Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
338 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10592606 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10590929 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#63545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#4516 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10589144 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69260 | — | 3 | 2 | no | maximal |
| 7 | #64110 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×C3×D24 | C22 | 1 | 2 | yes | — |
| 9 | #63830 | — | 2 | 2 | no | — |
| 10 | C32×M32 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3⋊(C3⋊C16) | C22 | 1 | 1 | yes | characteristic |
| 12 | #63625 | — | 2 | 1 | no | — |
| 13 | C16×C3⋊D3 | — | 2 | 1 | no | — |
| 14 | C3×#819 | C22 | 1 | 2 | yes | — |
| 15 | #63558 | — | 2 | 2 | no | — |
| 16 | #63545 | — | 2 | 1 | no | — |
| 17 | #63545 | — | 2 | 1 | no | — |
| 18 | #5160 | — | 3 | 2 | no | — |
| 19 | C2×#826 | — | 3 | 2 | no | — |
| 20 | #4907 | — | 3 | 2 | no | — |
| 21 | #4907 | — | 6 | 1 | no | — |
| 22 | #4897 | — | 3 | 2 | no | — |
| 23 | C3×#361 | — | 3 | 2 | no | — |
| 24 | #4516 | D3 | 1 | 2 | yes | complemented |
| 25 | #4493 | — | 3 | 2 | no | — |
| 26 | #3828 | D4 | 1 | 1 | yes | characteristic |
| 27 | C2×C3×D12 | — | 2 | 2 | no | — |
| 28 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 29 | #3748 | D4 | 1 | 1 | yes | characteristic |
| 30 | #3743 | — | 2 | 1 | no | — |
| 31 | C8×C3⋊D3 | — | 2 | 1 | no | — |
| 32 | C3×#208 | — | 2 | 2 | no | — |
| 33 | C3×D24 | — | 2 | 2 | no | — |
| 34 | C3×D24 | — | 2 | 2 | no | — |
| 35 | #3716 | — | 4 | 2 | no | — |
| 36 | #3714 | — | 4 | 2 | no | — |
| 37 | C32×C16 | — | 2 | 1 | no | — |
| 38 | C3⋊(C3⋊C16) | D4 | 1 | 1 | yes | characteristic |
| 39 | C3⋊(C3⋊C16) | D4 | 1 | 1 | yes | characteristic |
| 40 | #2221 | — | 9 | 1 | no | Sylow |
| 41 | C2×C3×D8 | — | 3 | 2 | no | — |
| 42 | #932 | — | 6 | 2 | no | — |
| 43 | #908 | — | 6 | 2 | no | — |
| 44 | C2×D24 | C2×D3 | 1 | 2 | yes | — |
| 45 | #901 | — | 3 | 2 | no | — |
| 46 | #901 | — | 6 | 1 | no | — |
| 47 | C3×M32 | — | 2 | 1 | no | — |
| 48 | C3×M32 | C2×D3 | 1 | 2 | yes | — |
| 49 | C3×#108 | — | 3 | 2 | no | — |
| 50 | #833 | — | 6 | 2 | no | — |
| 51 | #826 | — | 6 | 2 | no | — |
| 52 | #826 | — | 6 | 2 | no | — |
| 53 | #823 | — | 6 | 2 | no | — |
| 54 | #819 | C2×D3 | 1 | 2 | yes | — |
| 55 | C2×C3⋊C16 | — | 3 | 2 | no | — |
| 56 | C2×C3⋊C16 | — | 6 | 1 | no | — |
| 57 | #798 | — | 6 | 2 | no | — |
| 58 | #798 | — | 6 | 2 | no | — |
| 59 | D3×C16 | — | 6 | 2 | no | — |
| 60 | D3×C16 | — | 6 | 2 | no | — |
| 61 | C22×C3×D3 | — | 4 | 2 | no | — |
| 62 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 63 | #638 | — | 2 | 1 | no | — |
| 64 | C4⋊(C3⋊D3) | D8 | 1 | 1 | yes | characteristic |
| 65 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 66 | #634 | D8 | 1 | 1 | yes | characteristic |
| 67 | C3×D12 | — | 4 | 2 | no | — |
| 68 | C3×D12 | — | 4 | 2 | no | — |
| 69 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C32×C8 | #41 | 1 | 1 | yes | characteristic |
| 71 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 72 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 73 | C2×D16 | — | 9 | 1 | no | — |
| 74 | #504 | — | 9 | 1 | no | — |
| 75 | #472 | — | 9 | 2 | no | — |
| 76 | #368 | — | 9 | 1 | no | — |
| 77 | #361 | — | 3 | 2 | no | — |
| 78 | C2×C3×D4 | — | 6 | 2 | no | — |
| 79 | #235 | — | 3 | 2 | no | — |
| 80 | #235 | — | 6 | 1 | no | — |
| 81 | C2×D12 | — | 2 | 2 | no | — |
| 82 | C3×D8 | — | 6 | 2 | no | — |
| 83 | C3×D8 | — | 6 | 2 | no | — |
| 84 | C3×M16 | — | 6 | 2 | no | — |
| 85 | C2×C3×C8 | — | 2 | 1 | no | — |
| 86 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 87 | #214 | — | 12 | 2 | no | — |
| 88 | #213 | — | 12 | 2 | no | — |
| 89 | #208 | — | 2 | 2 | no | — |
| 90 | #208 | — | 3 | 2 | no | — |
| 91 | #208 | — | 6 | 1 | no | — |
| 92 | D24 | — | 2 | 2 | no | — |
| 93 | D24 | — | 2 | 2 | no | — |
| 94 | D24 | — | 12 | 2 | no | — |
| 95 | #204 | — | 12 | 2 | no | — |
| 96 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 97 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 98 | D3×C8 | — | 6 | 2 | no | — |
| 99 | D3×C8 | — | 6 | 2 | no | — |
| 100 | C3×C16 | — | 2 | 2 | no | — |
| 101 | C3×C16 | — | 2 | 2 | no | — |
| 102 | C3⋊C16 | — | 3 | 2 | no | — |
| 103 | C3⋊C16 | — | 3 | 2 | no | — |
| 104 | C3⋊C16 | — | 6 | 1 | no | — |
| 105 | C3⋊C16 | — | 6 | 1 | no | — |
| 106 | C22×C32 | #135 | 1 | 1 | yes | characteristic |
| 107 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 108 | C2×C3×D3 | — | 8 | 2 | no | — |
| 109 | C2×C3×D3 | — | 16 | 2 | no | — |
| 110 | C32×C4 | #121 | 1 | 1 | yes | characteristic |
| 111 | C32×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 112 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 113 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 114 | C2×D8 | — | 3 | 2 | no | — |
| 115 | #131 | — | 9 | 1 | no | — |
| 116 | D16 | — | 18 | 1 | no | — |
| 117 | D16 | — | 18 | 1 | no | — |
| 118 | M32 | — | 18 | 1 | no | — |
| 119 | M32 | D32 | 1 | 1 | yes | characteristic |
| 120 | C2×C16 | — | 9 | 1 | no | — |
| 121 | C2×C16 | — | 18 | 1 | no | — |
| 122 | #108 | — | 3 | 2 | no | — |
| 123 | #100 | — | 18 | 2 | no | — |
| 124 | C23×C3 | — | 12 | 2 | no | — |
| 125 | C22×D3 | — | 4 | 2 | no | — |
| 126 | C3×D4 | — | 12 | 2 | no | — |
| 127 | C3×D4 | — | 12 | 2 | no | — |
| 128 | C2×C3×C4 | — | 2 | 1 | no | — |
| 129 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 130 | #67 | — | 6 | 2 | no | — |
| 131 | #67 | — | 6 | 2 | no | — |
| 132 | D12 | — | 3 | 2 | no | — |
| 133 | D12 | — | 4 | 2 | no | — |
| 134 | D12 | — | 4 | 2 | no | — |
| 135 | D12 | — | 6 | 1 | no | — |
| 136 | C4×D3 | — | 6 | 2 | no | — |
| 137 | C4×D3 | — | 6 | 2 | no | — |
| 138 | Dic6 | — | 3 | 2 | no | — |
| 139 | Dic6 | — | 6 | 1 | no | — |
| 140 | C3×C8 | — | 2 | 1 | no | — |
| 141 | C3×C8 | — | 2 | 1 | no | — |
| 142 | C3×C8 | — | 12 | 2 | no | — |
| 143 | C3×C8 | #235 | 1 | 2 | yes | — |
| 144 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 145 | C3⋊C8 | — | 4 | 2 | no | — |
| 146 | C3⋊C8 | — | 6 | 2 | no | — |
| 147 | C3⋊C8 | — | 6 | 2 | no | — |
| 148 | C2×C32 | — | 2 | 1 | no | — |
| 149 | C2×C32 | #466 | 1 | 1 | yes | characteristic |
| 150 | C3⋊D3 | — | 4 | 1 | no | — |
| 151 | C3×D3 | — | 16 | 2 | no | — |
| 152 | #41 | — | 9 | 1 | no | — |
| 153 | C2×D4 | — | 6 | 2 | no | — |
| 154 | SD16 | — | 36 | 2 | no | — |
| 155 | D8 | — | 6 | 2 | no | — |
| 156 | D8 | — | 6 | 2 | no | — |
| 157 | D8 | — | 36 | 2 | no | — |
| 158 | M16 | — | 6 | 2 | no | — |
| 159 | M16 | — | 9 | 1 | no | — |
| 160 | M16 | — | 18 | 1 | no | — |
| 161 | C2×C8 | — | 18 | 1 | no | — |
| 162 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 163 | C16 | — | 2 | 1 | no | — |
| 164 | C16 | — | 9 | 1 | no | — |
| 165 | C16 | — | 9 | 1 | no | — |
| 166 | C22×C3 | — | 2 | 1 | no | — |
| 167 | C22×C3 | — | 24 | 2 | no | — |
| 168 | C22×C3 | — | 48 | 2 | no | — |
| 169 | C22×C3 | #916 | 1 | 2 | yes | — |
| 170 | C2×D3 | — | 6 | 2 | no | — |
| 171 | C2×D3 | — | 6 | 2 | no | — |
| 172 | C2×D3 | — | 8 | 2 | no | — |
| 173 | C2×D3 | — | 16 | 2 | no | — |
| 174 | C3×C4 | — | 2 | 1 | no | — |
| 175 | C3×C4 | — | 2 | 1 | no | — |
| 176 | C3×C4 | #884 | 1 | 2 | yes | — |
| 177 | C3×C4 | D3×D8 | 1 | 2 | yes | — |
| 178 | Dic3 | — | 6 | 2 | no | — |
| 179 | Dic3 | — | 6 | 2 | no | — |
| 180 | C32 | #2221 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 181 | C23 | — | 12 | 2 | no | — |
| 182 | Q8 | — | 9 | 1 | no | — |
| 183 | D4 | — | 9 | 1 | no | — |
| 184 | D4 | — | 12 | 2 | no | — |
| 185 | D4 | — | 12 | 2 | no | — |
| 186 | D4 | — | 18 | 1 | no | — |
| 187 | C2×C4 | — | 18 | 1 | no | — |
| 188 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 189 | C8 | — | 12 | 2 | no | — |
| 190 | C8 | — | 18 | 1 | no | — |
| 191 | C8 | #3798 | 1 | 1 | yes | characteristic |
| 192 | C8 | #3811 | 1 | 1 | yes | characteristic |
| 193 | C2×C3 | — | 2 | 2 | no | — |
| 194 | C2×C3 | — | 2 | 1 | no | — |
| 195 | C2×C3 | — | 4 | 1 | no | — |
| 196 | C2×C3 | — | 48 | 2 | no | — |
| 197 | C2×C3 | #4775 | 1 | 2 | yes | — |
| 198 | D3 | — | 12 | 2 | no | — |
| 199 | D3 | — | 12 | 2 | no | — |
| 200 | D3 | — | 16 | 2 | no | — |
| 201 | C22 | — | 18 | 1 | no | — |
| 202 | C22 | — | 24 | 2 | no | — |
| 203 | C22 | — | 48 | 2 | no | — |
| 204 | C22 | #63809 | 1 | 1 | yes | characteristic |
| 205 | C4 | — | 18 | 1 | no | — |
| 206 | C4 | #63797 | 1 | 1 | yes | characteristic |
| 207 | C4 | #63912 | 1 | 1 | yes | characteristic |
| 208 | C3 | — | 2 | 1 | no | — |
| 209 | C3 | #69260 | 1 | 2 | yes | complemented |
| 210 | C2 | — | 2 | 1 | no | — |
| 211 | C2 | — | 36 | 1 | no | — |
| 212 | C2 | — | 48 | 2 | no | — |
| 213 | C2 | #10590839 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10592606 | C2 | semidirect |
| 2. #10590929 | C2 | semidirect |
| 3. C2×#63545 | C2 | semidirect |
| 4. C3×#4516 | C2 | semidirect |
| 5. #10589144 | C2 | semidirect |
| 24. #4516 | D3 | semidirect |
| 180. C32 | #2221 | semidirect |
| 209. C3 | #69260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592606 | 2 |
| #10590929 | 2 |
| C2×#63545 | 2 |
| C3×#4516 | 2 |
| #10589144 | 2 |
| #69260 | 3 |