Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6175 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63039 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62469 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #62331 | C2 | 1 | 9 | yes | maximal, complemented |
| 4 | #62150 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #62147 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #61792 | C2 | 1 | 18 | yes | maximal, complemented |
| 7 | #61434 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #61288 | C2 | 1 | 9 | yes | maximal, complemented |
| 9 | #60308 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #3548 | C22 | 1 | 18 | yes | — |
| 11 | #3547 | — | 2 | 18 | no | — |
| 12 | #3517 | — | 2 | 6 | no | — |
| 13 | #3511 | C22 | 1 | 18 | yes | — |
| 14 | #3503 | C22 | 1 | 6 | yes | — |
| 15 | #3499 | C22 | 1 | 6 | yes | — |
| 16 | #3497 | — | 2 | 6 | no | — |
| 17 | #3483 | C22 | 1 | 6 | yes | — |
| 18 | #3483 | C22 | 1 | 1 | yes | characteristic |
| 19 | #3482 | C22 | 1 | 6 | yes | — |
| 20 | Q8×#41 | — | 2 | 2 | no | — |
| 21 | #3392 | C22 | 1 | 2 | yes | — |
| 22 | Q8×SD16 | C22 | 1 | 6 | yes | — |
| 23 | Q8×SD16 | C22 | 1 | 12 | yes | — |
| 24 | #3363 | C22 | 1 | 6 | yes | — |
| 25 | #3358 | C22 | 1 | 6 | yes | — |
| 26 | #3356 | C22 | 1 | 36 | yes | — |
| 27 | #3354 | C22 | 1 | 36 | yes | — |
| 28 | #3340 | C22 | 1 | 18 | yes | — |
| 29 | #3335 | C22 | 1 | 36 | yes | — |
| 30 | #3335 | C22 | 1 | 36 | yes | — |
| 31 | #3332 | C22 | 1 | 36 | yes | — |
| 32 | #3331 | C22 | 1 | 36 | yes | — |
| 33 | #3304 | C22 | 1 | 18 | yes | — |
| 34 | #3303 | C22 | 1 | 18 | yes | — |
| 35 | #3284 | C22 | 1 | 18 | yes | — |
| 36 | #3255 | C22 | 1 | 9 | yes | — |
| 37 | #3253 | C22 | 1 | 9 | yes | — |
| 38 | #3229 | C22 | 1 | 18 | yes | — |
| 39 | #3227 | C22 | 1 | 18 | yes | — |
| 40 | #3204 | C22 | 1 | 36 | yes | — |
| 41 | #3167 | C22 | 1 | 18 | yes | — |
| 42 | C2×#498 | C22 | 1 | 9 | yes | — |
| 43 | #3107 | C22 | 1 | 18 | yes | — |
| 44 | #3106 | C22 | 1 | 18 | yes | — |
| 45 | #3099 | C22 | 1 | 36 | yes | — |
| 46 | #3079 | C22 | 1 | 18 | yes | — |
| 47 | #3060 | C22 | 1 | 18 | yes | — |
| 48 | #2991 | C22 | 1 | 6 | yes | — |
| 49 | #2979 | C22 | 1 | 9 | yes | — |
| 50 | C8×#41 | C22 | 1 | 6 | yes | — |
| 51 | C4×#135 | C22 | 1 | 9 | yes | — |
| 52 | #2931 | C22 | 1 | 9 | yes | — |
| 53 | #2912 | C22 | 1 | 6 | yes | — |
| 54 | C2×2−1+4 | — | 2 | 6 | no | — |
| 55 | C2×#135 | C23 | 1 | 9 | yes | — |
| 56 | C2×#131 | C23 | 1 | 6 | yes | — |
| 57 | #562 | — | 2 | 36 | no | — |
| 58 | Q82 | D4 | 1 | 1 | yes | characteristic |
| 59 | Q82 | C23 | 1 | 6 | yes | — |
| 60 | #557 | — | 2 | 6 | no | — |
| 61 | #557 | C23 | 1 | 2 | yes | — |
| 62 | #556 | C23 | 1 | 18 | yes | — |
| 63 | #555 | — | 2 | 18 | no | — |
| 64 | #555 | D4 | 1 | 9 | yes | — |
| 65 | #555 | C23 | 1 | 18 | yes | — |
| 66 | #554 | — | 2 | 18 | no | — |
| 67 | #554 | C23 | 1 | 36 | yes | — |
| 68 | #553 | — | 2 | 36 | no | — |
| 69 | #552 | — | 2 | 18 | no | — |
| 70 | #550 | — | 2 | 6 | no | — |
| 71 | #550 | — | 2 | 18 | no | — |
| 72 | #550 | D4 | 1 | 6 | yes | — |
| 73 | #550 | C23 | 1 | 18 | yes | — |
| 74 | #550 | C23 | 1 | 2 | yes | — |
| 75 | D4×Q8 | — | 2 | 6 | no | — |
| 76 | D4×Q8 | — | 2 | 18 | no | — |
| 77 | D4×Q8 | C23 | 1 | 6 | yes | — |
| 78 | #548 | — | 2 | 6 | no | — |
| 79 | #548 | — | 2 | 36 | no | — |
| 80 | #547 | — | 2 | 18 | no | — |
| 81 | #547 | C23 | 1 | 18 | yes | — |
| 82 | #547 | C23 | 1 | 36 | yes | — |
| 83 | #544 | — | 2 | 18 | no | — |
| 84 | #542 | — | 2 | 36 | no | — |
| 85 | #540 | — | 2 | 36 | no | — |
| 86 | #537 | — | 2 | 36 | no | — |
| 87 | #537 | C23 | 1 | 36 | yes | — |
| 88 | #536 | — | 2 | 18 | no | — |
| 89 | #533 | — | 2 | 18 | no | — |
| 90 | #533 | C23 | 1 | 18 | yes | — |
| 91 | #532 | — | 2 | 18 | no | — |
| 92 | #532 | — | 2 | 18 | no | — |
| 93 | #532 | C23 | 1 | 18 | yes | — |
| 94 | #532 | C23 | 1 | 9 | yes | — |
| 95 | C2×C4⋊Q8 | C23 | 1 | 18 | yes | — |
| 96 | #529 | — | 2 | 18 | no | — |
| 97 | #520 | — | 2 | 6 | no | — |
| 98 | #520 | C23 | 1 | 12 | yes | — |
| 99 | C4×#41 | — | 2 | 6 | no | — |
| 100 | C4×#41 | C23 | 1 | 18 | yes | — |
| 101 | C4×#41 | C23 | 1 | 6 | yes | — |
| 102 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 103 | #498 | C23 | 1 | 18 | yes | — |
| 104 | #498 | C23 | 1 | 36 | yes | — |
| 105 | #492 | C23 | 1 | 6 | yes | — |
| 106 | #487 | C23 | 1 | 18 | yes | — |
| 107 | #486 | C23 | 1 | 18 | yes | — |
| 108 | #485 | C23 | 1 | 36 | yes | — |
| 109 | #483 | C23 | 1 | 72 | yes | — |
| 110 | #482 | C23 | 1 | 36 | yes | — |
| 111 | #481 | C23 | 1 | 72 | yes | — |
| 112 | #477 | C23 | 1 | 18 | yes | — |
| 113 | #476 | C23 | 1 | 36 | yes | — |
| 114 | #476 | C23 | 1 | 18 | yes | — |
| 115 | #475 | C23 | 1 | 36 | yes | — |
| 116 | #475 | C23 | 1 | 18 | yes | — |
| 117 | #474 | C23 | 1 | 18 | yes | — |
| 118 | #470 | C23 | 1 | 36 | yes | — |
| 119 | #469 | C23 | 1 | 36 | yes | — |
| 120 | #465 | C23 | 1 | 36 | yes | — |
| 121 | #465 | C23 | 1 | 36 | yes | — |
| 122 | #462 | C23 | 1 | 18 | yes | — |
| 123 | #461 | C23 | 1 | 6 | yes | — |
| 124 | #460 | C23 | 1 | 6 | yes | — |
| 125 | #459 | C23 | 1 | 18 | yes | — |
| 126 | #452 | C23 | 1 | 36 | yes | — |
| 127 | #449 | C23 | 1 | 36 | yes | — |
| 128 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 129 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 130 | C4×Q16 | C23 | 1 | 18 | yes | — |
| 131 | C4×SD16 | C23 | 1 | 36 | yes | — |
| 132 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 133 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 134 | C4×D8 | C23 | 1 | 18 | yes | — |
| 135 | #436 | C23 | 1 | 36 | yes | — |
| 136 | C8×D4 | C23 | 1 | 18 | yes | — |
| 137 | C8×D4 | C23 | 1 | 18 | yes | — |
| 138 | #431 | C23 | 1 | 18 | yes | — |
| 139 | #428 | C23 | 1 | 36 | yes | — |
| 140 | #427 | C23 | 1 | 9 | yes | — |
| 141 | C2×#106 | C23 | 1 | 18 | yes | — |
| 142 | C2×#106 | C23 | 1 | 18 | yes | — |
| 143 | #423 | C23 | 1 | 9 | yes | — |
| 144 | #417 | C23 | 1 | 36 | yes | — |
| 145 | #416 | C23 | 1 | 18 | yes | — |
| 146 | #408 | C23 | 1 | 18 | yes | — |
| 147 | C2×C4×C8 | C23 | 1 | 9 | yes | — |
| 148 | 2−1+4 | — | 8 | 24 | no | — |
| 149 | C2×#41 | — | 2 | 2 | no | — |
| 150 | C2×#41 | — | 2 | 36 | no | — |
| 151 | C2×#41 | — | 2 | 18 | no | — |
| 152 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 153 | C2×#41 | C24 | 1 | 18 | yes | — |
| 154 | C2×#41 | C24 | 1 | 6 | yes | — |
| 155 | C22×Q8 | — | 2 | 6 | no | — |
| 156 | C22×Q8 | — | 2 | 18 | no | — |
| 157 | #135 | — | 4 | 18 | no | — |
| 158 | C2×Q16 | C24 | 1 | 9 | yes | — |
| 159 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 160 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 161 | C2×D8 | C24 | 1 | 9 | yes | — |
| 162 | #131 | — | 4 | 12 | no | — |
| 163 | C2×M16 | C24 | 1 | 18 | yes | — |
| 164 | C22×C8 | C24 | 1 | 9 | yes | — |
| 165 | C22×C8 | C24 | 1 | 9 | yes | — |
| 166 | C4⋊Q8 | — | 2 | 18 | no | — |
| 167 | C4⋊Q8 | — | 2 | 18 | no | — |
| 168 | C4⋊Q8 | — | 2 | 18 | no | — |
| 169 | C4⋊Q8 | C2×D4 | 1 | 9 | yes | — |
| 170 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 171 | C4⋊Q8 | C24 | 1 | 18 | yes | — |
| 172 | C4⋊Q8 | C24 | 1 | 18 | yes | — |
| 173 | #127 | — | 2 | 18 | no | — |
| 174 | #127 | C2×D4 | 1 | 9 | yes | — |
| 175 | #127 | C24 | 1 | 6 | yes | — |
| 176 | #126 | — | 2 | 36 | no | — |
| 177 | #125 | — | 2 | 6 | no | — |
| 178 | #125 | — | 2 | 36 | no | — |
| 179 | #125 | — | 2 | 18 | no | — |
| 180 | #124 | — | 2 | 18 | no | — |
| 181 | #124 | — | 2 | 36 | no | — |
| 182 | #124 | — | 2 | 18 | no | — |
| 183 | #124 | C2×D4 | 1 | 18 | yes | — |
| 184 | #123 | — | 2 | 36 | no | — |
| 185 | #123 | — | 2 | 72 | no | — |
| 186 | C22⋊Q8 | — | 2 | 36 | no | — |
| 187 | C22⋊Q8 | — | 2 | 18 | no | — |
| 188 | C22⋊Q8 | — | 2 | 18 | no | — |
| 189 | C22⋊Q8 | — | 2 | 36 | no | — |
| 190 | C22⋊Q8 | — | 2 | 72 | no | — |
| 191 | C22⋊Q8 | C24 | 1 | 36 | yes | — |
| 192 | #121 | — | 2 | 18 | no | — |
| 193 | #121 | — | 2 | 18 | no | — |
| 194 | #121 | — | 2 | 36 | no | — |
| 195 | #121 | — | 2 | 72 | no | — |
| 196 | #121 | — | 2 | 18 | no | — |
| 197 | #121 | — | 2 | 6 | no | — |
| 198 | #121 | — | 2 | 36 | no | — |
| 199 | #121 | C2×D4 | 1 | 36 | yes | — |
| 200 | #121 | C24 | 1 | 36 | yes | — |
| 201 | C4×Q8 | — | 2 | 2 | no | — |
| 202 | C4×Q8 | — | 2 | 6 | no | — |
| 203 | C4×Q8 | — | 2 | 12 | no | — |
| 204 | C4×Q8 | — | 2 | 18 | no | — |
| 205 | C4×Q8 | — | 2 | 18 | no | — |
| 206 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 207 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 208 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 209 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 210 | C4×D4 | — | 2 | 36 | no | — |
| 211 | C4×D4 | — | 2 | 36 | no | — |
| 212 | C4×D4 | — | 2 | 18 | no | — |
| 213 | C4×D4 | — | 2 | 18 | no | — |
| 214 | C4×D4 | — | 2 | 18 | no | — |
| 215 | C4×D4 | — | 2 | 18 | no | — |
| 216 | C4×D4 | C2×D4 | 1 | 18 | yes | — |
| 217 | C4×D4 | C24 | 1 | 6 | yes | — |
| 218 | C4×D4 | C24 | 1 | 18 | yes | — |
| 219 | C4×D4 | C24 | 1 | 18 | yes | — |
| 220 | #117 | — | 2 | 18 | no | — |
| 221 | #117 | — | 2 | 18 | no | — |
| 222 | #117 | — | 2 | 18 | no | — |
| 223 | #117 | C2×D4 | 1 | 18 | yes | — |
| 224 | #117 | C24 | 1 | 18 | yes | — |
| 225 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 226 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 227 | C2×C4⋊C4 | C24 | 1 | 36 | yes | — |
| 228 | C2×C42 | — | 2 | 18 | no | — |
| 229 | C2×C42 | C24 | 1 | 9 | yes | — |
| 230 | #107 | C24 | 1 | 18 | yes | — |
| 231 | #106 | C24 | 1 | 9 | yes | — |
| 232 | #106 | C24 | 1 | 36 | yes | — |
| 233 | #106 | C24 | 1 | 36 | yes | — |
| 234 | #106 | C24 | 1 | 1 | yes | characteristic |
| 235 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 236 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 237 | #103 | C24 | 1 | 6 | yes | — |
| 238 | #103 | C24 | 1 | 18 | yes | — |
| 239 | #103 | C24 | 1 | 36 | yes | — |
| 240 | #102 | C24 | 1 | 6 | yes | — |
| 241 | #102 | C24 | 1 | 18 | yes | — |
| 242 | #102 | C24 | 1 | 36 | yes | — |
| 243 | C22⋊C8 | C24 | 1 | 36 | yes | — |
| 244 | C4×C8 | C24 | 1 | 6 | yes | — |
| 245 | C4×C8 | C24 | 1 | 18 | yes | — |
| 246 | #41 | — | 2 | 24 | no | — |
| 247 | #41 | — | 4 | 6 | no | — |
| 248 | #41 | — | 4 | 6 | no | — |
| 249 | #41 | — | 4 | 18 | no | — |
| 250 | #41 | — | 4 | 18 | no | — |
| 251 | #41 | — | 4 | 8 | no | — |
| 252 | #41 | — | 8 | 36 | no | — |
| 253 | #41 | — | 8 | 72 | no | — |
| 254 | C2×Q8 | — | 2 | 18 | no | — |
| 255 | C2×Q8 | — | 2 | 18 | no | — |
| 256 | C2×Q8 | — | 4 | 24 | no | — |
| 257 | C2×Q8 | — | 8 | 36 | no | — |
| 258 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 259 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 260 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 261 | C2×D4 | — | 2 | 18 | no | — |
| 262 | C2×D4 | — | 2 | 36 | no | — |
| 263 | C2×D4 | — | 2 | 6 | no | — |
| 264 | C2×D4 | — | 2 | 6 | no | — |
| 265 | C2×D4 | C22×D4 | 1 | 18 | yes | — |
| 266 | C2×D4 | C22×D4 | 1 | 18 | yes | — |
| 267 | C2×D4 | C25 | 1 | 6 | yes | — |
| 268 | C22×C4 | — | 2 | 36 | no | — |
| 269 | C22×C4 | — | 2 | 6 | no | — |
| 270 | C22×C4 | — | 2 | 18 | no | — |
| 271 | C22×C4 | — | 2 | 18 | no | — |
| 272 | C22×C4 | C22×D4 | 1 | 18 | yes | — |
| 273 | C22×C4 | C25 | 1 | 9 | yes | — |
| 274 | Q16 | — | 4 | 9 | no | — |
| 275 | SD16 | — | 2 | 12 | no | — |
| 276 | SD16 | — | 4 | 12 | no | — |
| 277 | D8 | — | 4 | 9 | no | — |
| 278 | M16 | — | 4 | 18 | no | — |
| 279 | C2×C8 | — | 2 | 18 | no | — |
| 280 | C2×C8 | — | 4 | 9 | no | — |
| 281 | C2×C8 | C25 | 1 | 6 | yes | — |
| 282 | C2×C8 | C25 | 1 | 9 | yes | — |
| 283 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 284 | C4⋊C4 | — | 2 | 6 | no | — |
| 285 | C4⋊C4 | — | 2 | 18 | no | — |
| 286 | C4⋊C4 | — | 2 | 18 | no | — |
| 287 | C4⋊C4 | — | 2 | 36 | no | — |
| 288 | C4⋊C4 | — | 2 | 36 | no | — |
| 289 | C4⋊C4 | — | 2 | 6 | no | — |
| 290 | C4⋊C4 | — | 2 | 6 | no | — |
| 291 | C4⋊C4 | — | 2 | 18 | no | — |
| 292 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 293 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 294 | C4⋊C4 | C25 | 1 | 18 | yes | — |
| 295 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 296 | C22⋊C4 | — | 2 | 36 | no | — |
| 297 | C22⋊C4 | — | 2 | 18 | no | — |
| 298 | C22⋊C4 | — | 2 | 6 | no | — |
| 299 | C22⋊C4 | — | 2 | 36 | no | — |
| 300 | C22⋊C4 | — | 2 | 18 | no | — |
| 301 | C22⋊C4 | C22×D4 | 1 | 36 | yes | — |
| 302 | C42 | — | 2 | 6 | no | — |
| 303 | C42 | — | 2 | 18 | no | — |
| 304 | C42 | — | 2 | 18 | no | — |
| 305 | C42 | C22×D4 | 1 | 9 | yes | — |
| 306 | C42 | C22×D4 | 1 | 9 | yes | — |
| 307 | C42 | C25 | 1 | 6 | yes | — |
| 308 | C23 | — | 2 | 6 | no | — |
| 309 | C23 | C23×D4 | 1 | 9 | yes | — |
| 310 | Q8 | — | 2 | 6 | no | — |
| 311 | Q8 | — | 2 | 6 | no | — |
| 312 | Q8 | — | 4 | 6 | no | — |
| 313 | Q8 | — | 4 | 36 | no | — |
| 314 | Q8 | — | 8 | 18 | no | — |
| 315 | Q8 | #577 | 1 | 8 | yes | — |
| 316 | D4 | — | 2 | 6 | no | — |
| 317 | D4 | — | 2 | 6 | no | — |
| 318 | D4 | — | 2 | 36 | no | — |
| 319 | D4 | — | 4 | 18 | no | — |
| 320 | D4 | — | 4 | 12 | no | — |
| 321 | D4 | — | 8 | 6 | no | — |
| 322 | D4 | — | 8 | 18 | no | — |
| 323 | D4 | — | 8 | 36 | no | — |
| 324 | C2×C4 | — | 2 | 9 | no | — |
| 325 | C2×C4 | — | 2 | 9 | no | — |
| 326 | C2×C4 | — | 2 | 36 | no | — |
| 327 | C2×C4 | — | 2 | 2 | no | — |
| 328 | C2×C4 | — | 2 | 6 | no | — |
| 329 | C2×C4 | — | 2 | 18 | no | — |
| 330 | C2×C4 | — | 4 | 36 | no | — |
| 331 | C2×C4 | — | 4 | 12 | no | — |
| 332 | C2×C4 | — | 8 | 18 | no | — |
| 333 | C2×C4 | — | 8 | 36 | no | — |
| 334 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 335 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 336 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 337 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 338 | C8 | — | 2 | 9 | no | — |
| 339 | C8 | — | 2 | 6 | no | — |
| 340 | C8 | #585 | 1 | 2 | yes | — |
| 341 | C22 | — | 2 | 9 | no | — |
| 342 | C22 | — | 2 | 18 | no | — |
| 343 | C22 | — | 4 | 6 | no | — |
| 344 | C22 | — | 4 | 6 | no | — |
| 345 | C22 | — | 4 | 6 | no | — |
| 346 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 347 | C4 | — | 2 | 9 | no | — |
| 348 | C4 | — | 2 | 6 | no | — |
| 349 | C4 | — | 4 | 6 | no | — |
| 350 | C4 | — | 4 | 2 | no | — |
| 351 | C4 | — | 4 | 18 | no | — |
| 352 | C4 | C2×#577 | 1 | 12 | yes | — |
| 353 | C4 | C2×#585 | 1 | 1 | yes | characteristic |
| 354 | C4 | 2−1+6 | 1 | 1 | yes | characteristic |
| 355 | C2 | — | 4 | 9 | no | — |
| 356 | C2 | — | 8 | 6 | no | — |
| 357 | C2 | #62988 | 1 | 1 | yes | characteristic |
| 358 | C2 | C22×#577 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #3483 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63039 | C2 | semidirect |
| 2. #62469 | C2 | semidirect |
| 3. #62331 | C2 | semidirect |
| 4. #62150 | C2 | semidirect |
| 5. #62147 | C2 | semidirect |
| 6. #61792 | C2 | semidirect |
| 7. #61434 | C2 | semidirect |
| 8. #61288 | C2 | semidirect |
| 9. #60308 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63039 | 2 |
| #62469 | 2 |
| #62331 | 2 |
| #62150 | 2 |
| #62147 | 2 |
| #61792 | 2 |
| #61434 | 2 |
| #61288 | 2 |
| #60308 | 2 |