← #34030419
Subgroups — #34030419
Order 18688.
556 conjugacy classes of subgroups.
The subgroup lattice has 292 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22626313 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #22626312 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22626293 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22626162 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22626161 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22618639 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C2×#14556666 | C22 | 1 | 2 | yes | — |
| 8 | C2×#14556665 | C22 | 1 | 2 | yes | — |
| 9 | C2×#14556664 | C22 | 1 | 2 | yes | — |
| 10 | C22×#11924031 | C22 | 1 | 2 | yes | — |
| 11 | #17989508 | C22 | 1 | 2 | yes | — |
| 12 | #17989508 | C22 | 1 | 2 | yes | — |
| 13 | #17989482 | C22 | 1 | 4 | yes | — |
| 14 | C22⋊#11924031 | C22 | 1 | 4 | yes | — |
| 15 | C22⋊#11924031 | C22 | 1 | 4 | yes | — |
| 16 | #17989476 | C22 | 1 | 4 | yes | — |
| 17 | C2×#14556599 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#14556598 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17989133 | C4 | 1 | 1 | yes | characteristic |
| 20 | #17988662 | C4 | 1 | 4 | yes | — |
| 21 | #17988650 | C22 | 1 | 4 | yes | — |
| 22 | #17988610 | C4 | 1 | 1 | yes | characteristic |
| 23 | #17988553 | C4 | 1 | 1 | yes | characteristic |
| 24 | C2×C8×Dic73 | C22 | 1 | 1 | yes | characteristic |
| 25 | #408×C73 | C4 | 1 | 1 | yes | characteristic |
| 26 | #14556666 | — | 4 | 2 | no | — |
| 27 | #14556665 | — | 4 | 2 | no | — |
| 28 | #14556664 | — | 4 | 2 | no | — |
| 29 | C2×#11924031 | — | 4 | 2 | no | — |
| 30 | C2×#11924031 | C23 | 1 | 4 | yes | — |
| 31 | C2×#11924031 | C23 | 1 | 4 | yes | — |
| 32 | C2×#11924028 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | #14556599 | — | 4 | 1 | no | — |
| 34 | #14556599 | — | 4 | 1 | no | — |
| 35 | #14556598 | — | 4 | 1 | no | — |
| 36 | #14556598 | — | 4 | 1 | no | — |
| 37 | C2×#11924012 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×#11924012 | C2×C4 | 1 | 2 | yes | — |
| 39 | C2×#11924011 | C2×C4 | 1 | 2 | yes | — |
| 40 | C22×#10596831 | C23 | 1 | 2 | yes | — |
| 41 | C22×#10596831 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×C8×D73 | C23 | 1 | 2 | yes | — |
| 43 | #14556589 | C8 | 1 | 1 | yes | characteristic |
| 44 | #14556587 | C8 | 1 | 1 | yes | characteristic |
| 45 | #14556580 | C8 | 1 | 1 | yes | characteristic |
| 46 | #14556578 | C8 | 1 | 1 | yes | characteristic |
| 47 | #14556563 | C8 | 1 | 4 | yes | — |
| 48 | C4×C22⋊D73 | C2×C4 | 1 | 4 | yes | — |
| 49 | C2×C4×Dic73 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | #14556520 | C2×C4 | 1 | 4 | yes | — |
| 51 | #14556503 | C2×C4 | 1 | 4 | yes | — |
| 52 | C8×Dic73 | C2×C4 | 1 | 2 | yes | — |
| 53 | C8×Dic73 | C23 | 1 | 2 | yes | — |
| 54 | C2×#41×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×M16×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C22×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C22⋊C8×C73 | C2×C4 | 1 | 4 | yes | — |
| 58 | #11924031 | — | 2 | 4 | no | — |
| 59 | #11924031 | — | 2 | 4 | no | — |
| 60 | #11924028 | — | 4 | 1 | no | — |
| 61 | #11924028 | — | 4 | 1 | no | — |
| 62 | C2×Dic146 | C2×C8 | 1 | 1 | yes | characteristic |
| 63 | C2×D292 | C2×C8 | 1 | 1 | yes | characteristic |
| 64 | C2×C22⋊D73 | C2×C8 | 1 | 4 | yes | — |
| 65 | C2×C22⋊D73 | C2×C8 | 1 | 2 | yes | — |
| 66 | C22×Dic73 | C2×C8 | 1 | 2 | yes | — |
| 67 | C2×C4×D73 | C22×C4 | 1 | 2 | yes | — |
| 68 | #11924012 | — | 4 | 2 | no | — |
| 69 | #11924012 | — | 4 | 1 | no | — |
| 70 | #11924011 | — | 4 | 2 | no | — |
| 71 | C2×#10596831 | — | 2 | 1 | no | — |
| 72 | C2×#10596831 | — | 2 | 1 | no | — |
| 73 | C2×#10596831 | — | 2 | 2 | no | — |
| 74 | C2×#10596831 | — | 2 | 2 | no | — |
| 75 | C2×#10596831 | C22×C4 | 1 | 1 | yes | characteristic |
| 76 | C2×#10596831 | C22×C4 | 1 | 2 | yes | — |
| 77 | C2×#10596831 | C24 | 1 | 1 | yes | characteristic |
| 78 | C8×D73 | — | 2 | 2 | no | — |
| 79 | C8×D73 | — | 2 | 2 | no | — |
| 80 | #11924007 | C2×C8 | 1 | 4 | yes | — |
| 81 | C22⋊Dic73 | C2×C8 | 1 | 4 | yes | — |
| 82 | #11924005 | C2×C8 | 1 | 4 | yes | — |
| 83 | C4×Dic73 | C2×C8 | 1 | 1 | yes | characteristic |
| 84 | C4×Dic73 | C2×C8 | 1 | 1 | yes | characteristic |
| 85 | C4×Dic73 | C22×C4 | 1 | 2 | yes | — |
| 86 | #41×C73 | — | 4 | 1 | no | — |
| 87 | #41×C73 | — | 4 | 1 | no | — |
| 88 | C2×Q8×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 89 | C2×D4×C73 | C2×C8 | 1 | 2 | yes | — |
| 90 | C2×D4×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×C73 | C22×C4 | 1 | 2 | yes | — |
| 92 | C22×C4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 93 | M16×C73 | — | 4 | 1 | no | — |
| 94 | C2×C8×C73 | — | 4 | 1 | no | — |
| 95 | C2×C8×C73 | C22×C4 | 1 | 2 | yes | — |
| 96 | C2×C8×C73 | C22×C4 | 1 | 2 | yes | — |
| 97 | C23×C73 | C22×C8 | 1 | 2 | yes | — |
| 98 | C23×C73 | C22×C8 | 1 | 1 | yes | characteristic |
| 99 | C22×D73 | C22×C8 | 1 | 2 | yes | — |
| 100 | Q8×C73 | — | 4 | 1 | no | — |
| 101 | D4×C73 | — | 4 | 1 | no | — |
| 102 | D4×C73 | — | 4 | 2 | no | — |
| 103 | C2×C4×C73 | — | 2 | 1 | no | — |
| 104 | C2×C4×C73 | — | 2 | 2 | no | — |
| 105 | C2×C4×C73 | — | 2 | 1 | no | — |
| 106 | C2×C4×C73 | — | 2 | 2 | no | — |
| 107 | C2×C4×C73 | C22×C8 | 1 | 1 | yes | characteristic |
| 108 | C2×C4×C73 | C22×C8 | 1 | 2 | yes | — |
| 109 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 110 | C22⋊D73 | — | 4 | 4 | no | — |
| 111 | C22⋊D73 | — | 4 | 2 | no | — |
| 112 | C2×Dic73 | — | 4 | 2 | no | — |
| 113 | C2×Dic73 | C22×C8 | 1 | 2 | yes | — |
| 114 | C2×Dic73 | C22×C8 | 1 | 2 | yes | — |
| 115 | C2×Dic73 | C22×C8 | 1 | 2 | yes | — |
| 116 | D292 | — | 4 | 1 | no | — |
| 117 | C4×D73 | — | 2 | 2 | no | — |
| 118 | C4×D73 | — | 2 | 2 | no | — |
| 119 | Dic146 | — | 4 | 1 | no | — |
| 120 | C8×C73 | — | 2 | 2 | no | — |
| 121 | C8×C73 | — | 2 | 2 | no | — |
| 122 | #10596831 | — | 2 | 1 | no | — |
| 123 | #10596831 | — | 2 | 2 | no | — |
| 124 | #10596831 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 125 | #10596831 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 126 | C22×C73 | — | 2 | 2 | no | — |
| 127 | C22×C73 | — | 2 | 4 | no | — |
| 128 | C22×C73 | — | 2 | 1 | no | — |
| 129 | C22×C73 | — | 2 | 2 | no | — |
| 130 | C22×C73 | C23×C8 | 1 | 1 | yes | characteristic |
| 131 | C2×D73 | — | 2 | 4 | no | — |
| 132 | C2×D73 | — | 2 | 2 | no | — |
| 133 | C4×C73 | — | 2 | 1 | no | — |
| 134 | C4×C73 | — | 2 | 2 | no | — |
| 135 | C4×C73 | #518 | 1 | 1 | yes | characteristic |
| 136 | C4×C73 | #568 | 1 | 1 | yes | characteristic |
| 137 | Dic73 | — | 2 | 2 | no | — |
| 138 | Dic73 | — | 2 | 2 | no | — |
| 139 | Dic73 | — | 2 | 2 | no | — |
| 140 | #33494 | — | 73 | 1 | no | maximal, Sylow |
| 141 | C2×C73 | — | 4 | 1 | no | — |
| 142 | C2×C73 | — | 4 | 2 | no | — |
| 143 | C2×C73 | #2972 | 1 | 1 | yes | characteristic |
| 144 | C2×C73 | #3407 | 1 | 2 | yes | — |
| 145 | D73 | — | 4 | 2 | no | — |
| 146 | #2931 | — | 73 | 1 | no | — |
| 147 | #2168 | — | 73 | 4 | no | — |
| 148 | #2168 | — | 73 | 4 | no | — |
| 149 | #2163 | — | 73 | 2 | no | — |
| 150 | #2113 | — | 73 | 2 | no | — |
| 151 | #2113 | — | 73 | 2 | no | — |
| 152 | C73 | #33494 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 153 | C2×#131 | — | 73 | 1 | no | — |
| 154 | C2×#131 | — | 73 | 1 | no | — |
| 155 | #532 | — | 73 | 1 | no | — |
| 156 | C2×M32 | — | 73 | 2 | no | — |
| 157 | C2×M32 | — | 73 | 2 | no | — |
| 158 | C22×C16 | — | 73 | 2 | no | — |
| 159 | C22×C16 | — | 73 | 2 | no | — |
| 160 | #436 | — | 73 | 4 | no | — |
| 161 | C8×D4 | — | 73 | 4 | no | — |
| 162 | #423 | — | 73 | 1 | no | — |
| 163 | #408 | — | 73 | 1 | no | — |
| 164 | #408 | #64408 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C8 | — | 73 | 1 | no | — |
| 166 | C4⋊C16 | — | 73 | 2 | no | — |
| 167 | C4⋊C16 | — | 73 | 2 | no | — |
| 168 | C22⋊C16 | — | 73 | 4 | no | — |
| 169 | C22⋊C16 | — | 73 | 4 | no | — |
| 170 | C22⋊C16 | — | 73 | 4 | no | — |
| 171 | #346 | — | 73 | 4 | no | — |
| 172 | C2×#41 | — | 73 | 1 | no | — |
| 173 | C2×#41 | C2×#64408 | 1 | 1 | yes | characteristic |
| 174 | #131 | — | 292 | 1 | no | — |
| 175 | #131 | — | 292 | 1 | no | — |
| 176 | #131 | — | 292 | 1 | no | — |
| 177 | #131 | — | 292 | 1 | no | — |
| 178 | C2×M16 | — | 73 | 1 | no | — |
| 179 | C2×M16 | — | 73 | 2 | no | — |
| 180 | C2×M16 | — | 73 | 2 | no | — |
| 181 | C2×M16 | C2×#64408 | 1 | 1 | yes | characteristic |
| 182 | C22×C8 | — | 73 | 1 | no | — |
| 183 | C22×C8 | — | 73 | 2 | no | — |
| 184 | C22×C8 | — | 73 | 2 | no | — |
| 185 | C22×C8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 186 | C4⋊Q8 | — | 73 | 1 | no | — |
| 187 | #127 | — | 73 | 1 | no | — |
| 188 | #124 | — | 73 | 1 | no | — |
| 189 | #124 | — | 73 | 1 | no | — |
| 190 | #121 | — | 73 | 4 | no | — |
| 191 | C4×D4 | — | 73 | 4 | no | — |
| 192 | C2×C42 | — | 73 | 1 | no | — |
| 193 | M32 | — | 292 | 2 | no | — |
| 194 | M32 | — | 292 | 2 | no | — |
| 195 | C2×C16 | — | 292 | 2 | no | — |
| 196 | C2×C16 | — | 292 | 2 | no | — |
| 197 | C2×C16 | — | 73 | 4 | no | — |
| 198 | C2×C16 | — | 73 | 4 | no | — |
| 199 | C4⋊C8 | — | 73 | 4 | no | — |
| 200 | C22⋊C8 | — | 73 | 4 | no | — |
| 201 | C22⋊C8 | C2×#64408 | 1 | 4 | yes | — |
| 202 | C4×C8 | — | 73 | 2 | no | — |
| 203 | C4×C8 | — | 73 | 2 | no | — |
| 204 | #41 | — | 4 | 1 | no | — |
| 205 | #41 | — | 4 | 1 | no | — |
| 206 | #41 | — | 292 | 1 | no | — |
| 207 | #41 | — | 292 | 1 | no | — |
| 208 | C2×Q8 | — | 73 | 1 | no | — |
| 209 | C2×Q8 | #11924036 | 1 | 1 | yes | characteristic |
| 210 | C2×D4 | — | 73 | 4 | no | — |
| 211 | C2×D4 | — | 73 | 2 | no | — |
| 212 | C2×D4 | — | 73 | 1 | no | — |
| 213 | C2×D4 | #11924036 | 1 | 2 | yes | — |
| 214 | C2×D4 | #11924036 | 1 | 1 | yes | characteristic |
| 215 | C22×C4 | — | 73 | 2 | no | — |
| 216 | C22×C4 | — | 73 | 2 | no | — |
| 217 | C22×C4 | C22×#64408 | 1 | 2 | yes | — |
| 218 | C22×C4 | C22×#64408 | 1 | 1 | yes | characteristic |
| 219 | M16 | — | 4 | 1 | no | — |
| 220 | M16 | — | 292 | 2 | no | — |
| 221 | M16 | — | 292 | 2 | no | — |
| 222 | M16 | — | 292 | 1 | no | — |
| 223 | C2×C8 | — | 4 | 1 | no | — |
| 224 | C2×C8 | — | 73 | 1 | no | — |
| 225 | C2×C8 | — | 73 | 1 | no | — |
| 226 | C2×C8 | — | 73 | 2 | no | — |
| 227 | C2×C8 | — | 146 | 2 | no | — |
| 228 | C2×C8 | — | 146 | 2 | no | — |
| 229 | C2×C8 | — | 146 | 2 | no | — |
| 230 | C2×C8 | — | 146 | 2 | no | — |
| 231 | C2×C8 | — | 146 | 1 | no | — |
| 232 | C2×C8 | — | 146 | 1 | no | — |
| 233 | C2×C8 | C22×#64408 | 1 | 2 | yes | — |
| 234 | C2×C8 | C22×#64408 | 1 | 2 | yes | — |
| 235 | C4⋊C4 | — | 73 | 4 | no | — |
| 236 | C22⋊C4 | — | 73 | 4 | no | — |
| 237 | C22⋊C4 | — | 73 | 4 | no | — |
| 238 | C42 | — | 73 | 1 | no | — |
| 239 | C42 | — | 73 | 1 | no | — |
| 240 | C42 | — | 73 | 2 | no | — |
| 241 | C16 | — | 146 | 4 | no | — |
| 242 | C16 | — | 146 | 4 | no | — |
| 243 | C23 | — | 73 | 2 | no | — |
| 244 | C23 | C2×#11924036 | 1 | 2 | yes | — |
| 245 | C23 | C2×#11924036 | 1 | 1 | yes | characteristic |
| 246 | Q8 | — | 4 | 1 | no | — |
| 247 | Q8 | — | 292 | 1 | no | — |
| 248 | D4 | — | 4 | 1 | no | — |
| 249 | D4 | — | 4 | 2 | no | — |
| 250 | D4 | — | 292 | 1 | no | — |
| 251 | D4 | — | 292 | 2 | no | — |
| 252 | D4 | — | 292 | 4 | no | — |
| 253 | C2×C4 | — | 2 | 1 | no | — |
| 254 | C2×C4 | — | 2 | 2 | no | — |
| 255 | C2×C4 | — | 2 | 1 | no | — |
| 256 | C2×C4 | — | 2 | 2 | no | — |
| 257 | C2×C4 | — | 292 | 2 | no | — |
| 258 | C2×C4 | — | 73 | 2 | no | — |
| 259 | C2×C4 | — | 73 | 2 | no | — |
| 260 | C2×C4 | — | 73 | 2 | no | — |
| 261 | C2×C4 | — | 146 | 2 | no | — |
| 262 | C2×C4 | — | 146 | 2 | no | — |
| 263 | C2×C4 | C2×#11924036 | 1 | 1 | yes | characteristic |
| 264 | C2×C4 | C2×#11924036 | 1 | 2 | yes | — |
| 265 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 266 | C8 | — | 2 | 2 | no | — |
| 267 | C8 | — | 2 | 2 | no | — |
| 268 | C8 | — | 73 | 1 | no | — |
| 269 | C8 | — | 73 | 1 | no | — |
| 270 | C8 | — | 146 | 1 | no | — |
| 271 | C8 | — | 146 | 2 | no | — |
| 272 | C22 | — | 2 | 2 | no | — |
| 273 | C22 | — | 2 | 4 | no | — |
| 274 | C22 | — | 2 | 1 | no | — |
| 275 | C22 | — | 2 | 2 | no | — |
| 276 | C22 | — | 146 | 4 | no | — |
| 277 | C22 | — | 146 | 2 | no | — |
| 278 | C22 | C22×#11924036 | 1 | 1 | yes | characteristic |
| 279 | C4 | — | 2 | 1 | no | — |
| 280 | C4 | — | 2 | 2 | no | — |
| 281 | C4 | — | 146 | 2 | no | — |
| 282 | C4 | — | 146 | 2 | no | — |
| 283 | C4 | — | 146 | 2 | no | — |
| 284 | C4 | #17989654 | 1 | 1 | yes | characteristic |
| 285 | C4 | #17989665 | 1 | 1 | yes | characteristic |
| 286 | C2 | — | 4 | 1 | no | — |
| 287 | C2 | — | 4 | 2 | no | — |
| 288 | C2 | — | 292 | 2 | no | — |
| 289 | C2 | #22626780 | 1 | 1 | yes | characteristic |
| 290 | C2 | #22626899 | 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