Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2400 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 2400 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 | C2×C32×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596275 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10592943 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #10592942 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C2×#63661 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #84110 | — | 3 | 4 | no | maximal |
| 7 | C32×H(5,𝔽2) | — | 2 | 6 | no | — |
| 8 | C32×H(5,𝔽2) | C22 | 1 | 4 | yes | — |
| 9 | C2×C32×#41 | — | 2 | 3 | no | — |
| 10 | C22×C32×D4 | — | 2 | 3 | no | — |
| 11 | C22×C32×D4 | C22 | 1 | 3 | yes | — |
| 12 | C22×#638 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #64162 | — | 2 | 3 | no | — |
| 14 | C2×#3757 | C22 | 1 | 3 | yes | complemented |
| 15 | #64148 | — | 2 | 6 | no | — |
| 16 | #64146 | C22 | 1 | 6 | yes | complemented |
| 17 | #64144 | C22 | 1 | 6 | yes | complemented |
| 18 | #64138 | — | 2 | 3 | no | — |
| 19 | #63661 | C22 | 1 | 12 | yes | complemented |
| 20 | C2×C3×H(5,𝔽2) | D3 | 1 | 4 | yes | complemented |
| 21 | #5804 | — | 3 | 12 | no | — |
| 22 | #5244 | — | 3 | 16 | no | — |
| 23 | #5243 | — | 3 | 16 | no | — |
| 24 | C2×#834 | — | 3 | 12 | no | — |
| 25 | C24×C32 | — | 2 | 1 | no | — |
| 26 | C24×C32 | D4 | 1 | 3 | yes | complemented |
| 27 | C24×C32 | C23 | 1 | 1 | yes | characteristic |
| 28 | C23×C3⋊D3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 29 | C32×#41 | — | 2 | 12 | no | — |
| 30 | C32×#41 | — | 2 | 12 | no | — |
| 31 | C2×C32×Q8 | — | 2 | 1 | no | — |
| 32 | C2×C32×D4 | — | 2 | 3 | no | — |
| 33 | C2×C32×D4 | — | 2 | 12 | no | — |
| 34 | C2×C32×D4 | — | 2 | 6 | no | — |
| 35 | C2×C32×D4 | — | 2 | 12 | no | — |
| 36 | C2×C32×D4 | — | 2 | 6 | no | — |
| 37 | C2×C32×D4 | D4 | 1 | 6 | yes | complemented |
| 38 | C2×C32×D4 | C23 | 1 | 6 | yes | — |
| 39 | C22×C32×C4 | — | 2 | 3 | no | — |
| 40 | C22×C32×C4 | D4 | 1 | 3 | yes | complemented |
| 41 | C2×#638 | — | 2 | 3 | no | — |
| 42 | C2×#638 | — | 2 | 3 | no | — |
| 43 | C2×#638 | — | 2 | 6 | no | — |
| 44 | C22×C3⋊Dic3 | — | 2 | 3 | no | — |
| 45 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 46 | #3757 | — | 2 | 3 | no | — |
| 47 | #3757 | — | 2 | 6 | no | — |
| 48 | #3757 | C23 | 1 | 6 | yes | complemented |
| 49 | #3752 | — | 2 | 6 | no | — |
| 50 | #3750 | — | 2 | 6 | no | — |
| 51 | #3026 | — | 9 | 1 | no | Sylow |
| 52 | C3×H(5,𝔽2) | — | 2 | 24 | no | — |
| 53 | C3×H(5,𝔽2) | C2×D3 | 1 | 16 | yes | — |
| 54 | C2×C3×#41 | — | 2 | 12 | no | — |
| 55 | C22×C3×D4 | — | 2 | 12 | no | — |
| 56 | C22×C3×D4 | C2×D3 | 1 | 12 | yes | — |
| 57 | C22×#67 | — | 3 | 4 | no | — |
| 58 | #953 | — | 6 | 12 | no | — |
| 59 | C2×#217 | — | 3 | 12 | no | — |
| 60 | #939 | — | 6 | 24 | no | — |
| 61 | #937 | — | 3 | 24 | no | — |
| 62 | #935 | — | 3 | 24 | no | — |
| 63 | #929 | — | 6 | 12 | no | — |
| 64 | #834 | — | 3 | 48 | no | — |
| 65 | C23×C32 | — | 2 | 4 | no | — |
| 66 | C23×C32 | — | 2 | 3 | no | — |
| 67 | C23×C32 | — | 2 | 3 | no | — |
| 68 | C23×C32 | — | 8 | 1 | no | — |
| 69 | C23×C32 | — | 8 | 3 | no | — |
| 70 | C23×C32 | — | 8 | 2 | no | — |
| 71 | C23×C32 | C2×D4 | 1 | 6 | yes | — |
| 72 | C23×C32 | C2×D4 | 1 | 3 | yes | — |
| 73 | C23×C32 | C2×D4 | 1 | 3 | yes | — |
| 74 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 75 | C22×C3⋊D3 | — | 2 | 3 | no | — |
| 76 | C22×C3⋊D3 | — | 8 | 1 | no | — |
| 77 | C32×Q8 | — | 2 | 4 | no | — |
| 78 | C32×D4 | — | 2 | 12 | no | — |
| 79 | C32×D4 | — | 2 | 12 | no | — |
| 80 | C32×D4 | — | 2 | 12 | no | — |
| 81 | C2×C32×C4 | — | 2 | 12 | no | — |
| 82 | C2×C32×C4 | — | 2 | 3 | no | — |
| 83 | C2×C32×C4 | — | 2 | 3 | no | — |
| 84 | C2×C32×C4 | C2×D4 | 1 | 6 | yes | — |
| 85 | #638 | — | 4 | 1 | no | — |
| 86 | #638 | — | 4 | 3 | no | — |
| 87 | #638 | — | 8 | 6 | no | — |
| 88 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 89 | C2×C3⋊Dic3 | — | 2 | 6 | no | — |
| 90 | C2×C3⋊Dic3 | — | 8 | 3 | no | — |
| 91 | C2×H(5,𝔽2) | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 92 | #534 | — | 9 | 3 | no | — |
| 93 | #458 | — | 9 | 4 | no | — |
| 94 | B(4,𝔽2) | — | 9 | 4 | no | — |
| 95 | C2×#99 | — | 9 | 3 | no | — |
| 96 | C24×C3 | — | 2 | 4 | no | — |
| 97 | C24×C3 | #67 | 1 | 12 | yes | complemented |
| 98 | C24×C3 | C22×D3 | 1 | 4 | yes | — |
| 99 | C23×D3 | — | 3 | 4 | no | — |
| 100 | C3×#41 | — | 2 | 48 | no | — |
| 101 | C3×#41 | — | 2 | 48 | no | — |
| 102 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 103 | C2×C3×D4 | — | 2 | 12 | no | — |
| 104 | C2×C3×D4 | — | 2 | 48 | no | — |
| 105 | C2×C3×D4 | — | 2 | 24 | no | — |
| 106 | C2×C3×D4 | — | 2 | 48 | no | — |
| 107 | C2×C3×D4 | — | 2 | 24 | no | — |
| 108 | C2×C3×D4 | #67 | 1 | 24 | yes | complemented |
| 109 | C2×C3×D4 | C22×D3 | 1 | 24 | yes | — |
| 110 | C22×C3×C4 | — | 2 | 12 | no | — |
| 111 | C22×C3×C4 | #67 | 1 | 12 | yes | complemented |
| 112 | C2×#67 | — | 6 | 12 | no | — |
| 113 | C2×#67 | — | 6 | 12 | no | — |
| 114 | C2×#67 | — | 6 | 24 | no | — |
| 115 | C22×Dic3 | — | 3 | 4 | no | — |
| 116 | C22×Dic3 | — | 6 | 12 | no | — |
| 117 | #217 | — | 3 | 24 | no | — |
| 118 | #217 | — | 6 | 12 | no | — |
| 119 | #217 | — | 6 | 24 | no | — |
| 120 | (C2×D3)⋊C4 | — | 6 | 24 | no | — |
| 121 | Dic3⋊C4 | — | 6 | 24 | no | — |
| 122 | C22×C32 | — | 2 | 6 | no | — |
| 123 | C22×C32 | — | 4 | 3 | no | — |
| 124 | C22×C32 | — | 4 | 1 | no | — |
| 125 | C22×C32 | — | 4 | 3 | no | — |
| 126 | C22×C32 | — | 4 | 6 | no | — |
| 127 | C22×C32 | — | 4 | 6 | no | — |
| 128 | C22×C32 | — | 8 | 3 | no | — |
| 129 | C22×C32 | — | 8 | 4 | no | — |
| 130 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 131 | C22×C32 | #120 | 1 | 3 | yes | — |
| 132 | C22×C32 | C22×D4 | 1 | 3 | yes | — |
| 133 | C2×C3⋊D3 | — | 4 | 6 | no | — |
| 134 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 135 | C32×C4 | — | 2 | 6 | no | — |
| 136 | C3⋊Dic3 | — | 4 | 6 | no | — |
| 137 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 138 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 139 | H(5,𝔽2) | C2×C3⋊D3 | 1 | 4 | yes | — |
| 140 | C2×#41 | — | 2 | 3 | no | — |
| 141 | C22×D4 | — | 2 | 3 | no | — |
| 142 | C22×D4 | — | 9 | 1 | no | — |
| 143 | C22×D4 | C2×C3⋊D3 | 1 | 3 | yes | — |
| 144 | #123 | — | 9 | 6 | no | — |
| 145 | #123 | — | 18 | 3 | no | — |
| 146 | #121 | — | 18 | 6 | no | — |
| 147 | #120 | — | 9 | 6 | no | — |
| 148 | #120 | — | 18 | 3 | no | — |
| 149 | C2×C22⋊C4 | — | 9 | 3 | no | — |
| 150 | #99 | — | 9 | 12 | no | — |
| 151 | C23×C3 | — | 2 | 16 | no | — |
| 152 | C23×C3 | — | 2 | 12 | no | — |
| 153 | C23×C3 | — | 2 | 12 | no | — |
| 154 | C23×C3 | — | 8 | 4 | no | — |
| 155 | C23×C3 | — | 8 | 12 | no | — |
| 156 | C23×C3 | — | 8 | 8 | no | — |
| 157 | C23×C3 | C2×#67 | 1 | 24 | yes | — |
| 158 | C23×C3 | C2×#67 | 1 | 12 | yes | — |
| 159 | C23×C3 | C2×#67 | 1 | 12 | yes | — |
| 160 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 161 | C22×D3 | — | 6 | 12 | no | — |
| 162 | C22×D3 | — | 24 | 4 | no | — |
| 163 | C3×Q8 | — | 2 | 16 | no | — |
| 164 | C3×D4 | — | 2 | 48 | no | — |
| 165 | C3×D4 | — | 2 | 48 | no | — |
| 166 | C3×D4 | — | 2 | 48 | no | — |
| 167 | C2×C3×C4 | — | 2 | 48 | no | — |
| 168 | C2×C3×C4 | — | 2 | 12 | no | — |
| 169 | C2×C3×C4 | — | 2 | 12 | no | — |
| 170 | C2×C3×C4 | C2×#67 | 1 | 24 | yes | — |
| 171 | #67 | — | 12 | 4 | no | — |
| 172 | #67 | — | 12 | 12 | no | — |
| 173 | #67 | — | 24 | 24 | no | — |
| 174 | C2×Dic3 | — | 6 | 12 | no | — |
| 175 | C2×Dic3 | — | 6 | 24 | no | — |
| 176 | C2×Dic3 | — | 24 | 12 | no | — |
| 177 | C2×C32 | — | 2 | 3 | no | — |
| 178 | C2×C32 | — | 2 | 1 | no | — |
| 179 | C2×C32 | — | 2 | 3 | no | — |
| 180 | C2×C32 | — | 4 | 6 | no | — |
| 181 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 182 | C3⋊D3 | — | 8 | 1 | no | — |
| 183 | C24 | — | 2 | 1 | no | — |
| 184 | C24 | — | 9 | 1 | no | — |
| 185 | C24 | #638 | 1 | 3 | yes | complemented |
| 186 | C24 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 187 | #41 | — | 2 | 12 | no | — |
| 188 | #41 | — | 2 | 12 | no | — |
| 189 | C2×Q8 | — | 2 | 1 | no | — |
| 190 | C2×D4 | — | 2 | 3 | no | — |
| 191 | C2×D4 | — | 2 | 12 | no | — |
| 192 | C2×D4 | — | 2 | 6 | no | — |
| 193 | C2×D4 | — | 2 | 12 | no | — |
| 194 | C2×D4 | — | 2 | 6 | no | — |
| 195 | C2×D4 | — | 18 | 3 | no | — |
| 196 | C2×D4 | — | 18 | 3 | no | — |
| 197 | C2×D4 | — | 18 | 6 | no | — |
| 198 | C2×D4 | #638 | 1 | 6 | yes | complemented |
| 199 | C2×D4 | C22×C3⋊D3 | 1 | 6 | yes | — |
| 200 | C22×C4 | — | 2 | 3 | no | — |
| 201 | C22×C4 | — | 9 | 1 | no | — |
| 202 | C22×C4 | — | 18 | 3 | no | — |
| 203 | C22×C4 | #638 | 1 | 3 | yes | complemented |
| 204 | C4⋊C4 | — | 18 | 6 | no | — |
| 205 | C22⋊C4 | — | 9 | 6 | no | — |
| 206 | C22⋊C4 | — | 18 | 3 | no | — |
| 207 | C22⋊C4 | — | 18 | 6 | no | — |
| 208 | C22⋊C4 | — | 18 | 6 | no | — |
| 209 | C22×C3 | — | 2 | 24 | no | — |
| 210 | C22×C3 | — | 4 | 12 | no | — |
| 211 | C22×C3 | — | 4 | 4 | no | — |
| 212 | C22×C3 | — | 4 | 12 | no | — |
| 213 | C22×C3 | — | 4 | 24 | no | — |
| 214 | C22×C3 | — | 4 | 24 | no | — |
| 215 | C22×C3 | — | 8 | 12 | no | — |
| 216 | C22×C3 | — | 8 | 16 | no | — |
| 217 | C22×C3 | #953 | 1 | 4 | yes | — |
| 218 | C22×C3 | #953 | 1 | 12 | yes | — |
| 219 | C22×C3 | C22×#67 | 1 | 12 | yes | — |
| 220 | C2×D3 | — | 12 | 24 | no | — |
| 221 | C2×D3 | — | 12 | 4 | no | — |
| 222 | C3×C4 | — | 2 | 24 | no | — |
| 223 | Dic3 | — | 12 | 24 | no | — |
| 224 | Dic3 | — | 12 | 4 | no | — |
| 225 | C32 | #3026 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 226 | C23 | — | 2 | 4 | no | — |
| 227 | C23 | — | 2 | 3 | no | — |
| 228 | C23 | — | 2 | 3 | no | — |
| 229 | C23 | — | 8 | 1 | no | — |
| 230 | C23 | — | 8 | 3 | no | — |
| 231 | C23 | — | 8 | 2 | no | — |
| 232 | C23 | — | 18 | 3 | no | — |
| 233 | C23 | — | 72 | 1 | no | — |
| 234 | C23 | C2×#638 | 1 | 6 | yes | — |
| 235 | C23 | C2×#638 | 1 | 3 | yes | — |
| 236 | C23 | C2×#638 | 1 | 3 | yes | — |
| 237 | C23 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 238 | Q8 | — | 2 | 4 | no | — |
| 239 | D4 | — | 2 | 12 | no | — |
| 240 | D4 | — | 2 | 12 | no | — |
| 241 | D4 | — | 2 | 12 | no | — |
| 242 | D4 | — | 36 | 1 | no | — |
| 243 | D4 | — | 36 | 3 | no | — |
| 244 | D4 | — | 72 | 6 | no | — |
| 245 | C2×C4 | — | 2 | 12 | no | — |
| 246 | C2×C4 | — | 2 | 3 | no | — |
| 247 | C2×C4 | — | 2 | 3 | no | — |
| 248 | C2×C4 | — | 18 | 6 | no | — |
| 249 | C2×C4 | — | 18 | 3 | no | — |
| 250 | C2×C4 | — | 72 | 3 | no | — |
| 251 | C2×C4 | C2×#638 | 1 | 6 | yes | — |
| 252 | C2×C3 | — | 2 | 12 | no | — |
| 253 | C2×C3 | — | 2 | 4 | no | — |
| 254 | C2×C3 | — | 2 | 12 | no | — |
| 255 | C2×C3 | — | 4 | 24 | no | — |
| 256 | C2×C3 | C2×#953 | 1 | 4 | yes | — |
| 257 | D3 | — | 24 | 4 | no | — |
| 258 | C22 | — | 2 | 6 | no | — |
| 259 | C22 | — | 4 | 3 | no | — |
| 260 | C22 | — | 4 | 3 | no | — |
| 261 | C22 | — | 4 | 1 | no | — |
| 262 | C22 | — | 4 | 6 | no | — |
| 263 | C22 | — | 4 | 6 | no | — |
| 264 | C22 | — | 8 | 3 | no | — |
| 265 | C22 | — | 8 | 4 | no | — |
| 266 | C22 | — | 36 | 6 | no | — |
| 267 | C22 | — | 36 | 1 | no | — |
| 268 | C22 | #64162 | 1 | 1 | yes | characteristic |
| 269 | C22 | #64162 | 1 | 3 | yes | — |
| 270 | C22 | C22×#638 | 1 | 3 | yes | — |
| 271 | C4 | — | 2 | 6 | no | — |
| 272 | C4 | — | 36 | 6 | no | — |
| 273 | C4 | — | 36 | 1 | no | — |
| 274 | C3 | #84110 | 1 | 4 | yes | complemented |
| 275 | C2 | — | 2 | 3 | no | — |
| 276 | C2 | — | 2 | 1 | no | — |
| 277 | C2 | — | 2 | 3 | no | — |
| 278 | C2 | — | 4 | 6 | no | — |
| 279 | C2 | — | 72 | 1 | no | — |
| 280 | C2 | C2×#64162 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×H(5,𝔽2) | C2 | semidirect |
| 2. #10596275 | C2 | semidirect |
| 3. #10592943 | C2 | semidirect |
| 4. #10592942 | C2 | semidirect |
| 5. C2×#63661 | C2 | semidirect |
| 12. C22×#638 | C22 | semidirect |
| 14. C2×#3757 | C22 | semidirect |
| 16. #64146 | C22 | semidirect |
| 17. #64144 | C22 | semidirect |
| 19. #63661 | C22 | semidirect |
| 20. C2×C3×H(5,𝔽2) | D3 | semidirect |
| 26. C24×C32 | D4 | semidirect |
| 28. C23×C3⋊D3 | C23 | semidirect |
| 37. C2×C32×D4 | D4 | semidirect |
| 40. C22×C32×C4 | D4 | semidirect |
| 45. C22×C3⋊Dic3 | C23 | semidirect |
| 48. #3757 | C23 | semidirect |
| 91. C2×H(5,𝔽2) | C3⋊D3 | semidirect |
| 97. C24×C3 | #67 | semidirect |
| 108. C2×C3×D4 | #67 | semidirect |
| 111. C22×C3×C4 | #67 | semidirect |
| 185. C24 | #638 | semidirect |
| 198. C2×D4 | #638 | semidirect |
| 203. C22×C4 | #638 | semidirect |
| 225. C32 | #3026 | semidirect |
| 274. C3 | #84110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×H(5,𝔽2) | 2 |
| #10596275 | 2 |
| #10592943 | 2 |
| #10592942 | 2 |
| C2×#63661 | 2 |
| #84110 | 3 |