Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2148 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 2148 conjugacy classes of subgroups — too many to draw. Only its 381 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 | C32×#585 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10596296 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10592942 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #10592939 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #84124 | — | 3 | 4 | no | maximal |
| 6 | C32×2−1+4 | — | 2 | 3 | no | — |
| 7 | C32×H(5,𝔽2) | — | 2 | 3 | no | — |
| 8 | C32×H(5,𝔽2) | C22 | 1 | 4 | yes | — |
| 9 | C2×C32×#41 | — | 2 | 6 | no | — |
| 10 | C2×C32×#41 | C22 | 1 | 3 | yes | — |
| 11 | C22×#634 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #64153 | — | 2 | 3 | no | — |
| 13 | #64145 | — | 2 | 3 | no | — |
| 14 | #64144 | C22 | 1 | 12 | yes | complemented |
| 15 | #64135 | C22 | 1 | 3 | yes | complemented |
| 16 | #64133 | — | 2 | 6 | no | — |
| 17 | #63661 | C22 | 1 | 12 | yes | complemented |
| 18 | C3×#585 | D3 | 1 | 4 | yes | — |
| 19 | #5825 | — | 3 | 12 | no | — |
| 20 | #5243 | — | 3 | 32 | no | — |
| 21 | #5240 | — | 3 | 12 | no | — |
| 22 | C32×#41 | — | 2 | 4 | no | — |
| 23 | C32×#41 | — | 2 | 12 | no | — |
| 24 | C32×#41 | — | 2 | 6 | no | — |
| 25 | C32×#41 | — | 2 | 12 | no | — |
| 26 | C32×#41 | — | 2 | 6 | no | — |
| 27 | C2×C32×Q8 | — | 2 | 6 | no | — |
| 28 | C2×C32×Q8 | D4 | 1 | 3 | yes | — |
| 29 | C2×C32×D4 | — | 2 | 6 | no | — |
| 30 | C2×C32×D4 | — | 2 | 12 | no | — |
| 31 | C2×C32×D4 | D4 | 1 | 3 | yes | — |
| 32 | C2×C32×D4 | C23 | 1 | 6 | yes | — |
| 33 | C22×C32×C4 | — | 2 | 4 | no | — |
| 34 | C22×C32×C4 | D4 | 1 | 6 | yes | — |
| 35 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 36 | C22×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 37 | C2×#634 | — | 2 | 3 | no | — |
| 38 | C2×#634 | — | 2 | 3 | no | — |
| 39 | #3757 | — | 2 | 12 | no | — |
| 40 | #3757 | C23 | 1 | 6 | yes | — |
| 41 | C4⋊(C3⋊Dic3) | — | 2 | 3 | no | — |
| 42 | #3750 | — | 2 | 12 | no | — |
| 43 | C4×C3⋊Dic3 | — | 2 | 3 | no | — |
| 44 | #3028 | — | 9 | 1 | no | Sylow |
| 45 | C3×2−1+4 | — | 2 | 12 | no | — |
| 46 | C3×H(5,𝔽2) | — | 2 | 12 | no | — |
| 47 | C3×H(5,𝔽2) | C2×D3 | 1 | 16 | yes | — |
| 48 | C2×C3×#41 | — | 2 | 24 | no | — |
| 49 | C2×C3×#41 | C2×D3 | 1 | 12 | yes | — |
| 50 | C22×Dic6 | — | 3 | 4 | no | — |
| 51 | #944 | — | 6 | 12 | no | — |
| 52 | #936 | — | 6 | 12 | no | — |
| 53 | #935 | — | 3 | 48 | no | — |
| 54 | #926 | — | 3 | 12 | no | — |
| 55 | #924 | — | 6 | 24 | no | — |
| 56 | #834 | — | 3 | 48 | no | — |
| 57 | C23×C32 | — | 2 | 4 | no | — |
| 58 | C23×C32 | C2×D4 | 1 | 6 | yes | — |
| 59 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 60 | C32×Q8 | — | 2 | 4 | no | — |
| 61 | C32×Q8 | — | 2 | 6 | no | — |
| 62 | C32×D4 | — | 2 | 12 | no | — |
| 63 | C32×D4 | — | 2 | 12 | no | — |
| 64 | C32×D4 | — | 2 | 6 | no | — |
| 65 | C2×C32×C4 | — | 2 | 12 | no | — |
| 66 | C2×C32×C4 | — | 2 | 6 | no | — |
| 67 | C2×C32×C4 | — | 2 | 6 | no | — |
| 68 | C2×C32×C4 | C2×D4 | 1 | 6 | yes | — |
| 69 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 70 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 71 | C2×C3⋊Dic3 | — | 2 | 6 | no | — |
| 72 | C2×C3⋊Dic3 | — | 2 | 6 | no | — |
| 73 | #634 | — | 4 | 1 | no | — |
| 74 | #634 | — | 4 | 3 | no | — |
| 75 | #585 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 76 | #536 | — | 9 | 3 | no | — |
| 77 | #458 | — | 9 | 8 | no | — |
| 78 | #410 | — | 9 | 3 | no | — |
| 79 | C3×#41 | — | 2 | 16 | no | — |
| 80 | C3×#41 | — | 2 | 48 | no | — |
| 81 | C3×#41 | — | 2 | 24 | no | — |
| 82 | C3×#41 | — | 2 | 48 | no | — |
| 83 | C3×#41 | — | 2 | 24 | no | — |
| 84 | C2×C3×Q8 | — | 2 | 24 | no | — |
| 85 | C2×C3×Q8 | #67 | 1 | 12 | yes | — |
| 86 | C2×C3×D4 | — | 2 | 24 | no | — |
| 87 | C2×C3×D4 | — | 2 | 48 | no | — |
| 88 | C2×C3×D4 | #67 | 1 | 12 | yes | — |
| 89 | C2×C3×D4 | C22×D3 | 1 | 24 | yes | — |
| 90 | C22×C3×C4 | — | 2 | 16 | no | — |
| 91 | C22×C3×C4 | #67 | 1 | 24 | yes | — |
| 92 | C22×C3×C4 | C22×D3 | 1 | 4 | yes | — |
| 93 | C22×Dic3 | — | 3 | 8 | no | — |
| 94 | C2×Dic6 | — | 6 | 12 | no | — |
| 95 | C2×Dic6 | — | 6 | 12 | no | — |
| 96 | #217 | — | 3 | 24 | no | — |
| 97 | #217 | — | 6 | 48 | no | — |
| 98 | C4⋊Dic3 | — | 6 | 12 | no | — |
| 99 | Dic3⋊C4 | — | 6 | 48 | no | — |
| 100 | C4×Dic3 | — | 6 | 12 | no | — |
| 101 | C22×C32 | — | 2 | 6 | no | — |
| 102 | C22×C32 | — | 4 | 1 | no | — |
| 103 | C22×C32 | — | 4 | 6 | no | — |
| 104 | C22×C32 | — | 8 | 4 | no | — |
| 105 | C22×C32 | C22×D4 | 1 | 3 | yes | — |
| 106 | C32×C4 | — | 2 | 6 | no | — |
| 107 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 108 | C32×C4 | #120 | 1 | 3 | yes | — |
| 109 | C3⋊Dic3 | — | 4 | 6 | no | — |
| 110 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 111 | 2−1+4 | — | 2 | 3 | no | — |
| 112 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 113 | H(5,𝔽2) | C2×C3⋊D3 | 1 | 4 | yes | — |
| 114 | C2×#41 | — | 2 | 6 | no | — |
| 115 | C2×#41 | C2×C3⋊D3 | 1 | 3 | yes | — |
| 116 | C22×Q8 | — | 9 | 1 | no | — |
| 117 | C4⋊Q8 | — | 18 | 3 | no | — |
| 118 | #124 | — | 18 | 3 | no | — |
| 119 | #123 | — | 9 | 12 | no | — |
| 120 | C22⋊Q8 | — | 18 | 6 | no | — |
| 121 | #117 | — | 9 | 3 | no | — |
| 122 | #99 | — | 9 | 12 | no | — |
| 123 | C23×C3 | — | 2 | 16 | no | — |
| 124 | C23×C3 | C2×#67 | 1 | 24 | yes | — |
| 125 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 126 | C3×Q8 | — | 2 | 16 | no | — |
| 127 | C3×Q8 | — | 2 | 24 | no | — |
| 128 | C3×D4 | — | 2 | 48 | no | — |
| 129 | C3×D4 | — | 2 | 48 | no | — |
| 130 | C3×D4 | — | 2 | 24 | no | — |
| 131 | C2×C3×C4 | — | 2 | 48 | no | — |
| 132 | C2×C3×C4 | — | 2 | 24 | no | — |
| 133 | C2×C3×C4 | — | 2 | 24 | no | — |
| 134 | C2×C3×C4 | C2×#67 | 1 | 24 | yes | — |
| 135 | C2×C3×C4 | C2×#67 | 1 | 12 | yes | — |
| 136 | C2×C3×C4 | C2×#67 | 1 | 12 | yes | — |
| 137 | C2×Dic3 | — | 6 | 24 | no | — |
| 138 | C2×Dic3 | — | 6 | 24 | no | — |
| 139 | Dic6 | — | 12 | 4 | no | — |
| 140 | Dic6 | — | 12 | 12 | no | — |
| 141 | C2×C32 | — | 2 | 3 | no | — |
| 142 | C2×C32 | — | 4 | 6 | no | — |
| 143 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 144 | #41 | — | 2 | 4 | no | — |
| 145 | #41 | — | 2 | 12 | no | — |
| 146 | #41 | — | 2 | 6 | no | — |
| 147 | #41 | — | 2 | 12 | no | — |
| 148 | #41 | — | 2 | 6 | no | — |
| 149 | C2×Q8 | — | 2 | 6 | no | — |
| 150 | C2×Q8 | — | 18 | 3 | no | — |
| 151 | C2×Q8 | — | 18 | 3 | no | — |
| 152 | C2×Q8 | #638 | 1 | 3 | yes | — |
| 153 | C2×D4 | — | 2 | 6 | no | — |
| 154 | C2×D4 | — | 2 | 12 | no | — |
| 155 | C2×D4 | #638 | 1 | 3 | yes | — |
| 156 | C2×D4 | C22×C3⋊D3 | 1 | 6 | yes | — |
| 157 | C22×C4 | — | 2 | 4 | no | — |
| 158 | C22×C4 | — | 9 | 2 | no | — |
| 159 | C22×C4 | #638 | 1 | 6 | yes | — |
| 160 | C22×C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 161 | C4⋊C4 | — | 18 | 3 | no | — |
| 162 | C4⋊C4 | — | 18 | 12 | no | — |
| 163 | C22⋊C4 | — | 9 | 6 | no | — |
| 164 | C22⋊C4 | — | 18 | 12 | no | — |
| 165 | C42 | — | 18 | 3 | no | — |
| 166 | C22×C3 | — | 2 | 24 | no | — |
| 167 | C22×C3 | — | 4 | 4 | no | — |
| 168 | C22×C3 | — | 4 | 24 | no | — |
| 169 | C22×C3 | — | 8 | 16 | no | — |
| 170 | C22×C3 | C22×#67 | 1 | 12 | yes | — |
| 171 | C3×C4 | — | 2 | 24 | no | — |
| 172 | C3×C4 | #953 | 1 | 4 | yes | — |
| 173 | C3×C4 | #953 | 1 | 12 | yes | — |
| 174 | Dic3 | — | 12 | 24 | no | — |
| 175 | Dic3 | — | 12 | 8 | no | — |
| 176 | C32 | #3028 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 177 | C23 | — | 2 | 4 | no | — |
| 178 | C23 | C2×#638 | 1 | 6 | yes | — |
| 179 | C23 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 180 | Q8 | — | 2 | 4 | no | — |
| 181 | Q8 | — | 2 | 6 | no | — |
| 182 | Q8 | — | 36 | 1 | no | — |
| 183 | Q8 | — | 36 | 3 | no | — |
| 184 | D4 | — | 2 | 12 | no | — |
| 185 | D4 | — | 2 | 12 | no | — |
| 186 | D4 | — | 2 | 6 | no | — |
| 187 | C2×C4 | — | 2 | 12 | no | — |
| 188 | C2×C4 | — | 2 | 6 | no | — |
| 189 | C2×C4 | — | 2 | 6 | no | — |
| 190 | C2×C4 | — | 18 | 6 | no | — |
| 191 | C2×C4 | — | 18 | 6 | no | — |
| 192 | C2×C4 | C2×#638 | 1 | 6 | yes | — |
| 193 | C2×C4 | C2×#638 | 1 | 3 | yes | — |
| 194 | C2×C4 | C2×#638 | 1 | 3 | yes | — |
| 195 | C2×C3 | — | 2 | 12 | no | — |
| 196 | C2×C3 | — | 4 | 24 | no | — |
| 197 | C2×C3 | C2×#953 | 1 | 4 | yes | — |
| 198 | C22 | — | 2 | 6 | no | — |
| 199 | C22 | — | 4 | 1 | no | — |
| 200 | C22 | — | 4 | 6 | no | — |
| 201 | C22 | — | 8 | 4 | no | — |
| 202 | C22 | C22×#638 | 1 | 3 | yes | — |
| 203 | C4 | — | 2 | 6 | no | — |
| 204 | C4 | — | 36 | 6 | no | — |
| 205 | C4 | — | 36 | 2 | no | — |
| 206 | C4 | #64162 | 1 | 1 | yes | characteristic |
| 207 | C4 | #64162 | 1 | 3 | yes | — |
| 208 | C3 | #84124 | 1 | 4 | yes | complemented |
| 209 | C2 | — | 2 | 3 | no | — |
| 210 | C2 | — | 4 | 6 | no | — |
| 211 | C2 | C2×#64162 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10596296 | C2 | semidirect |
| 3. #10592942 | C2 | semidirect |
| 4. #10592939 | C2 | semidirect |
| 11. C22×#634 | C22 | semidirect |
| 14. #64144 | C22 | semidirect |
| 15. #64135 | C22 | semidirect |
| 17. #63661 | C22 | semidirect |
| 176. C32 | #3028 | semidirect |
| 208. C3 | #84124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#585 | 2 |
| #10596296 | 2 |
| #10592942 | 2 |
| #10592939 | 2 |
| #84124 | 3 |