Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1608 conjugacy classes of subgroups.
The subgroup lattice has 782 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72226926 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72226877 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72226848 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D8×#367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225600 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#123363 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72225386 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72225377 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72225202 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #72225188 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #72216196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #498562 | — | 2 | 1 | no | — |
| 13 | #498306 | — | 2 | 2 | no | — |
| 14 | D4×#367 | — | 2 | 1 | no | — |
| 15 | C2×#12515 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#12424 | C22 | 1 | 2 | yes | — |
| 17 | C2×C16×D8 | C22 | 1 | 1 | yes | characteristic |
| 18 | #231561 | C22 | 1 | 2 | yes | — |
| 19 | D8×#107 | C22 | 1 | 2 | yes | — |
| 20 | #141665 | C22 | 1 | 2 | yes | — |
| 21 | #141665 | C22 | 1 | 2 | yes | — |
| 22 | #141258 | — | 2 | 1 | no | — |
| 23 | #141247 | C22 | 1 | 2 | yes | — |
| 24 | #140433 | C22 | 1 | 2 | yes | — |
| 25 | #140433 | C22 | 1 | 2 | yes | — |
| 26 | #140233 | — | 2 | 2 | no | — |
| 27 | #137536 | — | 2 | 2 | no | — |
| 28 | #136893 | — | 2 | 2 | no | — |
| 29 | #136495 | — | 2 | 2 | no | — |
| 30 | #136331 | — | 2 | 2 | no | — |
| 31 | #135778 | C22 | 1 | 1 | yes | characteristic |
| 32 | #134960 | — | 2 | 1 | no | — |
| 33 | C8×#367 | C22 | 1 | 1 | yes | characteristic |
| 34 | #129140 | C22 | 1 | 1 | yes | characteristic |
| 35 | #129140 | C22 | 1 | 2 | yes | — |
| 36 | C8×#357 | C22 | 1 | 1 | yes | characteristic |
| 37 | #123363 | C4 | 1 | 8 | yes | complemented |
| 38 | C2×#7100 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#7096 | C22 | 1 | 2 | yes | — |
| 40 | C2×#7068 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#7052 | C22 | 1 | 1 | yes | characteristic |
| 42 | #93064 | C22 | 1 | 2 | yes | — |
| 43 | #92931 | C22 | 1 | 2 | yes | — |
| 44 | #92931 | C22 | 1 | 1 | yes | characteristic |
| 45 | #92911 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×#2246 | — | 2 | 1 | no | — |
| 47 | C2×#2246 | — | 2 | 1 | no | — |
| 48 | C2×#2206 | — | 2 | 2 | no | — |
| 49 | C2×#2177 | — | 4 | 1 | no | — |
| 50 | C2×#2177 | — | 4 | 2 | no | — |
| 51 | C2×D4×C16 | — | 2 | 1 | no | — |
| 52 | C22×#367 | — | 4 | 1 | no | — |
| 53 | #23185 | — | 2 | 2 | no | — |
| 54 | #23185 | — | 2 | 2 | no | — |
| 55 | C4⋊C4×D8 | — | 2 | 2 | no | — |
| 56 | D4×#107 | — | 2 | 2 | no | — |
| 57 | C2×#1712 | C23 | 1 | 2 | yes | — |
| 58 | C2×C8×D8 | C23 | 1 | 1 | yes | characteristic |
| 59 | #13252 | — | 2 | 2 | no | — |
| 60 | #13239 | — | 4 | 1 | no | — |
| 61 | #13202 | — | 2 | 2 | no | — |
| 62 | #13202 | — | 2 | 2 | no | — |
| 63 | #13202 | — | 4 | 2 | no | — |
| 64 | #13177 | — | 2 | 2 | no | — |
| 65 | #13177 | — | 2 | 2 | no | — |
| 66 | #13149 | — | 4 | 2 | no | — |
| 67 | #13012 | — | 4 | 2 | no | — |
| 68 | #13012 | — | 4 | 2 | no | — |
| 69 | #12937 | — | 4 | 2 | no | — |
| 70 | #12920 | — | 4 | 2 | no | — |
| 71 | #12906 | — | 2 | 1 | no | — |
| 72 | #12906 | — | 2 | 1 | no | — |
| 73 | #12835 | — | 4 | 1 | no | — |
| 74 | C4×#367 | D4 | 1 | 1 | yes | characteristic |
| 75 | #12662 | — | 2 | 2 | no | — |
| 76 | #12662 | — | 2 | 1 | no | — |
| 77 | C4×#357 | D4 | 1 | 1 | yes | characteristic |
| 78 | #12515 | — | 2 | 2 | no | — |
| 79 | #12515 | C2×C4 | 1 | 4 | yes | complemented |
| 80 | #12424 | — | 2 | 4 | no | — |
| 81 | #12424 | C2×C4 | 1 | 8 | yes | complemented |
| 82 | C16×D8 | — | 2 | 2 | no | — |
| 83 | C16×D8 | C2×C4 | 1 | 4 | yes | complemented |
| 84 | C2×#1372 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×#1370 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×#1370 | C23 | 1 | 2 | yes | — |
| 87 | C2×#1370 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#1361 | — | 2 | 2 | no | — |
| 89 | C2×#1361 | — | 2 | 2 | no | — |
| 90 | C2×#1331 | D4 | 1 | 1 | yes | characteristic |
| 91 | C2×D4⋊C16 | — | 2 | 1 | no | — |
| 92 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 95 | #9734 | — | 2 | 2 | no | — |
| 96 | #9734 | — | 2 | 2 | no | — |
| 97 | #9614 | — | 2 | 2 | no | — |
| 98 | #9061 | — | 4 | 2 | no | — |
| 99 | #8882 | — | 4 | 2 | no | — |
| 100 | #8818 | C23 | 1 | 2 | yes | — |
| 101 | #8644 | — | 2 | 2 | no | — |
| 102 | C8×#107 | C23 | 1 | 2 | yes | — |
| 103 | C8×#107 | C23 | 1 | 1 | yes | characteristic |
| 104 | #7274 | — | 2 | 2 | no | — |
| 105 | #7274 | — | 2 | 2 | no | — |
| 106 | #7171 | D4 | 1 | 1 | yes | characteristic |
| 107 | #7171 | D4 | 1 | 2 | yes | — |
| 108 | #7167 | — | 2 | 2 | no | — |
| 109 | #7167 | — | 2 | 1 | no | — |
| 110 | #7154 | D4 | 1 | 1 | yes | characteristic |
| 111 | #7100 | C2×C4 | 1 | 4 | yes | complemented |
| 112 | #7096 | C2×C4 | 1 | 8 | yes | complemented |
| 113 | #7068 | — | 2 | 2 | no | — |
| 114 | #7052 | — | 2 | 2 | no | — |
| 115 | C22×D16 | — | 4 | 1 | no | — |
| 116 | C22×D16 | — | 4 | 1 | no | — |
| 117 | C22×D16 | — | 4 | 2 | no | — |
| 118 | C22×D16 | — | 8 | 1 | no | — |
| 119 | C23×C16 | — | 4 | 1 | no | — |
| 120 | C2×#493 | — | 2 | 2 | no | — |
| 121 | C2×#493 | — | 2 | 2 | no | — |
| 122 | C2×#493 | — | 2 | 2 | no | — |
| 123 | C2×C4×D8 | — | 4 | 2 | no | — |
| 124 | C2×C4×D8 | — | 4 | 2 | no | — |
| 125 | C2×C4×D8 | — | 4 | 2 | no | — |
| 126 | C2×C4×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C2×C8×D4 | — | 2 | 1 | no | — |
| 128 | C22×#107 | — | 4 | 2 | no | — |
| 129 | #2366 | — | 4 | 2 | no | — |
| 130 | D4×C4⋊C4 | — | 4 | 2 | no | — |
| 131 | #2246 | — | 2 | 4 | no | — |
| 132 | #2246 | — | 2 | 4 | no | — |
| 133 | #2246 | — | 4 | 2 | no | — |
| 134 | #2246 | — | 8 | 1 | no | — |
| 135 | #2206 | — | 2 | 8 | no | — |
| 136 | #2206 | — | 4 | 4 | no | — |
| 137 | #2177 | — | 8 | 8 | no | — |
| 138 | #2177 | — | 8 | 4 | no | — |
| 139 | D4×C16 | — | 2 | 4 | no | — |
| 140 | D4×C16 | — | 4 | 2 | no | — |
| 141 | C2×#367 | — | 4 | 1 | no | — |
| 142 | C2×#367 | — | 4 | 2 | no | — |
| 143 | C2×#367 | — | 4 | 2 | no | — |
| 144 | C2×#367 | — | 4 | 1 | no | — |
| 145 | C2×#367 | — | 8 | 4 | no | — |
| 146 | C2×#367 | — | 8 | 1 | no | — |
| 147 | C2×#367 | D8 | 1 | 1 | yes | characteristic |
| 148 | C2×#367 | D8 | 1 | 1 | yes | characteristic |
| 149 | C2×C4⋊C16 | — | 2 | 2 | no | — |
| 150 | C2×C4⋊C16 | — | 2 | 1 | no | — |
| 151 | C2×C4⋊C16 | — | 2 | 1 | no | — |
| 152 | C2×#357 | — | 4 | 2 | no | — |
| 153 | C2×#357 | — | 4 | 2 | no | — |
| 154 | C2×#357 | — | 4 | 2 | no | — |
| 155 | C2×#357 | — | 4 | 2 | no | — |
| 156 | C2×#357 | — | 4 | 2 | no | — |
| 157 | C2×#357 | — | 8 | 2 | no | — |
| 158 | C2×#357 | — | 8 | 4 | no | — |
| 159 | C2×#357 | D8 | 1 | 2 | yes | — |
| 160 | C2×C22⋊C16 | — | 4 | 1 | no | — |
| 161 | C2×#346 | — | 4 | 2 | no | — |
| 162 | C2×#346 | — | 4 | 1 | no | — |
| 163 | C2×C4×C16 | — | 2 | 1 | no | — |
| 164 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | #1982 | — | 4 | 2 | no | — |
| 169 | #1982 | — | 4 | 2 | no | — |
| 170 | #1970 | — | 4 | 2 | no | — |
| 171 | #1970 | — | 4 | 2 | no | — |
| 172 | #1947 | — | 4 | 2 | no | — |
| 173 | #1942 | — | 4 | 2 | no | — |
| 174 | #1879 | — | 8 | 2 | no | — |
| 175 | #1879 | — | 8 | 2 | no | — |
| 176 | #1862 | — | 8 | 2 | no | — |
| 177 | #1852 | — | 8 | 2 | no | — |
| 178 | #1845 | — | 2 | 2 | no | — |
| 179 | #1845 | — | 2 | 2 | no | — |
| 180 | #1845 | — | 2 | 2 | no | — |
| 181 | #1808 | — | 4 | 2 | no | — |
| 182 | #1802 | — | 4 | 2 | no | — |
| 183 | C4×#107 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C4×#107 | C2×D4 | 1 | 2 | yes | — |
| 185 | C8×C4⋊C4 | — | 2 | 1 | no | — |
| 186 | C8×C4⋊C4 | — | 2 | 2 | no | — |
| 187 | #1712 | — | 2 | 2 | no | — |
| 188 | #1712 | — | 2 | 2 | no | — |
| 189 | #1712 | — | 2 | 2 | no | — |
| 190 | #1712 | C22×C4 | 1 | 4 | yes | — |
| 191 | C8×D8 | — | 2 | 1 | no | — |
| 192 | C8×D8 | — | 2 | 1 | no | — |
| 193 | C8×D8 | C22×C4 | 1 | 2 | yes | — |
| 194 | C8×D8 | #41 | 1 | 2 | yes | — |
| 195 | C2×#335 | C2×D4 | 1 | 2 | yes | — |
| 196 | C2×#335 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×#335 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×#331 | — | 4 | 2 | no | — |
| 199 | C2×D4⋊C8 | — | 2 | 1 | no | — |
| 200 | C2×C82 | C24 | 1 | 1 | yes | characteristic |
| 201 | #1380 | — | 4 | 2 | no | — |
| 202 | #1380 | — | 4 | 2 | no | — |
| 203 | #1380 | D8 | 1 | 2 | yes | — |
| 204 | #1380 | D8 | 1 | 2 | yes | — |
| 205 | #1374 | — | 4 | 2 | no | — |
| 206 | #1374 | — | 4 | 1 | no | — |
| 207 | #1372 | — | 2 | 2 | no | — |
| 208 | #1370 | — | 2 | 1 | no | — |
| 209 | #1370 | — | 2 | 2 | no | — |
| 210 | #1370 | — | 2 | 1 | no | — |
| 211 | #1370 | — | 2 | 1 | no | — |
| 212 | #1370 | C22×C4 | 1 | 2 | yes | — |
| 213 | #1370 | C22×C4 | 1 | 4 | yes | — |
| 214 | #1361 | — | 2 | 8 | no | — |
| 215 | #1361 | — | 8 | 2 | no | — |
| 216 | #1331 | — | 2 | 2 | no | — |
| 217 | D4⋊C16 | — | 2 | 4 | no | — |
| 218 | C8×C16 | — | 2 | 1 | no | — |
| 219 | C8×C16 | — | 2 | 1 | no | — |
| 220 | C8×C16 | — | 2 | 1 | no | — |
| 221 | C8×C16 | — | 2 | 1 | no | — |
| 222 | C8×C16 | C22×C4 | 1 | 2 | yes | — |
| 223 | C8×C16 | #41 | 1 | 2 | yes | — |
| 224 | #1296 | — | 4 | 2 | no | — |
| 225 | #1279 | — | 2 | 1 | no | — |
| 226 | #1279 | — | 2 | 2 | no | — |
| 227 | C22×D8 | — | 4 | 2 | no | — |
| 228 | C22×D8 | — | 4 | 2 | no | — |
| 229 | C22×D8 | — | 4 | 2 | no | — |
| 230 | C22×D8 | — | 4 | 2 | no | — |
| 231 | C22×D8 | — | 8 | 2 | no | — |
| 232 | C22×D8 | C2×D8 | 1 | 1 | yes | characteristic |
| 233 | C23×C8 | — | 4 | 1 | no | — |
| 234 | C2×#127 | — | 4 | 2 | no | — |
| 235 | C2×C4×D4 | — | 2 | 1 | no | — |
| 236 | C2×C4×D4 | — | 8 | 2 | no | — |
| 237 | C2×C4×D4 | — | 8 | 2 | no | — |
| 238 | C2×C4×D4 | — | 8 | 2 | no | — |
| 239 | C22×C4⋊C4 | — | 8 | 2 | no | — |
| 240 | C2×D16 | — | 4 | 8 | no | — |
| 241 | C2×D16 | — | 4 | 4 | no | — |
| 242 | C2×D16 | — | 4 | 4 | no | — |
| 243 | C2×D16 | — | 8 | 4 | no | — |
| 244 | C2×D16 | — | 8 | 4 | no | — |
| 245 | C2×D16 | — | 8 | 4 | no | — |
| 246 | C2×D16 | — | 8 | 2 | no | — |
| 247 | C2×D16 | — | 8 | 2 | no | — |
| 248 | C2×D16 | — | 16 | 1 | no | — |
| 249 | C2×D16 | — | 16 | 1 | no | — |
| 250 | C2×D16 | — | 16 | 2 | no | — |
| 251 | C2×D16 | — | 16 | 2 | no | — |
| 252 | C22×C16 | — | 2 | 1 | no | — |
| 253 | C22×C16 | — | 2 | 2 | no | — |
| 254 | C22×C16 | — | 2 | 1 | no | — |
| 255 | C22×C16 | — | 4 | 2 | no | — |
| 256 | C22×C16 | — | 4 | 1 | no | — |
| 257 | C22×C16 | — | 4 | 4 | no | — |
| 258 | C22×C16 | — | 4 | 1 | no | — |
| 259 | C22×C16 | — | 8 | 2 | no | — |
| 260 | C22×C16 | — | 8 | 2 | no | — |
| 261 | C22×C16 | C2×D8 | 1 | 2 | yes | — |
| 262 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 263 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 264 | #493 | — | 2 | 4 | no | — |
| 265 | #493 | — | 2 | 4 | no | — |
| 266 | #493 | — | 2 | 4 | no | — |
| 267 | #493 | — | 4 | 2 | no | — |
| 268 | #493 | — | 4 | 2 | no | — |
| 269 | #493 | — | 4 | 2 | no | — |
| 270 | #493 | — | 4 | 2 | no | — |
| 271 | #493 | — | 4 | 2 | no | — |
| 272 | #493 | — | 4 | 2 | no | — |
| 273 | #493 | — | 4 | 2 | no | — |
| 274 | #493 | — | 8 | 2 | no | — |
| 275 | C4×D8 | — | 2 | 1 | no | — |
| 276 | C4×D8 | — | 2 | 1 | no | — |
| 277 | C4×D8 | — | 8 | 4 | no | — |
| 278 | C4×D8 | — | 8 | 4 | no | — |
| 279 | C4×D8 | — | 8 | 4 | no | — |
| 280 | C4×D8 | — | 16 | 2 | no | — |
| 281 | C4×D8 | — | 16 | 2 | no | — |
| 282 | C4×D8 | — | 16 | 2 | no | — |
| 283 | C4×D8 | C4×D4 | 1 | 2 | yes | — |
| 284 | C4×D8 | #135 | 1 | 2 | yes | — |
| 285 | C8×D4 | — | 2 | 2 | no | — |
| 286 | C8×D4 | — | 2 | 2 | no | — |
| 287 | C8×D4 | — | 4 | 1 | no | — |
| 288 | C8×D4 | — | 4 | 1 | no | — |
| 289 | C2×#107 | — | 4 | 2 | no | — |
| 290 | C2×#107 | — | 4 | 2 | no | — |
| 291 | C2×#107 | — | 4 | 2 | no | — |
| 292 | C2×#107 | — | 4 | 2 | no | — |
| 293 | C2×#107 | — | 8 | 4 | no | — |
| 294 | C2×#107 | — | 8 | 2 | no | — |
| 295 | C2×#107 | — | 8 | 2 | no | — |
| 296 | C2×#107 | — | 16 | 2 | no | — |
| 297 | C2×#107 | C2×D8 | 1 | 2 | yes | — |
| 298 | C2×#107 | C2×D8 | 1 | 2 | yes | — |
| 299 | C2×#107 | C2×D8 | 1 | 2 | yes | — |
| 300 | C2×#107 | C2×D8 | 1 | 1 | yes | characteristic |
| 301 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 302 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 303 | C2×C4⋊C8 | — | 2 | 2 | no | — |
| 304 | C2×#102 | — | 2 | 1 | no | — |
| 305 | C2×#102 | — | 8 | 2 | no | — |
| 306 | C2×#102 | — | 8 | 2 | no | — |
| 307 | C2×#102 | — | 8 | 2 | no | — |
| 308 | C2×#102 | — | 8 | 2 | no | — |
| 309 | C2×#102 | — | 8 | 2 | no | — |
| 310 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 311 | C2×C4×C8 | — | 4 | 2 | no | — |
| 312 | C2×C4×C8 | — | 4 | 1 | no | — |
| 313 | C2×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | C2×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 315 | C2×C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 316 | #390 | — | 8 | 2 | no | — |
| 317 | #390 | — | 8 | 2 | no | — |
| 318 | #389 | — | 8 | 2 | no | — |
| 319 | #386 | — | 16 | 2 | no | — |
| 320 | #385 | — | 16 | 2 | no | — |
| 321 | #384 | — | 4 | 2 | no | — |
| 322 | #380 | — | 8 | 2 | no | — |
| 323 | C4×C4⋊C4 | — | 2 | 2 | no | — |
| 324 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 325 | #367 | — | 2 | 2 | no | — |
| 326 | #367 | — | 2 | 2 | no | — |
| 327 | #367 | — | 8 | 4 | no | — |
| 328 | #367 | — | 8 | 4 | no | — |
| 329 | #367 | — | 8 | 2 | no | — |
| 330 | #367 | — | 16 | 1 | no | — |
| 331 | #367 | — | 16 | 2 | no | — |
| 332 | C4⋊C16 | — | 2 | 2 | no | — |
| 333 | C4⋊C16 | — | 2 | 4 | no | — |
| 334 | C4⋊C16 | — | 4 | 1 | no | — |
| 335 | C4⋊C16 | — | 4 | 1 | no | — |
| 336 | C4⋊C16 | — | 4 | 2 | no | — |
| 337 | C4⋊C16 | — | 4 | 1 | no | — |
| 338 | #357 | — | 2 | 4 | no | — |
| 339 | #357 | — | 4 | 8 | no | — |
| 340 | #357 | — | 8 | 4 | no | — |
| 341 | #357 | — | 8 | 4 | no | — |
| 342 | #357 | — | 16 | 2 | no | — |
| 343 | #357 | — | 16 | 2 | no | — |
| 344 | #357 | — | 16 | 4 | no | — |
| 345 | #357 | — | 16 | 8 | no | — |
| 346 | C22⋊C16 | — | 4 | 4 | no | — |
| 347 | #346 | — | 8 | 4 | no | — |
| 348 | #346 | — | 8 | 2 | no | — |
| 349 | C4×C16 | — | 2 | 1 | no | — |
| 350 | C4×C16 | — | 2 | 1 | no | — |
| 351 | C4×C16 | — | 2 | 1 | no | — |
| 352 | C4×C16 | — | 2 | 1 | no | — |
| 353 | C4×C16 | — | 2 | 1 | no | — |
| 354 | C4×C16 | — | 4 | 1 | no | — |
| 355 | C4×C16 | — | 4 | 1 | no | — |
| 356 | C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 357 | C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 358 | C4×C16 | #135 | 1 | 2 | yes | — |
| 359 | #340 | — | 2 | 2 | no | — |
| 360 | #340 | — | 2 | 1 | no | — |
| 361 | #340 | — | 8 | 2 | no | — |
| 362 | #340 | — | 8 | 2 | no | — |
| 363 | #336 | — | 4 | 2 | no | — |
| 364 | #336 | — | 4 | 1 | no | — |
| 365 | #335 | — | 2 | 1 | no | — |
| 366 | #335 | — | 2 | 1 | no | — |
| 367 | #335 | — | 2 | 2 | no | — |
| 368 | #335 | — | 2 | 2 | no | — |
| 369 | #335 | — | 2 | 1 | no | — |
| 370 | #335 | C4×D4 | 1 | 2 | yes | — |
| 371 | #331 | — | 16 | 2 | no | — |
| 372 | D4⋊C8 | — | 2 | 2 | no | — |
| 373 | D4⋊C8 | — | 2 | 2 | no | — |
| 374 | C82 | C23×C4 | 1 | 1 | yes | characteristic |
| 375 | C82 | C2×#41 | 1 | 1 | yes | characteristic |
| 376 | C82 | C2×#41 | 1 | 1 | yes | characteristic |
| 377 | C82 | 2−1+4 | 1 | 1 | yes | characteristic |
| 378 | C22×D4 | — | 2 | 1 | no | — |
| 379 | C22×D4 | — | 8 | 2 | no | — |
| 380 | C22×D4 | — | 8 | 2 | no | — |
| 381 | C22×D4 | — | 8 | 2 | no | — |
| 382 | C23×C4 | — | 4 | 1 | no | — |
| 383 | C23×C4 | — | 16 | 2 | no | — |
| 384 | C23×C4 | — | 16 | 2 | no | — |
| 385 | C2×D8 | — | 2 | 1 | no | — |
| 386 | C2×D8 | — | 2 | 2 | no | — |
| 387 | C2×D8 | — | 4 | 4 | no | — |
| 388 | C2×D8 | — | 4 | 4 | no | — |
| 389 | C2×D8 | — | 4 | 4 | no | — |
| 390 | C2×D8 | — | 4 | 4 | no | — |
| 391 | C2×D8 | — | 8 | 4 | no | — |
| 392 | C2×D8 | — | 8 | 2 | no | — |
| 393 | C2×D8 | — | 8 | 2 | no | — |
| 394 | C2×D8 | — | 8 | 2 | no | — |
| 395 | C2×D8 | — | 8 | 2 | no | — |
| 396 | C2×D8 | — | 8 | 2 | no | — |
| 397 | C2×D8 | — | 8 | 2 | no | — |
| 398 | C2×D8 | — | 8 | 2 | no | — |
| 399 | C2×D8 | — | 8 | 2 | no | — |
| 400 | C2×D8 | — | 8 | 2 | no | — |
| 401 | C2×D8 | — | 8 | 2 | no | — |
| 402 | C2×D8 | — | 8 | 2 | no | — |
| 403 | C2×D8 | — | 8 | 2 | no | — |
| 404 | C2×D8 | — | 16 | 2 | no | — |
| 405 | C2×D8 | — | 16 | 2 | no | — |
| 406 | C2×D8 | — | 16 | 2 | no | — |
| 407 | C2×D8 | — | 16 | 2 | no | — |
| 408 | C2×D8 | — | 16 | 4 | no | — |
| 409 | C2×D8 | — | 16 | 4 | no | — |
| 410 | C2×D8 | — | 16 | 2 | no | — |
| 411 | C2×D8 | C4×D8 | 1 | 2 | yes | — |
| 412 | C2×D8 | #509 | 1 | 4 | yes | — |
| 413 | C22×C8 | — | 2 | 1 | no | — |
| 414 | C22×C8 | — | 4 | 1 | no | — |
| 415 | C22×C8 | — | 4 | 2 | no | — |
| 416 | C22×C8 | — | 4 | 2 | no | — |
| 417 | C22×C8 | — | 4 | 2 | no | — |
| 418 | C22×C8 | — | 4 | 1 | no | — |
| 419 | C22×C8 | — | 8 | 1 | no | — |
| 420 | C22×C8 | — | 8 | 1 | no | — |
| 421 | C22×C8 | — | 8 | 1 | no | — |
| 422 | C22×C8 | — | 8 | 1 | no | — |
| 423 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 424 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 425 | C22×C8 | #576 | 1 | 1 | yes | characteristic |
| 426 | C22×C8 | #576 | 1 | 1 | yes | characteristic |
| 427 | #127 | — | 4 | 4 | no | — |
| 428 | #127 | — | 8 | 2 | no | — |
| 429 | #127 | — | 8 | 2 | no | — |
| 430 | #127 | — | 8 | 2 | no | — |
| 431 | C4×D4 | — | 2 | 2 | no | — |
| 432 | C4×D4 | — | 2 | 2 | no | — |
| 433 | C4×D4 | — | 4 | 1 | no | — |
| 434 | C4×D4 | — | 4 | 1 | no | — |
| 435 | C4×D4 | — | 16 | 4 | no | — |
| 436 | C4×D4 | — | 16 | 4 | no | — |
| 437 | C4×D4 | — | 16 | 4 | no | — |
| 438 | C4×D4 | — | 32 | 2 | no | — |
| 439 | C4×D4 | — | 32 | 2 | no | — |
| 440 | C4×D4 | — | 32 | 2 | no | — |
| 441 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 442 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 443 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 444 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 445 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 446 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 447 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 448 | C2×C4⋊C4 | — | 16 | 4 | no | — |
| 449 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 450 | C2×C4⋊C4 | — | 32 | 2 | no | — |
| 451 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 452 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 453 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 454 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 455 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 456 | C2×C42 | — | 4 | 2 | no | — |
| 457 | C2×C42 | — | 4 | 1 | no | — |
| 458 | C2×C42 | D42 | 1 | 1 | yes | characteristic |
| 459 | D16 | — | 8 | 16 | no | — |
| 460 | D16 | — | 8 | 8 | no | — |
| 461 | D16 | — | 16 | 4 | no | — |
| 462 | D16 | — | 16 | 8 | no | — |
| 463 | C2×C16 | — | 2 | 2 | no | — |
| 464 | C2×C16 | — | 2 | 2 | no | — |
| 465 | C2×C16 | — | 2 | 1 | no | — |
| 466 | C2×C16 | — | 2 | 1 | no | — |
| 467 | C2×C16 | — | 2 | 2 | no | — |
| 468 | C2×C16 | — | 2 | 2 | no | — |
| 469 | C2×C16 | — | 2 | 2 | no | — |
| 470 | C2×C16 | — | 2 | 2 | no | — |
| 471 | C2×C16 | — | 4 | 2 | no | — |
| 472 | C2×C16 | — | 4 | 4 | no | — |
| 473 | C2×C16 | — | 4 | 2 | no | — |
| 474 | C2×C16 | — | 4 | 1 | no | — |
| 475 | C2×C16 | — | 4 | 2 | no | — |
| 476 | C2×C16 | — | 4 | 4 | no | — |
| 477 | C2×C16 | — | 8 | 2 | no | — |
| 478 | C2×C16 | — | 8 | 1 | no | — |
| 479 | C2×C16 | — | 8 | 1 | no | — |
| 480 | C2×C16 | — | 8 | 2 | no | — |
| 481 | C2×C16 | — | 8 | 8 | no | — |
| 482 | C2×C16 | — | 8 | 1 | no | — |
| 483 | C2×C16 | — | 8 | 1 | no | — |
| 484 | C2×C16 | — | 8 | 1 | no | — |
| 485 | C2×C16 | C4×D8 | 1 | 2 | yes | — |
| 486 | C2×C16 | C4×D8 | 1 | 2 | yes | — |
| 487 | C2×C16 | #509 | 1 | 2 | yes | — |
| 488 | C2×C16 | #509 | 1 | 2 | yes | — |
| 489 | #107 | — | 2 | 1 | no | — |
| 490 | #107 | — | 2 | 2 | no | — |
| 491 | #107 | — | 2 | 2 | no | — |
| 492 | #107 | — | 2 | 2 | no | — |
| 493 | #107 | — | 2 | 2 | no | — |
| 494 | #107 | — | 2 | 2 | no | — |
| 495 | #107 | — | 2 | 2 | no | — |
| 496 | #107 | — | 8 | 2 | no | — |
| 497 | #107 | — | 8 | 2 | no | — |
| 498 | #107 | — | 8 | 2 | no | — |
| 499 | #107 | — | 8 | 2 | no | — |
| 500 | #107 | — | 16 | 4 | no | — |
| 501 | #107 | — | 16 | 2 | no | — |
| 502 | #107 | — | 16 | 2 | no | — |
| 503 | #107 | — | 16 | 4 | no | — |
| 504 | #107 | C4×D8 | 1 | 2 | yes | — |
| 505 | C4⋊C8 | — | 2 | 2 | no | — |
| 506 | C4⋊C8 | — | 4 | 1 | no | — |
| 507 | C4⋊C8 | — | 4 | 2 | no | — |
| 508 | C4⋊C8 | — | 4 | 1 | no | — |
| 509 | C4⋊C8 | — | 4 | 1 | no | — |
| 510 | C4⋊C8 | — | 4 | 2 | no | — |
| 511 | #102 | — | 2 | 2 | no | — |
| 512 | #102 | — | 2 | 2 | no | — |
| 513 | #102 | — | 16 | 4 | no | — |
| 514 | #102 | — | 16 | 4 | no | — |
| 515 | #102 | — | 16 | 4 | no | — |
| 516 | #102 | — | 32 | 2 | no | — |
| 517 | #102 | — | 32 | 2 | no | — |
| 518 | C22⋊C8 | — | 4 | 2 | no | — |
| 519 | C22⋊C8 | — | 4 | 2 | no | — |
| 520 | C4×C8 | — | 2 | 1 | no | — |
| 521 | C4×C8 | — | 8 | 2 | no | — |
| 522 | C4×C8 | — | 8 | 1 | no | — |
| 523 | C4×C8 | — | 8 | 2 | no | — |
| 524 | C4×C8 | — | 8 | 1 | no | — |
| 525 | C4×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 526 | C4×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 527 | C4×C8 | #520 | 1 | 1 | yes | characteristic |
| 528 | C4×C8 | #547 | 1 | 1 | yes | characteristic |
| 529 | C4×C8 | #548 | 1 | 1 | yes | characteristic |
| 530 | C4×C8 | #553 | 1 | 1 | yes | characteristic |
| 531 | C4×C8 | C2×#135 | 1 | 1 | yes | characteristic |
| 532 | C4×C8 | C2×#135 | 1 | 1 | yes | characteristic |
| 533 | C4×C8 | #577 | 1 | 1 | yes | characteristic |
| 534 | C4×C8 | #578 | 1 | 1 | yes | characteristic |
| 535 | #95 | — | 4 | 2 | no | — |
| 536 | #95 | — | 4 | 1 | no | — |
| 537 | #95 | — | 16 | 2 | no | — |
| 538 | C24 | — | 4 | 1 | no | — |
| 539 | C24 | — | 16 | 2 | no | — |
| 540 | C2×D4 | — | 2 | 4 | no | — |
| 541 | C2×D4 | — | 2 | 2 | no | — |
| 542 | C2×D4 | — | 4 | 1 | no | — |
| 543 | C2×D4 | — | 4 | 2 | no | — |
| 544 | C2×D4 | — | 8 | 4 | no | — |
| 545 | C2×D4 | — | 8 | 4 | no | — |
| 546 | C2×D4 | — | 8 | 4 | no | — |
| 547 | C2×D4 | — | 16 | 2 | no | — |
| 548 | C2×D4 | — | 16 | 2 | no | — |
| 549 | C2×D4 | — | 16 | 2 | no | — |
| 550 | C2×D4 | — | 16 | 2 | no | — |
| 551 | C2×D4 | — | 16 | 2 | no | — |
| 552 | C2×D4 | — | 16 | 2 | no | — |
| 553 | C2×D4 | — | 16 | 2 | no | — |
| 554 | C2×D4 | — | 16 | 2 | no | — |
| 555 | C2×D4 | — | 16 | 2 | no | — |
| 556 | C2×D4 | — | 16 | 2 | no | — |
| 557 | C2×D4 | — | 16 | 2 | no | — |
| 558 | C2×D4 | — | 32 | 2 | no | — |
| 559 | C2×D4 | — | 32 | 2 | no | — |
| 560 | C22×C4 | — | 4 | 1 | no | — |
| 561 | C22×C4 | — | 4 | 2 | no | — |
| 562 | C22×C4 | — | 4 | 2 | no | — |
| 563 | C22×C4 | — | 4 | 2 | no | — |
| 564 | C22×C4 | — | 4 | 2 | no | — |
| 565 | C22×C4 | — | 4 | 2 | no | — |
| 566 | C22×C4 | — | 8 | 1 | no | — |
| 567 | C22×C4 | — | 8 | 1 | no | — |
| 568 | C22×C4 | — | 8 | 1 | no | — |
| 569 | C22×C4 | — | 8 | 1 | no | — |
| 570 | C22×C4 | — | 16 | 2 | no | — |
| 571 | C22×C4 | — | 32 | 4 | no | — |
| 572 | C22×C4 | — | 32 | 4 | no | — |
| 573 | C22×C4 | — | 32 | 4 | no | — |
| 574 | C22×C4 | — | 32 | 4 | no | — |
| 575 | C22×C4 | — | 64 | 2 | no | — |
| 576 | C22×C4 | — | 64 | 2 | no | — |
| 577 | C22×C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 578 | C22×C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 579 | C22×C4 | #3292 | 1 | 1 | yes | characteristic |
| 580 | D8 | — | 2 | 4 | no | — |
| 581 | D8 | — | 2 | 2 | no | — |
| 582 | D8 | — | 8 | 4 | no | — |
| 583 | D8 | — | 8 | 4 | no | — |
| 584 | D8 | — | 8 | 4 | no | — |
| 585 | D8 | — | 8 | 4 | no | — |
| 586 | D8 | — | 16 | 4 | no | — |
| 587 | D8 | — | 16 | 4 | no | — |
| 588 | D8 | — | 16 | 8 | no | — |
| 589 | D8 | — | 16 | 2 | no | — |
| 590 | D8 | — | 16 | 2 | no | — |
| 591 | D8 | — | 16 | 2 | no | — |
| 592 | D8 | — | 16 | 2 | no | — |
| 593 | D8 | — | 32 | 2 | no | — |
| 594 | D8 | — | 32 | 2 | no | — |
| 595 | D8 | — | 32 | 4 | no | — |
| 596 | D8 | #2177 | 1 | 4 | yes | complemented |
| 597 | C2×C8 | — | 2 | 4 | no | — |
| 598 | C2×C8 | — | 2 | 1 | no | — |
| 599 | C2×C8 | — | 2 | 1 | no | — |
| 600 | C2×C8 | — | 2 | 2 | no | — |
| 601 | C2×C8 | — | 2 | 1 | no | — |
| 602 | C2×C8 | — | 2 | 1 | no | — |
| 603 | C2×C8 | — | 4 | 2 | no | — |
| 604 | C2×C8 | — | 8 | 1 | no | — |
| 605 | C2×C8 | — | 8 | 1 | no | — |
| 606 | C2×C8 | — | 8 | 2 | no | — |
| 607 | C2×C8 | — | 8 | 2 | no | — |
| 608 | C2×C8 | — | 8 | 2 | no | — |
| 609 | C2×C8 | — | 8 | 2 | no | — |
| 610 | C2×C8 | — | 8 | 2 | no | — |
| 611 | C2×C8 | — | 8 | 1 | no | — |
| 612 | C2×C8 | — | 8 | 2 | no | — |
| 613 | C2×C8 | — | 8 | 1 | no | — |
| 614 | C2×C8 | — | 8 | 2 | no | — |
| 615 | C2×C8 | — | 8 | 1 | no | — |
| 616 | C2×C8 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 617 | C2×C8 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 618 | C2×C8 | #2946 | 1 | 1 | yes | characteristic |
| 619 | C2×C8 | #2951 | 1 | 1 | yes | characteristic |
| 620 | C2×C8 | #3334 | 1 | 1 | yes | characteristic |
| 621 | C2×C8 | #3339 | 1 | 1 | yes | characteristic |
| 622 | C2×C8 | #3358 | 1 | 1 | yes | characteristic |
| 623 | C2×C8 | #3361 | 1 | 1 | yes | characteristic |
| 624 | C2×C8 | C2×#509 | 1 | 2 | yes | — |
| 625 | C2×C8 | C2×#509 | 1 | 1 | yes | characteristic |
| 626 | C2×C8 | C2×#509 | 1 | 1 | yes | characteristic |
| 627 | C2×C8 | #3415 | 1 | 1 | yes | characteristic |
| 628 | C2×C8 | #3416 | 1 | 2 | yes | — |
| 629 | C2×C8 | #3416 | 1 | 1 | yes | characteristic |
| 630 | C4⋊C4 | — | 2 | 2 | no | — |
| 631 | C4⋊C4 | — | 4 | 1 | no | — |
| 632 | C4⋊C4 | — | 4 | 2 | no | — |
| 633 | C4⋊C4 | — | 4 | 2 | no | — |
| 634 | C4⋊C4 | — | 4 | 2 | no | — |
| 635 | C4⋊C4 | — | 4 | 2 | no | — |
| 636 | C4⋊C4 | — | 4 | 2 | no | — |
| 637 | C4⋊C4 | — | 4 | 2 | no | — |
| 638 | C4⋊C4 | — | 16 | 2 | no | — |
| 639 | C4⋊C4 | — | 16 | 2 | no | — |
| 640 | C4⋊C4 | — | 16 | 2 | no | — |
| 641 | C4⋊C4 | — | 16 | 2 | no | — |
| 642 | C4⋊C4 | — | 32 | 2 | no | — |
| 643 | C4⋊C4 | — | 32 | 4 | no | — |
| 644 | C22⋊C4 | — | 4 | 2 | no | — |
| 645 | C22⋊C4 | — | 4 | 2 | no | — |
| 646 | C22⋊C4 | — | 32 | 4 | no | — |
| 647 | C22⋊C4 | — | 32 | 4 | no | — |
| 648 | C22⋊C4 | — | 32 | 4 | no | — |
| 649 | C22⋊C4 | — | 64 | 2 | no | — |
| 650 | C42 | — | 8 | 2 | no | — |
| 651 | C42 | — | 8 | 1 | no | — |
| 652 | C42 | — | 8 | 2 | no | — |
| 653 | C42 | — | 8 | 1 | no | — |
| 654 | C42 | #2361 | 1 | 1 | yes | characteristic |
| 655 | C42 | #3284 | 1 | 1 | yes | characteristic |
| 656 | C42 | #3285 | 1 | 1 | yes | characteristic |
| 657 | C42 | #3290 | 1 | 1 | yes | characteristic |
| 658 | C16 | — | 2 | 4 | no | — |
| 659 | C16 | — | 2 | 2 | no | — |
| 660 | C16 | — | 4 | 2 | no | — |
| 661 | C16 | — | 8 | 2 | no | — |
| 662 | C16 | — | 8 | 1 | no | — |
| 663 | C16 | — | 8 | 2 | no | — |
| 664 | C16 | — | 8 | 4 | no | — |
| 665 | C16 | — | 16 | 1 | no | — |
| 666 | C16 | #2177 | 1 | 4 | yes | complemented |
| 667 | C23 | — | 4 | 2 | no | — |
| 668 | C23 | — | 4 | 4 | no | — |
| 669 | C23 | — | 8 | 1 | no | — |
| 670 | C23 | — | 8 | 1 | no | — |
| 671 | C23 | — | 8 | 2 | no | — |
| 672 | C23 | — | 16 | 4 | no | — |
| 673 | C23 | — | 32 | 2 | no | — |
| 674 | C23 | — | 32 | 2 | no | — |
| 675 | C23 | — | 32 | 2 | no | — |
| 676 | C23 | — | 32 | 2 | no | — |
| 677 | C23 | — | 32 | 2 | no | — |
| 678 | C23 | — | 32 | 2 | no | — |
| 679 | C23 | D82 | 1 | 1 | yes | characteristic |
| 680 | D4 | — | 2 | 4 | no | — |
| 681 | D4 | — | 4 | 4 | no | — |
| 682 | D4 | — | 4 | 2 | no | — |
| 683 | D4 | — | 16 | 4 | no | — |
| 684 | D4 | — | 16 | 4 | no | — |
| 685 | D4 | — | 16 | 4 | no | — |
| 686 | D4 | — | 16 | 4 | no | — |
| 687 | D4 | — | 32 | 4 | no | — |
| 688 | D4 | — | 32 | 2 | no | — |
| 689 | D4 | — | 32 | 2 | no | — |
| 690 | D4 | — | 32 | 2 | no | — |
| 691 | D4 | — | 32 | 2 | no | — |
| 692 | D4 | — | 64 | 2 | no | — |
| 693 | C2×C4 | — | 2 | 2 | no | — |
| 694 | C2×C4 | — | 4 | 2 | no | — |
| 695 | C2×C4 | — | 8 | 1 | no | — |
| 696 | C2×C4 | — | 8 | 1 | no | — |
| 697 | C2×C4 | — | 8 | 2 | no | — |
| 698 | C2×C4 | — | 8 | 2 | no | — |
| 699 | C2×C4 | — | 8 | 2 | no | — |
| 700 | C2×C4 | — | 8 | 2 | no | — |
| 701 | C2×C4 | — | 8 | 2 | no | — |
| 702 | C2×C4 | — | 8 | 2 | no | — |
| 703 | C2×C4 | — | 8 | 2 | no | — |
| 704 | C2×C4 | — | 8 | 2 | no | — |
| 705 | C2×C4 | — | 8 | 2 | no | — |
| 706 | C2×C4 | — | 8 | 2 | no | — |
| 707 | C2×C4 | — | 8 | 2 | no | — |
| 708 | C2×C4 | — | 8 | 2 | no | — |
| 709 | C2×C4 | — | 8 | 2 | no | — |
| 710 | C2×C4 | — | 32 | 2 | no | — |
| 711 | C2×C4 | — | 32 | 2 | no | — |
| 712 | C2×C4 | — | 32 | 2 | no | — |
| 713 | C2×C4 | — | 64 | 8 | no | — |
| 714 | C2×C4 | — | 64 | 8 | no | — |
| 715 | C2×C4 | #19972 | 1 | 1 | yes | characteristic |
| 716 | C2×C4 | #19973 | 1 | 1 | yes | characteristic |
| 717 | C2×C4 | #20012 | 1 | 1 | yes | characteristic |
| 718 | C2×C4 | #22995 | 1 | 1 | yes | characteristic |
| 719 | C2×C4 | #23025 | 1 | 1 | yes | characteristic |
| 720 | C2×C4 | #23046 | 1 | 1 | yes | characteristic |
| 721 | C2×C4 | #33831 | 1 | 2 | yes | — |
| 722 | C2×C4 | #33838 | 1 | 1 | yes | characteristic |
| 723 | C2×C4 | #33840 | 1 | 1 | yes | characteristic |
| 724 | C2×C4 | #33854 | 1 | 2 | yes | — |
| 725 | C2×C4 | #33856 | 1 | 1 | yes | characteristic |
| 726 | C2×C4 | #33858 | 1 | 1 | yes | characteristic |
| 727 | C8 | — | 2 | 2 | no | — |
| 728 | C8 | — | 2 | 2 | no | — |
| 729 | C8 | — | 2 | 1 | no | — |
| 730 | C8 | — | 2 | 1 | no | — |
| 731 | C8 | — | 2 | 1 | no | — |
| 732 | C8 | — | 2 | 1 | no | — |
| 733 | C8 | — | 8 | 2 | no | — |
| 734 | C8 | — | 16 | 2 | no | — |
| 735 | C8 | — | 16 | 1 | no | — |
| 736 | C8 | C2×#2177 | 1 | 1 | yes | characteristic |
| 737 | C8 | C2×#2177 | 1 | 1 | yes | characteristic |
| 738 | C8 | #33454 | 1 | 1 | yes | characteristic |
| 739 | C8 | #33460 | 1 | 1 | yes | characteristic |
| 740 | C8 | #33912 | 1 | 2 | yes | — |
| 741 | C8 | #33933 | 1 | 1 | yes | characteristic |
| 742 | C8 | #33940 | 1 | 1 | yes | characteristic |
| 743 | C22 | — | 4 | 4 | no | — |
| 744 | C22 | — | 8 | 2 | no | — |
| 745 | C22 | — | 8 | 2 | no | — |
| 746 | C22 | — | 8 | 4 | no | — |
| 747 | C22 | — | 8 | 4 | no | — |
| 748 | C22 | — | 32 | 4 | no | — |
| 749 | C22 | — | 32 | 4 | no | — |
| 750 | C22 | — | 32 | 4 | no | — |
| 751 | C22 | — | 64 | 2 | no | — |
| 752 | C22 | — | 64 | 2 | no | — |
| 753 | C22 | — | 64 | 2 | no | — |
| 754 | C22 | — | 64 | 2 | no | — |
| 755 | C22 | #229257 | 1 | 1 | yes | characteristic |
| 756 | C22 | #492505 | 1 | 2 | yes | — |
| 757 | C22 | #492512 | 1 | 1 | yes | characteristic |
| 758 | C22 | #492514 | 1 | 1 | yes | characteristic |
| 759 | C22 | #492528 | 1 | 2 | yes | — |
| 760 | C4 | — | 2 | 1 | no | — |
| 761 | C4 | — | 2 | 1 | no | — |
| 762 | C4 | — | 8 | 2 | no | — |
| 763 | C4 | — | 16 | 2 | no | — |
| 764 | C4 | — | 16 | 2 | no | — |
| 765 | C4 | — | 16 | 2 | no | — |
| 766 | C4 | — | 64 | 2 | no | — |
| 767 | C4 | #492712 | 1 | 2 | yes | — |
| 768 | C4 | #492748 | 1 | 1 | yes | characteristic |
| 769 | C4 | #492754 | 1 | 1 | yes | characteristic |
| 770 | C4 | #498306 | 1 | 1 | yes | characteristic |
| 771 | C4 | #498318 | 1 | 1 | yes | characteristic |
| 772 | C4 | #498355 | 1 | 1 | yes | characteristic |
| 773 | C4 | #498373 | 1 | 1 | yes | characteristic |
| 774 | C2 | — | 8 | 4 | no | — |
| 775 | C2 | — | 64 | 4 | no | — |
| 776 | C2 | #72216414 | 1 | 1 | yes | characteristic |
| 777 | C2 | #72226877 | 1 | 1 | yes | characteristic |
| 778 | C2 | #72226899 | 1 | 1 | yes | characteristic |
| 779 | C2 | #72226945 | 1 | 2 | yes | — |
| 780 | C2 | #72226947 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | D82 |
| commutator | C82 | C23×C4 |
| Frattini, cosocle | C2×C82 | C24 |
| prime radical | C2×#123363 | 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. #72226926 | C2 | semidirect |
| 2. #72226877 | C2 | semidirect |
| 3. #72226848 | C2 | semidirect |
| 4. D8×#367 | C2 | semidirect |
| 5. #72225600 | C2 | semidirect |
| 7. #72225386 | C2 | semidirect |
| 8. #72225377 | C2 | semidirect |
| 9. #72225202 | C2 | semidirect |
| 10. #72225188 | C2 | semidirect |
| 11. #72216196 | C2 | semidirect |
| 37. #123363 | C4 | semidirect |
| 79. #12515 | C2×C4 | semidirect |
| 81. #12424 | C2×C4 | semidirect |
| 83. C16×D8 | C2×C4 | semidirect |
| 111. #7100 | C2×C4 | semidirect |
| 112. #7096 | C2×C4 | semidirect |
| 596. D8 | #2177 | semidirect |
| 666. C16 | #2177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72226926 | 2 |
| #72226877 | 2 |
| #72226848 | 2 |
| D8×#367 | 2 |
| #72225600 | 2 |
| C2×#123363 | 2 |
| #72225386 | 2 |
| #72225377 | 2 |
| #72225202 | 2 |
| #72225188 | 2 |
| #72216196 | 2 |