← #6404613
Subgroups — #6404613
Order 512.
1810 conjugacy classes of subgroups.
The subgroup lattice has 401 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #61393 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #60274 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #23179 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #23015 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | Q8×#108 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22688 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #22550 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22165 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #21705 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #21292 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C4×C8×Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3480 | C22 | 1 | 2 | yes | — |
| 13 | #3396 | C4 | 1 | 3 | yes | complemented |
| 14 | #3395 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | #3394 | C4 | 1 | 6 | yes | complemented |
| 16 | #3393 | C4 | 1 | 3 | yes | complemented |
| 17 | #3392 | C4 | 1 | 2 | yes | complemented |
| 18 | #3391 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #3147 | C22 | 1 | 3 | yes | — |
| 20 | #3035 | C22 | 1 | 6 | yes | — |
| 21 | #2994 | — | 2 | 6 | no | — |
| 22 | #2993 | — | 2 | 6 | no | — |
| 23 | #2991 | — | 2 | 2 | no | — |
| 24 | #2988 | — | 2 | 2 | no | — |
| 25 | Q8×M16 | C22 | 1 | 2 | yes | — |
| 26 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#443 | C22 | 1 | 6 | yes | — |
| 29 | C2×#443 | C22 | 1 | 6 | yes | — |
| 30 | C4×#135 | C22 | 1 | 3 | yes | — |
| 31 | #2935 | C22 | 1 | 6 | yes | — |
| 32 | #2931 | C22 | 1 | 6 | yes | — |
| 33 | #2922 | C22 | 1 | 6 | yes | — |
| 34 | #2906 | C22 | 1 | 6 | yes | — |
| 35 | C42×Q8 | C22 | 1 | 1 | yes | characteristic |
| 36 | #1980 | C22 | 1 | 6 | yes | — |
| 37 | #1974 | C22 | 1 | 3 | yes | — |
| 38 | #1974 | C22 | 1 | 3 | yes | — |
| 39 | #1974 | C22 | 1 | 6 | yes | — |
| 40 | #1962 | C22 | 1 | 6 | yes | — |
| 41 | #1950 | C22 | 1 | 6 | yes | — |
| 42 | #1945 | C22 | 1 | 1 | yes | characteristic |
| 43 | #1945 | C22 | 1 | 3 | yes | — |
| 44 | #1937 | C22 | 1 | 6 | yes | — |
| 45 | #1937 | C22 | 1 | 6 | yes | — |
| 46 | #1876 | C22 | 1 | 12 | yes | — |
| 47 | #1866 | C22 | 1 | 12 | yes | — |
| 48 | #1848 | C22 | 1 | 3 | yes | — |
| 49 | #1806 | C22 | 1 | 6 | yes | — |
| 50 | C4×#108 | C22 | 1 | 3 | yes | — |
| 51 | C8×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 52 | C8×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 53 | C4×C4⋊C8 | C22 | 1 | 3 | yes | — |
| 54 | C4×#104 | C22 | 1 | 6 | yes | — |
| 55 | C42×C8 | C22 | 1 | 3 | yes | — |
| 56 | C2×#135 | C23 | 1 | 3 | yes | — |
| 57 | C2×#135 | C23 | 1 | 6 | yes | — |
| 58 | C2×#131 | C23 | 1 | 12 | yes | — |
| 59 | #559 | C2×C4 | 1 | 6 | yes | — |
| 60 | #557 | C2×C4 | 1 | 2 | yes | — |
| 61 | #556 | C2×C4 | 1 | 6 | yes | — |
| 62 | #553 | — | 2 | 6 | no | — |
| 63 | #550 | C2×C4 | 1 | 2 | yes | — |
| 64 | #548 | — | 2 | 2 | no | — |
| 65 | #532 | C23 | 1 | 6 | yes | — |
| 66 | #529 | — | 2 | 6 | no | — |
| 67 | C4×#41 | — | 2 | 2 | no | — |
| 68 | C4×#41 | C23 | 1 | 6 | yes | — |
| 69 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 70 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 71 | #495 | C2×C4 | 1 | 6 | yes | — |
| 72 | #495 | C2×C4 | 1 | 6 | yes | — |
| 73 | #494 | C2×C4 | 1 | 3 | yes | — |
| 74 | #493 | C2×C4 | 1 | 3 | yes | — |
| 75 | #492 | C2×C4 | 1 | 6 | yes | — |
| 76 | #464 | C2×C4 | 1 | 12 | yes | — |
| 77 | #463 | C2×C4 | 1 | 12 | yes | — |
| 78 | #462 | C2×C4 | 1 | 6 | yes | — |
| 79 | #461 | C2×C4 | 1 | 6 | yes | — |
| 80 | #460 | C2×C4 | 1 | 6 | yes | — |
| 81 | #459 | C2×C4 | 1 | 6 | yes | — |
| 82 | #446 | — | 2 | 6 | no | — |
| 83 | C8×Q8 | — | 2 | 2 | no | — |
| 84 | C8×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C8×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C8×Q8 | C2×C4 | 1 | 3 | yes | — |
| 87 | C8×Q8 | C2×C4 | 1 | 3 | yes | — |
| 88 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 89 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 90 | C8×Q8 | D4 | 1 | 3 | yes | — |
| 91 | C8×Q8 | D4 | 1 | 3 | yes | — |
| 92 | #443 | — | 4 | 12 | no | — |
| 93 | #443 | — | 4 | 12 | no | — |
| 94 | C4×Q16 | C2×C4 | 1 | 3 | yes | — |
| 95 | C4×Q16 | C2×C4 | 1 | 3 | yes | — |
| 96 | C4×SD16 | C2×C4 | 1 | 6 | yes | — |
| 97 | C4×SD16 | C2×C4 | 1 | 6 | yes | — |
| 98 | C4×D8 | C2×C4 | 1 | 3 | yes | — |
| 99 | C4×D8 | C2×C4 | 1 | 3 | yes | — |
| 100 | #436 | — | 2 | 6 | no | — |
| 101 | #436 | — | 2 | 6 | no | — |
| 102 | #436 | — | 2 | 6 | no | — |
| 103 | #435 | — | 2 | 12 | no | — |
| 104 | C8×D4 | — | 2 | 6 | no | — |
| 105 | C8×D4 | — | 2 | 6 | no | — |
| 106 | C8×D4 | — | 2 | 6 | no | — |
| 107 | #433 | — | 2 | 6 | no | — |
| 108 | #433 | — | 2 | 6 | no | — |
| 109 | #431 | — | 2 | 6 | no | — |
| 110 | #431 | — | 2 | 6 | no | — |
| 111 | C2×#108 | C23 | 1 | 3 | yes | — |
| 112 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×#108 | C23 | 1 | 6 | yes | — |
| 114 | #427 | C23 | 1 | 1 | yes | characteristic |
| 115 | #424 | — | 2 | 12 | no | — |
| 116 | #424 | C23 | 1 | 6 | yes | — |
| 117 | #424 | C23 | 1 | 2 | yes | — |
| 118 | #423 | — | 2 | 6 | no | — |
| 119 | #423 | C23 | 1 | 6 | yes | — |
| 120 | C2×C4⋊C8 | — | 2 | 6 | no | — |
| 121 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 122 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 123 | C2×#104 | C23 | 1 | 6 | yes | — |
| 124 | C2×#104 | C23 | 1 | 12 | yes | — |
| 125 | C2×#104 | C23 | 1 | 6 | yes | — |
| 126 | #416 | C23 | 1 | 6 | yes | — |
| 127 | #408 | C23 | 1 | 6 | yes | — |
| 128 | #408 | C23 | 1 | 6 | yes | — |
| 129 | C4×M16 | C23 | 1 | 6 | yes | — |
| 130 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 131 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 132 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 134 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 135 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 136 | C4×C4⋊C4 | — | 2 | 3 | no | — |
| 137 | C4×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 138 | C43 | C23 | 1 | 3 | yes | — |
| 139 | #341 | C23 | 1 | 6 | yes | — |
| 140 | #339 | C23 | 1 | 6 | yes | — |
| 141 | #339 | C23 | 1 | 2 | yes | — |
| 142 | #336 | C23 | 1 | 6 | yes | — |
| 143 | C2×#41 | — | 2 | 2 | no | — |
| 144 | C2×#41 | C24 | 1 | 6 | yes | — |
| 145 | C22×Q8 | #41 | 1 | 1 | yes | characteristic |
| 146 | #135 | — | 2 | 6 | no | — |
| 147 | #135 | — | 2 | 6 | no | — |
| 148 | #135 | — | 4 | 6 | no | — |
| 149 | #135 | — | 4 | 6 | no | — |
| 150 | C2×Q16 | C22×C4 | 1 | 3 | yes | — |
| 151 | C2×Q16 | C22×C4 | 1 | 6 | yes | — |
| 152 | C2×SD16 | C22×C4 | 1 | 6 | yes | — |
| 153 | C2×SD16 | C22×C4 | 1 | 12 | yes | — |
| 154 | C2×D8 | C22×C4 | 1 | 3 | yes | — |
| 155 | C2×D8 | C22×C4 | 1 | 6 | yes | — |
| 156 | #131 | — | 4 | 12 | no | — |
| 157 | #131 | — | 4 | 12 | no | — |
| 158 | C2×M16 | — | 2 | 12 | no | — |
| 159 | C2×M16 | C24 | 1 | 6 | yes | — |
| 160 | C2×M16 | C24 | 1 | 2 | yes | — |
| 161 | C22×C8 | — | 2 | 12 | no | — |
| 162 | C22×C8 | C24 | 1 | 3 | yes | — |
| 163 | C22×C8 | C24 | 1 | 3 | yes | — |
| 164 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 165 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 166 | C4⋊Q8 | C22×C4 | 1 | 6 | yes | — |
| 167 | #127 | C22×C4 | 1 | 6 | yes | — |
| 168 | #126 | — | 2 | 12 | no | — |
| 169 | #125 | — | 2 | 6 | no | — |
| 170 | #124 | — | 2 | 6 | no | — |
| 171 | #124 | C22×C4 | 1 | 12 | yes | — |
| 172 | #123 | — | 2 | 12 | no | — |
| 173 | C22⋊Q8 | — | 2 | 6 | no | — |
| 174 | #121 | — | 2 | 6 | no | — |
| 175 | #121 | — | 2 | 6 | no | — |
| 176 | #121 | — | 2 | 6 | no | — |
| 177 | C4×Q8 | — | 2 | 8 | no | — |
| 178 | C4×Q8 | — | 2 | 2 | no | — |
| 179 | C4×Q8 | C22×C4 | 1 | 6 | yes | — |
| 180 | C4×Q8 | C22×C4 | 1 | 6 | yes | — |
| 181 | C4×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 182 | C4×Q8 | C22×C4 | 1 | 3 | yes | — |
| 183 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 185 | C4×D4 | — | 2 | 6 | no | — |
| 186 | C4×D4 | — | 2 | 6 | no | — |
| 187 | C4×D4 | — | 2 | 6 | no | — |
| 188 | C4×D4 | — | 2 | 6 | no | — |
| 189 | C4×D4 | — | 2 | 6 | no | — |
| 190 | C4×D4 | C22×C4 | 1 | 6 | yes | — |
| 191 | C4×D4 | C22×C4 | 1 | 6 | yes | — |
| 192 | #117 | — | 2 | 6 | no | — |
| 193 | #117 | — | 2 | 6 | no | — |
| 194 | #117 | C24 | 1 | 2 | yes | — |
| 195 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 196 | C2×C4⋊C4 | #41 | 1 | 3 | yes | — |
| 197 | C2×C42 | — | 2 | 3 | no | — |
| 198 | C2×C42 | — | 2 | 6 | no | — |
| 199 | C2×C42 | — | 2 | 3 | no | — |
| 200 | C2×C42 | C24 | 1 | 3 | yes | — |
| 201 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 202 | C2×C42 | C24 | 1 | 3 | yes | — |
| 203 | #108 | — | 2 | 6 | no | — |
| 204 | #108 | — | 2 | 2 | no | — |
| 205 | #108 | — | 4 | 6 | no | — |
| 206 | #107 | C22×C4 | 1 | 1 | yes | characteristic |
| 207 | #107 | C22×C4 | 1 | 1 | yes | characteristic |
| 208 | #106 | C22×C4 | 1 | 2 | yes | — |
| 209 | C4⋊C8 | — | 2 | 6 | no | — |
| 210 | C4⋊C8 | — | 2 | 6 | no | — |
| 211 | C4⋊C8 | — | 2 | 2 | no | — |
| 212 | C4⋊C8 | — | 2 | 2 | no | — |
| 213 | C4⋊C8 | — | 2 | 6 | no | — |
| 214 | C4⋊C8 | — | 2 | 6 | no | — |
| 215 | C4⋊C8 | C22×C4 | 1 | 3 | yes | — |
| 216 | C4⋊C8 | C22×C4 | 1 | 3 | yes | — |
| 217 | C4⋊C8 | C22×C4 | 1 | 6 | yes | — |
| 218 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 219 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 220 | C4⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 221 | #104 | — | 2 | 12 | no | — |
| 222 | #104 | — | 4 | 6 | no | — |
| 223 | #104 | — | 4 | 12 | no | — |
| 224 | #103 | C22×C4 | 1 | 6 | yes | — |
| 225 | #103 | C22×C4 | 1 | 6 | yes | — |
| 226 | #102 | C22×C4 | 1 | 6 | yes | — |
| 227 | #102 | C22×C4 | 1 | 6 | yes | — |
| 228 | C22⋊C8 | — | 2 | 6 | no | — |
| 229 | C22⋊C8 | — | 2 | 6 | no | — |
| 230 | C22⋊C8 | — | 2 | 6 | no | — |
| 231 | C22⋊C8 | — | 2 | 6 | no | — |
| 232 | #97 | — | 2 | 6 | no | — |
| 233 | C4×C8 | — | 2 | 6 | no | — |
| 234 | C4×C8 | — | 2 | 2 | no | — |
| 235 | C4×C8 | — | 2 | 6 | no | — |
| 236 | C4×C8 | — | 2 | 6 | no | — |
| 237 | C4×C8 | — | 4 | 3 | no | — |
| 238 | C4×C8 | C22×C4 | 1 | 3 | yes | — |
| 239 | C4×C8 | C22×C4 | 1 | 3 | yes | — |
| 240 | C4×C8 | C22×C4 | 1 | 3 | yes | — |
| 241 | C4×C8 | C22×C4 | 1 | 3 | yes | — |
| 242 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 243 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 244 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 245 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 246 | #95 | — | 2 | 3 | no | — |
| 247 | #41 | — | 2 | 6 | no | — |
| 248 | #41 | — | 2 | 6 | no | — |
| 249 | #41 | — | 2 | 6 | no | — |
| 250 | #41 | — | 2 | 6 | no | — |
| 251 | #41 | — | 4 | 8 | no | — |
| 252 | C2×Q8 | — | 2 | 4 | no | — |
| 253 | C2×Q8 | C4×D4 | 1 | 3 | yes | — |
| 254 | C2×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×Q8 | C23×C4 | 1 | 6 | yes | — |
| 256 | C2×D4 | — | 2 | 6 | no | — |
| 257 | C2×D4 | — | 2 | 6 | no | — |
| 258 | C2×D4 | — | 2 | 6 | no | — |
| 259 | C2×D4 | C23×C4 | 1 | 6 | yes | — |
| 260 | C22×C4 | — | 2 | 1 | no | — |
| 261 | C22×C4 | — | 2 | 3 | no | — |
| 262 | C22×C4 | — | 2 | 6 | no | — |
| 263 | C22×C4 | — | 2 | 6 | no | — |
| 264 | C22×C4 | — | 2 | 6 | no | — |
| 265 | C22×C4 | C2×#41 | 1 | 3 | yes | — |
| 266 | C22×C4 | C2×#41 | 1 | 3 | yes | — |
| 267 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 268 | Q16 | — | 2 | 6 | no | — |
| 269 | Q16 | — | 4 | 6 | no | — |
| 270 | SD16 | — | 2 | 12 | no | — |
| 271 | SD16 | — | 4 | 12 | no | — |
| 272 | D8 | — | 2 | 6 | no | — |
| 273 | D8 | — | 4 | 6 | no | — |
| 274 | M16 | — | 2 | 6 | no | — |
| 275 | M16 | — | 2 | 6 | no | — |
| 276 | M16 | — | 2 | 2 | no | — |
| 277 | M16 | — | 2 | 2 | no | — |
| 278 | M16 | — | 8 | 12 | no | — |
| 279 | C2×C8 | — | 2 | 3 | no | — |
| 280 | C2×C8 | — | 2 | 3 | no | — |
| 281 | C2×C8 | — | 2 | 3 | no | — |
| 282 | C2×C8 | — | 2 | 1 | no | — |
| 283 | C2×C8 | — | 2 | 1 | no | — |
| 284 | C2×C8 | — | 2 | 3 | no | — |
| 285 | C2×C8 | — | 2 | 2 | no | — |
| 286 | C2×C8 | — | 2 | 6 | no | — |
| 287 | C2×C8 | — | 8 | 12 | no | — |
| 288 | C2×C8 | C23×C4 | 1 | 3 | yes | — |
| 289 | C2×C8 | C23×C4 | 1 | 3 | yes | — |
| 290 | C2×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 291 | C2×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 292 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 294 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 295 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 296 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 297 | C2×C8 | 2−1+4 | 1 | 2 | yes | — |
| 298 | C4⋊C4 | — | 2 | 12 | no | — |
| 299 | C4⋊C4 | — | 2 | 6 | no | — |
| 300 | C4⋊C4 | — | 2 | 6 | no | — |
| 301 | C4⋊C4 | — | 2 | 6 | no | — |
| 302 | C4⋊C4 | — | 2 | 6 | no | — |
| 303 | C4⋊C4 | C4×D4 | 1 | 3 | yes | — |
| 304 | C4⋊C4 | C4×D4 | 1 | 3 | yes | — |
| 305 | C4⋊C4 | C4×D4 | 1 | 6 | yes | — |
| 306 | C4⋊C4 | C23×C4 | 1 | 2 | yes | — |
| 307 | C4⋊C4 | C23×C4 | 1 | 2 | yes | — |
| 308 | C22⋊C4 | — | 2 | 2 | no | — |
| 309 | C22⋊C4 | — | 2 | 12 | no | — |
| 310 | C22⋊C4 | — | 2 | 6 | no | — |
| 311 | C22⋊C4 | — | 2 | 6 | no | — |
| 312 | C22⋊C4 | — | 2 | 12 | no | — |
| 313 | C42 | — | 2 | 12 | no | — |
| 314 | C42 | — | 2 | 6 | no | — |
| 315 | C42 | — | 2 | 6 | no | — |
| 316 | C42 | — | 2 | 2 | no | — |
| 317 | C42 | — | 2 | 1 | no | — |
| 318 | C42 | — | 2 | 3 | no | — |
| 319 | C42 | — | 2 | 3 | no | — |
| 320 | C42 | — | 4 | 6 | no | — |
| 321 | C42 | C23×C4 | 1 | 3 | yes | — |
| 322 | C42 | C23×C4 | 1 | 3 | yes | — |
| 323 | C42 | C22×D4 | 1 | 3 | yes | — |
| 324 | C42 | C22×D4 | 1 | 3 | yes | — |
| 325 | C42 | H(5,𝔽2) | 1 | 2 | yes | — |
| 326 | C23 | — | 2 | 6 | no | — |
| 327 | C23 | C22×#41 | 1 | 1 | yes | characteristic |
| 328 | Q8 | — | 2 | 6 | no | — |
| 329 | Q8 | — | 2 | 6 | no | — |
| 330 | Q8 | — | 2 | 6 | no | — |
| 331 | Q8 | #443 | 1 | 4 | yes | complemented |
| 332 | D4 | — | 2 | 6 | no | — |
| 333 | D4 | — | 2 | 6 | no | — |
| 334 | D4 | — | 4 | 6 | no | — |
| 335 | D4 | — | 4 | 6 | no | — |
| 336 | D4 | — | 4 | 12 | no | — |
| 337 | D4 | — | 8 | 6 | no | — |
| 338 | C2×C4 | — | 2 | 2 | no | — |
| 339 | C2×C4 | — | 2 | 2 | no | — |
| 340 | C2×C4 | — | 2 | 2 | no | — |
| 341 | C2×C4 | — | 2 | 6 | no | — |
| 342 | C2×C4 | — | 2 | 6 | no | — |
| 343 | C2×C4 | — | 2 | 2 | no | — |
| 344 | C2×C4 | — | 2 | 2 | no | — |
| 345 | C2×C4 | — | 2 | 6 | no | — |
| 346 | C2×C4 | — | 4 | 3 | no | — |
| 347 | C2×C4 | — | 4 | 3 | no | — |
| 348 | C2×C4 | — | 4 | 3 | no | — |
| 349 | C2×C4 | — | 4 | 12 | no | — |
| 350 | C2×C4 | — | 4 | 6 | no | — |
| 351 | C2×C4 | — | 4 | 6 | no | — |
| 352 | C2×C4 | — | 8 | 6 | no | — |
| 353 | C2×C4 | C2×C4×D4 | 1 | 3 | yes | — |
| 354 | C2×C4 | C2×C4×D4 | 1 | 3 | yes | — |
| 355 | C2×C4 | C2×C4×D4 | 1 | 3 | yes | — |
| 356 | C2×C4 | C2×C4×D4 | 1 | 3 | yes | — |
| 357 | C2×C4 | C24×C4 | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 362 | C2×C4 | #585 | 1 | 1 | yes | characteristic |
| 363 | C8 | — | 2 | 3 | no | — |
| 364 | C8 | — | 2 | 3 | no | — |
| 365 | C8 | — | 2 | 1 | no | — |
| 366 | C8 | — | 2 | 1 | no | — |
| 367 | C8 | — | 2 | 3 | no | — |
| 368 | C8 | — | 2 | 3 | no | — |
| 369 | C8 | — | 4 | 2 | no | — |
| 370 | C8 | — | 4 | 6 | no | — |
| 371 | C8 | #520 | 1 | 2 | yes | — |
| 372 | C8 | #520 | 1 | 2 | yes | — |
| 373 | C22 | — | 2 | 1 | no | — |
| 374 | C22 | — | 2 | 1 | no | — |
| 375 | C22 | — | 4 | 6 | no | — |
| 376 | C22 | — | 4 | 6 | no | — |
| 377 | C22 | — | 4 | 6 | no | — |
| 378 | C22 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 379 | C22 | #3517 | 1 | 1 | yes | characteristic |
| 380 | C22 | #3522 | 1 | 1 | yes | characteristic |
| 381 | C4 | — | 2 | 4 | no | — |
| 382 | C4 | — | 2 | 3 | no | — |
| 383 | C4 | — | 2 | 3 | no | — |
| 384 | C4 | — | 2 | 3 | no | — |
| 385 | C4 | — | 4 | 6 | no | — |
| 386 | C4 | — | 4 | 6 | no | — |
| 387 | C4 | — | 4 | 2 | no | — |
| 388 | C4 | — | 4 | 2 | no | — |
| 389 | C4 | C2×#443 | 1 | 6 | yes | — |
| 390 | C4 | C2×#520 | 1 | 1 | yes | characteristic |
| 391 | C4 | C4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 392 | C4 | #3497 | 1 | 1 | yes | characteristic |
| 393 | C4 | #3498 | 1 | 1 | yes | characteristic |
| 394 | C2 | — | 2 | 1 | no | — |
| 395 | C2 | — | 2 | 1 | no | — |
| 396 | C2 | — | 8 | 6 | no | — |
| 397 | C2 | #34313 | 1 | 1 | yes | characteristic |
| 398 | C2 | C22×#443 | 1 | 1 | yes | characteristic |
| 399 | C2 | #60183 | 1 | 1 | yes | characteristic |
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