← #7623272
Subgroups — #7623272
Order 512.
1354 conjugacy classes of subgroups.
The subgroup lattice has 382 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #60717 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #33750 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #33743 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #33741 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #33740 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #33735 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C2×#2253 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #33713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #33708 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #33611 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #33610 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #33460 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #33459 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | C4×#504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #3512 | — | 2 | 2 | no | — |
| 16 | C2×#508 | C22 | 1 | 2 | yes | — |
| 17 | C2×#508 | C22 | 1 | 2 | yes | — |
| 18 | C2×#504 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#504 | C22 | 1 | 1 | yes | characteristic |
| 20 | #3183 | — | 2 | 4 | no | — |
| 21 | #3177 | C22 | 1 | 4 | yes | — |
| 22 | #3176 | C22 | 1 | 4 | yes | — |
| 23 | #3174 | — | 2 | 4 | no | — |
| 24 | #3168 | C22 | 1 | 8 | yes | — |
| 25 | C2×#499 | C22 | 1 | 2 | yes | — |
| 26 | #3147 | C22 | 1 | 2 | yes | — |
| 27 | #3142 | — | 2 | 2 | no | — |
| 28 | #3061 | C22 | 1 | 4 | yes | — |
| 29 | #3060 | — | 2 | 2 | no | — |
| 30 | #2952 | — | 2 | 2 | no | — |
| 31 | #2951 | C22 | 1 | 4 | yes | — |
| 32 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 33 | #2253 | C22 | 1 | 2 | yes | — |
| 34 | #2253 | C22 | 1 | 2 | yes | — |
| 35 | #2253 | C22 | 1 | 2 | yes | — |
| 36 | #2253 | C22 | 1 | 2 | yes | — |
| 37 | #2249 | C22 | 1 | 2 | yes | — |
| 38 | #2249 | C22 | 1 | 2 | yes | — |
| 39 | #2248 | C22 | 1 | 2 | yes | — |
| 40 | #2247 | C22 | 1 | 1 | yes | characteristic |
| 41 | #2246 | C22 | 1 | 1 | yes | characteristic |
| 42 | #2245 | C22 | 1 | 4 | yes | — |
| 43 | #2244 | C22 | 1 | 4 | yes | — |
| 44 | #2242 | C22 | 1 | 8 | yes | — |
| 45 | #2220 | C22 | 1 | 8 | yes | — |
| 46 | #2219 | C22 | 1 | 4 | yes | — |
| 47 | #2218 | C22 | 1 | 4 | yes | — |
| 48 | #2217 | C22 | 1 | 8 | yes | — |
| 49 | #2216 | C22 | 1 | 4 | yes | — |
| 50 | #2215 | C22 | 1 | 4 | yes | — |
| 51 | #2177 | C22 | 1 | 4 | yes | — |
| 52 | #2176 | C22 | 1 | 4 | yes | — |
| 53 | #2175 | C22 | 1 | 8 | yes | — |
| 54 | C4×Q32 | C22 | 1 | 4 | yes | — |
| 55 | C4×SD32 | C22 | 1 | 8 | yes | — |
| 56 | C4×D16 | C22 | 1 | 4 | yes | — |
| 57 | C2×#367 | C22 | 1 | 2 | yes | — |
| 58 | C2×#366 | C22 | 1 | 2 | yes | — |
| 59 | #2139 | C22 | 1 | 4 | yes | — |
| 60 | #2139 | C22 | 1 | 4 | yes | — |
| 61 | #2108 | C22 | 1 | 1 | yes | characteristic |
| 62 | #2108 | C22 | 1 | 1 | yes | characteristic |
| 63 | #2108 | C22 | 1 | 2 | yes | — |
| 64 | #2108 | C22 | 1 | 2 | yes | — |
| 65 | C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 66 | C4×M32 | C22 | 1 | 2 | yes | — |
| 67 | C2×C4×C16 | C22 | 1 | 1 | yes | characteristic |
| 68 | C2×C4×C16 | C22 | 1 | 2 | yes | — |
| 69 | C2×#135 | — | 2 | 2 | no | — |
| 70 | C2×#135 | C23 | 1 | 4 | yes | — |
| 71 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 73 | #553 | — | 4 | 8 | no | — |
| 74 | #553 | — | 4 | 4 | no | — |
| 75 | #552 | — | 4 | 4 | no | — |
| 76 | #541 | — | 2 | 4 | no | — |
| 77 | #540 | — | 2 | 4 | no | — |
| 78 | #537 | — | 2 | 4 | no | — |
| 79 | #532 | — | 2 | 2 | no | — |
| 80 | #529 | — | 2 | 8 | no | — |
| 81 | C2×#125 | — | 2 | 2 | no | — |
| 82 | #520 | — | 2 | 4 | no | — |
| 83 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 84 | #508 | — | 2 | 8 | no | — |
| 85 | #508 | — | 2 | 8 | no | — |
| 86 | C2×Q32 | C23 | 1 | 2 | yes | — |
| 87 | C2×Q32 | C23 | 1 | 2 | yes | — |
| 88 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 89 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 90 | C2×D16 | C23 | 1 | 2 | yes | — |
| 91 | C2×D16 | C23 | 1 | 2 | yes | — |
| 92 | #504 | — | 2 | 4 | no | — |
| 93 | #504 | — | 2 | 4 | no | — |
| 94 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×M32 | C23 | 1 | 2 | yes | — |
| 97 | C2×M32 | C23 | 1 | 2 | yes | — |
| 98 | C22×C16 | C23 | 1 | 2 | yes | — |
| 99 | C22×C16 | C23 | 1 | 2 | yes | — |
| 100 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 101 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 102 | #499 | — | 2 | 2 | no | — |
| 103 | #499 | — | 2 | 2 | no | — |
| 104 | #499 | C23 | 1 | 4 | yes | — |
| 105 | #499 | C23 | 1 | 4 | yes | — |
| 106 | #495 | — | 2 | 2 | no | — |
| 107 | #495 | C23 | 1 | 4 | yes | — |
| 108 | #494 | C23 | 1 | 2 | yes | — |
| 109 | #493 | C23 | 1 | 2 | yes | — |
| 110 | #492 | — | 2 | 2 | no | — |
| 111 | #491 | — | 2 | 4 | no | — |
| 112 | #490 | — | 2 | 4 | no | — |
| 113 | #488 | — | 2 | 8 | no | — |
| 114 | #470 | — | 2 | 4 | no | — |
| 115 | #469 | — | 2 | 4 | no | — |
| 116 | #468 | — | 2 | 8 | no | — |
| 117 | #467 | C23 | 1 | 8 | yes | — |
| 118 | #466 | C23 | 1 | 8 | yes | — |
| 119 | #465 | — | 2 | 8 | no | — |
| 120 | #442 | — | 2 | 4 | no | — |
| 121 | #441 | — | 2 | 4 | no | — |
| 122 | #440 | — | 2 | 8 | no | — |
| 123 | C4×Q16 | C23 | 1 | 8 | yes | — |
| 124 | C4×SD16 | — | 2 | 8 | no | — |
| 125 | C4×D8 | C23 | 1 | 8 | yes | — |
| 126 | C2×#107 | C23 | 1 | 4 | yes | — |
| 127 | C2×#106 | — | 2 | 2 | no | — |
| 128 | #417 | — | 2 | 4 | no | — |
| 129 | #417 | — | 2 | 4 | no | — |
| 130 | #405 | D4 | 1 | 2 | yes | — |
| 131 | #405 | D4 | 1 | 1 | yes | characteristic |
| 132 | #405 | C23 | 1 | 2 | yes | — |
| 133 | #405 | C23 | 1 | 1 | yes | characteristic |
| 134 | C4×M16 | D4 | 1 | 1 | yes | characteristic |
| 135 | C4×M16 | D4 | 1 | 2 | yes | — |
| 136 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 138 | #367 | C23 | 1 | 4 | yes | — |
| 139 | #367 | C23 | 1 | 4 | yes | — |
| 140 | #366 | C23 | 1 | 4 | yes | — |
| 141 | #366 | C23 | 1 | 4 | yes | — |
| 142 | #358 | C23 | 1 | 8 | yes | — |
| 143 | #358 | C23 | 1 | 8 | yes | — |
| 144 | #357 | C23 | 1 | 8 | yes | — |
| 145 | #357 | C23 | 1 | 8 | yes | — |
| 146 | #346 | C23 | 1 | 2 | yes | — |
| 147 | #346 | C23 | 1 | 2 | yes | — |
| 148 | #346 | C23 | 1 | 2 | yes | — |
| 149 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 150 | C4×C16 | C23 | 1 | 2 | yes | — |
| 151 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 152 | C4×C16 | C23 | 1 | 2 | yes | — |
| 153 | C4×C16 | C23 | 1 | 2 | yes | — |
| 154 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 155 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 156 | C2×#41 | — | 2 | 4 | no | — |
| 157 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | #135 | — | 2 | 8 | no | — |
| 159 | #135 | — | 2 | 8 | no | — |
| 160 | #135 | — | 4 | 8 | no | — |
| 161 | C2×Q16 | — | 2 | 2 | no | — |
| 162 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 163 | C2×SD16 | — | 2 | 4 | no | — |
| 164 | C2×SD16 | — | 2 | 4 | no | — |
| 165 | C2×D8 | — | 2 | 2 | no | — |
| 166 | C2×D8 | C24 | 1 | 4 | yes | — |
| 167 | #131 | — | 2 | 4 | no | — |
| 168 | #131 | — | 2 | 2 | no | — |
| 169 | #131 | — | 2 | 2 | no | — |
| 170 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 174 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 175 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C22×C8 | C24 | 1 | 2 | yes | — |
| 177 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 178 | C4⋊Q8 | — | 2 | 2 | no | — |
| 179 | #127 | — | 2 | 2 | no | — |
| 180 | #126 | — | 4 | 8 | no | — |
| 181 | #126 | — | 4 | 8 | no | — |
| 182 | #125 | — | 2 | 4 | no | — |
| 183 | #125 | — | 2 | 4 | no | — |
| 184 | #125 | — | 4 | 8 | no | — |
| 185 | #125 | — | 4 | 4 | no | — |
| 186 | #124 | — | 2 | 4 | no | — |
| 187 | #123 | — | 4 | 8 | no | — |
| 188 | #123 | — | 4 | 8 | no | — |
| 189 | C22⋊Q8 | — | 2 | 8 | no | — |
| 190 | C22⋊Q8 | — | 4 | 4 | no | — |
| 191 | #121 | — | 2 | 8 | no | — |
| 192 | #121 | — | 4 | 4 | no | — |
| 193 | #121 | — | 4 | 8 | no | — |
| 194 | #121 | — | 4 | 4 | no | — |
| 195 | #121 | — | 4 | 8 | no | — |
| 196 | C4×Q8 | — | 2 | 8 | no | — |
| 197 | C4×Q8 | D8 | 1 | 2 | yes | — |
| 198 | C4×D4 | — | 2 | 8 | no | — |
| 199 | C4×D4 | — | 4 | 8 | no | — |
| 200 | C4×D4 | — | 4 | 8 | no | — |
| 201 | C4×D4 | — | 4 | 4 | no | — |
| 202 | C4×D4 | D8 | 1 | 4 | yes | — |
| 203 | C4×D4 | D8 | 1 | 2 | yes | — |
| 204 | #117 | — | 4 | 4 | no | — |
| 205 | #117 | — | 4 | 8 | no | — |
| 206 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | #117 | C2×D4 | 1 | 2 | yes | — |
| 208 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 209 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 210 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 211 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 213 | Q32 | — | 2 | 4 | no | — |
| 214 | Q32 | — | 2 | 4 | no | — |
| 215 | SD32 | — | 2 | 8 | no | — |
| 216 | SD32 | — | 2 | 8 | no | — |
| 217 | D16 | — | 2 | 4 | no | — |
| 218 | D16 | — | 2 | 4 | no | — |
| 219 | M32 | — | 2 | 2 | no | — |
| 220 | M32 | — | 2 | 2 | no | — |
| 221 | M32 | — | 2 | 4 | no | — |
| 222 | M32 | — | 2 | 4 | no | — |
| 223 | C2×C16 | — | 2 | 4 | no | — |
| 224 | C2×C16 | — | 2 | 4 | no | — |
| 225 | C2×C16 | #41 | 1 | 4 | yes | — |
| 226 | C2×C16 | #41 | 1 | 4 | yes | — |
| 227 | C2×C16 | C24 | 1 | 2 | yes | — |
| 228 | C2×C16 | C24 | 1 | 2 | yes | — |
| 229 | C2×C16 | C24 | 1 | 1 | yes | characteristic |
| 230 | C2×C16 | C24 | 1 | 1 | yes | characteristic |
| 231 | C2×C16 | C24 | 1 | 1 | yes | characteristic |
| 232 | C2×C16 | C24 | 1 | 1 | yes | characteristic |
| 233 | #107 | — | 2 | 4 | no | — |
| 234 | #107 | C24 | 1 | 8 | yes | — |
| 235 | #106 | — | 2 | 4 | no | — |
| 236 | #106 | — | 2 | 4 | no | — |
| 237 | #103 | — | 2 | 8 | no | — |
| 238 | #103 | — | 2 | 8 | no | — |
| 239 | #102 | — | 2 | 8 | no | — |
| 240 | #102 | — | 2 | 8 | no | — |
| 241 | #97 | C2×D4 | 1 | 2 | yes | — |
| 242 | #97 | C2×D4 | 1 | 2 | yes | — |
| 243 | #97 | C2×D4 | 1 | 2 | yes | — |
| 244 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 245 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 247 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 249 | C4×C8 | C24 | 1 | 2 | yes | — |
| 250 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 251 | #41 | — | 2 | 2 | no | — |
| 252 | #41 | — | 2 | 2 | no | — |
| 253 | #41 | — | 4 | 8 | no | — |
| 254 | #41 | — | 4 | 8 | no | — |
| 255 | C2×Q8 | — | 2 | 4 | no | — |
| 256 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 257 | C2×D4 | — | 2 | 4 | no | — |
| 258 | C2×D4 | — | 4 | 4 | no | — |
| 259 | C2×D4 | — | 4 | 8 | no | — |
| 260 | C2×D4 | — | 4 | 4 | no | — |
| 261 | C2×D4 | C2×D8 | 1 | 2 | yes | — |
| 262 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 263 | C22×C4 | — | 4 | 4 | no | — |
| 264 | C22×C4 | — | 4 | 4 | no | — |
| 265 | C22×C4 | — | 4 | 8 | no | — |
| 266 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 267 | C22×C4 | C2×D8 | 1 | 4 | yes | — |
| 268 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 269 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 270 | Q16 | — | 2 | 4 | no | — |
| 271 | Q16 | — | 2 | 4 | no | — |
| 272 | Q16 | — | 4 | 4 | no | — |
| 273 | SD16 | — | 4 | 8 | no | — |
| 274 | SD16 | — | 4 | 8 | no | — |
| 275 | D8 | — | 2 | 4 | no | — |
| 276 | D8 | — | 2 | 4 | no | — |
| 277 | D8 | — | 4 | 4 | no | — |
| 278 | M16 | — | 2 | 2 | no | — |
| 279 | M16 | — | 2 | 2 | no | — |
| 280 | M16 | — | 2 | 4 | no | — |
| 281 | M16 | — | 2 | 4 | no | — |
| 282 | C2×C8 | — | 2 | 4 | no | — |
| 283 | C2×C8 | — | 2 | 2 | no | — |
| 284 | C2×C8 | — | 2 | 2 | no | — |
| 285 | C2×C8 | #135 | 1 | 4 | yes | — |
| 286 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 287 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 288 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 289 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 290 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 292 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 293 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 294 | C4⋊C4 | — | 2 | 8 | no | — |
| 295 | C4⋊C4 | — | 4 | 4 | no | — |
| 296 | C4⋊C4 | — | 4 | 8 | no | — |
| 297 | C4⋊C4 | — | 4 | 8 | no | — |
| 298 | C4⋊C4 | — | 4 | 8 | no | — |
| 299 | C4⋊C4 | — | 4 | 8 | no | — |
| 300 | C4⋊C4 | — | 4 | 4 | no | — |
| 301 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 302 | C4⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 303 | C22⋊C4 | — | 4 | 8 | no | — |
| 304 | C22⋊C4 | — | 4 | 4 | no | — |
| 305 | C22⋊C4 | — | 4 | 8 | no | — |
| 306 | C22⋊C4 | — | 4 | 8 | no | — |
| 307 | C22⋊C4 | — | 4 | 4 | no | — |
| 308 | C22⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 309 | C22⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 310 | C42 | — | 4 | 8 | no | — |
| 311 | C42 | C2×D8 | 1 | 4 | yes | — |
| 312 | C42 | C2×D8 | 1 | 2 | yes | — |
| 313 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | C42 | C22×D4 | 1 | 2 | yes | — |
| 315 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 316 | C16 | — | 2 | 2 | no | — |
| 317 | C16 | — | 2 | 2 | no | — |
| 318 | C16 | C2×#41 | 1 | 2 | yes | — |
| 319 | C16 | C2×#41 | 1 | 2 | yes | — |
| 320 | C16 | C2×#41 | 1 | 2 | yes | — |
| 321 | C16 | C2×#41 | 1 | 2 | yes | — |
| 322 | C23 | — | 4 | 4 | no | — |
| 323 | C23 | C22×D8 | 1 | 2 | yes | — |
| 324 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 325 | Q8 | — | 2 | 2 | no | — |
| 326 | Q8 | — | 4 | 4 | no | — |
| 327 | Q8 | — | 4 | 4 | no | — |
| 328 | D4 | — | 2 | 4 | no | — |
| 329 | D4 | — | 2 | 2 | no | — |
| 330 | D4 | — | 4 | 4 | no | — |
| 331 | D4 | — | 4 | 4 | no | — |
| 332 | D4 | — | 8 | 8 | no | — |
| 333 | D4 | — | 16 | 4 | no | — |
| 334 | D4 | — | 16 | 8 | no | — |
| 335 | C2×C4 | — | 2 | 2 | no | — |
| 336 | C2×C4 | — | 2 | 2 | no | — |
| 337 | C2×C4 | — | 4 | 4 | no | — |
| 338 | C2×C4 | — | 4 | 2 | no | — |
| 339 | C2×C4 | — | 4 | 4 | no | — |
| 340 | C2×C4 | — | 4 | 8 | no | — |
| 341 | C2×C4 | — | 8 | 8 | no | — |
| 342 | C2×C4 | — | 16 | 8 | no | — |
| 343 | C2×C4 | — | 16 | 4 | no | — |
| 344 | C2×C4 | #532 | 1 | 2 | yes | — |
| 345 | C2×C4 | C22×D8 | 1 | 4 | yes | — |
| 346 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 347 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 348 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 349 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 350 | C2×C4 | C2×#135 | 1 | 2 | yes | — |
| 351 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 352 | C8 | — | 2 | 2 | no | — |
| 353 | C8 | — | 2 | 2 | no | — |
| 354 | C8 | #532 | 1 | 2 | yes | — |
| 355 | C8 | C2×#135 | 1 | 2 | yes | — |
| 356 | C8 | C2×#135 | 1 | 2 | yes | — |
| 357 | C8 | C22×#41 | 1 | 1 | yes | characteristic |
| 358 | C8 | C22×#41 | 1 | 1 | yes | characteristic |
| 359 | C22 | — | 2 | 2 | no | — |
| 360 | C22 | — | 2 | 4 | no | — |
| 361 | C22 | — | 2 | 2 | no | — |
| 362 | C22 | — | 8 | 4 | no | — |
| 363 | C22 | — | 8 | 4 | no | — |
| 364 | C22 | — | 8 | 4 | no | — |
| 365 | C22 | #3169 | 1 | 2 | yes | — |
| 366 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 367 | C4 | — | 2 | 2 | no | — |
| 368 | C4 | — | 2 | 4 | no | — |
| 369 | C4 | — | 2 | 2 | no | — |
| 370 | C4 | — | 2 | 2 | no | — |
| 371 | C4 | — | 8 | 8 | no | — |
| 372 | C4 | — | 8 | 4 | no | — |
| 373 | C4 | #3169 | 1 | 2 | yes | — |
| 374 | C4 | C2×#532 | 1 | 1 | yes | characteristic |
| 375 | C4 | C22×#135 | 1 | 1 | yes | characteristic |
| 376 | C2 | — | 2 | 2 | no | — |
| 377 | C2 | — | 4 | 2 | no | — |
| 378 | C2 | — | 16 | 4 | no | — |
| 379 | C2 | C2×#3169 | 1 | 1 | yes | characteristic |
| 380 | C2 | #62635 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta