Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
861 conjugacy classes of subgroups.
The subgroup lattice has 538 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #491550 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #484147 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #231721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #231542 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #141341 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #141326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #141213 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #137501 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #137499 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #129200 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #129184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #33748 | C22 | 1 | 2 | yes | — |
| 13 | #33748 | C22 | 1 | 2 | yes | — |
| 14 | #23180 | — | 2 | 1 | no | — |
| 15 | #19603 | C22 | 1 | 1 | yes | characteristic |
| 16 | #19603 | C22 | 1 | 1 | yes | characteristic |
| 17 | #18091 | C22 | 1 | 2 | yes | — |
| 18 | #18084 | — | 2 | 1 | no | — |
| 19 | #18073 | C22 | 1 | 2 | yes | — |
| 20 | C4×#365 | C22 | 1 | 1 | yes | characteristic |
| 21 | #12532 | C4 | 1 | 2 | yes | complemented |
| 22 | #12532 | C4 | 1 | 2 | yes | complemented |
| 23 | #12525 | C4 | 1 | 2 | yes | complemented |
| 24 | #12525 | C4 | 1 | 2 | yes | complemented |
| 25 | #12089 | — | 2 | 2 | no | — |
| 26 | #12078 | — | 2 | 2 | no | — |
| 27 | #12078 | — | 2 | 2 | no | — |
| 28 | #12067 | — | 2 | 2 | no | — |
| 29 | #12013 | C22 | 1 | 1 | yes | characteristic |
| 30 | #12000 | C22 | 1 | 1 | yes | characteristic |
| 31 | #11751 | C22 | 1 | 2 | yes | — |
| 32 | #11744 | C22 | 1 | 2 | yes | — |
| 33 | #11654 | C22 | 1 | 2 | yes | — |
| 34 | #11652 | C22 | 1 | 2 | yes | — |
| 35 | #11414 | C22 | 1 | 2 | yes | — |
| 36 | #11402 | C22 | 1 | 1 | yes | characteristic |
| 37 | #9753 | — | 2 | 1 | no | — |
| 38 | #9726 | C22 | 1 | 2 | yes | — |
| 39 | #9724 | — | 2 | 1 | no | — |
| 40 | #9721 | C22 | 1 | 2 | yes | — |
| 41 | #9069 | — | 2 | 2 | no | — |
| 42 | #9053 | — | 2 | 2 | no | — |
| 43 | #8293 | C22 | 1 | 1 | yes | characteristic |
| 44 | C8×#108 | C22 | 1 | 1 | yes | characteristic |
| 45 | #8283 | C22 | 1 | 1 | yes | characteristic |
| 46 | #7174 | C22 | 1 | 1 | yes | characteristic |
| 47 | #7173 | C22 | 1 | 1 | yes | characteristic |
| 48 | #7164 | C22 | 1 | 2 | yes | — |
| 49 | #3169 | — | 2 | 1 | no | — |
| 50 | #3169 | — | 2 | 1 | no | — |
| 51 | #3169 | C23 | 1 | 2 | yes | — |
| 52 | #3169 | C23 | 1 | 2 | yes | — |
| 53 | #3147 | — | 2 | 1 | no | — |
| 54 | #3147 | — | 2 | 1 | no | — |
| 55 | #2979 | — | 2 | 2 | no | — |
| 56 | C2×#444 | — | 4 | 1 | no | — |
| 57 | #2935 | — | 2 | 2 | no | — |
| 58 | #2254 | C2×C4 | 1 | 2 | yes | — |
| 59 | #2254 | C2×C4 | 1 | 2 | yes | — |
| 60 | #2246 | C2×C4 | 1 | 2 | yes | — |
| 61 | #2246 | C2×C4 | 1 | 2 | yes | — |
| 62 | #2240 | C2×C4 | 1 | 2 | yes | — |
| 63 | #2240 | C2×C4 | 1 | 2 | yes | — |
| 64 | #2240 | C2×C4 | 1 | 2 | yes | — |
| 65 | #2240 | C2×C4 | 1 | 2 | yes | — |
| 66 | #2218 | — | 2 | 2 | no | — |
| 67 | #2218 | — | 2 | 2 | no | — |
| 68 | #2218 | — | 4 | 2 | no | — |
| 69 | #2177 | — | 2 | 2 | no | — |
| 70 | #2177 | — | 2 | 2 | no | — |
| 71 | #2177 | — | 4 | 2 | no | — |
| 72 | #2163 | C23 | 1 | 2 | yes | — |
| 73 | C2×#365 | — | 2 | 1 | no | — |
| 74 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 75 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 76 | #1980 | — | 2 | 2 | no | — |
| 77 | #1975 | — | 4 | 1 | no | — |
| 78 | #1876 | — | 4 | 2 | no | — |
| 79 | C4×#108 | D4 | 1 | 1 | yes | characteristic |
| 80 | C4×#108 | C23 | 1 | 1 | yes | characteristic |
| 81 | C4×#106 | C23 | 1 | 1 | yes | characteristic |
| 82 | #1770 | — | 2 | 1 | no | — |
| 83 | #1713 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #1713 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | #1712 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | #1712 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #1709 | — | 2 | 1 | no | — |
| 88 | #1709 | — | 2 | 1 | no | — |
| 89 | #1706 | — | 2 | 1 | no | — |
| 90 | #1706 | — | 2 | 1 | no | — |
| 91 | #1706 | C2×C4 | 1 | 2 | yes | — |
| 92 | #1706 | C2×C4 | 1 | 2 | yes | — |
| 93 | #1594 | — | 2 | 2 | no | — |
| 94 | #1594 | — | 2 | 2 | no | — |
| 95 | #1589 | — | 4 | 1 | no | — |
| 96 | #1586 | — | 4 | 2 | no | — |
| 97 | #1586 | — | 4 | 2 | no | — |
| 98 | #1581 | — | 4 | 2 | no | — |
| 99 | #1580 | — | 2 | 2 | no | — |
| 100 | #1580 | — | 2 | 2 | no | — |
| 101 | C8×D8 | — | 4 | 1 | no | — |
| 102 | #1564 | D4 | 1 | 1 | yes | characteristic |
| 103 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×#334 | C23 | 1 | 1 | yes | characteristic |
| 105 | #1525 | — | 2 | 2 | no | — |
| 106 | #1502 | — | 2 | 2 | no | — |
| 107 | #1484 | — | 2 | 2 | no | — |
| 108 | #1484 | — | 2 | 2 | no | — |
| 109 | #1480 | — | 2 | 2 | no | — |
| 110 | #1451 | C23 | 1 | 2 | yes | — |
| 111 | C8×M16 | — | 2 | 1 | no | — |
| 112 | C2×C82 | C23 | 1 | 1 | yes | characteristic |
| 113 | #1383 | — | 2 | 1 | no | — |
| 114 | #1370 | — | 2 | 1 | no | — |
| 115 | #1368 | D4 | 1 | 2 | yes | — |
| 116 | #1368 | D4 | 1 | 2 | yes | — |
| 117 | #1367 | — | 2 | 1 | no | — |
| 118 | #1349 | — | 4 | 2 | no | — |
| 119 | #1347 | — | 4 | 2 | no | — |
| 120 | #1333 | — | 2 | 2 | no | — |
| 121 | #1333 | — | 2 | 2 | no | — |
| 122 | #1333 | — | 2 | 2 | no | — |
| 123 | #1333 | — | 2 | 2 | no | — |
| 124 | #1313 | — | 2 | 2 | no | — |
| 125 | #1313 | — | 2 | 2 | no | — |
| 126 | #1312 | C2×C4 | 1 | 2 | yes | — |
| 127 | #1312 | C2×C4 | 1 | 2 | yes | — |
| 128 | #1279 | — | 2 | 1 | no | — |
| 129 | #1278 | — | 2 | 1 | no | — |
| 130 | #1278 | D4 | 1 | 2 | yes | — |
| 131 | C2×#135 | — | 4 | 1 | no | — |
| 132 | C2×#135 | — | 4 | 1 | no | — |
| 133 | C2×#135 | — | 8 | 1 | no | — |
| 134 | C2×#131 | — | 4 | 2 | no | — |
| 135 | #532 | — | 2 | 2 | no | — |
| 136 | #532 | — | 2 | 2 | no | — |
| 137 | C2×D16 | — | 2 | 2 | no | — |
| 138 | C2×D16 | — | 2 | 2 | no | — |
| 139 | C2×D16 | — | 4 | 2 | no | — |
| 140 | C2×M32 | — | 2 | 1 | no | — |
| 141 | C2×M32 | #41 | 1 | 1 | yes | characteristic |
| 142 | C2×M32 | #41 | 1 | 1 | yes | characteristic |
| 143 | #500 | — | 2 | 1 | no | — |
| 144 | #500 | — | 2 | 1 | no | — |
| 145 | #500 | C22×C4 | 1 | 2 | yes | — |
| 146 | #500 | C22×C4 | 1 | 2 | yes | — |
| 147 | #495 | — | 4 | 1 | no | — |
| 148 | #495 | — | 4 | 1 | no | — |
| 149 | #495 | — | 8 | 1 | no | — |
| 150 | #494 | — | 2 | 1 | no | — |
| 151 | #494 | — | 2 | 1 | no | — |
| 152 | #493 | — | 2 | 1 | no | — |
| 153 | #493 | — | 2 | 1 | no | — |
| 154 | #493 | — | 2 | 1 | no | — |
| 155 | #493 | — | 2 | 1 | no | — |
| 156 | #493 | C22×C4 | 1 | 2 | yes | — |
| 157 | #493 | C22×C4 | 1 | 2 | yes | — |
| 158 | #492 | — | 2 | 2 | no | — |
| 159 | #492 | — | 2 | 2 | no | — |
| 160 | #486 | — | 2 | 2 | no | — |
| 161 | #486 | — | 2 | 2 | no | — |
| 162 | #486 | — | 2 | 2 | no | — |
| 163 | #486 | — | 2 | 2 | no | — |
| 164 | #466 | — | 2 | 2 | no | — |
| 165 | #466 | — | 2 | 2 | no | — |
| 166 | #466 | — | 2 | 2 | no | — |
| 167 | #466 | — | 2 | 2 | no | — |
| 168 | #466 | — | 4 | 1 | no | — |
| 169 | #466 | — | 4 | 1 | no | — |
| 170 | #466 | — | 8 | 1 | no | — |
| 171 | #444 | — | 8 | 4 | no | — |
| 172 | C4×D8 | — | 2 | 2 | no | — |
| 173 | C4×D8 | — | 2 | 2 | no | — |
| 174 | C4×D8 | — | 2 | 2 | no | — |
| 175 | C4×D8 | — | 2 | 2 | no | — |
| 176 | C4×D8 | — | 4 | 1 | no | — |
| 177 | C4×D8 | — | 4 | 1 | no | — |
| 178 | C4×D8 | — | 8 | 1 | no | — |
| 179 | #436 | — | 4 | 2 | no | — |
| 180 | #436 | — | 4 | 2 | no | — |
| 181 | #436 | — | 4 | 2 | no | — |
| 182 | #435 | — | 8 | 2 | no | — |
| 183 | C8×D4 | — | 4 | 2 | no | — |
| 184 | C8×D4 | — | 4 | 2 | no | — |
| 185 | C8×D4 | — | 4 | 2 | no | — |
| 186 | #431 | — | 2 | 1 | no | — |
| 187 | #431 | C2×D4 | 1 | 2 | yes | — |
| 188 | C2×#108 | — | 2 | 1 | no | — |
| 189 | C2×#108 | — | 2 | 1 | no | — |
| 190 | C2×#106 | — | 2 | 1 | no | — |
| 191 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 192 | C2×#104 | — | 4 | 2 | no | — |
| 193 | C2×#104 | — | 4 | 2 | no | — |
| 194 | #408 | — | 4 | 2 | no | — |
| 195 | #408 | — | 8 | 2 | no | — |
| 196 | C4×M16 | — | 2 | 1 | no | — |
| 197 | C4×M16 | C2×D4 | 1 | 2 | yes | — |
| 198 | C2×#97 | — | 4 | 1 | no | — |
| 199 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 202 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 203 | #367 | — | 2 | 2 | no | — |
| 204 | #367 | — | 2 | 2 | no | — |
| 205 | #367 | — | 4 | 2 | no | — |
| 206 | #365 | — | 4 | 2 | no | — |
| 207 | C4⋊C16 | — | 2 | 2 | no | — |
| 208 | #357 | — | 2 | 2 | no | — |
| 209 | #357 | — | 2 | 2 | no | — |
| 210 | #357 | — | 2 | 2 | no | — |
| 211 | #357 | — | 2 | 2 | no | — |
| 212 | #357 | — | 4 | 2 | no | — |
| 213 | #357 | — | 4 | 2 | no | — |
| 214 | C22⋊C16 | — | 2 | 2 | no | — |
| 215 | #346 | — | 2 | 2 | no | — |
| 216 | #346 | — | 2 | 1 | no | — |
| 217 | #346 | C2×D4 | 1 | 2 | yes | — |
| 218 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 219 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 220 | #341 | — | 2 | 1 | no | — |
| 221 | #341 | — | 2 | 1 | no | — |
| 222 | #340 | — | 2 | 1 | no | — |
| 223 | #336 | — | 4 | 1 | no | — |
| 224 | #335 | — | 2 | 1 | no | — |
| 225 | #335 | — | 2 | 1 | no | — |
| 226 | #334 | — | 2 | 1 | no | — |
| 227 | #334 | — | 2 | 1 | no | — |
| 228 | #334 | C2×D4 | 1 | 2 | yes | — |
| 229 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 231 | #329 | — | 8 | 2 | no | — |
| 232 | #327 | — | 8 | 2 | no | — |
| 233 | D4⋊C8 | — | 4 | 2 | no | — |
| 234 | D4⋊C8 | — | 4 | 2 | no | — |
| 235 | D4⋊C8 | — | 4 | 2 | no | — |
| 236 | D4⋊C8 | — | 4 | 2 | no | — |
| 237 | D4⋊C8 | — | 4 | 2 | no | — |
| 238 | D4⋊C8 | — | 4 | 2 | no | — |
| 239 | #322 | — | 2 | 2 | no | — |
| 240 | #322 | — | 2 | 2 | no | — |
| 241 | #322 | — | 4 | 1 | no | — |
| 242 | C82 | — | 4 | 1 | no | — |
| 243 | C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 244 | C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 245 | C82 | #41 | 1 | 1 | yes | characteristic |
| 246 | C82 | #41 | 1 | 1 | yes | characteristic |
| 247 | C2×#41 | — | 4 | 2 | no | — |
| 248 | C2×#41 | — | 4 | 2 | no | — |
| 249 | #135 | — | 8 | 2 | no | — |
| 250 | #135 | — | 8 | 2 | no | — |
| 251 | #135 | — | 16 | 1 | no | — |
| 252 | #135 | — | 16 | 1 | no | — |
| 253 | #135 | — | 16 | 4 | no | — |
| 254 | C2×Q16 | — | 4 | 1 | no | — |
| 255 | C2×Q16 | — | 4 | 1 | no | — |
| 256 | C2×Q16 | — | 8 | 1 | no | — |
| 257 | C2×SD16 | — | 4 | 2 | no | — |
| 258 | C2×SD16 | — | 4 | 2 | no | — |
| 259 | C2×SD16 | — | 8 | 2 | no | — |
| 260 | C2×D8 | — | 2 | 2 | no | — |
| 261 | C2×D8 | — | 2 | 2 | no | — |
| 262 | C2×D8 | — | 2 | 2 | no | — |
| 263 | C2×D8 | — | 2 | 2 | no | — |
| 264 | C2×D8 | — | 4 | 1 | no | — |
| 265 | C2×D8 | — | 4 | 1 | no | — |
| 266 | C2×D8 | — | 4 | 1 | no | — |
| 267 | C2×D8 | — | 4 | 1 | no | — |
| 268 | C2×D8 | — | 8 | 1 | no | — |
| 269 | C2×D8 | — | 8 | 1 | no | — |
| 270 | #131 | — | 8 | 4 | no | — |
| 271 | #131 | — | 16 | 2 | no | — |
| 272 | C2×M16 | — | 2 | 2 | no | — |
| 273 | C2×M16 | — | 4 | 1 | no | — |
| 274 | C2×M16 | — | 8 | 2 | no | — |
| 275 | C2×M16 | — | 8 | 2 | no | — |
| 276 | C22×C8 | — | 2 | 1 | no | — |
| 277 | C22×C8 | — | 4 | 1 | no | — |
| 278 | C22×C8 | — | 8 | 2 | no | — |
| 279 | C22×C8 | — | 8 | 2 | no | — |
| 280 | C22×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 281 | C22×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 282 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 283 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 284 | C4⋊Q8 | — | 2 | 2 | no | — |
| 285 | C4⋊Q8 | — | 2 | 2 | no | — |
| 286 | #127 | — | 2 | 2 | no | — |
| 287 | #127 | — | 2 | 2 | no | — |
| 288 | #124 | — | 4 | 2 | no | — |
| 289 | #124 | — | 4 | 2 | no | — |
| 290 | #121 | — | 4 | 2 | no | — |
| 291 | #121 | — | 4 | 2 | no | — |
| 292 | #121 | — | 4 | 2 | no | — |
| 293 | #121 | — | 4 | 2 | no | — |
| 294 | C4×D4 | — | 4 | 2 | no | — |
| 295 | C4×D4 | — | 4 | 2 | no | — |
| 296 | C4×D4 | — | 4 | 2 | no | — |
| 297 | C4×D4 | — | 4 | 2 | no | — |
| 298 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 299 | C2×C42 | — | 4 | 1 | no | — |
| 300 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 301 | D16 | — | 4 | 4 | no | — |
| 302 | D16 | — | 8 | 2 | no | — |
| 303 | D16 | — | 8 | 4 | no | — |
| 304 | M32 | — | 4 | 1 | no | — |
| 305 | M32 | — | 4 | 1 | no | — |
| 306 | M32 | — | 8 | 1 | no | — |
| 307 | C2×C16 | — | 2 | 2 | no | — |
| 308 | C2×C16 | — | 4 | 2 | no | — |
| 309 | C2×C16 | C4×D4 | 1 | 2 | yes | — |
| 310 | C2×C16 | C4×D4 | 1 | 2 | yes | — |
| 311 | #108 | — | 2 | 2 | no | — |
| 312 | #108 | — | 4 | 1 | no | — |
| 313 | #108 | — | 4 | 2 | no | — |
| 314 | #107 | — | 2 | 2 | no | — |
| 315 | #107 | — | 2 | 2 | no | — |
| 316 | #107 | — | 2 | 2 | no | — |
| 317 | #107 | — | 2 | 2 | no | — |
| 318 | #107 | — | 4 | 1 | no | — |
| 319 | #107 | — | 4 | 1 | no | — |
| 320 | #107 | — | 8 | 1 | no | — |
| 321 | #106 | — | 4 | 1 | no | — |
| 322 | #106 | — | 4 | 1 | no | — |
| 323 | C4⋊C8 | — | 2 | 2 | no | — |
| 324 | C4⋊C8 | — | 2 | 1 | no | — |
| 325 | C4⋊C8 | — | 2 | 1 | no | — |
| 326 | C4⋊C8 | — | 2 | 2 | no | — |
| 327 | C4⋊C8 | — | 4 | 1 | no | — |
| 328 | #104 | — | 8 | 4 | no | — |
| 329 | #104 | — | 16 | 2 | no | — |
| 330 | #102 | — | 4 | 2 | no | — |
| 331 | #102 | — | 4 | 2 | no | — |
| 332 | #102 | — | 4 | 2 | no | — |
| 333 | #102 | — | 4 | 2 | no | — |
| 334 | #102 | — | 4 | 2 | no | — |
| 335 | #102 | — | 4 | 2 | no | — |
| 336 | #102 | — | 8 | 2 | no | — |
| 337 | C22⋊C8 | — | 2 | 2 | no | — |
| 338 | C22⋊C8 | — | 4 | 1 | no | — |
| 339 | C22⋊C8 | — | 8 | 2 | no | — |
| 340 | C22⋊C8 | — | 8 | 2 | no | — |
| 341 | C22⋊C8 | — | 8 | 2 | no | — |
| 342 | C22⋊C8 | — | 8 | 2 | no | — |
| 343 | #97 | — | 2 | 2 | no | — |
| 344 | #97 | — | 4 | 1 | no | — |
| 345 | #97 | — | 8 | 2 | no | — |
| 346 | C4×C8 | — | 2 | 2 | no | — |
| 347 | C4×C8 | — | 2 | 2 | no | — |
| 348 | C4×C8 | — | 2 | 1 | no | — |
| 349 | C4×C8 | — | 4 | 1 | no | — |
| 350 | C4×C8 | — | 4 | 1 | no | — |
| 351 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 352 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 353 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 354 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 355 | C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 356 | C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 357 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 358 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 359 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 360 | C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 361 | #95 | — | 4 | 1 | no | — |
| 362 | #41 | — | 8 | 2 | no | — |
| 363 | #41 | — | 8 | 2 | no | — |
| 364 | #41 | — | 8 | 2 | no | — |
| 365 | #41 | — | 8 | 2 | no | — |
| 366 | #41 | — | 16 | 2 | no | — |
| 367 | #41 | — | 16 | 2 | no | — |
| 368 | C2×Q8 | — | 4 | 2 | no | — |
| 369 | C2×Q8 | — | 4 | 2 | no | — |
| 370 | C2×D4 | — | 4 | 2 | no | — |
| 371 | C2×D4 | — | 4 | 2 | no | — |
| 372 | C2×D4 | — | 4 | 2 | no | — |
| 373 | C2×D4 | — | 4 | 2 | no | — |
| 374 | C2×D4 | — | 4 | 2 | no | — |
| 375 | C2×D4 | — | 4 | 2 | no | — |
| 376 | C2×D4 | — | 8 | 2 | no | — |
| 377 | C2×D4 | — | 8 | 2 | no | — |
| 378 | C22×C4 | — | 8 | 2 | no | — |
| 379 | C22×C4 | — | 8 | 2 | no | — |
| 380 | C22×C4 | — | 8 | 1 | no | — |
| 381 | C22×C4 | #550 | 1 | 1 | yes | characteristic |
| 382 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 383 | C22×C4 | #576 | 1 | 1 | yes | characteristic |
| 384 | Q16 | — | 8 | 2 | no | — |
| 385 | Q16 | — | 16 | 1 | no | — |
| 386 | Q16 | — | 16 | 2 | no | — |
| 387 | SD16 | — | 8 | 4 | no | — |
| 388 | SD16 | — | 16 | 2 | no | — |
| 389 | SD16 | — | 16 | 4 | no | — |
| 390 | D8 | — | 4 | 2 | no | — |
| 391 | D8 | — | 4 | 2 | no | — |
| 392 | D8 | — | 4 | 2 | no | — |
| 393 | D8 | — | 4 | 2 | no | — |
| 394 | D8 | — | 8 | 2 | no | — |
| 395 | D8 | — | 8 | 2 | no | — |
| 396 | D8 | — | 8 | 2 | no | — |
| 397 | D8 | — | 8 | 2 | no | — |
| 398 | D8 | — | 16 | 1 | no | — |
| 399 | D8 | — | 16 | 1 | no | — |
| 400 | D8 | — | 16 | 2 | no | — |
| 401 | D8 | — | 16 | 2 | no | — |
| 402 | M16 | — | 4 | 2 | no | — |
| 403 | M16 | — | 4 | 2 | no | — |
| 404 | M16 | — | 4 | 2 | no | — |
| 405 | M16 | — | 8 | 1 | no | — |
| 406 | M16 | — | 16 | 4 | no | — |
| 407 | M16 | — | 32 | 2 | no | — |
| 408 | C2×C8 | — | 2 | 1 | no | — |
| 409 | C2×C8 | — | 2 | 2 | no | — |
| 410 | C2×C8 | — | 2 | 1 | no | — |
| 411 | C2×C8 | — | 2 | 1 | no | — |
| 412 | C2×C8 | — | 2 | 1 | no | — |
| 413 | C2×C8 | — | 4 | 1 | no | — |
| 414 | C2×C8 | — | 4 | 1 | no | — |
| 415 | C2×C8 | — | 4 | 2 | no | — |
| 416 | C2×C8 | — | 4 | 2 | no | — |
| 417 | C2×C8 | — | 4 | 2 | no | — |
| 418 | C2×C8 | — | 4 | 1 | no | — |
| 419 | C2×C8 | — | 4 | 1 | no | — |
| 420 | C2×C8 | — | 4 | 2 | no | — |
| 421 | C2×C8 | — | 8 | 1 | no | — |
| 422 | C2×C8 | — | 8 | 1 | no | — |
| 423 | C2×C8 | — | 8 | 1 | no | — |
| 424 | C2×C8 | — | 16 | 4 | no | — |
| 425 | C2×C8 | — | 32 | 2 | no | — |
| 426 | C2×C8 | #442 | 1 | 1 | yes | characteristic |
| 427 | C2×C8 | #442 | 1 | 1 | yes | characteristic |
| 428 | C2×C8 | #442 | 1 | 1 | yes | characteristic |
| 429 | C2×C8 | #442 | 1 | 1 | yes | characteristic |
| 430 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 431 | C2×C8 | #518 | 1 | 1 | yes | characteristic |
| 432 | C2×C8 | #550 | 1 | 1 | yes | characteristic |
| 433 | C2×C8 | #559 | 1 | 1 | yes | characteristic |
| 434 | C4⋊C4 | — | 4 | 2 | no | — |
| 435 | C4⋊C4 | — | 4 | 2 | no | — |
| 436 | C4⋊C4 | — | 4 | 2 | no | — |
| 437 | C4⋊C4 | — | 4 | 2 | no | — |
| 438 | C4⋊C4 | — | 8 | 1 | no | — |
| 439 | C4⋊C4 | — | 8 | 1 | no | — |
| 440 | C22⋊C4 | — | 8 | 2 | no | — |
| 441 | C22⋊C4 | — | 8 | 2 | no | — |
| 442 | C22⋊C4 | — | 8 | 2 | no | — |
| 443 | C22⋊C4 | — | 8 | 2 | no | — |
| 444 | C42 | — | 8 | 1 | no | — |
| 445 | C42 | — | 8 | 1 | no | — |
| 446 | C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 447 | C42 | D42 | 1 | 1 | yes | characteristic |
| 448 | C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 449 | C42 | #576 | 1 | 1 | yes | characteristic |
| 450 | C16 | — | 2 | 2 | no | — |
| 451 | C16 | — | 2 | 2 | no | — |
| 452 | C16 | — | 4 | 2 | no | — |
| 453 | C16 | — | 8 | 2 | no | — |
| 454 | C23 | — | 8 | 2 | no | — |
| 455 | C23 | — | 8 | 2 | no | — |
| 456 | C23 | #3399 | 1 | 1 | yes | characteristic |
| 457 | Q8 | — | 8 | 2 | no | — |
| 458 | Q8 | — | 8 | 2 | no | — |
| 459 | Q8 | — | 16 | 2 | no | — |
| 460 | D4 | — | 8 | 2 | no | — |
| 461 | D4 | — | 8 | 2 | no | — |
| 462 | D4 | — | 8 | 2 | no | — |
| 463 | D4 | — | 8 | 2 | no | — |
| 464 | D4 | — | 8 | 2 | no | — |
| 465 | D4 | — | 8 | 2 | no | — |
| 466 | D4 | — | 8 | 2 | no | — |
| 467 | D4 | — | 8 | 2 | no | — |
| 468 | D4 | — | 16 | 2 | no | — |
| 469 | D4 | — | 16 | 2 | no | — |
| 470 | D4 | — | 16 | 2 | no | — |
| 471 | D4 | — | 16 | 2 | no | — |
| 472 | D4 | — | 32 | 2 | no | — |
| 473 | C2×C4 | — | 2 | 1 | no | — |
| 474 | C2×C4 | — | 2 | 1 | no | — |
| 475 | C2×C4 | — | 2 | 1 | no | — |
| 476 | C2×C4 | — | 2 | 1 | no | — |
| 477 | C2×C4 | — | 4 | 1 | no | — |
| 478 | C2×C4 | — | 8 | 2 | no | — |
| 479 | C2×C4 | — | 8 | 2 | no | — |
| 480 | C2×C4 | — | 16 | 2 | no | — |
| 481 | C2×C4 | — | 16 | 2 | no | — |
| 482 | C2×C4 | — | 16 | 2 | no | — |
| 483 | C2×C4 | — | 16 | 2 | no | — |
| 484 | C2×C4 | — | 16 | 1 | no | — |
| 485 | C2×C4 | — | 16 | 1 | no | — |
| 486 | C2×C4 | — | 16 | 1 | no | — |
| 487 | C2×C4 | #2366 | 1 | 1 | yes | characteristic |
| 488 | C2×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 489 | C2×C4 | #2948 | 1 | 1 | yes | characteristic |
| 490 | C2×C4 | #3274 | 1 | 1 | yes | characteristic |
| 491 | C2×C4 | #3274 | 1 | 1 | yes | characteristic |
| 492 | C2×C4 | #3399 | 1 | 1 | yes | characteristic |
| 493 | C8 | — | 2 | 2 | no | — |
| 494 | C8 | — | 2 | 1 | no | — |
| 495 | C8 | — | 2 | 1 | no | — |
| 496 | C8 | — | 2 | 1 | no | — |
| 497 | C8 | — | 2 | 1 | no | — |
| 498 | C8 | — | 2 | 1 | no | — |
| 499 | C8 | — | 2 | 1 | no | — |
| 500 | C8 | — | 4 | 1 | no | — |
| 501 | C8 | — | 8 | 2 | no | — |
| 502 | C8 | — | 8 | 2 | no | — |
| 503 | C8 | — | 8 | 1 | no | — |
| 504 | C8 | — | 8 | 2 | no | — |
| 505 | C8 | — | 8 | 1 | no | — |
| 506 | C8 | — | 8 | 2 | no | — |
| 507 | C8 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 508 | C8 | #2955 | 1 | 1 | yes | characteristic |
| 509 | C8 | #2956 | 1 | 1 | yes | characteristic |
| 510 | C22 | — | 2 | 1 | no | — |
| 511 | C22 | — | 2 | 1 | no | — |
| 512 | C22 | — | 2 | 1 | no | — |
| 513 | C22 | — | 16 | 2 | no | — |
| 514 | C22 | — | 16 | 2 | no | — |
| 515 | C22 | — | 16 | 2 | no | — |
| 516 | C22 | — | 16 | 2 | no | — |
| 517 | C22 | — | 16 | 2 | no | — |
| 518 | C22 | — | 16 | 2 | no | — |
| 519 | C22 | #23188 | 1 | 1 | yes | characteristic |
| 520 | C4 | — | 2 | 1 | no | — |
| 521 | C4 | — | 2 | 1 | no | — |
| 522 | C4 | — | 2 | 1 | no | — |
| 523 | C4 | — | 2 | 1 | no | — |
| 524 | C4 | — | 16 | 2 | no | — |
| 525 | C4 | — | 16 | 2 | no | — |
| 526 | C4 | — | 32 | 1 | no | — |
| 527 | C4 | #23181 | 1 | 1 | yes | characteristic |
| 528 | C4 | #23197 | 1 | 1 | yes | characteristic |
| 529 | C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 530 | C4 | #33471 | 1 | 1 | yes | characteristic |
| 531 | C2 | — | 4 | 1 | no | — |
| 532 | C2 | — | 32 | 2 | no | — |
| 533 | C2 | — | 32 | 2 | no | — |
| 534 | C2 | #231547 | 1 | 1 | yes | characteristic |
| 535 | C2 | #498578 | 1 | 1 | yes | characteristic |
| 536 | C2 | #498582 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #23188 |
| commutator | C4×C8 | C23×C4 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| prime radical | #491550 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #8293 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #484147 | C2 | semidirect |
| 3. #231721 | C2 | semidirect |
| 4. #231542 | C2 | semidirect |
| 5. #141341 | C2 | semidirect |
| 6. #141326 | C2 | semidirect |
| 7. #141213 | C2 | semidirect |
| 8. #137501 | C2 | semidirect |
| 9. #137499 | C2 | semidirect |
| 10. #129200 | C2 | semidirect |
| 11. #129184 | C2 | semidirect |
| 21. #12532 | C4 | semidirect |
| 22. #12532 | C4 | semidirect |
| 23. #12525 | C4 | semidirect |
| 24. #12525 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #491550 | 2 |
| #484147 | 2 |
| #231721 | 2 |
| #231542 | 2 |
| #141341 | 2 |
| #141326 | 2 |
| #141213 | 2 |
| #137501 | 2 |
| #137499 | 2 |
| #129200 | 2 |
| #129184 | 2 |