← #34034533
Subgroups — #34034533
Order 18688.
678 conjugacy classes of subgroups.
The subgroup lattice has 324 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22627174 | C2 | 1 | 2 | yes | maximal |
| 2 | #22627061 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | Q16×#10596842 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22627055 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22627052 | C2 | 1 | 2 | yes | maximal |
| 6 | #22627040 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C2×Q16×#64408 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | Q8×#10596842 | — | 2 | 4 | no | — |
| 9 | Q8×#10596842 | C22 | 1 | 8 | yes | — |
| 10 | #17989700 | — | 2 | 4 | no | — |
| 11 | #17989700 | C22 | 1 | 2 | yes | — |
| 12 | #17989700 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17989700 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17989677 | C22 | 1 | 2 | yes | — |
| 15 | #17989676 | C22 | 1 | 2 | yes | — |
| 16 | Q8⋊#10596842 | C22 | 1 | 8 | yes | — |
| 17 | #17989671 | C22 | 1 | 2 | yes | — |
| 18 | C8×#10596842 | C22 | 1 | 2 | yes | — |
| 19 | C2×Q8×#64408 | C22 | 1 | 2 | yes | — |
| 20 | Q16×#64408 | C4 | 1 | 2 | yes | — |
| 21 | Q16×#64408 | C4 | 1 | 2 | yes | — |
| 22 | Q16×#64408 | C22 | 1 | 2 | yes | — |
| 23 | Q16×#64408 | C22 | 1 | 2 | yes | — |
| 24 | C2×#14556660 | C4 | 1 | 1 | yes | characteristic |
| 25 | C2×#14556654 | C4 | 1 | 2 | yes | — |
| 26 | C2×C8×#64408 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×Q16×D73 | C4 | 1 | 1 | yes | characteristic |
| 28 | C4⋊#10596842 | — | 2 | 8 | no | — |
| 29 | C4⋊#10596842 | — | 2 | 1 | no | — |
| 30 | C4⋊#10596842 | D4 | 1 | 2 | yes | — |
| 31 | C4⋊#10596842 | C23 | 1 | 4 | yes | — |
| 32 | C22⋊#10596842 | — | 2 | 2 | no | — |
| 33 | C22⋊#10596842 | — | 2 | 1 | no | — |
| 34 | C22⋊#10596842 | D4 | 1 | 2 | yes | — |
| 35 | C4×#10596842 | — | 2 | 8 | no | — |
| 36 | C4×#10596842 | — | 2 | 2 | no | — |
| 37 | C4×#10596842 | C23 | 1 | 2 | yes | — |
| 38 | C4×#10596842 | C23 | 1 | 2 | yes | — |
| 39 | C2×#11924036 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | Q8×#64408 | — | 2 | 2 | no | — |
| 41 | Q8×#64408 | — | 2 | 2 | no | — |
| 42 | Q8×#64408 | C2×C4 | 1 | 4 | yes | — |
| 43 | Q8×#64408 | C23 | 1 | 4 | yes | — |
| 44 | C2×C4⋊#64408 | — | 2 | 2 | no | — |
| 45 | C2×C4⋊#64408 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×C4×#64408 | — | 2 | 2 | no | — |
| 47 | C2×C4×#64408 | C23 | 1 | 1 | yes | characteristic |
| 48 | #14556660 | C2×C4 | 1 | 2 | yes | — |
| 49 | #14556660 | C2×C4 | 1 | 2 | yes | — |
| 50 | #14556654 | C2×C4 | 1 | 4 | yes | — |
| 51 | #14556654 | C2×C4 | 1 | 4 | yes | — |
| 52 | C8×#64408 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C8×#64408 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C8×#64408 | C23 | 1 | 1 | yes | characteristic |
| 55 | C8×#64408 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×Q8×D73 | C2×C4 | 1 | 2 | yes | — |
| 57 | C2×Dic292 | C8 | 1 | 1 | yes | characteristic, complemented |
| 58 | C2×#11924018 | C8 | 1 | 2 | yes | complemented |
| 59 | Q16×D73 | C8 | 1 | 2 | yes | complemented |
| 60 | Q16×D73 | C8 | 1 | 2 | yes | complemented |
| 61 | Q16×D73 | C2×C4 | 1 | 2 | yes | — |
| 62 | Q16×D73 | C2×C4 | 1 | 2 | yes | — |
| 63 | C2×C8×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | C2×Q16×C73 | C8 | 1 | 1 | yes | characteristic, complemented |
| 65 | C2×#10596842 | — | 2 | 4 | no | — |
| 66 | C2×#10596842 | — | 2 | 2 | no | — |
| 67 | C2×#10596842 | C2×D4 | 1 | 4 | yes | — |
| 68 | C22×#64408 | — | 2 | 2 | no | — |
| 69 | C22×#64408 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C22×#64408 | #41 | 1 | 1 | yes | characteristic |
| 71 | #11924036 | — | 2 | 1 | no | — |
| 72 | #11924036 | C22×C4 | 1 | 1 | yes | characteristic |
| 73 | #11924036 | C22×C4 | 1 | 1 | yes | characteristic |
| 74 | C2×#10596833 | — | 2 | 1 | no | — |
| 75 | C4⋊#64408 | — | 2 | 4 | no | — |
| 76 | C4⋊#64408 | — | 2 | 4 | no | — |
| 77 | C4⋊#64408 | — | 2 | 2 | no | — |
| 78 | C4⋊#64408 | C22×C4 | 1 | 4 | yes | — |
| 79 | C4×#64408 | — | 2 | 4 | no | — |
| 80 | C4×#64408 | — | 2 | 4 | no | — |
| 81 | C4×#64408 | C22×C4 | 1 | 1 | yes | characteristic |
| 82 | C4×#64408 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C4×#64408 | #41 | 1 | 1 | yes | characteristic |
| 84 | C4×#64408 | C24 | 1 | 1 | yes | characteristic |
| 85 | C2×Dic146 | — | 2 | 2 | no | — |
| 86 | C2×Dic146 | C2×C8 | 1 | 2 | yes | — |
| 87 | Q8×D73 | — | 2 | 2 | no | — |
| 88 | Q8×D73 | — | 2 | 2 | no | — |
| 89 | Q8×D73 | C2×C8 | 1 | 4 | yes | — |
| 90 | Q8×D73 | C22×C4 | 1 | 4 | yes | — |
| 91 | C2×C4×D73 | — | 2 | 2 | no | — |
| 92 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 93 | Dic292 | C2×C8 | 1 | 2 | yes | — |
| 94 | Dic292 | C2×C8 | 1 | 2 | yes | — |
| 95 | #11924018 | C2×C8 | 1 | 4 | yes | — |
| 96 | #11924018 | C2×C8 | 1 | 4 | yes | — |
| 97 | C2×#10596831 | C2×C8 | 1 | 1 | yes | characteristic |
| 98 | C8×D73 | C2×C8 | 1 | 1 | yes | characteristic |
| 99 | C8×D73 | C2×C8 | 1 | 1 | yes | characteristic |
| 100 | C8×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | C8×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C2×Q8×C73 | C2×C8 | 1 | 2 | yes | — |
| 103 | Q16×C73 | C2×C8 | 1 | 2 | yes | — |
| 104 | Q16×C73 | C2×C8 | 1 | 2 | yes | — |
| 105 | C2×C8×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 106 | C22×D73 | C4×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×#64408 | — | 2 | 2 | no | — |
| 108 | C2×#64408 | — | 2 | 4 | no | — |
| 109 | C2×#64408 | — | 4 | 1 | no | — |
| 110 | C2×#64408 | — | 8 | 2 | no | — |
| 111 | C2×#64408 | C4×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×#64408 | C4×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×#64408 | C22×D4 | 1 | 1 | yes | characteristic |
| 114 | C2×#64408 | C2×#41 | 1 | 1 | yes | characteristic |
| 115 | #10596842 | — | 2 | 4 | no | — |
| 116 | #10596842 | — | 4 | 2 | no | — |
| 117 | #10596842 | — | 4 | 4 | no | — |
| 118 | Q8×C73 | — | 2 | 2 | no | — |
| 119 | Q8×C73 | C22×C8 | 1 | 4 | yes | — |
| 120 | C2×C4×C73 | — | 2 | 2 | no | — |
| 121 | C2×C4×C73 | C22×C8 | 1 | 1 | yes | characteristic |
| 122 | C2×Dic73 | — | 2 | 2 | no | — |
| 123 | C2×Dic73 | #131 | 1 | 1 | yes | characteristic |
| 124 | C4×D73 | — | 2 | 4 | no | — |
| 125 | C4×D73 | — | 2 | 4 | no | — |
| 126 | C4×D73 | C4×D4 | 1 | 1 | yes | characteristic |
| 127 | C4×D73 | C22×C8 | 1 | 1 | yes | characteristic |
| 128 | C4×D73 | #131 | 1 | 1 | yes | characteristic |
| 129 | C4×D73 | C23×C4 | 1 | 1 | yes | characteristic |
| 130 | Dic146 | — | 2 | 2 | no | — |
| 131 | Dic146 | — | 2 | 4 | no | — |
| 132 | Dic146 | — | 2 | 4 | no | — |
| 133 | Dic146 | C22×C8 | 1 | 4 | yes | — |
| 134 | #10596833 | — | 2 | 1 | no | — |
| 135 | #10596833 | — | 2 | 1 | no | — |
| 136 | C8×C73 | C22×C8 | 1 | 1 | yes | characteristic |
| 137 | C8×C73 | C22×C8 | 1 | 1 | yes | characteristic |
| 138 | #10596831 | C22×C8 | 1 | 1 | yes | characteristic |
| 139 | #10596831 | C22×C8 | 1 | 1 | yes | characteristic |
| 140 | C22×C73 | C8×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×D73 | — | 2 | 1 | no | — |
| 142 | C2×D73 | — | 2 | 1 | no | — |
| 143 | C2×D73 | C8×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×D73 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 145 | #64408 | — | 2 | 1 | no | — |
| 146 | #64408 | — | 2 | 1 | no | — |
| 147 | #64408 | — | 2 | 1 | no | — |
| 148 | #64408 | — | 4 | 4 | no | — |
| 149 | #64408 | #578 | 1 | 2 | yes | — |
| 150 | C4×C73 | — | 2 | 4 | no | — |
| 151 | C4×C73 | C8×D4 | 1 | 1 | yes | characteristic |
| 152 | C4×C73 | C23×C8 | 1 | 1 | yes | characteristic |
| 153 | Dic73 | — | 2 | 4 | no | — |
| 154 | Dic73 | C8×D4 | 1 | 1 | yes | characteristic |
| 155 | Dic73 | C2×#131 | 1 | 1 | yes | characteristic |
| 156 | #17856 | — | 73 | 1 | no | maximal, Sylow |
| 157 | C2×C73 | — | 2 | 1 | no | — |
| 158 | C2×C73 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 159 | D73 | — | 2 | 1 | no | — |
| 160 | D73 | #2950 | 1 | 1 | yes | characteristic |
| 161 | D73 | #2957 | 1 | 1 | yes | characteristic |
| 162 | #2982 | — | 73 | 2 | no | — |
| 163 | C2×C4×Q16 | — | 73 | 1 | no | — |
| 164 | #1579 | — | 73 | 4 | no | — |
| 165 | C8×Q16 | — | 73 | 4 | no | — |
| 166 | #1564 | — | 73 | 1 | no | — |
| 167 | #1479 | — | 73 | 2 | no | — |
| 168 | #1450 | — | 73 | 1 | no | — |
| 169 | C73 | #17856 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 170 | C22×Q16 | — | 73 | 1 | no | — |
| 171 | C2×C4×Q8 | — | 73 | 2 | no | — |
| 172 | C8×Q8 | — | 73 | 8 | no | — |
| 173 | C8×Q8 | — | 146 | 4 | no | — |
| 174 | C4×Q16 | — | 73 | 2 | no | — |
| 175 | C4×Q16 | — | 73 | 2 | no | — |
| 176 | C4×Q16 | — | 73 | 2 | no | — |
| 177 | C4×Q16 | — | 73 | 2 | no | — |
| 178 | #431 | — | 73 | 1 | no | — |
| 179 | #431 | — | 73 | 1 | no | — |
| 180 | #431 | — | 73 | 2 | no | — |
| 181 | #431 | — | 146 | 4 | no | — |
| 182 | C2×#107 | — | 73 | 1 | no | — |
| 183 | C2×#103 | — | 73 | 2 | no | — |
| 184 | C2×C4×C8 | — | 73 | 1 | no | — |
| 185 | #335 | — | 73 | 2 | no | — |
| 186 | #334 | — | 73 | 2 | no | — |
| 187 | Q8⋊C8 | — | 73 | 8 | no | — |
| 188 | #322 | — | 73 | 2 | no | — |
| 189 | C82 | — | 73 | 2 | no | — |
| 190 | C22×Q8 | — | 73 | 2 | no | — |
| 191 | C2×Q16 | — | 73 | 2 | no | — |
| 192 | C2×Q16 | — | 73 | 2 | no | — |
| 193 | C2×Q16 | — | 73 | 2 | no | — |
| 194 | C2×Q16 | — | 73 | 2 | no | — |
| 195 | C2×Q16 | — | 73 | 2 | no | — |
| 196 | C2×Q16 | — | 73 | 1 | no | — |
| 197 | C2×Q16 | #10596842 | 1 | 1 | yes | characteristic, complemented |
| 198 | C22×C8 | — | 73 | 1 | no | — |
| 199 | C22×C8 | — | 73 | 1 | no | — |
| 200 | C4×Q8 | — | 73 | 4 | no | — |
| 201 | C4×Q8 | — | 73 | 4 | no | — |
| 202 | C4×Q8 | — | 146 | 2 | no | — |
| 203 | C4×Q8 | — | 146 | 2 | no | — |
| 204 | C2×C4⋊C4 | — | 73 | 2 | no | — |
| 205 | C2×C4⋊C4 | — | 146 | 2 | no | — |
| 206 | C2×C42 | — | 73 | 1 | no | — |
| 207 | C2×C42 | — | 146 | 2 | no | — |
| 208 | #107 | — | 73 | 2 | no | — |
| 209 | #107 | — | 73 | 2 | no | — |
| 210 | C4⋊C8 | — | 73 | 2 | no | — |
| 211 | C4⋊C8 | — | 73 | 4 | no | — |
| 212 | C4⋊C8 | — | 146 | 1 | no | — |
| 213 | C4⋊C8 | — | 146 | 8 | no | — |
| 214 | #103 | — | 73 | 4 | no | — |
| 215 | #103 | — | 73 | 4 | no | — |
| 216 | C22⋊C8 | — | 73 | 2 | no | — |
| 217 | C22⋊C8 | — | 146 | 1 | no | — |
| 218 | C22⋊C8 | — | 146 | 2 | no | — |
| 219 | C4×C8 | — | 73 | 2 | no | — |
| 220 | C4×C8 | — | 73 | 1 | no | — |
| 221 | C4×C8 | — | 73 | 1 | no | — |
| 222 | C4×C8 | — | 73 | 1 | no | — |
| 223 | C4×C8 | — | 73 | 1 | no | — |
| 224 | C4×C8 | — | 73 | 2 | no | — |
| 225 | C4×C8 | — | 146 | 2 | no | — |
| 226 | C4×C8 | — | 146 | 8 | no | — |
| 227 | C2×Q8 | — | 73 | 4 | no | — |
| 228 | C2×Q8 | — | 73 | 4 | no | — |
| 229 | C2×Q8 | — | 73 | 2 | no | — |
| 230 | C2×Q8 | — | 146 | 2 | no | — |
| 231 | C2×Q8 | — | 146 | 2 | no | — |
| 232 | C2×Q8 | — | 146 | 2 | no | — |
| 233 | C2×Q8 | C2×#10596842 | 1 | 2 | yes | — |
| 234 | C22×C4 | — | 73 | 1 | no | — |
| 235 | C22×C4 | — | 73 | 1 | no | — |
| 236 | C22×C4 | — | 73 | 1 | no | — |
| 237 | C22×C4 | — | 146 | 2 | no | — |
| 238 | C22×C4 | — | 146 | 2 | no | — |
| 239 | Q16 | — | 73 | 4 | no | — |
| 240 | Q16 | — | 73 | 4 | no | — |
| 241 | Q16 | — | 73 | 2 | no | — |
| 242 | Q16 | — | 73 | 2 | no | — |
| 243 | Q16 | C2×#10596842 | 1 | 2 | yes | — |
| 244 | Q16 | C2×#10596842 | 1 | 2 | yes | — |
| 245 | C2×C8 | — | 73 | 1 | no | — |
| 246 | C2×C8 | — | 73 | 1 | no | — |
| 247 | C2×C8 | — | 73 | 1 | no | — |
| 248 | C2×C8 | — | 73 | 1 | no | — |
| 249 | C2×C8 | — | 73 | 1 | no | — |
| 250 | C2×C8 | — | 73 | 1 | no | — |
| 251 | C2×C8 | — | 73 | 1 | no | — |
| 252 | C2×C8 | — | 73 | 4 | no | — |
| 253 | C2×C8 | — | 146 | 2 | no | — |
| 254 | C2×C8 | — | 146 | 4 | no | — |
| 255 | C2×C8 | — | 146 | 1 | no | — |
| 256 | C2×C8 | — | 146 | 1 | no | — |
| 257 | C2×C8 | C2×#10596842 | 1 | 1 | yes | characteristic |
| 258 | C4⋊C4 | — | 73 | 4 | no | — |
| 259 | C4⋊C4 | — | 146 | 2 | no | — |
| 260 | C4⋊C4 | — | 146 | 4 | no | — |
| 261 | C4⋊C4 | — | 146 | 4 | no | — |
| 262 | C42 | — | 73 | 1 | no | — |
| 263 | C42 | — | 73 | 1 | no | — |
| 264 | C42 | — | 73 | 1 | no | — |
| 265 | C42 | — | 73 | 1 | no | — |
| 266 | C42 | — | 146 | 4 | no | — |
| 267 | C42 | — | 146 | 4 | no | — |
| 268 | C23 | — | 73 | 1 | no | — |
| 269 | Q8 | — | 2 | 2 | no | — |
| 270 | Q8 | — | 73 | 4 | no | — |
| 271 | Q8 | — | 146 | 4 | no | — |
| 272 | Q8 | — | 146 | 4 | no | — |
| 273 | Q8 | — | 146 | 2 | no | — |
| 274 | Q8 | C22×#10596842 | 1 | 4 | yes | — |
| 275 | C2×C4 | — | 2 | 2 | no | — |
| 276 | C2×C4 | — | 292 | 1 | no | — |
| 277 | C2×C4 | — | 584 | 2 | no | — |
| 278 | C2×C4 | — | 73 | 1 | no | — |
| 279 | C2×C4 | — | 73 | 1 | no | — |
| 280 | C2×C4 | — | 73 | 1 | no | — |
| 281 | C2×C4 | — | 73 | 1 | no | — |
| 282 | C2×C4 | — | 73 | 1 | no | — |
| 283 | C2×C4 | — | 73 | 1 | no | — |
| 284 | C2×C4 | — | 73 | 1 | no | — |
| 285 | C2×C4 | — | 73 | 1 | no | — |
| 286 | C2×C4 | — | 73 | 1 | no | — |
| 287 | C2×C4 | — | 146 | 4 | no | — |
| 288 | C2×C4 | — | 146 | 4 | no | — |
| 289 | C2×C4 | — | 146 | 4 | no | — |
| 290 | C2×C4 | — | 146 | 2 | no | — |
| 291 | C2×C4 | — | 146 | 2 | no | — |
| 292 | C2×C4 | C22×#10596842 | 1 | 1 | yes | characteristic |
| 293 | C8 | — | 292 | 4 | no | — |
| 294 | C8 | — | 292 | 2 | no | — |
| 295 | C8 | — | 73 | 1 | no | — |
| 296 | C8 | — | 73 | 1 | no | — |
| 297 | C8 | — | 146 | 1 | no | — |
| 298 | C8 | — | 146 | 1 | no | — |
| 299 | C8 | — | 146 | 4 | no | — |
| 300 | C8 | C22×#10596842 | 1 | 1 | yes | characteristic |
| 301 | C8 | C22×#10596842 | 1 | 1 | yes | characteristic |
| 302 | C22 | — | 73 | 1 | no | — |
| 303 | C22 | — | 73 | 1 | no | — |
| 304 | C22 | — | 146 | 1 | no | — |
| 305 | C22 | — | 146 | 1 | no | — |
| 306 | C22 | D4×#10596842 | 1 | 1 | yes | characteristic |
| 307 | C4 | — | 2 | 4 | no | — |
| 308 | C4 | — | 292 | 4 | no | — |
| 309 | C4 | — | 73 | 2 | no | — |
| 310 | C4 | — | 73 | 1 | no | — |
| 311 | C4 | — | 73 | 1 | no | — |
| 312 | C4 | — | 146 | 1 | no | — |
| 313 | C4 | — | 146 | 1 | no | — |
| 314 | C4 | — | 146 | 1 | no | — |
| 315 | C4 | — | 146 | 4 | no | — |
| 316 | C4 | D4×#10596842 | 1 | 1 | yes | characteristic |
| 317 | C4 | C23×#10596842 | 1 | 1 | yes | characteristic |
| 318 | C2 | — | 2 | 1 | no | — |
| 319 | C2 | — | 73 | 1 | no | — |
| 320 | C2 | — | 73 | 1 | no | — |
| 321 | C2 | — | 146 | 1 | no | — |
| 322 | C2 | C2×D4×#10596842 | 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