Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
2790 conjugacy classes of subgroups.
The subgroup lattice has 974 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72226914 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | D8×#357 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72226853 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72226833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225597 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×D8×D16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72225386 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#122946 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72225188 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #72225182 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #72216196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×D4×D16 | — | 2 | 1 | no | — |
| 13 | C2×D82 | C22 | 1 | 2 | yes | — |
| 14 | #497870 | — | 2 | 1 | no | — |
| 15 | D4×#357 | — | 2 | 2 | no | — |
| 16 | D8×D16 | — | 2 | 4 | no | — |
| 17 | D8×D16 | C4 | 1 | 8 | yes | complemented |
| 18 | C2×#12515 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#12430 | — | 2 | 1 | no | — |
| 20 | C2×#12424 | C22 | 1 | 2 | yes | — |
| 21 | C2×#12316 | — | 2 | 2 | no | — |
| 22 | C2×C8×D16 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C16×D8 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C16×D8 | C22 | 1 | 2 | yes | complemented |
| 25 | D8×#107 | C22 | 1 | 2 | yes | complemented |
| 26 | #141665 | C22 | 1 | 2 | yes | complemented |
| 27 | #141665 | C22 | 1 | 2 | yes | complemented |
| 28 | #141247 | C22 | 1 | 2 | yes | complemented |
| 29 | #140429 | — | 2 | 1 | no | — |
| 30 | #138642 | — | 2 | 2 | no | — |
| 31 | #136878 | — | 2 | 2 | no | — |
| 32 | #136339 | — | 2 | 2 | no | — |
| 33 | #135778 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #134950 | C22 | 1 | 2 | yes | — |
| 35 | #134950 | C22 | 1 | 2 | yes | complemented |
| 36 | #131848 | — | 2 | 2 | no | — |
| 37 | #129140 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C8×#357 | C22 | 1 | 1 | yes | characteristic |
| 39 | #122946 | — | 2 | 4 | no | — |
| 40 | C2×#7101 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#7096 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×#7068 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#7068 | C22 | 1 | 2 | yes | complemented |
| 44 | C2×#7052 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #93064 | C22 | 1 | 2 | yes | complemented |
| 46 | #92931 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #92911 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C23×D16 | — | 4 | 1 | no | — |
| 49 | C2×D4×D8 | — | 2 | 2 | no | — |
| 50 | C2×D4×D8 | — | 2 | 2 | no | — |
| 51 | D4×D16 | — | 2 | 8 | no | — |
| 52 | D4×D16 | — | 4 | 4 | no | — |
| 53 | C2×#2246 | — | 2 | 1 | no | — |
| 54 | C2×#2246 | — | 2 | 1 | no | — |
| 55 | C2×#2215 | — | 4 | 1 | no | — |
| 56 | C2×#2206 | — | 2 | 2 | no | — |
| 57 | C2×#2184 | — | 4 | 2 | no | — |
| 58 | C2×#2177 | — | 4 | 1 | no | — |
| 59 | C2×C4×D16 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×D4×C16 | — | 2 | 1 | no | — |
| 61 | C2×D4×C16 | — | 2 | 2 | no | — |
| 62 | C22×#357 | — | 4 | 2 | no | — |
| 63 | C4⋊C4×D8 | — | 2 | 2 | no | — |
| 64 | D4×#107 | — | 2 | 2 | no | — |
| 65 | D82 | — | 2 | 4 | no | — |
| 66 | D82 | — | 2 | 4 | no | — |
| 67 | D82 | — | 4 | 2 | no | — |
| 68 | D82 | C2×C4 | 1 | 8 | yes | complemented |
| 69 | C2×#1712 | C23 | 1 | 2 | yes | — |
| 70 | C2×#1667 | — | 2 | 2 | no | — |
| 71 | C2×#1667 | — | 2 | 2 | no | — |
| 72 | C2×#1619 | — | 4 | 2 | no | — |
| 73 | C2×C8×D8 | C23 | 1 | 2 | yes | — |
| 74 | C2×C8×D8 | C23 | 1 | 1 | yes | characteristic |
| 75 | #13252 | — | 2 | 2 | no | — |
| 76 | #13202 | — | 2 | 2 | no | — |
| 77 | #13202 | — | 2 | 2 | no | — |
| 78 | #13202 | — | 4 | 2 | no | — |
| 79 | #13168 | — | 4 | 1 | no | — |
| 80 | #13059 | — | 4 | 2 | no | — |
| 81 | #12991 | — | 4 | 2 | no | — |
| 82 | #12937 | — | 4 | 2 | no | — |
| 83 | #12906 | — | 2 | 1 | no | — |
| 84 | #12906 | — | 2 | 1 | no | — |
| 85 | #12811 | — | 2 | 2 | no | — |
| 86 | #12811 | — | 2 | 2 | no | — |
| 87 | #12731 | — | 4 | 2 | no | — |
| 88 | #12662 | — | 2 | 1 | no | — |
| 89 | C4×#357 | D4 | 1 | 1 | yes | characteristic |
| 90 | #12515 | — | 2 | 2 | no | — |
| 91 | #12515 | C2×C4 | 1 | 4 | yes | complemented |
| 92 | #12430 | — | 2 | 8 | no | — |
| 93 | #12424 | — | 2 | 4 | no | — |
| 94 | #12424 | C2×C4 | 1 | 8 | yes | complemented |
| 95 | #12316 | — | 2 | 16 | no | — |
| 96 | C8×D16 | C2×C4 | 1 | 4 | yes | — |
| 97 | C8×D16 | D4 | 1 | 4 | yes | — |
| 98 | C16×D8 | — | 2 | 4 | no | — |
| 99 | C16×D8 | — | 2 | 2 | no | — |
| 100 | C16×D8 | — | 4 | 2 | no | — |
| 101 | C16×D8 | C2×C4 | 1 | 4 | yes | complemented |
| 102 | C2×#1371 | D4 | 1 | 1 | yes | characteristic |
| 103 | C2×#1370 | C23 | 1 | 2 | yes | — |
| 104 | C2×#1370 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×#1370 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×#1361 | — | 2 | 2 | no | — |
| 107 | C2×#1361 | — | 2 | 2 | no | — |
| 108 | C2×#1331 | D4 | 1 | 1 | yes | characteristic |
| 109 | C2×#1331 | D4 | 1 | 2 | yes | — |
| 110 | C2×D4⋊C16 | — | 2 | 1 | no | — |
| 111 | C2×D4⋊C16 | — | 2 | 2 | no | — |
| 112 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 115 | #9614 | — | 2 | 2 | no | — |
| 116 | #8882 | — | 4 | 2 | no | — |
| 117 | #8818 | C23 | 1 | 2 | yes | — |
| 118 | #8644 | — | 2 | 2 | no | — |
| 119 | C8×#107 | C23 | 1 | 1 | yes | characteristic |
| 120 | #7274 | — | 2 | 2 | no | — |
| 121 | #7274 | — | 2 | 2 | no | — |
| 122 | #7171 | D4 | 1 | 1 | yes | characteristic |
| 123 | #7167 | — | 2 | 1 | no | — |
| 124 | #7154 | D4 | 1 | 1 | yes | characteristic |
| 125 | #7101 | — | 2 | 2 | no | — |
| 126 | #7096 | — | 4 | 2 | no | — |
| 127 | #7068 | — | 2 | 4 | no | — |
| 128 | #7068 | — | 2 | 2 | no | — |
| 129 | #7052 | — | 2 | 2 | no | — |
| 130 | C23×D8 | — | 4 | 2 | no | — |
| 131 | C23×D8 | — | 4 | 2 | no | — |
| 132 | C2×D42 | — | 4 | 2 | no | — |
| 133 | C22×D16 | — | 4 | 8 | no | — |
| 134 | C22×D16 | — | 4 | 1 | no | — |
| 135 | C22×D16 | — | 4 | 1 | no | — |
| 136 | C22×D16 | — | 4 | 2 | no | — |
| 137 | C22×D16 | — | 8 | 1 | no | — |
| 138 | C22×D16 | — | 8 | 4 | no | — |
| 139 | C22×D16 | — | 8 | 4 | no | — |
| 140 | C22×D16 | D8 | 1 | 1 | yes | characteristic |
| 141 | C23×C16 | — | 4 | 1 | no | — |
| 142 | C23×C16 | — | 4 | 2 | no | — |
| 143 | D4×D8 | — | 2 | 8 | no | — |
| 144 | D4×D8 | — | 2 | 8 | no | — |
| 145 | D4×D8 | — | 4 | 4 | no | — |
| 146 | D4×D8 | — | 4 | 4 | no | — |
| 147 | D4×D8 | — | 4 | 4 | no | — |
| 148 | D4×D8 | — | 4 | 4 | no | — |
| 149 | D4×D8 | — | 8 | 2 | no | — |
| 150 | D4×D8 | — | 8 | 2 | no | — |
| 151 | C2×#493 | — | 2 | 2 | no | — |
| 152 | C2×#493 | — | 2 | 2 | no | — |
| 153 | C2×#493 | — | 2 | 2 | no | — |
| 154 | C2×#466 | — | 4 | 2 | no | — |
| 155 | C2×#466 | — | 4 | 2 | no | — |
| 156 | C2×#459 | — | 4 | 2 | no | — |
| 157 | C2×#459 | — | 4 | 2 | no | — |
| 158 | C2×#447 | — | 8 | 2 | no | — |
| 159 | C2×#447 | — | 8 | 2 | no | — |
| 160 | C2×C4×D8 | — | 4 | 2 | no | — |
| 161 | C2×C4×D8 | C2×D4 | 1 | 2 | yes | — |
| 162 | C2×C4×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C8×D4 | — | 2 | 1 | no | — |
| 164 | C2×C8×D4 | — | 2 | 2 | no | — |
| 165 | C22×#107 | — | 4 | 2 | no | — |
| 166 | D4×C4⋊C4 | — | 4 | 2 | no | — |
| 167 | #2246 | — | 2 | 4 | no | — |
| 168 | #2246 | — | 2 | 4 | no | — |
| 169 | #2246 | — | 4 | 2 | no | — |
| 170 | #2246 | — | 8 | 1 | no | — |
| 171 | #2215 | — | 4 | 8 | no | — |
| 172 | #2206 | — | 2 | 8 | no | — |
| 173 | #2206 | — | 4 | 4 | no | — |
| 174 | #2184 | — | 4 | 16 | no | — |
| 175 | #2177 | — | 8 | 4 | no | — |
| 176 | C4×D16 | C22⋊C4 | 1 | 4 | yes | — |
| 177 | C4×D16 | SD16 | 1 | 4 | yes | — |
| 178 | D4×C16 | — | 2 | 4 | no | — |
| 179 | D4×C16 | — | 4 | 4 | no | — |
| 180 | D4×C16 | — | 4 | 2 | no | — |
| 181 | D4×C16 | — | 8 | 2 | no | — |
| 182 | C2×#367 | — | 4 | 1 | no | — |
| 183 | C2×#367 | — | 4 | 1 | no | — |
| 184 | C2×#367 | — | 8 | 1 | no | — |
| 185 | C2×#366 | D8 | 1 | 1 | yes | characteristic |
| 186 | C2×C4⋊C16 | — | 2 | 1 | no | — |
| 187 | C2×C4⋊C16 | — | 2 | 1 | no | — |
| 188 | C2×C4⋊C16 | — | 2 | 2 | no | — |
| 189 | C2×#357 | — | 4 | 2 | no | — |
| 190 | C2×#357 | — | 4 | 2 | no | — |
| 191 | C2×#357 | — | 4 | 2 | no | — |
| 192 | C2×#357 | — | 4 | 2 | no | — |
| 193 | C2×#357 | — | 4 | 2 | no | — |
| 194 | C2×#357 | — | 4 | 2 | no | — |
| 195 | C2×#357 | — | 4 | 2 | no | — |
| 196 | C2×#357 | — | 8 | 2 | no | — |
| 197 | C2×#357 | — | 8 | 8 | no | — |
| 198 | C2×#357 | — | 8 | 4 | no | — |
| 199 | C2×#357 | D8 | 1 | 2 | yes | — |
| 200 | C2×#357 | D8 | 1 | 2 | yes | — |
| 201 | C2×C22⋊C16 | — | 4 | 1 | no | — |
| 202 | C2×C22⋊C16 | — | 4 | 2 | no | — |
| 203 | C2×#346 | — | 4 | 1 | no | — |
| 204 | C2×C4×C16 | — | 2 | 1 | no | — |
| 205 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | #1947 | — | 4 | 2 | no | — |
| 210 | #1942 | — | 4 | 2 | no | — |
| 211 | #1862 | — | 8 | 2 | no | — |
| 212 | #1852 | — | 8 | 2 | no | — |
| 213 | #1845 | — | 2 | 2 | no | — |
| 214 | #1845 | — | 2 | 2 | no | — |
| 215 | #1845 | — | 2 | 2 | no | — |
| 216 | #1808 | — | 4 | 2 | no | — |
| 217 | #1802 | — | 4 | 2 | no | — |
| 218 | C4×#107 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C8×C4⋊C4 | — | 2 | 1 | no | — |
| 220 | #1712 | — | 2 | 2 | no | — |
| 221 | #1712 | — | 2 | 2 | no | — |
| 222 | #1712 | — | 2 | 2 | no | — |
| 223 | #1712 | C22×C4 | 1 | 4 | yes | — |
| 224 | #1667 | — | 2 | 8 | no | — |
| 225 | #1667 | — | 2 | 8 | no | — |
| 226 | #1667 | — | 4 | 4 | no | — |
| 227 | #1667 | — | 4 | 4 | no | — |
| 228 | #1619 | — | 4 | 8 | no | — |
| 229 | #1619 | — | 4 | 8 | no | — |
| 230 | C8×D8 | — | 2 | 1 | no | — |
| 231 | C8×D8 | — | 2 | 2 | no | — |
| 232 | C8×D8 | — | 2 | 2 | no | — |
| 233 | C8×D8 | — | 2 | 1 | no | — |
| 234 | C8×D8 | C22×C4 | 1 | 4 | yes | — |
| 235 | C8×D8 | C22×C4 | 1 | 2 | yes | — |
| 236 | C8×D8 | C2×D4 | 1 | 4 | yes | — |
| 237 | C8×D8 | #41 | 1 | 2 | yes | — |
| 238 | C2×#335 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C2×#335 | C2×D4 | 1 | 2 | yes | — |
| 240 | C2×#335 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C2×#331 | — | 4 | 2 | no | — |
| 242 | C2×D4⋊C8 | — | 2 | 1 | no | — |
| 243 | C2×D4⋊C8 | — | 2 | 2 | no | — |
| 244 | C2×C82 | C24 | 1 | 1 | yes | characteristic |
| 245 | #1380 | — | 4 | 2 | no | — |
| 246 | #1380 | — | 4 | 2 | no | — |
| 247 | #1380 | D8 | 1 | 2 | yes | — |
| 248 | #1374 | — | 4 | 1 | no | — |
| 249 | #1371 | C22⋊C4 | 1 | 4 | yes | — |
| 250 | #1370 | — | 2 | 1 | no | — |
| 251 | #1370 | — | 2 | 2 | no | — |
| 252 | #1370 | — | 2 | 1 | no | — |
| 253 | #1370 | — | 2 | 2 | no | — |
| 254 | #1370 | — | 2 | 1 | no | — |
| 255 | #1370 | C22×C4 | 1 | 2 | yes | — |
| 256 | #1361 | — | 2 | 8 | no | — |
| 257 | #1361 | — | 8 | 2 | no | — |
| 258 | #1331 | — | 2 | 2 | no | — |
| 259 | #1331 | C22⋊C4 | 1 | 8 | yes | — |
| 260 | D4⋊C16 | — | 2 | 4 | no | — |
| 261 | D4⋊C16 | — | 4 | 4 | no | — |
| 262 | C8×C16 | — | 2 | 1 | no | — |
| 263 | C8×C16 | — | 2 | 1 | no | — |
| 264 | C8×C16 | — | 2 | 1 | no | — |
| 265 | C8×C16 | — | 2 | 1 | no | — |
| 266 | C8×C16 | C22×C4 | 1 | 2 | yes | — |
| 267 | C8×C16 | C2×D4 | 1 | 2 | yes | — |
| 268 | #1296 | — | 4 | 2 | no | — |
| 269 | #1279 | — | 2 | 1 | no | — |
| 270 | C23×D4 | — | 8 | 2 | no | — |
| 271 | C23×D4 | — | 8 | 2 | no | — |
| 272 | C22×D8 | — | 4 | 8 | no | — |
| 273 | C22×D8 | — | 4 | 8 | no | — |
| 274 | C22×D8 | — | 4 | 2 | no | — |
| 275 | C22×D8 | — | 4 | 2 | no | — |
| 276 | C22×D8 | — | 4 | 2 | no | — |
| 277 | C22×D8 | — | 4 | 2 | no | — |
| 278 | C22×D8 | — | 8 | 2 | no | — |
| 279 | C22×D8 | — | 8 | 4 | no | — |
| 280 | C22×D8 | — | 8 | 4 | no | — |
| 281 | C22×D8 | — | 8 | 2 | no | — |
| 282 | C22×D8 | — | 8 | 2 | no | — |
| 283 | C22×D8 | — | 8 | 4 | no | — |
| 284 | C22×D8 | — | 8 | 4 | no | — |
| 285 | C22×D8 | — | 8 | 4 | no | — |
| 286 | C22×D8 | — | 8 | 4 | no | — |
| 287 | C22×D8 | — | 16 | 2 | no | — |
| 288 | C22×D8 | — | 16 | 2 | no | — |
| 289 | C22×D8 | — | 16 | 2 | no | — |
| 290 | C22×D8 | — | 16 | 2 | no | — |
| 291 | C22×D8 | C2×D8 | 1 | 2 | yes | — |
| 292 | C22×D8 | C2×D8 | 1 | 1 | yes | characteristic |
| 293 | C23×C8 | — | 4 | 2 | no | — |
| 294 | C23×C8 | — | 4 | 1 | no | — |
| 295 | D42 | — | 4 | 8 | no | — |
| 296 | D42 | — | 8 | 4 | no | — |
| 297 | D42 | — | 8 | 4 | no | — |
| 298 | D42 | — | 16 | 2 | no | — |
| 299 | C2×#127 | — | 4 | 2 | no | — |
| 300 | C2×#121 | — | 8 | 2 | no | — |
| 301 | C2×#121 | — | 8 | 2 | no | — |
| 302 | C2×#120 | — | 16 | 2 | no | — |
| 303 | C2×C4×D4 | — | 2 | 2 | no | — |
| 304 | C2×C4×D4 | — | 2 | 1 | no | — |
| 305 | C2×C4×D4 | — | 8 | 2 | no | — |
| 306 | C22×C4⋊C4 | — | 8 | 2 | no | — |
| 307 | C2×D16 | — | 4 | 8 | no | — |
| 308 | C2×D16 | — | 4 | 4 | no | — |
| 309 | C2×D16 | — | 4 | 4 | no | — |
| 310 | C2×D16 | — | 8 | 4 | no | — |
| 311 | C2×D16 | — | 8 | 4 | no | — |
| 312 | C2×D16 | — | 8 | 4 | no | — |
| 313 | C2×D16 | — | 8 | 32 | no | — |
| 314 | C2×D16 | — | 8 | 2 | no | — |
| 315 | C2×D16 | — | 8 | 2 | no | — |
| 316 | C2×D16 | — | 16 | 1 | no | — |
| 317 | C2×D16 | — | 16 | 1 | no | — |
| 318 | C2×D16 | — | 16 | 2 | no | — |
| 319 | C2×D16 | — | 16 | 2 | no | — |
| 320 | C2×D16 | #102 | 1 | 4 | yes | — |
| 321 | C2×D16 | D16 | 1 | 4 | yes | — |
| 322 | C2×D16 | SD32 | 1 | 4 | yes | — |
| 323 | C22×C16 | — | 2 | 1 | no | — |
| 324 | C22×C16 | — | 2 | 2 | no | — |
| 325 | C22×C16 | — | 2 | 1 | no | — |
| 326 | C22×C16 | — | 4 | 1 | no | — |
| 327 | C22×C16 | — | 4 | 4 | no | — |
| 328 | C22×C16 | — | 4 | 1 | no | — |
| 329 | C22×C16 | — | 4 | 2 | no | — |
| 330 | C22×C16 | — | 8 | 4 | no | — |
| 331 | C22×C16 | — | 8 | 4 | no | — |
| 332 | C22×C16 | — | 8 | 2 | no | — |
| 333 | C22×C16 | — | 8 | 2 | no | — |
| 334 | C22×C16 | — | 16 | 2 | no | — |
| 335 | C22×C16 | C2×D8 | 1 | 2 | yes | — |
| 336 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 337 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 338 | #493 | — | 2 | 4 | no | — |
| 339 | #493 | — | 2 | 4 | no | — |
| 340 | #493 | — | 2 | 4 | no | — |
| 341 | #493 | — | 4 | 2 | no | — |
| 342 | #493 | — | 4 | 2 | no | — |
| 343 | #493 | — | 4 | 2 | no | — |
| 344 | #493 | — | 4 | 2 | no | — |
| 345 | #493 | — | 4 | 2 | no | — |
| 346 | #493 | — | 4 | 2 | no | — |
| 347 | #493 | — | 4 | 2 | no | — |
| 348 | #493 | — | 8 | 2 | no | — |
| 349 | #466 | — | 4 | 8 | no | — |
| 350 | #466 | — | 4 | 8 | no | — |
| 351 | #466 | — | 8 | 4 | no | — |
| 352 | #466 | — | 8 | 4 | no | — |
| 353 | #459 | — | 4 | 8 | no | — |
| 354 | #459 | — | 4 | 8 | no | — |
| 355 | #459 | — | 8 | 4 | no | — |
| 356 | #459 | — | 8 | 4 | no | — |
| 357 | #447 | — | 8 | 8 | no | — |
| 358 | #447 | — | 8 | 8 | no | — |
| 359 | #447 | — | 8 | 8 | no | — |
| 360 | #447 | — | 8 | 8 | no | — |
| 361 | C4×D8 | — | 2 | 1 | no | — |
| 362 | C4×D8 | — | 2 | 2 | no | — |
| 363 | C4×D8 | — | 2 | 1 | no | — |
| 364 | C4×D8 | — | 2 | 2 | no | — |
| 365 | C4×D8 | — | 8 | 4 | no | — |
| 366 | C4×D8 | — | 16 | 2 | no | — |
| 367 | C4×D8 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 368 | C4×D8 | C4×D4 | 1 | 2 | yes | — |
| 369 | C4×D8 | C2×SD16 | 1 | 4 | yes | — |
| 370 | C4×D8 | #135 | 1 | 2 | yes | — |
| 371 | C8×D4 | — | 2 | 2 | no | — |
| 372 | C8×D4 | — | 2 | 4 | no | — |
| 373 | C8×D4 | — | 2 | 4 | no | — |
| 374 | C8×D4 | — | 2 | 2 | no | — |
| 375 | C8×D4 | — | 4 | 1 | no | — |
| 376 | C8×D4 | — | 4 | 2 | no | — |
| 377 | C8×D4 | — | 4 | 2 | no | — |
| 378 | C8×D4 | — | 4 | 1 | no | — |
| 379 | C2×#107 | — | 4 | 2 | no | — |
| 380 | C2×#107 | — | 4 | 2 | no | — |
| 381 | C2×#107 | — | 4 | 2 | no | — |
| 382 | C2×#107 | — | 4 | 2 | no | — |
| 383 | C2×#107 | — | 8 | 4 | no | — |
| 384 | C2×#107 | — | 8 | 2 | no | — |
| 385 | C2×#107 | — | 8 | 2 | no | — |
| 386 | C2×#107 | — | 16 | 2 | no | — |
| 387 | C2×#107 | C2×D8 | 1 | 2 | yes | — |
| 388 | C2×#107 | C2×D8 | 1 | 2 | yes | — |
| 389 | C2×#107 | C2×D8 | 1 | 1 | yes | characteristic |
| 390 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 391 | C2×C4⋊C8 | — | 2 | 2 | no | — |
| 392 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 393 | C2×#102 | — | 2 | 2 | no | — |
| 394 | C2×#102 | — | 2 | 1 | no | — |
| 395 | C2×#102 | — | 8 | 2 | no | — |
| 396 | C2×#102 | — | 8 | 2 | no | — |
| 397 | C2×#102 | — | 8 | 2 | no | — |
| 398 | C2×C22⋊C8 | — | 4 | 2 | no | — |
| 399 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 400 | C2×C4×C8 | — | 4 | 1 | no | — |
| 401 | C2×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 402 | C2×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 403 | C2×C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 404 | #389 | — | 8 | 2 | no | — |
| 405 | #385 | — | 16 | 2 | no | — |
| 406 | #384 | — | 4 | 2 | no | — |
| 407 | #380 | — | 8 | 2 | no | — |
| 408 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 409 | #367 | — | 8 | 2 | no | — |
| 410 | #367 | — | 16 | 1 | no | — |
| 411 | #367 | — | 16 | 2 | no | — |
| 412 | #366 | #102 | 1 | 4 | yes | — |
| 413 | C4⋊C16 | — | 2 | 2 | no | — |
| 414 | C4⋊C16 | — | 4 | 2 | no | — |
| 415 | C4⋊C16 | — | 4 | 1 | no | — |
| 416 | C4⋊C16 | — | 4 | 1 | no | — |
| 417 | C4⋊C16 | — | 4 | 2 | no | — |
| 418 | C4⋊C16 | — | 4 | 1 | no | — |
| 419 | #357 | — | 2 | 4 | no | — |
| 420 | #357 | — | 4 | 8 | no | — |
| 421 | #357 | — | 8 | 4 | no | — |
| 422 | #357 | — | 8 | 4 | no | — |
| 423 | #357 | — | 8 | 4 | no | — |
| 424 | #357 | — | 8 | 4 | no | — |
| 425 | #357 | — | 16 | 2 | no | — |
| 426 | #357 | — | 16 | 2 | no | — |
| 427 | #357 | — | 16 | 4 | no | — |
| 428 | #357 | — | 16 | 8 | no | — |
| 429 | #357 | #102 | 1 | 8 | yes | — |
| 430 | C22⋊C16 | — | 4 | 4 | no | — |
| 431 | C22⋊C16 | — | 8 | 4 | no | — |
| 432 | #346 | — | 8 | 2 | no | — |
| 433 | C4×C16 | — | 2 | 1 | no | — |
| 434 | C4×C16 | — | 2 | 1 | no | — |
| 435 | C4×C16 | — | 2 | 1 | no | — |
| 436 | C4×C16 | — | 2 | 1 | no | — |
| 437 | C4×C16 | — | 2 | 1 | no | — |
| 438 | C4×C16 | — | 4 | 1 | no | — |
| 439 | C4×C16 | — | 4 | 1 | no | — |
| 440 | C4×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 441 | C4×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 442 | C4×C16 | C2×SD16 | 1 | 2 | yes | — |
| 443 | #340 | — | 2 | 1 | no | — |
| 444 | #340 | — | 8 | 2 | no | — |
| 445 | #340 | — | 8 | 2 | no | — |
| 446 | #336 | — | 4 | 1 | no | — |
| 447 | #335 | — | 2 | 1 | no | — |
| 448 | #335 | — | 2 | 2 | no | — |
| 449 | #335 | — | 2 | 1 | no | — |
| 450 | #335 | — | 2 | 1 | no | — |
| 451 | #335 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 452 | #335 | C4×D4 | 1 | 2 | yes | — |
| 453 | #331 | — | 4 | 8 | no | — |
| 454 | D4⋊C8 | — | 2 | 2 | no | — |
| 455 | D4⋊C8 | — | 2 | 4 | no | — |
| 456 | D4⋊C8 | — | 2 | 4 | no | — |
| 457 | D4⋊C8 | — | 2 | 2 | no | — |
| 458 | C82 | C23×C4 | 1 | 1 | yes | characteristic |
| 459 | C82 | C22×D4 | 1 | 1 | yes | characteristic |
| 460 | C82 | C2×#41 | 1 | 1 | yes | characteristic |
| 461 | C82 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 462 | C25 | — | 16 | 2 | no | — |
| 463 | C22×D4 | — | 2 | 2 | no | — |
| 464 | C22×D4 | — | 2 | 1 | no | — |
| 465 | C22×D4 | — | 8 | 8 | no | — |
| 466 | C22×D4 | — | 8 | 8 | no | — |
| 467 | C22×D4 | — | 8 | 2 | no | — |
| 468 | C22×D4 | — | 8 | 2 | no | — |
| 469 | C22×D4 | — | 8 | 2 | no | — |
| 470 | C22×D4 | — | 16 | 4 | no | — |
| 471 | C22×D4 | — | 16 | 4 | no | — |
| 472 | C22×D4 | — | 16 | 2 | no | — |
| 473 | C22×D4 | — | 16 | 2 | no | — |
| 474 | C22×D4 | — | 16 | 4 | no | — |
| 475 | C22×D4 | — | 16 | 4 | no | — |
| 476 | C22×D4 | — | 16 | 4 | no | — |
| 477 | C22×D4 | — | 16 | 4 | no | — |
| 478 | C22×D4 | — | 32 | 2 | no | — |
| 479 | C22×D4 | — | 32 | 2 | no | — |
| 480 | C22×D4 | — | 32 | 2 | no | — |
| 481 | C22×D4 | — | 32 | 2 | no | — |
| 482 | C23×C4 | — | 4 | 2 | no | — |
| 483 | C23×C4 | — | 4 | 1 | no | — |
| 484 | C23×C4 | — | 16 | 2 | no | — |
| 485 | C2×D8 | — | 2 | 2 | no | — |
| 486 | C2×D8 | — | 2 | 2 | no | — |
| 487 | C2×D8 | — | 2 | 2 | no | — |
| 488 | C2×D8 | — | 2 | 1 | no | — |
| 489 | C2×D8 | — | 2 | 2 | no | — |
| 490 | C2×D8 | — | 4 | 4 | no | — |
| 491 | C2×D8 | — | 4 | 4 | no | — |
| 492 | C2×D8 | — | 4 | 4 | no | — |
| 493 | C2×D8 | — | 4 | 4 | no | — |
| 494 | C2×D8 | — | 8 | 4 | no | — |
| 495 | C2×D8 | — | 8 | 8 | no | — |
| 496 | C2×D8 | — | 8 | 8 | no | — |
| 497 | C2×D8 | — | 8 | 16 | no | — |
| 498 | C2×D8 | — | 8 | 16 | no | — |
| 499 | C2×D8 | — | 8 | 2 | no | — |
| 500 | C2×D8 | — | 8 | 2 | no | — |
| 501 | C2×D8 | — | 8 | 2 | no | — |
| 502 | C2×D8 | — | 8 | 2 | no | — |
| 503 | C2×D8 | — | 8 | 2 | no | — |
| 504 | C2×D8 | — | 8 | 2 | no | — |
| 505 | C2×D8 | — | 8 | 2 | no | — |
| 506 | C2×D8 | — | 8 | 2 | no | — |
| 507 | C2×D8 | — | 8 | 2 | no | — |
| 508 | C2×D8 | — | 8 | 2 | no | — |
| 509 | C2×D8 | — | 8 | 2 | no | — |
| 510 | C2×D8 | — | 8 | 2 | no | — |
| 511 | C2×D8 | — | 16 | 2 | no | — |
| 512 | C2×D8 | — | 16 | 2 | no | — |
| 513 | C2×D8 | — | 16 | 2 | no | — |
| 514 | C2×D8 | — | 16 | 2 | no | — |
| 515 | C2×D8 | — | 16 | 4 | no | — |
| 516 | C2×D8 | — | 16 | 4 | no | — |
| 517 | C2×D8 | — | 16 | 2 | no | — |
| 518 | C2×D8 | — | 16 | 8 | no | — |
| 519 | C2×D8 | — | 16 | 8 | no | — |
| 520 | C2×D8 | — | 16 | 8 | no | — |
| 521 | C2×D8 | — | 16 | 8 | no | — |
| 522 | C2×D8 | — | 16 | 8 | no | — |
| 523 | C2×D8 | — | 16 | 8 | no | — |
| 524 | C2×D8 | — | 16 | 4 | no | — |
| 525 | C2×D8 | — | 16 | 4 | no | — |
| 526 | C2×D8 | — | 16 | 4 | no | — |
| 527 | C2×D8 | — | 16 | 4 | no | — |
| 528 | C2×D8 | C2×#102 | 1 | 4 | yes | — |
| 529 | C2×D8 | C4×D8 | 1 | 2 | yes | — |
| 530 | C2×D8 | C2×D16 | 1 | 4 | yes | — |
| 531 | C2×D8 | C2×SD32 | 1 | 4 | yes | — |
| 532 | C2×D8 | #509 | 1 | 4 | yes | — |
| 533 | C22×C8 | — | 2 | 1 | no | — |
| 534 | C22×C8 | — | 4 | 1 | no | — |
| 535 | C22×C8 | — | 4 | 2 | no | — |
| 536 | C22×C8 | — | 4 | 2 | no | — |
| 537 | C22×C8 | — | 4 | 4 | no | — |
| 538 | C22×C8 | — | 4 | 4 | no | — |
| 539 | C22×C8 | — | 4 | 2 | no | — |
| 540 | C22×C8 | — | 4 | 1 | no | — |
| 541 | C22×C8 | — | 8 | 1 | no | — |
| 542 | C22×C8 | — | 8 | 1 | no | — |
| 543 | C22×C8 | — | 8 | 2 | no | — |
| 544 | C22×C8 | — | 8 | 2 | no | — |
| 545 | C22×C8 | — | 8 | 1 | no | — |
| 546 | C22×C8 | — | 8 | 2 | no | — |
| 547 | C22×C8 | — | 8 | 2 | no | — |
| 548 | C22×C8 | — | 8 | 1 | no | — |
| 549 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 550 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 551 | C22×C8 | #576 | 1 | 1 | yes | characteristic |
| 552 | C22×C8 | #576 | 1 | 1 | yes | characteristic |
| 553 | #127 | — | 4 | 4 | no | — |
| 554 | #127 | — | 8 | 2 | no | — |
| 555 | #127 | — | 8 | 2 | no | — |
| 556 | #127 | — | 8 | 2 | no | — |
| 557 | #121 | — | 8 | 8 | no | — |
| 558 | #121 | — | 8 | 8 | no | — |
| 559 | #121 | — | 16 | 4 | no | — |
| 560 | #121 | — | 16 | 4 | no | — |
| 561 | #120 | — | 16 | 8 | no | — |
| 562 | #120 | — | 16 | 8 | no | — |
| 563 | C4×D4 | — | 2 | 2 | no | — |
| 564 | C4×D4 | — | 2 | 4 | no | — |
| 565 | C4×D4 | — | 2 | 2 | no | — |
| 566 | C4×D4 | — | 2 | 4 | no | — |
| 567 | C4×D4 | — | 4 | 2 | no | — |
| 568 | C4×D4 | — | 4 | 1 | no | — |
| 569 | C4×D4 | — | 4 | 2 | no | — |
| 570 | C4×D4 | — | 4 | 1 | no | — |
| 571 | C4×D4 | — | 16 | 4 | no | — |
| 572 | C4×D4 | — | 32 | 2 | no | — |
| 573 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 574 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 575 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 576 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 577 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 578 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 579 | C2×C4⋊C4 | — | 16 | 4 | no | — |
| 580 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 581 | C2×C4⋊C4 | — | 32 | 2 | no | — |
| 582 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 583 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 584 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 585 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 586 | C2×C42 | — | 4 | 1 | no | — |
| 587 | C2×C42 | D42 | 1 | 1 | yes | characteristic |
| 588 | D16 | — | 8 | 16 | no | — |
| 589 | D16 | — | 8 | 8 | no | — |
| 590 | D16 | — | 16 | 4 | no | — |
| 591 | D16 | — | 16 | 8 | no | — |
| 592 | D16 | #357 | 1 | 16 | yes | complemented |
| 593 | C2×C16 | — | 2 | 2 | no | — |
| 594 | C2×C16 | — | 2 | 2 | no | — |
| 595 | C2×C16 | — | 2 | 2 | no | — |
| 596 | C2×C16 | — | 2 | 1 | no | — |
| 597 | C2×C16 | — | 2 | 1 | no | — |
| 598 | C2×C16 | — | 2 | 2 | no | — |
| 599 | C2×C16 | — | 2 | 2 | no | — |
| 600 | C2×C16 | — | 2 | 2 | no | — |
| 601 | C2×C16 | — | 4 | 2 | no | — |
| 602 | C2×C16 | — | 4 | 4 | no | — |
| 603 | C2×C16 | — | 4 | 2 | no | — |
| 604 | C2×C16 | — | 4 | 2 | no | — |
| 605 | C2×C16 | — | 4 | 1 | no | — |
| 606 | C2×C16 | — | 8 | 1 | no | — |
| 607 | C2×C16 | — | 8 | 1 | no | — |
| 608 | C2×C16 | — | 8 | 8 | no | — |
| 609 | C2×C16 | — | 8 | 1 | no | — |
| 610 | C2×C16 | — | 8 | 2 | no | — |
| 611 | C2×C16 | — | 8 | 2 | no | — |
| 612 | C2×C16 | — | 8 | 1 | no | — |
| 613 | C2×C16 | — | 8 | 2 | no | — |
| 614 | C2×C16 | — | 8 | 1 | no | — |
| 615 | C2×C16 | — | 16 | 8 | no | — |
| 616 | C2×C16 | C2×#102 | 1 | 2 | yes | — |
| 617 | C2×C16 | C2×#102 | 1 | 2 | yes | — |
| 618 | C2×C16 | C2×D16 | 1 | 2 | yes | — |
| 619 | C2×C16 | C2×SD32 | 1 | 2 | yes | — |
| 620 | #107 | — | 2 | 1 | no | — |
| 621 | #107 | — | 2 | 2 | no | — |
| 622 | #107 | — | 2 | 2 | no | — |
| 623 | #107 | — | 2 | 2 | no | — |
| 624 | #107 | — | 8 | 2 | no | — |
| 625 | #107 | — | 8 | 2 | no | — |
| 626 | #107 | — | 8 | 2 | no | — |
| 627 | #107 | — | 8 | 2 | no | — |
| 628 | #107 | — | 16 | 4 | no | — |
| 629 | #107 | — | 16 | 2 | no | — |
| 630 | #107 | — | 16 | 2 | no | — |
| 631 | #107 | — | 16 | 4 | no | — |
| 632 | #107 | C2×#102 | 1 | 4 | yes | — |
| 633 | #107 | C4×D8 | 1 | 2 | yes | — |
| 634 | C4⋊C8 | — | 2 | 2 | no | — |
| 635 | C4⋊C8 | — | 2 | 4 | no | — |
| 636 | C4⋊C8 | — | 4 | 2 | no | — |
| 637 | C4⋊C8 | — | 4 | 1 | no | — |
| 638 | C4⋊C8 | — | 4 | 1 | no | — |
| 639 | C4⋊C8 | — | 4 | 1 | no | — |
| 640 | #102 | — | 2 | 4 | no | — |
| 641 | #102 | — | 2 | 2 | no | — |
| 642 | #102 | — | 2 | 2 | no | — |
| 643 | #102 | — | 2 | 4 | no | — |
| 644 | #102 | — | 8 | 8 | no | — |
| 645 | #102 | — | 8 | 8 | no | — |
| 646 | #102 | — | 16 | 4 | no | — |
| 647 | C22⋊C8 | — | 4 | 2 | no | — |
| 648 | C22⋊C8 | — | 4 | 4 | no | — |
| 649 | C22⋊C8 | — | 4 | 4 | no | — |
| 650 | C22⋊C8 | — | 4 | 2 | no | — |
| 651 | C4×C8 | — | 2 | 1 | no | — |
| 652 | C4×C8 | — | 8 | 1 | no | — |
| 653 | C4×C8 | — | 8 | 1 | no | — |
| 654 | C4×C8 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 655 | C4×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 656 | C4×C8 | #518 | 1 | 1 | yes | characteristic |
| 657 | C4×C8 | D42 | 1 | 1 | yes | characteristic |
| 658 | C4×C8 | #546 | 1 | 1 | yes | characteristic |
| 659 | C4×C8 | #546 | 1 | 1 | yes | characteristic |
| 660 | C4×C8 | C22×SD16 | 1 | 1 | yes | characteristic |
| 661 | C4×C8 | C2×#135 | 1 | 1 | yes | characteristic |
| 662 | C4×C8 | #576 | 1 | 1 | yes | characteristic |
| 663 | C4×C8 | #577 | 1 | 1 | yes | characteristic |
| 664 | #95 | — | 4 | 1 | no | — |
| 665 | #95 | — | 16 | 2 | no | — |
| 666 | C24 | — | 4 | 2 | no | — |
| 667 | C24 | — | 4 | 1 | no | — |
| 668 | C24 | — | 16 | 8 | no | — |
| 669 | C24 | — | 16 | 2 | no | — |
| 670 | C24 | — | 32 | 4 | no | — |
| 671 | C24 | — | 32 | 4 | no | — |
| 672 | C24 | — | 32 | 4 | no | — |
| 673 | C24 | — | 32 | 4 | no | — |
| 674 | C24 | — | 64 | 2 | no | — |
| 675 | C24 | — | 64 | 2 | no | — |
| 676 | C2×D4 | — | 2 | 4 | no | — |
| 677 | C2×D4 | — | 2 | 4 | no | — |
| 678 | C2×D4 | — | 2 | 4 | no | — |
| 679 | C2×D4 | — | 2 | 4 | no | — |
| 680 | C2×D4 | — | 2 | 2 | no | — |
| 681 | C2×D4 | — | 4 | 2 | no | — |
| 682 | C2×D4 | — | 4 | 1 | no | — |
| 683 | C2×D4 | — | 4 | 2 | no | — |
| 684 | C2×D4 | — | 4 | 2 | no | — |
| 685 | C2×D4 | — | 4 | 2 | no | — |
| 686 | C2×D4 | — | 8 | 4 | no | — |
| 687 | C2×D4 | — | 8 | 4 | no | — |
| 688 | C2×D4 | — | 8 | 4 | no | — |
| 689 | C2×D4 | — | 16 | 8 | no | — |
| 690 | C2×D4 | — | 16 | 8 | no | — |
| 691 | C2×D4 | — | 16 | 16 | no | — |
| 692 | C2×D4 | — | 16 | 16 | no | — |
| 693 | C2×D4 | — | 16 | 2 | no | — |
| 694 | C2×D4 | — | 16 | 2 | no | — |
| 695 | C2×D4 | — | 16 | 2 | no | — |
| 696 | C2×D4 | — | 16 | 2 | no | — |
| 697 | C2×D4 | — | 16 | 2 | no | — |
| 698 | C2×D4 | — | 16 | 2 | no | — |
| 699 | C2×D4 | — | 16 | 2 | no | — |
| 700 | C2×D4 | — | 16 | 2 | no | — |
| 701 | C2×D4 | — | 16 | 2 | no | — |
| 702 | C2×D4 | — | 16 | 2 | no | — |
| 703 | C2×D4 | — | 16 | 2 | no | — |
| 704 | C2×D4 | — | 32 | 2 | no | — |
| 705 | C2×D4 | — | 32 | 2 | no | — |
| 706 | C2×D4 | — | 32 | 8 | no | — |
| 707 | C2×D4 | — | 32 | 8 | no | — |
| 708 | C2×D4 | — | 32 | 8 | no | — |
| 709 | C2×D4 | — | 32 | 8 | no | — |
| 710 | C2×D4 | — | 32 | 8 | no | — |
| 711 | C2×D4 | — | 32 | 8 | no | — |
| 712 | C2×D4 | — | 32 | 4 | no | — |
| 713 | C2×D4 | — | 32 | 4 | no | — |
| 714 | C2×D4 | — | 32 | 4 | no | — |
| 715 | C2×D4 | — | 32 | 4 | no | — |
| 716 | C22×C4 | — | 4 | 2 | no | — |
| 717 | C22×C4 | — | 4 | 1 | no | — |
| 718 | C22×C4 | — | 4 | 2 | no | — |
| 719 | C22×C4 | — | 4 | 4 | no | — |
| 720 | C22×C4 | — | 4 | 2 | no | — |
| 721 | C22×C4 | — | 4 | 4 | no | — |
| 722 | C22×C4 | — | 4 | 2 | no | — |
| 723 | C22×C4 | — | 8 | 2 | no | — |
| 724 | C22×C4 | — | 8 | 2 | no | — |
| 725 | C22×C4 | — | 8 | 1 | no | — |
| 726 | C22×C4 | — | 8 | 1 | no | — |
| 727 | C22×C4 | — | 8 | 2 | no | — |
| 728 | C22×C4 | — | 8 | 2 | no | — |
| 729 | C22×C4 | — | 8 | 1 | no | — |
| 730 | C22×C4 | — | 8 | 1 | no | — |
| 731 | C22×C4 | — | 16 | 2 | no | — |
| 732 | C22×C4 | — | 32 | 4 | no | — |
| 733 | C22×C4 | — | 32 | 4 | no | — |
| 734 | C22×C4 | — | 64 | 2 | no | — |
| 735 | C22×C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 736 | C22×C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 737 | C22×C4 | #3292 | 1 | 1 | yes | characteristic |
| 738 | D8 | — | 2 | 4 | no | — |
| 739 | D8 | — | 2 | 4 | no | — |
| 740 | D8 | — | 2 | 4 | no | — |
| 741 | D8 | — | 2 | 4 | no | — |
| 742 | D8 | — | 2 | 2 | no | — |
| 743 | D8 | — | 8 | 4 | no | — |
| 744 | D8 | — | 8 | 4 | no | — |
| 745 | D8 | — | 8 | 4 | no | — |
| 746 | D8 | — | 8 | 4 | no | — |
| 747 | D8 | — | 16 | 4 | no | — |
| 748 | D8 | — | 16 | 4 | no | — |
| 749 | D8 | — | 16 | 8 | no | — |
| 750 | D8 | — | 16 | 16 | no | — |
| 751 | D8 | — | 16 | 16 | no | — |
| 752 | D8 | — | 16 | 2 | no | — |
| 753 | D8 | — | 16 | 2 | no | — |
| 754 | D8 | — | 16 | 2 | no | — |
| 755 | D8 | — | 16 | 2 | no | — |
| 756 | D8 | — | 32 | 2 | no | — |
| 757 | D8 | — | 32 | 2 | no | — |
| 758 | D8 | — | 32 | 4 | no | — |
| 759 | D8 | C2×#357 | 1 | 8 | yes | complemented |
| 760 | D8 | #2177 | 1 | 4 | yes | complemented |
| 761 | C2×C8 | — | 2 | 4 | no | — |
| 762 | C2×C8 | — | 2 | 2 | no | — |
| 763 | C2×C8 | — | 2 | 1 | no | — |
| 764 | C2×C8 | — | 2 | 1 | no | — |
| 765 | C2×C8 | — | 2 | 1 | no | — |
| 766 | C2×C8 | — | 2 | 1 | no | — |
| 767 | C2×C8 | — | 4 | 2 | no | — |
| 768 | C2×C8 | — | 4 | 4 | no | — |
| 769 | C2×C8 | — | 8 | 2 | no | — |
| 770 | C2×C8 | — | 8 | 2 | no | — |
| 771 | C2×C8 | — | 8 | 1 | no | — |
| 772 | C2×C8 | — | 8 | 1 | no | — |
| 773 | C2×C8 | — | 8 | 4 | no | — |
| 774 | C2×C8 | — | 8 | 4 | no | — |
| 775 | C2×C8 | — | 8 | 2 | no | — |
| 776 | C2×C8 | — | 8 | 2 | no | — |
| 777 | C2×C8 | — | 8 | 2 | no | — |
| 778 | C2×C8 | — | 8 | 2 | no | — |
| 779 | C2×C8 | — | 8 | 4 | no | — |
| 780 | C2×C8 | — | 8 | 4 | no | — |
| 781 | C2×C8 | — | 8 | 1 | no | — |
| 782 | C2×C8 | — | 8 | 1 | no | — |
| 783 | C2×C8 | — | 8 | 1 | no | — |
| 784 | C2×C8 | C22×#102 | 1 | 1 | yes | characteristic |
| 785 | C2×C8 | #2897 | 1 | 1 | yes | characteristic |
| 786 | C2×C8 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 787 | C2×C8 | #2948 | 1 | 1 | yes | characteristic |
| 788 | C2×C8 | D4×D8 | 1 | 1 | yes | characteristic |
| 789 | C2×C8 | #3280 | 1 | 1 | yes | characteristic |
| 790 | C2×C8 | #3294 | 1 | 1 | yes | characteristic |
| 791 | C2×C8 | #3295 | 1 | 1 | yes | characteristic |
| 792 | C2×C8 | C22×D16 | 1 | 1 | yes | characteristic |
| 793 | C2×C8 | C22×SD32 | 1 | 1 | yes | characteristic |
| 794 | C2×C8 | C2×#509 | 1 | 2 | yes | — |
| 795 | C2×C8 | #3415 | 1 | 2 | yes | — |
| 796 | C2×C8 | #3415 | 1 | 1 | yes | characteristic |
| 797 | C2×C8 | #3416 | 1 | 1 | yes | characteristic |
| 798 | C4⋊C4 | — | 2 | 4 | no | — |
| 799 | C4⋊C4 | — | 2 | 2 | no | — |
| 800 | C4⋊C4 | — | 4 | 2 | no | — |
| 801 | C4⋊C4 | — | 4 | 1 | no | — |
| 802 | C4⋊C4 | — | 4 | 2 | no | — |
| 803 | C4⋊C4 | — | 4 | 2 | no | — |
| 804 | C4⋊C4 | — | 16 | 2 | no | — |
| 805 | C4⋊C4 | — | 16 | 2 | no | — |
| 806 | C4⋊C4 | — | 16 | 2 | no | — |
| 807 | C4⋊C4 | — | 16 | 2 | no | — |
| 808 | C4⋊C4 | — | 32 | 2 | no | — |
| 809 | C4⋊C4 | — | 32 | 4 | no | — |
| 810 | C22⋊C4 | — | 4 | 4 | no | — |
| 811 | C22⋊C4 | — | 4 | 2 | no | — |
| 812 | C22⋊C4 | — | 4 | 4 | no | — |
| 813 | C22⋊C4 | — | 4 | 2 | no | — |
| 814 | C22⋊C4 | — | 16 | 8 | no | — |
| 815 | C22⋊C4 | — | 32 | 4 | no | — |
| 816 | C42 | — | 8 | 1 | no | — |
| 817 | C42 | — | 8 | 1 | no | — |
| 818 | C42 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 819 | C42 | #3280 | 1 | 1 | yes | characteristic |
| 820 | C42 | D4×SD16 | 1 | 1 | yes | characteristic |
| 821 | C42 | #3290 | 1 | 1 | yes | characteristic |
| 822 | C16 | — | 2 | 4 | no | — |
| 823 | C16 | — | 2 | 2 | no | — |
| 824 | C16 | — | 4 | 2 | no | — |
| 825 | C16 | — | 8 | 2 | no | — |
| 826 | C16 | — | 8 | 1 | no | — |
| 827 | C16 | — | 8 | 2 | no | — |
| 828 | C16 | — | 16 | 2 | no | — |
| 829 | C16 | — | 16 | 1 | no | — |
| 830 | C16 | C2×#357 | 1 | 4 | yes | complemented |
| 831 | C23 | — | 4 | 2 | no | — |
| 832 | C23 | — | 4 | 4 | no | — |
| 833 | C23 | — | 4 | 4 | no | — |
| 834 | C23 | — | 4 | 4 | no | — |
| 835 | C23 | — | 4 | 4 | no | — |
| 836 | C23 | — | 8 | 2 | no | — |
| 837 | C23 | — | 8 | 2 | no | — |
| 838 | C23 | — | 8 | 1 | no | — |
| 839 | C23 | — | 8 | 1 | no | — |
| 840 | C23 | — | 8 | 2 | no | — |
| 841 | C23 | — | 8 | 2 | no | — |
| 842 | C23 | — | 8 | 2 | no | — |
| 843 | C23 | — | 16 | 4 | no | — |
| 844 | C23 | — | 32 | 16 | no | — |
| 845 | C23 | — | 32 | 16 | no | — |
| 846 | C23 | — | 32 | 2 | no | — |
| 847 | C23 | — | 32 | 2 | no | — |
| 848 | C23 | — | 32 | 2 | no | — |
| 849 | C23 | — | 32 | 2 | no | — |
| 850 | C23 | — | 32 | 2 | no | — |
| 851 | C23 | — | 32 | 2 | no | — |
| 852 | C23 | — | 64 | 8 | no | — |
| 853 | C23 | — | 64 | 8 | no | — |
| 854 | C23 | — | 64 | 8 | no | — |
| 855 | C23 | — | 64 | 8 | no | — |
| 856 | C23 | — | 64 | 8 | no | — |
| 857 | C23 | D82 | 1 | 1 | yes | characteristic |
| 858 | D4 | — | 2 | 4 | no | — |
| 859 | D4 | — | 2 | 8 | no | — |
| 860 | D4 | — | 4 | 4 | no | — |
| 861 | D4 | — | 4 | 2 | no | — |
| 862 | D4 | — | 4 | 4 | no | — |
| 863 | D4 | — | 4 | 4 | no | — |
| 864 | D4 | — | 4 | 4 | no | — |
| 865 | D4 | — | 16 | 4 | no | — |
| 866 | D4 | — | 16 | 4 | no | — |
| 867 | D4 | — | 16 | 4 | no | — |
| 868 | D4 | — | 16 | 4 | no | — |
| 869 | D4 | — | 32 | 4 | no | — |
| 870 | D4 | — | 32 | 16 | no | — |
| 871 | D4 | — | 32 | 16 | no | — |
| 872 | D4 | — | 32 | 2 | no | — |
| 873 | D4 | — | 32 | 2 | no | — |
| 874 | D4 | — | 32 | 2 | no | — |
| 875 | D4 | — | 32 | 2 | no | — |
| 876 | D4 | — | 64 | 2 | no | — |
| 877 | C2×C4 | — | 2 | 2 | no | — |
| 878 | C2×C4 | — | 4 | 2 | no | — |
| 879 | C2×C4 | — | 4 | 4 | no | — |
| 880 | C2×C4 | — | 8 | 2 | no | — |
| 881 | C2×C4 | — | 8 | 2 | no | — |
| 882 | C2×C4 | — | 8 | 1 | no | — |
| 883 | C2×C4 | — | 8 | 1 | no | — |
| 884 | C2×C4 | — | 8 | 4 | no | — |
| 885 | C2×C4 | — | 8 | 4 | no | — |
| 886 | C2×C4 | — | 8 | 4 | no | — |
| 887 | C2×C4 | — | 8 | 4 | no | — |
| 888 | C2×C4 | — | 8 | 2 | no | — |
| 889 | C2×C4 | — | 8 | 2 | no | — |
| 890 | C2×C4 | — | 8 | 2 | no | — |
| 891 | C2×C4 | — | 8 | 2 | no | — |
| 892 | C2×C4 | — | 8 | 2 | no | — |
| 893 | C2×C4 | — | 8 | 2 | no | — |
| 894 | C2×C4 | — | 8 | 2 | no | — |
| 895 | C2×C4 | — | 32 | 2 | no | — |
| 896 | C2×C4 | — | 32 | 2 | no | — |
| 897 | C2×C4 | — | 32 | 2 | no | — |
| 898 | C2×C4 | — | 64 | 8 | no | — |
| 899 | C2×C4 | #19968 | 1 | 1 | yes | characteristic |
| 900 | C2×C4 | D8×SD16 | 1 | 1 | yes | characteristic |
| 901 | C2×C4 | #19976 | 1 | 1 | yes | characteristic |
| 902 | C2×C4 | D4×#102 | 1 | 1 | yes | characteristic |
| 903 | C2×C4 | C22⋊C4×D8 | 1 | 1 | yes | characteristic |
| 904 | C2×C4 | #22466 | 1 | 1 | yes | characteristic |
| 905 | C2×C4 | #33830 | 1 | 2 | yes | — |
| 906 | C2×C4 | D4×D16 | 1 | 1 | yes | characteristic |
| 907 | C2×C4 | D4×SD32 | 1 | 1 | yes | characteristic |
| 908 | C2×C4 | #33854 | 1 | 2 | yes | — |
| 909 | C2×C4 | #33856 | 1 | 1 | yes | characteristic |
| 910 | C2×C4 | #33858 | 1 | 1 | yes | characteristic |
| 911 | C8 | — | 2 | 2 | no | — |
| 912 | C8 | — | 2 | 2 | no | — |
| 913 | C8 | — | 2 | 1 | no | — |
| 914 | C8 | — | 2 | 1 | no | — |
| 915 | C8 | — | 2 | 1 | no | — |
| 916 | C8 | — | 2 | 1 | no | — |
| 917 | C8 | — | 8 | 4 | no | — |
| 918 | C8 | — | 8 | 2 | no | — |
| 919 | C8 | — | 16 | 1 | no | — |
| 920 | C8 | C22×#357 | 1 | 1 | yes | characteristic |
| 921 | C8 | #33381 | 1 | 1 | yes | characteristic |
| 922 | C8 | C2×#2177 | 1 | 1 | yes | characteristic |
| 923 | C8 | #33456 | 1 | 1 | yes | characteristic |
| 924 | C8 | #33830 | 1 | 2 | yes | — |
| 925 | C8 | #33861 | 1 | 1 | yes | characteristic |
| 926 | C8 | #33862 | 1 | 1 | yes | characteristic |
| 927 | C22 | — | 4 | 8 | no | — |
| 928 | C22 | — | 4 | 4 | no | — |
| 929 | C22 | — | 8 | 2 | no | — |
| 930 | C22 | — | 8 | 4 | no | — |
| 931 | C22 | — | 8 | 4 | no | — |
| 932 | C22 | — | 8 | 2 | no | — |
| 933 | C22 | — | 8 | 4 | no | — |
| 934 | C22 | — | 8 | 4 | no | — |
| 935 | C22 | — | 8 | 4 | no | — |
| 936 | C22 | — | 8 | 4 | no | — |
| 937 | C22 | — | 8 | 4 | no | — |
| 938 | C22 | — | 8 | 4 | no | — |
| 939 | C22 | — | 32 | 4 | no | — |
| 940 | C22 | — | 32 | 4 | no | — |
| 941 | C22 | — | 32 | 4 | no | — |
| 942 | C22 | — | 64 | 32 | no | — |
| 943 | C22 | — | 64 | 2 | no | — |
| 944 | C22 | — | 64 | 2 | no | — |
| 945 | C22 | — | 64 | 2 | no | — |
| 946 | C22 | — | 64 | 2 | no | — |
| 947 | C22 | D8×#102 | 1 | 1 | yes | characteristic |
| 948 | C22 | #492504 | 1 | 2 | yes | — |
| 949 | C22 | D8×D16 | 1 | 1 | yes | characteristic |
| 950 | C22 | D8×SD32 | 1 | 1 | yes | characteristic |
| 951 | C22 | #492528 | 1 | 2 | yes | — |
| 952 | C4 | — | 2 | 1 | no | — |
| 953 | C4 | — | 2 | 1 | no | — |
| 954 | C4 | — | 8 | 2 | no | — |
| 955 | C4 | — | 8 | 4 | no | — |
| 956 | C4 | — | 16 | 2 | no | — |
| 957 | C4 | — | 64 | 2 | no | — |
| 958 | C4 | #492534 | 1 | 1 | yes | characteristic |
| 959 | C4 | #492535 | 1 | 1 | yes | characteristic |
| 960 | C4 | #492586 | 1 | 2 | yes | — |
| 961 | C4 | D4×#357 | 1 | 1 | yes | characteristic |
| 962 | C4 | #497404 | 1 | 1 | yes | characteristic |
| 963 | C4 | #497432 | 1 | 1 | yes | characteristic |
| 964 | C4 | #497459 | 1 | 1 | yes | characteristic |
| 965 | C2 | — | 8 | 8 | no | — |
| 966 | C2 | — | 8 | 4 | no | — |
| 967 | C2 | — | 64 | 4 | no | — |
| 968 | C2 | #72216412 | 1 | 1 | yes | characteristic |
| 969 | C2 | D8×#357 | 1 | 1 | yes | characteristic |
| 970 | C2 | #72226890 | 1 | 1 | yes | characteristic |
| 971 | C2 | #72226920 | 1 | 2 | yes | — |
| 972 | C2 | #72226921 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | D82 |
| commutator | C82 | C23×C4 |
| Frattini, cosocle | C2×C82 | C24 |
| prime radical | C2×D8×D16 | C2 |
| LCS | G ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C42 ◁ C2×C82 ◁ G | |
| LECS | G ▷ C2×C82 ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72226914 | C2 | semidirect |
| 2. D8×#357 | C2 | semidirect |
| 3. #72226853 | C2 | semidirect |
| 4. #72226833 | C2 | semidirect |
| 5. #72225597 | C2 | semidirect |
| 7. #72225386 | C2 | semidirect |
| 8. C2×#122946 | C2 | semidirect |
| 9. #72225188 | C2 | semidirect |
| 10. #72225182 | C2 | semidirect |
| 11. #72216196 | C2 | semidirect |
| 17. D8×D16 | C4 | semidirect |
| 24. C2×C16×D8 | C22 | semidirect |
| 25. D8×#107 | C22 | semidirect |
| 26. #141665 | C22 | semidirect |
| 27. #141665 | C22 | semidirect |
| 28. #141247 | C22 | semidirect |
| 33. #135778 | C22 | semidirect |
| 35. #134950 | C22 | semidirect |
| 37. #129140 | C22 | semidirect |
| 40. C2×#7101 | C22 | semidirect |
| 41. C2×#7096 | C22 | semidirect |
| 43. C2×#7068 | C22 | semidirect |
| 44. C2×#7052 | C22 | semidirect |
| 45. #93064 | C22 | semidirect |
| 46. #92931 | C22 | semidirect |
| 47. #92911 | C22 | semidirect |
| 68. D82 | C2×C4 | semidirect |
| 91. #12515 | C2×C4 | semidirect |
| 94. #12424 | C2×C4 | semidirect |
| 101. C16×D8 | C2×C4 | semidirect |
| 592. D16 | #357 | semidirect |
| 759. D8 | C2×#357 | semidirect |
| 760. D8 | #2177 | semidirect |
| 830. C16 | C2×#357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72226914 | 2 |
| D8×#357 | 2 |
| #72226853 | 2 |
| #72226833 | 2 |
| #72225597 | 2 |
| C2×D8×D16 | 2 |
| #72225386 | 2 |
| C2×#122946 | 2 |
| #72225188 | 2 |
| #72225182 | 2 |
| #72216196 | 2 |