← C113×#13262 #43281282
Subgroups — C113×#13262 #43281282
Order 28928.
462 conjugacy classes of subgroups.
The subgroup lattice has 250 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#494×C113 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#364×C113 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#362×C113 | C2 | 1 | 2 | yes | maximal |
| 4 | C113×#2141 | C2 | 1 | 2 | yes | maximal |
| 5 | C113×#1772 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C22×Q16×C113 | — | 2 | 1 | no | — |
| 7 | C22×Q16×C113 | C22 | 1 | 2 | yes | — |
| 8 | C2×C4⋊Q8×C113 | — | 2 | 1 | no | — |
| 9 | C2×M32×C113 | C22 | 1 | 2 | yes | — |
| 10 | #494×C113 | — | 2 | 2 | no | — |
| 11 | #494×C113 | C4 | 1 | 4 | yes | complemented |
| 12 | C2×#108×C113 | C22 | 1 | 1 | yes | characteristic |
| 13 | #427×C113 | C22 | 1 | 1 | yes | characteristic |
| 14 | #405×C113 | — | 2 | 1 | no | — |
| 15 | C2×C4×C8×C113 | C22 | 1 | 1 | yes | characteristic |
| 16 | #364×C113 | — | 2 | 2 | no | — |
| 17 | #362×C113 | — | 2 | 4 | no | — |
| 18 | #358×C113 | — | 2 | 4 | no | — |
| 19 | #339×C113 | — | 2 | 1 | no | — |
| 20 | C22×Q8×C113 | — | 2 | 2 | no | — |
| 21 | C2×Q16×C113 | — | 2 | 4 | no | — |
| 22 | C2×Q16×C113 | — | 2 | 2 | no | — |
| 23 | C2×Q16×C113 | — | 2 | 2 | no | — |
| 24 | C2×Q16×C113 | — | 2 | 2 | no | — |
| 25 | C2×Q16×C113 | — | 2 | 2 | no | — |
| 26 | C2×Q16×C113 | — | 2 | 2 | no | — |
| 27 | C2×Q16×C113 | — | 4 | 1 | no | — |
| 28 | C2×Q16×C113 | — | 4 | 1 | no | — |
| 29 | C2×Q16×C113 | — | 4 | 2 | no | — |
| 30 | C2×Q16×C113 | C2×C4 | 1 | 4 | yes | — |
| 31 | C2×M16×C113 | — | 2 | 1 | no | — |
| 32 | C22×C8×C113 | D4 | 1 | 1 | yes | characteristic |
| 33 | C22×C8×C113 | C23 | 1 | 1 | yes | characteristic |
| 34 | C4⋊Q8×C113 | — | 2 | 4 | no | — |
| 35 | C4⋊Q8×C113 | — | 4 | 2 | no | — |
| 36 | #117×C113 | — | 2 | 1 | no | — |
| 37 | C2×C4⋊C4×C113 | — | 4 | 2 | no | — |
| 38 | C2×C42×C113 | D4 | 1 | 1 | yes | characteristic |
| 39 | M32×C113 | — | 2 | 2 | no | — |
| 40 | M32×C113 | — | 2 | 2 | no | — |
| 41 | C2×C16×C113 | — | 2 | 2 | no | — |
| 42 | #108×C113 | — | 2 | 1 | no | — |
| 43 | #108×C113 | D4 | 1 | 2 | yes | — |
| 44 | #107×C113 | D4 | 1 | 2 | yes | — |
| 45 | #106×C113 | — | 2 | 1 | no | — |
| 46 | #97×C113 | — | 4 | 1 | no | — |
| 47 | C4×C8×C113 | — | 4 | 1 | no | — |
| 48 | C4×C8×C113 | C2×C4 | 1 | 2 | yes | — |
| 49 | C4×C8×C113 | D4 | 1 | 2 | yes | — |
| 50 | C2×Q8×C113 | — | 2 | 4 | no | — |
| 51 | C2×Q8×C113 | — | 4 | 2 | no | — |
| 52 | C2×Q8×C113 | — | 4 | 2 | no | — |
| 53 | C2×Q8×C113 | — | 4 | 2 | no | — |
| 54 | C2×Q8×C113 | — | 4 | 2 | no | — |
| 55 | C2×Q8×C113 | — | 4 | 2 | no | — |
| 56 | C22×C4×C113 | — | 2 | 1 | no | — |
| 57 | C22×C4×C113 | — | 4 | 2 | no | — |
| 58 | C22×C4×C113 | C2×D4 | 1 | 1 | yes | characteristic |
| 59 | Q16×C113 | — | 2 | 4 | no | — |
| 60 | Q16×C113 | — | 2 | 4 | no | — |
| 61 | Q16×C113 | — | 4 | 4 | no | — |
| 62 | Q16×C113 | — | 4 | 4 | no | — |
| 63 | Q16×C113 | — | 4 | 2 | no | — |
| 64 | Q16×C113 | — | 4 | 2 | no | — |
| 65 | M16×C113 | — | 2 | 2 | no | — |
| 66 | M16×C113 | — | 4 | 1 | no | — |
| 67 | C2×C8×C113 | — | 4 | 1 | no | — |
| 68 | C2×C8×C113 | C22⋊C4 | 1 | 2 | yes | — |
| 69 | C2×C8×C113 | D8 | 1 | 1 | yes | characteristic |
| 70 | C2×C8×C113 | D8 | 1 | 1 | yes | characteristic |
| 71 | C2×C8×C113 | SD16 | 1 | 2 | yes | — |
| 72 | C2×C8×C113 | C22×C4 | 1 | 1 | yes | characteristic |
| 73 | C2×C8×C113 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C2×C8×C113 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C8×C113 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C2×C8×C113 | #41 | 1 | 1 | yes | characteristic |
| 77 | C2×C8×C113 | #41 | 1 | 1 | yes | characteristic |
| 78 | C4⋊C4×C113 | — | 2 | 2 | no | — |
| 79 | C4⋊C4×C113 | — | 4 | 8 | no | — |
| 80 | C22⋊C4×C113 | — | 4 | 1 | no | — |
| 81 | C42×C113 | — | 2 | 1 | no | — |
| 82 | C42×C113 | — | 4 | 1 | no | — |
| 83 | C42×C113 | C22⋊C4 | 1 | 2 | yes | — |
| 84 | C16×C113 | — | 4 | 2 | no | — |
| 85 | C23×C113 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 86 | Q8×C113 | — | 4 | 4 | no | — |
| 87 | Q8×C113 | — | 4 | 4 | no | — |
| 88 | Q8×C113 | — | 8 | 2 | no | — |
| 89 | Q8×C113 | — | 8 | 2 | no | — |
| 90 | C2×C4×C113 | — | 2 | 4 | no | — |
| 91 | C2×C4×C113 | — | 2 | 2 | no | — |
| 92 | C2×C4×C113 | — | 4 | 4 | no | — |
| 93 | C2×C4×C113 | — | 4 | 2 | no | — |
| 94 | C2×C4×C113 | — | 8 | 2 | no | — |
| 95 | C2×C4×C113 | — | 8 | 2 | no | — |
| 96 | C2×C4×C113 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C2×C4×C113 | #121 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×C113 | #121 | 1 | 1 | yes | characteristic |
| 99 | C2×C4×C113 | C2×D8 | 1 | 1 | yes | characteristic |
| 100 | C2×C4×C113 | C2×SD16 | 1 | 1 | yes | characteristic |
| 101 | C2×C4×C113 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 102 | C8×C113 | — | 4 | 2 | no | — |
| 103 | C8×C113 | #102 | 1 | 2 | yes | — |
| 104 | C8×C113 | #102 | 1 | 2 | yes | — |
| 105 | C8×C113 | C4×D4 | 1 | 1 | yes | characteristic |
| 106 | C8×C113 | C4×D4 | 1 | 1 | yes | characteristic |
| 107 | C8×C113 | #124 | 1 | 1 | yes | characteristic |
| 108 | C8×C113 | #127 | 1 | 1 | yes | characteristic |
| 109 | C22×C113 | — | 2 | 2 | no | — |
| 110 | C22×C113 | #418 | 1 | 1 | yes | characteristic |
| 111 | C22×C113 | #459 | 1 | 1 | yes | characteristic |
| 112 | C22×C113 | #460 | 1 | 1 | yes | characteristic |
| 113 | C4×C113 | — | 2 | 4 | no | — |
| 114 | C4×C113 | — | 8 | 2 | no | — |
| 115 | C4×C113 | — | 8 | 4 | no | — |
| 116 | C4×C113 | #390 | 1 | 1 | yes | characteristic |
| 117 | C4×C113 | C2×#102 | 1 | 1 | yes | characteristic |
| 118 | C4×C113 | #459 | 1 | 1 | yes | characteristic |
| 119 | C4×C113 | #460 | 1 | 1 | yes | characteristic |
| 120 | #13262 | C113 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 121 | C2×C113 | — | 2 | 1 | no | — |
| 122 | C2×C113 | — | 2 | 1 | no | — |
| 123 | C2×C113 | #1982 | 1 | 1 | yes | characteristic |
| 124 | C2×C113 | #2214 | 1 | 2 | yes | — |
| 125 | C2×#494 | C2×C113 | 1 | 1 | yes | characteristic |
| 126 | C2×#364 | C2×C113 | 1 | 1 | yes | characteristic |
| 127 | C2×#362 | C2×C113 | 1 | 2 | yes | — |
| 128 | #2141 | C2×C113 | 1 | 2 | yes | — |
| 129 | #1772 | C2×C113 | 1 | 1 | yes | characteristic |
| 130 | C113 | #13262 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 131 | C22×Q16 | — | 2 | 1 | no | — |
| 132 | C22×Q16 | C22×C113 | 1 | 2 | yes | — |
| 133 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 134 | C2×M32 | C22×C113 | 1 | 2 | yes | — |
| 135 | #494 | — | 2 | 2 | no | — |
| 136 | #494 | C4×C113 | 1 | 4 | yes | complemented |
| 137 | C2×#108 | C22×C113 | 1 | 1 | yes | characteristic |
| 138 | #427 | C22×C113 | 1 | 1 | yes | characteristic |
| 139 | #405 | — | 2 | 1 | no | — |
| 140 | C2×C4×C8 | C22×C113 | 1 | 1 | yes | characteristic |
| 141 | #364 | — | 2 | 2 | no | — |
| 142 | #362 | — | 2 | 4 | no | — |
| 143 | #358 | — | 2 | 4 | no | — |
| 144 | #339 | — | 2 | 1 | no | — |
| 145 | C22×Q8 | — | 2 | 2 | no | — |
| 146 | C2×Q16 | — | 2 | 4 | no | — |
| 147 | C2×Q16 | — | 2 | 2 | no | — |
| 148 | C2×Q16 | — | 2 | 2 | no | — |
| 149 | C2×Q16 | — | 2 | 2 | no | — |
| 150 | C2×Q16 | — | 2 | 2 | no | — |
| 151 | C2×Q16 | — | 2 | 2 | no | — |
| 152 | C2×Q16 | — | 4 | 1 | no | — |
| 153 | C2×Q16 | — | 4 | 1 | no | — |
| 154 | C2×Q16 | — | 4 | 2 | no | — |
| 155 | C2×Q16 | C2×C4×C113 | 1 | 4 | yes | — |
| 156 | C2×M16 | — | 2 | 1 | no | — |
| 157 | C22×C8 | D4×C113 | 1 | 1 | yes | characteristic |
| 158 | C22×C8 | C23×C113 | 1 | 1 | yes | characteristic |
| 159 | C4⋊Q8 | — | 2 | 4 | no | — |
| 160 | C4⋊Q8 | — | 4 | 2 | no | — |
| 161 | #117 | — | 2 | 1 | no | — |
| 162 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 163 | C2×C42 | D4×C113 | 1 | 1 | yes | characteristic |
| 164 | M32 | — | 2 | 2 | no | — |
| 165 | M32 | — | 2 | 2 | no | — |
| 166 | C2×C16 | — | 2 | 2 | no | — |
| 167 | #108 | — | 2 | 1 | no | — |
| 168 | #108 | D4×C113 | 1 | 2 | yes | — |
| 169 | #107 | D4×C113 | 1 | 2 | yes | — |
| 170 | #106 | — | 2 | 1 | no | — |
| 171 | #97 | — | 4 | 1 | no | — |
| 172 | C4×C8 | — | 4 | 1 | no | — |
| 173 | C4×C8 | C2×C4×C113 | 1 | 2 | yes | — |
| 174 | C4×C8 | D4×C113 | 1 | 2 | yes | — |
| 175 | C2×Q8 | — | 2 | 4 | no | — |
| 176 | C2×Q8 | — | 4 | 2 | no | — |
| 177 | C2×Q8 | — | 4 | 2 | no | — |
| 178 | C2×Q8 | — | 4 | 2 | no | — |
| 179 | C2×Q8 | — | 4 | 2 | no | — |
| 180 | C2×Q8 | — | 4 | 2 | no | — |
| 181 | C22×C4 | — | 2 | 1 | no | — |
| 182 | C22×C4 | — | 4 | 2 | no | — |
| 183 | C22×C4 | C2×D4×C113 | 1 | 1 | yes | characteristic |
| 184 | Q16 | — | 2 | 4 | no | — |
| 185 | Q16 | — | 2 | 4 | no | — |
| 186 | Q16 | — | 4 | 4 | no | — |
| 187 | Q16 | — | 4 | 4 | no | — |
| 188 | Q16 | — | 4 | 2 | no | — |
| 189 | Q16 | — | 4 | 2 | no | — |
| 190 | M16 | — | 2 | 2 | no | — |
| 191 | M16 | — | 4 | 1 | no | — |
| 192 | C2×C8 | — | 4 | 1 | no | — |
| 193 | C2×C8 | C22⋊C4×C113 | 1 | 2 | yes | — |
| 194 | C2×C8 | D8×C113 | 1 | 1 | yes | characteristic |
| 195 | C2×C8 | D8×C113 | 1 | 1 | yes | characteristic |
| 196 | C2×C8 | SD16×C113 | 1 | 2 | yes | — |
| 197 | C2×C8 | C22×C4×C113 | 1 | 1 | yes | characteristic |
| 198 | C2×C8 | C2×D4×C113 | 1 | 1 | yes | characteristic |
| 199 | C2×C8 | C2×D4×C113 | 1 | 1 | yes | characteristic |
| 200 | C2×C8 | C2×D4×C113 | 1 | 1 | yes | characteristic |
| 201 | C2×C8 | #41×C113 | 1 | 1 | yes | characteristic |
| 202 | C2×C8 | #41×C113 | 1 | 1 | yes | characteristic |
| 203 | C4⋊C4 | — | 2 | 2 | no | — |
| 204 | C4⋊C4 | — | 4 | 8 | no | — |
| 205 | C22⋊C4 | — | 4 | 1 | no | — |
| 206 | C42 | — | 2 | 1 | no | — |
| 207 | C42 | — | 4 | 1 | no | — |
| 208 | C42 | C22⋊C4×C113 | 1 | 2 | yes | — |
| 209 | C16 | — | 4 | 2 | no | — |
| 210 | C23 | AGL(1,ℤ/8)×C113 | 1 | 1 | yes | characteristic |
| 211 | Q8 | — | 4 | 4 | no | — |
| 212 | Q8 | — | 4 | 4 | no | — |
| 213 | Q8 | — | 8 | 2 | no | — |
| 214 | Q8 | — | 8 | 2 | no | — |
| 215 | C2×C4 | — | 2 | 4 | no | — |
| 216 | C2×C4 | — | 2 | 2 | no | — |
| 217 | C2×C4 | — | 4 | 4 | no | — |
| 218 | C2×C4 | — | 4 | 2 | no | — |
| 219 | C2×C4 | — | 8 | 2 | no | — |
| 220 | C2×C4 | — | 8 | 2 | no | — |
| 221 | C2×C4 | C2×C22⋊C4×C113 | 1 | 1 | yes | characteristic |
| 222 | C2×C4 | #121×C113 | 1 | 1 | yes | characteristic |
| 223 | C2×C4 | #121×C113 | 1 | 1 | yes | characteristic |
| 224 | C2×C4 | C2×D8×C113 | 1 | 1 | yes | characteristic |
| 225 | C2×C4 | C2×SD16×C113 | 1 | 1 | yes | characteristic |
| 226 | C2×C4 | AGL(1,ℤ/8)×C113 | 1 | 1 | yes | characteristic |
| 227 | C8 | — | 4 | 2 | no | — |
| 228 | C8 | #102×C113 | 1 | 2 | yes | — |
| 229 | C8 | #102×C113 | 1 | 2 | yes | — |
| 230 | C8 | C4×D4×C113 | 1 | 1 | yes | characteristic |
| 231 | C8 | C4×D4×C113 | 1 | 1 | yes | characteristic |
| 232 | C8 | #124×C113 | 1 | 1 | yes | characteristic |
| 233 | C8 | #127×C113 | 1 | 1 | yes | characteristic |
| 234 | C22 | — | 2 | 2 | no | — |
| 235 | C22 | #418×C113 | 1 | 1 | yes | characteristic |
| 236 | C22 | #459×C113 | 1 | 1 | yes | characteristic |
| 237 | C22 | #460×C113 | 1 | 1 | yes | characteristic |
| 238 | C4 | — | 2 | 4 | no | — |
| 239 | C4 | — | 8 | 2 | no | — |
| 240 | C4 | — | 8 | 4 | no | — |
| 241 | C4 | #390×C113 | 1 | 1 | yes | characteristic |
| 242 | C4 | C2×#102×C113 | 1 | 1 | yes | characteristic |
| 243 | C4 | #459×C113 | 1 | 1 | yes | characteristic |
| 244 | C4 | #460×C113 | 1 | 1 | yes | characteristic |
| 245 | C2 | — | 2 | 1 | no | — |
| 246 | C2 | — | 2 | 1 | no | — |
| 247 | C2 | C113×#1982 | 1 | 1 | yes | characteristic |
| 248 | C2 | C113×#2214 | 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