 | semidirect |
| 418. #123 | C22×D3 | semidirect |
| 438. #120 | C22×D3 | semidirect |
| 453. #99 | C22×D3 | semidirect |
| 820. C3 | #60398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5966 | 2 |
| #86294 | 2 |
| C3×#3026 | 2 |
| #84110 | 2 |
| #83375 | 2 |
| #80309 | 2 |
| #80308 | 2 |
| #80305 | 2 |
| #80304 | 2 |
| #78686 | 2 |
| C2×#4740 | 2 |
| #60398 | 3 |