Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #10596154 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10592759 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10592413 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C32×#329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589330 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #68353 | — | 3 | 4 | no | maximal |
| 7 | C32×#124 | C22 | 1 | 1 | yes | characteristic |
| 8 | #64156 | — | 2 | 1 | no | — |
| 9 | C2×#3756 | — | 2 | 1 | no | — |
| 10 | #64146 | — | 2 | 1 | no | — |
| 11 | C2×#3754 | — | 2 | 1 | no | — |
| 12 | #64094 | — | 2 | 2 | no | — |
| 13 | #64091 | — | 2 | 2 | no | — |
| 14 | #64084 | C22 | 1 | 2 | yes | — |
| 15 | #64078 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C32×#97 | C22 | 1 | 2 | yes | complemented |
| 17 | #63648 | — | 2 | 2 | no | — |
| 18 | #63643 | — | 2 | 2 | no | — |
| 19 | #63630 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #5683 | — | 3 | 4 | no | — |
| 21 | #5060 | — | 3 | 4 | no | — |
| 22 | #4714 | — | 3 | 8 | no | — |
| 23 | C3×#329 | D3 | 1 | 4 | yes | complemented |
| 24 | #4464 | — | 3 | 8 | no | — |
| 25 | C23×C3⋊D3 | — | 2 | 1 | no | — |
| 26 | C2×C32×Q8 | D4 | 1 | 1 | yes | characteristic |
| 27 | C2×C32×D4 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×#638 | — | 2 | 2 | no | — |
| 29 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 30 | C2×C4⋊(C3⋊D3) | D4 | 1 | 2 | yes | — |
| 31 | C2×#634 | — | 2 | 1 | no | — |
| 32 | C2×#634 | D4 | 1 | 2 | yes | — |
| 33 | C2×C32×C8 | — | 2 | 2 | no | — |
| 34 | C32×C22⋊C4 | — | 2 | 2 | no | — |
| 35 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 36 | #3757 | — | 2 | 1 | no | — |
| 37 | #3756 | — | 4 | 2 | no | — |
| 38 | #3754 | — | 4 | 2 | no | — |
| 39 | #3752 | — | 2 | 2 | no | — |
| 40 | #3752 | — | 2 | 2 | no | — |
| 41 | #3752 | — | 2 | 2 | no | — |
| 42 | C4⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 43 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 44 | C2×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 45 | #1659 | — | 9 | 1 | no | Sylow |
| 46 | C3×#124 | C2×D3 | 1 | 4 | yes | — |
| 47 | #947 | — | 6 | 4 | no | — |
| 48 | C2×#216 | — | 6 | 4 | no | — |
| 49 | #937 | — | 6 | 4 | no | — |
| 50 | C2×#214 | — | 6 | 4 | no | — |
| 51 | #885 | — | 6 | 8 | no | — |
| 52 | #882 | — | 6 | 8 | no | — |
| 53 | #875 | — | 3 | 8 | no | — |
| 54 | #869 | — | 3 | 4 | no | — |
| 55 | C3×#97 | C2×D3 | 1 | 8 | yes | complemented |
| 56 | #821 | — | 6 | 8 | no | — |
| 57 | #816 | — | 6 | 8 | no | — |
| 58 | #803 | — | 3 | 4 | no | — |
| 59 | C23×C32 | — | 2 | 1 | no | — |
| 60 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 61 | C22×C3⋊D3 | — | 8 | 1 | no | — |
| 62 | C22×C3⋊D3 | — | 8 | 2 | no | — |
| 63 | C32×Q8 | — | 4 | 1 | no | — |
| 64 | C32×D4 | — | 4 | 1 | no | — |
| 65 | C2×C32×C4 | — | 2 | 1 | no | — |
| 66 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 67 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 68 | #638 | — | 8 | 2 | no | — |
| 69 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 70 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 71 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 72 | C4⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 73 | #634 | — | 4 | 2 | no | — |
| 74 | #634 | — | 4 | 1 | no | — |
| 75 | #634 | — | 4 | 1 | no | — |
| 76 | C32×C8 | — | 4 | 2 | no | — |
| 77 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 78 | H(3,𝔽4) | — | 9 | 1 | no | — |
| 79 | #497 | — | 9 | 1 | no | — |
| 80 | #489 | — | 9 | 2 | no | — |
| 81 | #329 | — | 9 | 2 | no | — |
| 82 | #329 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 83 | C23×D3 | — | 6 | 4 | no | — |
| 84 | C2×C3×Q8 | D12 | 1 | 4 | yes | — |
| 85 | C2×C3×D4 | D12 | 1 | 4 | yes | — |
| 86 | C2×#67 | — | 6 | 8 | no | — |
| 87 | C2×D12 | — | 3 | 8 | no | — |
| 88 | C2×D12 | — | 6 | 4 | no | — |
| 89 | C2×Dic6 | — | 3 | 8 | no | — |
| 90 | C2×Dic6 | — | 6 | 4 | no | — |
| 91 | C2×C3×C8 | — | 2 | 8 | no | — |
| 92 | C3×C22⋊C4 | — | 2 | 8 | no | — |
| 93 | C3×C42 | C22×D3 | 1 | 4 | yes | — |
| 94 | #217 | — | 6 | 4 | no | — |
| 95 | #216 | — | 12 | 8 | no | — |
| 96 | #214 | — | 12 | 8 | no | — |
| 97 | (C2×D3)⋊C4 | — | 6 | 8 | no | — |
| 98 | (C2×D3)⋊C4 | — | 6 | 8 | no | — |
| 99 | (C2×D3)⋊C4 | — | 6 | 8 | no | — |
| 100 | C4⋊Dic3 | — | 6 | 8 | no | — |
| 101 | C4×Dic3 | — | 6 | 4 | no | — |
| 102 | C2×C3⋊C8 | — | 6 | 4 | no | — |
| 103 | C22×C32 | — | 4 | 1 | no | — |
| 104 | C22×C32 | — | 4 | 2 | no | — |
| 105 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 106 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 107 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 108 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 109 | C2×C3⋊D3 | — | 8 | 4 | no | — |
| 110 | C32×C4 | — | 2 | 1 | no | — |
| 111 | C32×C4 | — | 2 | 2 | no | — |
| 112 | C32×C4 | — | 4 | 1 | no | — |
| 113 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 114 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 115 | C2×Q16 | — | 18 | 1 | no | — |
| 116 | C2×SD16 | — | 18 | 1 | no | — |
| 117 | C4⋊Q8 | — | 9 | 1 | no | — |
| 118 | #124 | — | 9 | 2 | no | — |
| 119 | #124 | — | 18 | 2 | no | — |
| 120 | #124 | — | 18 | 1 | no | — |
| 121 | #124 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 122 | #120 | — | 18 | 2 | no | — |
| 123 | #120 | — | 18 | 1 | no | — |
| 124 | #103 | — | 18 | 2 | no | — |
| 125 | #102 | — | 18 | 2 | no | — |
| 126 | #97 | — | 9 | 1 | no | — |
| 127 | #97 | C2×C3⋊D3 | 1 | 2 | yes | complemented |
| 128 | C23×C3 | — | 2 | 4 | no | — |
| 129 | C22×D3 | — | 6 | 8 | no | — |
| 130 | C22×D3 | — | 24 | 4 | no | — |
| 131 | C22×D3 | — | 24 | 8 | no | — |
| 132 | C3×Q8 | — | 4 | 4 | no | — |
| 133 | C3×D4 | — | 4 | 4 | no | — |
| 134 | C2×C3×C4 | — | 2 | 4 | no | — |
| 135 | C2×C3×C4 | C2×D12 | 1 | 4 | yes | — |
| 136 | C2×C3×C4 | D3×D4 | 1 | 8 | yes | — |
| 137 | #67 | — | 24 | 8 | no | — |
| 138 | C2×Dic3 | — | 6 | 8 | no | — |
| 139 | C2×Dic3 | — | 12 | 4 | no | — |
| 140 | D12 | — | 12 | 8 | no | — |
| 141 | D12 | — | 24 | 4 | no | — |
| 142 | Dic6 | — | 12 | 8 | no | — |
| 143 | Dic6 | — | 12 | 4 | no | — |
| 144 | Dic6 | — | 12 | 4 | no | — |
| 145 | C3×C8 | — | 4 | 8 | no | — |
| 146 | C3⋊C8 | — | 6 | 8 | no | — |
| 147 | C2×C32 | — | 8 | 1 | no | — |
| 148 | C2×C32 | #453 | 1 | 1 | yes | characteristic |
| 149 | C2×C32 | #455 | 1 | 2 | yes | — |
| 150 | C3⋊D3 | — | 8 | 2 | no | — |
| 151 | C24 | — | 18 | 1 | no | — |
| 152 | C2×Q8 | — | 9 | 2 | no | — |
| 153 | C2×Q8 | — | 18 | 1 | no | — |
| 154 | C2×Q8 | C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 155 | C2×D4 | — | 9 | 2 | no | — |
| 156 | C2×D4 | — | 18 | 1 | no | — |
| 157 | C2×D4 | — | 18 | 2 | no | — |
| 158 | C2×D4 | C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 159 | Q16 | — | 36 | 2 | no | — |
| 160 | SD16 | — | 36 | 2 | no | — |
| 161 | C2×C8 | — | 2 | 2 | no | — |
| 162 | C2×C8 | — | 18 | 1 | no | — |
| 163 | C4⋊C4 | — | 18 | 2 | no | — |
| 164 | C22⋊C4 | — | 2 | 2 | no | — |
| 165 | C22⋊C4 | — | 18 | 2 | no | — |
| 166 | C22⋊C4 | — | 18 | 1 | no | — |
| 167 | C22⋊C4 | — | 18 | 2 | no | — |
| 168 | C22⋊C4 | — | 18 | 2 | no | — |
| 169 | C42 | — | 18 | 1 | no | — |
| 170 | C42 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 171 | C22×C3 | — | 4 | 4 | no | — |
| 172 | C22×C3 | — | 4 | 8 | no | — |
| 173 | C22×C3 | #882 | 1 | 4 | yes | — |
| 174 | C2×D3 | — | 12 | 8 | no | — |
| 175 | C2×D3 | — | 12 | 8 | no | — |
| 176 | C2×D3 | — | 12 | 8 | no | — |
| 177 | C2×D3 | — | 24 | 16 | no | — |
| 178 | C3×C4 | — | 2 | 4 | no | — |
| 179 | C3×C4 | — | 2 | 8 | no | — |
| 180 | C3×C4 | — | 4 | 4 | no | — |
| 181 | Dic3 | — | 12 | 8 | no | — |
| 182 | Dic3 | — | 24 | 4 | no | — |
| 183 | C32 | #1659 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 184 | C23 | — | 2 | 1 | no | — |
| 185 | C23 | — | 18 | 2 | no | — |
| 186 | C23 | — | 72 | 2 | no | — |
| 187 | C23 | — | 72 | 1 | no | — |
| 188 | Q8 | — | 4 | 1 | no | — |
| 189 | Q8 | — | 36 | 2 | no | — |
| 190 | Q8 | — | 36 | 1 | no | — |
| 191 | Q8 | — | 36 | 1 | no | — |
| 192 | D4 | — | 4 | 1 | no | — |
| 193 | D4 | — | 36 | 2 | no | — |
| 194 | D4 | — | 72 | 1 | no | — |
| 195 | D4 | — | 72 | 2 | no | — |
| 196 | C2×C4 | — | 2 | 1 | no | — |
| 197 | C2×C4 | — | 18 | 2 | no | — |
| 198 | C2×C4 | — | 36 | 1 | no | — |
| 199 | C2×C4 | C2×C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 200 | C2×C4 | D4×C3⋊D3 | 1 | 2 | yes | — |
| 201 | C8 | — | 4 | 2 | no | — |
| 202 | C8 | — | 18 | 2 | no | — |
| 203 | C2×C3 | — | 8 | 4 | no | — |
| 204 | C2×C3 | #4747 | 1 | 4 | yes | — |
| 205 | C2×C3 | #4825 | 1 | 8 | yes | — |
| 206 | D3 | — | 24 | 8 | no | — |
| 207 | C22 | — | 4 | 2 | no | — |
| 208 | C22 | — | 4 | 1 | no | — |
| 209 | C22 | — | 36 | 2 | no | — |
| 210 | C22 | — | 36 | 2 | no | — |
| 211 | C22 | — | 36 | 2 | no | — |
| 212 | C22 | — | 72 | 4 | no | — |
| 213 | C22 | #64091 | 1 | 1 | yes | characteristic |
| 214 | C4 | — | 2 | 2 | no | — |
| 215 | C4 | — | 2 | 1 | no | — |
| 216 | C4 | — | 4 | 1 | no | — |
| 217 | C4 | — | 36 | 2 | no | — |
| 218 | C4 | — | 72 | 1 | no | — |
| 219 | C3 | #68353 | 1 | 4 | yes | complemented |
| 220 | C2 | — | 8 | 1 | no | — |
| 221 | C2 | — | 72 | 2 | no | — |
| 222 | C2 | #10592446 | 1 | 1 | yes | characteristic |
| 223 | C2 | #10592524 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10592759 | C2 | semidirect |
| 3. #10592413 | C2 | semidirect |
| 4. C32×#329 | C2 | semidirect |
| 5. #10589330 | C2 | semidirect |
| 15. #64078 | C22 | semidirect |
| 16. C32×#97 | C22 | semidirect |
| 19. #63630 | C22 | semidirect |
| 23. C3×#329 | D3 | semidirect |
| 55. C3×#97 | C2×D3 | semidirect |
| 82. #329 | C3⋊D3 | semidirect |
| 127. #97 | C2×C3⋊D3 | semidirect |
| 183. C32 | #1659 | semidirect |
| 219. C3 | #68353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596154 | 2 |
| #10592759 | 2 |
| #10592413 | 2 |
| C32×#329 | 2 |
| #10589330 | 2 |
| #68353 | 3 |