← #26034664
Subgroups — #26034664
Order 11392.
1002 conjugacy classes of subgroups.
The subgroup lattice has 266 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #19152351 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #19152334 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×Dic178 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #19152317 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | D4×Dic178 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #19152217 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #19152213 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #19152170 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #19152152 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #19152146 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #559×C89 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#13083573 | C22 | 1 | 2 | yes | — |
| 13 | C22×Dic178 | C22 | 1 | 4 | yes | — |
| 14 | #15668012 | C22 | 1 | 1 | yes | characteristic |
| 15 | #15668012 | C22 | 1 | 4 | yes | — |
| 16 | #15668011 | C22 | 1 | 2 | yes | — |
| 17 | #15668011 | C22 | 1 | 8 | yes | — |
| 18 | #15668011 | C22 | 1 | 4 | yes | — |
| 19 | #15668010 | C22 | 1 | 2 | yes | — |
| 20 | #15668005 | C22 | 1 | 8 | yes | — |
| 21 | #15668005 | C22 | 1 | 8 | yes | — |
| 22 | #15668002 | C22 | 1 | 4 | yes | — |
| 23 | #15667999 | C22 | 1 | 2 | yes | — |
| 24 | #15667999 | C22 | 1 | 4 | yes | — |
| 25 | #15667998 | C22 | 1 | 8 | yes | — |
| 26 | #15667996 | C22 | 1 | 4 | yes | — |
| 27 | #15667995 | C22 | 1 | 4 | yes | — |
| 28 | #15667993 | C22 | 1 | 4 | yes | — |
| 29 | #15667992 | C22 | 1 | 2 | yes | — |
| 30 | #15667991 | C22 | 1 | 8 | yes | — |
| 31 | #15667990 | C22 | 1 | 4 | yes | — |
| 32 | #15667989 | C22 | 1 | 8 | yes | — |
| 33 | #15667989 | C22 | 1 | 8 | yes | — |
| 34 | #15667988 | C22 | 1 | 2 | yes | — |
| 35 | #15667983 | C22 | 1 | 4 | yes | — |
| 36 | Q8×Dic89 | C22 | 1 | 4 | yes | — |
| 37 | C4×Dic178 | C22 | 1 | 4 | yes | — |
| 38 | C4×Dic178 | C22 | 1 | 2 | yes | — |
| 39 | C4×Dic178 | C22 | 1 | 4 | yes | — |
| 40 | D4×Dic89 | C22 | 1 | 4 | yes | — |
| 41 | D4×Dic89 | C22 | 1 | 4 | yes | — |
| 42 | #15667969 | C22 | 1 | 4 | yes | — |
| 43 | #15667968 | C22 | 1 | 4 | yes | — |
| 44 | C42×D89 | C22 | 1 | 1 | yes | characteristic |
| 45 | #127×C89 | C22 | 1 | 1 | yes | characteristic |
| 46 | #124×C89 | C22 | 1 | 4 | yes | — |
| 47 | #123×C89 | C22 | 1 | 4 | yes | — |
| 48 | C4×Q8×C89 | C22 | 1 | 2 | yes | — |
| 49 | C4×D4×C89 | C22 | 1 | 4 | yes | — |
| 50 | #13083573 | — | 4 | 4 | no | — |
| 51 | C2×Dic178 | — | 4 | 8 | no | — |
| 52 | C2×Dic178 | C23 | 1 | 2 | yes | — |
| 53 | C2×Dic178 | C23 | 1 | 4 | yes | — |
| 54 | C2×Dic178 | C23 | 1 | 8 | yes | — |
| 55 | C2×Dic178 | C23 | 1 | 2 | yes | — |
| 56 | C2×C22⋊D89 | C23 | 1 | 4 | yes | — |
| 57 | C22×Dic89 | C23 | 1 | 4 | yes | — |
| 58 | C22×Dic89 | C23 | 1 | 4 | yes | — |
| 59 | C2×C4×D89 | C23 | 1 | 2 | yes | — |
| 60 | C2×C4×D89 | C23 | 1 | 1 | yes | characteristic |
| 61 | C4⋊Dic89 | C23 | 1 | 2 | yes | — |
| 62 | C4⋊Dic89 | C23 | 1 | 4 | yes | — |
| 63 | C4⋊Dic89 | C23 | 1 | 4 | yes | — |
| 64 | C4⋊Dic89 | C23 | 1 | 8 | yes | — |
| 65 | #13083553 | C23 | 1 | 4 | yes | — |
| 66 | #13083553 | C23 | 1 | 4 | yes | — |
| 67 | #13083553 | C23 | 1 | 4 | yes | — |
| 68 | #13083553 | C23 | 1 | 4 | yes | — |
| 69 | #13083553 | C23 | 1 | 8 | yes | — |
| 70 | #13083553 | C23 | 1 | 4 | yes | — |
| 71 | C22⋊Dic89 | C23 | 1 | 4 | yes | — |
| 72 | C22⋊Dic89 | C23 | 1 | 8 | yes | — |
| 73 | C22⋊Dic89 | C23 | 1 | 8 | yes | — |
| 74 | #13083551 | C23 | 1 | 4 | yes | — |
| 75 | #13083551 | C23 | 1 | 4 | yes | — |
| 76 | C4×Dic89 | C23 | 1 | 8 | yes | — |
| 77 | C4×Dic89 | C23 | 1 | 4 | yes | — |
| 78 | C4×Dic89 | C23 | 1 | 2 | yes | — |
| 79 | C4×Dic89 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×Q8×C89 | C23 | 1 | 2 | yes | — |
| 81 | C2×D4×C89 | C23 | 1 | 4 | yes | — |
| 82 | C2×D4×C89 | C23 | 1 | 2 | yes | — |
| 83 | C22×C4×C89 | C23 | 1 | 4 | yes | — |
| 84 | C4⋊C4×C89 | C23 | 1 | 4 | yes | — |
| 85 | C4⋊C4×C89 | C23 | 1 | 2 | yes | — |
| 86 | C22⋊C4×C89 | C23 | 1 | 4 | yes | — |
| 87 | C22⋊C4×C89 | C23 | 1 | 8 | yes | — |
| 88 | C42×C89 | C23 | 1 | 4 | yes | — |
| 89 | C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 90 | C23×C89 | C24 | 1 | 4 | yes | — |
| 91 | C22×D89 | C24 | 1 | 1 | yes | characteristic |
| 92 | Q8×C89 | — | 2 | 4 | no | — |
| 93 | D4×C89 | — | 2 | 8 | no | — |
| 94 | D4×C89 | — | 4 | 2 | no | — |
| 95 | C2×C4×C89 | — | 4 | 4 | no | — |
| 96 | C2×C4×C89 | C24 | 1 | 4 | yes | — |
| 97 | C2×C4×C89 | C24 | 1 | 4 | yes | — |
| 98 | C2×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 99 | C2×C4×C89 | C24 | 1 | 2 | yes | — |
| 100 | C22⋊D89 | — | 4 | 4 | no | — |
| 101 | C2×Dic89 | — | 2 | 8 | no | — |
| 102 | C2×Dic89 | — | 4 | 4 | no | — |
| 103 | C2×Dic89 | C24 | 1 | 4 | yes | — |
| 104 | C2×Dic89 | C24 | 1 | 2 | yes | — |
| 105 | C2×Dic89 | C24 | 1 | 4 | yes | — |
| 106 | C2×Dic89 | C24 | 1 | 4 | yes | — |
| 107 | C2×Dic89 | C24 | 1 | 1 | yes | characteristic |
| 108 | C4×D89 | — | 2 | 4 | no | — |
| 109 | C4×D89 | — | 2 | 2 | no | — |
| 110 | Dic178 | — | 2 | 4 | no | — |
| 111 | Dic178 | — | 2 | 8 | no | — |
| 112 | Dic178 | — | 4 | 8 | no | — |
| 113 | Dic178 | — | 4 | 2 | no | — |
| 114 | C22×C89 | — | 2 | 4 | no | — |
| 115 | C22×C89 | — | 2 | 8 | no | — |
| 116 | C22×C89 | C25 | 1 | 1 | yes | characteristic |
| 117 | C2×D89 | — | 2 | 1 | no | — |
| 118 | C2×D89 | — | 2 | 2 | no | — |
| 119 | C4×C89 | — | 2 | 4 | no | — |
| 120 | C4×C89 | — | 2 | 1 | no | — |
| 121 | C4×C89 | — | 2 | 4 | no | — |
| 122 | C4×C89 | 2−1+4 | 1 | 4 | yes | — |
| 123 | Dic89 | — | 2 | 4 | no | — |
| 124 | Dic89 | — | 2 | 4 | no | — |
| 125 | Dic89 | — | 2 | 4 | no | — |
| 126 | Dic89 | — | 2 | 2 | no | — |
| 127 | Dic89 | H(5,𝔽2) | 1 | 2 | yes | — |
| 128 | C2×C89 | — | 4 | 4 | no | — |
| 129 | C2×C89 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 130 | C2×C89 | C2×2−1+4 | 1 | 2 | yes | — |
| 131 | D89 | — | 4 | 1 | no | — |
| 132 | #3550 | — | 89 | 1 | no | maximal, Sylow |
| 133 | C89 | #3550 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 134 | #563 | — | 89 | 4 | no | — |
| 135 | #559 | — | 89 | 1 | no | — |
| 136 | #559 | D89 | 1 | 1 | yes | characteristic, complemented |
| 137 | Q82 | — | 89 | 2 | no | — |
| 138 | #556 | — | 89 | 4 | no | — |
| 139 | D4×Q8 | — | 89 | 4 | no | — |
| 140 | #542 | — | 89 | 4 | no | — |
| 141 | #542 | — | 89 | 4 | no | — |
| 142 | #536 | — | 89 | 4 | no | — |
| 143 | #533 | — | 89 | 2 | no | — |
| 144 | #532 | — | 89 | 1 | no | — |
| 145 | C2×#41 | — | 89 | 2 | no | — |
| 146 | C22×Q8 | — | 89 | 4 | no | — |
| 147 | C4⋊Q8 | — | 89 | 2 | no | — |
| 148 | C4⋊Q8 | — | 89 | 2 | no | — |
| 149 | C4⋊Q8 | — | 89 | 8 | no | — |
| 150 | C4⋊Q8 | — | 89 | 4 | no | — |
| 151 | C4⋊Q8 | — | 89 | 1 | no | — |
| 152 | C4⋊Q8 | — | 89 | 4 | no | — |
| 153 | #127 | C2×D89 | 1 | 1 | yes | characteristic |
| 154 | #126 | — | 89 | 8 | no | — |
| 155 | #126 | — | 89 | 8 | no | — |
| 156 | #125 | — | 89 | 4 | no | — |
| 157 | #124 | — | 89 | 2 | no | — |
| 158 | #124 | — | 89 | 4 | no | — |
| 159 | #124 | — | 89 | 8 | no | — |
| 160 | #124 | C2×D89 | 1 | 4 | yes | — |
| 161 | #123 | — | 89 | 4 | no | — |
| 162 | #123 | — | 89 | 4 | no | — |
| 163 | #123 | — | 89 | 4 | no | — |
| 164 | #123 | C2×D89 | 1 | 4 | yes | — |
| 165 | C22⋊Q8 | — | 89 | 2 | no | — |
| 166 | C22⋊Q8 | — | 89 | 8 | no | — |
| 167 | C22⋊Q8 | — | 89 | 4 | no | — |
| 168 | C22⋊Q8 | — | 89 | 2 | no | — |
| 169 | C22⋊Q8 | — | 89 | 8 | no | — |
| 170 | C22⋊Q8 | — | 89 | 8 | no | — |
| 171 | #121 | — | 89 | 4 | no | — |
| 172 | C4×Q8 | — | 89 | 4 | no | — |
| 173 | C4×Q8 | — | 89 | 4 | no | — |
| 174 | C4×Q8 | — | 89 | 2 | no | — |
| 175 | C4×Q8 | — | 89 | 4 | no | — |
| 176 | C4×Q8 | C2×D89 | 1 | 2 | yes | — |
| 177 | C4×D4 | — | 89 | 4 | no | — |
| 178 | C4×D4 | — | 89 | 4 | no | — |
| 179 | C4×D4 | C2×D89 | 1 | 4 | yes | — |
| 180 | #117 | — | 89 | 4 | no | — |
| 181 | #117 | — | 89 | 4 | no | — |
| 182 | C2×C42 | — | 89 | 1 | no | — |
| 183 | #41 | — | 356 | 4 | no | — |
| 184 | C2×Q8 | — | 89 | 8 | no | — |
| 185 | C2×Q8 | — | 89 | 2 | no | — |
| 186 | C2×Q8 | — | 89 | 2 | no | — |
| 187 | C2×Q8 | — | 89 | 4 | no | — |
| 188 | C2×Q8 | — | 356 | 8 | no | — |
| 189 | C2×Q8 | C22×D89 | 1 | 2 | yes | — |
| 190 | C2×D4 | — | 89 | 4 | no | — |
| 191 | C2×D4 | C22×D89 | 1 | 4 | yes | — |
| 192 | C2×D4 | C22×D89 | 1 | 2 | yes | — |
| 193 | C22×C4 | — | 89 | 4 | no | — |
| 194 | C22×C4 | — | 89 | 4 | no | — |
| 195 | C22×C4 | — | 89 | 2 | no | — |
| 196 | C22×C4 | — | 89 | 1 | no | — |
| 197 | C22×C4 | C22×D89 | 1 | 4 | yes | — |
| 198 | C4⋊C4 | — | 89 | 4 | no | — |
| 199 | C4⋊C4 | — | 89 | 4 | no | — |
| 200 | C4⋊C4 | — | 89 | 4 | no | — |
| 201 | C4⋊C4 | — | 89 | 2 | no | — |
| 202 | C4⋊C4 | — | 89 | 4 | no | — |
| 203 | C4⋊C4 | — | 89 | 4 | no | — |
| 204 | C4⋊C4 | — | 89 | 4 | no | — |
| 205 | C4⋊C4 | — | 89 | 8 | no | — |
| 206 | C4⋊C4 | — | 89 | 8 | no | — |
| 207 | C4⋊C4 | — | 89 | 4 | no | — |
| 208 | C4⋊C4 | C22×D89 | 1 | 2 | yes | — |
| 209 | C4⋊C4 | C22×D89 | 1 | 4 | yes | — |
| 210 | C22⋊C4 | — | 89 | 4 | no | — |
| 211 | C22⋊C4 | — | 89 | 8 | no | — |
| 212 | C22⋊C4 | — | 89 | 8 | no | — |
| 213 | C22⋊C4 | — | 89 | 4 | no | — |
| 214 | C22⋊C4 | — | 89 | 4 | no | — |
| 215 | C22⋊C4 | C22×D89 | 1 | 4 | yes | — |
| 216 | C22⋊C4 | C22×D89 | 1 | 8 | yes | — |
| 217 | C42 | — | 89 | 2 | no | — |
| 218 | C42 | — | 89 | 1 | no | — |
| 219 | C42 | — | 89 | 4 | no | — |
| 220 | C42 | — | 89 | 8 | no | — |
| 221 | C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 222 | C42 | C22×D89 | 1 | 4 | yes | — |
| 223 | C23 | — | 89 | 1 | no | — |
| 224 | C23 | C23×D89 | 1 | 4 | yes | — |
| 225 | Q8 | — | 2 | 4 | no | — |
| 226 | Q8 | — | 356 | 8 | no | — |
| 227 | Q8 | — | 356 | 2 | no | — |
| 228 | Q8 | — | 178 | 8 | no | — |
| 229 | Q8 | — | 178 | 4 | no | — |
| 230 | D4 | — | 2 | 8 | no | — |
| 231 | D4 | — | 4 | 2 | no | — |
| 232 | D4 | — | 356 | 4 | no | — |
| 233 | C2×C4 | — | 4 | 4 | no | — |
| 234 | C2×C4 | — | 89 | 1 | no | — |
| 235 | C2×C4 | — | 89 | 4 | no | — |
| 236 | C2×C4 | — | 89 | 2 | no | — |
| 237 | C2×C4 | — | 89 | 4 | no | — |
| 238 | C2×C4 | — | 89 | 4 | no | — |
| 239 | C2×C4 | — | 356 | 4 | no | — |
| 240 | C2×C4 | — | 178 | 2 | no | — |
| 241 | C2×C4 | — | 178 | 8 | no | — |
| 242 | C2×C4 | — | 178 | 4 | no | — |
| 243 | C2×C4 | C23×D89 | 1 | 4 | yes | — |
| 244 | C2×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 245 | C2×C4 | C23×D89 | 1 | 4 | yes | — |
| 246 | C2×C4 | C23×D89 | 1 | 2 | yes | — |
| 247 | C22 | — | 2 | 4 | no | — |
| 248 | C22 | — | 2 | 8 | no | — |
| 249 | C22 | — | 178 | 1 | no | — |
| 250 | C22 | — | 178 | 2 | no | — |
| 251 | C22 | C24×D89 | 1 | 1 | yes | characteristic |
| 252 | C4 | — | 2 | 4 | no | — |
| 253 | C4 | — | 2 | 1 | no | — |
| 254 | C4 | — | 2 | 4 | no | — |
| 255 | C4 | — | 89 | 2 | no | — |
| 256 | C4 | — | 178 | 4 | no | — |
| 257 | C4 | — | 178 | 4 | no | — |
| 258 | C4 | — | 178 | 2 | no | — |
| 259 | C4 | — | 178 | 4 | no | — |
| 260 | C4 | #15668059 | 1 | 4 | yes | — |
| 261 | C2 | — | 4 | 4 | no | — |
| 262 | C2 | — | 356 | 1 | no | — |
| 263 | C2 | H(5,𝔽2)×D89 | 1 | 1 | yes | characteristic |
| 264 | C2 | C2×#15668059 | 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