Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
2356 conjugacy classes of subgroups.
The subgroup lattice has 496 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7623523 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #6345753 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #484058 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | #483996 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #483965 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #483445 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #481345 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #479959 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#3169 | C22 | 1 | 2 | yes | — |
| 10 | #60232 | — | 2 | 2 | no | — |
| 11 | #33819 | C4 | 1 | 4 | yes | — |
| 12 | #33793 | C4 | 1 | 4 | yes | — |
| 13 | #33771 | C4 | 1 | 4 | yes | — |
| 14 | #33758 | C4 | 1 | 4 | yes | — |
| 15 | #33748 | C22 | 1 | 4 | yes | — |
| 16 | #33669 | C22 | 1 | 8 | yes | — |
| 17 | #33418 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 19 | #18091 | C22 | 1 | 8 | yes | — |
| 20 | #18084 | — | 2 | 4 | no | — |
| 21 | #18044 | C22 | 1 | 8 | yes | complemented |
| 22 | M16×D8 | — | 2 | 4 | no | — |
| 23 | #17989 | — | 2 | 4 | no | — |
| 24 | #17970 | C22 | 1 | 8 | yes | complemented |
| 25 | #17793 | C22 | 1 | 2 | yes | — |
| 26 | #17490 | — | 2 | 2 | no | — |
| 27 | #17323 | C22 | 1 | 1 | yes | characteristic |
| 28 | #12089 | C22 | 1 | 16 | yes | complemented |
| 29 | #12078 | C22 | 1 | 32 | yes | complemented |
| 30 | #12067 | C22 | 1 | 16 | yes | complemented |
| 31 | #12029 | C22 | 1 | 8 | yes | complemented |
| 32 | #12021 | C22 | 1 | 4 | yes | complemented |
| 33 | #11680 | C22 | 1 | 8 | yes | — |
| 34 | #11678 | C22 | 1 | 4 | yes | complemented |
| 35 | #11678 | C22 | 1 | 4 | yes | complemented |
| 36 | #11599 | C22 | 1 | 8 | yes | complemented |
| 37 | #11414 | C22 | 1 | 8 | yes | complemented |
| 38 | #11406 | C22 | 1 | 2 | yes | complemented |
| 39 | #11405 | C22 | 1 | 2 | yes | complemented |
| 40 | C2×#532 | — | 2 | 2 | no | — |
| 41 | C22×M32 | — | 2 | 1 | no | — |
| 42 | #3169 | — | 2 | 2 | no | — |
| 43 | #3169 | — | 2 | 2 | no | — |
| 44 | #3169 | — | 2 | 2 | no | — |
| 45 | #3169 | — | 2 | 2 | no | — |
| 46 | #3169 | C2×C4 | 1 | 4 | yes | — |
| 47 | #3169 | C2×C4 | 1 | 4 | yes | — |
| 48 | #3169 | C23 | 1 | 4 | yes | — |
| 49 | #3169 | C23 | 1 | 4 | yes | — |
| 50 | C2×#500 | C2×C4 | 1 | 2 | yes | — |
| 51 | C2×#493 | C2×C4 | 1 | 2 | yes | — |
| 52 | C2×#486 | — | 2 | 2 | no | — |
| 53 | C2×#466 | — | 2 | 2 | no | — |
| 54 | C2×#466 | C2×C4 | 1 | 4 | yes | — |
| 55 | #2981 | — | 2 | 8 | no | — |
| 56 | #2981 | — | 4 | 4 | no | — |
| 57 | #2980 | — | 4 | 4 | no | — |
| 58 | #2979 | — | 2 | 8 | no | — |
| 59 | C2×C4×D8 | — | 2 | 2 | no | — |
| 60 | C2×C4×D8 | C23 | 1 | 4 | yes | — |
| 61 | D4×M16 | — | 2 | 8 | no | — |
| 62 | D4×M16 | — | 4 | 4 | no | — |
| 63 | #2920 | — | 2 | 2 | no | — |
| 64 | #2920 | D4 | 1 | 2 | yes | — |
| 65 | #2879 | — | 4 | 4 | no | — |
| 66 | C22×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 67 | #2254 | C2×C4 | 1 | 4 | yes | — |
| 68 | #2246 | C2×C4 | 1 | 4 | yes | — |
| 69 | #2240 | C2×C4 | 1 | 8 | yes | — |
| 70 | #2233 | C2×C4 | 1 | 16 | yes | — |
| 71 | #2226 | C2×C4 | 1 | 16 | yes | — |
| 72 | #2218 | C2×C4 | 1 | 16 | yes | — |
| 73 | #2206 | C2×C4 | 1 | 16 | yes | — |
| 74 | #2184 | C2×C4 | 1 | 16 | yes | — |
| 75 | #2177 | C23 | 1 | 16 | yes | — |
| 76 | #2163 | C23 | 1 | 4 | yes | — |
| 77 | #2162 | C2×C4 | 1 | 4 | yes | — |
| 78 | #2150 | C2×C4 | 1 | 2 | yes | — |
| 79 | #2112 | C2×C4 | 1 | 2 | yes | — |
| 80 | C4×M32 | — | 2 | 2 | no | — |
| 81 | C4×M32 | C23 | 1 | 4 | yes | — |
| 82 | C4×M32 | C23 | 1 | 2 | yes | — |
| 83 | C2×#346 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#346 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×C16 | — | 2 | 1 | no | — |
| 86 | #1594 | C23 | 1 | 16 | yes | — |
| 87 | #1589 | — | 2 | 8 | no | — |
| 88 | #1586 | — | 2 | 16 | no | — |
| 89 | #1581 | — | 2 | 16 | no | — |
| 90 | #1580 | C23 | 1 | 16 | yes | — |
| 91 | C8×D8 | — | 2 | 8 | no | — |
| 92 | #1568 | — | 2 | 2 | no | — |
| 93 | #1568 | C23 | 1 | 4 | yes | — |
| 94 | #1567 | — | 2 | 2 | no | — |
| 95 | #1566 | C23 | 1 | 4 | yes | — |
| 96 | #1564 | — | 2 | 2 | no | — |
| 97 | #1564 | C23 | 1 | 4 | yes | — |
| 98 | #1496 | — | 2 | 8 | no | — |
| 99 | #1486 | — | 2 | 8 | no | — |
| 100 | #1484 | — | 2 | 8 | no | — |
| 101 | #1452 | D4 | 1 | 2 | yes | — |
| 102 | #1451 | C23 | 1 | 4 | yes | — |
| 103 | #1450 | C23 | 1 | 2 | yes | — |
| 104 | C8×M16 | D4 | 1 | 4 | yes | — |
| 105 | #1368 | C23 | 1 | 16 | yes | — |
| 106 | #1333 | C23 | 1 | 16 | yes | — |
| 107 | #1333 | C23 | 1 | 16 | yes | — |
| 108 | #1313 | C23 | 1 | 8 | yes | — |
| 109 | #1313 | C23 | 1 | 8 | yes | — |
| 110 | C22×#41 | — | 4 | 2 | no | — |
| 111 | C22×D8 | — | 2 | 2 | no | — |
| 112 | C22×D8 | C22×C4 | 1 | 4 | yes | — |
| 113 | C22×M16 | — | 4 | 8 | no | — |
| 114 | C23×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 115 | C23×C8 | #41 | 1 | 1 | yes | characteristic |
| 116 | #532 | — | 2 | 4 | no | — |
| 117 | #532 | — | 2 | 4 | no | — |
| 118 | #532 | — | 2 | 4 | no | — |
| 119 | #532 | — | 2 | 4 | no | — |
| 120 | #532 | — | 4 | 2 | no | — |
| 121 | #532 | — | 4 | 2 | no | — |
| 122 | #532 | — | 4 | 2 | no | — |
| 123 | #532 | — | 4 | 2 | no | — |
| 124 | C2×C4⋊Q8 | — | 2 | 2 | no | — |
| 125 | C2×#127 | — | 2 | 2 | no | — |
| 126 | C2×#124 | — | 4 | 2 | no | — |
| 127 | C2×#121 | — | 2 | 4 | no | — |
| 128 | C2×#121 | — | 4 | 2 | no | — |
| 129 | C2×C4×D4 | — | 2 | 4 | no | — |
| 130 | C2×C4×D4 | — | 4 | 2 | no | — |
| 131 | C22×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×D16 | C22×C4 | 1 | 16 | yes | — |
| 133 | C2×M32 | — | 2 | 4 | no | — |
| 134 | C2×M32 | — | 4 | 4 | no | — |
| 135 | C2×M32 | C22×C4 | 1 | 4 | yes | — |
| 136 | C22×C16 | — | 2 | 1 | no | — |
| 137 | C22×C16 | — | 2 | 1 | no | — |
| 138 | #500 | — | 2 | 2 | no | — |
| 139 | #500 | — | 2 | 2 | no | — |
| 140 | #500 | C22×C4 | 1 | 4 | yes | — |
| 141 | #500 | C22×C4 | 1 | 4 | yes | — |
| 142 | #493 | — | 2 | 2 | no | — |
| 143 | #493 | — | 2 | 2 | no | — |
| 144 | #493 | C22×C4 | 1 | 4 | yes | — |
| 145 | #493 | C22×C4 | 1 | 4 | yes | — |
| 146 | #486 | — | 2 | 4 | no | — |
| 147 | #486 | — | 2 | 4 | no | — |
| 148 | #486 | — | 2 | 4 | no | — |
| 149 | #486 | — | 2 | 4 | no | — |
| 150 | #466 | — | 2 | 4 | no | — |
| 151 | #466 | — | 2 | 4 | no | — |
| 152 | #466 | — | 2 | 4 | no | — |
| 153 | #466 | — | 2 | 4 | no | — |
| 154 | #466 | — | 2 | 4 | no | — |
| 155 | #466 | — | 2 | 4 | no | — |
| 156 | #466 | C22×C4 | 1 | 8 | yes | — |
| 157 | #466 | C22×C4 | 1 | 8 | yes | — |
| 158 | C4×D8 | — | 2 | 4 | no | — |
| 159 | C4×D8 | — | 2 | 4 | no | — |
| 160 | C4×D8 | — | 2 | 4 | no | — |
| 161 | C4×D8 | — | 2 | 4 | no | — |
| 162 | C4×D8 | — | 2 | 4 | no | — |
| 163 | C4×D8 | — | 2 | 4 | no | — |
| 164 | C4×D8 | C22×C4 | 1 | 8 | yes | — |
| 165 | C4×D8 | C24 | 1 | 8 | yes | — |
| 166 | #436 | — | 2 | 16 | no | — |
| 167 | #436 | — | 4 | 8 | no | — |
| 168 | #435 | — | 4 | 16 | no | — |
| 169 | #435 | — | 4 | 16 | no | — |
| 170 | C8×D4 | — | 2 | 16 | no | — |
| 171 | C8×D4 | — | 4 | 8 | no | — |
| 172 | #432 | — | 2 | 2 | no | — |
| 173 | #432 | — | 2 | 2 | no | — |
| 174 | #432 | — | 2 | 4 | no | — |
| 175 | #432 | — | 4 | 2 | no | — |
| 176 | #431 | — | 2 | 4 | no | — |
| 177 | #431 | — | 4 | 2 | no | — |
| 178 | #431 | C2×D4 | 1 | 4 | yes | — |
| 179 | #431 | C2×D4 | 1 | 4 | yes | — |
| 180 | C2×#107 | — | 2 | 2 | no | — |
| 181 | C2×#107 | C22×C4 | 1 | 4 | yes | — |
| 182 | #423 | — | 2 | 2 | no | — |
| 183 | #423 | — | 2 | 4 | no | — |
| 184 | C2×#102 | — | 2 | 4 | no | — |
| 185 | C2×#102 | — | 2 | 4 | no | — |
| 186 | #408 | — | 4 | 16 | no | — |
| 187 | #408 | — | 4 | 16 | no | — |
| 188 | #407 | — | 2 | 2 | no | — |
| 189 | #407 | — | 4 | 8 | no | — |
| 190 | #407 | — | 4 | 2 | no | — |
| 191 | C4×M16 | — | 4 | 2 | no | — |
| 192 | C4×M16 | C2×D4 | 1 | 4 | yes | — |
| 193 | C2×C4×C8 | C22×C4 | 1 | 2 | yes | — |
| 194 | C2×C4×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 195 | C2×C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 196 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C8 | #41 | 1 | 2 | yes | — |
| 198 | C2×C4×C8 | #41 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×C8 | C24 | 1 | 2 | yes | — |
| 200 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 201 | #367 | C22×C4 | 1 | 16 | yes | — |
| 202 | C4⋊C16 | C22×C4 | 1 | 8 | yes | — |
| 203 | #357 | C22×C4 | 1 | 32 | yes | — |
| 204 | C22⋊C16 | C22×C4 | 1 | 8 | yes | — |
| 205 | #346 | — | 2 | 1 | no | — |
| 206 | #346 | — | 2 | 1 | no | — |
| 207 | #346 | C24 | 1 | 2 | yes | — |
| 208 | #346 | C24 | 1 | 2 | yes | — |
| 209 | #346 | C24 | 1 | 4 | yes | — |
| 210 | C4×C16 | — | 2 | 4 | no | — |
| 211 | C4×C16 | C22×C4 | 1 | 4 | yes | — |
| 212 | #335 | — | 2 | 4 | no | — |
| 213 | #335 | — | 2 | 4 | no | — |
| 214 | #334 | — | 2 | 4 | no | — |
| 215 | #334 | C24 | 1 | 8 | yes | — |
| 216 | D4⋊C8 | — | 2 | 16 | no | — |
| 217 | D4⋊C8 | — | 2 | 16 | no | — |
| 218 | #322 | C2×D4 | 1 | 8 | yes | — |
| 219 | #322 | C24 | 1 | 4 | yes | — |
| 220 | C82 | C2×D4 | 1 | 4 | yes | — |
| 221 | C2×#41 | — | 4 | 4 | no | — |
| 222 | C2×#41 | — | 4 | 4 | no | — |
| 223 | C2×#41 | — | 4 | 4 | no | — |
| 224 | C2×#41 | — | 4 | 4 | no | — |
| 225 | C2×#41 | — | 16 | 8 | no | — |
| 226 | C22×Q8 | — | 4 | 2 | no | — |
| 227 | C22×D4 | — | 2 | 4 | no | — |
| 228 | C22×D4 | — | 4 | 4 | no | — |
| 229 | C22×D4 | — | 4 | 2 | no | — |
| 230 | C22×D4 | — | 4 | 2 | no | — |
| 231 | C23×C4 | — | 4 | 4 | no | — |
| 232 | C23×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 233 | C23×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 234 | C2×D8 | — | 2 | 4 | no | — |
| 235 | C2×D8 | — | 2 | 4 | no | — |
| 236 | C2×D8 | — | 2 | 4 | no | — |
| 237 | C2×D8 | — | 4 | 8 | no | — |
| 238 | C2×D8 | — | 8 | 4 | no | — |
| 239 | C2×D8 | C23×C4 | 1 | 8 | yes | — |
| 240 | C2×M16 | — | 2 | 4 | no | — |
| 241 | C2×M16 | — | 4 | 16 | no | — |
| 242 | C2×M16 | — | 4 | 4 | no | — |
| 243 | C2×M16 | — | 16 | 16 | no | — |
| 244 | C22×C8 | — | 4 | 2 | no | — |
| 245 | C22×C8 | — | 4 | 2 | no | — |
| 246 | C22×C8 | — | 4 | 16 | no | — |
| 247 | C22×C8 | C4×D4 | 1 | 2 | yes | — |
| 248 | C22×C8 | C4×D4 | 1 | 2 | yes | — |
| 249 | C22×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 250 | C22×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 251 | C22×C8 | C23×C4 | 1 | 2 | yes | — |
| 252 | C22×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 253 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 254 | C22×C8 | C2×#41 | 1 | 2 | yes | — |
| 255 | C4⋊Q8 | — | 2 | 4 | no | — |
| 256 | C4⋊Q8 | — | 2 | 4 | no | — |
| 257 | C4⋊Q8 | — | 4 | 2 | no | — |
| 258 | C4⋊Q8 | — | 4 | 2 | no | — |
| 259 | #127 | — | 2 | 4 | no | — |
| 260 | #127 | — | 2 | 4 | no | — |
| 261 | #127 | — | 4 | 2 | no | — |
| 262 | #127 | — | 4 | 2 | no | — |
| 263 | #124 | — | 4 | 4 | no | — |
| 264 | #124 | — | 4 | 4 | no | — |
| 265 | #124 | — | 4 | 4 | no | — |
| 266 | #124 | — | 4 | 4 | no | — |
| 267 | #121 | — | 2 | 8 | no | — |
| 268 | #121 | — | 2 | 8 | no | — |
| 269 | #121 | — | 4 | 4 | no | — |
| 270 | #121 | — | 4 | 4 | no | — |
| 271 | #121 | — | 4 | 4 | no | — |
| 272 | #121 | — | 4 | 4 | no | — |
| 273 | #121 | — | 4 | 4 | no | — |
| 274 | #121 | — | 4 | 4 | no | — |
| 275 | C4×D4 | — | 2 | 8 | no | — |
| 276 | C4×D4 | — | 2 | 8 | no | — |
| 277 | C4×D4 | — | 4 | 4 | no | — |
| 278 | C4×D4 | — | 4 | 4 | no | — |
| 279 | C4×D4 | — | 4 | 4 | no | — |
| 280 | C4×D4 | — | 4 | 4 | no | — |
| 281 | C4×D4 | — | 4 | 4 | no | — |
| 282 | C4×D4 | — | 4 | 4 | no | — |
| 283 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 284 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 285 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 286 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 287 | C2×C42 | C4×D4 | 1 | 2 | yes | — |
| 288 | C2×C42 | C4×D4 | 1 | 1 | yes | characteristic |
| 289 | C2×C42 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 290 | C2×C42 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 291 | C2×C42 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 292 | C2×C42 | C22×D4 | 1 | 2 | yes | — |
| 293 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 294 | D16 | — | 4 | 16 | no | — |
| 295 | M32 | — | 4 | 4 | no | — |
| 296 | M32 | — | 4 | 8 | no | — |
| 297 | C2×C16 | — | 2 | 4 | no | — |
| 298 | C2×C16 | — | 2 | 2 | no | — |
| 299 | C2×C16 | — | 2 | 2 | no | — |
| 300 | C2×C16 | — | 4 | 2 | no | — |
| 301 | C2×C16 | C23×C4 | 1 | 8 | yes | — |
| 302 | #107 | — | 2 | 4 | no | — |
| 303 | #107 | — | 2 | 4 | no | — |
| 304 | #107 | — | 2 | 4 | no | — |
| 305 | #107 | C23×C4 | 1 | 8 | yes | — |
| 306 | C4⋊C8 | — | 2 | 4 | no | — |
| 307 | C4⋊C8 | — | 2 | 4 | no | — |
| 308 | C4⋊C8 | — | 2 | 8 | no | — |
| 309 | C4⋊C8 | — | 4 | 4 | no | — |
| 310 | #102 | — | 2 | 8 | no | — |
| 311 | #102 | — | 2 | 8 | no | — |
| 312 | #102 | — | 2 | 8 | no | — |
| 313 | #102 | — | 2 | 8 | no | — |
| 314 | C22⋊C8 | — | 2 | 4 | no | — |
| 315 | C22⋊C8 | — | 2 | 4 | no | — |
| 316 | C22⋊C8 | — | 4 | 16 | no | — |
| 317 | C22⋊C8 | — | 4 | 16 | no | — |
| 318 | C22⋊C8 | — | 4 | 4 | no | — |
| 319 | C22⋊C8 | — | 4 | 4 | no | — |
| 320 | #97 | — | 2 | 4 | no | — |
| 321 | #97 | — | 4 | 4 | no | — |
| 322 | C4×C8 | — | 4 | 4 | no | — |
| 323 | C4×C8 | C4×D4 | 1 | 2 | yes | — |
| 324 | C4×C8 | C4×D4 | 1 | 2 | yes | — |
| 325 | C4×C8 | C4×D4 | 1 | 2 | yes | — |
| 326 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 327 | C4×C8 | C23×C4 | 1 | 2 | yes | — |
| 328 | C4×C8 | C22×D4 | 1 | 8 | yes | — |
| 329 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | C4×C8 | C22×D4 | 1 | 2 | yes | — |
| 331 | C4×C8 | C2×#41 | 1 | 2 | yes | — |
| 332 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 333 | C4×C8 | C25 | 1 | 1 | yes | characteristic |
| 334 | C24 | — | 4 | 4 | no | — |
| 335 | C24 | #442 | 1 | 1 | yes | characteristic |
| 336 | #41 | — | 16 | 8 | no | — |
| 337 | #41 | — | 16 | 8 | no | — |
| 338 | #41 | — | 16 | 4 | no | — |
| 339 | #41 | — | 16 | 8 | no | — |
| 340 | #41 | — | 16 | 4 | no | — |
| 341 | C2×Q8 | — | 4 | 4 | no | — |
| 342 | C2×Q8 | — | 4 | 4 | no | — |
| 343 | C2×Q8 | — | 16 | 4 | no | — |
| 344 | C2×D4 | — | 2 | 8 | no | — |
| 345 | C2×D4 | — | 4 | 8 | no | — |
| 346 | C2×D4 | — | 4 | 8 | no | — |
| 347 | C2×D4 | — | 4 | 4 | no | — |
| 348 | C2×D4 | — | 4 | 4 | no | — |
| 349 | C2×D4 | — | 4 | 4 | no | — |
| 350 | C2×D4 | — | 4 | 4 | no | — |
| 351 | C2×D4 | — | 4 | 4 | no | — |
| 352 | C2×D4 | — | 8 | 4 | no | — |
| 353 | C2×D4 | — | 8 | 4 | no | — |
| 354 | C2×D4 | — | 16 | 4 | no | — |
| 355 | C2×D4 | — | 16 | 4 | no | — |
| 356 | C2×D4 | — | 16 | 8 | no | — |
| 357 | C22×C4 | — | 4 | 1 | no | — |
| 358 | C22×C4 | — | 4 | 1 | no | — |
| 359 | C22×C4 | — | 4 | 4 | no | — |
| 360 | C22×C4 | — | 4 | 4 | no | — |
| 361 | C22×C4 | — | 4 | 8 | no | — |
| 362 | C22×C4 | — | 4 | 8 | no | — |
| 363 | C22×C4 | — | 8 | 16 | no | — |
| 364 | C22×C4 | #442 | 1 | 2 | yes | — |
| 365 | C22×C4 | #442 | 1 | 2 | yes | — |
| 366 | C22×C4 | #442 | 1 | 2 | yes | — |
| 367 | C22×C4 | #442 | 1 | 2 | yes | — |
| 368 | C22×C4 | #442 | 1 | 1 | yes | characteristic |
| 369 | C22×C4 | C2×C4×D4 | 1 | 2 | yes | — |
| 370 | C22×C4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 371 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 372 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 373 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 374 | D8 | — | 2 | 16 | no | — |
| 375 | D8 | — | 4 | 8 | no | — |
| 376 | D8 | — | 8 | 4 | no | — |
| 377 | D8 | — | 8 | 4 | no | — |
| 378 | M16 | — | 4 | 8 | no | — |
| 379 | M16 | — | 8 | 8 | no | — |
| 380 | M16 | — | 16 | 16 | no | — |
| 381 | C2×C8 | — | 2 | 2 | no | — |
| 382 | C2×C8 | — | 2 | 4 | no | — |
| 383 | C2×C8 | — | 2 | 2 | no | — |
| 384 | C2×C8 | — | 2 | 4 | no | — |
| 385 | C2×C8 | — | 2 | 8 | no | — |
| 386 | C2×C8 | — | 4 | 2 | no | — |
| 387 | C2×C8 | — | 4 | 1 | no | — |
| 388 | C2×C8 | — | 4 | 2 | no | — |
| 389 | C2×C8 | — | 4 | 1 | no | — |
| 390 | C2×C8 | — | 4 | 8 | no | — |
| 391 | C2×C8 | — | 16 | 16 | no | — |
| 392 | C2×C8 | C2×C4×D4 | 1 | 2 | yes | — |
| 393 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 394 | C2×C8 | C2×C4×D4 | 1 | 2 | yes | — |
| 395 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 396 | C2×C8 | C24×C4 | 1 | 1 | yes | characteristic |
| 397 | C2×C8 | C22×#41 | 1 | 1 | yes | characteristic |
| 398 | C4⋊C4 | — | 2 | 8 | no | — |
| 399 | C4⋊C4 | — | 4 | 4 | no | — |
| 400 | C4⋊C4 | — | 4 | 4 | no | — |
| 401 | C4⋊C4 | — | 4 | 4 | no | — |
| 402 | C22⋊C4 | — | 4 | 8 | no | — |
| 403 | C22⋊C4 | — | 4 | 8 | no | — |
| 404 | C22⋊C4 | — | 4 | 8 | no | — |
| 405 | C22⋊C4 | — | 4 | 8 | no | — |
| 406 | C42 | #442 | 1 | 1 | yes | characteristic |
| 407 | C42 | #442 | 1 | 2 | yes | — |
| 408 | C42 | #442 | 1 | 1 | yes | characteristic |
| 409 | C42 | #442 | 1 | 2 | yes | — |
| 410 | C42 | C2×C4×D4 | 1 | 2 | yes | — |
| 411 | C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 412 | C42 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 413 | C42 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 414 | C42 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 415 | C42 | C23×D4 | 1 | 1 | yes | characteristic |
| 416 | C16 | — | 2 | 4 | no | — |
| 417 | C16 | — | 2 | 8 | no | — |
| 418 | C16 | — | 4 | 2 | no | — |
| 419 | C23 | — | 4 | 2 | no | — |
| 420 | C23 | — | 4 | 1 | no | — |
| 421 | C23 | — | 4 | 8 | no | — |
| 422 | C23 | — | 8 | 8 | no | — |
| 423 | C23 | — | 16 | 4 | no | — |
| 424 | C23 | — | 16 | 4 | no | — |
| 425 | C23 | C2×#442 | 1 | 2 | yes | — |
| 426 | C23 | C2×#442 | 1 | 1 | yes | characteristic |
| 427 | Q8 | — | 16 | 4 | no | — |
| 428 | Q8 | — | 16 | 4 | no | — |
| 429 | D4 | — | 4 | 8 | no | — |
| 430 | D4 | — | 4 | 8 | no | — |
| 431 | D4 | — | 8 | 8 | no | — |
| 432 | D4 | — | 16 | 4 | no | — |
| 433 | D4 | — | 16 | 4 | no | — |
| 434 | D4 | — | 16 | 4 | no | — |
| 435 | D4 | — | 16 | 4 | no | — |
| 436 | D4 | — | 16 | 8 | no | — |
| 437 | D4 | — | 16 | 8 | no | — |
| 438 | C2×C4 | — | 2 | 1 | no | — |
| 439 | C2×C4 | — | 2 | 2 | no | — |
| 440 | C2×C4 | — | 2 | 4 | no | — |
| 441 | C2×C4 | — | 2 | 4 | no | — |
| 442 | C2×C4 | — | 2 | 4 | no | — |
| 443 | C2×C4 | — | 2 | 1 | no | — |
| 444 | C2×C4 | — | 2 | 2 | no | — |
| 445 | C2×C4 | — | 4 | 2 | no | — |
| 446 | C2×C4 | — | 4 | 2 | no | — |
| 447 | C2×C4 | — | 4 | 2 | no | — |
| 448 | C2×C4 | — | 4 | 1 | no | — |
| 449 | C2×C4 | — | 4 | 2 | no | — |
| 450 | C2×C4 | — | 4 | 8 | no | — |
| 451 | C2×C4 | — | 8 | 8 | no | — |
| 452 | C2×C4 | — | 8 | 8 | no | — |
| 453 | C2×C4 | — | 8 | 8 | no | — |
| 454 | C2×C4 | — | 8 | 16 | no | — |
| 455 | C2×C4 | C2×#442 | 1 | 2 | yes | — |
| 456 | C2×C4 | C2×#442 | 1 | 2 | yes | — |
| 457 | C2×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 458 | C2×C4 | C2×#442 | 1 | 2 | yes | — |
| 459 | C2×C4 | C2×#442 | 1 | 2 | yes | — |
| 460 | C2×C4 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | C22×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 462 | C8 | — | 2 | 1 | no | — |
| 463 | C8 | — | 2 | 2 | no | — |
| 464 | C8 | — | 2 | 1 | no | — |
| 465 | C8 | — | 2 | 2 | no | — |
| 466 | C8 | — | 4 | 8 | no | — |
| 467 | C8 | — | 8 | 8 | no | — |
| 468 | C8 | #2956 | 1 | 2 | yes | — |
| 469 | C8 | #3573 | 1 | 2 | yes | — |
| 470 | C22 | — | 2 | 2 | no | — |
| 471 | C22 | — | 2 | 1 | no | — |
| 472 | C22 | — | 2 | 2 | no | — |
| 473 | C22 | — | 2 | 2 | no | — |
| 474 | C22 | — | 2 | 2 | no | — |
| 475 | C22 | — | 8 | 2 | no | — |
| 476 | C22 | — | 8 | 8 | no | — |
| 477 | C22 | — | 8 | 8 | no | — |
| 478 | C22 | — | 8 | 8 | no | — |
| 479 | C22 | — | 32 | 8 | no | — |
| 480 | C22 | C22×#442 | 1 | 1 | yes | characteristic |
| 481 | C4 | — | 2 | 1 | no | — |
| 482 | C4 | — | 2 | 2 | no | — |
| 483 | C4 | — | 2 | 2 | no | — |
| 484 | C4 | — | 2 | 2 | no | — |
| 485 | C4 | — | 2 | 2 | no | — |
| 486 | C4 | — | 8 | 8 | no | — |
| 487 | C4 | #33471 | 1 | 4 | yes | — |
| 488 | C4 | #60143 | 1 | 1 | yes | characteristic |
| 489 | C4 | C2×#2956 | 1 | 1 | yes | characteristic |
| 490 | C2 | — | 4 | 1 | no | — |
| 491 | C2 | — | 4 | 2 | no | — |
| 492 | C2 | — | 16 | 8 | no | — |
| 493 | C2 | #6345612 | 1 | 1 | yes | characteristic |
| 494 | C2 | C2×#33471 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#442 |
| commutator | C2×C8 | C24×C4 |
| Frattini, cosocle | C4×C8 | C25 |
| prime radical | #7623523 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C42 ◁ #17323 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #6345753 | C2 | semidirect |
| 3. #484058 | C2 | semidirect |
| 4. #483996 | C2 | semidirect |
| 5. #483965 | C2 | semidirect |
| 6. #483445 | C2 | semidirect |
| 7. #481345 | C2 | semidirect |
| 8. #479959 | C2 | semidirect |
| 21. #18044 | C22 | semidirect |
| 24. #17970 | C22 | semidirect |
| 28. #12089 | C22 | semidirect |
| 29. #12078 | C22 | semidirect |
| 30. #12067 | C22 | semidirect |
| 31. #12029 | C22 | semidirect |
| 32. #12021 | C22 | semidirect |
| 34. #11678 | C22 | semidirect |
| 35. #11678 | C22 | semidirect |
| 36. #11599 | C22 | semidirect |
| 37. #11414 | C22 | semidirect |
| 38. #11406 | C22 | semidirect |
| 39. #11405 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7623523 | 2 |
| #6345753 | 2 |
| #484058 | 2 |
| #483996 | 2 |
| #483965 | 2 |
| #483445 | 2 |
| #481345 | 2 |
| #479959 | 2 |