Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1463 conjugacy classes of subgroups.
The subgroup lattice has 763 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72227226 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72227225 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72227184 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72227103 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72227102 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72225246 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72225245 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72214397 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72213956 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #498578 | — | 2 | 2 | no | — |
| 11 | #491500 | C22 | 1 | 2 | yes | — |
| 12 | #491500 | C22 | 1 | 1 | yes | characteristic |
| 13 | #491469 | C22 | 1 | 2 | yes | — |
| 14 | #491469 | C22 | 1 | 1 | yes | characteristic |
| 15 | #484147 | — | 2 | 2 | no | — |
| 16 | #231729 | C22 | 1 | 1 | yes | characteristic |
| 17 | #231631 | C22 | 1 | 1 | yes | characteristic |
| 18 | #231542 | C22 | 1 | 2 | yes | — |
| 19 | #141341 | C22 | 1 | 2 | yes | — |
| 20 | #141339 | C22 | 1 | 2 | yes | — |
| 21 | #141298 | — | 2 | 2 | no | — |
| 22 | #141296 | C22 | 1 | 2 | yes | — |
| 23 | #141294 | C22 | 1 | 2 | yes | — |
| 24 | #141213 | — | 2 | 2 | no | — |
| 25 | #137549 | — | 2 | 2 | no | — |
| 26 | #137546 | — | 2 | 2 | no | — |
| 27 | #137501 | — | 2 | 2 | no | — |
| 28 | #137499 | — | 2 | 2 | no | — |
| 29 | #129195 | C22 | 1 | 2 | yes | — |
| 30 | #129160 | C22 | 1 | 2 | yes | — |
| 31 | #129158 | C22 | 1 | 2 | yes | — |
| 32 | #123419 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #123419 | C4 | 1 | 2 | yes | complemented |
| 34 | #123412 | C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | #123412 | C4 | 1 | 2 | yes | complemented |
| 36 | #123411 | C4 | 1 | 1 | yes | characteristic, complemented |
| 37 | #123403 | C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | #122923 | C22 | 1 | 2 | yes | — |
| 39 | #122910 | C22 | 1 | 2 | yes | — |
| 40 | #122887 | C22 | 1 | 1 | yes | characteristic |
| 41 | #122868 | C22 | 1 | 1 | yes | characteristic |
| 42 | #122211 | C22 | 1 | 1 | yes | characteristic |
| 43 | #92938 | C22 | 1 | 2 | yes | — |
| 44 | #92937 | C22 | 1 | 2 | yes | — |
| 45 | #33748 | — | 2 | 2 | no | — |
| 46 | #33748 | — | 2 | 2 | no | — |
| 47 | #33748 | — | 4 | 1 | no | — |
| 48 | #33717 | — | 2 | 2 | no | — |
| 49 | #33717 | — | 2 | 2 | no | — |
| 50 | #33717 | — | 4 | 1 | no | — |
| 51 | C2×AGL(1,ℤ/16) | — | 4 | 2 | no | — |
| 52 | #23188 | — | 2 | 2 | no | — |
| 53 | #23180 | — | 2 | 2 | no | — |
| 54 | #19603 | C23 | 1 | 2 | yes | — |
| 55 | #19603 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#1712 | C23 | 1 | 1 | yes | characteristic |
| 57 | #18091 | — | 2 | 2 | no | — |
| 58 | #18073 | — | 2 | 2 | no | — |
| 59 | #13257 | — | 2 | 2 | no | — |
| 60 | #13255 | — | 2 | 2 | no | — |
| 61 | #13249 | — | 4 | 2 | no | — |
| 62 | #13040 | — | 4 | 2 | no | — |
| 63 | #13037 | — | 4 | 2 | no | — |
| 64 | C4×#365 | D4 | 1 | 2 | yes | — |
| 65 | #12666 | — | 2 | 2 | no | — |
| 66 | #12523 | C2×C4 | 1 | 2 | yes | complemented |
| 67 | #12523 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 68 | #12519 | — | 2 | 2 | no | — |
| 69 | #12519 | — | 2 | 2 | no | — |
| 70 | #12519 | — | 4 | 1 | no | — |
| 71 | #12517 | C2×C4 | 1 | 2 | yes | — |
| 72 | #12517 | C2×C4 | 1 | 2 | yes | — |
| 73 | #12517 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #12517 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | #12515 | C2×C4 | 1 | 2 | yes | — |
| 76 | #12515 | C2×C4 | 1 | 2 | yes | — |
| 77 | #12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | #12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | #12515 | C2×C4 | 1 | 2 | yes | complemented |
| 80 | #12515 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 81 | #12509 | C2×C4 | 1 | 2 | yes | complemented |
| 82 | #12509 | C2×C4 | 1 | 2 | yes | complemented |
| 83 | #12509 | C2×C4 | 1 | 2 | yes | complemented |
| 84 | #12506 | — | 2 | 2 | no | — |
| 85 | #12506 | — | 2 | 2 | no | — |
| 86 | #12506 | — | 4 | 1 | no | — |
| 87 | #12089 | — | 4 | 2 | no | — |
| 88 | #12078 | — | 4 | 2 | no | — |
| 89 | #12078 | — | 4 | 2 | no | — |
| 90 | #12067 | — | 4 | 2 | no | — |
| 91 | #12013 | C23 | 1 | 2 | yes | — |
| 92 | #12000 | D4 | 1 | 2 | yes | — |
| 93 | #11996 | C23 | 1 | 2 | yes | — |
| 94 | #11931 | — | 2 | 2 | no | — |
| 95 | #11925 | — | 2 | 2 | no | — |
| 96 | #11751 | — | 2 | 2 | no | — |
| 97 | #11744 | — | 2 | 2 | no | — |
| 98 | #11654 | — | 2 | 2 | no | — |
| 99 | #11652 | — | 2 | 2 | no | — |
| 100 | #11414 | — | 2 | 2 | no | — |
| 101 | C8×M32 | C23 | 1 | 1 | yes | characteristic |
| 102 | C8×M32 | C23 | 1 | 2 | yes | — |
| 103 | #9753 | — | 2 | 2 | no | — |
| 104 | #9743 | — | 2 | 2 | no | — |
| 105 | #9726 | — | 2 | 2 | no | — |
| 106 | #9721 | — | 2 | 2 | no | — |
| 107 | #9069 | — | 4 | 1 | no | — |
| 108 | #9061 | — | 4 | 1 | no | — |
| 109 | #9053 | — | 4 | 2 | no | — |
| 110 | #8293 | C23 | 1 | 2 | yes | — |
| 111 | #8283 | C23 | 1 | 2 | yes | — |
| 112 | #7174 | D4 | 1 | 2 | yes | — |
| 113 | #7173 | D4 | 1 | 2 | yes | — |
| 114 | #7168 | — | 2 | 2 | no | — |
| 115 | #7164 | — | 2 | 2 | no | — |
| 116 | #7099 | — | 2 | 2 | no | — |
| 117 | #7099 | — | 2 | 2 | no | — |
| 118 | #7096 | — | 4 | 1 | no | — |
| 119 | #7094 | — | 4 | 2 | no | — |
| 120 | #7092 | — | 4 | 1 | no | — |
| 121 | #7052 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 122 | #7052 | C2×C4 | 1 | 2 | yes | complemented |
| 123 | C162 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 124 | C2×#509 | — | 4 | 2 | no | — |
| 125 | C2×#509 | — | 4 | 2 | no | — |
| 126 | C2×#509 | — | 8 | 2 | no | — |
| 127 | C2×#509 | — | 8 | 2 | no | — |
| 128 | #3169 | — | 2 | 2 | no | — |
| 129 | #3169 | — | 2 | 2 | no | — |
| 130 | #3169 | — | 2 | 2 | no | — |
| 131 | #3147 | — | 2 | 2 | no | — |
| 132 | #3147 | — | 2 | 1 | no | — |
| 133 | C2×#493 | — | 2 | 2 | no | — |
| 134 | C2×#493 | — | 2 | 1 | no | — |
| 135 | #2979 | — | 4 | 1 | no | — |
| 136 | C2×#444 | — | 4 | 2 | no | — |
| 137 | C2×#442 | — | 4 | 2 | no | — |
| 138 | #2935 | — | 4 | 2 | no | — |
| 139 | #2366 | — | 4 | 1 | no | — |
| 140 | #2254 | — | 2 | 2 | no | — |
| 141 | #2254 | — | 2 | 2 | no | — |
| 142 | #2254 | — | 4 | 1 | no | — |
| 143 | #2250 | — | 4 | 2 | no | — |
| 144 | #2250 | — | 4 | 2 | no | — |
| 145 | #2250 | — | 8 | 2 | no | — |
| 146 | #2250 | — | 8 | 2 | no | — |
| 147 | #2248 | — | 2 | 2 | no | — |
| 148 | #2248 | — | 2 | 2 | no | — |
| 149 | #2248 | — | 2 | 2 | no | — |
| 150 | #2248 | — | 2 | 2 | no | — |
| 151 | #2248 | — | 4 | 1 | no | — |
| 152 | #2248 | — | 4 | 1 | no | — |
| 153 | #2246 | — | 2 | 2 | no | — |
| 154 | #2246 | — | 2 | 2 | no | — |
| 155 | #2246 | — | 2 | 2 | no | — |
| 156 | #2246 | — | 2 | 2 | no | — |
| 157 | #2246 | — | 2 | 2 | no | — |
| 158 | #2246 | — | 2 | 2 | no | — |
| 159 | #2246 | — | 4 | 1 | no | — |
| 160 | #2246 | — | 4 | 1 | no | — |
| 161 | #2246 | — | 4 | 1 | no | — |
| 162 | #2240 | — | 2 | 2 | no | — |
| 163 | #2240 | — | 2 | 2 | no | — |
| 164 | #2240 | — | 2 | 2 | no | — |
| 165 | #2240 | — | 2 | 2 | no | — |
| 166 | #2240 | — | 4 | 2 | no | — |
| 167 | #2218 | — | 4 | 2 | no | — |
| 168 | #2218 | — | 4 | 2 | no | — |
| 169 | #2218 | — | 8 | 2 | no | — |
| 170 | #2218 | — | 8 | 2 | no | — |
| 171 | AGL(1,ℤ/16) | — | 8 | 8 | no | — |
| 172 | #2177 | — | 4 | 2 | no | — |
| 173 | #2177 | — | 4 | 2 | no | — |
| 174 | #2177 | — | 8 | 2 | no | — |
| 175 | #2177 | — | 8 | 2 | no | — |
| 176 | #2163 | — | 2 | 2 | no | — |
| 177 | C2×#365 | — | 2 | 2 | no | — |
| 178 | #2150 | — | 2 | 2 | no | — |
| 179 | C2×#361 | — | 4 | 2 | no | — |
| 180 | C2×#361 | — | 4 | 2 | no | — |
| 181 | C2×#360 | — | 4 | 2 | no | — |
| 182 | C2×#360 | — | 4 | 2 | no | — |
| 183 | C2×#347 | — | 4 | 2 | no | — |
| 184 | C4×M32 | — | 2 | 1 | no | — |
| 185 | C4×M32 | C2×D4 | 1 | 2 | yes | — |
| 186 | C4×M32 | C2×D4 | 1 | 2 | yes | — |
| 187 | #1982 | — | 4 | 2 | no | — |
| 188 | #1980 | — | 4 | 2 | no | — |
| 189 | #1975 | — | 4 | 2 | no | — |
| 190 | #1972 | — | 4 | 2 | no | — |
| 191 | #1879 | — | 8 | 2 | no | — |
| 192 | #1876 | — | 8 | 2 | no | — |
| 193 | C4×#108 | C2×D4 | 1 | 2 | yes | — |
| 194 | C4×#106 | C2×D4 | 1 | 2 | yes | — |
| 195 | #1770 | — | 2 | 2 | no | — |
| 196 | #1713 | C22×C4 | 1 | 2 | yes | — |
| 197 | #1713 | C22×C4 | 1 | 1 | yes | characteristic |
| 198 | #1712 | — | 2 | 2 | no | — |
| 199 | #1712 | — | 2 | 1 | no | — |
| 200 | #1712 | C22×C4 | 1 | 1 | yes | characteristic |
| 201 | #1712 | C22×C4 | 1 | 1 | yes | characteristic |
| 202 | #1712 | C22×C4 | 1 | 2 | yes | — |
| 203 | #1712 | C22×C4 | 1 | 1 | yes | characteristic |
| 204 | #1709 | — | 2 | 2 | no | — |
| 205 | #1709 | — | 2 | 1 | no | — |
| 206 | #1706 | — | 2 | 2 | no | — |
| 207 | #1706 | — | 2 | 2 | no | — |
| 208 | #1706 | — | 2 | 2 | no | — |
| 209 | #1594 | — | 4 | 2 | no | — |
| 210 | #1594 | — | 4 | 2 | no | — |
| 211 | #1586 | — | 8 | 2 | no | — |
| 212 | #1581 | — | 8 | 2 | no | — |
| 213 | #1580 | — | 4 | 2 | no | — |
| 214 | #1580 | — | 4 | 2 | no | — |
| 215 | #1564 | C2×D4 | 1 | 2 | yes | — |
| 216 | C2×#334 | C2×D4 | 1 | 2 | yes | — |
| 217 | C2×#331 | — | 4 | 1 | no | — |
| 218 | #1525 | — | 4 | 1 | no | — |
| 219 | #1502 | — | 4 | 2 | no | — |
| 220 | #1484 | — | 4 | 2 | no | — |
| 221 | #1480 | — | 4 | 2 | no | — |
| 222 | #1451 | — | 2 | 2 | no | — |
| 223 | C2×C82 | C24 | 1 | 1 | yes | characteristic |
| 224 | #1383 | — | 2 | 2 | no | — |
| 225 | #1375 | — | 4 | 2 | no | — |
| 226 | #1370 | — | 2 | 2 | no | — |
| 227 | #1368 | — | 2 | 2 | no | — |
| 228 | #1368 | — | 2 | 2 | no | — |
| 229 | #1367 | — | 2 | 2 | no | — |
| 230 | #1367 | — | 2 | 2 | no | — |
| 231 | #1367 | — | 2 | 2 | no | — |
| 232 | #1361 | — | 8 | 2 | no | — |
| 233 | #1360 | — | 8 | 2 | no | — |
| 234 | #1349 | — | 8 | 2 | no | — |
| 235 | #1347 | — | 8 | 2 | no | — |
| 236 | #1333 | — | 4 | 2 | no | — |
| 237 | #1333 | — | 4 | 2 | no | — |
| 238 | #1333 | — | 4 | 2 | no | — |
| 239 | #1333 | — | 4 | 2 | no | — |
| 240 | #1313 | — | 4 | 2 | no | — |
| 241 | #1313 | — | 4 | 2 | no | — |
| 242 | #1311 | — | 2 | 1 | no | — |
| 243 | #1311 | #41 | 1 | 2 | yes | — |
| 244 | #1311 | #41 | 1 | 2 | yes | — |
| 245 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 246 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 247 | C8×C16 | C22×C4 | 1 | 2 | yes | — |
| 248 | C8×C16 | C22×C4 | 1 | 2 | yes | — |
| 249 | #1279 | — | 2 | 2 | no | — |
| 250 | #1278 | — | 2 | 2 | no | — |
| 251 | C2×#135 | — | 4 | 2 | no | — |
| 252 | C2×#135 | — | 4 | 2 | no | — |
| 253 | C2×#135 | — | 8 | 1 | no | — |
| 254 | C22×D8 | — | 4 | 2 | no | — |
| 255 | C22×D8 | — | 4 | 2 | no | — |
| 256 | C22×D8 | — | 8 | 1 | no | — |
| 257 | C2×#131 | — | 8 | 2 | no | — |
| 258 | #532 | — | 4 | 2 | no | — |
| 259 | #532 | — | 4 | 1 | no | — |
| 260 | C2×#127 | — | 4 | 1 | no | — |
| 261 | C2×C4×D4 | — | 8 | 2 | no | — |
| 262 | #509 | — | 8 | 4 | no | — |
| 263 | #509 | — | 8 | 4 | no | — |
| 264 | #509 | — | 16 | 2 | no | — |
| 265 | #509 | — | 16 | 2 | no | — |
| 266 | #509 | — | 16 | 4 | no | — |
| 267 | #509 | — | 16 | 4 | no | — |
| 268 | #509 | — | 16 | 4 | no | — |
| 269 | #509 | — | 16 | 4 | no | — |
| 270 | C2×SD32 | — | 4 | 2 | no | — |
| 271 | C2×SD32 | — | 4 | 2 | no | — |
| 272 | C2×SD32 | — | 4 | 2 | no | — |
| 273 | C2×SD32 | — | 4 | 2 | no | — |
| 274 | C2×SD32 | — | 8 | 2 | no | — |
| 275 | C2×SD32 | — | 8 | 2 | no | — |
| 276 | C2×SD32 | — | 8 | 2 | no | — |
| 277 | C2×SD32 | — | 8 | 2 | no | — |
| 278 | C2×D16 | — | 4 | 2 | no | — |
| 279 | C2×D16 | — | 4 | 2 | no | — |
| 280 | C2×D16 | — | 4 | 2 | no | — |
| 281 | C2×D16 | — | 4 | 2 | no | — |
| 282 | C2×D16 | — | 4 | 2 | no | — |
| 283 | C2×D16 | — | 4 | 2 | no | — |
| 284 | C2×D16 | — | 8 | 2 | no | — |
| 285 | C2×D16 | — | 8 | 2 | no | — |
| 286 | C2×D16 | — | 8 | 2 | no | — |
| 287 | C2×D16 | — | 8 | 2 | no | — |
| 288 | C2×D16 | — | 8 | 2 | no | — |
| 289 | C2×D16 | — | 8 | 2 | no | — |
| 290 | C2×M32 | — | 2 | 2 | no | — |
| 291 | C2×M32 | — | 2 | 2 | no | — |
| 292 | C2×M32 | — | 4 | 2 | no | — |
| 293 | C2×M32 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 294 | C2×M32 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 295 | #500 | — | 2 | 2 | no | — |
| 296 | #500 | — | 2 | 2 | no | — |
| 297 | #500 | — | 2 | 2 | no | — |
| 298 | #495 | — | 4 | 2 | no | — |
| 299 | #495 | — | 4 | 2 | no | — |
| 300 | #495 | — | 8 | 1 | no | — |
| 301 | #494 | — | 2 | 2 | no | — |
| 302 | #494 | — | 2 | 1 | no | — |
| 303 | #493 | — | 2 | 2 | no | — |
| 304 | #493 | — | 2 | 2 | no | — |
| 305 | #493 | — | 2 | 2 | no | — |
| 306 | #493 | — | 2 | 2 | no | — |
| 307 | #493 | — | 2 | 2 | no | — |
| 308 | #493 | — | 2 | 1 | no | — |
| 309 | #493 | — | 2 | 1 | no | — |
| 310 | #493 | — | 2 | 1 | no | — |
| 311 | #493 | — | 2 | 2 | no | — |
| 312 | #493 | — | 4 | 2 | no | — |
| 313 | #493 | — | 4 | 1 | no | — |
| 314 | #493 | — | 4 | 2 | no | — |
| 315 | #493 | — | 4 | 2 | no | — |
| 316 | #493 | — | 8 | 1 | no | — |
| 317 | #492 | — | 4 | 2 | no | — |
| 318 | #492 | — | 4 | 1 | no | — |
| 319 | #486 | — | 4 | 2 | no | — |
| 320 | #486 | — | 4 | 2 | no | — |
| 321 | #486 | — | 4 | 2 | no | — |
| 322 | #466 | — | 4 | 2 | no | — |
| 323 | #466 | — | 4 | 2 | no | — |
| 324 | #466 | — | 4 | 2 | no | — |
| 325 | #466 | — | 4 | 2 | no | — |
| 326 | #466 | — | 8 | 2 | no | — |
| 327 | #444 | — | 8 | 4 | no | — |
| 328 | #444 | — | 16 | 2 | no | — |
| 329 | #442 | — | 8 | 4 | no | — |
| 330 | #442 | — | 16 | 2 | no | — |
| 331 | C4×D8 | — | 4 | 2 | no | — |
| 332 | C4×D8 | — | 4 | 2 | no | — |
| 333 | C4×D8 | — | 4 | 2 | no | — |
| 334 | C4×D8 | — | 4 | 2 | no | — |
| 335 | C4×D8 | — | 8 | 2 | no | — |
| 336 | #436 | — | 8 | 2 | no | — |
| 337 | #436 | — | 8 | 2 | no | — |
| 338 | #435 | — | 16 | 2 | no | — |
| 339 | C8×D4 | — | 8 | 2 | no | — |
| 340 | C8×D4 | — | 8 | 2 | no | — |
| 341 | #431 | — | 2 | 2 | no | — |
| 342 | C2×#108 | — | 2 | 2 | no | — |
| 343 | C2×#106 | — | 2 | 2 | no | — |
| 344 | C2×C4⋊C8 | — | 2 | 2 | no | — |
| 345 | C2×#104 | — | 8 | 2 | no | — |
| 346 | C2×#104 | — | 8 | 2 | no | — |
| 347 | C2×#102 | — | 8 | 2 | no | — |
| 348 | C2×#102 | — | 8 | 2 | no | — |
| 349 | #408 | — | 8 | 2 | no | — |
| 350 | #408 | — | 16 | 1 | no | — |
| 351 | C4×M16 | — | 2 | 2 | no | — |
| 352 | C2×#97 | — | 4 | 2 | no | — |
| 353 | C2×C4×C8 | C22×D4 | 1 | 2 | yes | — |
| 354 | C2×C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 355 | #390 | — | 8 | 2 | no | — |
| 356 | #386 | — | 16 | 1 | no | — |
| 357 | C4×C4⋊C4 | — | 2 | 2 | no | — |
| 358 | #367 | — | 4 | 2 | no | — |
| 359 | #367 | — | 4 | 2 | no | — |
| 360 | #367 | — | 8 | 2 | no | — |
| 361 | #367 | — | 8 | 2 | no | — |
| 362 | #365 | — | 4 | 4 | no | — |
| 363 | C4⋊C16 | — | 4 | 2 | no | — |
| 364 | C4⋊C16 | — | 4 | 2 | no | — |
| 365 | C4⋊C16 | — | 4 | 2 | no | — |
| 366 | #361 | — | 8 | 4 | no | — |
| 367 | #361 | — | 16 | 2 | no | — |
| 368 | #360 | — | 8 | 4 | no | — |
| 369 | #360 | — | 16 | 2 | no | — |
| 370 | #357 | — | 4 | 2 | no | — |
| 371 | #357 | — | 4 | 2 | no | — |
| 372 | #357 | — | 4 | 2 | no | — |
| 373 | #357 | — | 4 | 2 | no | — |
| 374 | #357 | — | 8 | 2 | no | — |
| 375 | #357 | — | 8 | 2 | no | — |
| 376 | #357 | — | 8 | 4 | no | — |
| 377 | C22⋊C16 | — | 4 | 2 | no | — |
| 378 | #347 | — | 8 | 4 | no | — |
| 379 | #346 | — | 2 | 2 | no | — |
| 380 | #346 | — | 2 | 2 | no | — |
| 381 | #346 | — | 4 | 2 | no | — |
| 382 | #346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 383 | #346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 384 | C4×C16 | — | 2 | 1 | no | — |
| 385 | C4×C16 | — | 2 | 1 | no | — |
| 386 | C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 387 | C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 388 | C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 389 | C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 390 | #341 | — | 2 | 2 | no | — |
| 391 | #340 | — | 2 | 2 | no | — |
| 392 | #336 | — | 4 | 2 | no | — |
| 393 | #335 | — | 2 | 2 | no | — |
| 394 | #334 | — | 2 | 2 | no | — |
| 395 | #334 | — | 2 | 2 | no | — |
| 396 | #334 | — | 2 | 2 | no | — |
| 397 | #331 | — | 16 | 1 | no | — |
| 398 | #329 | — | 16 | 1 | no | — |
| 399 | #327 | — | 16 | 2 | no | — |
| 400 | D4⋊C8 | — | 8 | 2 | no | — |
| 401 | D4⋊C8 | — | 8 | 2 | no | — |
| 402 | D4⋊C8 | — | 8 | 2 | no | — |
| 403 | D4⋊C8 | — | 8 | 2 | no | — |
| 404 | #322 | — | 4 | 2 | no | — |
| 405 | #322 | — | 4 | 2 | no | — |
| 406 | C82 | C23×C4 | 1 | 1 | yes | characteristic |
| 407 | C82 | C2×#41 | 1 | 2 | yes | — |
| 408 | C82 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 409 | C2×#41 | — | 8 | 2 | no | — |
| 410 | C2×#41 | — | 8 | 1 | no | — |
| 411 | C22×D4 | — | 8 | 2 | no | — |
| 412 | C22×D4 | — | 8 | 1 | no | — |
| 413 | C23×C4 | — | 16 | 1 | no | — |
| 414 | #135 | — | 8 | 2 | no | — |
| 415 | #135 | — | 8 | 2 | no | — |
| 416 | #135 | — | 8 | 2 | no | — |
| 417 | #135 | — | 8 | 2 | no | — |
| 418 | #135 | — | 16 | 2 | no | — |
| 419 | #135 | — | 16 | 2 | no | — |
| 420 | #135 | — | 16 | 2 | no | — |
| 421 | #135 | — | 16 | 2 | no | — |
| 422 | C2×Q16 | — | 4 | 2 | no | — |
| 423 | C2×Q16 | — | 4 | 2 | no | — |
| 424 | C2×Q16 | — | 8 | 1 | no | — |
| 425 | C2×SD16 | — | 8 | 2 | no | — |
| 426 | C2×SD16 | — | 8 | 2 | no | — |
| 427 | C2×SD16 | — | 16 | 1 | no | — |
| 428 | C2×D8 | — | 4 | 2 | no | — |
| 429 | C2×D8 | — | 4 | 2 | no | — |
| 430 | C2×D8 | — | 4 | 2 | no | — |
| 431 | C2×D8 | — | 4 | 2 | no | — |
| 432 | C2×D8 | — | 4 | 2 | no | — |
| 433 | C2×D8 | — | 4 | 2 | no | — |
| 434 | C2×D8 | — | 4 | 2 | no | — |
| 435 | C2×D8 | — | 4 | 2 | no | — |
| 436 | C2×D8 | — | 4 | 2 | no | — |
| 437 | C2×D8 | — | 4 | 2 | no | — |
| 438 | C2×D8 | — | 8 | 2 | no | — |
| 439 | C2×D8 | — | 8 | 2 | no | — |
| 440 | C2×D8 | — | 8 | 2 | no | — |
| 441 | C2×D8 | — | 8 | 2 | no | — |
| 442 | C2×D8 | — | 8 | 1 | no | — |
| 443 | C2×D8 | — | 8 | 1 | no | — |
| 444 | C2×D8 | — | 8 | 1 | no | — |
| 445 | C2×D8 | — | 8 | 2 | no | — |
| 446 | C2×D8 | — | 8 | 2 | no | — |
| 447 | C2×D8 | — | 8 | 2 | no | — |
| 448 | C2×D8 | — | 16 | 1 | no | — |
| 449 | C2×D8 | — | 16 | 2 | no | — |
| 450 | C2×D8 | — | 16 | 2 | no | — |
| 451 | C2×D8 | — | 16 | 2 | no | — |
| 452 | C2×D8 | — | 16 | 2 | no | — |
| 453 | #131 | — | 16 | 4 | no | — |
| 454 | #131 | — | 32 | 2 | no | — |
| 455 | C2×M16 | — | 4 | 2 | no | — |
| 456 | C2×M16 | — | 16 | 2 | no | — |
| 457 | C2×M16 | — | 16 | 1 | no | — |
| 458 | C22×C8 | — | 2 | 1 | no | — |
| 459 | C22×C8 | — | 4 | 2 | no | — |
| 460 | C22×C8 | — | 16 | 2 | no | — |
| 461 | C22×C8 | — | 16 | 1 | no | — |
| 462 | C22×C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 463 | C22×C8 | #576 | 1 | 2 | yes | — |
| 464 | C4⋊Q8 | — | 4 | 1 | no | — |
| 465 | C4⋊Q8 | — | 4 | 2 | no | — |
| 466 | #127 | — | 4 | 1 | no | — |
| 467 | #127 | — | 4 | 1 | no | — |
| 468 | #127 | — | 4 | 1 | no | — |
| 469 | #127 | — | 4 | 2 | no | — |
| 470 | #127 | — | 8 | 2 | no | — |
| 471 | #127 | — | 8 | 1 | no | — |
| 472 | #124 | — | 8 | 2 | no | — |
| 473 | #124 | — | 8 | 1 | no | — |
| 474 | #121 | — | 8 | 2 | no | — |
| 475 | #121 | — | 8 | 2 | no | — |
| 476 | #121 | — | 8 | 2 | no | — |
| 477 | C4×D4 | — | 8 | 2 | no | — |
| 478 | C4×D4 | — | 8 | 2 | no | — |
| 479 | C4×D4 | — | 8 | 2 | no | — |
| 480 | C4×D4 | — | 16 | 4 | no | — |
| 481 | C4×D4 | — | 32 | 2 | no | — |
| 482 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 483 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 484 | C2×C22⋊C4 | — | 16 | 1 | no | — |
| 485 | C2×C42 | — | 4 | 2 | no | — |
| 486 | C2×C42 | D42 | 1 | 1 | yes | characteristic |
| 487 | SD32 | — | 8 | 4 | no | — |
| 488 | SD32 | — | 8 | 4 | no | — |
| 489 | SD32 | — | 16 | 2 | no | — |
| 490 | SD32 | — | 16 | 2 | no | — |
| 491 | SD32 | — | 16 | 4 | no | — |
| 492 | SD32 | — | 16 | 4 | no | — |
| 493 | SD32 | — | 16 | 4 | no | — |
| 494 | SD32 | — | 16 | 4 | no | — |
| 495 | D16 | — | 8 | 4 | no | — |
| 496 | D16 | — | 8 | 4 | no | — |
| 497 | D16 | — | 8 | 4 | no | — |
| 498 | D16 | — | 16 | 2 | no | — |
| 499 | D16 | — | 16 | 2 | no | — |
| 500 | D16 | — | 16 | 2 | no | — |
| 501 | D16 | — | 16 | 4 | no | — |
| 502 | D16 | — | 16 | 4 | no | — |
| 503 | D16 | — | 16 | 4 | no | — |
| 504 | D16 | — | 16 | 4 | no | — |
| 505 | D16 | — | 16 | 4 | no | — |
| 506 | D16 | — | 16 | 4 | no | — |
| 507 | M32 | — | 2 | 4 | no | — |
| 508 | M32 | — | 4 | 2 | no | — |
| 509 | M32 | — | 4 | 4 | no | — |
| 510 | M32 | — | 4 | 4 | no | — |
| 511 | M32 | — | 8 | 2 | no | — |
| 512 | M32 | — | 8 | 2 | no | — |
| 513 | C2×C16 | — | 2 | 2 | no | — |
| 514 | C2×C16 | — | 2 | 2 | no | — |
| 515 | C2×C16 | — | 2 | 2 | no | — |
| 516 | C2×C16 | — | 2 | 2 | no | — |
| 517 | C2×C16 | — | 8 | 2 | no | — |
| 518 | C2×C16 | — | 8 | 2 | no | — |
| 519 | C2×C16 | #442 | 1 | 2 | yes | — |
| 520 | C2×C16 | #442 | 1 | 2 | yes | — |
| 521 | C2×C16 | #442 | 1 | 2 | yes | — |
| 522 | C2×C16 | #442 | 1 | 2 | yes | — |
| 523 | #108 | — | 4 | 2 | no | — |
| 524 | #108 | — | 4 | 2 | no | — |
| 525 | #107 | — | 4 | 2 | no | — |
| 526 | #107 | — | 4 | 2 | no | — |
| 527 | #107 | — | 4 | 2 | no | — |
| 528 | #107 | — | 4 | 2 | no | — |
| 529 | #107 | — | 8 | 2 | no | — |
| 530 | #106 | — | 4 | 2 | no | — |
| 531 | #106 | — | 4 | 2 | no | — |
| 532 | C4⋊C8 | — | 4 | 2 | no | — |
| 533 | C4⋊C8 | — | 4 | 2 | no | — |
| 534 | C4⋊C8 | — | 4 | 2 | no | — |
| 535 | #104 | — | 16 | 4 | no | — |
| 536 | #104 | — | 32 | 2 | no | — |
| 537 | #102 | — | 8 | 2 | no | — |
| 538 | #102 | — | 8 | 2 | no | — |
| 539 | #102 | — | 8 | 2 | no | — |
| 540 | #102 | — | 8 | 2 | no | — |
| 541 | #102 | — | 16 | 2 | no | — |
| 542 | #102 | — | 16 | 4 | no | — |
| 543 | #102 | — | 32 | 2 | no | — |
| 544 | C22⋊C8 | — | 4 | 2 | no | — |
| 545 | C22⋊C8 | — | 16 | 2 | no | — |
| 546 | C22⋊C8 | — | 16 | 2 | no | — |
| 547 | C22⋊C8 | — | 16 | 2 | no | — |
| 548 | #97 | — | 4 | 2 | no | — |
| 549 | #97 | — | 8 | 2 | no | — |
| 550 | #97 | — | 8 | 2 | no | — |
| 551 | C4×C8 | — | 2 | 1 | no | — |
| 552 | C4×C8 | — | 4 | 2 | no | — |
| 553 | C4×C8 | — | 4 | 2 | no | — |
| 554 | C4×C8 | C2×C4×D4 | 1 | 2 | yes | — |
| 555 | C4×C8 | #518 | 1 | 1 | yes | characteristic |
| 556 | C4×C8 | #550 | 1 | 2 | yes | — |
| 557 | C4×C8 | #559 | 1 | 1 | yes | characteristic |
| 558 | C4×C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 559 | C4×C8 | #576 | 1 | 2 | yes | — |
| 560 | #95 | — | 4 | 2 | no | — |
| 561 | C24 | — | 16 | 1 | no | — |
| 562 | #41 | — | 16 | 2 | no | — |
| 563 | #41 | — | 16 | 2 | no | — |
| 564 | #41 | — | 16 | 2 | no | — |
| 565 | #41 | — | 16 | 2 | no | — |
| 566 | #41 | — | 32 | 1 | no | — |
| 567 | #41 | — | 32 | 1 | no | — |
| 568 | C2×Q8 | — | 8 | 2 | no | — |
| 569 | C2×Q8 | — | 8 | 1 | no | — |
| 570 | C2×D4 | — | 8 | 2 | no | — |
| 571 | C2×D4 | — | 8 | 2 | no | — |
| 572 | C2×D4 | — | 8 | 2 | no | — |
| 573 | C2×D4 | — | 8 | 2 | no | — |
| 574 | C2×D4 | — | 8 | 2 | no | — |
| 575 | C2×D4 | — | 8 | 2 | no | — |
| 576 | C2×D4 | — | 8 | 1 | no | — |
| 577 | C2×D4 | — | 8 | 1 | no | — |
| 578 | C2×D4 | — | 8 | 1 | no | — |
| 579 | C2×D4 | — | 16 | 2 | no | — |
| 580 | C2×D4 | — | 16 | 2 | no | — |
| 581 | C2×D4 | — | 16 | 2 | no | — |
| 582 | C2×D4 | — | 16 | 2 | no | — |
| 583 | C2×D4 | — | 16 | 2 | no | — |
| 584 | C2×D4 | — | 16 | 1 | no | — |
| 585 | C2×D4 | — | 16 | 2 | no | — |
| 586 | C2×D4 | — | 16 | 1 | no | — |
| 587 | C2×D4 | — | 32 | 1 | no | — |
| 588 | C2×D4 | — | 32 | 1 | no | — |
| 589 | C22×C4 | — | 8 | 2 | no | — |
| 590 | C22×C4 | — | 16 | 2 | no | — |
| 591 | C22×C4 | — | 16 | 1 | no | — |
| 592 | C22×C4 | — | 32 | 4 | no | — |
| 593 | C22×C4 | — | 64 | 1 | no | — |
| 594 | C22×C4 | #3274 | 1 | 2 | yes | — |
| 595 | C22×C4 | #3292 | 1 | 1 | yes | characteristic |
| 596 | Q16 | — | 8 | 2 | no | — |
| 597 | Q16 | — | 8 | 2 | no | — |
| 598 | Q16 | — | 16 | 2 | no | — |
| 599 | Q16 | — | 16 | 2 | no | — |
| 600 | SD16 | — | 16 | 2 | no | — |
| 601 | SD16 | — | 16 | 2 | no | — |
| 602 | SD16 | — | 32 | 2 | no | — |
| 603 | SD16 | — | 32 | 2 | no | — |
| 604 | D8 | — | 8 | 2 | no | — |
| 605 | D8 | — | 8 | 2 | no | — |
| 606 | D8 | — | 8 | 2 | no | — |
| 607 | D8 | — | 8 | 2 | no | — |
| 608 | D8 | — | 8 | 2 | no | — |
| 609 | D8 | — | 8 | 2 | no | — |
| 610 | D8 | — | 8 | 2 | no | — |
| 611 | D8 | — | 8 | 2 | no | — |
| 612 | D8 | — | 8 | 2 | no | — |
| 613 | D8 | — | 8 | 2 | no | — |
| 614 | D8 | — | 16 | 2 | no | — |
| 615 | D8 | — | 16 | 2 | no | — |
| 616 | D8 | — | 16 | 2 | no | — |
| 617 | D8 | — | 16 | 2 | no | — |
| 618 | D8 | — | 16 | 2 | no | — |
| 619 | D8 | — | 16 | 2 | no | — |
| 620 | D8 | — | 16 | 2 | no | — |
| 621 | D8 | — | 16 | 2 | no | — |
| 622 | D8 | — | 16 | 2 | no | — |
| 623 | D8 | — | 16 | 2 | no | — |
| 624 | D8 | — | 16 | 4 | no | — |
| 625 | D8 | — | 32 | 2 | no | — |
| 626 | D8 | — | 32 | 2 | no | — |
| 627 | M16 | — | 8 | 2 | no | — |
| 628 | M16 | — | 8 | 2 | no | — |
| 629 | M16 | — | 32 | 4 | no | — |
| 630 | M16 | — | 64 | 1 | no | — |
| 631 | C2×C8 | — | 2 | 1 | no | — |
| 632 | C2×C8 | — | 2 | 2 | no | — |
| 633 | C2×C8 | — | 2 | 2 | no | — |
| 634 | C2×C8 | — | 2 | 1 | no | — |
| 635 | C2×C8 | — | 4 | 2 | no | — |
| 636 | C2×C8 | — | 4 | 2 | no | — |
| 637 | C2×C8 | — | 8 | 2 | no | — |
| 638 | C2×C8 | — | 8 | 2 | no | — |
| 639 | C2×C8 | — | 8 | 2 | no | — |
| 640 | C2×C8 | — | 8 | 2 | no | — |
| 641 | C2×C8 | — | 8 | 2 | no | — |
| 642 | C2×C8 | — | 32 | 4 | no | — |
| 643 | C2×C8 | — | 64 | 1 | no | — |
| 644 | C2×C8 | C2×#442 | 1 | 2 | yes | — |
| 645 | C2×C8 | #2948 | 1 | 2 | yes | — |
| 646 | C2×C8 | #3399 | 1 | 2 | yes | — |
| 647 | C2×C8 | #3399 | 1 | 2 | yes | — |
| 648 | C4⋊C4 | — | 8 | 2 | no | — |
| 649 | C4⋊C4 | — | 8 | 2 | no | — |
| 650 | C4⋊C4 | — | 8 | 2 | no | — |
| 651 | C4⋊C4 | — | 8 | 2 | no | — |
| 652 | C4⋊C4 | — | 8 | 2 | no | — |
| 653 | C22⋊C4 | — | 16 | 2 | no | — |
| 654 | C22⋊C4 | — | 16 | 2 | no | — |
| 655 | C22⋊C4 | — | 16 | 2 | no | — |
| 656 | C22⋊C4 | — | 32 | 4 | no | — |
| 657 | C22⋊C4 | — | 64 | 1 | no | — |
| 658 | C42 | — | 8 | 2 | no | — |
| 659 | C42 | — | 8 | 2 | no | — |
| 660 | C42 | #2366 | 1 | 1 | yes | characteristic |
| 661 | C42 | #3274 | 1 | 2 | yes | — |
| 662 | C42 | #3292 | 1 | 1 | yes | characteristic |
| 663 | C16 | — | 2 | 4 | no | — |
| 664 | C16 | — | 2 | 4 | no | — |
| 665 | C16 | — | 2 | 2 | no | — |
| 666 | C16 | — | 2 | 2 | no | — |
| 667 | C16 | — | 2 | 2 | no | — |
| 668 | C16 | — | 4 | 2 | no | — |
| 669 | C16 | — | 4 | 2 | no | — |
| 670 | C16 | — | 16 | 2 | no | — |
| 671 | C16 | — | 16 | 2 | no | — |
| 672 | C16 | AGL(1,ℤ/16) | 1 | 4 | yes | complemented |
| 673 | C23 | — | 16 | 2 | no | — |
| 674 | C23 | — | 16 | 1 | no | — |
| 675 | C23 | — | 16 | 1 | no | — |
| 676 | C23 | — | 16 | 1 | no | — |
| 677 | C23 | — | 32 | 2 | no | — |
| 678 | C23 | — | 32 | 1 | no | — |
| 679 | C23 | — | 32 | 1 | no | — |
| 680 | C23 | — | 32 | 2 | no | — |
| 681 | C23 | #20310 | 1 | 1 | yes | characteristic |
| 682 | Q8 | — | 16 | 2 | no | — |
| 683 | Q8 | — | 16 | 2 | no | — |
| 684 | Q8 | — | 32 | 1 | no | — |
| 685 | D4 | — | 16 | 2 | no | — |
| 686 | D4 | — | 16 | 2 | no | — |
| 687 | D4 | — | 16 | 2 | no | — |
| 688 | D4 | — | 16 | 2 | no | — |
| 689 | D4 | — | 16 | 2 | no | — |
| 690 | D4 | — | 16 | 2 | no | — |
| 691 | D4 | — | 16 | 2 | no | — |
| 692 | D4 | — | 16 | 2 | no | — |
| 693 | D4 | — | 16 | 2 | no | — |
| 694 | D4 | — | 16 | 2 | no | — |
| 695 | D4 | — | 32 | 1 | no | — |
| 696 | D4 | — | 32 | 1 | no | — |
| 697 | D4 | — | 32 | 1 | no | — |
| 698 | D4 | — | 32 | 2 | no | — |
| 699 | D4 | — | 32 | 2 | no | — |
| 700 | D4 | — | 32 | 2 | no | — |
| 701 | D4 | — | 32 | 2 | no | — |
| 702 | D4 | — | 32 | 2 | no | — |
| 703 | D4 | — | 64 | 1 | no | — |
| 704 | D4 | — | 64 | 1 | no | — |
| 705 | C2×C4 | — | 2 | 2 | no | — |
| 706 | C2×C4 | — | 2 | 2 | no | — |
| 707 | C2×C4 | — | 4 | 1 | no | — |
| 708 | C2×C4 | — | 16 | 2 | no | — |
| 709 | C2×C4 | — | 16 | 2 | no | — |
| 710 | C2×C4 | — | 16 | 2 | no | — |
| 711 | C2×C4 | — | 16 | 2 | no | — |
| 712 | C2×C4 | — | 16 | 1 | no | — |
| 713 | C2×C4 | — | 32 | 2 | no | — |
| 714 | C2×C4 | — | 32 | 1 | no | — |
| 715 | C2×C4 | — | 32 | 1 | no | — |
| 716 | C2×C4 | — | 32 | 2 | no | — |
| 717 | C2×C4 | — | 64 | 4 | no | — |
| 718 | C2×C4 | #20310 | 1 | 1 | yes | characteristic |
| 719 | C2×C4 | #20310 | 1 | 2 | yes | — |
| 720 | C2×C4 | #23188 | 1 | 2 | yes | — |
| 721 | C2×C4 | #23201 | 1 | 1 | yes | characteristic |
| 722 | C8 | — | 2 | 2 | no | — |
| 723 | C8 | — | 2 | 2 | no | — |
| 724 | C8 | — | 2 | 2 | no | — |
| 725 | C8 | — | 2 | 2 | no | — |
| 726 | C8 | — | 4 | 1 | no | — |
| 727 | C8 | — | 16 | 2 | no | — |
| 728 | C8 | — | 16 | 2 | no | — |
| 729 | C8 | — | 16 | 2 | no | — |
| 730 | C8 | C2×AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 731 | C8 | #33471 | 1 | 2 | yes | — |
| 732 | C22 | — | 2 | 2 | no | — |
| 733 | C22 | — | 2 | 1 | no | — |
| 734 | C22 | — | 32 | 2 | no | — |
| 735 | C22 | — | 32 | 2 | no | — |
| 736 | C22 | — | 32 | 2 | no | — |
| 737 | C22 | — | 32 | 2 | no | — |
| 738 | C22 | — | 32 | 2 | no | — |
| 739 | C22 | — | 32 | 1 | no | — |
| 740 | C22 | — | 32 | 1 | no | — |
| 741 | C22 | — | 32 | 1 | no | — |
| 742 | C22 | — | 32 | 2 | no | — |
| 743 | C22 | — | 64 | 1 | no | — |
| 744 | C22 | — | 64 | 2 | no | — |
| 745 | C22 | — | 64 | 1 | no | — |
| 746 | C22 | #231631 | 1 | 1 | yes | characteristic |
| 747 | C4 | — | 2 | 2 | no | — |
| 748 | C4 | — | 2 | 1 | no | — |
| 749 | C4 | — | 2 | 1 | no | — |
| 750 | C4 | — | 32 | 2 | no | — |
| 751 | C4 | — | 32 | 2 | no | — |
| 752 | C4 | — | 32 | 1 | no | — |
| 753 | C4 | #498578 | 1 | 2 | yes | — |
| 754 | C4 | #498582 | 1 | 2 | yes | — |
| 755 | C2 | — | 4 | 1 | no | — |
| 756 | C2 | — | 64 | 2 | no | — |
| 757 | C2 | — | 64 | 1 | no | — |
| 758 | C2 | — | 64 | 1 | no | — |
| 759 | C2 | — | 64 | 1 | no | — |
| 760 | C2 | #72214332 | 1 | 1 | yes | characteristic |
| 761 | C2 | #72227103 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #231631 |
| commutator | C82 | C23×C4 |
| Frattini, cosocle | C2×C82 | C24 |
| prime radical | #72213956 | C2 |
| LCS | G ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ 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. #72227226 | C2 | semidirect |
| 2. #72227225 | C2 | semidirect |
| 3. #72227184 | C2 | semidirect |
| 4. #72227103 | C2 | semidirect |
| 5. #72227102 | C2 | semidirect |
| 6. #72225246 | C2 | semidirect |
| 7. #72225245 | C2 | semidirect |
| 8. #72214397 | C2 | semidirect |
| 32. #123419 | C4 | semidirect |
| 33. #123419 | C4 | semidirect |
| 34. #123412 | C4 | semidirect |
| 35. #123412 | C4 | semidirect |
| 36. #123411 | C4 | semidirect |
| 37. #123403 | C4 | semidirect |
| 66. #12523 | C2×C4 | semidirect |
| 67. #12523 | C2×C4 | semidirect |
| 79. #12515 | C2×C4 | semidirect |
| 80. #12515 | C2×C4 | semidirect |
| 81. #12509 | C2×C4 | semidirect |
| 82. #12509 | C2×C4 | semidirect |
| 83. #12509 | C2×C4 | semidirect |
| 121. #7052 | C2×C4 | semidirect |
| 122. #7052 | C2×C4 | semidirect |
| 123. C162 | C2×C4 | semidirect |
| 672. C16 | AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227226 | 2 |
| #72227225 | 2 |
| #72227184 | 2 |
| #72227103 | 2 |
| #72227102 | 2 |
| #72225246 | 2 |
| #72225245 | 2 |
| #72214397 | 2 |
| #72213956 | 2 |