← #11795931
Subgroups — #11795931
Order 1152.
240 conjugacy classes of subgroups.
The subgroup lattice has 174 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C9×M32 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10588782 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#63371 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10588189 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #71425 | — | 3 | 1 | no | maximal |
| 6 | C22×C8×C9 | C22 | 1 | 1 | yes | characteristic |
| 7 | #63488 | C4 | 1 | 1 | yes | characteristic |
| 8 | C2×#3667 | C4 | 1 | 1 | yes | characteristic |
| 9 | C9×M32 | C4 | 1 | 2 | yes | complemented |
| 10 | C9×M32 | C22 | 1 | 2 | yes | — |
| 11 | C2×C9×C16 | C4 | 1 | 2 | yes | complemented |
| 12 | #63375 | C22 | 1 | 2 | yes | — |
| 13 | C8×Dic9 | C4 | 1 | 2 | yes | — |
| 14 | #63371 | C4 | 1 | 2 | yes | complemented |
| 15 | #63371 | C22 | 1 | 2 | yes | — |
| 16 | C2×C9⋊C16 | C4 | 1 | 2 | yes | complemented |
| 17 | C2×C3×M32 | D3 | 1 | 1 | yes | characteristic |
| 18 | #5101 | — | 3 | 1 | no | — |
| 19 | C2×#812 | — | 3 | 1 | no | — |
| 20 | #4512 | — | 3 | 4 | no | — |
| 21 | C22×C4×C9 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C2×C8×C9 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | C2×C8×C9 | C2×C4 | 1 | 1 | yes | characteristic |
| 24 | C2×C8×C9 | C2×C4 | 1 | 1 | yes | characteristic |
| 25 | C2×C8×C9 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C2×C8×C9 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C2×C8×C9 | C23 | 1 | 1 | yes | characteristic |
| 28 | #3676 | — | 2 | 1 | no | — |
| 29 | C4⋊Dic9 | — | 2 | 1 | no | — |
| 30 | C4×Dic9 | C2×C4 | 1 | 2 | yes | — |
| 31 | #3667 | — | 2 | 1 | no | — |
| 32 | #3667 | — | 2 | 1 | no | — |
| 33 | C2×C9⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 34 | C9×C16 | C2×C4 | 1 | 4 | yes | — |
| 35 | C9⋊C16 | C2×C4 | 1 | 4 | yes | — |
| 36 | #2110 | — | 9 | 1 | no | Sylow |
| 37 | C22×C3×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 38 | #926 | — | 3 | 1 | no | — |
| 39 | C2×#208 | — | 3 | 1 | no | — |
| 40 | C3×M32 | Dic3 | 1 | 2 | yes | — |
| 41 | C3×M32 | C2×D3 | 1 | 2 | yes | — |
| 42 | C2×C3×C16 | Dic3 | 1 | 2 | yes | — |
| 43 | #815 | — | 3 | 2 | no | — |
| 44 | C8×Dic3 | — | 3 | 2 | no | — |
| 45 | #812 | — | 3 | 2 | no | — |
| 46 | #812 | — | 3 | 2 | no | — |
| 47 | C2×C3⋊C16 | — | 3 | 2 | no | — |
| 48 | C23×C9 | M16 | 1 | 1 | yes | characteristic |
| 49 | C2×C4×C9 | C42 | 1 | 1 | yes | characteristic |
| 50 | C2×C4×C9 | C42 | 1 | 1 | yes | characteristic |
| 51 | C2×C4×C9 | M16 | 1 | 1 | yes | characteristic |
| 52 | C2×C4×C9 | M16 | 1 | 1 | yes | characteristic |
| 53 | C2×C4×C9 | M16 | 1 | 1 | yes | characteristic |
| 54 | C2×C4×C9 | C22×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×Dic9 | — | 2 | 2 | no | — |
| 56 | C8×C9 | C42 | 1 | 1 | yes | characteristic |
| 57 | C8×C9 | C42 | 1 | 1 | yes | characteristic |
| 58 | C8×C9 | C22×C4 | 1 | 1 | yes | characteristic |
| 59 | C8×C9 | C22×C4 | 1 | 1 | yes | characteristic |
| 60 | C9⋊C8 | — | 2 | 2 | no | — |
| 61 | C2×M32 | — | 9 | 1 | no | — |
| 62 | C2×M32 | D9 | 1 | 1 | yes | characteristic |
| 63 | #405 | — | 9 | 1 | no | — |
| 64 | #347 | — | 9 | 4 | no | — |
| 65 | C22×C3×C4 | C4×D3 | 1 | 1 | yes | characteristic |
| 66 | C2×C3×C8 | C4×D3 | 1 | 1 | yes | characteristic |
| 67 | C2×C3×C8 | C4×D3 | 1 | 1 | yes | characteristic |
| 68 | C2×C3×C8 | C4×D3 | 1 | 1 | yes | characteristic |
| 69 | C2×C3×C8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 70 | C2×C3×C8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 71 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 72 | #217 | — | 6 | 1 | no | — |
| 73 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 74 | C4×Dic3 | — | 3 | 2 | no | — |
| 75 | #208 | — | 6 | 1 | no | — |
| 76 | #208 | — | 6 | 1 | no | — |
| 77 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 78 | C3×C16 | C2×Dic3 | 1 | 4 | yes | — |
| 79 | C3⋊C16 | — | 3 | 4 | no | — |
| 80 | C22×C9 | — | 4 | 1 | no | — |
| 81 | C22×C9 | #97 | 1 | 1 | yes | characteristic |
| 82 | C22×C9 | #97 | 1 | 1 | yes | characteristic |
| 83 | C22×C9 | C2×M16 | 1 | 1 | yes | characteristic |
| 84 | C4×C9 | #97 | 1 | 1 | yes | characteristic |
| 85 | C4×C9 | #97 | 1 | 1 | yes | characteristic |
| 86 | C4×C9 | C2×C42 | 1 | 1 | yes | characteristic |
| 87 | C4×C9 | C2×M16 | 1 | 1 | yes | characteristic |
| 88 | Dic9 | — | 4 | 2 | no | — |
| 89 | C2×M16 | — | 9 | 1 | no | — |
| 90 | C22×C8 | C2×D9 | 1 | 1 | yes | characteristic |
| 91 | #117 | — | 9 | 1 | no | — |
| 92 | M32 | — | 9 | 2 | no | — |
| 93 | M32 | — | 9 | 2 | no | — |
| 94 | M32 | Dic9 | 1 | 2 | yes | complemented |
| 95 | M32 | C2×D9 | 1 | 2 | yes | — |
| 96 | C2×C16 | — | 9 | 2 | no | — |
| 97 | C2×C16 | Dic9 | 1 | 2 | yes | complemented |
| 98 | #97 | — | 9 | 2 | no | — |
| 99 | C4×C8 | — | 9 | 2 | no | — |
| 100 | C23×C3 | ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 101 | C2×C3×C4 | ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 102 | C2×C3×C4 | ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 103 | C2×C3×C4 | ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 104 | C2×C3×C4 | C4×Dic3 | 1 | 1 | yes | characteristic |
| 105 | C2×C3×C4 | C4×Dic3 | 1 | 1 | yes | characteristic |
| 106 | C2×C3×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 107 | C2×Dic3 | — | 6 | 2 | no | — |
| 108 | C3×C8 | C4×Dic3 | 1 | 1 | yes | characteristic |
| 109 | C3×C8 | C4×Dic3 | 1 | 1 | yes | characteristic |
| 110 | C3×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 111 | C3×C8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 112 | C3⋊C8 | — | 6 | 2 | no | — |
| 113 | C2×C9 | — | 2 | 1 | no | — |
| 114 | C2×C9 | — | 2 | 1 | no | — |
| 115 | C2×C9 | — | 2 | 1 | no | — |
| 116 | C2×C9 | C2×#97 | 1 | 1 | yes | characteristic |
| 117 | C22×C4 | C4×D9 | 1 | 1 | yes | characteristic |
| 118 | M16 | — | 18 | 1 | no | — |
| 119 | M16 | — | 18 | 1 | no | — |
| 120 | C2×C8 | — | 9 | 2 | no | — |
| 121 | C2×C8 | C4×D9 | 1 | 1 | yes | characteristic |
| 122 | C2×C8 | C4×D9 | 1 | 1 | yes | characteristic |
| 123 | C2×C8 | C4×D9 | 1 | 1 | yes | characteristic |
| 124 | C2×C8 | C2×Dic9 | 1 | 1 | yes | characteristic |
| 125 | C2×C8 | C2×Dic9 | 1 | 1 | yes | characteristic |
| 126 | C2×C8 | C22×D9 | 1 | 1 | yes | characteristic |
| 127 | C4⋊C4 | — | 18 | 1 | no | — |
| 128 | C22⋊C4 | — | 18 | 1 | no | — |
| 129 | C42 | — | 9 | 2 | no | — |
| 130 | C16 | — | 9 | 4 | no | — |
| 131 | C16 | C2×Dic9 | 1 | 4 | yes | — |
| 132 | C22×C3 | — | 4 | 1 | no | — |
| 133 | C22×C3 | #815 | 1 | 1 | yes | characteristic |
| 134 | C22×C3 | #815 | 1 | 1 | yes | characteristic |
| 135 | C22×C3 | C2×ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 136 | C3×C4 | #815 | 1 | 1 | yes | characteristic |
| 137 | C3×C4 | #815 | 1 | 1 | yes | characteristic |
| 138 | C3×C4 | C2×ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 139 | C3×C4 | C2×C4×Dic3 | 1 | 1 | yes | characteristic |
| 140 | Dic3 | — | 12 | 2 | no | — |
| 141 | C9 | #2110 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 142 | C23 | #3663 | 1 | 1 | yes | characteristic |
| 143 | C2×C4 | — | 18 | 2 | no | — |
| 144 | C2×C4 | #3663 | 1 | 1 | yes | characteristic |
| 145 | C2×C4 | #3663 | 1 | 1 | yes | characteristic |
| 146 | C2×C4 | #3663 | 1 | 1 | yes | characteristic |
| 147 | C2×C4 | C4×Dic9 | 1 | 1 | yes | characteristic |
| 148 | C2×C4 | C4×Dic9 | 1 | 1 | yes | characteristic |
| 149 | C2×C4 | C2×C4×D9 | 1 | 1 | yes | characteristic |
| 150 | C8 | — | 18 | 2 | no | — |
| 151 | C8 | C4×Dic9 | 1 | 1 | yes | characteristic |
| 152 | C8 | C4×Dic9 | 1 | 1 | yes | characteristic |
| 153 | C8 | C2×C4×D9 | 1 | 1 | yes | characteristic |
| 154 | C8 | C22×Dic9 | 1 | 1 | yes | characteristic |
| 155 | C2×C3 | — | 2 | 1 | no | — |
| 156 | C2×C3 | — | 2 | 1 | no | — |
| 157 | C2×C3 | — | 2 | 1 | no | — |
| 158 | C2×C3 | C2×#815 | 1 | 1 | yes | characteristic |
| 159 | C22 | — | 4 | 1 | no | — |
| 160 | C22 | #63375 | 1 | 1 | yes | characteristic |
| 161 | C22 | #63375 | 1 | 1 | yes | characteristic |
| 162 | C22 | C2×#3663 | 1 | 1 | yes | characteristic |
| 163 | C4 | — | 36 | 2 | no | — |
| 164 | C4 | #63375 | 1 | 1 | yes | characteristic |
| 165 | C4 | #63375 | 1 | 1 | yes | characteristic |
| 166 | C4 | C2×#3663 | 1 | 1 | yes | characteristic |
| 167 | C4 | C2×C4×Dic9 | 1 | 1 | yes | characteristic |
| 168 | C3 | #71425 | 1 | 1 | yes | characteristic |
| 169 | C2 | — | 2 | 1 | no | — |
| 170 | C2 | — | 2 | 1 | no | — |
| 171 | C2 | — | 2 | 1 | no | — |
| 172 | C2 | C2×#63375 | 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