Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
628 conjugacy classes of subgroups.
The subgroup lattice has 364 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #33435 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33385 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #27693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #24287 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13466 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13406 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13152 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13071 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #12878 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #12832 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12745 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#504 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#504 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #3067 | C22 | 1 | 2 | yes | — |
| 16 | #3018 | — | 2 | 1 | no | — |
| 17 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 18 | #2916 | C22 | 1 | 1 | yes | characteristic |
| 19 | #2168 | — | 2 | 2 | no | — |
| 20 | #2168 | — | 2 | 2 | no | — |
| 21 | #2155 | C22 | 1 | 2 | yes | complemented |
| 22 | #2150 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #2145 | C22 | 1 | 2 | yes | — |
| 24 | #2143 | — | 2 | 2 | no | — |
| 25 | #2143 | C22 | 1 | 2 | yes | — |
| 26 | C2×#359 | — | 2 | 2 | no | — |
| 27 | C2×#359 | C22 | 1 | 2 | yes | — |
| 28 | #2138 | C22 | 1 | 2 | yes | — |
| 29 | #2113 | C22 | 1 | 1 | yes | characteristic |
| 30 | #2113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C2×#346 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #2102 | — | 2 | 1 | no | — |
| 33 | #2098 | — | 2 | 1 | no | — |
| 34 | #2050 | — | 2 | 1 | no | — |
| 35 | #2017 | — | 2 | 1 | no | — |
| 36 | #1974 | C22 | 1 | 2 | yes | — |
| 37 | #1945 | C22 | 1 | 2 | yes | complemented |
| 38 | #1884 | — | 2 | 1 | no | — |
| 39 | #1868 | — | 2 | 1 | no | — |
| 40 | #1814 | C22 | 1 | 2 | yes | complemented |
| 41 | #1813 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1812 | C22 | 1 | 1 | yes | characteristic |
| 43 | #1791 | — | 2 | 1 | no | — |
| 44 | #1388 | C22 | 1 | 2 | yes | complemented |
| 45 | #1382 | C22 | 1 | 2 | yes | complemented |
| 46 | #1381 | C22 | 1 | 2 | yes | complemented |
| 47 | #585 | — | 2 | 1 | no | — |
| 48 | #578 | — | 2 | 2 | no | — |
| 49 | #577 | — | 4 | 2 | no | — |
| 50 | #576 | — | 2 | 2 | no | — |
| 51 | #575 | — | 2 | 2 | no | — |
| 52 | #575 | — | 2 | 1 | no | — |
| 53 | #575 | — | 2 | 2 | no | — |
| 54 | C2×#135 | — | 2 | 2 | no | — |
| 55 | C2×#135 | C23 | 1 | 2 | yes | — |
| 56 | #568 | — | 2 | 1 | no | — |
| 57 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 59 | #532 | D4 | 1 | 1 | yes | characteristic |
| 60 | #504 | — | 4 | 2 | no | — |
| 61 | #504 | — | 4 | 2 | no | — |
| 62 | C2×M32 | — | 2 | 1 | no | — |
| 63 | C2×M32 | D4 | 1 | 2 | yes | — |
| 64 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22×C16 | — | 2 | 1 | no | — |
| 67 | C22×C16 | D4 | 1 | 2 | yes | — |
| 68 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 70 | #473 | — | 2 | 2 | no | — |
| 71 | #472 | — | 2 | 2 | no | — |
| 72 | #471 | — | 4 | 2 | no | — |
| 73 | #456 | — | 4 | 1 | no | — |
| 74 | #455 | — | 4 | 1 | no | — |
| 75 | #454 | — | 4 | 1 | no | — |
| 76 | #453 | — | 4 | 1 | no | — |
| 77 | #436 | — | 2 | 2 | no | — |
| 78 | C8×D4 | — | 2 | 2 | no | — |
| 79 | #430 | — | 2 | 2 | no | — |
| 80 | #430 | — | 2 | 1 | no | — |
| 81 | C2×#108 | — | 2 | 2 | no | — |
| 82 | C2×#108 | C23 | 1 | 2 | yes | — |
| 83 | C2×#108 | C23 | 1 | 2 | yes | — |
| 84 | #427 | C23 | 1 | 2 | yes | — |
| 85 | #424 | — | 2 | 2 | no | — |
| 86 | #423 | D4 | 1 | 1 | yes | characteristic |
| 87 | #421 | — | 2 | 2 | no | — |
| 88 | C2×#104 | — | 2 | 2 | no | — |
| 89 | #413 | — | 2 | 1 | no | — |
| 90 | #413 | — | 2 | 2 | no | — |
| 91 | #410 | — | 2 | 1 | no | — |
| 92 | #408 | — | 2 | 2 | no | — |
| 93 | #408 | D4 | 1 | 1 | yes | characteristic |
| 94 | #408 | D4 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 96 | #365 | — | 4 | 2 | no | — |
| 97 | C4⋊C16 | — | 2 | 2 | no | — |
| 98 | #360 | — | 4 | 2 | no | — |
| 99 | #359 | — | 2 | 2 | no | — |
| 100 | #359 | — | 2 | 4 | no | — |
| 101 | #359 | — | 2 | 2 | no | — |
| 102 | #358 | — | 2 | 2 | no | — |
| 103 | #357 | — | 2 | 2 | no | — |
| 104 | C22⋊C16 | — | 2 | 2 | no | — |
| 105 | C22⋊C16 | — | 2 | 2 | no | — |
| 106 | #346 | — | 2 | 1 | no | — |
| 107 | #346 | — | 2 | 1 | no | — |
| 108 | #344 | — | 2 | 2 | no | — |
| 109 | #339 | — | 2 | 2 | no | — |
| 110 | #338 | — | 2 | 1 | no | — |
| 111 | H(3,ℤ/4) | — | 2 | 1 | no | — |
| 112 | 2−1+4 | — | 4 | 2 | no | — |
| 113 | 2−1+4 | — | 4 | 1 | no | — |
| 114 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 115 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 116 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 117 | C2×#41 | — | 2 | 2 | no | — |
| 118 | C2×#41 | — | 4 | 2 | no | — |
| 119 | C2×#41 | — | 8 | 2 | no | — |
| 120 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | #137 | — | 4 | 4 | no | — |
| 123 | #137 | — | 4 | 2 | no | — |
| 124 | #137 | — | 4 | 2 | no | — |
| 125 | #137 | — | 4 | 2 | no | — |
| 126 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 127 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 128 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 129 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 130 | #135 | — | 2 | 4 | no | — |
| 131 | #135 | — | 2 | 2 | no | — |
| 132 | #135 | — | 2 | 2 | no | — |
| 133 | #135 | — | 2 | 2 | no | — |
| 134 | #135 | — | 2 | 2 | no | — |
| 135 | #135 | — | 4 | 2 | no | — |
| 136 | #135 | — | 4 | 2 | no | — |
| 137 | #135 | — | 8 | 2 | no | — |
| 138 | C2×Q16 | — | 2 | 2 | no | — |
| 139 | C2×Q16 | #41 | 1 | 2 | yes | — |
| 140 | C2×SD16 | — | 2 | 2 | no | — |
| 141 | C2×SD16 | — | 4 | 2 | no | — |
| 142 | C2×D8 | — | 2 | 2 | no | — |
| 143 | C2×D8 | #41 | 1 | 2 | yes | — |
| 144 | #131 | — | 2 | 2 | no | — |
| 145 | #131 | — | 2 | 2 | no | — |
| 146 | #131 | — | 2 | 2 | no | — |
| 147 | #131 | — | 2 | 2 | no | — |
| 148 | #131 | — | 8 | 2 | no | — |
| 149 | C2×M16 | — | 2 | 1 | no | — |
| 150 | C2×M16 | — | 2 | 2 | no | — |
| 151 | C2×M16 | — | 2 | 2 | no | — |
| 152 | C2×M16 | — | 4 | 2 | no | — |
| 153 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×M16 | #41 | 1 | 2 | yes | — |
| 156 | C22×C8 | — | 2 | 1 | no | — |
| 157 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 159 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 160 | C4⋊Q8 | SD16 | 1 | 1 | yes | characteristic |
| 161 | #127 | SD16 | 1 | 1 | yes | characteristic |
| 162 | #124 | SD16 | 1 | 1 | yes | characteristic |
| 163 | #124 | SD16 | 1 | 1 | yes | characteristic |
| 164 | #121 | — | 2 | 2 | no | — |
| 165 | C4×D4 | — | 2 | 2 | no | — |
| 166 | #117 | — | 2 | 2 | no | — |
| 167 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | M32 | — | 2 | 2 | no | — |
| 169 | M32 | — | 2 | 2 | no | — |
| 170 | M32 | — | 4 | 2 | no | — |
| 171 | M32 | — | 4 | 2 | no | — |
| 172 | C2×C16 | — | 2 | 2 | no | — |
| 173 | C2×C16 | — | 2 | 1 | no | — |
| 174 | C2×C16 | — | 2 | 1 | no | — |
| 175 | C2×C16 | — | 2 | 2 | no | — |
| 176 | C2×C16 | — | 4 | 2 | no | — |
| 177 | C2×C16 | — | 4 | 2 | no | — |
| 178 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×C16 | C2×D4 | 1 | 2 | yes | — |
| 181 | #108 | — | 2 | 2 | no | — |
| 182 | #108 | — | 2 | 2 | no | — |
| 183 | #108 | — | 2 | 2 | no | — |
| 184 | #108 | — | 2 | 2 | no | — |
| 185 | #108 | — | 4 | 2 | no | — |
| 186 | #107 | — | 2 | 2 | no | — |
| 187 | #106 | — | 2 | 2 | no | — |
| 188 | C4⋊C8 | — | 2 | 2 | no | — |
| 189 | C4⋊C8 | — | 8 | 2 | no | — |
| 190 | #104 | — | 4 | 2 | no | — |
| 191 | #104 | — | 4 | 2 | no | — |
| 192 | #104 | — | 8 | 2 | no | — |
| 193 | #101 | — | 4 | 2 | no | — |
| 194 | #101 | — | 4 | 1 | no | — |
| 195 | #100 | — | 4 | 2 | no | — |
| 196 | #100 | — | 4 | 1 | no | — |
| 197 | #99 | — | 4 | 2 | no | — |
| 198 | C22⋊C8 | — | 2 | 2 | no | — |
| 199 | C22⋊C8 | — | 2 | 2 | no | — |
| 200 | C22⋊C8 | — | 8 | 2 | no | — |
| 201 | C4×C8 | — | 2 | 1 | no | — |
| 202 | C4×C8 | — | 2 | 1 | no | — |
| 203 | #41 | — | 2 | 2 | no | — |
| 204 | #41 | — | 2 | 2 | no | — |
| 205 | #41 | — | 2 | 2 | no | — |
| 206 | #41 | — | 2 | 2 | no | — |
| 207 | #41 | — | 4 | 4 | no | — |
| 208 | #41 | — | 4 | 2 | no | — |
| 209 | #41 | — | 4 | 2 | no | — |
| 210 | #41 | — | 4 | 2 | no | — |
| 211 | #41 | — | 4 | 2 | no | — |
| 212 | #41 | — | 8 | 2 | no | — |
| 213 | #41 | — | 8 | 4 | no | — |
| 214 | #41 | — | 8 | 2 | no | — |
| 215 | #41 | — | 8 | 2 | no | — |
| 216 | #41 | — | 8 | 2 | no | — |
| 217 | C2×Q8 | — | 2 | 2 | no | — |
| 218 | C2×Q8 | — | 4 | 2 | no | — |
| 219 | C2×Q8 | — | 8 | 2 | no | — |
| 220 | C2×Q8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 221 | C2×Q8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 222 | C2×D4 | — | 2 | 1 | no | — |
| 223 | C2×D4 | — | 2 | 2 | no | — |
| 224 | C2×D4 | — | 2 | 2 | no | — |
| 225 | C2×D4 | — | 4 | 2 | no | — |
| 226 | C2×D4 | — | 4 | 2 | no | — |
| 227 | C2×D4 | — | 8 | 2 | no | — |
| 228 | C2×D4 | — | 8 | 4 | no | — |
| 229 | C2×D4 | — | 8 | 2 | no | — |
| 230 | C2×D4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 231 | C2×D4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 232 | C2×D4 | #135 | 1 | 2 | yes | — |
| 233 | C22×C4 | — | 2 | 1 | no | — |
| 234 | C22×C4 | — | 2 | 1 | no | — |
| 235 | C22×C4 | — | 4 | 2 | no | — |
| 236 | C22×C4 | — | 8 | 2 | no | — |
| 237 | C22×C4 | #121 | 1 | 2 | yes | — |
| 238 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 239 | Q16 | — | 2 | 2 | no | — |
| 240 | Q16 | — | 2 | 2 | no | — |
| 241 | Q16 | — | 4 | 2 | no | — |
| 242 | Q16 | — | 8 | 2 | no | — |
| 243 | SD16 | — | 4 | 4 | no | — |
| 244 | SD16 | — | 4 | 2 | no | — |
| 245 | SD16 | — | 4 | 2 | no | — |
| 246 | SD16 | — | 8 | 2 | no | — |
| 247 | SD16 | — | 8 | 2 | no | — |
| 248 | D8 | — | 2 | 2 | no | — |
| 249 | D8 | — | 2 | 2 | no | — |
| 250 | D8 | — | 4 | 2 | no | — |
| 251 | D8 | — | 8 | 2 | no | — |
| 252 | M16 | — | 2 | 2 | no | — |
| 253 | M16 | — | 2 | 4 | no | — |
| 254 | M16 | — | 2 | 2 | no | — |
| 255 | M16 | — | 4 | 2 | no | — |
| 256 | M16 | — | 4 | 2 | no | — |
| 257 | M16 | — | 4 | 2 | no | — |
| 258 | M16 | — | 4 | 2 | no | — |
| 259 | M16 | — | 4 | 2 | no | — |
| 260 | M16 | — | 8 | 2 | no | — |
| 261 | C2×C8 | — | 2 | 2 | no | — |
| 262 | C2×C8 | — | 2 | 2 | no | — |
| 263 | C2×C8 | — | 2 | 1 | no | — |
| 264 | C2×C8 | — | 2 | 1 | no | — |
| 265 | C2×C8 | — | 2 | 2 | no | — |
| 266 | C2×C8 | — | 4 | 1 | no | — |
| 267 | C2×C8 | — | 4 | 1 | no | — |
| 268 | C2×C8 | — | 4 | 2 | no | — |
| 269 | C2×C8 | — | 4 | 2 | no | — |
| 270 | C2×C8 | — | 8 | 2 | no | — |
| 271 | C2×C8 | #121 | 1 | 2 | yes | — |
| 272 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 274 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 275 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 276 | C4⋊C4 | — | 2 | 2 | no | — |
| 277 | C4⋊C4 | — | 4 | 2 | no | — |
| 278 | C22⋊C4 | — | 2 | 2 | no | — |
| 279 | C22⋊C4 | — | 2 | 2 | no | — |
| 280 | C22⋊C4 | — | 4 | 2 | no | — |
| 281 | C42 | — | 2 | 1 | no | — |
| 282 | C42 | — | 4 | 2 | no | — |
| 283 | C42 | C2×SD16 | 1 | 1 | yes | characteristic |
| 284 | C42 | C2×SD16 | 1 | 1 | yes | characteristic |
| 285 | C16 | — | 2 | 1 | no | — |
| 286 | C16 | — | 2 | 1 | no | — |
| 287 | C16 | — | 2 | 2 | no | — |
| 288 | C16 | — | 4 | 1 | no | — |
| 289 | C16 | — | 4 | 1 | no | — |
| 290 | C23 | — | 2 | 1 | no | — |
| 291 | C23 | — | 4 | 2 | no | — |
| 292 | C23 | — | 8 | 2 | no | — |
| 293 | C23 | #465 | 1 | 2 | yes | — |
| 294 | C23 | C2×#135 | 1 | 1 | yes | characteristic |
| 295 | Q8 | — | 2 | 2 | no | — |
| 296 | Q8 | — | 2 | 2 | no | — |
| 297 | Q8 | — | 4 | 2 | no | — |
| 298 | Q8 | — | 4 | 2 | no | — |
| 299 | Q8 | — | 8 | 2 | no | — |
| 300 | D4 | — | 2 | 4 | no | — |
| 301 | D4 | — | 2 | 2 | no | — |
| 302 | D4 | — | 2 | 2 | no | — |
| 303 | D4 | — | 4 | 2 | no | — |
| 304 | D4 | — | 4 | 2 | no | — |
| 305 | D4 | — | 4 | 2 | no | — |
| 306 | D4 | — | 8 | 2 | no | — |
| 307 | D4 | — | 8 | 2 | no | — |
| 308 | D4 | — | 8 | 4 | no | — |
| 309 | D4 | — | 8 | 2 | no | — |
| 310 | D4 | — | 8 | 2 | no | — |
| 311 | C2×C4 | — | 2 | 2 | no | — |
| 312 | C2×C4 | — | 2 | 2 | no | — |
| 313 | C2×C4 | — | 2 | 1 | no | — |
| 314 | C2×C4 | — | 2 | 1 | no | — |
| 315 | C2×C4 | — | 2 | 1 | no | — |
| 316 | C2×C4 | — | 4 | 1 | no | — |
| 317 | C2×C4 | — | 4 | 1 | no | — |
| 318 | C2×C4 | — | 4 | 2 | no | — |
| 319 | C2×C4 | — | 8 | 4 | no | — |
| 320 | C2×C4 | — | 8 | 1 | no | — |
| 321 | C2×C4 | — | 8 | 2 | no | — |
| 322 | C2×C4 | — | 8 | 2 | no | — |
| 323 | C2×C4 | — | 8 | 2 | no | — |
| 324 | C2×C4 | — | 8 | 2 | no | — |
| 325 | C2×C4 | #465 | 1 | 2 | yes | — |
| 326 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 327 | C2×C4 | #546 | 1 | 2 | yes | — |
| 328 | C2×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 329 | C2×C4 | #576 | 1 | 2 | yes | — |
| 330 | C8 | — | 2 | 2 | no | — |
| 331 | C8 | — | 4 | 1 | no | — |
| 332 | C8 | — | 4 | 1 | no | — |
| 333 | C8 | — | 8 | 2 | no | — |
| 334 | C8 | — | 8 | 2 | no | — |
| 335 | C8 | #525 | 1 | 1 | yes | characteristic |
| 336 | C8 | #534 | 1 | 1 | yes | characteristic |
| 337 | C8 | #551 | 1 | 2 | yes | — |
| 338 | C22 | — | 2 | 2 | no | — |
| 339 | C22 | — | 4 | 1 | no | — |
| 340 | C22 | — | 4 | 2 | no | — |
| 341 | C22 | — | 4 | 2 | no | — |
| 342 | C22 | — | 4 | 1 | no | — |
| 343 | C22 | — | 8 | 2 | no | — |
| 344 | C22 | — | 16 | 2 | no | — |
| 345 | C22 | — | 32 | 2 | no | — |
| 346 | C22 | C2×#465 | 1 | 1 | yes | characteristic |
| 347 | C22 | #3297 | 1 | 2 | yes | — |
| 348 | C4 | — | 2 | 2 | no | — |
| 349 | C4 | — | 4 | 1 | no | — |
| 350 | C4 | — | 4 | 1 | no | — |
| 351 | C4 | — | 4 | 1 | no | — |
| 352 | C4 | — | 8 | 2 | no | — |
| 353 | C4 | — | 16 | 2 | no | — |
| 354 | C4 | #2534 | 1 | 1 | yes | characteristic |
| 355 | C4 | #3058 | 1 | 1 | yes | characteristic |
| 356 | C4 | #3295 | 1 | 2 | yes | — |
| 357 | C2 | — | 2 | 1 | no | — |
| 358 | C2 | — | 2 | 2 | no | — |
| 359 | C2 | — | 4 | 2 | no | — |
| 360 | C2 | — | 8 | 1 | no | — |
| 361 | C2 | — | 16 | 2 | no | — |
| 362 | C2 | #28097 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #3058 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| socle | C2 | #28097 |
| prime radical | #24287 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #2931 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #33435 | C2 | semidirect |
| 2. #33385 | C2 | semidirect |
| 3. #27693 | C2 | semidirect |
| 5. #13466 | C2 | semidirect |
| 6. #13406 | C2 | semidirect |
| 7. #13152 | C2 | semidirect |
| 8. #13071 | C2 | semidirect |
| 9. #12878 | C2 | semidirect |
| 10. #12832 | C2 | semidirect |
| 11. #12745 | C2 | semidirect |
| 14. C2×#504 | C22 | semidirect |
| 21. #2155 | C22 | semidirect |
| 22. #2150 | C22 | semidirect |
| 30. #2113 | C22 | semidirect |
| 31. C2×#346 | C22 | semidirect |
| 37. #1945 | C22 | semidirect |
| 40. #1814 | C22 | semidirect |
| 44. #1388 | C22 | semidirect |
| 45. #1382 | C22 | semidirect |
| 46. #1381 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #33435 | 2 |
| #33385 | 2 |
| #27693 | 2 |
| #24287 | 2 |
| #13466 | 2 |
| #13406 | 2 |
| #13152 | 2 |
| #13071 | 2 |
| #12878 | 2 |
| #12832 | 2 |
| #12745 | 2 |