Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
303 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #10592566 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10590914 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#4487 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10589131 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10589110 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #69314 | — | 3 | 2 | no | maximal |
| 7 | C2×#3746 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#3743 | C22 | 1 | 1 | yes | characteristic |
| 9 | #64106 | — | 2 | 1 | no | — |
| 10 | #63818 | — | 2 | 1 | no | — |
| 11 | C32×#106 | C22 | 1 | 1 | yes | characteristic |
| 12 | #63637 | — | 2 | 1 | no | — |
| 13 | C3×#819 | C22 | 1 | 2 | yes | — |
| 14 | C3×#812 | C22 | 1 | 2 | yes | — |
| 15 | #63578 | — | 2 | 1 | no | — |
| 16 | #4893 | — | 3 | 2 | no | — |
| 17 | #4867 | — | 3 | 2 | no | — |
| 18 | #4867 | — | 6 | 1 | no | — |
| 19 | C3×#365 | — | 3 | 2 | no | — |
| 20 | #4517 | — | 3 | 2 | no | — |
| 21 | #4514 | — | 3 | 2 | no | — |
| 22 | #4496 | — | 3 | 2 | no | — |
| 23 | #4487 | D3 | 1 | 2 | yes | complemented |
| 24 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 25 | C2×#634 | — | 2 | 1 | no | — |
| 26 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 27 | C32×C4⋊C4 | — | 2 | 1 | no | — |
| 28 | #3752 | — | 4 | 1 | no | — |
| 29 | C4⋊(C3⋊Dic3) | — | 4 | 1 | no | — |
| 30 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 31 | #3746 | — | 2 | 2 | no | — |
| 32 | #3743 | — | 2 | 2 | no | — |
| 33 | C3×#208 | — | 2 | 2 | no | — |
| 34 | #3712 | — | 4 | 1 | no | — |
| 35 | #3710 | — | 4 | 1 | no | — |
| 36 | C3×C3⋊C16 | — | 2 | 2 | no | — |
| 37 | #2239 | — | 9 | 1 | no | Sylow |
| 38 | D3×M16 | — | 6 | 2 | no | — |
| 39 | C2×Dic12 | — | 3 | 2 | no | — |
| 40 | C2×Dic12 | — | 6 | 1 | no | — |
| 41 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 42 | C2×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 43 | #897 | — | 6 | 2 | no | — |
| 44 | #897 | — | 6 | 2 | no | — |
| 45 | C3×M32 | — | 3 | 2 | no | — |
| 46 | C3×#108 | — | 3 | 2 | no | — |
| 47 | C3×#106 | — | 2 | 1 | no | — |
| 48 | C3×#106 | C2×D3 | 1 | 2 | yes | — |
| 49 | #822 | — | 6 | 2 | no | — |
| 50 | #819 | C2×D3 | 1 | 2 | yes | — |
| 51 | #812 | C2×D3 | 1 | 2 | yes | — |
| 52 | #810 | — | 6 | 2 | no | — |
| 53 | #810 | — | 6 | 2 | no | — |
| 54 | C22×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic |
| 55 | C2×C32×C4 | — | 4 | 1 | no | — |
| 56 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 57 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 58 | C2×C3⋊Dic3 | SD16 | 1 | 1 | yes | characteristic |
| 59 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 60 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 61 | #634 | — | 4 | 1 | no | — |
| 62 | #634 | — | 4 | 1 | no | — |
| 63 | C32×C8 | #41 | 1 | 2 | yes | — |
| 64 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 65 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 66 | #470 | — | 9 | 1 | no | — |
| 67 | #430 | — | 9 | 1 | no | — |
| 68 | #365 | — | 3 | 2 | no | — |
| 69 | #362 | — | 9 | 2 | no | — |
| 70 | #349 | — | 9 | 1 | no | — |
| 71 | C2×C4×D3 | — | 3 | 2 | no | — |
| 72 | C2×C4×D3 | — | 6 | 1 | no | — |
| 73 | C2×Dic6 | — | 6 | 2 | no | — |
| 74 | C2×Dic6 | — | 6 | 2 | no | — |
| 75 | C3×M16 | — | 6 | 2 | no | — |
| 76 | C2×C3×C8 | — | 2 | 1 | no | — |
| 77 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 78 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 79 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 80 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 81 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 82 | C4⋊Dic3 | — | 12 | 2 | no | — |
| 83 | C4⋊Dic3 | — | 12 | 2 | no | — |
| 84 | #208 | — | 2 | 2 | no | — |
| 85 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 86 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 87 | Dic12 | — | 6 | 2 | no | — |
| 88 | Dic12 | — | 6 | 2 | no | — |
| 89 | Dic12 | — | 12 | 2 | no | — |
| 90 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 91 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 92 | ΓL(1,𝔽25) | — | 12 | 2 | no | — |
| 93 | ΓL(1,𝔽25) | — | 12 | 2 | no | — |
| 94 | D3×C8 | — | 12 | 2 | no | — |
| 95 | C3×C16 | — | 6 | 2 | no | — |
| 96 | C3⋊C16 | — | 2 | 2 | no | — |
| 97 | C22×C32 | C2×SD16 | 1 | 1 | yes | characteristic |
| 98 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 99 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 100 | C32×C4 | — | 8 | 1 | no | — |
| 101 | C32×C4 | #123 | 1 | 1 | yes | characteristic |
| 102 | C32×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 103 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 104 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 105 | C2×Q16 | — | 9 | 1 | no | — |
| 106 | C2×M16 | — | 9 | 1 | no | — |
| 107 | C2×M16 | — | 18 | 1 | no | — |
| 108 | C22⋊Q8 | — | 18 | 1 | no | — |
| 109 | M32 | — | 3 | 2 | no | — |
| 110 | #108 | — | 3 | 2 | no | — |
| 111 | #108 | — | 18 | 1 | no | — |
| 112 | #106 | D32 | 1 | 1 | yes | characteristic |
| 113 | #103 | — | 18 | 1 | no | — |
| 114 | C22×D3 | — | 3 | 2 | no | — |
| 115 | C22×D3 | — | 6 | 1 | no | — |
| 116 | C2×C3×C4 | — | 2 | 1 | no | — |
| 117 | C2×C3×C4 | — | 4 | 2 | no | — |
| 118 | C2×C3×C4 | — | 4 | 2 | no | — |
| 119 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 120 | C2×Dic3 | — | 3 | 2 | no | — |
| 121 | C2×Dic3 | — | 6 | 1 | no | — |
| 122 | C2×Dic3 | — | 12 | 2 | no | — |
| 123 | C2×Dic3 | — | 12 | 2 | no | — |
| 124 | C4×D3 | — | 6 | 2 | no | — |
| 125 | C4×D3 | — | 6 | 2 | no | — |
| 126 | C4×D3 | — | 12 | 1 | no | — |
| 127 | C4×D3 | — | 12 | 1 | no | — |
| 128 | Dic6 | — | 12 | 2 | no | — |
| 129 | Dic6 | — | 12 | 2 | no | — |
| 130 | Dic6 | — | 12 | 2 | no | — |
| 131 | Dic6 | — | 12 | 2 | no | — |
| 132 | C3×C8 | — | 2 | 2 | no | — |
| 133 | C3×C8 | — | 12 | 2 | no | — |
| 134 | C3×C8 | #235 | 1 | 2 | yes | — |
| 135 | C3×C8 | #239 | 1 | 2 | yes | — |
| 136 | C3⋊C8 | — | 4 | 2 | no | — |
| 137 | C3⋊C8 | — | 6 | 2 | no | — |
| 138 | C3⋊C8 | — | 12 | 1 | no | — |
| 139 | C2×C32 | — | 2 | 1 | no | — |
| 140 | C2×C32 | #481 | 1 | 1 | yes | characteristic |
| 141 | C3⋊D3 | — | 4 | 1 | no | — |
| 142 | C2×Q8 | — | 18 | 1 | no | — |
| 143 | C22×C4 | — | 9 | 1 | no | — |
| 144 | Q16 | — | 18 | 2 | no | — |
| 145 | M16 | — | 6 | 2 | no | — |
| 146 | M16 | — | 18 | 2 | no | — |
| 147 | M16 | — | 36 | 1 | no | — |
| 148 | C2×C8 | — | 9 | 1 | no | — |
| 149 | C2×C8 | — | 36 | 1 | no | — |
| 150 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 151 | C4⋊C4 | — | 2 | 1 | no | — |
| 152 | C4⋊C4 | — | 36 | 1 | no | — |
| 153 | C22⋊C4 | — | 36 | 1 | no | — |
| 154 | C16 | — | 6 | 2 | no | — |
| 155 | C22×C3 | — | 2 | 1 | no | — |
| 156 | C22×C3 | D3×SD16 | 1 | 2 | yes | — |
| 157 | C2×D3 | — | 6 | 2 | no | — |
| 158 | C2×D3 | — | 12 | 1 | no | — |
| 159 | C2×D3 | — | 12 | 2 | no | — |
| 160 | C2×D3 | — | 12 | 2 | no | — |
| 161 | C3×C4 | — | 2 | 1 | no | — |
| 162 | C3×C4 | — | 2 | 1 | no | — |
| 163 | C3×C4 | — | 8 | 2 | no | — |
| 164 | C3×C4 | — | 8 | 2 | no | — |
| 165 | C3×C4 | #894 | 1 | 2 | yes | — |
| 166 | C3×C4 | #914 | 1 | 2 | yes | — |
| 167 | Dic3 | — | 6 | 2 | no | — |
| 168 | Dic3 | — | 12 | 1 | no | — |
| 169 | Dic3 | — | 24 | 2 | no | — |
| 170 | Dic3 | — | 24 | 2 | no | — |
| 171 | C32 | #2239 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 172 | C23 | — | 9 | 1 | no | — |
| 173 | Q8 | — | 36 | 1 | no | — |
| 174 | Q8 | — | 36 | 1 | no | — |
| 175 | C2×C4 | — | 4 | 1 | no | — |
| 176 | C2×C4 | — | 9 | 1 | no | — |
| 177 | C2×C4 | — | 18 | 1 | no | — |
| 178 | C2×C4 | — | 18 | 1 | no | — |
| 179 | C2×C4 | — | 36 | 1 | no | — |
| 180 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 181 | C8 | — | 12 | 2 | no | — |
| 182 | C8 | — | 18 | 1 | no | — |
| 183 | C8 | #3799 | 1 | 2 | yes | — |
| 184 | C2×C3 | — | 2 | 2 | no | — |
| 185 | C2×C3 | — | 2 | 2 | no | — |
| 186 | C2×C3 | — | 2 | 1 | no | — |
| 187 | C2×C3 | #4863 | 1 | 2 | yes | — |
| 188 | D3 | — | 12 | 2 | no | — |
| 189 | D3 | — | 24 | 1 | no | — |
| 190 | C22 | — | 18 | 1 | no | — |
| 191 | C22 | — | 36 | 1 | no | — |
| 192 | C22 | #63930 | 1 | 1 | yes | characteristic |
| 193 | C4 | — | 8 | 1 | no | — |
| 194 | C4 | — | 18 | 1 | no | — |
| 195 | C4 | — | 72 | 1 | no | — |
| 196 | C4 | #63897 | 1 | 1 | yes | characteristic |
| 197 | C4 | #63941 | 1 | 1 | yes | characteristic |
| 198 | C3 | — | 2 | 1 | no | — |
| 199 | C3 | #69314 | 1 | 2 | yes | complemented |
| 200 | C2 | — | 2 | 1 | no | — |
| 201 | C2 | — | 36 | 1 | no | — |
| 202 | C2 | #10590445 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#4487 | C2 | semidirect |
| 4. #10589131 | C2 | semidirect |
| 23. #4487 | D3 | semidirect |
| 171. C32 | #2239 | semidirect |
| 199. C3 | #69314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592566 | 2 |
| #10590914 | 2 |
| C3×#4487 | 2 |
| #10589131 | 2 |
| #10589110 | 2 |
| #69314 | 3 |