Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1164 conjugacy classes of subgroups.
The subgroup lattice has 928 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86019 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #84004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #82936 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #78992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2010 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72114 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71715 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #70417 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #70395 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #70394 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #69992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #69966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68711 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #23995 | — | 3 | 1 | no | maximal, Sylow |
| 17 | #5964 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#575 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#525 | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×#525 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #5832 | C22 | 1 | 1 | yes | characteristic |
| 22 | Dic3×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #5822 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5791 | C22 | 1 | 1 | yes | characteristic |
| 25 | #5791 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#926 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #5745 | C22 | 1 | 1 | yes | characteristic |
| 28 | #5665 | — | 2 | 2 | no | — |
| 29 | #5643 | — | 2 | 1 | no | — |
| 30 | #5625 | — | 2 | 1 | no | — |
| 31 | #5619 | — | 2 | 1 | no | — |
| 32 | #5603 | — | 2 | 1 | no | — |
| 33 | #5593 | — | 2 | 2 | no | — |
| 34 | #5557 | — | 2 | 2 | no | — |
| 35 | #5538 | — | 2 | 2 | no | — |
| 36 | #5522 | C22 | 1 | 1 | yes | characteristic |
| 37 | #5517 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C3×#421 | C22 | 1 | 1 | yes | characteristic |
| 39 | C3×#421 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C3×#407 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5240 | C22 | 1 | 1 | yes | characteristic |
| 42 | #5236 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×#837 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#837 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5207 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #5205 | — | 2 | 1 | no | — |
| 47 | #5202 | — | 2 | 1 | no | — |
| 48 | #5201 | — | 2 | 1 | no | — |
| 49 | #5198 | — | 2 | 1 | no | — |
| 50 | C2×#825 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#825 | C22 | 1 | 1 | yes | characteristic |
| 52 | #5132 | C22 | 1 | 1 | yes | characteristic |
| 53 | #5053 | — | 2 | 2 | no | — |
| 54 | #5032 | — | 2 | 2 | no | — |
| 55 | #5006 | C22 | 1 | 1 | yes | characteristic |
| 56 | #5006 | C22 | 1 | 1 | yes | characteristic |
| 57 | #5005 | C22 | 1 | 1 | yes | characteristic |
| 58 | #4821 | — | 2 | 2 | no | — |
| 59 | D3×#104 | — | 2 | 2 | no | — |
| 60 | C3×H(3,ℤ/4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #4559 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #4556 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #4555 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #4555 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #4532 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #4532 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #4531 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #3455 | — | 3 | 1 | no | — |
| 69 | #3025 | — | 3 | 1 | no | — |
| 70 | #3018 | — | 3 | 1 | no | — |
| 71 | #2901 | — | 3 | 1 | no | — |
| 72 | #2031 | — | 3 | 1 | no | — |
| 73 | #2031 | — | 3 | 1 | no | — |
| 74 | #2010 | — | 3 | 1 | no | — |
| 75 | #2010 | D3 | 1 | 1 | yes | characteristic, complemented |
| 76 | #1906 | — | 3 | 1 | no | — |
| 77 | #1906 | — | 3 | 1 | no | — |
| 78 | #1897 | — | 3 | 1 | no | — |
| 79 | #1897 | — | 3 | 1 | no | — |
| 80 | #1891 | — | 3 | 1 | no | — |
| 81 | #1884 | — | 3 | 1 | no | — |
| 82 | #1827 | — | 3 | 1 | no | — |
| 83 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 85 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 86 | #1010 | — | 2 | 1 | no | — |
| 87 | #1010 | — | 2 | 1 | no | — |
| 88 | #1009 | — | 2 | 1 | no | — |
| 89 | #1009 | — | 2 | 1 | no | — |
| 90 | D3×#41 | — | 2 | 2 | no | — |
| 91 | D3×#41 | — | 4 | 1 | no | — |
| 92 | #1007 | — | 2 | 1 | no | — |
| 93 | #1004 | — | 2 | 1 | no | — |
| 94 | #1004 | — | 2 | 2 | no | — |
| 95 | C2×#235 | — | 4 | 1 | no | — |
| 96 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 98 | C3×#137 | — | 2 | 1 | no | — |
| 99 | C3×#137 | — | 2 | 1 | no | — |
| 100 | C3×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 101 | C3×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 102 | C3×#135 | — | 4 | 1 | no | — |
| 103 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 105 | C3×#123 | — | 2 | 1 | no | — |
| 106 | C3×#123 | — | 2 | 1 | no | — |
| 107 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 108 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 109 | C3×#121 | — | 2 | 1 | no | — |
| 110 | C3×#121 | — | 2 | 1 | no | — |
| 111 | C3×#120 | — | 2 | 1 | no | — |
| 112 | C3×#120 | — | 2 | 1 | no | — |
| 113 | C3×C4×D4 | — | 2 | 2 | no | — |
| 114 | C3×C4×D4 | — | 4 | 1 | no | — |
| 115 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 116 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 117 | #953 | — | 2 | 1 | no | — |
| 118 | #953 | D4 | 1 | 2 | yes | — |
| 119 | C2×#217 | — | 2 | 1 | no | — |
| 120 | #951 | — | 2 | 1 | no | — |
| 121 | #950 | — | 4 | 1 | no | — |
| 122 | #949 | — | 2 | 1 | no | — |
| 123 | #947 | D4 | 1 | 1 | yes | characteristic, complemented |
| 124 | Q8×Dic3 | — | 2 | 1 | no | — |
| 125 | #944 | D4 | 1 | 1 | yes | characteristic, complemented |
| 126 | #942 | — | 2 | 1 | no | — |
| 127 | #940 | D4 | 1 | 1 | yes | characteristic, complemented |
| 128 | #939 | — | 2 | 2 | no | — |
| 129 | #939 | — | 2 | 2 | no | — |
| 130 | #938 | — | 2 | 2 | no | — |
| 131 | #936 | — | 2 | 2 | no | — |
| 132 | #936 | D4 | 1 | 1 | yes | characteristic, complemented |
| 133 | #935 | — | 2 | 2 | no | — |
| 134 | D4×Dic3 | — | 2 | 1 | no | — |
| 135 | D4×Dic3 | — | 2 | 2 | no | — |
| 136 | #932 | — | 2 | 1 | no | — |
| 137 | #930 | — | 2 | 1 | no | — |
| 138 | #930 | — | 2 | 1 | no | — |
| 139 | #929 | — | 2 | 1 | no | — |
| 140 | #929 | D4 | 1 | 2 | yes | — |
| 141 | C4×#67 | — | 2 | 2 | no | — |
| 142 | C4×#67 | — | 2 | 2 | no | — |
| 143 | C4×#67 | — | 4 | 1 | no | — |
| 144 | #926 | — | 2 | 1 | no | — |
| 145 | #926 | — | 2 | 1 | no | — |
| 146 | #926 | — | 2 | 1 | no | — |
| 147 | #926 | — | 2 | 1 | no | — |
| 148 | #926 | — | 2 | 1 | no | — |
| 149 | #926 | C23 | 1 | 1 | yes | characteristic |
| 150 | #926 | C23 | 1 | 1 | yes | characteristic |
| 151 | C2×C4⋊Dic3 | — | 2 | 1 | no | — |
| 152 | #924 | — | 2 | 1 | no | — |
| 153 | #924 | — | 2 | 1 | no | — |
| 154 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 155 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 157 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 158 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 159 | #907 | — | 4 | 1 | no | — |
| 160 | D3×M16 | — | 2 | 2 | no | — |
| 161 | #901 | — | 4 | 1 | no | — |
| 162 | #898 | — | 2 | 2 | no | — |
| 163 | #897 | — | 2 | 2 | no | — |
| 164 | #893 | — | 2 | 1 | no | — |
| 165 | #890 | — | 2 | 2 | no | — |
| 166 | #890 | — | 2 | 1 | no | — |
| 167 | #889 | — | 2 | 2 | no | — |
| 168 | #888 | — | 2 | 1 | no | — |
| 169 | #887 | — | 2 | 1 | no | — |
| 170 | #886 | — | 2 | 2 | no | — |
| 171 | #885 | — | 2 | 2 | no | — |
| 172 | #883 | — | 2 | 2 | no | — |
| 173 | #883 | — | 2 | 2 | no | — |
| 174 | #67⋊C4 | — | 2 | 2 | no | — |
| 175 | #879 | — | 2 | 2 | no | — |
| 176 | #879 | — | 2 | 2 | no | — |
| 177 | #879 | — | 2 | 2 | no | — |
| 178 | #878 | — | 2 | 2 | no | — |
| 179 | #878 | — | 2 | 2 | no | — |
| 180 | #872 | D4 | 1 | 2 | yes | complemented |
| 181 | C42×D3 | D4 | 1 | 2 | yes | complemented |
| 182 | C4×Dic6 | — | 2 | 2 | no | — |
| 183 | C3×#104 | — | 2 | 2 | no | — |
| 184 | C3×#104 | — | 4 | 1 | no | — |
| 185 | C3×C22⋊C8 | — | 4 | 1 | no | — |
| 186 | #837 | — | 2 | 1 | no | — |
| 187 | #837 | — | 2 | 1 | no | — |
| 188 | #837 | — | 2 | 1 | no | — |
| 189 | #837 | — | 2 | 1 | no | — |
| 190 | #837 | — | 4 | 1 | no | — |
| 191 | #834 | — | 2 | 2 | no | — |
| 192 | #830 | — | 4 | 1 | no | — |
| 193 | #825 | — | 2 | 1 | no | — |
| 194 | #825 | — | 2 | 1 | no | — |
| 195 | #825 | — | 2 | 1 | no | — |
| 196 | #825 | — | 2 | 1 | no | — |
| 197 | #824 | — | 2 | 1 | no | — |
| 198 | #823 | — | 2 | 1 | no | — |
| 199 | #806 | — | 2 | 2 | no | — |
| 200 | #806 | — | 2 | 2 | no | — |
| 201 | #805 | — | 2 | 2 | no | — |
| 202 | #585 | — | 3 | 1 | no | — |
| 203 | #575 | — | 3 | 1 | no | — |
| 204 | #575 | C2×D3 | 1 | 1 | yes | characteristic |
| 205 | #568 | — | 3 | 1 | no | — |
| 206 | #542 | — | 6 | 1 | no | — |
| 207 | #542 | — | 6 | 1 | no | — |
| 208 | #541 | — | 6 | 1 | no | — |
| 209 | #540 | — | 6 | 1 | no | — |
| 210 | #539 | — | 6 | 2 | no | — |
| 211 | #538 | — | 6 | 2 | no | — |
| 212 | #533 | — | 3 | 1 | no | — |
| 213 | #532 | — | 3 | 1 | no | — |
| 214 | #529 | — | 6 | 2 | no | — |
| 215 | #529 | — | 6 | 2 | no | — |
| 216 | #525 | — | 3 | 1 | no | — |
| 217 | #525 | — | 3 | 1 | no | — |
| 218 | #525 | C2×D3 | 1 | 1 | yes | characteristic |
| 219 | #525 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 220 | C4×#41 | — | 3 | 1 | no | — |
| 221 | C4×#41 | — | 3 | 1 | no | — |
| 222 | C2×#117 | — | 3 | 1 | no | — |
| 223 | #458 | — | 6 | 2 | no | — |
| 224 | B(4,𝔽2) | — | 6 | 2 | no | — |
| 225 | #456 | — | 6 | 1 | no | — |
| 226 | #455 | — | 6 | 1 | no | — |
| 227 | #454 | — | 6 | 1 | no | — |
| 228 | #453 | — | 6 | 1 | no | — |
| 229 | #421 | — | 3 | 1 | no | — |
| 230 | #421 | — | 3 | 1 | no | — |
| 231 | #421 | — | 6 | 2 | no | — |
| 232 | #421 | C2×D3 | 1 | 1 | yes | characteristic |
| 233 | #421 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 234 | C2×#104 | — | 3 | 1 | no | — |
| 235 | C2×#104 | — | 3 | 1 | no | — |
| 236 | C2×#104 | — | 3 | 1 | no | — |
| 237 | C2×#104 | — | 3 | 1 | no | — |
| 238 | C2×#104 | — | 6 | 2 | no | — |
| 239 | #413 | — | 3 | 1 | no | — |
| 240 | #410 | — | 3 | 1 | no | — |
| 241 | #410 | — | 3 | 1 | no | — |
| 242 | #410 | — | 3 | 1 | no | — |
| 243 | #407 | — | 3 | 1 | no | — |
| 244 | #407 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 245 | #344 | — | 3 | 1 | no | — |
| 246 | #344 | — | 3 | 1 | no | — |
| 247 | #339 | — | 3 | 1 | no | — |
| 248 | #339 | — | 3 | 1 | no | — |
| 249 | #339 | — | 3 | 1 | no | — |
| 250 | #339 | — | 3 | 1 | no | — |
| 251 | H(3,ℤ/4) | — | 3 | 1 | no | — |
| 252 | H(3,ℤ/4) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 253 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C3×#41 | — | 2 | 1 | no | — |
| 255 | C3×#41 | — | 2 | 1 | no | — |
| 256 | C3×#41 | — | 2 | 1 | no | — |
| 257 | C3×#41 | — | 2 | 1 | no | — |
| 258 | C3×#41 | — | 2 | 1 | no | — |
| 259 | C3×#41 | — | 2 | 1 | no | — |
| 260 | C3×#41 | — | 2 | 1 | no | — |
| 261 | C3×#41 | — | 2 | 1 | no | — |
| 262 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×C3×Q8 | #41 | 1 | 1 | yes | characteristic |
| 264 | C2×C3×D4 | — | 2 | 1 | no | — |
| 265 | C2×C3×D4 | — | 2 | 1 | no | — |
| 266 | C2×C3×D4 | — | 2 | 2 | no | — |
| 267 | C2×C3×D4 | — | 4 | 1 | no | — |
| 268 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×C3×D4 | #41 | 1 | 1 | yes | characteristic |
| 270 | C22×C3×C4 | — | 2 | 1 | no | — |
| 271 | C22×C3×C4 | — | 2 | 1 | no | — |
| 272 | C22×C3×C4 | — | 2 | 1 | no | — |
| 273 | C22×C3×C4 | — | 2 | 1 | no | — |
| 274 | C22×C3×C4 | — | 2 | 1 | no | — |
| 275 | C22×C3×C4 | — | 2 | 1 | no | — |
| 276 | C22×C3×C4 | — | 2 | 1 | no | — |
| 277 | C22×C3×C4 | — | 2 | 1 | no | — |
| 278 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 280 | C2×#67 | — | 2 | 1 | no | — |
| 281 | C2×#67 | — | 2 | 2 | no | — |
| 282 | C2×#67 | — | 2 | 2 | no | — |
| 283 | C2×#67 | — | 4 | 2 | no | — |
| 284 | C2×#67 | — | 4 | 1 | no | — |
| 285 | C2×#67 | C2×D4 | 1 | 2 | yes | — |
| 286 | C22×Dic3 | — | 2 | 2 | no | — |
| 287 | C22×Dic3 | — | 2 | 1 | no | — |
| 288 | C22×Dic3 | — | 2 | 1 | no | — |
| 289 | #239 | — | 2 | 2 | no | — |
| 290 | #239 | — | 4 | 1 | no | — |
| 291 | D3×Q8 | — | 2 | 2 | no | — |
| 292 | D3×Q8 | — | 4 | 1 | no | — |
| 293 | #237 | — | 2 | 2 | no | — |
| 294 | #237 | — | 4 | 1 | no | — |
| 295 | #237 | — | 4 | 2 | no | — |
| 296 | #237 | — | 4 | 2 | no | — |
| 297 | D3×D4 | — | 2 | 2 | no | — |
| 298 | D3×D4 | — | 4 | 1 | no | — |
| 299 | D3×D4 | — | 4 | 2 | no | — |
| 300 | D3×D4 | — | 4 | 2 | no | — |
| 301 | #235 | — | 2 | 1 | no | — |
| 302 | #235 | — | 2 | 1 | no | — |
| 303 | #235 | — | 2 | 1 | no | — |
| 304 | #235 | — | 2 | 1 | no | — |
| 305 | #235 | — | 2 | 1 | no | — |
| 306 | #235 | — | 2 | 1 | no | — |
| 307 | #235 | — | 2 | 1 | no | — |
| 308 | #235 | — | 2 | 1 | no | — |
| 309 | #235 | — | 4 | 1 | no | — |
| 310 | #235 | — | 4 | 1 | no | — |
| 311 | #235 | — | 4 | 2 | no | — |
| 312 | #235 | — | 4 | 2 | no | — |
| 313 | C2×D12 | — | 4 | 1 | no | — |
| 314 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 315 | C2×D12 | #41 | 1 | 1 | yes | characteristic |
| 316 | C2×C4×D3 | — | 2 | 1 | no | — |
| 317 | C2×C4×D3 | — | 2 | 2 | no | — |
| 318 | C2×C4×D3 | — | 4 | 2 | no | — |
| 319 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 320 | C2×Dic6 | — | 2 | 2 | no | — |
| 321 | C2×Dic6 | — | 4 | 1 | no | — |
| 322 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | C2×Dic6 | #41 | 1 | 1 | yes | characteristic |
| 324 | C3×Q16 | — | 4 | 1 | no | — |
| 325 | C3×SD16 | — | 4 | 1 | no | — |
| 326 | C3×SD16 | — | 4 | 1 | no | — |
| 327 | C3×D8 | — | 4 | 1 | no | — |
| 328 | C3×M16 | — | 2 | 1 | no | — |
| 329 | C3×M16 | — | 2 | 1 | no | — |
| 330 | C3×M16 | — | 2 | 1 | no | — |
| 331 | C3×M16 | — | 2 | 1 | no | — |
| 332 | C2×C3×C8 | — | 2 | 1 | no | — |
| 333 | C2×C3×C8 | — | 2 | 1 | no | — |
| 334 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 335 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 336 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 337 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 338 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 339 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 340 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 341 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 342 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 343 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 344 | C3×C42 | — | 2 | 1 | no | — |
| 345 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 346 | #217 | — | 2 | 1 | no | — |
| 347 | #217 | — | 2 | 1 | no | — |
| 348 | #217 | — | 2 | 2 | no | — |
| 349 | #217 | — | 2 | 1 | no | — |
| 350 | #217 | — | 2 | 1 | no | — |
| 351 | #217 | — | 2 | 2 | no | — |
| 352 | #217 | — | 2 | 2 | no | — |
| 353 | #217 | — | 2 | 1 | no | — |
| 354 | #217 | — | 4 | 1 | no | — |
| 355 | #217 | C2×D4 | 1 | 2 | yes | — |
| 356 | #216 | — | 4 | 1 | no | — |
| 357 | #215 | — | 4 | 1 | no | — |
| 358 | #214 | — | 4 | 1 | no | — |
| 359 | #213 | — | 4 | 1 | no | — |
| 360 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 361 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 362 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 363 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 364 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 365 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 366 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 367 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 368 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 369 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 370 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 371 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 372 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 373 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 374 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 375 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 376 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 377 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 378 | C4×Dic3 | — | 2 | 2 | no | — |
| 379 | C4×Dic3 | — | 2 | 1 | no | — |
| 380 | C4×Dic3 | — | 2 | 1 | no | — |
| 381 | C4×Dic3 | — | 2 | 1 | no | — |
| 382 | C4×Dic3 | — | 2 | 2 | no | — |
| 383 | C4×Dic3 | — | 2 | 1 | no | — |
| 384 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 385 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 386 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 387 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 388 | #208 | — | 2 | 1 | no | — |
| 389 | #208 | — | 2 | 1 | no | — |
| 390 | #208 | — | 2 | 1 | no | — |
| 391 | #208 | — | 2 | 1 | no | — |
| 392 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 393 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 394 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 395 | D3×C8 | — | 4 | 2 | no | — |
| 396 | 2−1+4 | — | 6 | 1 | no | — |
| 397 | 2−1+4 | — | 6 | 1 | no | — |
| 398 | 2−1+4 | — | 6 | 1 | no | — |
| 399 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 400 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 401 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 402 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 403 | C2×#41 | — | 3 | 1 | no | — |
| 404 | C2×#41 | — | 3 | 1 | no | — |
| 405 | C2×#41 | — | 6 | 2 | no | — |
| 406 | C2×#41 | — | 12 | 1 | no | — |
| 407 | C2×#41 | — | 12 | 1 | no | — |
| 408 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 409 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 410 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 411 | #137 | — | 2 | 1 | no | — |
| 412 | #137 | — | 2 | 1 | no | — |
| 413 | #137 | — | 6 | 1 | no | — |
| 414 | #137 | — | 6 | 1 | no | — |
| 415 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 416 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 417 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 418 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 419 | #135 | — | 4 | 1 | no | — |
| 420 | #135 | — | 12 | 1 | no | — |
| 421 | #131 | — | 12 | 1 | no | — |
| 422 | #131 | — | 12 | 1 | no | — |
| 423 | C2×M16 | — | 3 | 1 | no | — |
| 424 | C2×M16 | — | 3 | 1 | no | — |
| 425 | C2×M16 | — | 6 | 2 | no | — |
| 426 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 427 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 428 | C4⋊Q8 | — | 3 | 1 | no | — |
| 429 | C4⋊Q8 | — | 6 | 1 | no | — |
| 430 | #127 | — | 3 | 1 | no | — |
| 431 | #126 | — | 6 | 2 | no | — |
| 432 | #126 | — | 6 | 2 | no | — |
| 433 | #126 | — | 6 | 2 | no | — |
| 434 | #126 | — | 6 | 2 | no | — |
| 435 | #125 | — | 6 | 1 | no | — |
| 436 | #125 | — | 6 | 2 | no | — |
| 437 | #125 | — | 6 | 2 | no | — |
| 438 | #124 | — | 3 | 1 | no | — |
| 439 | #124 | — | 3 | 1 | no | — |
| 440 | #124 | — | 6 | 2 | no | — |
| 441 | #124 | — | 6 | 2 | no | — |
| 442 | #123 | — | 2 | 1 | no | — |
| 443 | #123 | — | 2 | 1 | no | — |
| 444 | #123 | — | 3 | 2 | no | — |
| 445 | #123 | — | 6 | 2 | no | — |
| 446 | #123 | — | 6 | 2 | no | — |
| 447 | #123 | — | 6 | 2 | no | — |
| 448 | #123 | — | 6 | 2 | no | — |
| 449 | #123 | — | 6 | 1 | no | — |
| 450 | C22⋊Q8 | — | 2 | 1 | no | — |
| 451 | C22⋊Q8 | — | 2 | 1 | no | — |
| 452 | C22⋊Q8 | — | 6 | 2 | no | — |
| 453 | C22⋊Q8 | — | 6 | 2 | no | — |
| 454 | C22⋊Q8 | — | 6 | 2 | no | — |
| 455 | C22⋊Q8 | — | 6 | 1 | no | — |
| 456 | C22⋊Q8 | — | 6 | 1 | no | — |
| 457 | #121 | — | 2 | 1 | no | — |
| 458 | #121 | — | 2 | 1 | no | — |
| 459 | #121 | — | 6 | 1 | no | — |
| 460 | #121 | — | 6 | 2 | no | — |
| 461 | #121 | — | 6 | 2 | no | — |
| 462 | #121 | — | 6 | 2 | no | — |
| 463 | #121 | — | 6 | 1 | no | — |
| 464 | #120 | — | 2 | 1 | no | — |
| 465 | #120 | — | 2 | 1 | no | — |
| 466 | #120 | — | 3 | 2 | no | — |
| 467 | #120 | — | 6 | 1 | no | — |
| 468 | C4×Q8 | — | 6 | 1 | no | — |
| 469 | C4×Q8 | — | 6 | 1 | no | — |
| 470 | C4×Q8 | — | 6 | 2 | no | — |
| 471 | C4×D4 | — | 2 | 2 | no | — |
| 472 | C4×D4 | — | 4 | 1 | no | — |
| 473 | C4×D4 | — | 6 | 2 | no | — |
| 474 | C4×D4 | — | 6 | 2 | no | — |
| 475 | C4×D4 | — | 6 | 1 | no | — |
| 476 | C4×D4 | — | 6 | 2 | no | — |
| 477 | C4×D4 | — | 6 | 2 | no | — |
| 478 | C4×D4 | — | 6 | 1 | no | — |
| 479 | C4×D4 | — | 12 | 1 | no | — |
| 480 | #117 | — | 3 | 2 | no | — |
| 481 | #117 | — | 3 | 1 | no | — |
| 482 | #117 | — | 3 | 1 | no | — |
| 483 | #117 | — | 6 | 1 | no | — |
| 484 | #117 | — | 6 | 1 | no | — |
| 485 | #117 | — | 6 | 1 | no | — |
| 486 | #117 | — | 6 | 1 | no | — |
| 487 | #117 | — | 6 | 1 | no | — |
| 488 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 489 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 490 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 491 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 492 | C2×C42 | — | 3 | 1 | no | — |
| 493 | C2×C42 | — | 3 | 1 | no | — |
| 494 | C2×C42 | — | 3 | 2 | no | — |
| 495 | C2×C42 | — | 6 | 1 | no | — |
| 496 | #104 | — | 2 | 2 | no | — |
| 497 | #104 | — | 4 | 1 | no | — |
| 498 | #104 | — | 6 | 1 | no | — |
| 499 | #104 | — | 6 | 1 | no | — |
| 500 | #104 | — | 6 | 1 | no | — |
| 501 | #104 | — | 6 | 1 | no | — |
| 502 | #104 | — | 6 | 1 | no | — |
| 503 | #104 | — | 6 | 1 | no | — |
| 504 | #104 | — | 6 | 1 | no | — |
| 505 | #104 | — | 6 | 1 | no | — |
| 506 | #104 | — | 6 | 2 | no | — |
| 507 | #104 | — | 12 | 1 | no | — |
| 508 | #101 | — | 6 | 1 | no | — |
| 509 | #100 | — | 6 | 1 | no | — |
| 510 | #99 | — | 6 | 2 | no | — |
| 511 | #99 | — | 6 | 2 | no | — |
| 512 | #99 | — | 6 | 2 | no | — |
| 513 | C22⋊C8 | — | 4 | 1 | no | — |
| 514 | C22⋊C8 | — | 12 | 1 | no | — |
| 515 | C23×C3 | — | 2 | 1 | no | — |
| 516 | C23×C3 | — | 2 | 1 | no | — |
| 517 | C23×C3 | — | 2 | 1 | no | — |
| 518 | C23×C3 | — | 2 | 1 | no | — |
| 519 | C23×C3 | — | 2 | 1 | no | — |
| 520 | C23×C3 | — | 8 | 1 | no | — |
| 521 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 522 | C22×D3 | — | 2 | 1 | no | — |
| 523 | C22×D3 | — | 4 | 2 | no | — |
| 524 | C22×D3 | #120 | 1 | 2 | yes | — |
| 525 | C3×Q8 | — | 2 | 1 | no | — |
| 526 | C3×Q8 | — | 2 | 1 | no | — |
| 527 | C3×Q8 | — | 2 | 1 | no | — |
| 528 | C3×Q8 | — | 2 | 1 | no | — |
| 529 | C3×D4 | — | 2 | 1 | no | — |
| 530 | C3×D4 | — | 2 | 1 | no | — |
| 531 | C3×D4 | — | 2 | 1 | no | — |
| 532 | C3×D4 | — | 2 | 1 | no | — |
| 533 | C3×D4 | — | 4 | 1 | no | — |
| 534 | C3×D4 | — | 4 | 1 | no | — |
| 535 | C3×D4 | — | 4 | 1 | no | — |
| 536 | C3×D4 | — | 4 | 1 | no | — |
| 537 | C3×D4 | — | 8 | 2 | no | — |
| 538 | C3×D4 | — | 8 | 2 | no | — |
| 539 | C2×C3×C4 | — | 2 | 1 | no | — |
| 540 | C2×C3×C4 | — | 2 | 2 | no | — |
| 541 | C2×C3×C4 | — | 2 | 1 | no | — |
| 542 | C2×C3×C4 | — | 2 | 1 | no | — |
| 543 | C2×C3×C4 | — | 2 | 1 | no | — |
| 544 | C2×C3×C4 | — | 2 | 1 | no | — |
| 545 | C2×C3×C4 | — | 4 | 1 | no | — |
| 546 | C2×C3×C4 | — | 4 | 1 | no | — |
| 547 | C2×C3×C4 | — | 4 | 1 | no | — |
| 548 | C2×C3×C4 | — | 4 | 1 | no | — |
| 549 | C2×C3×C4 | — | 4 | 1 | no | — |
| 550 | C2×C3×C4 | — | 4 | 1 | no | — |
| 551 | C2×C3×C4 | — | 4 | 1 | no | — |
| 552 | C2×C3×C4 | — | 4 | 1 | no | — |
| 553 | C2×C3×C4 | — | 4 | 1 | no | — |
| 554 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 555 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 556 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 557 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 558 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 559 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 560 | #67 | — | 2 | 2 | no | — |
| 561 | #67 | — | 2 | 2 | no | — |
| 562 | #67 | — | 4 | 2 | no | — |
| 563 | #67 | — | 4 | 2 | no | — |
| 564 | #67 | — | 4 | 1 | no | — |
| 565 | #67 | — | 4 | 1 | no | — |
| 566 | #67 | — | 8 | 2 | no | — |
| 567 | #67 | — | 8 | 2 | no | — |
| 568 | #67 | — | 8 | 2 | no | — |
| 569 | C2×Dic3 | — | 2 | 1 | no | — |
| 570 | C2×Dic3 | — | 2 | 1 | no | — |
| 571 | C2×Dic3 | — | 2 | 2 | no | — |
| 572 | C2×Dic3 | — | 2 | 1 | no | — |
| 573 | C2×Dic3 | — | 2 | 1 | no | — |
| 574 | C2×Dic3 | — | 2 | 1 | no | — |
| 575 | C2×Dic3 | — | 4 | 2 | no | — |
| 576 | C2×Dic3 | — | 4 | 1 | no | — |
| 577 | C2×Dic3 | — | 8 | 1 | no | — |
| 578 | C2×Dic3 | — | 8 | 2 | no | — |
| 579 | C2×Dic3 | — | 8 | 1 | no | — |
| 580 | C2×Dic3 | #120 | 1 | 2 | yes | — |
| 581 | D12 | — | 2 | 1 | no | — |
| 582 | D12 | — | 2 | 1 | no | — |
| 583 | D12 | — | 2 | 1 | no | — |
| 584 | D12 | — | 2 | 1 | no | — |
| 585 | D12 | — | 4 | 2 | no | — |
| 586 | C4×D3 | — | 2 | 2 | no | — |
| 587 | C4×D3 | — | 2 | 2 | no | — |
| 588 | C4×D3 | — | 4 | 2 | no | — |
| 589 | C4×D3 | — | 4 | 2 | no | — |
| 590 | C4×D3 | — | 4 | 1 | no | — |
| 591 | C4×D3 | — | 4 | 1 | no | — |
| 592 | C4×D3 | — | 8 | 2 | no | — |
| 593 | Dic6 | — | 2 | 1 | no | — |
| 594 | Dic6 | — | 2 | 1 | no | — |
| 595 | Dic6 | — | 2 | 1 | no | — |
| 596 | Dic6 | — | 2 | 1 | no | — |
| 597 | Dic6 | — | 4 | 2 | no | — |
| 598 | Dic6 | — | 8 | 2 | no | — |
| 599 | C3×C8 | — | 4 | 1 | no | — |
| 600 | C3×C8 | — | 4 | 1 | no | — |
| 601 | C3⋊C8 | — | 4 | 1 | no | — |
| 602 | C3⋊C8 | — | 4 | 1 | no | — |
| 603 | C24 | D3×D4 | 1 | 1 | yes | characteristic |
| 604 | #41 | — | 2 | 1 | no | — |
| 605 | #41 | — | 2 | 1 | no | — |
| 606 | #41 | — | 2 | 1 | no | — |
| 607 | #41 | — | 2 | 1 | no | — |
| 608 | #41 | — | 2 | 1 | no | — |
| 609 | #41 | — | 2 | 1 | no | — |
| 610 | #41 | — | 2 | 1 | no | — |
| 611 | #41 | — | 2 | 1 | no | — |
| 612 | #41 | — | 6 | 1 | no | — |
| 613 | #41 | — | 6 | 1 | no | — |
| 614 | #41 | — | 6 | 1 | no | — |
| 615 | #41 | — | 6 | 1 | no | — |
| 616 | #41 | — | 6 | 2 | no | — |
| 617 | #41 | — | 6 | 2 | no | — |
| 618 | #41 | — | 6 | 1 | no | — |
| 619 | #41 | — | 6 | 1 | no | — |
| 620 | #41 | — | 6 | 1 | no | — |
| 621 | #41 | — | 6 | 1 | no | — |
| 622 | #41 | — | 12 | 2 | no | — |
| 623 | #41 | — | 12 | 2 | no | — |
| 624 | #41 | — | 12 | 2 | no | — |
| 625 | #41 | — | 12 | 1 | no | — |
| 626 | #41 | — | 12 | 1 | no | — |
| 627 | #41 | — | 12 | 2 | no | — |
| 628 | #41 | — | 12 | 1 | no | — |
| 629 | #41 | — | 12 | 1 | no | — |
| 630 | C2×Q8 | — | 3 | 1 | no | — |
| 631 | C2×Q8 | — | 3 | 1 | no | — |
| 632 | C2×Q8 | — | 6 | 2 | no | — |
| 633 | C2×Q8 | — | 6 | 2 | no | — |
| 634 | C2×Q8 | — | 12 | 1 | no | — |
| 635 | C2×Q8 | — | 12 | 1 | no | — |
| 636 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 637 | C2×Q8 | #237 | 1 | 1 | yes | characteristic |
| 638 | C2×D4 | — | 2 | 1 | no | — |
| 639 | C2×D4 | — | 2 | 1 | no | — |
| 640 | C2×D4 | — | 2 | 2 | no | — |
| 641 | C2×D4 | — | 3 | 2 | no | — |
| 642 | C2×D4 | — | 3 | 1 | no | — |
| 643 | C2×D4 | — | 3 | 1 | no | — |
| 644 | C2×D4 | — | 4 | 1 | no | — |
| 645 | C2×D4 | — | 6 | 2 | no | — |
| 646 | C2×D4 | — | 6 | 1 | no | — |
| 647 | C2×D4 | — | 6 | 2 | no | — |
| 648 | C2×D4 | — | 6 | 2 | no | — |
| 649 | C2×D4 | — | 12 | 1 | no | — |
| 650 | C2×D4 | — | 12 | 1 | no | — |
| 651 | C2×D4 | — | 12 | 2 | no | — |
| 652 | C2×D4 | — | 12 | 2 | no | — |
| 653 | C2×D4 | — | 12 | 2 | no | — |
| 654 | C2×D4 | — | 12 | 1 | no | — |
| 655 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 656 | C2×D4 | #237 | 1 | 1 | yes | characteristic |
| 657 | C22×C4 | — | 2 | 1 | no | — |
| 658 | C22×C4 | — | 2 | 1 | no | — |
| 659 | C22×C4 | — | 2 | 1 | no | — |
| 660 | C22×C4 | — | 2 | 1 | no | — |
| 661 | C22×C4 | — | 2 | 1 | no | — |
| 662 | C22×C4 | — | 2 | 1 | no | — |
| 663 | C22×C4 | — | 2 | 1 | no | — |
| 664 | C22×C4 | — | 2 | 1 | no | — |
| 665 | C22×C4 | — | 3 | 2 | no | — |
| 666 | C22×C4 | — | 6 | 2 | no | — |
| 667 | C22×C4 | — | 6 | 2 | no | — |
| 668 | C22×C4 | — | 6 | 1 | no | — |
| 669 | C22×C4 | — | 6 | 1 | no | — |
| 670 | C22×C4 | — | 6 | 1 | no | — |
| 671 | C22×C4 | — | 12 | 2 | no | — |
| 672 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 673 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 674 | Q16 | — | 4 | 1 | no | — |
| 675 | Q16 | — | 12 | 1 | no | — |
| 676 | SD16 | — | 4 | 1 | no | — |
| 677 | SD16 | — | 4 | 1 | no | — |
| 678 | SD16 | — | 12 | 1 | no | — |
| 679 | SD16 | — | 12 | 1 | no | — |
| 680 | D8 | — | 4 | 1 | no | — |
| 681 | D8 | — | 12 | 1 | no | — |
| 682 | M16 | — | 2 | 1 | no | — |
| 683 | M16 | — | 2 | 1 | no | — |
| 684 | M16 | — | 2 | 1 | no | — |
| 685 | M16 | — | 2 | 1 | no | — |
| 686 | M16 | — | 6 | 1 | no | — |
| 687 | M16 | — | 6 | 1 | no | — |
| 688 | M16 | — | 6 | 1 | no | — |
| 689 | M16 | — | 6 | 1 | no | — |
| 690 | M16 | — | 12 | 2 | no | — |
| 691 | C2×C8 | — | 2 | 1 | no | — |
| 692 | C2×C8 | — | 2 | 1 | no | — |
| 693 | C2×C8 | — | 6 | 1 | no | — |
| 694 | C2×C8 | — | 6 | 1 | no | — |
| 695 | C2×C8 | — | 12 | 2 | no | — |
| 696 | C4⋊C4 | — | 2 | 2 | no | — |
| 697 | C4⋊C4 | — | 2 | 1 | no | — |
| 698 | C4⋊C4 | — | 2 | 1 | no | — |
| 699 | C4⋊C4 | — | 4 | 1 | no | — |
| 700 | C4⋊C4 | — | 6 | 2 | no | — |
| 701 | C4⋊C4 | — | 6 | 2 | no | — |
| 702 | C4⋊C4 | — | 6 | 2 | no | — |
| 703 | C4⋊C4 | — | 6 | 1 | no | — |
| 704 | C4⋊C4 | — | 6 | 1 | no | — |
| 705 | C4⋊C4 | — | 6 | 1 | no | — |
| 706 | C4⋊C4 | — | 6 | 1 | no | — |
| 707 | C4⋊C4 | — | 6 | 2 | no | — |
| 708 | C4⋊C4 | — | 6 | 2 | no | — |
| 709 | C4⋊C4 | — | 6 | 2 | no | — |
| 710 | C4⋊C4 | — | 6 | 2 | no | — |
| 711 | C4⋊C4 | — | 6 | 1 | no | — |
| 712 | C4⋊C4 | — | 6 | 1 | no | — |
| 713 | C4⋊C4 | — | 12 | 1 | no | — |
| 714 | C22⋊C4 | — | 2 | 2 | no | — |
| 715 | C22⋊C4 | — | 2 | 2 | no | — |
| 716 | C22⋊C4 | — | 2 | 1 | no | — |
| 717 | C22⋊C4 | — | 2 | 1 | no | — |
| 718 | C22⋊C4 | — | 3 | 2 | no | — |
| 719 | C22⋊C4 | — | 4 | 1 | no | — |
| 720 | C22⋊C4 | — | 4 | 1 | no | — |
| 721 | C22⋊C4 | — | 6 | 2 | no | — |
| 722 | C22⋊C4 | — | 6 | 2 | no | — |
| 723 | C22⋊C4 | — | 6 | 2 | no | — |
| 724 | C22⋊C4 | — | 6 | 2 | no | — |
| 725 | C22⋊C4 | — | 6 | 2 | no | — |
| 726 | C22⋊C4 | — | 6 | 1 | no | — |
| 727 | C22⋊C4 | — | 6 | 1 | no | — |
| 728 | C22⋊C4 | — | 6 | 1 | no | — |
| 729 | C22⋊C4 | — | 6 | 1 | no | — |
| 730 | C22⋊C4 | — | 6 | 2 | no | — |
| 731 | C22⋊C4 | — | 6 | 1 | no | — |
| 732 | C22⋊C4 | — | 12 | 1 | no | — |
| 733 | C22⋊C4 | — | 12 | 1 | no | — |
| 734 | C42 | — | 2 | 1 | no | — |
| 735 | C42 | — | 3 | 1 | no | — |
| 736 | C42 | — | 3 | 1 | no | — |
| 737 | C42 | — | 3 | 1 | no | — |
| 738 | C42 | — | 3 | 1 | no | — |
| 739 | C42 | — | 6 | 2 | no | — |
| 740 | C42 | — | 6 | 2 | no | — |
| 741 | C42 | — | 6 | 1 | no | — |
| 742 | C42 | — | 6 | 1 | no | — |
| 743 | C42 | — | 6 | 1 | no | — |
| 744 | C42 | — | 6 | 1 | no | — |
| 745 | C42 | D3×D4 | 1 | 2 | yes | — |
| 746 | C22×C3 | — | 4 | 1 | no | — |
| 747 | C22×C3 | — | 4 | 2 | no | — |
| 748 | C22×C3 | — | 4 | 1 | no | — |
| 749 | C22×C3 | — | 4 | 1 | no | — |
| 750 | C22×C3 | — | 4 | 1 | no | — |
| 751 | C22×C3 | — | 4 | 1 | no | — |
| 752 | C22×C3 | — | 4 | 1 | no | — |
| 753 | C22×C3 | — | 4 | 1 | no | — |
| 754 | C22×C3 | — | 4 | 1 | no | — |
| 755 | C22×C3 | — | 4 | 1 | no | — |
| 756 | C22×C3 | — | 4 | 1 | no | — |
| 757 | C22×C3 | — | 8 | 1 | no | — |
| 758 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 759 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 760 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 761 | C2×D3 | — | 2 | 2 | no | — |
| 762 | C2×D3 | — | 4 | 2 | no | — |
| 763 | C2×D3 | — | 4 | 1 | no | — |
| 764 | C2×D3 | — | 8 | 1 | no | — |
| 765 | C2×D3 | — | 16 | 2 | no | — |
| 766 | C3×C4 | — | 4 | 2 | no | — |
| 767 | C3×C4 | — | 4 | 1 | no | — |
| 768 | C3×C4 | — | 4 | 1 | no | — |
| 769 | C3×C4 | — | 4 | 1 | no | — |
| 770 | C3×C4 | — | 8 | 1 | no | — |
| 771 | C3×C4 | #525 | 1 | 1 | yes | characteristic |
| 772 | C3×C4 | #535 | 1 | 1 | yes | characteristic |
| 773 | C3×C4 | #546 | 1 | 1 | yes | characteristic |
| 774 | C3×C4 | #546 | 1 | 1 | yes | characteristic |
| 775 | Dic3 | — | 2 | 2 | no | — |
| 776 | Dic3 | — | 4 | 1 | no | — |
| 777 | Dic3 | — | 4 | 2 | no | — |
| 778 | Dic3 | — | 4 | 1 | no | — |
| 779 | Dic3 | — | 4 | 1 | no | — |
| 780 | Dic3 | — | 4 | 1 | no | — |
| 781 | Dic3 | — | 4 | 1 | no | — |
| 782 | Dic3 | — | 8 | 1 | no | — |
| 783 | C23 | — | 2 | 1 | no | — |
| 784 | C23 | — | 2 | 1 | no | — |
| 785 | C23 | — | 2 | 1 | no | — |
| 786 | C23 | — | 2 | 1 | no | — |
| 787 | C23 | — | 2 | 1 | no | — |
| 788 | C23 | — | 3 | 2 | no | — |
| 789 | C23 | — | 6 | 1 | no | — |
| 790 | C23 | — | 8 | 1 | no | — |
| 791 | C23 | — | 12 | 2 | no | — |
| 792 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 793 | Q8 | — | 2 | 1 | no | — |
| 794 | Q8 | — | 2 | 1 | no | — |
| 795 | Q8 | — | 2 | 1 | no | — |
| 796 | Q8 | — | 2 | 1 | no | — |
| 797 | Q8 | — | 6 | 1 | no | — |
| 798 | Q8 | — | 6 | 1 | no | — |
| 799 | Q8 | — | 6 | 1 | no | — |
| 800 | Q8 | — | 6 | 1 | no | — |
| 801 | Q8 | — | 12 | 2 | no | — |
| 802 | Q8 | — | 24 | 2 | no | — |
| 803 | D4 | — | 2 | 1 | no | — |
| 804 | D4 | — | 2 | 1 | no | — |
| 805 | D4 | — | 2 | 1 | no | — |
| 806 | D4 | — | 2 | 1 | no | — |
| 807 | D4 | — | 4 | 1 | no | — |
| 808 | D4 | — | 4 | 1 | no | — |
| 809 | D4 | — | 4 | 1 | no | — |
| 810 | D4 | — | 4 | 1 | no | — |
| 811 | D4 | — | 6 | 2 | no | — |
| 812 | D4 | — | 6 | 2 | no | — |
| 813 | D4 | — | 6 | 1 | no | — |
| 814 | D4 | — | 6 | 1 | no | — |
| 815 | D4 | — | 6 | 1 | no | — |
| 816 | D4 | — | 6 | 1 | no | — |
| 817 | D4 | — | 8 | 2 | no | — |
| 818 | D4 | — | 8 | 2 | no | — |
| 819 | D4 | — | 12 | 2 | no | — |
| 820 | D4 | — | 12 | 2 | no | — |
| 821 | D4 | — | 12 | 2 | no | — |
| 822 | D4 | — | 12 | 1 | no | — |
| 823 | D4 | — | 12 | 1 | no | — |
| 824 | D4 | — | 24 | 2 | no | — |
| 825 | D4 | — | 24 | 2 | no | — |
| 826 | D4 | — | 24 | 2 | no | — |
| 827 | C2×C4 | — | 2 | 1 | no | — |
| 828 | C2×C4 | — | 2 | 2 | no | — |
| 829 | C2×C4 | — | 2 | 1 | no | — |
| 830 | C2×C4 | — | 2 | 1 | no | — |
| 831 | C2×C4 | — | 2 | 1 | no | — |
| 832 | C2×C4 | — | 2 | 1 | no | — |
| 833 | C2×C4 | — | 3 | 2 | no | — |
| 834 | C2×C4 | — | 4 | 1 | no | — |
| 835 | C2×C4 | — | 4 | 1 | no | — |
| 836 | C2×C4 | — | 4 | 1 | no | — |
| 837 | C2×C4 | — | 4 | 1 | no | — |
| 838 | C2×C4 | — | 4 | 1 | no | — |
| 839 | C2×C4 | — | 4 | 1 | no | — |
| 840 | C2×C4 | — | 4 | 1 | no | — |
| 841 | C2×C4 | — | 4 | 1 | no | — |
| 842 | C2×C4 | — | 4 | 1 | no | — |
| 843 | C2×C4 | — | 6 | 2 | no | — |
| 844 | C2×C4 | — | 6 | 2 | no | — |
| 845 | C2×C4 | — | 6 | 1 | no | — |
| 846 | C2×C4 | — | 6 | 1 | no | — |
| 847 | C2×C4 | — | 6 | 1 | no | — |
| 848 | C2×C4 | — | 6 | 1 | no | — |
| 849 | C2×C4 | — | 6 | 2 | no | — |
| 850 | C2×C4 | — | 6 | 1 | no | — |
| 851 | C2×C4 | — | 12 | 2 | no | — |
| 852 | C2×C4 | — | 12 | 2 | no | — |
| 853 | C2×C4 | — | 12 | 2 | no | — |
| 854 | C2×C4 | — | 12 | 1 | no | — |
| 855 | C2×C4 | — | 12 | 1 | no | — |
| 856 | C2×C4 | — | 12 | 1 | no | — |
| 857 | C2×C4 | — | 24 | 2 | no | — |
| 858 | C2×C4 | — | 24 | 1 | no | — |
| 859 | C2×C4 | — | 24 | 2 | no | — |
| 860 | C2×C4 | — | 24 | 1 | no | — |
| 861 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 862 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 863 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 864 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 865 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 866 | C2×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 867 | C8 | — | 4 | 1 | no | — |
| 868 | C8 | — | 4 | 1 | no | — |
| 869 | C8 | — | 12 | 1 | no | — |
| 870 | C8 | — | 12 | 1 | no | — |
| 871 | C2×C3 | — | 2 | 1 | no | — |
| 872 | C2×C3 | — | 2 | 1 | no | — |
| 873 | C2×C3 | — | 2 | 1 | no | — |
| 874 | C2×C3 | — | 8 | 1 | no | — |
| 875 | C2×C3 | — | 8 | 1 | no | — |
| 876 | C2×C3 | — | 8 | 1 | no | — |
| 877 | C2×C3 | #2404 | 1 | 1 | yes | characteristic |
| 878 | D3 | — | 4 | 2 | no | — |
| 879 | D3 | — | 8 | 1 | no | — |
| 880 | C22 | — | 4 | 1 | no | — |
| 881 | C22 | — | 4 | 2 | no | — |
| 882 | C22 | — | 4 | 1 | no | — |
| 883 | C22 | — | 4 | 1 | no | — |
| 884 | C22 | — | 4 | 1 | no | — |
| 885 | C22 | — | 4 | 1 | no | — |
| 886 | C22 | — | 4 | 1 | no | — |
| 887 | C22 | — | 4 | 1 | no | — |
| 888 | C22 | — | 4 | 1 | no | — |
| 889 | C22 | — | 4 | 1 | no | — |
| 890 | C22 | — | 4 | 1 | no | — |
| 891 | C22 | — | 6 | 2 | no | — |
| 892 | C22 | — | 8 | 1 | no | — |
| 893 | C22 | — | 12 | 2 | no | — |
| 894 | C22 | — | 12 | 1 | no | — |
| 895 | C22 | — | 24 | 1 | no | — |
| 896 | C22 | — | 48 | 2 | no | — |
| 897 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 898 | C22 | #5591 | 1 | 1 | yes | characteristic |
| 899 | C22 | #5610 | 1 | 1 | yes | characteristic |
| 900 | C4 | — | 4 | 2 | no | — |
| 901 | C4 | — | 4 | 1 | no | — |
| 902 | C4 | — | 4 | 1 | no | — |
| 903 | C4 | — | 4 | 1 | no | — |
| 904 | C4 | — | 6 | 2 | no | — |
| 905 | C4 | — | 8 | 1 | no | — |
| 906 | C4 | — | 12 | 1 | no | — |
| 907 | C4 | — | 12 | 1 | no | — |
| 908 | C4 | — | 12 | 1 | no | — |
| 909 | C4 | — | 12 | 2 | no | — |
| 910 | C4 | — | 12 | 1 | no | — |
| 911 | C4 | — | 12 | 1 | no | — |
| 912 | C4 | — | 24 | 1 | no | — |
| 913 | C4 | #5591 | 1 | 1 | yes | characteristic |
| 914 | C4 | #5606 | 1 | 1 | yes | characteristic |
| 915 | C4 | #5610 | 1 | 1 | yes | characteristic |
| 916 | C4 | #5715 | 1 | 1 | yes | characteristic |
| 917 | C3 | #23995 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 918 | C2 | — | 2 | 1 | no | — |
| 919 | C2 | — | 2 | 1 | no | — |
| 920 | C2 | — | 2 | 1 | no | — |
| 921 | C2 | — | 8 | 1 | no | — |
| 922 | C2 | — | 8 | 1 | no | — |
| 923 | C2 | — | 8 | 1 | no | — |
| 924 | C2 | — | 12 | 2 | no | — |
| 925 | C2 | — | 24 | 1 | no | — |
| 926 | C2 | #76754 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #5715 |
| commutator, cosocle | C22×C3×C4 | C24 |
| Frattini | C22×C4 | C23×D3 |
| Fitting | C3×#2010 | C2 |
| socle | C2×C3 | #2404 |
| hypercenter | #2010 | D3 |
| hypocenter | C3 | #23995 |
| LCS | G ▷ C22×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #2010 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86019 | C2 | semidirect |
| 2. #84004 | C2 | semidirect |
| 3. #82936 | C2 | semidirect |
| 4. #78992 | C2 | semidirect |
| 5. C3×#2010 | C2 | semidirect |
| 6. #72114 | C2 | semidirect |
| 7. #71715 | C2 | semidirect |
| 8. #71712 | C2 | semidirect |
| 9. #70417 | C2 | semidirect |
| 10. #70395 | C2 | semidirect |
| 11. #70394 | C2 | semidirect |
| 12. #69992 | C2 | semidirect |
| 13. #69966 | C2 | semidirect |
| 14. #68714 | C2 | semidirect |
| 15. #68711 | C2 | semidirect |
| 20. C3×#525 | C22 | semidirect |
| 22. Dic3×#41 | C22 | semidirect |
| 26. C2×#926 | C22 | semidirect |
| 37. #5517 | C22 | semidirect |
| 39. C3×#421 | C22 | semidirect |
| 40. C3×#407 | C22 | semidirect |
| 42. #5236 | C22 | semidirect |
| 45. #5207 | C22 | semidirect |
| 60. C3×H(3,ℤ/4) | C22 | semidirect |
| 61. #4559 | C22 | semidirect |
| 62. #4556 | C22 | semidirect |
| 63. #4555 | C22 | semidirect |
| 64. #4555 | C22 | semidirect |
| 65. #4532 | C22 | semidirect |
| 66. #4532 | C22 | semidirect |
| 67. #4531 | C22 | semidirect |
| 75. #2010 | D3 | semidirect |
| 123. #947 | D4 | semidirect |
| 125. #944 | D4 | semidirect |
| 127. #940 | D4 | semidirect |
| 132. #936 | D4 | semidirect |
| 180. #872 | D4 | semidirect |
| 181. C42×D3 | D4 | semidirect |
| 219. #525 | C2×D3 | semidirect |
| 233. #421 | C2×D3 | semidirect |
| 244. #407 | C2×D3 | semidirect |
| 252. H(3,ℤ/4) | C2×D3 | semidirect |
| 917. C3 | #23995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86019 | 2 |
| #84004 | 2 |
| #82936 | 2 |
| #78992 | 2 |
| C3×#2010 | 2 |
| #72114 | 2 |
| #71715 | 2 |
| #71712 | 2 |
| #70417 | 2 |
| #70395 | 2 |
| #70394 | 2 |
| #69992 | 2 |
| #69966 | 2 |
| #68714 | 2 |
| #68711 | 2 |
| #23995 | 3 |