Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3133 conjugacy classes of subgroups.
The subgroup lattice has 438 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64298 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#64096 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5510 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595032 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10594930 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10594929 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10594527 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10594526 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10594525 | C2 | 1 | 8 | yes | maximal, complemented |
| 10 | #86367 | — | 3 | 2 | no | maximal |
| 11 | C22×#634 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×#235 | C22 | 1 | 4 | yes | — |
| 13 | C2×#3805 | C22 | 1 | 8 | yes | — |
| 14 | #64298 | — | 2 | 16 | no | — |
| 15 | C2×#3795 | C22 | 1 | 8 | yes | — |
| 16 | C2×D3×Dic6 | C22 | 1 | 8 | yes | — |
| 17 | C2×C32×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#3750 | C22 | 1 | 2 | yes | — |
| 19 | C2×C4×C3⋊Dic3 | C22 | 1 | 2 | yes | — |
| 20 | C2×C4×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 21 | #64096 | C22 | 1 | 4 | yes | — |
| 22 | #64096 | C22 | 1 | 4 | yes | — |
| 23 | C3×#930 | C22 | 1 | 8 | yes | — |
| 24 | C3×#897 | C22 | 1 | 8 | yes | — |
| 25 | C3×#895 | C22 | 1 | 8 | yes | — |
| 26 | #63980 | C22 | 1 | 4 | yes | — |
| 27 | #63980 | C22 | 1 | 4 | yes | — |
| 28 | #63919 | C22 | 1 | 4 | yes | — |
| 29 | #63915 | C22 | 1 | 8 | yes | — |
| 30 | #63914 | C22 | 1 | 4 | yes | — |
| 31 | #63914 | C22 | 1 | 2 | yes | — |
| 32 | #63902 | C22 | 1 | 8 | yes | — |
| 33 | C4×#625 | C22 | 1 | 4 | yes | — |
| 34 | C4×#625 | C22 | 1 | 4 | yes | — |
| 35 | #63899 | C22 | 1 | 16 | yes | — |
| 36 | #63898 | C22 | 1 | 8 | yes | — |
| 37 | #63885 | C22 | 1 | 16 | yes | — |
| 38 | #63873 | C22 | 1 | 2 | yes | — |
| 39 | #63863 | C22 | 1 | 4 | yes | — |
| 40 | C2×#1010 | — | 3 | 4 | no | — |
| 41 | C3×#537 | — | 3 | 2 | no | — |
| 42 | #5832 | — | 3 | 4 | no | — |
| 43 | #5633 | — | 3 | 8 | no | — |
| 44 | #5632 | — | 3 | 8 | no | — |
| 45 | #5599 | — | 3 | 8 | no | — |
| 46 | #5598 | — | 3 | 8 | no | — |
| 47 | #5597 | — | 3 | 8 | no | — |
| 48 | #5596 | — | 3 | 8 | no | — |
| 49 | #5510 | D3 | 1 | 2 | yes | complemented |
| 50 | C2×#887 | — | 3 | 2 | no | — |
| 51 | C2×#887 | — | 6 | 1 | no | — |
| 52 | C22×C32×C4 | C23 | 1 | 2 | yes | — |
| 53 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 54 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 57 | C2×#634 | D4 | 1 | 8 | yes | complemented |
| 58 | C2×#634 | C23 | 1 | 4 | yes | — |
| 59 | C2×C3×#67 | C23 | 1 | 8 | yes | — |
| 60 | C3×#235 | — | 2 | 16 | no | — |
| 61 | C2×C3×D12 | C23 | 1 | 4 | yes | — |
| 62 | C2×C3×D12 | C23 | 1 | 8 | yes | — |
| 63 | C2×C3×C4×D3 | C23 | 1 | 8 | yes | — |
| 64 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 65 | C2×#627 | C23 | 1 | 8 | yes | — |
| 66 | C2×#625 | C23 | 1 | 8 | yes | — |
| 67 | C2×#625 | C23 | 1 | 4 | yes | — |
| 68 | C2×#625 | C23 | 1 | 4 | yes | — |
| 69 | #3805 | — | 2 | 32 | no | — |
| 70 | C2×D3×Dic3 | C23 | 1 | 16 | yes | — |
| 71 | #3795 | — | 2 | 32 | no | — |
| 72 | D3×Dic6 | — | 2 | 32 | no | — |
| 73 | C32×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 74 | #3750 | C23 | 1 | 8 | yes | — |
| 75 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 76 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 77 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 78 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 79 | C3×(C2×D3)⋊C4 | C23 | 1 | 16 | yes | — |
| 80 | C3×C4⋊Dic3 | C23 | 1 | 8 | yes | — |
| 81 | #3724 | C23 | 1 | 4 | yes | — |
| 82 | #3724 | C23 | 1 | 4 | yes | — |
| 83 | (C2×D3)⋊Dic3 | C23 | 1 | 8 | yes | — |
| 84 | (C2×D3)⋊Dic3 | C23 | 1 | 8 | yes | — |
| 85 | #3497 | — | 9 | 1 | no | Sylow |
| 86 | C2×C3×#41 | — | 3 | 4 | no | — |
| 87 | #1010 | — | 6 | 32 | no | — |
| 88 | C2×D3×Q8 | — | 3 | 8 | no | — |
| 89 | C2×#237 | — | 3 | 16 | no | — |
| 90 | C2×#237 | — | 3 | 8 | no | — |
| 91 | C2×#235 | — | 3 | 8 | no | — |
| 92 | C2×#235 | C2×D3 | 1 | 4 | yes | — |
| 93 | C22×Dic6 | — | 3 | 2 | no | — |
| 94 | C22×Dic6 | — | 3 | 8 | no | — |
| 95 | C22×Dic6 | — | 6 | 1 | no | — |
| 96 | C3×C22⋊Q8 | — | 3 | 8 | no | — |
| 97 | C3×#121 | — | 3 | 8 | no | — |
| 98 | C3×#121 | — | 3 | 8 | no | — |
| 99 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 100 | C2×C3×C4⋊C4 | C2×D3 | 1 | 2 | yes | — |
| 101 | #947 | — | 3 | 4 | no | — |
| 102 | #944 | — | 3 | 4 | no | — |
| 103 | #940 | — | 3 | 4 | no | — |
| 104 | #940 | — | 3 | 8 | no | — |
| 105 | #939 | — | 3 | 8 | no | — |
| 106 | #939 | — | 3 | 8 | no | — |
| 107 | #939 | — | 3 | 16 | no | — |
| 108 | #936 | — | 3 | 4 | no | — |
| 109 | D4×Dic3 | — | 3 | 8 | no | — |
| 110 | #930 | C2×D3 | 1 | 8 | yes | — |
| 111 | C4×#67 | — | 3 | 8 | no | — |
| 112 | C4×#67 | — | 3 | 8 | no | — |
| 113 | C2×Dic3⋊C4 | — | 3 | 4 | no | — |
| 114 | C2×Dic3⋊C4 | — | 6 | 2 | no | — |
| 115 | C2×C4×Dic3 | — | 3 | 2 | no | — |
| 116 | C2×C4×Dic3 | — | 3 | 4 | no | — |
| 117 | C2×C4×Dic3 | — | 6 | 2 | no | — |
| 118 | C2×C4×Dic3 | — | 6 | 1 | no | — |
| 119 | #897 | C2×D3 | 1 | 8 | yes | — |
| 120 | #896 | — | 3 | 16 | no | — |
| 121 | #895 | C2×D3 | 1 | 8 | yes | — |
| 122 | #893 | — | 3 | 8 | no | — |
| 123 | #888 | — | 3 | 8 | no | — |
| 124 | #887 | — | 3 | 8 | no | — |
| 125 | #887 | — | 3 | 8 | no | — |
| 126 | #887 | — | 6 | 4 | no | — |
| 127 | #887 | — | 6 | 4 | no | — |
| 128 | #885 | — | 3 | 16 | no | — |
| 129 | #884 | — | 3 | 16 | no | — |
| 130 | #67⋊C4 | — | 3 | 16 | no | — |
| 131 | #878 | — | 3 | 16 | no | — |
| 132 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 133 | C22×C3×D3 | C24 | 1 | 8 | yes | — |
| 134 | C2×C32×C4 | — | 4 | 2 | no | — |
| 135 | C2×C32×C4 | C2×D4 | 1 | 4 | yes | — |
| 136 | C2×C32×C4 | C24 | 1 | 4 | yes | — |
| 137 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 138 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 139 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 140 | C2×C3⋊Dic3 | C2×D4 | 1 | 8 | yes | — |
| 141 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 142 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 143 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 144 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 145 | #634 | C2×D4 | 1 | 16 | yes | — |
| 146 | C3×#67 | — | 2 | 16 | no | — |
| 147 | C2×C3×Dic3 | C24 | 1 | 8 | yes | — |
| 148 | C3×D12 | — | 2 | 8 | no | — |
| 149 | C3×D12 | — | 4 | 8 | no | — |
| 150 | C3×C4×D3 | — | 2 | 16 | no | — |
| 151 | C3×Dic6 | — | 2 | 8 | no | — |
| 152 | #627 | — | 2 | 16 | no | — |
| 153 | #625 | — | 2 | 16 | no | — |
| 154 | #625 | — | 2 | 8 | no | — |
| 155 | #625 | — | 4 | 4 | no | — |
| 156 | D3×Dic3 | — | 2 | 32 | no | — |
| 157 | C2×2−1+4 | — | 9 | 2 | no | — |
| 158 | #550 | — | 9 | 4 | no | — |
| 159 | D4×Q8 | — | 9 | 4 | no | — |
| 160 | #548 | — | 9 | 8 | no | — |
| 161 | #537 | — | 3 | 2 | no | — |
| 162 | #537 | — | 9 | 4 | no | — |
| 163 | #532 | — | 9 | 4 | no | — |
| 164 | #532 | — | 9 | 2 | no | — |
| 165 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 166 | C3×#41 | — | 6 | 16 | no | — |
| 167 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 168 | C2×C3×D4 | — | 3 | 8 | no | — |
| 169 | C2×C3×D4 | — | 3 | 4 | no | — |
| 170 | C2×C3×D4 | — | 3 | 8 | no | — |
| 171 | C22×C3×C4 | — | 2 | 1 | no | — |
| 172 | C22×C3×C4 | — | 2 | 2 | no | — |
| 173 | C22×C3×C4 | — | 3 | 8 | no | — |
| 174 | C22×C3×C4 | C22×D3 | 1 | 4 | yes | — |
| 175 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 176 | C2×#67 | — | 3 | 8 | no | — |
| 177 | C2×#67 | — | 3 | 16 | no | — |
| 178 | C2×#67 | — | 3 | 8 | no | — |
| 179 | C2×#67 | C22×D3 | 1 | 8 | yes | — |
| 180 | C22×Dic3 | — | 3 | 4 | no | — |
| 181 | C22×Dic3 | — | 3 | 2 | no | — |
| 182 | C22×Dic3 | — | 3 | 2 | no | — |
| 183 | C22×Dic3 | — | 3 | 16 | no | — |
| 184 | C22×Dic3 | — | 6 | 1 | no | — |
| 185 | C22×Dic3 | — | 6 | 2 | no | — |
| 186 | C22×Dic3 | — | 6 | 1 | no | — |
| 187 | D3×Q8 | — | 6 | 32 | no | — |
| 188 | #237 | — | 6 | 32 | no | — |
| 189 | #237 | — | 6 | 64 | no | — |
| 190 | #235 | — | 2 | 16 | no | — |
| 191 | #235 | — | 6 | 32 | no | — |
| 192 | C2×D12 | C22×D3 | 1 | 4 | yes | — |
| 193 | C2×D12 | C22×D3 | 1 | 8 | yes | — |
| 194 | C2×C4×D3 | — | 3 | 16 | no | — |
| 195 | C2×C4×D3 | C22×D3 | 1 | 8 | yes | — |
| 196 | C2×Dic6 | — | 3 | 16 | no | — |
| 197 | C2×Dic6 | — | 3 | 8 | no | — |
| 198 | C2×Dic6 | — | 3 | 16 | no | — |
| 199 | C2×Dic6 | — | 6 | 4 | no | — |
| 200 | C2×Dic6 | — | 6 | 8 | no | — |
| 201 | C2×Dic6 | — | 6 | 32 | no | — |
| 202 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 203 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 204 | C3×C4⋊C4 | — | 3 | 8 | no | — |
| 205 | C3×C4⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 206 | C3×C22⋊C4 | — | 3 | 16 | no | — |
| 207 | #217 | — | 3 | 8 | no | — |
| 208 | #217 | — | 3 | 8 | no | — |
| 209 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 210 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 211 | (C2×D3)⋊C4 | C22×D3 | 1 | 16 | yes | — |
| 212 | C4⋊Dic3 | C22×D3 | 1 | 8 | yes | — |
| 213 | Dic3⋊C4 | — | 3 | 16 | no | — |
| 214 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 215 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 216 | Dic3⋊C4 | — | 6 | 8 | no | — |
| 217 | C4×Dic3 | — | 3 | 8 | no | — |
| 218 | C4×Dic3 | — | 3 | 8 | no | — |
| 219 | C4×Dic3 | — | 3 | 4 | no | — |
| 220 | C4×Dic3 | — | 3 | 4 | no | — |
| 221 | C4×Dic3 | — | 6 | 4 | no | — |
| 222 | C4×Dic3 | — | 6 | 2 | no | — |
| 223 | C4×Dic3 | — | 6 | 4 | no | — |
| 224 | C4×Dic3 | — | 6 | 2 | no | — |
| 225 | C22×C32 | — | 2 | 1 | no | — |
| 226 | C22×C32 | — | 2 | 1 | no | — |
| 227 | C22×C32 | C22×D4 | 1 | 2 | yes | — |
| 228 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 229 | C2×C3×D3 | — | 2 | 8 | no | — |
| 230 | C2×C3×D3 | — | 2 | 8 | no | — |
| 231 | C2×C3×D3 | — | 2 | 8 | no | — |
| 232 | C32×C4 | — | 2 | 4 | no | — |
| 233 | C32×C4 | C22×D4 | 1 | 4 | yes | — |
| 234 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 235 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 236 | C3⋊Dic3 | C22×D4 | 1 | 8 | yes | — |
| 237 | C3⋊Dic3 | 2−1+4 | 1 | 2 | yes | complemented |
| 238 | C3×Dic3 | — | 2 | 8 | no | — |
| 239 | 2−1+4 | — | 18 | 16 | no | — |
| 240 | C2×#41 | — | 3 | 4 | no | — |
| 241 | C2×#41 | — | 9 | 8 | no | — |
| 242 | C2×#41 | — | 9 | 8 | no | — |
| 243 | C22×Q8 | — | 9 | 8 | no | — |
| 244 | C22×Q8 | — | 9 | 1 | no | — |
| 245 | C4⋊Q8 | — | 9 | 4 | no | — |
| 246 | C4⋊Q8 | — | 9 | 2 | no | — |
| 247 | #127 | — | 9 | 2 | no | — |
| 248 | #127 | — | 9 | 4 | no | — |
| 249 | #124 | — | 9 | 8 | no | — |
| 250 | #124 | — | 9 | 4 | no | — |
| 251 | C22⋊Q8 | — | 3 | 8 | no | — |
| 252 | C22⋊Q8 | — | 9 | 16 | no | — |
| 253 | #121 | — | 3 | 8 | no | — |
| 254 | #121 | — | 3 | 8 | no | — |
| 255 | #121 | — | 9 | 16 | no | — |
| 256 | #121 | — | 9 | 4 | no | — |
| 257 | #121 | — | 9 | 4 | no | — |
| 258 | C4×Q8 | — | 9 | 4 | no | — |
| 259 | C4×Q8 | — | 9 | 4 | no | — |
| 260 | C4×D4 | — | 9 | 8 | no | — |
| 261 | C4×D4 | — | 9 | 8 | no | — |
| 262 | C4×D4 | — | 9 | 4 | no | — |
| 263 | C4×D4 | — | 9 | 4 | no | — |
| 264 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 265 | C2×C4⋊C4 | D32 | 1 | 1 | yes | characteristic |
| 266 | C2×C42 | — | 9 | 2 | no | — |
| 267 | C2×C42 | — | 9 | 1 | no | — |
| 268 | C23×C3 | — | 2 | 1 | no | — |
| 269 | C23×C3 | — | 3 | 8 | no | — |
| 270 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 271 | C22×D3 | C23×D3 | 1 | 8 | yes | — |
| 272 | C3×Q8 | — | 6 | 8 | no | — |
| 273 | C3×D4 | — | 6 | 16 | no | — |
| 274 | C3×D4 | — | 6 | 8 | no | — |
| 275 | C3×D4 | — | 12 | 8 | no | — |
| 276 | C2×C3×C4 | — | 2 | 2 | no | — |
| 277 | C2×C3×C4 | — | 2 | 4 | no | — |
| 278 | C2×C3×C4 | — | 2 | 4 | no | — |
| 279 | C2×C3×C4 | — | 3 | 8 | no | — |
| 280 | C2×C3×C4 | — | 4 | 4 | no | — |
| 281 | C2×C3×C4 | — | 4 | 4 | no | — |
| 282 | C2×C3×C4 | — | 6 | 16 | no | — |
| 283 | C2×C3×C4 | D3×D4 | 1 | 8 | yes | — |
| 284 | C2×C3×C4 | C23×D3 | 1 | 8 | yes | — |
| 285 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 286 | #67 | — | 2 | 16 | no | — |
| 287 | #67 | — | 6 | 32 | no | — |
| 288 | #67 | — | 6 | 16 | no | — |
| 289 | #67 | — | 12 | 8 | no | — |
| 290 | C2×Dic3 | — | 3 | 16 | no | — |
| 291 | C2×Dic3 | — | 3 | 2 | no | — |
| 292 | C2×Dic3 | — | 3 | 8 | no | — |
| 293 | C2×Dic3 | — | 3 | 2 | no | — |
| 294 | C2×Dic3 | — | 3 | 4 | no | — |
| 295 | C2×Dic3 | — | 6 | 8 | no | — |
| 296 | C2×Dic3 | — | 6 | 1 | no | — |
| 297 | C2×Dic3 | — | 6 | 1 | no | — |
| 298 | C2×Dic3 | — | 6 | 4 | no | — |
| 299 | C2×Dic3 | — | 6 | 2 | no | — |
| 300 | C2×Dic3 | — | 6 | 32 | no | — |
| 301 | C2×Dic3 | — | 6 | 4 | no | — |
| 302 | C2×Dic3 | — | 6 | 4 | no | — |
| 303 | C2×Dic3 | — | 12 | 2 | no | — |
| 304 | C2×Dic3 | — | 12 | 2 | no | — |
| 305 | C2×Dic3 | C23×D3 | 1 | 8 | yes | — |
| 306 | D12 | — | 2 | 8 | no | — |
| 307 | D12 | — | 4 | 8 | no | — |
| 308 | C4×D3 | — | 2 | 16 | no | — |
| 309 | C4×D3 | — | 6 | 32 | no | — |
| 310 | Dic6 | — | 2 | 8 | no | — |
| 311 | Dic6 | — | 3 | 32 | no | — |
| 312 | Dic6 | — | 6 | 16 | no | — |
| 313 | Dic6 | — | 6 | 32 | no | — |
| 314 | C2×C32 | — | 2 | 2 | no | — |
| 315 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 316 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 317 | C2×C32 | #585 | 1 | 1 | yes | characteristic |
| 318 | C3×D3 | — | 4 | 8 | no | — |
| 319 | #41 | — | 6 | 16 | no | — |
| 320 | #41 | — | 18 | 32 | no | — |
| 321 | #41 | — | 18 | 32 | no | — |
| 322 | C2×Q8 | — | 3 | 4 | no | — |
| 323 | C2×Q8 | — | 9 | 8 | no | — |
| 324 | C2×Q8 | — | 9 | 4 | no | — |
| 325 | C2×Q8 | — | 9 | 8 | no | — |
| 326 | C2×Q8 | — | 18 | 32 | no | — |
| 327 | C2×D4 | — | 3 | 8 | no | — |
| 328 | C2×D4 | — | 3 | 4 | no | — |
| 329 | C2×D4 | — | 3 | 8 | no | — |
| 330 | C2×D4 | — | 9 | 4 | no | — |
| 331 | C2×D4 | — | 9 | 8 | no | — |
| 332 | C2×D4 | — | 9 | 4 | no | — |
| 333 | C22×C4 | — | 3 | 8 | no | — |
| 334 | C22×C4 | — | 9 | 16 | no | — |
| 335 | C22×C4 | — | 9 | 2 | no | — |
| 336 | C22×C4 | — | 9 | 1 | no | — |
| 337 | C22×C4 | — | 9 | 1 | no | — |
| 338 | C22×C4 | C2×D32 | 1 | 2 | yes | — |
| 339 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 340 | C4⋊C4 | — | 3 | 8 | no | — |
| 341 | C4⋊C4 | — | 9 | 4 | no | — |
| 342 | C4⋊C4 | — | 9 | 4 | no | — |
| 343 | C4⋊C4 | — | 9 | 8 | no | — |
| 344 | C4⋊C4 | C2×D32 | 1 | 4 | yes | — |
| 345 | C22⋊C4 | — | 3 | 16 | no | — |
| 346 | C22⋊C4 | — | 9 | 8 | no | — |
| 347 | C22⋊C4 | — | 9 | 8 | no | — |
| 348 | C42 | — | 9 | 4 | no | — |
| 349 | C42 | — | 9 | 2 | no | — |
| 350 | C42 | — | 9 | 4 | no | — |
| 351 | C42 | — | 9 | 2 | no | — |
| 352 | C22×C3 | — | 2 | 2 | no | — |
| 353 | C22×C3 | — | 2 | 2 | no | — |
| 354 | C22×C3 | — | 2 | 2 | no | — |
| 355 | C22×C3 | — | 2 | 2 | no | — |
| 356 | C22×C3 | — | 2 | 2 | no | — |
| 357 | C22×C3 | — | 2 | 1 | no | — |
| 358 | C22×C3 | — | 6 | 8 | no | — |
| 359 | C22×C3 | — | 6 | 8 | no | — |
| 360 | C22×C3 | — | 6 | 8 | no | — |
| 361 | C22×C3 | C2×D3×D4 | 1 | 4 | yes | — |
| 362 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 363 | C2×D3 | — | 2 | 8 | no | — |
| 364 | C2×D3 | — | 2 | 8 | no | — |
| 365 | C2×D3 | — | 2 | 8 | no | — |
| 366 | C3×C4 | — | 2 | 8 | no | — |
| 367 | C3×C4 | — | 2 | 4 | no | — |
| 368 | C3×C4 | — | 4 | 4 | no | — |
| 369 | C3×C4 | — | 6 | 8 | no | — |
| 370 | C3×C4 | C2×D3×D4 | 1 | 8 | yes | — |
| 371 | Dic3 | — | 2 | 8 | no | — |
| 372 | Dic3 | — | 3 | 16 | no | — |
| 373 | Dic3 | — | 3 | 4 | no | — |
| 374 | Dic3 | — | 6 | 8 | no | — |
| 375 | Dic3 | — | 6 | 2 | no | — |
| 376 | Dic3 | — | 6 | 2 | no | — |
| 377 | Dic3 | — | 6 | 4 | no | — |
| 378 | Dic3 | — | 6 | 2 | no | — |
| 379 | Dic3 | — | 12 | 2 | no | — |
| 380 | C32 | #3497 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 381 | C23 | — | 3 | 8 | no | — |
| 382 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 383 | Q8 | — | 6 | 8 | no | — |
| 384 | Q8 | — | 9 | 16 | no | — |
| 385 | Q8 | — | 18 | 16 | no | — |
| 386 | D4 | — | 6 | 16 | no | — |
| 387 | D4 | — | 6 | 8 | no | — |
| 388 | D4 | — | 12 | 8 | no | — |
| 389 | D4 | — | 18 | 16 | no | — |
| 390 | D4 | — | 18 | 8 | no | — |
| 391 | D4 | — | 36 | 4 | no | — |
| 392 | C2×C4 | — | 3 | 8 | no | — |
| 393 | C2×C4 | — | 4 | 2 | no | — |
| 394 | C2×C4 | — | 6 | 16 | no | — |
| 395 | C2×C4 | — | 9 | 8 | no | — |
| 396 | C2×C4 | — | 9 | 1 | no | — |
| 397 | C2×C4 | — | 9 | 4 | no | — |
| 398 | C2×C4 | — | 9 | 1 | no | — |
| 399 | C2×C4 | — | 9 | 2 | no | — |
| 400 | C2×C4 | — | 18 | 32 | no | — |
| 401 | C2×C4 | — | 18 | 2 | no | — |
| 402 | C2×C4 | — | 36 | 1 | no | — |
| 403 | C2×C4 | #3802 | 1 | 4 | yes | — |
| 404 | C2×C4 | C22×D32 | 1 | 4 | yes | — |
| 405 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 406 | C2×C3 | — | 2 | 4 | no | — |
| 407 | C2×C3 | — | 2 | 4 | no | — |
| 408 | C2×C3 | — | 2 | 1 | no | — |
| 409 | C2×C3 | — | 2 | 1 | no | — |
| 410 | C2×C3 | — | 2 | 1 | no | — |
| 411 | C2×C3 | — | 12 | 8 | no | — |
| 412 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 413 | C2×C3 | #5966 | 1 | 2 | yes | — |
| 414 | C2×C3 | D3×2−1+4 | 1 | 2 | yes | — |
| 415 | D3 | — | 4 | 8 | no | — |
| 416 | C22 | — | 2 | 1 | no | — |
| 417 | C22 | — | 2 | 1 | no | — |
| 418 | C22 | — | 6 | 8 | no | — |
| 419 | C22 | — | 6 | 8 | no | — |
| 420 | C22 | — | 6 | 8 | no | — |
| 421 | C22 | C2×#3802 | 1 | 2 | yes | — |
| 422 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 423 | C4 | — | 2 | 4 | no | — |
| 424 | C4 | — | 6 | 8 | no | — |
| 425 | C4 | — | 9 | 8 | no | — |
| 426 | C4 | — | 9 | 2 | no | — |
| 427 | C4 | — | 18 | 2 | no | — |
| 428 | C4 | — | 18 | 1 | no | — |
| 429 | C4 | C2×#3802 | 1 | 4 | yes | — |
| 430 | C3 | — | 2 | 1 | no | — |
| 431 | C3 | #86367 | 1 | 2 | yes | complemented |
| 432 | C2 | — | 2 | 2 | no | — |
| 433 | C2 | — | 12 | 8 | no | — |
| 434 | C2 | C22×#3802 | 1 | 1 | yes | characteristic |
| 435 | C2 | #10596679 | 1 | 1 | yes | characteristic |
| 436 | C2 | #10596687 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C2×C32×C4⋊C4 | C22 |
| hypercenter | C2×C4⋊C4 | D32 |
| hypocenter | C32 | #3497 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64298 | C2 | semidirect |
| 2. C2×#64096 | C2 | semidirect |
| 3. C3×#5510 | C2 | semidirect |
| 4. #10595032 | C2 | semidirect |
| 5. #10594930 | C2 | semidirect |
| 6. #10594929 | C2 | semidirect |
| 7. #10594527 | C2 | semidirect |
| 8. #10594526 | C2 | semidirect |
| 9. #10594525 | C2 | semidirect |
| 49. #5510 | D3 | semidirect |
| 57. C2×#634 | D4 | semidirect |
| 237. C3⋊Dic3 | 2−1+4 | semidirect |
| 380. C32 | #3497 | semidirect |
| 431. C3 | #86367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64298 | 2 |
| C2×#64096 | 2 |
| C3×#5510 | 2 |
| #10595032 | 2 |
| #10594930 | 2 |
| #10594929 | 2 |
| #10594527 | 2 |
| #10594526 | 2 |
| #10594525 | 2 |
| #86367 | 3 |