Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3606 conjugacy classes of subgroups.
The subgroup lattice has 429 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C32×#555 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10596193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10596141 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10596139 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10596070 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10596067 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10596024 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C4×#3830 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10596003 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #10595993 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #86959 | — | 3 | 4 | no | maximal |
| 13 | C2×#3832 | C22 | 1 | 2 | yes | — |
| 14 | C2×#3830 | C22 | 1 | 2 | yes | — |
| 15 | C2×#3830 | C22 | 1 | 4 | yes | — |
| 16 | C2×#3828 | C22 | 1 | 4 | yes | — |
| 17 | C32×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 18 | C32×#124 | C22 | 1 | 4 | yes | — |
| 19 | C32×#121 | C22 | 1 | 4 | yes | — |
| 20 | C32×C4×D4 | C22 | 1 | 2 | yes | — |
| 21 | C32×#117 | C22 | 1 | 4 | yes | — |
| 22 | #64156 | C22 | 1 | 2 | yes | — |
| 23 | #64153 | C22 | 1 | 4 | yes | — |
| 24 | #64149 | C22 | 1 | 4 | yes | — |
| 25 | #64149 | C22 | 1 | 4 | yes | — |
| 26 | #64148 | C22 | 1 | 8 | yes | — |
| 27 | D4×C3⋊Dic3 | C22 | 1 | 2 | yes | — |
| 28 | #64139 | C22 | 1 | 4 | yes | — |
| 29 | C4×#638 | C22 | 1 | 4 | yes | — |
| 30 | C2×C4×C3⋊Dic3 | C22 | 1 | 4 | yes | — |
| 31 | #64104 | C22 | 1 | 4 | yes | — |
| 32 | #64102 | C22 | 1 | 4 | yes | — |
| 33 | #64102 | C22 | 1 | 4 | yes | — |
| 34 | #64101 | C22 | 1 | 2 | yes | — |
| 35 | #64097 | C22 | 1 | 4 | yes | — |
| 36 | #64096 | C22 | 1 | 4 | yes | — |
| 37 | #64096 | C22 | 1 | 2 | yes | — |
| 38 | #64094 | C22 | 1 | 8 | yes | — |
| 39 | #64093 | C22 | 1 | 8 | yes | — |
| 40 | #64093 | C22 | 1 | 8 | yes | — |
| 41 | #64090 | C22 | 1 | 4 | yes | — |
| 42 | #64090 | C22 | 1 | 8 | yes | — |
| 43 | #64090 | C22 | 1 | 8 | yes | — |
| 44 | #64086 | C22 | 1 | 4 | yes | — |
| 45 | #64084 | C22 | 1 | 4 | yes | — |
| 46 | #64083 | C22 | 1 | 1 | yes | characteristic |
| 47 | #64081 | C22 | 1 | 8 | yes | — |
| 48 | C42×C3⋊D3 | C22 | 1 | 4 | yes | — |
| 49 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 50 | C4×#634 | C22 | 1 | 2 | yes | — |
| 51 | C3×#555 | D3 | 1 | 4 | yes | complemented |
| 52 | #5725 | — | 3 | 4 | no | — |
| 53 | #5722 | — | 3 | 4 | no | — |
| 54 | #5670 | — | 3 | 16 | no | — |
| 55 | #5668 | — | 3 | 16 | no | — |
| 56 | #5599 | — | 3 | 16 | no | — |
| 57 | #5596 | — | 3 | 16 | no | — |
| 58 | #5553 | — | 3 | 8 | no | — |
| 59 | C4×#237 | — | 3 | 8 | no | — |
| 60 | #5532 | — | 3 | 16 | no | — |
| 61 | #5522 | — | 3 | 16 | no | — |
| 62 | C2×C32×Q8 | C23 | 1 | 2 | yes | — |
| 63 | C2×C32×D4 | C23 | 1 | 2 | yes | — |
| 64 | C2×C32×D4 | C23 | 1 | 4 | yes | — |
| 65 | C22×C32×C4 | C23 | 1 | 4 | yes | — |
| 66 | C2×#638 | C23 | 1 | 8 | yes | — |
| 67 | C2×#638 | C23 | 1 | 4 | yes | — |
| 68 | C2×#638 | C23 | 1 | 8 | yes | — |
| 69 | C22×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 70 | C22×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 71 | #3832 | — | 4 | 4 | no | — |
| 72 | #3830 | — | 2 | 8 | no | — |
| 73 | #3830 | — | 4 | 8 | no | — |
| 74 | #3828 | — | 2 | 16 | no | — |
| 75 | C2×C4⋊(C3⋊D3) | C23 | 1 | 4 | yes | — |
| 76 | C2×C4⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 77 | C2×C4⋊(C3⋊D3) | C23 | 1 | 4 | yes | — |
| 78 | C2×C4×C3⋊D3 | C23 | 1 | 8 | yes | — |
| 79 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×C4×C3⋊D3 | C23 | 1 | 4 | yes | — |
| 81 | C2×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 82 | C2×#634 | C23 | 1 | 4 | yes | — |
| 83 | C2×#634 | C23 | 1 | 2 | yes | — |
| 84 | C32×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 85 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 86 | C32×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 87 | C32×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 88 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 89 | C32×C42 | C23 | 1 | 4 | yes | — |
| 90 | #3757 | C23 | 1 | 4 | yes | — |
| 91 | #3752 | C23 | 1 | 8 | yes | — |
| 92 | #3752 | C23 | 1 | 8 | yes | — |
| 93 | #3752 | C23 | 1 | 4 | yes | — |
| 94 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 95 | #3750 | C23 | 1 | 4 | yes | — |
| 96 | #3750 | C23 | 1 | 4 | yes | — |
| 97 | #3750 | C23 | 1 | 8 | yes | — |
| 98 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 99 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 100 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 101 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 102 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 103 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 104 | #3483 | — | 9 | 1 | no | Sylow |
| 105 | C2×#239 | — | 3 | 8 | no | — |
| 106 | C2×#237 | — | 3 | 8 | no | — |
| 107 | C2×#237 | — | 3 | 16 | no | — |
| 108 | C2×#235 | — | 3 | 16 | no | — |
| 109 | C3×C4⋊Q8 | C2×D3 | 1 | 4 | yes | — |
| 110 | C3×#124 | C2×D3 | 1 | 16 | yes | — |
| 111 | C3×#121 | C2×D3 | 1 | 16 | yes | — |
| 112 | C3×C4×D4 | C2×D3 | 1 | 8 | yes | — |
| 113 | C3×#117 | C2×D3 | 1 | 16 | yes | — |
| 114 | #947 | — | 3 | 8 | no | — |
| 115 | #944 | — | 3 | 16 | no | — |
| 116 | #940 | — | 3 | 16 | no | — |
| 117 | #940 | — | 3 | 16 | no | — |
| 118 | #939 | — | 3 | 32 | no | — |
| 119 | D4×Dic3 | — | 3 | 8 | no | — |
| 120 | #930 | — | 3 | 16 | no | — |
| 121 | C4×#67 | — | 3 | 16 | no | — |
| 122 | C2×C4×Dic3 | — | 3 | 16 | no | — |
| 123 | #895 | — | 3 | 16 | no | — |
| 124 | #893 | — | 3 | 16 | no | — |
| 125 | #893 | — | 3 | 16 | no | — |
| 126 | #892 | — | 3 | 8 | no | — |
| 127 | #888 | — | 3 | 16 | no | — |
| 128 | #887 | — | 3 | 16 | no | — |
| 129 | #887 | — | 3 | 8 | no | — |
| 130 | #885 | — | 3 | 32 | no | — |
| 131 | #884 | — | 3 | 32 | no | — |
| 132 | #884 | — | 3 | 32 | no | — |
| 133 | #67⋊C4 | — | 3 | 16 | no | — |
| 134 | #67⋊C4 | — | 3 | 32 | no | — |
| 135 | #67⋊C4 | — | 3 | 32 | no | — |
| 136 | #877 | — | 3 | 16 | no | — |
| 137 | #875 | — | 3 | 16 | no | — |
| 138 | #874 | — | 3 | 4 | no | — |
| 139 | #872 | — | 3 | 32 | no | — |
| 140 | C42×D3 | — | 3 | 16 | no | — |
| 141 | C42×D3 | — | 3 | 4 | no | — |
| 142 | C4×Dic6 | — | 3 | 8 | no | — |
| 143 | C23×C32 | C24 | 1 | 4 | yes | — |
| 144 | C22×C3⋊D3 | C24 | 1 | 4 | yes | — |
| 145 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 146 | C32×Q8 | — | 4 | 2 | no | — |
| 147 | C32×D4 | — | 2 | 4 | no | — |
| 148 | C32×D4 | — | 4 | 4 | no | — |
| 149 | C2×C32×C4 | — | 2 | 8 | no | — |
| 150 | C2×C32×C4 | C24 | 1 | 4 | yes | — |
| 151 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 152 | C2×C32×C4 | C24 | 1 | 4 | yes | — |
| 153 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 154 | #638 | — | 2 | 16 | no | — |
| 155 | #638 | — | 2 | 8 | no | — |
| 156 | #638 | — | 4 | 8 | no | — |
| 157 | C2×C3⋊Dic3 | — | 2 | 8 | no | — |
| 158 | C2×C3⋊Dic3 | — | 2 | 8 | no | — |
| 159 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 160 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 161 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 162 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 163 | C4⋊(C3⋊D3) | — | 2 | 8 | no | — |
| 164 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 165 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 166 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 167 | C4×C3⋊D3 | — | 2 | 16 | no | — |
| 168 | C4×C3⋊D3 | — | 2 | 8 | no | — |
| 169 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 170 | #634 | — | 4 | 4 | no | — |
| 171 | #634 | #41 | 1 | 8 | yes | complemented |
| 172 | Q82 | — | 9 | 1 | no | — |
| 173 | #555 | — | 9 | 4 | no | — |
| 174 | #555 | — | 9 | 4 | no | — |
| 175 | #555 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 176 | #550 | — | 9 | 4 | no | — |
| 177 | #550 | — | 9 | 2 | no | — |
| 178 | #532 | — | 9 | 1 | no | — |
| 179 | #532 | — | 9 | 4 | no | — |
| 180 | #532 | — | 9 | 4 | no | — |
| 181 | C4×#41 | — | 9 | 2 | no | — |
| 182 | C4×#41 | — | 9 | 4 | no | — |
| 183 | C2×C3×Q8 | C22×D3 | 1 | 8 | yes | — |
| 184 | C2×C3×D4 | C22×D3 | 1 | 8 | yes | — |
| 185 | C2×C3×D4 | C22×D3 | 1 | 16 | yes | — |
| 186 | C22×C3×C4 | C22×D3 | 1 | 16 | yes | — |
| 187 | C2×#67 | — | 3 | 32 | no | — |
| 188 | C2×#67 | — | 3 | 16 | no | — |
| 189 | C2×#67 | — | 3 | 32 | no | — |
| 190 | C22×Dic3 | — | 3 | 16 | no | — |
| 191 | C22×Dic3 | — | 3 | 16 | no | — |
| 192 | #239 | — | 12 | 16 | no | — |
| 193 | #237 | — | 6 | 32 | no | — |
| 194 | #237 | — | 12 | 32 | no | — |
| 195 | #235 | — | 6 | 64 | no | — |
| 196 | C2×D12 | — | 3 | 16 | no | — |
| 197 | C2×D12 | — | 3 | 8 | no | — |
| 198 | C2×D12 | — | 3 | 16 | no | — |
| 199 | C2×C4×D3 | — | 3 | 32 | no | — |
| 200 | C2×C4×D3 | — | 3 | 4 | no | — |
| 201 | C2×C4×D3 | — | 3 | 16 | no | — |
| 202 | C2×C4×D3 | — | 3 | 8 | no | — |
| 203 | C2×Dic6 | — | 3 | 8 | no | — |
| 204 | C2×Dic6 | — | 3 | 16 | no | — |
| 205 | C3×C4⋊C4 | C22×D3 | 1 | 16 | yes | — |
| 206 | C3×C4⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 207 | C3×C22⋊C4 | C22×D3 | 1 | 16 | yes | — |
| 208 | C3×C22⋊C4 | C22×D3 | 1 | 32 | yes | — |
| 209 | C3×C42 | C22×D3 | 1 | 4 | yes | — |
| 210 | C3×C42 | C22×D3 | 1 | 16 | yes | — |
| 211 | #217 | — | 3 | 16 | no | — |
| 212 | (C2×D3)⋊C4 | — | 3 | 32 | no | — |
| 213 | (C2×D3)⋊C4 | — | 3 | 32 | no | — |
| 214 | (C2×D3)⋊C4 | — | 3 | 16 | no | — |
| 215 | C4⋊Dic3 | — | 3 | 8 | no | — |
| 216 | Dic3⋊C4 | — | 3 | 16 | no | — |
| 217 | Dic3⋊C4 | — | 3 | 16 | no | — |
| 218 | Dic3⋊C4 | — | 3 | 32 | no | — |
| 219 | C4×Dic3 | — | 3 | 16 | no | — |
| 220 | C4×Dic3 | — | 3 | 16 | no | — |
| 221 | C4×Dic3 | — | 3 | 4 | no | — |
| 222 | C4×Dic3 | — | 3 | 16 | no | — |
| 223 | C4×Dic3 | — | 3 | 8 | no | — |
| 224 | C4×Dic3 | — | 3 | 16 | no | — |
| 225 | C22×C32 | — | 2 | 4 | no | — |
| 226 | C22×C32 | — | 2 | 4 | no | — |
| 227 | C22×C32 | — | 2 | 4 | no | — |
| 228 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 229 | C2×C3⋊D3 | — | 2 | 8 | no | — |
| 230 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 231 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 232 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 233 | C32×C4 | — | 2 | 4 | no | — |
| 234 | C32×C4 | — | 2 | 4 | no | — |
| 235 | C32×C4 | — | 2 | 1 | no | — |
| 236 | C32×C4 | C2×#41 | 1 | 4 | yes | — |
| 237 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 238 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 239 | C3⋊Dic3 | C2×#41 | 1 | 8 | yes | — |
| 240 | C3⋊Dic3 | H(5,𝔽2) | 1 | 2 | yes | — |
| 241 | C2×#41 | — | 9 | 2 | no | — |
| 242 | C2×#41 | — | 9 | 2 | no | — |
| 243 | C2×#41 | — | 9 | 4 | no | — |
| 244 | C2×#41 | — | 9 | 4 | no | — |
| 245 | C4⋊Q8 | — | 9 | 4 | no | — |
| 246 | C4⋊Q8 | — | 9 | 4 | no | — |
| 247 | C4⋊Q8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 248 | #127 | — | 9 | 4 | no | — |
| 249 | #127 | — | 9 | 4 | no | — |
| 250 | #127 | — | 9 | 1 | no | — |
| 251 | #124 | — | 9 | 2 | no | — |
| 252 | #124 | — | 9 | 8 | no | — |
| 253 | #124 | — | 9 | 4 | no | — |
| 254 | #124 | C2×C3⋊D3 | 1 | 4 | yes | — |
| 255 | #121 | — | 9 | 8 | no | — |
| 256 | #121 | — | 9 | 4 | no | — |
| 257 | #121 | — | 9 | 4 | no | — |
| 258 | #121 | — | 9 | 8 | no | — |
| 259 | #121 | — | 9 | 8 | no | — |
| 260 | #121 | C2×C3⋊D3 | 1 | 4 | yes | — |
| 261 | C4×Q8 | — | 9 | 2 | no | — |
| 262 | C4×Q8 | — | 9 | 4 | no | — |
| 263 | C4×Q8 | — | 9 | 2 | no | — |
| 264 | C4×D4 | — | 9 | 2 | no | — |
| 265 | C4×D4 | — | 9 | 4 | no | — |
| 266 | C4×D4 | — | 9 | 4 | no | — |
| 267 | C4×D4 | — | 9 | 4 | no | — |
| 268 | C4×D4 | — | 9 | 4 | no | — |
| 269 | C4×D4 | — | 9 | 8 | no | — |
| 270 | C4×D4 | — | 9 | 8 | no | — |
| 271 | C4×D4 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 272 | #117 | — | 9 | 2 | no | — |
| 273 | #117 | — | 9 | 4 | no | — |
| 274 | #117 | — | 9 | 8 | no | — |
| 275 | #117 | C2×C3⋊D3 | 1 | 4 | yes | — |
| 276 | C2×C42 | — | 9 | 4 | no | — |
| 277 | C2×C42 | — | 9 | 1 | no | — |
| 278 | C2×C42 | — | 9 | 4 | no | — |
| 279 | C23×C3 | C23×D3 | 1 | 16 | yes | — |
| 280 | C22×D3 | — | 3 | 16 | no | — |
| 281 | C22×D3 | — | 3 | 4 | no | — |
| 282 | C3×Q8 | — | 4 | 8 | no | — |
| 283 | C3×D4 | — | 2 | 16 | no | — |
| 284 | C3×D4 | — | 4 | 16 | no | — |
| 285 | C2×C3×C4 | — | 2 | 32 | no | — |
| 286 | C2×C3×C4 | C23×D3 | 1 | 16 | yes | — |
| 287 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 288 | C2×C3×C4 | C23×D3 | 1 | 16 | yes | — |
| 289 | C2×C3×C4 | C23×D3 | 1 | 8 | yes | — |
| 290 | #67 | — | 6 | 64 | no | — |
| 291 | #67 | — | 6 | 32 | no | — |
| 292 | #67 | — | 12 | 32 | no | — |
| 293 | C2×Dic3 | — | 3 | 4 | no | — |
| 294 | C2×Dic3 | — | 3 | 16 | no | — |
| 295 | C2×Dic3 | — | 3 | 8 | no | — |
| 296 | C2×Dic3 | — | 3 | 16 | no | — |
| 297 | C2×Dic3 | — | 6 | 32 | no | — |
| 298 | C2×Dic3 | — | 6 | 32 | no | — |
| 299 | D12 | — | 6 | 32 | no | — |
| 300 | D12 | — | 12 | 16 | no | — |
| 301 | D12 | — | 12 | 8 | no | — |
| 302 | C4×D3 | — | 6 | 64 | no | — |
| 303 | C4×D3 | — | 6 | 32 | no | — |
| 304 | C4×D3 | — | 6 | 8 | no | — |
| 305 | C4×D3 | — | 6 | 16 | no | — |
| 306 | Dic6 | — | 3 | 32 | no | — |
| 307 | Dic6 | — | 12 | 16 | no | — |
| 308 | C2×C32 | — | 4 | 4 | no | — |
| 309 | C2×C32 | C22×#41 | 1 | 2 | yes | — |
| 310 | C2×C32 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 311 | C3⋊D3 | — | 4 | 4 | no | — |
| 312 | C3⋊D3 | — | 4 | 1 | no | — |
| 313 | #41 | — | 18 | 16 | no | — |
| 314 | #41 | — | 18 | 8 | no | — |
| 315 | #41 | — | 36 | 8 | no | — |
| 316 | #41 | — | 36 | 4 | no | — |
| 317 | C2×Q8 | — | 9 | 2 | no | — |
| 318 | C2×Q8 | — | 9 | 4 | no | — |
| 319 | C2×Q8 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 320 | C2×D4 | — | 9 | 4 | no | — |
| 321 | C2×D4 | — | 9 | 8 | no | — |
| 322 | C2×D4 | — | 9 | 8 | no | — |
| 323 | C2×D4 | — | 9 | 4 | no | — |
| 324 | C2×D4 | — | 9 | 4 | no | — |
| 325 | C2×D4 | — | 9 | 2 | no | — |
| 326 | C2×D4 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 327 | C2×D4 | C22×C3⋊D3 | 1 | 4 | yes | — |
| 328 | C22×C4 | — | 9 | 4 | no | — |
| 329 | C22×C4 | — | 9 | 4 | no | — |
| 330 | C22×C4 | — | 9 | 8 | no | — |
| 331 | C22×C4 | — | 9 | 2 | no | — |
| 332 | C22×C4 | — | 9 | 4 | no | — |
| 333 | C22×C4 | — | 9 | 1 | no | — |
| 334 | C22×C4 | C22×C3⋊D3 | 1 | 4 | yes | — |
| 335 | C4⋊C4 | — | 9 | 4 | no | — |
| 336 | C4⋊C4 | — | 9 | 8 | no | — |
| 337 | C4⋊C4 | — | 9 | 4 | no | — |
| 338 | C4⋊C4 | — | 9 | 2 | no | — |
| 339 | C4⋊C4 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 340 | C4⋊C4 | C22×C3⋊D3 | 1 | 4 | yes | — |
| 341 | C22⋊C4 | — | 9 | 4 | no | — |
| 342 | C22⋊C4 | — | 9 | 8 | no | — |
| 343 | C22⋊C4 | — | 9 | 4 | no | — |
| 344 | C22⋊C4 | — | 9 | 8 | no | — |
| 345 | C22⋊C4 | C22×C3⋊D3 | 1 | 4 | yes | — |
| 346 | C22⋊C4 | C22×C3⋊D3 | 1 | 8 | yes | — |
| 347 | C42 | — | 9 | 4 | no | — |
| 348 | C42 | — | 9 | 2 | no | — |
| 349 | C42 | — | 9 | 1 | no | — |
| 350 | C42 | — | 9 | 4 | no | — |
| 351 | C42 | — | 9 | 4 | no | — |
| 352 | C42 | — | 9 | 4 | no | — |
| 353 | C42 | C22×C3⋊D3 | 1 | 4 | yes | — |
| 354 | C42 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 355 | C22×C3 | — | 2 | 16 | no | — |
| 356 | C22×C3 | — | 2 | 16 | no | — |
| 357 | C22×C3 | — | 2 | 16 | no | — |
| 358 | C22×C3 | C24×D3 | 1 | 4 | yes | — |
| 359 | C2×D3 | — | 6 | 32 | no | — |
| 360 | C2×D3 | — | 6 | 8 | no | — |
| 361 | C2×D3 | — | 6 | 4 | no | — |
| 362 | C2×D3 | — | 6 | 16 | no | — |
| 363 | C3×C4 | — | 2 | 16 | no | — |
| 364 | C3×C4 | — | 2 | 16 | no | — |
| 365 | C3×C4 | — | 2 | 4 | no | — |
| 366 | C3×C4 | D3×#41 | 1 | 16 | yes | — |
| 367 | Dic3 | — | 3 | 32 | no | — |
| 368 | Dic3 | — | 3 | 8 | no | — |
| 369 | Dic3 | — | 6 | 8 | no | — |
| 370 | Dic3 | — | 6 | 16 | no | — |
| 371 | C32 | #3483 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 372 | C23 | — | 9 | 1 | no | — |
| 373 | C23 | — | 9 | 4 | no | — |
| 374 | C23 | C23×C3⋊D3 | 1 | 4 | yes | — |
| 375 | Q8 | — | 4 | 2 | no | — |
| 376 | Q8 | — | 9 | 8 | no | — |
| 377 | Q8 | — | 36 | 4 | no | — |
| 378 | D4 | — | 2 | 4 | no | — |
| 379 | D4 | — | 4 | 4 | no | — |
| 380 | D4 | — | 18 | 16 | no | — |
| 381 | D4 | — | 18 | 8 | no | — |
| 382 | D4 | — | 18 | 8 | no | — |
| 383 | D4 | — | 36 | 4 | no | — |
| 384 | D4 | — | 36 | 2 | no | — |
| 385 | D4 | — | 36 | 8 | no | — |
| 386 | C2×C4 | — | 2 | 8 | no | — |
| 387 | C2×C4 | — | 9 | 1 | no | — |
| 388 | C2×C4 | — | 9 | 4 | no | — |
| 389 | C2×C4 | — | 9 | 2 | no | — |
| 390 | C2×C4 | — | 9 | 4 | no | — |
| 391 | C2×C4 | — | 18 | 16 | no | — |
| 392 | C2×C4 | — | 18 | 8 | no | — |
| 393 | C2×C4 | — | 18 | 2 | no | — |
| 394 | C2×C4 | — | 18 | 8 | no | — |
| 395 | C2×C4 | — | 18 | 8 | no | — |
| 396 | C2×C4 | — | 18 | 4 | no | — |
| 397 | C2×C4 | C23×C3⋊D3 | 1 | 4 | yes | — |
| 398 | C2×C4 | C23×C3⋊D3 | 1 | 4 | yes | — |
| 399 | C2×C4 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 400 | C2×C4 | C23×C3⋊D3 | 1 | 2 | yes | — |
| 401 | C2×C3 | — | 4 | 16 | no | — |
| 402 | C2×C3 | C2×D3×#41 | 1 | 8 | yes | — |
| 403 | C2×C3 | D3×H(5,𝔽2) | 1 | 4 | yes | — |
| 404 | D3 | — | 12 | 16 | no | — |
| 405 | D3 | — | 12 | 4 | no | — |
| 406 | C22 | — | 2 | 4 | no | — |
| 407 | C22 | — | 2 | 4 | no | — |
| 408 | C22 | — | 2 | 4 | no | — |
| 409 | C22 | — | 18 | 8 | no | — |
| 410 | C22 | — | 18 | 2 | no | — |
| 411 | C22 | — | 18 | 1 | no | — |
| 412 | C22 | — | 18 | 4 | no | — |
| 413 | C22 | C24×C3⋊D3 | 1 | 1 | yes | characteristic |
| 414 | C4 | — | 2 | 4 | no | — |
| 415 | C4 | — | 2 | 4 | no | — |
| 416 | C4 | — | 2 | 1 | no | — |
| 417 | C4 | — | 9 | 8 | no | — |
| 418 | C4 | — | 9 | 2 | no | — |
| 419 | C4 | — | 18 | 2 | no | — |
| 420 | C4 | — | 18 | 4 | no | — |
| 421 | C4 | #41×C3⋊D3 | 1 | 4 | yes | — |
| 422 | C3 | #86959 | 1 | 4 | yes | complemented |
| 423 | C2 | — | 4 | 4 | no | — |
| 424 | C2 | — | 36 | 4 | no | — |
| 425 | C2 | — | 36 | 1 | no | — |
| 426 | C2 | C2×#41×C3⋊D3 | 1 | 2 | yes | — |
| 427 | C2 | C3⋊D3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#555 | C2 |
| hypercenter | #555 | C3⋊D3 |
| hypocenter | C32 | #3483 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #555 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#555 | C2 | semidirect |
| 2. #10596196 | C2 | semidirect |
| 3. #10596193 | C2 | semidirect |
| 4. #10596141 | C2 | semidirect |
| 5. #10596139 | C2 | semidirect |
| 6. #10596070 | C2 | semidirect |
| 7. #10596067 | C2 | semidirect |
| 8. #10596024 | C2 | semidirect |
| 9. C4×#3830 | C2 | semidirect |
| 10. #10596003 | C2 | semidirect |
| 11. #10595993 | C2 | semidirect |
| 51. C3×#555 | D3 | semidirect |
| 171. #634 | #41 | semidirect |
| 175. #555 | C3⋊D3 | semidirect |
| 371. C32 | #3483 | semidirect |
| 422. C3 | #86959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#555 | 2 |
| #10596196 | 2 |
| #10596193 | 2 |
| #10596141 | 2 |
| #10596139 | 2 |
| #10596070 | 2 |
| #10596067 | 2 |
| #10596024 | 2 |
| C4×#3830 | 2 |
| #10596003 | 2 |
| #10595993 | 2 |
| #86959 | 3 |