Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
471 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 471 conjugacy classes of subgroups — too many to draw. Only its 76 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 | #10589819 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10588753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10588526 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C9×#331 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10588162 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #68391 | — | 3 | 1 | no | maximal |
| 7 | C2×D4×D9 | — | 2 | 2 | no | — |
| 8 | C9×#127 | C22 | 1 | 1 | yes | characteristic |
| 9 | #63500 | — | 2 | 2 | no | — |
| 10 | #63499 | — | 2 | 2 | no | — |
| 11 | C2×#3672 | — | 2 | 2 | no | — |
| 12 | C4×D36 | C22 | 1 | 2 | yes | — |
| 13 | #63431 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C9×C4⋊C8 | C22 | 1 | 2 | yes | complemented |
| 15 | #63380 | — | 2 | 2 | no | — |
| 16 | #63377 | — | 2 | 2 | no | — |
| 17 | C4×C9⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #5717 | — | 3 | 1 | no | — |
| 19 | #5076 | — | 3 | 1 | no | — |
| 20 | #4842 | — | 3 | 2 | no | — |
| 21 | C3×#331 | D3 | 1 | 1 | yes | characteristic |
| 22 | #4483 | — | 3 | 2 | no | — |
| 23 | C23×D9 | — | 2 | 2 | no | — |
| 24 | C2×D4×C9 | — | 2 | 2 | no | — |
| 25 | C2×D4×C9 | D4 | 1 | 2 | yes | — |
| 26 | C2×#611 | — | 2 | 4 | no | — |
| 27 | D4×D9 | — | 4 | 4 | no | — |
| 28 | D4×D9 | — | 4 | 4 | no | — |
| 29 | C2×D36 | D4 | 1 | 2 | yes | — |
| 30 | C2×C4×D9 | — | 2 | 2 | no | — |
| 31 | C2×Dic18 | — | 2 | 1 | no | — |
| 32 | C2×C8×C9 | — | 2 | 2 | no | — |
| 33 | C42×C9 | C23 | 1 | 1 | yes | characteristic |
| 34 | #3676 | — | 2 | 2 | no | — |
| 35 | #3672 | — | 4 | 4 | no | — |
| 36 | (C2×D9)⋊C4 | — | 2 | 2 | no | — |
| 37 | C4⋊Dic9 | — | 2 | 2 | no | — |
| 38 | C4⋊Dic9 | D4 | 1 | 2 | yes | — |
| 39 | C2×C9⋊C8 | — | 2 | 1 | no | — |
| 40 | #1629 | — | 9 | 1 | no | Sylow |
| 41 | C2×D3×D4 | — | 6 | 2 | no | — |
| 42 | C3×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 43 | #938 | — | 6 | 2 | no | — |
| 44 | #937 | — | 6 | 2 | no | — |
| 45 | C2×#214 | — | 6 | 2 | no | — |
| 46 | C4×D12 | — | 3 | 2 | no | — |
| 47 | #869 | — | 3 | 1 | no | — |
| 48 | C3×C4⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 49 | #821 | — | 6 | 2 | no | — |
| 50 | #817 | — | 6 | 2 | no | — |
| 51 | C4×C3⋊C8 | — | 3 | 1 | no | — |
| 52 | C23×C9 | — | 2 | 2 | no | — |
| 53 | C22×D9 | — | 2 | 2 | no | — |
| 54 | C22×D9 | — | 4 | 8 | no | — |
| 55 | C22×D9 | — | 8 | 2 | no | — |
| 56 | D4×C9 | — | 4 | 2 | no | — |
| 57 | D4×C9 | — | 4 | 2 | no | — |
| 58 | D4×C9 | — | 4 | 2 | no | — |
| 59 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C4×C9 | C2×D4 | 1 | 2 | yes | — |
| 61 | #611 | — | 4 | 8 | no | — |
| 62 | C2×Dic9 | — | 2 | 2 | no | — |
| 63 | C2×Dic9 | — | 4 | 1 | no | — |
| 64 | D36 | — | 2 | 2 | no | — |
| 65 | D36 | SD16 | 1 | 4 | yes | complemented |
| 66 | C4×D9 | — | 4 | 2 | no | — |
| 67 | C4×D9 | — | 4 | 2 | no | — |
| 68 | Dic18 | — | 4 | 2 | no | — |
| 69 | C8×C9 | — | 4 | 2 | no | — |
| 70 | C9⋊C8 | — | 2 | 2 | no | — |
| 71 | D42 | — | 9 | 1 | no | — |
| 72 | #492 | — | 9 | 1 | no | — |
| 73 | #476 | — | 9 | 2 | no | — |
| 74 | #331 | D9 | 1 | 1 | yes | characteristic, complemented |
| 75 | D4⋊C8 | — | 9 | 2 | no | — |
| 76 | C23×D3 | — | 6 | 2 | no | — |
| 77 | C2×C3×D4 | — | 2 | 2 | no | — |
| 78 | C2×C3×D4 | D12 | 1 | 2 | yes | — |
| 79 | C2×#67 | — | 6 | 4 | no | — |
| 80 | D3×D4 | — | 12 | 4 | no | — |
| 81 | D3×D4 | — | 12 | 4 | no | — |
| 82 | C2×D12 | — | 3 | 2 | no | — |
| 83 | C2×C4×D3 | — | 6 | 2 | no | — |
| 84 | C2×Dic6 | — | 6 | 1 | no | — |
| 85 | C2×C3×C8 | — | 2 | 2 | no | — |
| 86 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 87 | #217 | — | 6 | 2 | no | — |
| 88 | #214 | — | 12 | 4 | no | — |
| 89 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 90 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 91 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 92 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 93 | C22×C9 | — | 4 | 4 | no | — |
| 94 | C22×C9 | — | 4 | 2 | no | — |
| 95 | C22×C9 | #120 | 1 | 1 | yes | characteristic |
| 96 | C2×D9 | — | 2 | 4 | no | — |
| 97 | C2×D9 | — | 4 | 2 | no | — |
| 98 | C2×D9 | — | 4 | 2 | no | — |
| 99 | C2×D9 | — | 8 | 8 | no | — |
| 100 | C4×C9 | — | 2 | 1 | no | — |
| 101 | C4×C9 | C2×SD16 | 1 | 2 | yes | — |
| 102 | C4×C9 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 103 | Dic9 | — | 4 | 2 | no | — |
| 104 | Dic9 | — | 8 | 1 | no | — |
| 105 | C22×D4 | — | 18 | 2 | no | — |
| 106 | C2×SD16 | — | 18 | 2 | no | — |
| 107 | C4⋊Q8 | — | 9 | 1 | no | — |
| 108 | #127 | C2×D9 | 1 | 1 | yes | characteristic |
| 109 | #121 | — | 18 | 2 | no | — |
| 110 | #120 | — | 18 | 2 | no | — |
| 111 | C4×D4 | — | 9 | 2 | no | — |
| 112 | #106 | — | 18 | 2 | no | — |
| 113 | C4⋊C8 | C2×D9 | 1 | 2 | yes | complemented |
| 114 | #102 | — | 18 | 2 | no | — |
| 115 | C4×C8 | — | 9 | 1 | no | — |
| 116 | C23×C3 | — | 2 | 2 | no | — |
| 117 | C22×D3 | — | 6 | 2 | no | — |
| 118 | C22×D3 | — | 12 | 8 | no | — |
| 119 | C22×D3 | — | 24 | 2 | no | — |
| 120 | C3×D4 | — | 4 | 2 | no | — |
| 121 | C3×D4 | — | 4 | 2 | no | — |
| 122 | C3×D4 | — | 4 | 2 | no | — |
| 123 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 124 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 125 | #67 | — | 12 | 8 | no | — |
| 126 | C2×Dic3 | — | 6 | 2 | no | — |
| 127 | C2×Dic3 | — | 12 | 1 | no | — |
| 128 | D12 | — | 3 | 4 | no | — |
| 129 | D12 | — | 6 | 2 | no | — |
| 130 | C4×D3 | — | 12 | 2 | no | — |
| 131 | C4×D3 | — | 12 | 2 | no | — |
| 132 | Dic6 | — | 12 | 2 | no | — |
| 133 | C3×C8 | — | 4 | 2 | no | — |
| 134 | C3⋊C8 | — | 6 | 2 | no | — |
| 135 | C2×C9 | — | 8 | 2 | no | — |
| 136 | C2×C9 | #450 | 1 | 2 | yes | — |
| 137 | C2×C9 | #453 | 1 | 1 | yes | characteristic |
| 138 | D9 | — | 4 | 4 | no | — |
| 139 | C24 | — | 18 | 2 | no | — |
| 140 | C2×Q8 | — | 18 | 1 | no | — |
| 141 | C2×D4 | — | 2 | 2 | no | — |
| 142 | C2×D4 | — | 9 | 2 | no | — |
| 143 | C2×D4 | — | 18 | 4 | no | — |
| 144 | C2×D4 | — | 36 | 4 | no | — |
| 145 | C2×D4 | — | 36 | 4 | no | — |
| 146 | C2×D4 | D36 | 1 | 2 | yes | — |
| 147 | C22×C4 | — | 18 | 2 | no | — |
| 148 | SD16 | — | 36 | 4 | no | — |
| 149 | C2×C8 | — | 2 | 2 | no | — |
| 150 | C2×C8 | — | 18 | 1 | no | — |
| 151 | C4⋊C4 | — | 9 | 2 | no | — |
| 152 | C4⋊C4 | — | 18 | 2 | no | — |
| 153 | C22⋊C4 | — | 18 | 2 | no | — |
| 154 | C22⋊C4 | — | 18 | 2 | no | — |
| 155 | C42 | C22×D9 | 1 | 1 | yes | characteristic |
| 156 | C22×C3 | — | 4 | 2 | no | — |
| 157 | C22×C3 | — | 4 | 4 | no | — |
| 158 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 159 | C2×D3 | — | 6 | 4 | no | — |
| 160 | C2×D3 | — | 12 | 2 | no | — |
| 161 | C2×D3 | — | 12 | 2 | no | — |
| 162 | C2×D3 | — | 24 | 8 | no | — |
| 163 | C3×C4 | — | 2 | 1 | no | — |
| 164 | C3×C4 | #911 | 1 | 2 | yes | — |
| 165 | C3×C4 | D3×SD16 | 1 | 2 | yes | — |
| 166 | Dic3 | — | 12 | 2 | no | — |
| 167 | Dic3 | — | 24 | 1 | no | — |
| 168 | C9 | #1629 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 169 | C23 | — | 2 | 2 | no | — |
| 170 | C23 | — | 18 | 2 | no | — |
| 171 | C23 | — | 36 | 8 | no | — |
| 172 | C23 | — | 72 | 2 | no | — |
| 173 | Q8 | — | 36 | 2 | no | — |
| 174 | D4 | — | 4 | 2 | no | — |
| 175 | D4 | — | 4 | 2 | no | — |
| 176 | D4 | — | 4 | 2 | no | — |
| 177 | D4 | — | 9 | 4 | no | — |
| 178 | D4 | — | 18 | 2 | no | — |
| 179 | D4 | — | 36 | 8 | no | — |
| 180 | C2×C4 | — | 18 | 2 | no | — |
| 181 | C2×C4 | — | 36 | 2 | no | — |
| 182 | C2×C4 | — | 36 | 2 | no | — |
| 183 | C2×C4 | — | 36 | 1 | no | — |
| 184 | C2×C4 | C2×D36 | 1 | 1 | yes | characteristic |
| 185 | C2×C4 | D4×D9 | 1 | 2 | yes | — |
| 186 | C8 | — | 4 | 2 | no | — |
| 187 | C8 | — | 18 | 2 | no | — |
| 188 | C2×C3 | — | 8 | 2 | no | — |
| 189 | C2×C3 | #4747 | 1 | 1 | yes | characteristic |
| 190 | C2×C3 | #4776 | 1 | 2 | yes | — |
| 191 | D3 | — | 12 | 4 | no | — |
| 192 | C22 | — | 4 | 2 | no | — |
| 193 | C22 | — | 4 | 4 | no | — |
| 194 | C22 | — | 18 | 4 | no | — |
| 195 | C22 | — | 36 | 2 | no | — |
| 196 | C22 | — | 36 | 2 | no | — |
| 197 | C22 | — | 72 | 8 | no | — |
| 198 | C22 | #63444 | 1 | 1 | yes | characteristic |
| 199 | C4 | — | 2 | 1 | no | — |
| 200 | C4 | — | 36 | 2 | no | — |
| 201 | C4 | — | 72 | 1 | no | — |
| 202 | C4 | #63473 | 1 | 2 | yes | — |
| 203 | C4 | SD16×D9 | 1 | 2 | yes | — |
| 204 | C3 | #68391 | 1 | 1 | yes | characteristic |
| 205 | C2 | — | 8 | 2 | no | — |
| 206 | C2 | — | 36 | 4 | no | — |
| 207 | C2 | #10588427 | 1 | 1 | yes | characteristic |
| 208 | C2 | #10588456 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10588753 | C2 | semidirect |
| 3. #10588526 | C2 | semidirect |
| 4. C9×#331 | C2 | semidirect |
| 5. #10588162 | C2 | semidirect |
| 13. #63431 | C22 | semidirect |
| 14. C9×C4⋊C8 | C22 | semidirect |
| 17. C4×C9⋊C8 | C22 | semidirect |
| 65. D36 | SD16 | semidirect |
| 74. #331 | D9 | semidirect |
| 113. C4⋊C8 | C2×D9 | semidirect |
| 168. C9 | #1629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589819 | 2 |
| #10588753 | 2 |
| #10588526 | 2 |
| C9×#331 | 2 |
| #10588162 | 2 |
| #68391 | 3 |