← #36382366
Subgroups — #36382366
Order 22599.
662 conjugacy classes of subgroups.
The subgroup lattice has 240 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #21419354 | C3 | 1 | 3 | yes | maximal, complemented |
| 2 | #21419353 | C3 | 1 | 3 | yes | maximal, complemented |
| 3 | #21419349 | C3 | 1 | 3 | yes | maximal, complemented |
| 4 | #21419345 | C3 | 1 | 3 | yes | maximal, complemented |
| 5 | #21419344 | C3 | 1 | 3 | yes | maximal, complemented |
| 6 | #21419339 | C3 | 1 | 3 | yes | maximal, complemented |
| 7 | #21419336 | C3 | 1 | 2 | yes | maximal, complemented |
| 8 | #21419330 | C3 | 1 | 2 | yes | maximal, complemented |
| 9 | #21419329 | C3 | 1 | 2 | yes | maximal, complemented |
| 10 | #21419322 | C3 | 1 | 1 | yes | maximal, characteristic |
| 11 | #21419317 | C3 | 1 | 1 | yes | maximal, characteristic |
| 12 | #21419316 | C3 | 1 | 1 | yes | maximal, characteristic |
| 13 | C9×#11719687 | C3 | 1 | 3 | yes | maximal, complemented |
| 14 | C9×#11719686 | C3 | 1 | 3 | yes | maximal, complemented |
| 15 | C9×#11719689 | C3 | 1 | 2 | yes | maximal, complemented |
| 16 | C9×C32⋊(C31⋊C3) | C3 | 1 | 1 | yes | maximal, characteristic |
| 17 | #21419294 | C3 | 1 | 3 | yes | maximal, complemented |
| 18 | C3×C92×C31 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | C3×#11719689 | C32 | 1 | 2 | yes | — |
| 20 | C3×#11719686 | C32 | 1 | 3 | yes | — |
| 21 | C3×#11719687 | C32 | 1 | 3 | yes | — |
| 22 | C3×C32⋊(C31⋊C3) | C32 | 1 | 1 | yes | characteristic |
| 23 | C3×C9×C31⋊C3 | C32 | 1 | 3 | yes | — |
| 24 | #14578887 | C32 | 1 | 6 | yes | — |
| 25 | #14578886 | C32 | 1 | 6 | yes | — |
| 26 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 27 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 28 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 29 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 30 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 31 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 32 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 33 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 34 | (C31⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 35 | C32⋊(C31⋊C9) | C32 | 1 | 2 | yes | — |
| 36 | C32⋊(C31⋊C9) | C32 | 1 | 2 | yes | — |
| 37 | C32⋊(C31⋊C9) | C32 | 1 | 2 | yes | — |
| 38 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 39 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 40 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 41 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 42 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 43 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 44 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 45 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 46 | (C3×C31⋊C3)⋊C9 | C32 | 1 | 3 | yes | — |
| 47 | C9×C31⋊C9 | C32 | 1 | 6 | yes | — |
| 48 | C32×C9×C31 | C32 | 1 | 1 | yes | characteristic |
| 49 | C32×C9×C31 | C32 | 1 | 1 | yes | characteristic |
| 50 | C32×C9×C31 | C32 | 1 | 1 | yes | characteristic |
| 51 | C32×C9×C31 | C32 | 1 | 1 | yes | characteristic |
| 52 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 53 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 54 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 55 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 56 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 57 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 58 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 59 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 60 | C92×C31 | C32 | 1 | 1 | yes | characteristic |
| 61 | C33×C31 | C33 | 1 | 1 | yes | characteristic |
| 62 | C32×C31⋊C3 | C33 | 1 | 3 | yes | — |
| 63 | C3×C9×C31 | — | 3 | 3 | no | — |
| 64 | C3×C9×C31 | — | 3 | 3 | no | — |
| 65 | C3×C9×C31 | — | 3 | 3 | no | — |
| 66 | C3×C9×C31 | — | 3 | 3 | no | — |
| 67 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 68 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 69 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 70 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 71 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 72 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 73 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 74 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 75 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 76 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 77 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 78 | C3×C9×C31 | C33 | 1 | 1 | yes | characteristic |
| 79 | C32⋊(C31⋊C3) | — | 3 | 3 | no | — |
| 80 | #11719689 | — | 3 | 6 | no | — |
| 81 | C3×C31⋊C9 | C33 | 1 | 6 | yes | — |
| 82 | C3×C31⋊C9 | C33 | 1 | 6 | yes | — |
| 83 | C3×C31⋊C9 | C33 | 1 | 6 | yes | — |
| 84 | C3×C31⋊C9 | C33 | 1 | 6 | yes | — |
| 85 | #11719687 | — | 3 | 9 | no | — |
| 86 | #11719686 | — | 3 | 9 | no | — |
| 87 | C9×C31⋊C3 | — | 3 | 9 | no | — |
| 88 | #10624877 | — | 31 | 1 | no | maximal, Sylow |
| 89 | C32×C31 | — | 3 | 1 | no | — |
| 90 | C32×C31 | — | 3 | 1 | no | — |
| 91 | C32×C31 | — | 3 | 1 | no | — |
| 92 | C32×C31 | #737 | 1 | 3 | yes | — |
| 93 | C32×C31 | C34 | 1 | 1 | yes | characteristic |
| 94 | C3×C31⋊C3 | — | 3 | 3 | no | — |
| 95 | C3×C31⋊C3 | — | 3 | 3 | no | — |
| 96 | C3×C31⋊C3 | — | 3 | 3 | no | — |
| 97 | C3×C31⋊C3 | — | 3 | 3 | no | — |
| 98 | C9×C31 | — | 3 | 1 | no | — |
| 99 | C9×C31 | — | 3 | 1 | no | — |
| 100 | C9×C31 | — | 3 | 1 | no | — |
| 101 | C9×C31 | — | 3 | 1 | no | — |
| 102 | C9×C31 | — | 3 | 1 | no | — |
| 103 | C9×C31 | — | 3 | 1 | no | — |
| 104 | C9×C31 | — | 3 | 1 | no | — |
| 105 | C9×C31 | — | 3 | 1 | no | — |
| 106 | C9×C31 | — | 3 | 1 | no | — |
| 107 | C9×C31 | #737 | 1 | 3 | yes | — |
| 108 | C9×C31 | #737 | 1 | 3 | yes | — |
| 109 | C9×C31 | #737 | 1 | 3 | yes | — |
| 110 | C31⋊C9 | — | 3 | 6 | no | — |
| 111 | C31⋊C9 | — | 3 | 6 | no | — |
| 112 | C31⋊C9 | — | 3 | 6 | no | — |
| 113 | C31⋊C9 | — | 3 | 6 | no | — |
| 114 | #6899 | — | 31 | 3 | no | — |
| 115 | #6899 | — | 31 | 3 | no | — |
| 116 | #6898 | — | 31 | 3 | no | — |
| 117 | #6897 | — | 31 | 3 | no | — |
| 118 | #6897 | — | 31 | 3 | no | — |
| 119 | #6896 | — | 31 | 3 | no | — |
| 120 | #6895 | — | 31 | 2 | no | — |
| 121 | #6894 | — | 31 | 2 | no | — |
| 122 | #6894 | — | 31 | 2 | no | — |
| 123 | #6893 | — | 31 | 1 | no | — |
| 124 | C9⋊H(3,𝔽3) | — | 31 | 1 | no | — |
| 125 | C9⋊H(3,𝔽3) | — | 31 | 1 | no | — |
| 126 | C9×3−1+2 | — | 31 | 2 | no | — |
| 127 | C9×3−1+2 | — | 31 | 3 | no | — |
| 128 | C9×3−1+2 | — | 31 | 3 | no | — |
| 129 | C9×H(3,𝔽3) | — | 31 | 1 | no | — |
| 130 | #6887 | — | 31 | 3 | no | — |
| 131 | C3×C92 | C31⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 132 | C3×C31 | — | 3 | 3 | no | — |
| 133 | C3×C31 | C3×#737 | 1 | 1 | yes | characteristic |
| 134 | C3×C31 | C3×#737 | 1 | 1 | yes | characteristic |
| 135 | C3×C31 | C3×#737 | 1 | 1 | yes | characteristic |
| 136 | C3×C31 | C3×#737 | 1 | 1 | yes | characteristic |
| 137 | C31⋊C3 | — | 9 | 3 | no | — |
| 138 | C3×3−1+2 | — | 31 | 2 | no | — |
| 139 | C3×3−1+2 | — | 31 | 3 | no | — |
| 140 | C3×3−1+2 | — | 31 | 3 | no | — |
| 141 | C3×H(3,𝔽3) | — | 31 | 1 | no | — |
| 142 | C32×C9 | — | 31 | 3 | no | — |
| 143 | C32×C9 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 144 | C32×C9 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 145 | C32×C9 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 146 | C32×C9 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 147 | C9⋊C9 | — | 31 | 6 | no | — |
| 148 | C9⋊C9 | — | 31 | 6 | no | — |
| 149 | C9⋊C9 | — | 31 | 6 | no | — |
| 150 | C9⋊C9 | — | 31 | 6 | no | — |
| 151 | C9⋊C9 | — | 31 | 6 | no | — |
| 152 | C9⋊C9 | — | 31 | 6 | no | — |
| 153 | C9⋊C9 | — | 31 | 6 | no | — |
| 154 | C9⋊C9 | — | 31 | 6 | no | — |
| 155 | C9⋊C9 | — | 31 | 6 | no | — |
| 156 | C9⋊C9 | — | 31 | 6 | no | — |
| 157 | C9⋊C9 | — | 31 | 6 | no | — |
| 158 | C32⋊C9 | — | 31 | 2 | no | — |
| 159 | C32⋊C9 | — | 31 | 2 | no | — |
| 160 | C32⋊C9 | — | 31 | 2 | no | — |
| 161 | C32⋊C9 | — | 31 | 3 | no | — |
| 162 | C32⋊C9 | — | 31 | 3 | no | — |
| 163 | C32⋊C9 | — | 31 | 3 | no | — |
| 164 | C32⋊C9 | — | 31 | 3 | no | — |
| 165 | C32⋊C9 | — | 31 | 3 | no | — |
| 166 | C32⋊C9 | — | 31 | 3 | no | — |
| 167 | C32⋊C9 | — | 31 | 3 | no | — |
| 168 | C32⋊C9 | — | 31 | 3 | no | — |
| 169 | C32⋊C9 | — | 31 | 3 | no | — |
| 170 | C92 | — | 31 | 6 | no | — |
| 171 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 172 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 173 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 174 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 175 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 176 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 177 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 178 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 179 | C92 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 180 | C31 | #10624877 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 181 | C33 | — | 31 | 3 | no | — |
| 182 | C33 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 183 | 3−1+2 | — | 93 | 6 | no | — |
| 184 | 3−1+2 | — | 93 | 9 | no | — |
| 185 | 3−1+2 | — | 93 | 9 | no | — |
| 186 | H(3,𝔽3) | — | 93 | 3 | no | — |
| 187 | C3×C9 | — | 3 | 3 | no | — |
| 188 | C3×C9 | — | 3 | 3 | no | — |
| 189 | C3×C9 | — | 3 | 3 | no | — |
| 190 | C3×C9 | — | 3 | 3 | no | — |
| 191 | C3×C9 | — | 31 | 6 | no | — |
| 192 | C3×C9 | — | 31 | 6 | no | — |
| 193 | C3×C9 | — | 31 | 6 | no | — |
| 194 | C3×C9 | — | 31 | 6 | no | — |
| 195 | C3×C9 | — | 93 | 9 | no | — |
| 196 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 197 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 198 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 199 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 200 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 201 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 202 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 203 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 204 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 205 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 206 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 207 | C3×C9 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 208 | C32 | — | 3 | 1 | no | — |
| 209 | C32 | — | 3 | 1 | no | — |
| 210 | C32 | — | 3 | 1 | no | — |
| 211 | C32 | — | 93 | 3 | no | — |
| 212 | C32 | — | 93 | 3 | no | — |
| 213 | C32 | — | 93 | 3 | no | — |
| 214 | C32 | — | 93 | 3 | no | — |
| 215 | C32 | #14578912 | 1 | 3 | yes | — |
| 216 | C32 | C33×C31⋊C3 | 1 | 1 | yes | characteristic |
| 217 | C9 | — | 3 | 1 | no | — |
| 218 | C9 | — | 3 | 1 | no | — |
| 219 | C9 | — | 3 | 1 | no | — |
| 220 | C9 | — | 3 | 1 | no | — |
| 221 | C9 | — | 3 | 1 | no | — |
| 222 | C9 | — | 3 | 1 | no | — |
| 223 | C9 | — | 3 | 1 | no | — |
| 224 | C9 | — | 3 | 1 | no | — |
| 225 | C9 | — | 3 | 1 | no | — |
| 226 | C9 | — | 93 | 6 | no | — |
| 227 | C9 | — | 93 | 6 | no | — |
| 228 | C9 | — | 93 | 6 | no | — |
| 229 | C9 | — | 93 | 6 | no | — |
| 230 | C9 | #14578912 | 1 | 3 | yes | — |
| 231 | C9 | #14578912 | 1 | 3 | yes | — |
| 232 | C9 | #14578912 | 1 | 3 | yes | — |
| 233 | C3 | — | 3 | 3 | no | — |
| 234 | C3 | — | 279 | 3 | no | — |
| 235 | C3 | C3×#14578912 | 1 | 1 | yes | characteristic |
| 236 | C3 | C3×#14578912 | 1 | 1 | yes | characteristic |
| 237 | C3 | C3×#14578912 | 1 | 1 | yes | characteristic |
| 238 | C3 | C3×#14578912 | 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