← C109×#32872 #42150866
Subgroups — C109×#32872 #42150866
Order 27904.
482 conjugacy classes of subgroups.
The subgroup lattice has 282 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C109×#2103 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C109×#2098 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C109×#2082 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C109×#2070 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C109×#2049 | C2 | 1 | 2 | yes | maximal |
| 6 | C109×#2047 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C109×#2020 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C109×#1902 | C2 | 1 | 2 | yes | maximal |
| 9 | C109×#1858 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#137×C109 | C22 | 1 | 2 | yes | — |
| 11 | C22×Q16×C109 | C22 | 1 | 1 | yes | characteristic |
| 12 | #568×C109 | C22 | 1 | 1 | yes | characteristic |
| 13 | #430×C109 | C22 | 1 | 2 | yes | — |
| 14 | #430×C109 | C22 | 1 | 1 | yes | characteristic |
| 15 | #430×C109 | C22 | 1 | 2 | yes | — |
| 16 | #424×C109 | C22 | 1 | 2 | yes | — |
| 17 | #421×C109 | C22 | 1 | 2 | yes | — |
| 18 | #419×C109 | C22 | 1 | 2 | yes | — |
| 19 | #419×C109 | C22 | 1 | 2 | yes | — |
| 20 | #413×C109 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#101×C109 | C22 | 1 | 2 | yes | — |
| 22 | C2×#101×C109 | C22 | 1 | 2 | yes | — |
| 23 | C2×#101×C109 | C22 | 1 | 2 | yes | — |
| 24 | #408×C109 | C22 | 1 | 1 | yes | characteristic |
| 25 | #344×C109 | C22 | 1 | 2 | yes | — |
| 26 | #344×C109 | C22 | 1 | 2 | yes | — |
| 27 | #341×C109 | C22 | 1 | 1 | yes | characteristic |
| 28 | #341×C109 | C22 | 1 | 2 | yes | — |
| 29 | #338×C109 | C22 | 1 | 2 | yes | — |
| 30 | H(3,ℤ/4)×C109 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#41×C109 | C23 | 1 | 1 | yes | characteristic |
| 32 | C22×Q8×C109 | C23 | 1 | 2 | yes | — |
| 33 | #137×C109 | — | 4 | 2 | no | — |
| 34 | #137×C109 | — | 4 | 2 | no | — |
| 35 | C2×Q16×C109 | — | 2 | 2 | no | — |
| 36 | C2×Q16×C109 | — | 4 | 1 | no | — |
| 37 | C2×Q16×C109 | — | 4 | 2 | no | — |
| 38 | C2×SD16×C109 | — | 2 | 2 | no | — |
| 39 | #131×C109 | — | 4 | 2 | no | — |
| 40 | C2×M16×C109 | — | 4 | 1 | no | — |
| 41 | C2×M16×C109 | C23 | 1 | 2 | yes | — |
| 42 | C2×M16×C109 | C23 | 1 | 2 | yes | — |
| 43 | C2×M16×C109 | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×M16×C109 | C23 | 1 | 2 | yes | — |
| 45 | C2×M16×C109 | C23 | 1 | 2 | yes | — |
| 46 | C22×C8×C109 | C23 | 1 | 1 | yes | characteristic |
| 47 | #117×C109 | C23 | 1 | 2 | yes | — |
| 48 | #108×C109 | — | 4 | 1 | no | — |
| 49 | #108×C109 | — | 4 | 2 | no | — |
| 50 | #108×C109 | — | 4 | 2 | no | — |
| 51 | C4⋊C8×C109 | — | 4 | 2 | no | — |
| 52 | #104×C109 | — | 4 | 2 | no | — |
| 53 | #103×C109 | — | 4 | 2 | no | — |
| 54 | #103×C109 | — | 4 | 2 | no | — |
| 55 | #101×C109 | — | 2 | 1 | no | — |
| 56 | #101×C109 | — | 4 | 2 | no | — |
| 57 | #101×C109 | — | 4 | 2 | no | — |
| 58 | #101×C109 | — | 4 | 2 | no | — |
| 59 | #100×C109 | — | 2 | 1 | no | — |
| 60 | C22⋊C8×C109 | — | 4 | 1 | no | — |
| 61 | #41×C109 | — | 2 | 2 | no | — |
| 62 | #41×C109 | — | 2 | 2 | no | — |
| 63 | C2×Q8×C109 | — | 2 | 2 | no | — |
| 64 | C2×Q8×C109 | — | 2 | 2 | no | — |
| 65 | C2×Q8×C109 | — | 2 | 2 | no | — |
| 66 | C2×Q8×C109 | — | 2 | 2 | no | — |
| 67 | C2×Q8×C109 | — | 2 | 2 | no | — |
| 68 | C2×Q8×C109 | — | 2 | 2 | no | — |
| 69 | C2×Q8×C109 | #41 | 1 | 1 | yes | characteristic |
| 70 | C2×D4×C109 | — | 2 | 1 | no | — |
| 71 | C2×D4×C109 | #41 | 1 | 1 | yes | characteristic |
| 72 | C22×C4×C109 | — | 2 | 1 | no | — |
| 73 | C22×C4×C109 | — | 2 | 2 | no | — |
| 74 | C22×C4×C109 | C24 | 1 | 1 | yes | characteristic |
| 75 | Q16×C109 | — | 4 | 4 | no | — |
| 76 | Q16×C109 | — | 4 | 4 | no | — |
| 77 | SD16×C109 | — | 4 | 4 | no | — |
| 78 | M16×C109 | — | 2 | 2 | no | — |
| 79 | M16×C109 | — | 2 | 2 | no | — |
| 80 | M16×C109 | — | 2 | 2 | no | — |
| 81 | M16×C109 | — | 2 | 2 | no | — |
| 82 | M16×C109 | — | 2 | 2 | no | — |
| 83 | M16×C109 | — | 2 | 2 | no | — |
| 84 | M16×C109 | — | 2 | 2 | no | — |
| 85 | M16×C109 | — | 2 | 2 | no | — |
| 86 | M16×C109 | — | 2 | 2 | no | — |
| 87 | M16×C109 | — | 4 | 2 | no | — |
| 88 | C2×C8×C109 | — | 2 | 2 | no | — |
| 89 | C2×C8×C109 | — | 2 | 1 | no | — |
| 90 | C2×C8×C109 | — | 2 | 1 | no | — |
| 91 | C2×C8×C109 | — | 2 | 2 | no | — |
| 92 | C2×C8×C109 | — | 2 | 2 | no | — |
| 93 | C2×C8×C109 | — | 2 | 2 | no | — |
| 94 | C2×C8×C109 | — | 2 | 2 | no | — |
| 95 | C2×C8×C109 | — | 4 | 2 | no | — |
| 96 | C4⋊C4×C109 | — | 2 | 2 | no | — |
| 97 | C22⋊C4×C109 | — | 2 | 2 | no | — |
| 98 | C42×C109 | — | 2 | 2 | no | — |
| 99 | C23×C109 | — | 2 | 1 | no | — |
| 100 | C23×C109 | 2−1+4 | 1 | 1 | yes | characteristic |
| 101 | Q8×C109 | — | 2 | 2 | no | — |
| 102 | Q8×C109 | — | 4 | 2 | no | — |
| 103 | Q8×C109 | — | 4 | 2 | no | — |
| 104 | Q8×C109 | — | 4 | 2 | no | — |
| 105 | Q8×C109 | — | 4 | 2 | no | — |
| 106 | D4×C109 | — | 2 | 2 | no | — |
| 107 | D4×C109 | — | 4 | 2 | no | — |
| 108 | C2×C4×C109 | — | 2 | 1 | no | — |
| 109 | C2×C4×C109 | — | 4 | 1 | no | — |
| 110 | C2×C4×C109 | — | 4 | 1 | no | — |
| 111 | C2×C4×C109 | — | 4 | 2 | no | — |
| 112 | C2×C4×C109 | — | 4 | 2 | no | — |
| 113 | C2×C4×C109 | — | 4 | 2 | no | — |
| 114 | C2×C4×C109 | — | 4 | 2 | no | — |
| 115 | C2×C4×C109 | C2×#41 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C109 | H(5,𝔽2) | 1 | 2 | yes | — |
| 117 | C2×C4×C109 | H(5,𝔽2) | 1 | 2 | yes | — |
| 118 | C2×C4×C109 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 119 | C8×C109 | — | 4 | 2 | no | — |
| 120 | C8×C109 | — | 4 | 2 | no | — |
| 121 | C8×C109 | — | 4 | 1 | no | — |
| 122 | C8×C109 | — | 4 | 2 | no | — |
| 123 | C8×C109 | — | 4 | 1 | no | — |
| 124 | C8×C109 | — | 4 | 2 | no | — |
| 125 | C22×C109 | — | 4 | 1 | no | — |
| 126 | C22×C109 | — | 4 | 1 | no | — |
| 127 | C22×C109 | — | 8 | 1 | no | — |
| 128 | C22×C109 | #539 | 1 | 1 | yes | characteristic |
| 129 | C22×C109 | #562 | 1 | 2 | yes | — |
| 130 | C4×C109 | — | 4 | 1 | no | — |
| 131 | C4×C109 | — | 8 | 2 | no | — |
| 132 | C4×C109 | — | 8 | 2 | no | — |
| 133 | C4×C109 | #538 | 1 | 2 | yes | — |
| 134 | C4×C109 | #560 | 1 | 1 | yes | characteristic |
| 135 | C4×C109 | #560 | 1 | 1 | yes | characteristic |
| 136 | #32872 | C109 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 137 | C2×C109 | — | 2 | 2 | no | — |
| 138 | C2×C109 | — | 2 | 1 | no | — |
| 139 | C2×C109 | — | 8 | 1 | no | — |
| 140 | C2×C109 | #2826 | 1 | 1 | yes | characteristic |
| 141 | #2103 | C2×C109 | 1 | 2 | yes | complemented |
| 142 | #2098 | C2×C109 | 1 | 1 | yes | characteristic |
| 143 | #2082 | C2×C109 | 1 | 2 | yes | complemented |
| 144 | #2070 | C2×C109 | 1 | 2 | yes | complemented |
| 145 | #2049 | C2×C109 | 1 | 2 | yes | — |
| 146 | #2047 | C2×C109 | 1 | 2 | yes | complemented |
| 147 | #2020 | C2×C109 | 1 | 1 | yes | characteristic |
| 148 | #1902 | C2×C109 | 1 | 2 | yes | — |
| 149 | #1858 | C2×C109 | 1 | 1 | yes | characteristic |
| 150 | C109 | #32872 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 151 | C2×#137 | C22×C109 | 1 | 2 | yes | — |
| 152 | C22×Q16 | C22×C109 | 1 | 1 | yes | characteristic |
| 153 | #568 | C22×C109 | 1 | 1 | yes | characteristic |
| 154 | #430 | C22×C109 | 1 | 2 | yes | — |
| 155 | #430 | C22×C109 | 1 | 1 | yes | characteristic |
| 156 | #430 | C22×C109 | 1 | 2 | yes | — |
| 157 | #424 | C22×C109 | 1 | 2 | yes | — |
| 158 | #421 | C22×C109 | 1 | 2 | yes | — |
| 159 | #419 | C22×C109 | 1 | 2 | yes | — |
| 160 | #419 | C22×C109 | 1 | 2 | yes | — |
| 161 | #413 | C22×C109 | 1 | 1 | yes | characteristic |
| 162 | C2×#101 | C22×C109 | 1 | 2 | yes | — |
| 163 | C2×#101 | C22×C109 | 1 | 2 | yes | — |
| 164 | C2×#101 | C22×C109 | 1 | 2 | yes | — |
| 165 | #408 | C22×C109 | 1 | 1 | yes | characteristic |
| 166 | #344 | C22×C109 | 1 | 2 | yes | — |
| 167 | #344 | C22×C109 | 1 | 2 | yes | — |
| 168 | #341 | C22×C109 | 1 | 1 | yes | characteristic |
| 169 | #341 | C22×C109 | 1 | 2 | yes | — |
| 170 | #338 | C22×C109 | 1 | 2 | yes | — |
| 171 | H(3,ℤ/4) | C22×C109 | 1 | 1 | yes | characteristic |
| 172 | C2×#41 | C23×C109 | 1 | 1 | yes | characteristic |
| 173 | C22×Q8 | C23×C109 | 1 | 2 | yes | — |
| 174 | #137 | — | 4 | 2 | no | — |
| 175 | #137 | — | 4 | 2 | no | — |
| 176 | C2×Q16 | — | 2 | 2 | no | — |
| 177 | C2×Q16 | — | 4 | 1 | no | — |
| 178 | C2×Q16 | — | 4 | 2 | no | — |
| 179 | C2×SD16 | — | 2 | 2 | no | — |
| 180 | #131 | — | 4 | 2 | no | — |
| 181 | C2×M16 | — | 4 | 1 | no | — |
| 182 | C2×M16 | C23×C109 | 1 | 2 | yes | — |
| 183 | C2×M16 | C23×C109 | 1 | 2 | yes | — |
| 184 | C2×M16 | C23×C109 | 1 | 1 | yes | characteristic |
| 185 | C2×M16 | C23×C109 | 1 | 2 | yes | — |
| 186 | C2×M16 | C23×C109 | 1 | 2 | yes | — |
| 187 | C22×C8 | C23×C109 | 1 | 1 | yes | characteristic |
| 188 | #117 | C23×C109 | 1 | 2 | yes | — |
| 189 | #108 | — | 4 | 1 | no | — |
| 190 | #108 | — | 4 | 2 | no | — |
| 191 | #108 | — | 4 | 2 | no | — |
| 192 | C4⋊C8 | — | 4 | 2 | no | — |
| 193 | #104 | — | 4 | 2 | no | — |
| 194 | #103 | — | 4 | 2 | no | — |
| 195 | #103 | — | 4 | 2 | no | — |
| 196 | #101 | — | 2 | 1 | no | — |
| 197 | #101 | — | 4 | 2 | no | — |
| 198 | #101 | — | 4 | 2 | no | — |
| 199 | #101 | — | 4 | 2 | no | — |
| 200 | #100 | — | 2 | 1 | no | — |
| 201 | C22⋊C8 | — | 4 | 1 | no | — |
| 202 | #41 | — | 2 | 2 | no | — |
| 203 | #41 | — | 2 | 2 | no | — |
| 204 | C2×Q8 | — | 2 | 2 | no | — |
| 205 | C2×Q8 | — | 2 | 2 | no | — |
| 206 | C2×Q8 | — | 2 | 2 | no | — |
| 207 | C2×Q8 | — | 2 | 2 | no | — |
| 208 | C2×Q8 | — | 2 | 2 | no | — |
| 209 | C2×Q8 | — | 2 | 2 | no | — |
| 210 | C2×Q8 | #41×C109 | 1 | 1 | yes | characteristic |
| 211 | C2×D4 | — | 2 | 1 | no | — |
| 212 | C2×D4 | #41×C109 | 1 | 1 | yes | characteristic |
| 213 | C22×C4 | — | 2 | 1 | no | — |
| 214 | C22×C4 | — | 2 | 2 | no | — |
| 215 | C22×C4 | C24×C109 | 1 | 1 | yes | characteristic |
| 216 | Q16 | — | 4 | 4 | no | — |
| 217 | Q16 | — | 4 | 4 | no | — |
| 218 | SD16 | — | 4 | 4 | no | — |
| 219 | M16 | — | 2 | 2 | no | — |
| 220 | M16 | — | 2 | 2 | no | — |
| 221 | M16 | — | 2 | 2 | no | — |
| 222 | M16 | — | 2 | 2 | no | — |
| 223 | M16 | — | 2 | 2 | no | — |
| 224 | M16 | — | 2 | 2 | no | — |
| 225 | M16 | — | 2 | 2 | no | — |
| 226 | M16 | — | 2 | 2 | no | — |
| 227 | M16 | — | 2 | 2 | no | — |
| 228 | M16 | — | 4 | 2 | no | — |
| 229 | C2×C8 | — | 2 | 2 | no | — |
| 230 | C2×C8 | — | 2 | 1 | no | — |
| 231 | C2×C8 | — | 2 | 1 | no | — |
| 232 | C2×C8 | — | 2 | 2 | no | — |
| 233 | C2×C8 | — | 2 | 2 | no | — |
| 234 | C2×C8 | — | 2 | 2 | no | — |
| 235 | C2×C8 | — | 2 | 2 | no | — |
| 236 | C2×C8 | — | 4 | 2 | no | — |
| 237 | C4⋊C4 | — | 2 | 2 | no | — |
| 238 | C22⋊C4 | — | 2 | 2 | no | — |
| 239 | C42 | — | 2 | 2 | no | — |
| 240 | C23 | — | 2 | 1 | no | — |
| 241 | C23 | 2−1+4×C109 | 1 | 1 | yes | characteristic |
| 242 | Q8 | — | 2 | 2 | no | — |
| 243 | Q8 | — | 4 | 2 | no | — |
| 244 | Q8 | — | 4 | 2 | no | — |
| 245 | Q8 | — | 4 | 2 | no | — |
| 246 | Q8 | — | 4 | 2 | no | — |
| 247 | D4 | — | 2 | 2 | no | — |
| 248 | D4 | — | 4 | 2 | no | — |
| 249 | C2×C4 | — | 2 | 1 | no | — |
| 250 | C2×C4 | — | 4 | 1 | no | — |
| 251 | C2×C4 | — | 4 | 1 | no | — |
| 252 | C2×C4 | — | 4 | 2 | no | — |
| 253 | C2×C4 | — | 4 | 2 | no | — |
| 254 | C2×C4 | — | 4 | 2 | no | — |
| 255 | C2×C4 | — | 4 | 2 | no | — |
| 256 | C2×C4 | C2×#41×C109 | 1 | 1 | yes | characteristic |
| 257 | C2×C4 | H(5,𝔽2)×C109 | 1 | 2 | yes | — |
| 258 | C2×C4 | H(5,𝔽2)×C109 | 1 | 2 | yes | — |
| 259 | C2×C4 | H(5,𝔽2)×C109 | 1 | 1 | yes | characteristic |
| 260 | C8 | — | 4 | 2 | no | — |
| 261 | C8 | — | 4 | 2 | no | — |
| 262 | C8 | — | 4 | 1 | no | — |
| 263 | C8 | — | 4 | 2 | no | — |
| 264 | C8 | — | 4 | 1 | no | — |
| 265 | C8 | — | 4 | 2 | no | — |
| 266 | C22 | — | 4 | 1 | no | — |
| 267 | C22 | — | 4 | 1 | no | — |
| 268 | C22 | — | 8 | 1 | no | — |
| 269 | C22 | #539×C109 | 1 | 1 | yes | characteristic |
| 270 | C22 | #562×C109 | 1 | 2 | yes | — |
| 271 | C4 | — | 4 | 1 | no | — |
| 272 | C4 | — | 8 | 2 | no | — |
| 273 | C4 | — | 8 | 2 | no | — |
| 274 | C4 | #538×C109 | 1 | 2 | yes | — |
| 275 | C4 | #560×C109 | 1 | 1 | yes | characteristic |
| 276 | C4 | #560×C109 | 1 | 1 | yes | characteristic |
| 277 | C2 | — | 2 | 2 | no | — |
| 278 | C2 | — | 2 | 1 | no | — |
| 279 | C2 | — | 8 | 1 | no | — |
| 280 | C2 | C109×#2826 | 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