Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1002 conjugacy classes of subgroups.
The subgroup lattice has 358 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#563 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #5724 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #5722 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #5710 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #5702 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #5699 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #5688 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #5672 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #5668 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #5664 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #5648 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #5640 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #5632 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | #3550 | — | 3 | 1 | no | maximal, Sylow |
| 15 | C2×#239 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×D3×Q8 | C22 | 1 | 2 | yes | — |
| 17 | C2×#237 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×Dic6 | C22 | 1 | 2 | yes | — |
| 19 | C3×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 20 | C3×#126 | C22 | 1 | 4 | yes | — |
| 21 | C3×#125 | C22 | 1 | 2 | yes | — |
| 22 | C3×#124 | C22 | 1 | 1 | yes | characteristic |
| 23 | C3×#123 | C22 | 1 | 2 | yes | — |
| 24 | C3×C22⋊Q8 | C22 | 1 | 4 | yes | — |
| 25 | #947 | C22 | 1 | 2 | yes | — |
| 26 | #944 | C22 | 1 | 4 | yes | — |
| 27 | #944 | C22 | 1 | 1 | yes | characteristic |
| 28 | #944 | C22 | 1 | 2 | yes | — |
| 29 | #940 | C22 | 1 | 1 | yes | characteristic |
| 30 | #935 | C22 | 1 | 2 | yes | — |
| 31 | #929 | C22 | 1 | 2 | yes | — |
| 32 | C4×#67 | C22 | 1 | 4 | yes | — |
| 33 | #898 | C22 | 1 | 4 | yes | — |
| 34 | #898 | C22 | 1 | 4 | yes | — |
| 35 | #897 | C22 | 1 | 4 | yes | — |
| 36 | #896 | C22 | 1 | 4 | yes | — |
| 37 | #896 | C22 | 1 | 4 | yes | — |
| 38 | #896 | C22 | 1 | 4 | yes | — |
| 39 | #896 | C22 | 1 | 4 | yes | — |
| 40 | #894 | C22 | 1 | 4 | yes | — |
| 41 | #894 | C22 | 1 | 4 | yes | — |
| 42 | #892 | C22 | 1 | 2 | yes | — |
| 43 | #892 | C22 | 1 | 2 | yes | — |
| 44 | #888 | C22 | 1 | 2 | yes | — |
| 45 | #888 | C22 | 1 | 4 | yes | — |
| 46 | #888 | C22 | 1 | 4 | yes | — |
| 47 | #888 | C22 | 1 | 2 | yes | — |
| 48 | #887 | C22 | 1 | 4 | yes | — |
| 49 | #887 | C22 | 1 | 4 | yes | — |
| 50 | #887 | C22 | 1 | 4 | yes | — |
| 51 | #886 | C22 | 1 | 2 | yes | — |
| 52 | #885 | C22 | 1 | 4 | yes | — |
| 53 | #885 | C22 | 1 | 4 | yes | — |
| 54 | #885 | C22 | 1 | 4 | yes | — |
| 55 | #884 | C22 | 1 | 4 | yes | — |
| 56 | #67⋊C4 | C22 | 1 | 4 | yes | — |
| 57 | #67⋊C4 | C22 | 1 | 4 | yes | — |
| 58 | #879 | C22 | 1 | 4 | yes | — |
| 59 | #878 | C22 | 1 | 4 | yes | — |
| 60 | #878 | C22 | 1 | 4 | yes | — |
| 61 | #877 | C22 | 1 | 2 | yes | — |
| 62 | #875 | C22 | 1 | 1 | yes | characteristic |
| 63 | #875 | C22 | 1 | 2 | yes | — |
| 64 | #872 | C22 | 1 | 2 | yes | — |
| 65 | C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 66 | #870 | C22 | 1 | 2 | yes | — |
| 67 | C4×Dic6 | C22 | 1 | 4 | yes | — |
| 68 | #563 | — | 3 | 2 | no | — |
| 69 | #563 | — | 3 | 1 | no | — |
| 70 | #563 | D3 | 1 | 1 | yes | characteristic, complemented |
| 71 | #559 | — | 3 | 2 | no | — |
| 72 | Q82 | — | 3 | 2 | no | — |
| 73 | #556 | — | 3 | 4 | no | — |
| 74 | D4×Q8 | — | 3 | 4 | no | — |
| 75 | #542 | — | 3 | 4 | no | — |
| 76 | #542 | — | 3 | 4 | no | — |
| 77 | #536 | — | 3 | 2 | no | — |
| 78 | #536 | — | 3 | 2 | no | — |
| 79 | #533 | — | 3 | 2 | no | — |
| 80 | #532 | — | 3 | 1 | no | — |
| 81 | C2×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×C3×Q8 | C23 | 1 | 2 | yes | — |
| 83 | C2×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22×C3×C4 | C23 | 1 | 2 | yes | — |
| 85 | C2×#67 | C23 | 1 | 4 | yes | — |
| 86 | C2×#67 | C23 | 1 | 2 | yes | — |
| 87 | C22×Dic3 | C23 | 1 | 2 | yes | — |
| 88 | C22×Dic3 | C23 | 1 | 2 | yes | — |
| 89 | #239 | — | 4 | 2 | no | — |
| 90 | D3×Q8 | — | 4 | 4 | no | — |
| 91 | #237 | — | 4 | 2 | no | — |
| 92 | C2×D12 | C23 | 1 | 2 | yes | — |
| 93 | C2×D12 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C4×D3 | C23 | 1 | 2 | yes | — |
| 95 | C2×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×C4×D3 | C23 | 1 | 2 | yes | — |
| 97 | C2×C4×D3 | C23 | 1 | 4 | yes | — |
| 98 | C2×Dic6 | — | 4 | 4 | no | — |
| 99 | C2×Dic6 | C23 | 1 | 4 | yes | — |
| 100 | C2×Dic6 | C23 | 1 | 4 | yes | — |
| 101 | C2×Dic6 | C23 | 1 | 2 | yes | — |
| 102 | C2×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×Dic6 | C23 | 1 | 4 | yes | — |
| 104 | C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 105 | C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 106 | C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 107 | C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 108 | C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 109 | C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 110 | C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 111 | C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 112 | C3×C42 | C23 | 1 | 2 | yes | — |
| 113 | C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 114 | #217 | C23 | 1 | 2 | yes | — |
| 115 | #217 | C23 | 1 | 4 | yes | — |
| 116 | (C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 117 | (C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 118 | (C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 119 | (C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 120 | (C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 121 | (C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 122 | C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 123 | C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 124 | C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 125 | Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 126 | Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 127 | Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 128 | Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 129 | Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 130 | Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 131 | Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 132 | C4×Dic3 | C23 | 1 | 4 | yes | — |
| 133 | C4×Dic3 | C23 | 1 | 4 | yes | — |
| 134 | C4×Dic3 | C23 | 1 | 2 | yes | — |
| 135 | C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 136 | C4×Dic3 | C23 | 1 | 2 | yes | — |
| 137 | C4×Dic3 | C23 | 1 | 4 | yes | — |
| 138 | C2×#41 | — | 3 | 1 | no | — |
| 139 | C2×#41 | — | 3 | 1 | no | — |
| 140 | C22×Q8 | — | 3 | 2 | no | — |
| 141 | C22×Q8 | — | 3 | 2 | no | — |
| 142 | C4⋊Q8 | — | 3 | 1 | no | — |
| 143 | C4⋊Q8 | — | 3 | 2 | no | — |
| 144 | C4⋊Q8 | — | 3 | 4 | no | — |
| 145 | C4⋊Q8 | — | 3 | 2 | no | — |
| 146 | C4⋊Q8 | — | 3 | 2 | no | — |
| 147 | C4⋊Q8 | — | 3 | 4 | no | — |
| 148 | C4⋊Q8 | — | 3 | 4 | no | — |
| 149 | C4⋊Q8 | C2×D3 | 1 | 2 | yes | — |
| 150 | #127 | — | 3 | 1 | no | — |
| 151 | #126 | — | 3 | 4 | no | — |
| 152 | #126 | — | 3 | 4 | no | — |
| 153 | #126 | — | 3 | 4 | no | — |
| 154 | #126 | C2×D3 | 1 | 4 | yes | — |
| 155 | #125 | — | 3 | 2 | no | — |
| 156 | #125 | C2×D3 | 1 | 2 | yes | — |
| 157 | #124 | — | 3 | 2 | no | — |
| 158 | #124 | — | 3 | 4 | no | — |
| 159 | #124 | — | 3 | 4 | no | — |
| 160 | #124 | — | 3 | 4 | no | — |
| 161 | #124 | — | 3 | 1 | no | — |
| 162 | #124 | — | 3 | 2 | no | — |
| 163 | #124 | C2×D3 | 1 | 1 | yes | characteristic |
| 164 | #123 | — | 3 | 2 | no | — |
| 165 | #123 | — | 3 | 2 | no | — |
| 166 | #123 | — | 3 | 4 | no | — |
| 167 | #123 | — | 3 | 4 | no | — |
| 168 | #123 | — | 3 | 2 | no | — |
| 169 | #123 | C2×D3 | 1 | 2 | yes | — |
| 170 | C22⋊Q8 | — | 3 | 4 | no | — |
| 171 | C22⋊Q8 | — | 3 | 4 | no | — |
| 172 | C22⋊Q8 | — | 3 | 4 | no | — |
| 173 | C22⋊Q8 | — | 3 | 4 | no | — |
| 174 | C22⋊Q8 | — | 3 | 4 | no | — |
| 175 | C22⋊Q8 | — | 3 | 4 | no | — |
| 176 | C22⋊Q8 | — | 3 | 4 | no | — |
| 177 | C22⋊Q8 | C2×D3 | 1 | 4 | yes | — |
| 178 | #121 | — | 3 | 4 | no | — |
| 179 | C4×Q8 | — | 3 | 4 | no | — |
| 180 | C4×Q8 | — | 3 | 4 | no | — |
| 181 | C4×Q8 | — | 3 | 4 | no | — |
| 182 | C4×Q8 | — | 3 | 4 | no | — |
| 183 | C4×D4 | — | 3 | 4 | no | — |
| 184 | C4×D4 | — | 3 | 4 | no | — |
| 185 | C4×D4 | — | 3 | 4 | no | — |
| 186 | #117 | — | 3 | 2 | no | — |
| 187 | #117 | — | 3 | 2 | no | — |
| 188 | #117 | — | 3 | 2 | no | — |
| 189 | #117 | — | 3 | 2 | no | — |
| 190 | C2×C42 | — | 3 | 1 | no | — |
| 191 | C23×C3 | C24 | 1 | 2 | yes | — |
| 192 | C22×D3 | C24 | 1 | 2 | yes | — |
| 193 | C22×D3 | C24 | 1 | 1 | yes | characteristic |
| 194 | C3×Q8 | — | 4 | 2 | no | — |
| 195 | C3×Q8 | — | 4 | 1 | no | — |
| 196 | C3×D4 | — | 4 | 1 | no | — |
| 197 | C2×C3×C4 | — | 4 | 2 | no | — |
| 198 | C2×C3×C4 | C24 | 1 | 4 | yes | — |
| 199 | C2×C3×C4 | C24 | 1 | 2 | yes | — |
| 200 | C2×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 201 | C2×C3×C4 | C24 | 1 | 2 | yes | — |
| 202 | C2×C3×C4 | C24 | 1 | 4 | yes | — |
| 203 | #67 | — | 2 | 8 | no | — |
| 204 | #67 | — | 4 | 2 | no | — |
| 205 | C2×Dic3 | — | 2 | 4 | no | — |
| 206 | C2×Dic3 | — | 4 | 2 | no | — |
| 207 | C2×Dic3 | C24 | 1 | 4 | yes | — |
| 208 | C2×Dic3 | C24 | 1 | 2 | yes | — |
| 209 | C2×Dic3 | C24 | 1 | 4 | yes | — |
| 210 | C2×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 211 | C2×Dic3 | C24 | 1 | 2 | yes | — |
| 212 | D12 | — | 4 | 1 | no | — |
| 213 | D12 | — | 4 | 2 | no | — |
| 214 | C4×D3 | — | 2 | 2 | no | — |
| 215 | C4×D3 | — | 2 | 4 | no | — |
| 216 | C4×D3 | — | 2 | 4 | no | — |
| 217 | C4×D3 | — | 4 | 4 | no | — |
| 218 | Dic6 | — | 2 | 8 | no | — |
| 219 | Dic6 | — | 2 | 8 | no | — |
| 220 | Dic6 | — | 4 | 4 | no | — |
| 221 | Dic6 | — | 4 | 1 | no | — |
| 222 | Dic6 | — | 4 | 2 | no | — |
| 223 | #41 | — | 12 | 2 | no | — |
| 224 | #41 | — | 12 | 2 | no | — |
| 225 | C2×Q8 | — | 3 | 4 | no | — |
| 226 | C2×Q8 | — | 3 | 4 | no | — |
| 227 | C2×Q8 | — | 3 | 4 | no | — |
| 228 | C2×Q8 | — | 3 | 2 | no | — |
| 229 | C2×Q8 | — | 3 | 1 | no | — |
| 230 | C2×Q8 | — | 12 | 4 | no | — |
| 231 | C2×Q8 | — | 12 | 4 | no | — |
| 232 | C2×Q8 | C22×D3 | 1 | 2 | yes | — |
| 233 | C2×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 234 | C2×D4 | — | 3 | 4 | no | — |
| 235 | C2×D4 | — | 3 | 2 | no | — |
| 236 | C2×D4 | — | 3 | 2 | no | — |
| 237 | C2×D4 | — | 3 | 1 | no | — |
| 238 | C2×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 239 | C22×C4 | — | 3 | 2 | no | — |
| 240 | C22×C4 | — | 3 | 2 | no | — |
| 241 | C22×C4 | — | 3 | 2 | no | — |
| 242 | C22×C4 | — | 3 | 1 | no | — |
| 243 | C22×C4 | — | 3 | 2 | no | — |
| 244 | C22×C4 | — | 3 | 4 | no | — |
| 245 | C22×C4 | C22×D3 | 1 | 2 | yes | — |
| 246 | C4⋊C4 | — | 3 | 4 | no | — |
| 247 | C4⋊C4 | — | 3 | 2 | no | — |
| 248 | C4⋊C4 | — | 3 | 2 | no | — |
| 249 | C4⋊C4 | — | 3 | 4 | no | — |
| 250 | C4⋊C4 | — | 3 | 4 | no | — |
| 251 | C4⋊C4 | — | 3 | 4 | no | — |
| 252 | C4⋊C4 | — | 3 | 4 | no | — |
| 253 | C4⋊C4 | — | 3 | 4 | no | — |
| 254 | C4⋊C4 | — | 3 | 4 | no | — |
| 255 | C4⋊C4 | — | 3 | 4 | no | — |
| 256 | C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 257 | C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 258 | C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 259 | C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 260 | C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 261 | C22⋊C4 | — | 3 | 2 | no | — |
| 262 | C22⋊C4 | — | 3 | 4 | no | — |
| 263 | C22⋊C4 | — | 3 | 4 | no | — |
| 264 | C22⋊C4 | — | 3 | 4 | no | — |
| 265 | C22⋊C4 | — | 3 | 4 | no | — |
| 266 | C22⋊C4 | — | 3 | 4 | no | — |
| 267 | C22⋊C4 | — | 3 | 4 | no | — |
| 268 | C22⋊C4 | — | 3 | 4 | no | — |
| 269 | C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 270 | C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 271 | C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 272 | C42 | — | 3 | 2 | no | — |
| 273 | C42 | — | 3 | 1 | no | — |
| 274 | C42 | — | 3 | 4 | no | — |
| 275 | C42 | — | 3 | 4 | no | — |
| 276 | C42 | — | 3 | 2 | no | — |
| 277 | C42 | — | 3 | 4 | no | — |
| 278 | C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 279 | C42 | C22×D3 | 1 | 2 | yes | — |
| 280 | C22×C3 | — | 2 | 2 | no | — |
| 281 | C22×C3 | — | 2 | 4 | no | — |
| 282 | C22×C3 | C25 | 1 | 1 | yes | characteristic |
| 283 | C2×D3 | — | 2 | 2 | no | — |
| 284 | C2×D3 | — | 2 | 1 | no | — |
| 285 | C2×D3 | — | 2 | 2 | no | — |
| 286 | C2×D3 | — | 2 | 4 | no | — |
| 287 | C3×C4 | — | 2 | 4 | no | — |
| 288 | C3×C4 | — | 2 | 1 | no | — |
| 289 | C3×C4 | — | 2 | 2 | no | — |
| 290 | C3×C4 | — | 2 | 4 | no | — |
| 291 | C3×C4 | — | 2 | 2 | no | — |
| 292 | Dic3 | — | 2 | 4 | no | — |
| 293 | Dic3 | — | 2 | 2 | no | — |
| 294 | Dic3 | — | 2 | 4 | no | — |
| 295 | Dic3 | H(5,𝔽2) | 1 | 2 | yes | — |
| 296 | Dic3 | 2−1+4 | 1 | 4 | yes | — |
| 297 | C23 | — | 3 | 2 | no | — |
| 298 | C23 | — | 3 | 1 | no | — |
| 299 | C23 | C23×D3 | 1 | 2 | yes | — |
| 300 | Q8 | — | 4 | 2 | no | — |
| 301 | Q8 | — | 4 | 1 | no | — |
| 302 | Q8 | — | 6 | 8 | no | — |
| 303 | Q8 | — | 6 | 8 | no | — |
| 304 | Q8 | — | 12 | 4 | no | — |
| 305 | Q8 | — | 12 | 2 | no | — |
| 306 | Q8 | — | 12 | 1 | no | — |
| 307 | D4 | — | 4 | 1 | no | — |
| 308 | D4 | — | 6 | 8 | no | — |
| 309 | D4 | — | 12 | 1 | no | — |
| 310 | D4 | — | 12 | 2 | no | — |
| 311 | D4 | — | 12 | 2 | no | — |
| 312 | C2×C4 | — | 3 | 2 | no | — |
| 313 | C2×C4 | — | 3 | 1 | no | — |
| 314 | C2×C4 | — | 3 | 4 | no | — |
| 315 | C2×C4 | — | 3 | 2 | no | — |
| 316 | C2×C4 | — | 3 | 4 | no | — |
| 317 | C2×C4 | — | 4 | 2 | no | — |
| 318 | C2×C4 | — | 6 | 4 | no | — |
| 319 | C2×C4 | — | 6 | 2 | no | — |
| 320 | C2×C4 | — | 6 | 4 | no | — |
| 321 | C2×C4 | — | 6 | 4 | no | — |
| 322 | C2×C4 | — | 12 | 4 | no | — |
| 323 | C2×C4 | — | 12 | 2 | no | — |
| 324 | C2×C4 | C23×D3 | 1 | 4 | yes | — |
| 325 | C2×C4 | C23×D3 | 1 | 2 | yes | — |
| 326 | C2×C4 | C23×D3 | 1 | 2 | yes | — |
| 327 | C2×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 328 | C2×C4 | C23×D3 | 1 | 4 | yes | — |
| 329 | C2×C3 | — | 4 | 2 | no | — |
| 330 | C2×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 331 | C2×C3 | C2×2−1+4 | 1 | 2 | yes | — |
| 332 | D3 | — | 4 | 2 | no | — |
| 333 | D3 | — | 4 | 1 | no | — |
| 334 | C22 | — | 2 | 2 | no | — |
| 335 | C22 | — | 2 | 4 | no | — |
| 336 | C22 | — | 6 | 2 | no | — |
| 337 | C22 | — | 6 | 1 | no | — |
| 338 | C22 | — | 6 | 2 | no | — |
| 339 | C22 | — | 6 | 4 | no | — |
| 340 | C22 | C24×D3 | 1 | 1 | yes | characteristic |
| 341 | C4 | — | 2 | 4 | no | — |
| 342 | C4 | — | 2 | 1 | no | — |
| 343 | C4 | — | 2 | 2 | no | — |
| 344 | C4 | — | 2 | 2 | no | — |
| 345 | C4 | — | 2 | 4 | no | — |
| 346 | C4 | — | 3 | 2 | no | — |
| 347 | C4 | — | 3 | 4 | no | — |
| 348 | C4 | — | 6 | 2 | no | — |
| 349 | C4 | — | 6 | 4 | no | — |
| 350 | C4 | — | 6 | 4 | no | — |
| 351 | C3 | #3550 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 352 | C2 | — | 4 | 2 | no | — |
| 353 | C2 | — | 12 | 2 | no | — |
| 354 | C2 | — | 12 | 1 | no | — |
| 355 | C2 | D3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 356 | C2 | D3×2−1+4 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D3 |
| commutator, socle, cosocle | C22×C3 | C25 |
| Fitting | C3×#563 | C2 |
| prime radical | #5668 | C2 |
| hypercenter | #563 | D3 |
| hypocenter | C3 | #3550 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #563 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#563 | C2 | semidirect |
| 2. #5724 | C2 | semidirect |
| 3. #5722 | C2 | semidirect |
| 4. #5710 | C2 | semidirect |
| 5. #5702 | C2 | semidirect |
| 6. #5699 | C2 | semidirect |
| 7. #5688 | C2 | semidirect |
| 8. #5672 | C2 | semidirect |
| 10. #5664 | C2 | semidirect |
| 11. #5648 | C2 | semidirect |
| 12. #5640 | C2 | semidirect |
| 13. #5632 | C2 | semidirect |
| 70. #563 | D3 | semidirect |
| 351. C3 | #3550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#563 | 2 |
| #5724 | 2 |
| #5722 | 2 |
| #5710 | 2 |
| #5702 | 2 |
| #5699 | 2 |
| #5688 | 2 |
| #5672 | 2 |
| #5668 | 2 |
| #5664 | 2 |
| #5648 | 2 |
| #5640 | 2 |
| #5632 | 2 |
| #3550 | 3 |