Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
717 conjugacy classes of subgroups.
The subgroup lattice has 369 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23740 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #21184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #21071 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #20776 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11334 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11286 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11275 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11153 | C2 | 1 | 2 | yes | maximal |
| 10 | #11146 | C2 | 1 | 2 | yes | maximal |
| 11 | #11103 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×#430 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#430 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#430 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#430 | C22 | 1 | 2 | yes | — |
| 16 | #2905 | C22 | 1 | 2 | yes | — |
| 17 | C2×#421 | C22 | 1 | 2 | yes | — |
| 18 | C22×#104 | C22 | 1 | 1 | yes | characteristic |
| 19 | #2896 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#413 | C22 | 1 | 2 | yes | — |
| 21 | #2879 | C22 | 1 | 1 | yes | characteristic |
| 22 | #2873 | C22 | 1 | 1 | yes | characteristic |
| 23 | #2098 | — | 2 | 4 | no | — |
| 24 | #1953 | — | 2 | 4 | no | — |
| 25 | #1929 | — | 2 | 4 | no | — |
| 26 | #1841 | — | 2 | 4 | no | — |
| 27 | C2×#344 | C22 | 1 | 2 | yes | — |
| 28 | C2×#344 | C22 | 1 | 2 | yes | — |
| 29 | C2×#344 | C22 | 1 | 2 | yes | — |
| 30 | #1738 | C22 | 1 | 2 | yes | — |
| 31 | #1738 | C22 | 1 | 2 | yes | — |
| 32 | #1733 | C22 | 1 | 2 | yes | — |
| 33 | C2×#339 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#339 | C22 | 1 | 2 | yes | — |
| 35 | C2×#338 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×H(3,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 37 | #1728 | C22 | 1 | 1 | yes | characteristic |
| 38 | #1728 | C22 | 1 | 2 | yes | — |
| 39 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 40 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 41 | C22×M16 | C23 | 1 | 2 | yes | — |
| 42 | C22×M16 | C23 | 1 | 2 | yes | — |
| 43 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 44 | C22×M16 | C23 | 1 | 2 | yes | — |
| 45 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 46 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×#117 | C23 | 1 | 2 | yes | — |
| 49 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 50 | #430 | — | 2 | 4 | no | — |
| 51 | #430 | — | 2 | 2 | no | — |
| 52 | #430 | — | 2 | 4 | no | — |
| 53 | #430 | — | 2 | 2 | no | — |
| 54 | #430 | — | 4 | 2 | no | — |
| 55 | #430 | — | 4 | 2 | no | — |
| 56 | C2×#108 | — | 2 | 2 | no | — |
| 57 | C2×#108 | — | 2 | 2 | no | — |
| 58 | C2×#108 | — | 2 | 2 | no | — |
| 59 | C2×#108 | — | 4 | 2 | no | — |
| 60 | #424 | — | 2 | 4 | no | — |
| 61 | #424 | — | 4 | 2 | no | — |
| 62 | #423 | — | 4 | 2 | no | — |
| 63 | #421 | — | 2 | 4 | no | — |
| 64 | #421 | — | 4 | 2 | no | — |
| 65 | C2×#104 | — | 2 | 2 | no | — |
| 66 | C2×#104 | — | 4 | 2 | no | — |
| 67 | C2×#104 | — | 4 | 2 | no | — |
| 68 | #419 | — | 2 | 1 | no | — |
| 69 | #418 | — | 2 | 1 | no | — |
| 70 | #417 | — | 2 | 2 | no | — |
| 71 | #416 | — | 2 | 2 | no | — |
| 72 | #413 | — | 2 | 4 | no | — |
| 73 | #413 | — | 4 | 2 | no | — |
| 74 | C2×#101 | — | 2 | 2 | no | — |
| 75 | C2×#100 | — | 2 | 2 | no | — |
| 76 | #408 | — | 2 | 2 | no | — |
| 77 | #408 | — | 2 | 2 | no | — |
| 78 | #407 | — | 2 | 2 | no | — |
| 79 | #405 | — | 2 | 2 | no | — |
| 80 | #405 | D4 | 1 | 4 | yes | — |
| 81 | C4×M16 | — | 2 | 2 | no | — |
| 82 | #344 | — | 2 | 4 | no | — |
| 83 | #344 | — | 2 | 4 | no | — |
| 84 | #344 | — | 2 | 4 | no | — |
| 85 | #341 | — | 4 | 2 | no | — |
| 86 | #341 | — | 4 | 2 | no | — |
| 87 | #339 | — | 2 | 4 | no | — |
| 88 | #339 | — | 2 | 4 | no | — |
| 89 | #339 | — | 2 | 2 | no | — |
| 90 | #338 | — | 2 | 2 | no | — |
| 91 | H(3,ℤ/4) | D4 | 1 | 4 | yes | — |
| 92 | #336 | — | 2 | 2 | no | — |
| 93 | #336 | — | 4 | 2 | no | — |
| 94 | C2×#41 | — | 2 | 1 | no | — |
| 95 | C2×#41 | — | 2 | 1 | no | — |
| 96 | C2×#41 | — | 2 | 2 | no | — |
| 97 | C2×#41 | — | 2 | 1 | no | — |
| 98 | C2×#41 | — | 2 | 2 | no | — |
| 99 | C2×#41 | — | 2 | 2 | no | — |
| 100 | C2×#41 | — | 2 | 2 | no | — |
| 101 | C2×#41 | — | 2 | 1 | no | — |
| 102 | C22×Q8 | #41 | 1 | 1 | yes | characteristic |
| 103 | C22×D4 | — | 2 | 1 | no | — |
| 104 | C22×D4 | #41 | 1 | 1 | yes | characteristic |
| 105 | C23×C4 | — | 2 | 1 | no | — |
| 106 | C23×C4 | — | 2 | 1 | no | — |
| 107 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 108 | C2×M16 | — | 2 | 2 | no | — |
| 109 | C2×M16 | — | 2 | 2 | no | — |
| 110 | C2×M16 | — | 2 | 1 | no | — |
| 111 | C2×M16 | — | 2 | 2 | no | — |
| 112 | C2×M16 | — | 2 | 1 | no | — |
| 113 | C2×M16 | — | 2 | 2 | no | — |
| 114 | C2×M16 | — | 2 | 2 | no | — |
| 115 | C2×M16 | — | 2 | 2 | no | — |
| 116 | C2×M16 | — | 2 | 2 | no | — |
| 117 | C2×M16 | — | 2 | 2 | no | — |
| 118 | C2×M16 | — | 2 | 2 | no | — |
| 119 | C2×M16 | — | 2 | 2 | no | — |
| 120 | C2×M16 | — | 2 | 2 | no | — |
| 121 | C2×M16 | — | 2 | 2 | no | — |
| 122 | C2×M16 | — | 2 | 1 | no | — |
| 123 | C2×M16 | — | 2 | 2 | no | — |
| 124 | C2×M16 | — | 2 | 2 | no | — |
| 125 | C2×M16 | — | 2 | 1 | no | — |
| 126 | C2×M16 | — | 2 | 2 | no | — |
| 127 | C2×M16 | — | 2 | 2 | no | — |
| 128 | C2×M16 | — | 2 | 2 | no | — |
| 129 | C2×M16 | — | 2 | 2 | no | — |
| 130 | C2×M16 | — | 2 | 2 | no | — |
| 131 | C2×M16 | — | 2 | 2 | no | — |
| 132 | C2×M16 | — | 2 | 2 | no | — |
| 133 | C2×M16 | — | 2 | 2 | no | — |
| 134 | C2×M16 | — | 2 | 2 | no | — |
| 135 | C2×M16 | — | 2 | 2 | no | — |
| 136 | C2×M16 | — | 2 | 2 | no | — |
| 137 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 138 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 139 | C2×M16 | #41 | 1 | 4 | yes | — |
| 140 | C2×M16 | #41 | 1 | 2 | yes | — |
| 141 | C2×M16 | #41 | 1 | 2 | yes | — |
| 142 | C22×C8 | — | 2 | 1 | no | — |
| 143 | C22×C8 | — | 2 | 1 | no | — |
| 144 | C22×C8 | — | 2 | 2 | no | — |
| 145 | C22×C8 | — | 2 | 1 | no | — |
| 146 | C22×C8 | — | 2 | 2 | no | — |
| 147 | C22×C8 | — | 2 | 2 | no | — |
| 148 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 149 | #117 | — | 2 | 1 | no | — |
| 150 | #117 | — | 2 | 2 | no | — |
| 151 | #117 | — | 2 | 2 | no | — |
| 152 | #117 | — | 2 | 1 | no | — |
| 153 | #117 | — | 2 | 2 | no | — |
| 154 | #117 | — | 2 | 1 | no | — |
| 155 | #117 | C2×D4 | 1 | 4 | yes | — |
| 156 | #117 | C2×D4 | 1 | 2 | yes | — |
| 157 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 158 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 159 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 160 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 161 | C2×C42 | — | 2 | 1 | no | — |
| 162 | C2×C42 | — | 2 | 2 | no | — |
| 163 | C2×C42 | — | 2 | 1 | no | — |
| 164 | C2×C42 | — | 2 | 2 | no | — |
| 165 | C2×C42 | — | 2 | 2 | no | — |
| 166 | C2×C42 | — | 2 | 1 | no | — |
| 167 | #108 | — | 2 | 8 | no | — |
| 168 | #108 | — | 4 | 4 | no | — |
| 169 | #108 | — | 4 | 8 | no | — |
| 170 | #108 | — | 4 | 4 | no | — |
| 171 | C4⋊C8 | — | 4 | 8 | no | — |
| 172 | #104 | — | 4 | 8 | no | — |
| 173 | #104 | — | 4 | 4 | no | — |
| 174 | #103 | — | 2 | 4 | no | — |
| 175 | #102 | — | 2 | 4 | no | — |
| 176 | #101 | — | 4 | 4 | no | — |
| 177 | #100 | — | 4 | 4 | no | — |
| 178 | C22⋊C8 | — | 4 | 4 | no | — |
| 179 | #97 | — | 2 | 4 | no | — |
| 180 | C4×C8 | — | 2 | 4 | no | — |
| 181 | C24 | — | 2 | 1 | no | — |
| 182 | C24 | 2−1+4 | 1 | 1 | yes | characteristic |
| 183 | #41 | — | 4 | 1 | no | — |
| 184 | #41 | — | 4 | 1 | no | — |
| 185 | #41 | — | 4 | 2 | no | — |
| 186 | #41 | — | 4 | 1 | no | — |
| 187 | #41 | — | 4 | 1 | no | — |
| 188 | #41 | — | 4 | 2 | no | — |
| 189 | #41 | — | 4 | 2 | no | — |
| 190 | #41 | — | 4 | 2 | no | — |
| 191 | #41 | — | 4 | 2 | no | — |
| 192 | #41 | — | 4 | 2 | no | — |
| 193 | C2×Q8 | — | 2 | 1 | no | — |
| 194 | C2×Q8 | — | 2 | 2 | no | — |
| 195 | C2×Q8 | — | 2 | 1 | no | — |
| 196 | C2×Q8 | — | 2 | 2 | no | — |
| 197 | C2×D4 | — | 2 | 1 | no | — |
| 198 | C2×D4 | — | 2 | 2 | no | — |
| 199 | C2×D4 | — | 2 | 1 | no | — |
| 200 | C2×D4 | — | 2 | 2 | no | — |
| 201 | C2×D4 | — | 4 | 1 | no | — |
| 202 | C2×D4 | — | 4 | 2 | no | — |
| 203 | C2×D4 | — | 4 | 1 | no | — |
| 204 | C2×D4 | — | 4 | 2 | no | — |
| 205 | C22×C4 | — | 2 | 1 | no | — |
| 206 | C22×C4 | — | 4 | 1 | no | — |
| 207 | C22×C4 | — | 4 | 2 | no | — |
| 208 | C22×C4 | — | 4 | 1 | no | — |
| 209 | C22×C4 | — | 4 | 2 | no | — |
| 210 | C22×C4 | — | 4 | 1 | no | — |
| 211 | C22×C4 | — | 4 | 2 | no | — |
| 212 | C22×C4 | — | 4 | 2 | no | — |
| 213 | C22×C4 | — | 4 | 1 | no | — |
| 214 | C22×C4 | — | 8 | 2 | no | — |
| 215 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 216 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 217 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 218 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 219 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 220 | C22×C4 | C2×#41 | 1 | 2 | yes | — |
| 221 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 222 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 223 | C22×C4 | 2−1+4 | 1 | 2 | yes | — |
| 224 | C22×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 225 | M16 | — | 2 | 4 | no | — |
| 226 | M16 | — | 2 | 4 | no | — |
| 227 | M16 | — | 2 | 4 | no | — |
| 228 | M16 | — | 2 | 2 | no | — |
| 229 | M16 | — | 2 | 2 | no | — |
| 230 | M16 | — | 2 | 4 | no | — |
| 231 | M16 | — | 2 | 4 | no | — |
| 232 | M16 | — | 4 | 2 | no | — |
| 233 | M16 | — | 4 | 2 | no | — |
| 234 | M16 | — | 4 | 2 | no | — |
| 235 | M16 | — | 4 | 2 | no | — |
| 236 | M16 | — | 4 | 2 | no | — |
| 237 | M16 | — | 4 | 2 | no | — |
| 238 | M16 | — | 4 | 2 | no | — |
| 239 | M16 | — | 4 | 1 | no | — |
| 240 | M16 | — | 4 | 1 | no | — |
| 241 | M16 | — | 4 | 2 | no | — |
| 242 | M16 | — | 4 | 2 | no | — |
| 243 | M16 | — | 4 | 2 | no | — |
| 244 | M16 | — | 4 | 2 | no | — |
| 245 | M16 | — | 4 | 2 | no | — |
| 246 | M16 | — | 4 | 2 | no | — |
| 247 | C2×C8 | — | 2 | 2 | no | — |
| 248 | C2×C8 | — | 2 | 2 | no | — |
| 249 | C2×C8 | — | 2 | 2 | no | — |
| 250 | C2×C8 | — | 2 | 2 | no | — |
| 251 | C2×C8 | — | 2 | 4 | no | — |
| 252 | C2×C8 | — | 4 | 2 | no | — |
| 253 | C2×C8 | — | 4 | 1 | no | — |
| 254 | C2×C8 | — | 4 | 1 | no | — |
| 255 | C2×C8 | — | 4 | 2 | no | — |
| 256 | C2×C8 | — | 4 | 2 | no | — |
| 257 | C2×C8 | — | 4 | 1 | no | — |
| 258 | C2×C8 | — | 4 | 2 | no | — |
| 259 | C2×C8 | — | 4 | 2 | no | — |
| 260 | C2×C8 | — | 4 | 2 | no | — |
| 261 | C2×C8 | — | 4 | 2 | no | — |
| 262 | C2×C8 | — | 4 | 2 | no | — |
| 263 | C2×C8 | — | 4 | 2 | no | — |
| 264 | C2×C8 | — | 4 | 2 | no | — |
| 265 | C2×C8 | #121 | 1 | 4 | yes | — |
| 266 | C4⋊C4 | — | 2 | 2 | no | — |
| 267 | C4⋊C4 | — | 2 | 4 | no | — |
| 268 | C4⋊C4 | — | 4 | 2 | no | — |
| 269 | C4⋊C4 | — | 4 | 1 | no | — |
| 270 | C22⋊C4 | — | 2 | 2 | no | — |
| 271 | C22⋊C4 | — | 2 | 4 | no | — |
| 272 | C22⋊C4 | — | 4 | 2 | no | — |
| 273 | C22⋊C4 | — | 4 | 1 | no | — |
| 274 | C42 | — | 2 | 2 | no | — |
| 275 | C42 | — | 2 | 4 | no | — |
| 276 | C42 | — | 4 | 1 | no | — |
| 277 | C42 | — | 4 | 2 | no | — |
| 278 | C42 | — | 4 | 1 | no | — |
| 279 | C42 | — | 4 | 1 | no | — |
| 280 | C42 | — | 4 | 2 | no | — |
| 281 | C23 | — | 4 | 1 | no | — |
| 282 | C23 | — | 4 | 2 | no | — |
| 283 | C23 | — | 8 | 1 | no | — |
| 284 | C23 | — | 16 | 1 | no | — |
| 285 | C23 | #536 | 1 | 1 | yes | characteristic |
| 286 | C23 | #542 | 1 | 2 | yes | — |
| 287 | C23 | #547 | 1 | 1 | yes | characteristic |
| 288 | C23 | #552 | 1 | 1 | yes | characteristic |
| 289 | C23 | #563 | 1 | 2 | yes | — |
| 290 | Q8 | — | 4 | 1 | no | — |
| 291 | Q8 | — | 4 | 1 | no | — |
| 292 | Q8 | — | 4 | 2 | no | — |
| 293 | D4 | — | 4 | 1 | no | — |
| 294 | D4 | — | 4 | 1 | no | — |
| 295 | D4 | — | 4 | 2 | no | — |
| 296 | D4 | — | 8 | 1 | no | — |
| 297 | D4 | — | 8 | 1 | no | — |
| 298 | D4 | — | 8 | 2 | no | — |
| 299 | C2×C4 | — | 4 | 2 | no | — |
| 300 | C2×C4 | — | 4 | 4 | no | — |
| 301 | C2×C4 | — | 4 | 2 | no | — |
| 302 | C2×C4 | — | 4 | 1 | no | — |
| 303 | C2×C4 | — | 4 | 4 | no | — |
| 304 | C2×C4 | — | 4 | 2 | no | — |
| 305 | C2×C4 | — | 8 | 1 | no | — |
| 306 | C2×C4 | — | 8 | 2 | no | — |
| 307 | C2×C4 | — | 8 | 1 | no | — |
| 308 | C2×C4 | — | 8 | 1 | no | — |
| 309 | C2×C4 | — | 8 | 1 | no | — |
| 310 | C2×C4 | — | 8 | 2 | no | — |
| 311 | C2×C4 | — | 16 | 1 | no | — |
| 312 | C2×C4 | — | 16 | 2 | no | — |
| 313 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 314 | C2×C4 | #525 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | #525 | 1 | 1 | yes | characteristic |
| 316 | C2×C4 | #535 | 1 | 1 | yes | characteristic |
| 317 | C2×C4 | #535 | 1 | 1 | yes | characteristic |
| 318 | C2×C4 | #535 | 1 | 2 | yes | — |
| 319 | C2×C4 | #536 | 1 | 1 | yes | characteristic |
| 320 | C2×C4 | #539 | 1 | 2 | yes | — |
| 321 | C2×C4 | #539 | 1 | 2 | yes | — |
| 322 | C2×C4 | #540 | 1 | 2 | yes | — |
| 323 | C2×C4 | #542 | 1 | 2 | yes | — |
| 324 | C2×C4 | #547 | 1 | 2 | yes | — |
| 325 | C2×C4 | #548 | 1 | 1 | yes | characteristic |
| 326 | C2×C4 | #551 | 1 | 2 | yes | — |
| 327 | C2×C4 | #552 | 1 | 2 | yes | — |
| 328 | C2×C4 | #553 | 1 | 2 | yes | — |
| 329 | C2×C4 | #556 | 1 | 1 | yes | characteristic |
| 330 | C2×C4 | #563 | 1 | 2 | yes | — |
| 331 | C8 | — | 2 | 4 | no | — |
| 332 | C8 | — | 4 | 4 | no | — |
| 333 | C8 | — | 4 | 2 | no | — |
| 334 | C8 | — | 4 | 2 | no | — |
| 335 | C8 | — | 8 | 1 | no | — |
| 336 | C8 | — | 8 | 2 | no | — |
| 337 | C8 | — | 8 | 2 | no | — |
| 338 | C22 | — | 4 | 1 | no | — |
| 339 | C22 | — | 4 | 2 | no | — |
| 340 | C22 | — | 4 | 1 | no | — |
| 341 | C22 | — | 4 | 2 | no | — |
| 342 | C22 | — | 4 | 1 | no | — |
| 343 | C22 | — | 8 | 2 | no | — |
| 344 | C22 | — | 8 | 1 | no | — |
| 345 | C22 | — | 16 | 2 | no | — |
| 346 | C22 | #2415 | 1 | 1 | yes | characteristic |
| 347 | C22 | #2632 | 1 | 1 | yes | characteristic |
| 348 | C22 | #2718 | 1 | 2 | yes | — |
| 349 | C22 | #2738 | 1 | 2 | yes | — |
| 350 | C22 | #2821 | 1 | 1 | yes | characteristic |
| 351 | C4 | — | 8 | 2 | no | — |
| 352 | C4 | — | 8 | 2 | no | — |
| 353 | C4 | — | 8 | 4 | no | — |
| 354 | C4 | — | 8 | 1 | no | — |
| 355 | C4 | #2413 | 1 | 1 | yes | characteristic |
| 356 | C4 | #2598 | 1 | 1 | yes | characteristic |
| 357 | C4 | #2619 | 1 | 1 | yes | characteristic |
| 358 | C4 | #2633 | 1 | 1 | yes | characteristic |
| 359 | C4 | #2723 | 1 | 2 | yes | — |
| 360 | C4 | #2777 | 1 | 2 | yes | — |
| 361 | C2 | — | 2 | 1 | no | — |
| 362 | C2 | — | 2 | 1 | no | — |
| 363 | C2 | — | 2 | 2 | no | — |
| 364 | C2 | — | 2 | 2 | no | — |
| 365 | C2 | — | 2 | 1 | no | — |
| 366 | C2 | — | 16 | 1 | no | — |
| 367 | C2 | #16676 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #2619 |
| commutator, Frattini, cosocle | C23×C4 | C24 |
| socle | C2 | #16676 |
| prime radical | C22×#41 | C23 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21184 | C2 | semidirect |
| 4. #20776 | C2 | semidirect |
| 5. #11375 | C2 | semidirect |
| 6. #11334 | C2 | semidirect |
| 7. #11286 | C2 | semidirect |
| 8. #11275 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23740 | 2 |
| #21184 | 2 |
| #21071 | 2 |
| #20776 | 2 |
| #11375 | 2 |
| #11334 | 2 |
| #11286 | 2 |
| #11275 | 2 |
| #11153 | 2 |
| #11146 | 2 |
| #11103 | 2 |