Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
817 conjugacy classes of subgroups.
The subgroup lattice has 673 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #496303 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #494051 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #481290 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #479976 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #127410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #127316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #127134 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #60183 | C22 | 1 | 1 | yes | characteristic |
| 9 | #33428 | C22 | 1 | 1 | yes | characteristic |
| 10 | #33428 | C22 | 1 | 1 | yes | characteristic |
| 11 | #33421 | C22 | 1 | 1 | yes | characteristic |
| 12 | #33421 | C22 | 1 | 1 | yes | characteristic |
| 13 | #20787 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17336 | C22 | 1 | 1 | yes | characteristic |
| 15 | #13199 | C4 | 1 | 2 | yes | complemented |
| 16 | #13198 | C4 | 1 | 2 | yes | complemented |
| 17 | #13197 | — | 2 | 1 | no | — |
| 18 | #13196 | — | 2 | 1 | no | — |
| 19 | #12878 | C4 | 1 | 1 | yes | characteristic |
| 20 | #12877 | C4 | 1 | 1 | yes | characteristic |
| 21 | #12830 | — | 2 | 1 | no | — |
| 22 | #12829 | — | 2 | 1 | no | — |
| 23 | #12746 | C4 | 1 | 1 | yes | characteristic |
| 24 | #12745 | C4 | 1 | 1 | yes | characteristic |
| 25 | #12685 | — | 2 | 1 | no | — |
| 26 | #12684 | — | 2 | 1 | no | — |
| 27 | #12646 | — | 2 | 1 | no | — |
| 28 | #12642 | — | 2 | 1 | no | — |
| 29 | #11670 | — | 2 | 1 | no | — |
| 30 | #11670 | C4 | 1 | 2 | yes | complemented |
| 31 | #11669 | — | 2 | 1 | no | — |
| 32 | #11669 | C4 | 1 | 2 | yes | complemented |
| 33 | C2×#1336 | — | 2 | 1 | no | — |
| 34 | #11602 | — | 2 | 1 | no | — |
| 35 | #11416 | — | 2 | 1 | no | — |
| 36 | #11415 | — | 2 | 1 | no | — |
| 37 | #11414 | — | 2 | 1 | no | — |
| 38 | #11414 | — | 2 | 1 | no | — |
| 39 | #11413 | — | 2 | 1 | no | — |
| 40 | #11413 | — | 2 | 1 | no | — |
| 41 | #7240 | — | 2 | 1 | no | — |
| 42 | #7239 | — | 2 | 1 | no | — |
| 43 | #7226 | — | 2 | 1 | no | — |
| 44 | #7225 | — | 2 | 1 | no | — |
| 45 | #7208 | — | 2 | 1 | no | — |
| 46 | #7207 | — | 2 | 1 | no | — |
| 47 | #3584 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #3573 | — | 2 | 1 | no | — |
| 49 | #2965 | — | 2 | 1 | no | — |
| 50 | #2957 | — | 2 | 1 | no | — |
| 51 | #2957 | — | 2 | 1 | no | — |
| 52 | #2957 | — | 2 | 1 | no | — |
| 53 | #2956 | — | 2 | 1 | no | — |
| 54 | #2956 | — | 2 | 1 | no | — |
| 55 | #2956 | C2×C4 | 1 | 2 | yes | — |
| 56 | #2955 | — | 2 | 1 | no | — |
| 57 | #2955 | — | 2 | 1 | no | — |
| 58 | #2955 | C2×C4 | 1 | 2 | yes | — |
| 59 | C2×#443 | — | 2 | 1 | no | — |
| 60 | C2×#443 | — | 2 | 1 | no | — |
| 61 | C2×#443 | — | 2 | 1 | no | — |
| 62 | #2916 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | #2901 | — | 2 | 1 | no | — |
| 64 | C4×#131 | C23 | 1 | 1 | yes | characteristic |
| 65 | #2166 | — | 2 | 1 | no | — |
| 66 | #2166 | — | 2 | 1 | no | — |
| 67 | #2166 | — | 2 | 1 | no | — |
| 68 | #2166 | — | 2 | 1 | no | — |
| 69 | #2165 | — | 2 | 1 | no | — |
| 70 | #2165 | — | 2 | 1 | no | — |
| 71 | #2165 | — | 2 | 1 | no | — |
| 72 | #2165 | C2×C4 | 1 | 2 | yes | — |
| 73 | #2164 | — | 2 | 1 | no | — |
| 74 | #2164 | — | 2 | 1 | no | — |
| 75 | #2164 | — | 2 | 1 | no | — |
| 76 | #2164 | — | 2 | 1 | no | — |
| 77 | #2163 | — | 2 | 1 | no | — |
| 78 | #2163 | — | 2 | 1 | no | — |
| 79 | #2163 | — | 2 | 1 | no | — |
| 80 | #2163 | — | 2 | 1 | no | — |
| 81 | C2×#364 | — | 2 | 1 | no | — |
| 82 | C2×#364 | — | 2 | 1 | no | — |
| 83 | #2151 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #2151 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | #2151 | D4 | 1 | 1 | yes | characteristic |
| 86 | #2151 | D4 | 1 | 1 | yes | characteristic |
| 87 | #2148 | — | 2 | 1 | no | — |
| 88 | #2145 | — | 2 | 1 | no | — |
| 89 | C2×#359 | — | 2 | 1 | no | — |
| 90 | #2138 | — | 2 | 1 | no | — |
| 91 | #2117 | — | 2 | 2 | no | — |
| 92 | C2×#350 | — | 2 | 2 | no | — |
| 93 | #2115 | — | 2 | 2 | no | — |
| 94 | #2115 | — | 2 | 1 | no | — |
| 95 | #2115 | — | 2 | 1 | no | — |
| 96 | #2113 | — | 2 | 2 | no | — |
| 97 | #2113 | C2×C4 | 1 | 1 | yes | characteristic |
| 98 | #2113 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 100 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 101 | #2110 | — | 2 | 1 | no | — |
| 102 | #2110 | C2×C4 | 1 | 2 | yes | — |
| 103 | C4×M32 | D4 | 1 | 1 | yes | characteristic |
| 104 | C4×M32 | D4 | 1 | 1 | yes | characteristic |
| 105 | C2×#346 | D4 | 1 | 1 | yes | characteristic |
| 106 | C2×#346 | D4 | 1 | 1 | yes | characteristic |
| 107 | #1841 | — | 2 | 1 | no | — |
| 108 | #1833 | — | 2 | 1 | no | — |
| 109 | #1827 | — | 2 | 1 | no | — |
| 110 | #1813 | C2×C4 | 1 | 1 | yes | characteristic |
| 111 | #1812 | C2×C4 | 1 | 1 | yes | characteristic |
| 112 | #1772 | — | 2 | 1 | no | — |
| 113 | #1757 | — | 2 | 1 | no | — |
| 114 | #1747 | — | 2 | 1 | no | — |
| 115 | #1455 | C2×C4 | 1 | 1 | yes | characteristic |
| 116 | #1455 | D4 | 1 | 1 | yes | characteristic |
| 117 | #1453 | C2×C4 | 1 | 1 | yes | characteristic |
| 118 | #1453 | D4 | 1 | 1 | yes | characteristic |
| 119 | #1451 | — | 2 | 1 | no | — |
| 120 | #1451 | — | 2 | 1 | no | — |
| 121 | #1451 | — | 2 | 1 | no | — |
| 122 | #1450 | D4 | 1 | 1 | yes | characteristic |
| 123 | C2×#322 | D4 | 1 | 1 | yes | characteristic |
| 124 | #1389 | — | 2 | 1 | no | — |
| 125 | #1388 | — | 2 | 1 | no | — |
| 126 | #1382 | — | 2 | 1 | no | — |
| 127 | #1381 | — | 2 | 1 | no | — |
| 128 | #1336 | — | 2 | 2 | no | — |
| 129 | #1336 | — | 2 | 2 | no | — |
| 130 | #1335 | — | 2 | 2 | no | — |
| 131 | #1335 | — | 2 | 2 | no | — |
| 132 | #1313 | — | 2 | 1 | no | — |
| 133 | #1313 | — | 2 | 1 | no | — |
| 134 | #1313 | — | 2 | 1 | no | — |
| 135 | #1313 | — | 2 | 1 | no | — |
| 136 | #1313 | — | 2 | 1 | no | — |
| 137 | #1313 | — | 2 | 1 | no | — |
| 138 | #1313 | — | 2 | 1 | no | — |
| 139 | #1313 | — | 2 | 1 | no | — |
| 140 | #585 | — | 2 | 1 | no | — |
| 141 | #578 | — | 4 | 1 | no | — |
| 142 | #577 | — | 4 | 2 | no | — |
| 143 | #576 | — | 4 | 1 | no | — |
| 144 | #575 | — | 2 | 1 | no | — |
| 145 | #575 | — | 2 | 1 | no | — |
| 146 | #575 | C42 | 1 | 2 | yes | — |
| 147 | C2×#135 | — | 2 | 1 | no | — |
| 148 | C2×#135 | — | 2 | 1 | no | — |
| 149 | C2×#135 | — | 2 | 1 | no | — |
| 150 | #568 | — | 2 | 1 | no | — |
| 151 | #568 | — | 2 | 2 | no | — |
| 152 | #568 | — | 4 | 1 | no | — |
| 153 | #568 | — | 4 | 1 | no | — |
| 154 | #568 | — | 8 | 2 | no | — |
| 155 | C2×#131 | — | 2 | 2 | no | — |
| 156 | C2×#131 | — | 4 | 1 | no | — |
| 157 | C2×#131 | — | 4 | 1 | no | — |
| 158 | C2×#131 | — | 8 | 2 | no | — |
| 159 | C2×#131 | C22×C4 | 1 | 1 | yes | characteristic |
| 160 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C4×#41 | #41 | 1 | 1 | yes | characteristic |
| 162 | C2×M32 | — | 2 | 2 | no | — |
| 163 | C2×M32 | — | 4 | 1 | no | — |
| 164 | C2×M32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C2×M32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 166 | C2×M32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 167 | C2×M32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 168 | C22×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 169 | C22×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 170 | C22×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 171 | C22×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | #446 | — | 4 | 1 | no | — |
| 173 | #444 | — | 2 | 2 | no | — |
| 174 | #444 | — | 2 | 2 | no | — |
| 175 | #444 | — | 2 | 2 | no | — |
| 176 | #444 | — | 2 | 2 | no | — |
| 177 | #444 | — | 4 | 1 | no | — |
| 178 | #444 | — | 4 | 1 | no | — |
| 179 | #443 | — | 2 | 2 | no | — |
| 180 | #443 | — | 2 | 2 | no | — |
| 181 | #443 | — | 2 | 2 | no | — |
| 182 | #443 | — | 2 | 2 | no | — |
| 183 | #443 | — | 4 | 1 | no | — |
| 184 | #443 | — | 4 | 1 | no | — |
| 185 | #443 | — | 4 | 1 | no | — |
| 186 | #443 | — | 4 | 1 | no | — |
| 187 | #443 | — | 4 | 1 | no | — |
| 188 | #443 | — | 4 | 1 | no | — |
| 189 | #436 | — | 4 | 1 | no | — |
| 190 | #435 | — | 4 | 1 | no | — |
| 191 | #435 | — | 4 | 1 | no | — |
| 192 | #431 | — | 2 | 1 | no | — |
| 193 | #431 | — | 2 | 1 | no | — |
| 194 | #431 | — | 2 | 1 | no | — |
| 195 | #430 | — | 2 | 1 | no | — |
| 196 | #430 | — | 2 | 1 | no | — |
| 197 | #430 | C42 | 1 | 2 | yes | — |
| 198 | C2×#108 | — | 2 | 1 | no | — |
| 199 | C2×#108 | — | 2 | 1 | no | — |
| 200 | C2×#108 | — | 2 | 1 | no | — |
| 201 | C2×#108 | — | 2 | 1 | no | — |
| 202 | #427 | — | 2 | 1 | no | — |
| 203 | #421 | — | 2 | 2 | no | — |
| 204 | #421 | — | 4 | 1 | no | — |
| 205 | #421 | — | 4 | 1 | no | — |
| 206 | C2×#104 | — | 2 | 2 | no | — |
| 207 | C2×#104 | — | 4 | 1 | no | — |
| 208 | C2×#104 | — | 4 | 1 | no | — |
| 209 | #413 | — | 2 | 1 | no | — |
| 210 | #410 | — | 2 | 1 | no | — |
| 211 | #405 | — | 4 | 1 | no | — |
| 212 | #405 | C22×C4 | 1 | 1 | yes | characteristic |
| 213 | #405 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | #405 | #41 | 1 | 1 | yes | characteristic |
| 215 | #405 | #41 | 1 | 1 | yes | characteristic |
| 216 | #405 | #41 | 1 | 1 | yes | characteristic |
| 217 | #405 | #41 | 1 | 1 | yes | characteristic |
| 218 | C4×M16 | — | 2 | 1 | no | — |
| 219 | C4×M16 | — | 2 | 1 | no | — |
| 220 | C4×M16 | C22×C4 | 1 | 1 | yes | characteristic |
| 221 | C4×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C4×M16 | #41 | 1 | 1 | yes | characteristic |
| 223 | C2×C4×C8 | — | 2 | 1 | no | — |
| 224 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | #364 | — | 2 | 2 | no | — |
| 228 | #364 | — | 4 | 1 | no | — |
| 229 | #364 | — | 4 | 1 | no | — |
| 230 | #364 | — | 4 | 1 | no | — |
| 231 | C4⋊C16 | — | 2 | 1 | no | — |
| 232 | C4⋊C16 | — | 2 | 1 | no | — |
| 233 | C4⋊C16 | — | 2 | 1 | no | — |
| 234 | C4⋊C16 | — | 2 | 1 | no | — |
| 235 | C4⋊C16 | — | 2 | 1 | no | — |
| 236 | C4⋊C16 | — | 2 | 1 | no | — |
| 237 | C4⋊C16 | — | 2 | 1 | no | — |
| 238 | C4⋊C16 | — | 2 | 1 | no | — |
| 239 | #362 | — | 4 | 1 | no | — |
| 240 | #361 | — | 4 | 1 | no | — |
| 241 | #360 | — | 4 | 2 | no | — |
| 242 | #359 | — | 4 | 2 | no | — |
| 243 | #358 | — | 4 | 1 | no | — |
| 244 | #357 | — | 4 | 1 | no | — |
| 245 | #350 | — | 8 | 2 | no | — |
| 246 | #350 | — | 8 | 2 | no | — |
| 247 | #349 | — | 2 | 2 | no | — |
| 248 | #349 | — | 4 | 1 | no | — |
| 249 | #349 | — | 4 | 1 | no | — |
| 250 | #349 | — | 4 | 1 | no | — |
| 251 | #349 | — | 8 | 2 | no | — |
| 252 | C22⋊C16 | — | 2 | 1 | no | — |
| 253 | C22⋊C16 | — | 2 | 1 | no | — |
| 254 | C22⋊C16 | — | 2 | 1 | no | — |
| 255 | C22⋊C16 | — | 2 | 1 | no | — |
| 256 | C22⋊C16 | — | 2 | 1 | no | — |
| 257 | C22⋊C16 | — | 2 | 1 | no | — |
| 258 | C22⋊C16 | — | 2 | 1 | no | — |
| 259 | C22⋊C16 | — | 2 | 1 | no | — |
| 260 | C22⋊C16 | — | 8 | 2 | no | — |
| 261 | #347 | — | 2 | 2 | no | — |
| 262 | #347 | — | 2 | 2 | no | — |
| 263 | #347 | — | 2 | 2 | no | — |
| 264 | #347 | — | 4 | 1 | no | — |
| 265 | #346 | — | 2 | 1 | no | — |
| 266 | #346 | — | 2 | 1 | no | — |
| 267 | #346 | — | 2 | 1 | no | — |
| 268 | #346 | — | 2 | 1 | no | — |
| 269 | #346 | — | 2 | 1 | no | — |
| 270 | #346 | — | 2 | 1 | no | — |
| 271 | C4×C16 | — | 2 | 1 | no | — |
| 272 | C4×C16 | — | 2 | 1 | no | — |
| 273 | #344 | — | 4 | 1 | no | — |
| 274 | #339 | — | 4 | 1 | no | — |
| 275 | #338 | — | 2 | 1 | no | — |
| 276 | H(3,ℤ/4) | — | 2 | 1 | no | — |
| 277 | H(3,ℤ/4) | — | 4 | 1 | no | — |
| 278 | #322 | — | 2 | 1 | no | — |
| 279 | #322 | — | 2 | 1 | no | — |
| 280 | #322 | — | 2 | 1 | no | — |
| 281 | #322 | — | 2 | 1 | no | — |
| 282 | #322 | — | 2 | 1 | no | — |
| 283 | #322 | — | 2 | 1 | no | — |
| 284 | #322 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 285 | #322 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 286 | C82 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 287 | C82 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 288 | 2−1+4 | — | 4 | 2 | no | — |
| 289 | 2−1+4 | — | 4 | 1 | no | — |
| 290 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 291 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 292 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 293 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 294 | C2×#41 | — | 2 | 2 | no | — |
| 295 | C2×#41 | — | 4 | 1 | no | — |
| 296 | C2×#41 | — | 4 | 1 | no | — |
| 297 | C2×#41 | — | 8 | 2 | no | — |
| 298 | C2×#41 | C4×D4 | 1 | 1 | yes | characteristic |
| 299 | #137 | — | 4 | 2 | no | — |
| 300 | #137 | — | 4 | 2 | no | — |
| 301 | #137 | — | 4 | 2 | no | — |
| 302 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 303 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 304 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 305 | #135 | — | 2 | 2 | no | — |
| 306 | #135 | — | 2 | 2 | no | — |
| 307 | #135 | — | 2 | 2 | no | — |
| 308 | #135 | — | 2 | 2 | no | — |
| 309 | #135 | — | 4 | 1 | no | — |
| 310 | #135 | — | 4 | 1 | no | — |
| 311 | #135 | — | 4 | 1 | no | — |
| 312 | #135 | — | 4 | 1 | no | — |
| 313 | #135 | — | 4 | 1 | no | — |
| 314 | #135 | — | 4 | 1 | no | — |
| 315 | C2×Q16 | — | 2 | 1 | no | — |
| 316 | C2×Q16 | — | 2 | 1 | no | — |
| 317 | C2×Q16 | — | 2 | 1 | no | — |
| 318 | C2×SD16 | — | 2 | 2 | no | — |
| 319 | C2×SD16 | — | 4 | 1 | no | — |
| 320 | C2×SD16 | — | 4 | 1 | no | — |
| 321 | C2×D8 | — | 2 | 1 | no | — |
| 322 | C2×D8 | — | 2 | 1 | no | — |
| 323 | C2×D8 | — | 2 | 1 | no | — |
| 324 | #131 | — | 4 | 1 | no | — |
| 325 | #131 | — | 4 | 1 | no | — |
| 326 | #131 | — | 4 | 1 | no | — |
| 327 | #131 | — | 4 | 1 | no | — |
| 328 | #131 | — | 4 | 2 | no | — |
| 329 | #131 | — | 4 | 2 | no | — |
| 330 | #131 | — | 4 | 2 | no | — |
| 331 | #131 | — | 4 | 2 | no | — |
| 332 | #131 | — | 4 | 2 | no | — |
| 333 | #131 | — | 4 | 2 | no | — |
| 334 | #131 | — | 8 | 1 | no | — |
| 335 | #131 | — | 8 | 1 | no | — |
| 336 | #131 | — | 8 | 1 | no | — |
| 337 | #131 | — | 8 | 1 | no | — |
| 338 | #131 | — | 8 | 2 | no | — |
| 339 | #131 | — | 8 | 2 | no | — |
| 340 | #131 | — | 8 | 2 | no | — |
| 341 | #131 | — | 8 | 2 | no | — |
| 342 | C2×M16 | — | 2 | 2 | no | — |
| 343 | C2×M16 | — | 4 | 2 | no | — |
| 344 | C2×M16 | — | 4 | 1 | no | — |
| 345 | C2×M16 | — | 4 | 1 | no | — |
| 346 | C2×M16 | — | 4 | 1 | no | — |
| 347 | C2×M16 | — | 4 | 1 | no | — |
| 348 | C2×M16 | — | 4 | 1 | no | — |
| 349 | C2×M16 | — | 8 | 1 | no | — |
| 350 | C2×M16 | — | 8 | 1 | no | — |
| 351 | C2×M16 | — | 8 | 2 | no | — |
| 352 | C2×M16 | — | 8 | 2 | no | — |
| 353 | C2×M16 | — | 8 | 2 | no | — |
| 354 | C2×M16 | C2×C42 | 1 | 1 | yes | characteristic |
| 355 | C2×M16 | #117 | 1 | 1 | yes | characteristic |
| 356 | C2×M16 | C4×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×M16 | C4×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×M16 | #124 | 1 | 1 | yes | characteristic |
| 359 | C2×M16 | #127 | 1 | 1 | yes | characteristic |
| 360 | C22×C8 | — | 4 | 2 | no | — |
| 361 | C22×C8 | — | 4 | 1 | no | — |
| 362 | C22×C8 | — | 8 | 1 | no | — |
| 363 | C22×C8 | — | 8 | 1 | no | — |
| 364 | C22×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 365 | C22×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 366 | C22×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 367 | C22×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 368 | C22×C8 | #121 | 1 | 1 | yes | characteristic |
| 369 | C22×C8 | #121 | 1 | 1 | yes | characteristic |
| 370 | C4×Q8 | — | 2 | 1 | no | — |
| 371 | C4×D4 | — | 2 | 1 | no | — |
| 372 | C4×D4 | — | 2 | 1 | no | — |
| 373 | C4×D4 | — | 2 | 1 | no | — |
| 374 | #117 | — | 4 | 1 | no | — |
| 375 | #117 | #117 | 1 | 1 | yes | characteristic |
| 376 | #117 | #124 | 1 | 1 | yes | characteristic |
| 377 | #117 | #126 | 1 | 1 | yes | characteristic |
| 378 | C2×C42 | C4×D4 | 1 | 1 | yes | characteristic |
| 379 | C2×C42 | #121 | 1 | 1 | yes | characteristic |
| 380 | C2×C42 | #123 | 1 | 1 | yes | characteristic |
| 381 | M32 | — | 4 | 1 | no | — |
| 382 | M32 | — | 4 | 1 | no | — |
| 383 | M32 | — | 4 | 1 | no | — |
| 384 | M32 | — | 4 | 1 | no | — |
| 385 | M32 | — | 4 | 2 | no | — |
| 386 | M32 | — | 4 | 2 | no | — |
| 387 | M32 | — | 4 | 2 | no | — |
| 388 | M32 | — | 8 | 1 | no | — |
| 389 | C2×C16 | — | 2 | 1 | no | — |
| 390 | C2×C16 | — | 2 | 1 | no | — |
| 391 | C2×C16 | — | 2 | 1 | no | — |
| 392 | C2×C16 | — | 2 | 1 | no | — |
| 393 | C2×C16 | — | 2 | 1 | no | — |
| 394 | C2×C16 | — | 2 | 1 | no | — |
| 395 | C2×C16 | — | 2 | 1 | no | — |
| 396 | C2×C16 | — | 2 | 1 | no | — |
| 397 | C2×C16 | — | 4 | 1 | no | — |
| 398 | C2×C16 | — | 4 | 1 | no | — |
| 399 | C2×C16 | — | 4 | 1 | no | — |
| 400 | C2×C16 | — | 4 | 1 | no | — |
| 401 | C2×C16 | — | 4 | 2 | no | — |
| 402 | C2×C16 | — | 8 | 1 | no | — |
| 403 | #108 | — | 2 | 2 | no | — |
| 404 | #108 | — | 2 | 2 | no | — |
| 405 | #108 | — | 4 | 1 | no | — |
| 406 | #108 | — | 4 | 1 | no | — |
| 407 | #108 | — | 4 | 1 | no | — |
| 408 | #108 | — | 4 | 1 | no | — |
| 409 | #107 | — | 4 | 1 | no | — |
| 410 | #106 | — | 4 | 1 | no | — |
| 411 | C4⋊C8 | — | 4 | 1 | no | — |
| 412 | C4⋊C8 | — | 4 | 1 | no | — |
| 413 | C4⋊C8 | — | 4 | 1 | no | — |
| 414 | #104 | — | 4 | 2 | no | — |
| 415 | #104 | — | 4 | 2 | no | — |
| 416 | #104 | — | 4 | 2 | no | — |
| 417 | #104 | — | 4 | 2 | no | — |
| 418 | #101 | — | 4 | 1 | no | — |
| 419 | #100 | — | 4 | 1 | no | — |
| 420 | #99 | — | 4 | 1 | no | — |
| 421 | #99 | — | 4 | 1 | no | — |
| 422 | C22⋊C8 | — | 4 | 1 | no | — |
| 423 | C22⋊C8 | — | 4 | 1 | no | — |
| 424 | C22⋊C8 | — | 4 | 1 | no | — |
| 425 | #97 | — | 4 | 1 | no | — |
| 426 | #97 | — | 4 | 1 | no | — |
| 427 | #97 | — | 8 | 1 | no | — |
| 428 | #97 | #117 | 1 | 1 | yes | characteristic |
| 429 | #97 | C4×D4 | 1 | 1 | yes | characteristic |
| 430 | #97 | C4×D4 | 1 | 1 | yes | characteristic |
| 431 | #97 | C4×D4 | 1 | 1 | yes | characteristic |
| 432 | #97 | #124 | 1 | 1 | yes | characteristic |
| 433 | #97 | #126 | 1 | 1 | yes | characteristic |
| 434 | C4×C8 | — | 2 | 1 | no | — |
| 435 | C4×C8 | — | 2 | 1 | no | — |
| 436 | C4×C8 | — | 2 | 1 | no | — |
| 437 | C4×C8 | — | 2 | 1 | no | — |
| 438 | C4×C8 | — | 4 | 1 | no | — |
| 439 | C4×C8 | — | 8 | 1 | no | — |
| 440 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 441 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 442 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 443 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 444 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 445 | C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 446 | C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 447 | C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 448 | C4×C8 | #123 | 1 | 1 | yes | characteristic |
| 449 | C4×C8 | #123 | 1 | 1 | yes | characteristic |
| 450 | #41 | — | 4 | 1 | no | — |
| 451 | #41 | — | 4 | 1 | no | — |
| 452 | #41 | — | 4 | 2 | no | — |
| 453 | #41 | — | 4 | 2 | no | — |
| 454 | #41 | — | 4 | 2 | no | — |
| 455 | #41 | — | 4 | 2 | no | — |
| 456 | #41 | — | 4 | 2 | no | — |
| 457 | #41 | — | 4 | 2 | no | — |
| 458 | #41 | — | 8 | 1 | no | — |
| 459 | #41 | — | 8 | 1 | no | — |
| 460 | #41 | — | 8 | 2 | no | — |
| 461 | #41 | — | 8 | 2 | no | — |
| 462 | #41 | — | 8 | 2 | no | — |
| 463 | #41 | — | 8 | 2 | no | — |
| 464 | #41 | — | 8 | 1 | no | — |
| 465 | #41 | — | 8 | 1 | no | — |
| 466 | C2×Q8 | — | 2 | 2 | no | — |
| 467 | C2×Q8 | — | 4 | 1 | no | — |
| 468 | C2×Q8 | — | 4 | 1 | no | — |
| 469 | C2×Q8 | — | 8 | 2 | no | — |
| 470 | C2×Q8 | #444 | 1 | 1 | yes | characteristic |
| 471 | C2×D4 | — | 2 | 2 | no | — |
| 472 | C2×D4 | — | 4 | 1 | no | — |
| 473 | C2×D4 | — | 4 | 1 | no | — |
| 474 | C2×D4 | — | 4 | 2 | no | — |
| 475 | C2×D4 | — | 8 | 2 | no | — |
| 476 | C2×D4 | — | 8 | 2 | no | — |
| 477 | C2×D4 | — | 8 | 2 | no | — |
| 478 | C2×D4 | — | 8 | 1 | no | — |
| 479 | C2×D4 | — | 8 | 1 | no | — |
| 480 | C2×D4 | #444 | 1 | 1 | yes | characteristic |
| 481 | C2×D4 | #444 | 1 | 1 | yes | characteristic |
| 482 | C2×D4 | #444 | 1 | 1 | yes | characteristic |
| 483 | C22×C4 | — | 2 | 1 | no | — |
| 484 | C22×C4 | — | 2 | 1 | no | — |
| 485 | C22×C4 | — | 2 | 1 | no | — |
| 486 | C22×C4 | — | 4 | 2 | no | — |
| 487 | C22×C4 | — | 8 | 1 | no | — |
| 488 | C22×C4 | — | 8 | 1 | no | — |
| 489 | C22×C4 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 490 | C22×C4 | #388 | 1 | 1 | yes | characteristic |
| 491 | C22×C4 | #390 | 1 | 1 | yes | characteristic |
| 492 | Q16 | — | 2 | 2 | no | — |
| 493 | Q16 | — | 2 | 2 | no | — |
| 494 | Q16 | — | 4 | 1 | no | — |
| 495 | Q16 | — | 4 | 1 | no | — |
| 496 | SD16 | — | 4 | 2 | no | — |
| 497 | SD16 | — | 4 | 2 | no | — |
| 498 | SD16 | — | 4 | 2 | no | — |
| 499 | SD16 | — | 4 | 2 | no | — |
| 500 | D8 | — | 2 | 2 | no | — |
| 501 | D8 | — | 2 | 2 | no | — |
| 502 | D8 | — | 4 | 1 | no | — |
| 503 | D8 | — | 4 | 1 | no | — |
| 504 | M16 | — | 4 | 1 | no | — |
| 505 | M16 | — | 4 | 1 | no | — |
| 506 | M16 | — | 4 | 1 | no | — |
| 507 | M16 | — | 4 | 1 | no | — |
| 508 | M16 | — | 4 | 1 | no | — |
| 509 | M16 | — | 4 | 1 | no | — |
| 510 | M16 | — | 4 | 2 | no | — |
| 511 | M16 | — | 4 | 2 | no | — |
| 512 | M16 | — | 8 | 2 | no | — |
| 513 | M16 | — | 8 | 2 | no | — |
| 514 | M16 | — | 8 | 2 | no | — |
| 515 | M16 | — | 8 | 1 | no | — |
| 516 | M16 | — | 8 | 1 | no | — |
| 517 | M16 | — | 8 | 2 | no | — |
| 518 | M16 | — | 8 | 1 | no | — |
| 519 | M16 | — | 8 | 1 | no | — |
| 520 | M16 | — | 16 | 1 | no | — |
| 521 | M16 | — | 16 | 1 | no | — |
| 522 | C2×C8 | — | 2 | 1 | no | — |
| 523 | C2×C8 | — | 2 | 1 | no | — |
| 524 | C2×C8 | — | 2 | 1 | no | — |
| 525 | C2×C8 | — | 2 | 1 | no | — |
| 526 | C2×C8 | — | 2 | 1 | no | — |
| 527 | C2×C8 | — | 2 | 1 | no | — |
| 528 | C2×C8 | — | 2 | 1 | no | — |
| 529 | C2×C8 | — | 2 | 1 | no | — |
| 530 | C2×C8 | — | 2 | 1 | no | — |
| 531 | C2×C8 | — | 2 | 1 | no | — |
| 532 | C2×C8 | — | 2 | 1 | no | — |
| 533 | C2×C8 | — | 2 | 1 | no | — |
| 534 | C2×C8 | — | 4 | 1 | no | — |
| 535 | C2×C8 | — | 4 | 1 | no | — |
| 536 | C2×C8 | — | 4 | 1 | no | — |
| 537 | C2×C8 | — | 4 | 1 | no | — |
| 538 | C2×C8 | — | 4 | 2 | no | — |
| 539 | C2×C8 | — | 8 | 2 | no | — |
| 540 | C2×C8 | — | 8 | 2 | no | — |
| 541 | C2×C8 | — | 8 | 2 | no | — |
| 542 | C2×C8 | — | 8 | 1 | no | — |
| 543 | C2×C8 | — | 8 | 1 | no | — |
| 544 | C2×C8 | — | 8 | 2 | no | — |
| 545 | C2×C8 | — | 8 | 1 | no | — |
| 546 | C2×C8 | — | 16 | 1 | no | — |
| 547 | C2×C8 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 548 | C2×C8 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 549 | C2×C8 | #386 | 1 | 1 | yes | characteristic |
| 550 | C2×C8 | #386 | 1 | 1 | yes | characteristic |
| 551 | C2×C8 | #388 | 1 | 1 | yes | characteristic |
| 552 | C2×C8 | #388 | 1 | 1 | yes | characteristic |
| 553 | C2×C8 | #390 | 1 | 1 | yes | characteristic |
| 554 | C2×C8 | #390 | 1 | 1 | yes | characteristic |
| 555 | C4⋊C4 | — | 2 | 1 | no | — |
| 556 | C4⋊C4 | — | 2 | 1 | no | — |
| 557 | C4⋊C4 | — | 2 | 1 | no | — |
| 558 | C4⋊C4 | — | 8 | 1 | no | — |
| 559 | C22⋊C4 | — | 2 | 1 | no | — |
| 560 | C22⋊C4 | — | 2 | 1 | no | — |
| 561 | C22⋊C4 | — | 2 | 1 | no | — |
| 562 | C22⋊C4 | — | 8 | 1 | no | — |
| 563 | C42 | — | 2 | 1 | no | — |
| 564 | C42 | — | 2 | 1 | no | — |
| 565 | C42 | — | 2 | 1 | no | — |
| 566 | C42 | — | 8 | 1 | no | — |
| 567 | C42 | #386 | 1 | 1 | yes | characteristic |
| 568 | C42 | #388 | 1 | 1 | yes | characteristic |
| 569 | C42 | #388 | 1 | 1 | yes | characteristic |
| 570 | C42 | #388 | 1 | 1 | yes | characteristic |
| 571 | C16 | — | 4 | 1 | no | — |
| 572 | C16 | — | 4 | 1 | no | — |
| 573 | C16 | — | 4 | 1 | no | — |
| 574 | C16 | — | 4 | 1 | no | — |
| 575 | C16 | — | 4 | 1 | no | — |
| 576 | C16 | — | 4 | 1 | no | — |
| 577 | C16 | — | 4 | 1 | no | — |
| 578 | C16 | — | 4 | 1 | no | — |
| 579 | C16 | — | 8 | 2 | no | — |
| 580 | C16 | — | 8 | 2 | no | — |
| 581 | C23 | — | 4 | 2 | no | — |
| 582 | C23 | — | 8 | 1 | no | — |
| 583 | C23 | — | 8 | 1 | no | — |
| 584 | C23 | #1765 | 1 | 1 | yes | characteristic |
| 585 | C23 | #1938 | 1 | 1 | yes | characteristic |
| 586 | C23 | #1975 | 1 | 1 | yes | characteristic |
| 587 | Q8 | — | 4 | 1 | no | — |
| 588 | Q8 | — | 4 | 2 | no | — |
| 589 | Q8 | — | 4 | 2 | no | — |
| 590 | Q8 | — | 8 | 1 | no | — |
| 591 | Q8 | — | 8 | 1 | no | — |
| 592 | D4 | — | 4 | 1 | no | — |
| 593 | D4 | — | 4 | 1 | no | — |
| 594 | D4 | — | 4 | 1 | no | — |
| 595 | D4 | — | 4 | 2 | no | — |
| 596 | D4 | — | 4 | 2 | no | — |
| 597 | D4 | — | 8 | 1 | no | — |
| 598 | D4 | — | 8 | 1 | no | — |
| 599 | D4 | — | 8 | 2 | no | — |
| 600 | D4 | — | 8 | 2 | no | — |
| 601 | D4 | — | 8 | 2 | no | — |
| 602 | D4 | — | 8 | 2 | no | — |
| 603 | C2×C4 | — | 2 | 1 | no | — |
| 604 | C2×C4 | — | 2 | 1 | no | — |
| 605 | C2×C4 | — | 2 | 1 | no | — |
| 606 | C2×C4 | — | 2 | 1 | no | — |
| 607 | C2×C4 | — | 2 | 1 | no | — |
| 608 | C2×C4 | — | 2 | 1 | no | — |
| 609 | C2×C4 | — | 2 | 1 | no | — |
| 610 | C2×C4 | — | 2 | 1 | no | — |
| 611 | C2×C4 | — | 2 | 1 | no | — |
| 612 | C2×C4 | — | 2 | 1 | no | — |
| 613 | C2×C4 | — | 4 | 2 | no | — |
| 614 | C2×C4 | — | 8 | 2 | no | — |
| 615 | C2×C4 | — | 8 | 2 | no | — |
| 616 | C2×C4 | — | 8 | 2 | no | — |
| 617 | C2×C4 | — | 8 | 1 | no | — |
| 618 | C2×C4 | — | 8 | 1 | no | — |
| 619 | C2×C4 | — | 8 | 1 | no | — |
| 620 | C2×C4 | — | 8 | 1 | no | — |
| 621 | C2×C4 | — | 8 | 1 | no | — |
| 622 | C2×C4 | — | 8 | 2 | no | — |
| 623 | C2×C4 | — | 16 | 1 | no | — |
| 624 | C2×C4 | #1437 | 1 | 1 | yes | characteristic |
| 625 | C2×C4 | #1765 | 1 | 1 | yes | characteristic |
| 626 | C2×C4 | #1938 | 1 | 1 | yes | characteristic |
| 627 | C2×C4 | #1975 | 1 | 1 | yes | characteristic |
| 628 | C8 | — | 2 | 1 | no | — |
| 629 | C8 | — | 2 | 1 | no | — |
| 630 | C8 | — | 2 | 1 | no | — |
| 631 | C8 | — | 2 | 1 | no | — |
| 632 | C8 | — | 2 | 1 | no | — |
| 633 | C8 | — | 2 | 1 | no | — |
| 634 | C8 | — | 8 | 1 | no | — |
| 635 | C8 | — | 8 | 1 | no | — |
| 636 | C8 | — | 8 | 1 | no | — |
| 637 | C8 | — | 8 | 1 | no | — |
| 638 | C8 | — | 8 | 2 | no | — |
| 639 | C8 | — | 16 | 1 | no | — |
| 640 | C8 | #1891 | 1 | 1 | yes | characteristic |
| 641 | C8 | #1891 | 1 | 1 | yes | characteristic |
| 642 | C8 | #1910 | 1 | 1 | yes | characteristic |
| 643 | C8 | #1910 | 1 | 1 | yes | characteristic |
| 644 | C22 | — | 2 | 1 | no | — |
| 645 | C22 | — | 2 | 1 | no | — |
| 646 | C22 | — | 2 | 1 | no | — |
| 647 | C22 | — | 4 | 1 | no | — |
| 648 | C22 | — | 4 | 1 | no | — |
| 649 | C22 | — | 4 | 1 | no | — |
| 650 | C22 | — | 8 | 2 | no | — |
| 651 | C22 | — | 16 | 2 | no | — |
| 652 | C22 | — | 32 | 1 | no | — |
| 653 | C22 | — | 32 | 1 | no | — |
| 654 | C22 | #10930 | 1 | 1 | yes | characteristic |
| 655 | C4 | — | 2 | 1 | no | — |
| 656 | C4 | — | 2 | 1 | no | — |
| 657 | C4 | — | 2 | 1 | no | — |
| 658 | C4 | — | 4 | 1 | no | — |
| 659 | C4 | — | 4 | 1 | no | — |
| 660 | C4 | — | 4 | 1 | no | — |
| 661 | C4 | — | 4 | 1 | no | — |
| 662 | C4 | — | 8 | 2 | no | — |
| 663 | C4 | — | 32 | 1 | no | — |
| 664 | C4 | #10937 | 1 | 1 | yes | characteristic |
| 665 | C4 | #10948 | 1 | 1 | yes | characteristic |
| 666 | C2 | — | 2 | 1 | no | — |
| 667 | C2 | — | 4 | 1 | no | — |
| 668 | C2 | — | 4 | 1 | no | — |
| 669 | C2 | — | 4 | 1 | no | — |
| 670 | C2 | — | 16 | 2 | no | — |
| 671 | C2 | #111118 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #10948 |
| commutator | C2×M16 | C2×C42 |
| Frattini, cosocle | C4×#131 | C23 |
| socle | C2 | #111118 |
| prime radical | #3584 | C2×C4 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ C4×#131 ◁ G | |
| LECS | G ▷ C4×#131 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #479976 | C2 | semidirect |
| 5. #127410 | C2 | semidirect |
| 6. #127316 | C2 | semidirect |
| 7. #127134 | C2 | semidirect |
| 15. #13199 | C4 | semidirect |
| 16. #13198 | C4 | semidirect |
| 30. #11670 | C4 | semidirect |
| 32. #11669 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #496303 | 2 |
| #494051 | 2 |
| #481290 | 2 |
| #479976 | 2 |
| #127410 | 2 |
| #127316 | 2 |
| #127134 | 2 |