Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
340 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 56 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 | C2×GO+(4,𝔽2)⋊C4 | C2 | 1 | 2 | yes | maximal |
| 2 | #10593553 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10593454 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10593267 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10593166 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C22×GO+(4,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 7 | C22×AGL(1,𝔽9) | C22 | 1 | 2 | yes | — |
| 8 | C2×C4⋊#157 | — | 2 | 1 | no | — |
| 9 | C2×C4×#157 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#3777 | — | 2 | 1 | no | — |
| 11 | C2×#3777 | C22 | 1 | 2 | yes | — |
| 12 | C2×#3773 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×D32⋊C4 | — | 2 | 1 | no | — |
| 14 | GO+(4,𝔽2)⋊C4 | — | 2 | 4 | no | — |
| 15 | #63921 | — | 2 | 1 | no | — |
| 16 | C22×D32 | — | 2 | 1 | no | — |
| 17 | C22×#157 | — | 2 | 2 | no | — |
| 18 | C22×#157 | D4 | 1 | 1 | yes | characteristic |
| 19 | C22×#157 | C23 | 1 | 1 | yes | characteristic |
| 20 | C2×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 21 | C2×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 22 | C2×GO+(4,𝔽2) | — | 2 | 1 | no | — |
| 23 | C2×GO+(4,𝔽2) | D4 | 1 | 2 | yes | — |
| 24 | C2×AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 25 | C2×AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 26 | C2×AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 27 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×#624 | — | 2 | 1 | no | — |
| 29 | C4⋊#157 | — | 4 | 2 | no | — |
| 30 | C4×#157 | — | 2 | 2 | no | — |
| 31 | #3777 | — | 2 | 2 | no | — |
| 32 | #3777 | — | 2 | 2 | no | — |
| 33 | #3777 | — | 4 | 2 | no | — |
| 34 | #3773 | — | 2 | 2 | no | — |
| 35 | D32⋊C4 | — | 4 | 2 | no | — |
| 36 | C3×(C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 37 | (C2×D3)⋊Dic3 | — | 4 | 1 | no | — |
| 38 | #2071 | — | 9 | 1 | no | maximal, Sylow |
| 39 | D3×C22⋊C4 | — | 12 | 1 | no | — |
| 40 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 41 | C22×C3×D3 | — | 4 | 1 | no | — |
| 42 | C2×D32 | — | 2 | 2 | no | — |
| 43 | C2×D32 | — | 4 | 1 | no | — |
| 44 | C2×D32 | — | 4 | 1 | no | — |
| 45 | C2×D32 | — | 4 | 1 | no | — |
| 46 | C2×D32 | — | 4 | 1 | no | — |
| 47 | C2×D32 | — | 4 | 1 | no | — |
| 48 | C2×#157 | — | 2 | 1 | no | — |
| 49 | C2×#157 | — | 2 | 1 | no | — |
| 50 | C2×#157 | — | 4 | 2 | no | — |
| 51 | C2×#157 | — | 4 | 2 | no | — |
| 52 | C2×#157 | — | 4 | 2 | no | — |
| 53 | C2×#157 | D8 | 1 | 2 | yes | — |
| 54 | C2×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 55 | C2×#157 | #41 | 1 | 2 | yes | — |
| 56 | C2×#157 | #41 | 1 | 2 | yes | — |
| 57 | C2×#157 | #41 | 1 | 1 | yes | characteristic |
| 58 | GO+(4,𝔽2) | — | 2 | 4 | no | — |
| 59 | GO+(4,𝔽2) | — | 4 | 2 | no | — |
| 60 | AGL(1,𝔽9) | — | 4 | 2 | no | — |
| 61 | C2×C32×C4 | SD16 | 1 | 1 | yes | characteristic |
| 62 | C2×C3⋊Dic3 | SD16 | 1 | 1 | yes | characteristic |
| 63 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 64 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 65 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 66 | #624 | — | 4 | 1 | no | — |
| 67 | #624 | — | 4 | 1 | no | — |
| 68 | C2×#102 | — | 9 | 2 | no | — |
| 69 | #390 | — | 9 | 1 | no | — |
| 70 | #384 | — | 9 | 1 | no | — |
| 71 | #340 | — | 9 | 2 | no | — |
| 72 | #336 | — | 9 | 1 | no | — |
| 73 | C23×D3 | — | 12 | 1 | no | — |
| 74 | C2×C4×D3 | — | 12 | 1 | no | — |
| 75 | C2×C4×D3 | — | 12 | 1 | no | — |
| 76 | C3×C22⋊C4 | — | 12 | 1 | no | — |
| 77 | #217 | — | 12 | 1 | no | — |
| 78 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 79 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 80 | C22×C32 | C2×SD16 | 1 | 1 | yes | characteristic |
| 81 | C2×C3⋊D3 | #121 | 1 | 1 | yes | characteristic |
| 82 | C2×C3⋊D3 | #123 | 1 | 1 | yes | characteristic |
| 83 | C2×C3⋊D3 | #124 | 1 | 1 | yes | characteristic |
| 84 | C2×C3⋊D3 | C2×D8 | 1 | 1 | yes | characteristic |
| 85 | C2×C3⋊D3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 86 | C2×C3⋊D3 | #137 | 1 | 1 | yes | characteristic |
| 87 | C2×C3×D3 | — | 4 | 2 | no | — |
| 88 | C2×C3×D3 | — | 8 | 1 | no | — |
| 89 | C2×C3×D3 | — | 8 | 1 | no | — |
| 90 | D32 | — | 4 | 2 | no | — |
| 91 | D32 | — | 4 | 2 | no | — |
| 92 | D32 | — | 8 | 1 | no | — |
| 93 | D32 | — | 8 | 1 | no | — |
| 94 | #157 | — | 2 | 2 | no | — |
| 95 | #157 | — | 8 | 2 | no | — |
| 96 | #157 | #123 | 1 | 2 | yes | — |
| 97 | #157 | #126 | 1 | 2 | yes | — |
| 98 | C32×C4 | — | 2 | 1 | no | — |
| 99 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 100 | C3×Dic3 | — | 8 | 1 | no | — |
| 101 | C22×D4 | — | 9 | 1 | no | — |
| 102 | C22×C8 | — | 9 | 2 | no | — |
| 103 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 104 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 105 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 106 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 107 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 108 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 109 | C2×C42 | — | 9 | 1 | no | — |
| 110 | #102 | — | 18 | 4 | no | — |
| 111 | C23×C3 | — | 12 | 1 | no | — |
| 112 | C22×D3 | — | 4 | 1 | no | — |
| 113 | C22×D3 | — | 12 | 1 | no | — |
| 114 | C22×D3 | — | 12 | 2 | no | — |
| 115 | C22×D3 | — | 12 | 2 | no | — |
| 116 | C22×D3 | — | 24 | 1 | no | — |
| 117 | C22×D3 | — | 24 | 1 | no | — |
| 118 | C22×D3 | — | 24 | 1 | no | — |
| 119 | C22×D3 | — | 24 | 1 | no | — |
| 120 | C2×C3×C4 | — | 4 | 1 | no | — |
| 121 | C2×C3×C4 | — | 12 | 1 | no | — |
| 122 | C2×Dic3 | — | 4 | 1 | no | — |
| 123 | C2×Dic3 | — | 12 | 1 | no | — |
| 124 | C4×D3 | — | 24 | 1 | no | — |
| 125 | C4×D3 | — | 24 | 1 | no | — |
| 126 | C4×D3 | — | 24 | 1 | no | — |
| 127 | C4×D3 | — | 24 | 1 | no | — |
| 128 | C2×C32 | #461 | 1 | 1 | yes | characteristic |
| 129 | C2×C32 | #481 | 1 | 1 | yes | characteristic |
| 130 | C2×C32 | #486 | 1 | 1 | yes | characteristic |
| 131 | C3⋊D3 | #397 | 1 | 1 | yes | characteristic |
| 132 | C3⋊D3 | #459 | 1 | 1 | yes | characteristic |
| 133 | C3⋊D3 | #480 | 1 | 1 | yes | characteristic |
| 134 | C3⋊D3 | #489 | 1 | 1 | yes | characteristic |
| 135 | C3×D3 | — | 8 | 2 | no | — |
| 136 | C24 | — | 18 | 1 | no | — |
| 137 | C2×D4 | — | 9 | 2 | no | — |
| 138 | C2×D4 | — | 18 | 2 | no | — |
| 139 | C2×D4 | — | 18 | 2 | no | — |
| 140 | C2×D4 | — | 18 | 1 | no | — |
| 141 | C22×C4 | — | 9 | 1 | no | — |
| 142 | C22×C4 | — | 9 | 1 | no | — |
| 143 | C22×C4 | — | 9 | 1 | no | — |
| 144 | C22×C4 | — | 18 | 1 | no | — |
| 145 | C22×C4 | — | 18 | 2 | no | — |
| 146 | C2×C8 | — | 18 | 2 | no | — |
| 147 | C2×C8 | — | 18 | 2 | no | — |
| 148 | C2×C8 | — | 18 | 2 | no | — |
| 149 | C4⋊C4 | — | 18 | 2 | no | — |
| 150 | C4⋊C4 | — | 18 | 2 | no | — |
| 151 | C4⋊C4 | — | 18 | 2 | no | — |
| 152 | C4⋊C4 | — | 36 | 2 | no | — |
| 153 | C4⋊C4 | — | 36 | 2 | no | — |
| 154 | C22⋊C4 | — | 12 | 1 | no | — |
| 155 | C22⋊C4 | — | 36 | 1 | no | — |
| 156 | C22⋊C4 | — | 36 | 2 | no | — |
| 157 | C42 | — | 18 | 2 | no | — |
| 158 | C22×C3 | — | 4 | 1 | no | — |
| 159 | C22×C3 | — | 12 | 2 | no | — |
| 160 | C22×C3 | — | 24 | 1 | no | — |
| 161 | C22×C3 | — | 24 | 1 | no | — |
| 162 | C2×D3 | — | 4 | 2 | no | — |
| 163 | C2×D3 | — | 8 | 1 | no | — |
| 164 | C2×D3 | — | 8 | 1 | no | — |
| 165 | C2×D3 | — | 12 | 1 | no | — |
| 166 | C2×D3 | — | 12 | 1 | no | — |
| 167 | C2×D3 | — | 12 | 1 | no | — |
| 168 | C2×D3 | — | 12 | 1 | no | — |
| 169 | C2×D3 | — | 12 | 1 | no | — |
| 170 | C2×D3 | — | 12 | 1 | no | — |
| 171 | C2×D3 | — | 24 | 2 | no | — |
| 172 | C2×D3 | — | 24 | 2 | no | — |
| 173 | C2×D3 | — | 24 | 2 | no | — |
| 174 | C2×D3 | — | 24 | 2 | no | — |
| 175 | C3×C4 | — | 8 | 1 | no | — |
| 176 | C3×C4 | — | 24 | 1 | no | — |
| 177 | Dic3 | — | 8 | 1 | no | — |
| 178 | Dic3 | — | 24 | 1 | no | — |
| 179 | C32 | #2071 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 180 | C23 | — | 9 | 1 | no | — |
| 181 | C23 | — | 12 | 1 | no | — |
| 182 | C23 | — | 18 | 2 | no | — |
| 183 | C23 | — | 36 | 1 | no | — |
| 184 | C23 | — | 36 | 1 | no | — |
| 185 | C23 | — | 36 | 1 | no | — |
| 186 | C23 | — | 36 | 1 | no | — |
| 187 | C23 | — | 36 | 1 | no | — |
| 188 | D4 | — | 18 | 4 | no | — |
| 189 | D4 | — | 36 | 2 | no | — |
| 190 | C2×C4 | — | 9 | 2 | no | — |
| 191 | C2×C4 | — | 9 | 1 | no | — |
| 192 | C2×C4 | — | 9 | 1 | no | — |
| 193 | C2×C4 | — | 9 | 2 | no | — |
| 194 | C2×C4 | — | 9 | 2 | no | — |
| 195 | C2×C4 | — | 9 | 1 | no | — |
| 196 | C2×C4 | — | 12 | 1 | no | — |
| 197 | C2×C4 | — | 18 | 1 | no | — |
| 198 | C2×C4 | — | 18 | 1 | no | — |
| 199 | C2×C4 | — | 18 | 1 | no | — |
| 200 | C2×C4 | — | 18 | 1 | no | — |
| 201 | C2×C4 | — | 36 | 1 | no | — |
| 202 | C2×C4 | — | 36 | 1 | no | — |
| 203 | C2×C4 | — | 36 | 2 | no | — |
| 204 | C2×C4 | — | 36 | 2 | no | — |
| 205 | C2×C4 | — | 36 | 2 | no | — |
| 206 | C2×C4 | AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 207 | C8 | — | 36 | 2 | no | — |
| 208 | C2×C3 | — | 4 | 1 | no | — |
| 209 | C2×C3 | — | 4 | 1 | no | — |
| 210 | C2×C3 | — | 4 | 1 | no | — |
| 211 | C2×C3 | — | 24 | 2 | no | — |
| 212 | D3 | — | 8 | 2 | no | — |
| 213 | D3 | — | 12 | 1 | no | — |
| 214 | D3 | — | 12 | 1 | no | — |
| 215 | D3 | — | 12 | 1 | no | — |
| 216 | D3 | — | 12 | 1 | no | — |
| 217 | C22 | — | 9 | 1 | no | — |
| 218 | C22 | — | 9 | 1 | no | — |
| 219 | C22 | — | 9 | 1 | no | — |
| 220 | C22 | — | 9 | 1 | no | — |
| 221 | C22 | — | 9 | 1 | no | — |
| 222 | C22 | — | 9 | 1 | no | — |
| 223 | C22 | — | 12 | 2 | no | — |
| 224 | C22 | — | 24 | 1 | no | — |
| 225 | C22 | — | 24 | 1 | no | — |
| 226 | C22 | — | 36 | 2 | no | — |
| 227 | C22 | — | 36 | 2 | no | — |
| 228 | C22 | — | 72 | 1 | no | — |
| 229 | C22 | — | 72 | 1 | no | — |
| 230 | C22 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 231 | C4 | — | 2 | 1 | no | — |
| 232 | C4 | — | 9 | 2 | no | — |
| 233 | C4 | — | 9 | 2 | no | — |
| 234 | C4 | — | 18 | 2 | no | — |
| 235 | C4 | — | 18 | 1 | no | — |
| 236 | C4 | — | 24 | 1 | no | — |
| 237 | C4 | — | 72 | 2 | no | — |
| 238 | C3 | — | 4 | 1 | no | — |
| 239 | C2 | — | 9 | 1 | no | — |
| 240 | C2 | — | 9 | 1 | no | — |
| 241 | C2 | — | 9 | 1 | no | — |
| 242 | C2 | — | 9 | 1 | no | — |
| 243 | C2 | — | 24 | 2 | no | — |
| 244 | C2 | #10596402 | 1 | 1 | yes | characteristic |
| 245 | C2 | #10596409 | 1 | 1 | yes | characteristic |
| 246 | C2 | #10596412 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10593553 | C2 | semidirect |
| 4. #10593267 | C2 | semidirect |
| 5. #10593166 | C2 | semidirect |
| 179. C32 | #2071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×GO+(4,𝔽2)⋊C4 | 2 |
| #10593553 | 2 |
| #10593454 | 2 |
| #10593267 | 2 |
| #10593166 | 2 |
| #2071 | 9 |