← #34029822
Subgroups — #34029822
Order 18688.
716 conjugacy classes of subgroups.
The subgroup lattice has 270 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22626899 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22626501 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22626151 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22626150 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #22626146 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#17989478 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #22623032 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | D73⋊#131 | C4 | 1 | 1 | yes | characteristic |
| 9 | #41×#64408 | C4 | 1 | 1 | yes | characteristic |
| 10 | #17989646 | C4 | 1 | 6 | yes | complemented |
| 11 | #17989645 | C4 | 1 | 2 | yes | complemented |
| 12 | C2×#14556666 | C22 | 1 | 3 | yes | — |
| 13 | #17989643 | C22 | 1 | 3 | yes | — |
| 14 | #17989553 | C4 | 1 | 3 | yes | — |
| 15 | #17989550 | C22 | 1 | 3 | yes | — |
| 16 | M16×#64408 | C4 | 1 | 3 | yes | — |
| 17 | C2×#14556645 | C22 | 1 | 3 | yes | — |
| 18 | #17989478 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17989478 | C22 | 1 | 3 | yes | — |
| 20 | #17989478 | C22 | 1 | 3 | yes | — |
| 21 | #17989478 | C22 | 1 | 3 | yes | — |
| 22 | #17989477 | C22 | 1 | 6 | yes | — |
| 23 | #131×D73 | C22 | 1 | 1 | yes | characteristic |
| 24 | #17989005 | C4 | 1 | 3 | yes | complemented |
| 25 | #17989004 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | #17989003 | C4 | 1 | 3 | yes | complemented |
| 27 | C2×#14556530 | C22 | 1 | 3 | yes | — |
| 28 | M32×D73 | C22 | 1 | 3 | yes | — |
| 29 | #504×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 30 | #14556679 | — | 2 | 1 | no | — |
| 31 | #14556678 | — | 2 | 3 | no | — |
| 32 | D73⋊M16 | C2×C4 | 1 | 3 | yes | — |
| 33 | C2×#11924036 | C2×C4 | 1 | 3 | yes | — |
| 34 | Q8×#64408 | — | 2 | 1 | no | — |
| 35 | D4×#64408 | — | 2 | 3 | no | — |
| 36 | #14556670 | C2×C4 | 1 | 3 | yes | — |
| 37 | C2×C4×#64408 | C2×C4 | 1 | 3 | yes | — |
| 38 | #14556666 | C2×C4 | 1 | 6 | yes | complemented |
| 39 | #14556666 | C23 | 1 | 3 | yes | — |
| 40 | #14556666 | C23 | 1 | 1 | yes | characteristic |
| 41 | #14556665 | C2×C4 | 1 | 6 | yes | complemented |
| 42 | #14556664 | C2×C4 | 1 | 6 | yes | complemented |
| 43 | C2×#11924031 | C2×C4 | 1 | 6 | yes | complemented |
| 44 | #14556645 | C2×C4 | 1 | 3 | yes | — |
| 45 | #14556645 | C2×C4 | 1 | 3 | yes | — |
| 46 | #14556645 | C23 | 1 | 3 | yes | — |
| 47 | #14556645 | C23 | 1 | 1 | yes | characteristic |
| 48 | C8×#64408 | C2×C4 | 1 | 6 | yes | — |
| 49 | #41×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | #14556599 | C2×C4 | 1 | 3 | yes | — |
| 51 | #14556598 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | #14556597 | C2×C4 | 1 | 3 | yes | — |
| 53 | M16×D73 | C2×C4 | 1 | 3 | yes | — |
| 54 | C2×C8×D73 | C23 | 1 | 3 | yes | — |
| 55 | #14556531 | C2×C4 | 1 | 3 | yes | complemented |
| 56 | #14556530 | C2×C4 | 1 | 3 | yes | complemented |
| 57 | #14556530 | C2×C4 | 1 | 3 | yes | complemented |
| 58 | #14556530 | C23 | 1 | 3 | yes | — |
| 59 | #14556530 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#11924003 | C2×C4 | 1 | 3 | yes | complemented |
| 61 | C16×D73 | C2×C4 | 1 | 6 | yes | complemented |
| 62 | #131×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | M32×C73 | C2×C4 | 1 | 3 | yes | complemented |
| 64 | C2×C16×C73 | C2×C4 | 1 | 3 | yes | complemented |
| 65 | C22×#64408 | — | 2 | 3 | no | — |
| 66 | #11924038 | — | 2 | 3 | no | — |
| 67 | #11924037 | — | 2 | 3 | no | — |
| 68 | #11924036 | — | 2 | 3 | no | — |
| 69 | #11924036 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | #11924036 | C22×C4 | 1 | 3 | yes | — |
| 71 | C2×#10596833 | — | 2 | 3 | no | — |
| 72 | C4⋊#64408 | — | 2 | 3 | no | — |
| 73 | C22⋊#64408 | — | 2 | 3 | no | — |
| 74 | C4×#64408 | — | 2 | 3 | no | — |
| 75 | C4×#64408 | C22×C4 | 1 | 3 | yes | — |
| 76 | C4×#64408 | C22×C4 | 1 | 1 | yes | characteristic |
| 77 | #11924031 | C22×C4 | 1 | 2 | yes | — |
| 78 | #11924031 | C22×C4 | 1 | 6 | yes | — |
| 79 | #11924029 | M16 | 1 | 1 | yes | characteristic |
| 80 | #11924028 | C42 | 1 | 3 | yes | — |
| 81 | #11924027 | M16 | 1 | 3 | yes | — |
| 82 | Q8×D73 | M16 | 1 | 1 | yes | characteristic |
| 83 | D4×D73 | M16 | 1 | 3 | yes | — |
| 84 | C2×C4×D73 | C22×C4 | 1 | 3 | yes | — |
| 85 | #11924012 | C42 | 1 | 3 | yes | — |
| 86 | #11924011 | C42 | 1 | 6 | yes | — |
| 87 | C2×#10596831 | C22×C4 | 1 | 3 | yes | — |
| 88 | C8×D73 | C22×C4 | 1 | 3 | yes | — |
| 89 | C8×D73 | C22×C4 | 1 | 3 | yes | — |
| 90 | C8×D73 | C22×C4 | 1 | 3 | yes | — |
| 91 | C8×D73 | C24 | 1 | 1 | yes | characteristic |
| 92 | #11924003 | C22×C4 | 1 | 3 | yes | — |
| 93 | #11924003 | C22×C4 | 1 | 1 | yes | characteristic |
| 94 | #41×C73 | C42 | 1 | 1 | yes | characteristic |
| 95 | M16×C73 | C42 | 1 | 3 | yes | — |
| 96 | C2×C8×C73 | C22×C4 | 1 | 3 | yes | — |
| 97 | C16×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 98 | C16×C73 | C22×C4 | 1 | 3 | yes | — |
| 99 | C22×D73 | C2×M16 | 1 | 3 | yes | — |
| 100 | C2×#64408 | — | 2 | 1 | no | — |
| 101 | C2×#64408 | — | 2 | 3 | no | — |
| 102 | C2×#64408 | — | 8 | 3 | no | — |
| 103 | Q8×C73 | #97 | 1 | 1 | yes | characteristic |
| 104 | D4×C73 | #97 | 1 | 3 | yes | — |
| 105 | C2×C4×C73 | C2×C42 | 1 | 3 | yes | — |
| 106 | C22⋊D73 | #97 | 1 | 6 | yes | — |
| 107 | C2×Dic73 | C2×M16 | 1 | 3 | yes | — |
| 108 | D292 | #97 | 1 | 3 | yes | — |
| 109 | C4×D73 | C2×C42 | 1 | 3 | yes | — |
| 110 | C4×D73 | C2×M16 | 1 | 3 | yes | — |
| 111 | C4×D73 | C2×M16 | 1 | 3 | yes | — |
| 112 | C4×D73 | C23×C4 | 1 | 1 | yes | characteristic |
| 113 | Dic146 | #97 | 1 | 3 | yes | — |
| 114 | #10596833 | — | 2 | 1 | no | — |
| 115 | #10596833 | — | 2 | 3 | no | — |
| 116 | C8×C73 | C2×C42 | 1 | 3 | yes | — |
| 117 | C8×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 118 | #10596831 | C2×C42 | 1 | 3 | yes | — |
| 119 | #10596831 | C23×C4 | 1 | 1 | yes | characteristic |
| 120 | C22×C73 | C2×#97 | 1 | 3 | yes | — |
| 121 | C2×D73 | — | 4 | 3 | no | — |
| 122 | C2×D73 | C2×#97 | 1 | 3 | yes | — |
| 123 | C2×D73 | C22×M16 | 1 | 1 | yes | characteristic |
| 124 | #64408 | — | 4 | 3 | no | — |
| 125 | #64408 | — | 4 | 1 | no | — |
| 126 | C4×C73 | C2×#97 | 1 | 3 | yes | — |
| 127 | C4×C73 | C22×C42 | 1 | 1 | yes | characteristic |
| 128 | Dic73 | C2×#97 | 1 | 3 | yes | — |
| 129 | Dic73 | C22×M16 | 1 | 1 | yes | characteristic |
| 130 | #33329 | — | 73 | 1 | no | maximal, Sylow |
| 131 | C2×C73 | — | 2 | 3 | no | — |
| 132 | C2×C73 | C22×#97 | 1 | 1 | yes | characteristic |
| 133 | D73 | — | 2 | 1 | no | — |
| 134 | D73 | — | 2 | 3 | no | — |
| 135 | #3407 | — | 73 | 1 | no | — |
| 136 | #3407 | — | 73 | 1 | no | — |
| 137 | #2875 | — | 73 | 1 | no | — |
| 138 | #2110 | — | 73 | 3 | no | — |
| 139 | #2110 | — | 73 | 3 | no | — |
| 140 | C2×#347 | — | 73 | 3 | no | — |
| 141 | C2×#347 | — | 73 | 3 | no | — |
| 142 | C73 | #33329 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 143 | C2×#131 | — | 73 | 1 | no | — |
| 144 | C2×#131 | — | 73 | 1 | no | — |
| 145 | C4×#41 | — | 73 | 1 | no | — |
| 146 | #504 | — | 73 | 2 | no | — |
| 147 | #504 | — | 73 | 6 | no | — |
| 148 | #504 | — | 73 | 1 | no | — |
| 149 | #504 | — | 73 | 3 | no | — |
| 150 | #504 | — | 73 | 3 | no | — |
| 151 | #504 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 152 | C2×M32 | — | 73 | 3 | no | — |
| 153 | C2×M32 | — | 73 | 3 | no | — |
| 154 | C2×M32 | — | 73 | 3 | no | — |
| 155 | C2×M32 | — | 73 | 3 | no | — |
| 156 | #405 | — | 73 | 3 | no | — |
| 157 | #405 | — | 73 | 3 | no | — |
| 158 | C4×M16 | — | 73 | 3 | no | — |
| 159 | C2×#97 | — | 73 | 3 | no | — |
| 160 | #347 | — | 73 | 1 | no | — |
| 161 | #347 | — | 73 | 3 | no | — |
| 162 | #347 | — | 73 | 6 | no | — |
| 163 | #347 | — | 73 | 3 | no | — |
| 164 | #347 | — | 73 | 3 | no | — |
| 165 | C2×#41 | — | 73 | 1 | no | — |
| 166 | #131 | — | 73 | 1 | no | — |
| 167 | #131 | — | 73 | 3 | no | — |
| 168 | #131 | — | 73 | 3 | no | — |
| 169 | #131 | — | 146 | 3 | no | — |
| 170 | #131 | — | 146 | 1 | no | — |
| 171 | #131 | C2×#64408 | 1 | 1 | yes | characteristic |
| 172 | C2×M16 | — | 73 | 3 | no | — |
| 173 | C2×M16 | — | 73 | 3 | no | — |
| 174 | C22×C8 | — | 73 | 3 | no | — |
| 175 | C22×C8 | — | 73 | 3 | no | — |
| 176 | C4×Q8 | — | 146 | 1 | no | — |
| 177 | C4×D4 | — | 146 | 3 | no | — |
| 178 | #117 | — | 73 | 3 | no | — |
| 179 | C2×C42 | — | 73 | 3 | no | — |
| 180 | M32 | — | 73 | 3 | no | — |
| 181 | M32 | — | 73 | 1 | no | — |
| 182 | M32 | — | 73 | 6 | no | — |
| 183 | M32 | — | 73 | 6 | no | — |
| 184 | M32 | — | 73 | 3 | no | — |
| 185 | M32 | — | 73 | 3 | no | — |
| 186 | M32 | — | 73 | 1 | no | — |
| 187 | M32 | — | 73 | 3 | no | — |
| 188 | M32 | — | 73 | 3 | no | — |
| 189 | M32 | C2×#64408 | 1 | 3 | yes | complemented |
| 190 | C2×C16 | — | 73 | 6 | no | — |
| 191 | C2×C16 | — | 73 | 6 | no | — |
| 192 | C2×C16 | — | 73 | 3 | no | — |
| 193 | C2×C16 | — | 73 | 6 | no | — |
| 194 | C2×C16 | C2×#64408 | 1 | 3 | yes | complemented |
| 195 | #97 | — | 73 | 1 | no | — |
| 196 | #97 | — | 73 | 3 | no | — |
| 197 | #97 | — | 73 | 3 | no | — |
| 198 | #97 | — | 73 | 3 | no | — |
| 199 | C4×C8 | — | 73 | 6 | no | — |
| 200 | #41 | — | 73 | 1 | no | — |
| 201 | #41 | — | 73 | 3 | no | — |
| 202 | #41 | — | 73 | 3 | no | — |
| 203 | #41 | C4×#64408 | 1 | 1 | yes | characteristic |
| 204 | C2×Q8 | — | 73 | 1 | no | — |
| 205 | C2×D4 | — | 73 | 3 | no | — |
| 206 | C22×C4 | — | 73 | 3 | no | — |
| 207 | C22×C4 | — | 146 | 3 | no | — |
| 208 | M16 | — | 73 | 3 | no | — |
| 209 | M16 | — | 73 | 6 | no | — |
| 210 | M16 | — | 146 | 3 | no | — |
| 211 | M16 | — | 146 | 3 | no | — |
| 212 | M16 | C4×#64408 | 1 | 3 | yes | — |
| 213 | C2×C8 | — | 73 | 3 | no | — |
| 214 | C2×C8 | — | 73 | 3 | no | — |
| 215 | C2×C8 | — | 73 | 1 | no | — |
| 216 | C2×C8 | — | 73 | 3 | no | — |
| 217 | C2×C8 | — | 73 | 3 | no | — |
| 218 | C2×C8 | — | 73 | 3 | no | — |
| 219 | C2×C8 | — | 73 | 1 | no | — |
| 220 | C2×C8 | — | 146 | 3 | no | — |
| 221 | C2×C8 | — | 146 | 3 | no | — |
| 222 | C2×C8 | C22×#64408 | 1 | 3 | yes | — |
| 223 | C4⋊C4 | — | 146 | 3 | no | — |
| 224 | C22⋊C4 | — | 146 | 3 | no | — |
| 225 | C42 | — | 73 | 3 | no | — |
| 226 | C42 | — | 73 | 1 | no | — |
| 227 | C42 | — | 146 | 3 | no | — |
| 228 | C16 | — | 73 | 2 | no | — |
| 229 | C16 | — | 73 | 6 | no | — |
| 230 | C16 | — | 73 | 3 | no | — |
| 231 | C16 | — | 73 | 1 | no | — |
| 232 | C16 | C22×#64408 | 1 | 3 | yes | — |
| 233 | C16 | C22×#64408 | 1 | 1 | yes | characteristic |
| 234 | C23 | — | 73 | 3 | no | — |
| 235 | Q8 | — | 73 | 3 | no | — |
| 236 | Q8 | #14556645 | 1 | 1 | yes | characteristic |
| 237 | D4 | — | 73 | 6 | no | — |
| 238 | D4 | — | 73 | 3 | no | — |
| 239 | D4 | #14556645 | 1 | 3 | yes | — |
| 240 | C2×C4 | — | 584 | 3 | no | — |
| 241 | C2×C4 | — | 73 | 3 | no | — |
| 242 | C2×C4 | — | 73 | 1 | no | — |
| 243 | C2×C4 | — | 73 | 3 | no | — |
| 244 | C2×C4 | — | 73 | 3 | no | — |
| 245 | C2×C4 | — | 73 | 3 | no | — |
| 246 | C2×C4 | — | 146 | 1 | no | — |
| 247 | C2×C4 | — | 146 | 3 | no | — |
| 248 | C2×C4 | C2×C4×#64408 | 1 | 3 | yes | — |
| 249 | C8 | — | 73 | 1 | no | — |
| 250 | C8 | — | 73 | 3 | no | — |
| 251 | C8 | — | 146 | 1 | no | — |
| 252 | C8 | — | 146 | 3 | no | — |
| 253 | C8 | C2×C4×#64408 | 1 | 3 | yes | — |
| 254 | C8 | C23×#64408 | 1 | 1 | yes | characteristic |
| 255 | C22 | — | 292 | 3 | no | — |
| 256 | C22 | — | 73 | 1 | no | — |
| 257 | C22 | — | 73 | 3 | no | — |
| 258 | C22 | C2×#14556645 | 1 | 3 | yes | — |
| 259 | C4 | — | 292 | 1 | no | — |
| 260 | C4 | — | 292 | 3 | no | — |
| 261 | C4 | — | 73 | 1 | no | — |
| 262 | C4 | — | 73 | 3 | no | — |
| 263 | C4 | C2×#14556645 | 1 | 3 | yes | — |
| 264 | C4 | C22×C4×#64408 | 1 | 1 | yes | characteristic |
| 265 | C2 | — | 2 | 3 | no | — |
| 266 | C2 | — | 146 | 1 | no | — |
| 267 | C2 | — | 146 | 3 | no | — |
| 268 | C2 | C22×#14556645 | 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