Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
6184 conjugacy classes of subgroups.
The subgroup lattice has 530 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87144 | C2 | 1 | 10 | yes | maximal, complemented |
| 3 | #87144 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #87143 | C2 | 1 | 5 | yes | maximal, complemented |
| 5 | D3×#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #87140 | C2 | 1 | 5 | yes | maximal, complemented |
| 7 | #87139 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #86102 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | #86099 | C2 | 1 | 10 | yes | maximal, complemented |
| 10 | #86098 | C2 | 1 | 5 | yes | maximal, complemented |
| 11 | #86089 | C2 | 1 | 10 | yes | maximal, complemented |
| 12 | #63067 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C3×#564 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#564 | C22 | 1 | 5 | yes | — |
| 15 | C3×#564 | C22 | 1 | 10 | yes | — |
| 16 | C2×C3×#125 | C22 | 1 | 10 | yes | — |
| 17 | C2×C3×#125 | C22 | 1 | 5 | yes | — |
| 18 | #5700 | C22 | 1 | 5 | yes | — |
| 19 | #5699 | C22 | 1 | 10 | yes | — |
| 20 | #5699 | C22 | 1 | 10 | yes | — |
| 21 | #5699 | C22 | 1 | 10 | yes | — |
| 22 | #5698 | C22 | 1 | 20 | yes | — |
| 23 | #5696 | C22 | 1 | 20 | yes | — |
| 24 | #5696 | C22 | 1 | 20 | yes | — |
| 25 | #5696 | C22 | 1 | 20 | yes | — |
| 26 | #5696 | C22 | 1 | 20 | yes | — |
| 27 | #5695 | C22 | 1 | 10 | yes | — |
| 28 | #5694 | C22 | 1 | 20 | yes | — |
| 29 | #5694 | C22 | 1 | 10 | yes | — |
| 30 | #5693 | C22 | 1 | 20 | yes | — |
| 31 | #5693 | C22 | 1 | 20 | yes | — |
| 32 | #5693 | C22 | 1 | 20 | yes | — |
| 33 | #5692 | C22 | 1 | 20 | yes | — |
| 34 | #5692 | C22 | 1 | 20 | yes | — |
| 35 | #5691 | C22 | 1 | 10 | yes | — |
| 36 | #5691 | C22 | 1 | 10 | yes | — |
| 37 | #5690 | C22 | 1 | 20 | yes | — |
| 38 | #5690 | C22 | 1 | 10 | yes | — |
| 39 | #5689 | C22 | 1 | 20 | yes | — |
| 40 | #5689 | C22 | 1 | 10 | yes | — |
| 41 | #5689 | C22 | 1 | 10 | yes | — |
| 42 | #5688 | C22 | 1 | 5 | yes | — |
| 43 | #5688 | C22 | 1 | 5 | yes | — |
| 44 | #5688 | C22 | 1 | 10 | yes | — |
| 45 | D3×#125 | C22 | 1 | 5 | yes | — |
| 46 | D3×#125 | C22 | 1 | 5 | yes | — |
| 47 | D3×#125 | C22 | 1 | 10 | yes | — |
| 48 | C3⋊#564 | C22 | 1 | 10 | yes | — |
| 49 | C3⋊#564 | C22 | 1 | 10 | yes | — |
| 50 | C3⋊#564 | C22 | 1 | 5 | yes | — |
| 51 | #5685 | C22 | 1 | 20 | yes | — |
| 52 | #5685 | C22 | 1 | 20 | yes | — |
| 53 | #5685 | C22 | 1 | 10 | yes | — |
| 54 | #5515 | C22 | 1 | 20 | yes | — |
| 55 | #5514 | C22 | 1 | 10 | yes | — |
| 56 | #5513 | C22 | 1 | 10 | yes | — |
| 57 | #5513 | C22 | 1 | 20 | yes | — |
| 58 | #5511 | C22 | 1 | 20 | yes | — |
| 59 | #5511 | C22 | 1 | 10 | yes | — |
| 60 | #5507 | C22 | 1 | 10 | yes | — |
| 61 | #5504 | C22 | 1 | 10 | yes | — |
| 62 | #5500 | C22 | 1 | 10 | yes | — |
| 63 | #5479 | C22 | 1 | 10 | yes | — |
| 64 | C4×#235 | C22 | 1 | 5 | yes | — |
| 65 | #5470 | C22 | 1 | 5 | yes | — |
| 66 | #3563 | — | 3 | 10 | no | — |
| 67 | #3563 | — | 3 | 10 | no | — |
| 68 | #3563 | — | 3 | 10 | no | — |
| 69 | #3556 | — | 3 | 5 | no | — |
| 70 | #3553 | — | 3 | 5 | no | — |
| 71 | #3553 | — | 3 | 5 | no | — |
| 72 | #3531 | — | 3 | 1 | no | — |
| 73 | C2×#564 | — | 3 | 1 | no | — |
| 74 | C2×#564 | D3 | 1 | 1 | yes | characteristic, complemented |
| 75 | #3515 | — | 3 | 10 | no | — |
| 76 | #3504 | — | 3 | 5 | no | — |
| 77 | C2×#235 | C23 | 1 | 5 | yes | — |
| 78 | C3×#125 | C23 | 1 | 20 | yes | — |
| 79 | C3×#125 | C23 | 1 | 20 | yes | — |
| 80 | C3×#125 | C23 | 1 | 10 | yes | — |
| 81 | C3×#125 | C23 | 1 | 5 | yes | — |
| 82 | C3×#125 | C23 | 1 | 10 | yes | — |
| 83 | C3×#125 | C23 | 1 | 10 | yes | — |
| 84 | C3×#125 | C23 | 1 | 5 | yes | — |
| 85 | C3×#125 | C23 | 1 | 10 | yes | — |
| 86 | C3×#125 | C23 | 1 | 20 | yes | — |
| 87 | C3×#125 | C23 | 1 | 10 | yes | — |
| 88 | C2×C3×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 89 | C2×C3×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 90 | C2×C3×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 91 | C2×C3×C42 | C23 | 1 | 5 | yes | — |
| 92 | #930 | C23 | 1 | 10 | yes | — |
| 93 | #929 | C23 | 1 | 20 | yes | — |
| 94 | C4×#67 | C23 | 1 | 10 | yes | — |
| 95 | C4×#67 | C23 | 1 | 10 | yes | — |
| 96 | C4×#67 | C23 | 1 | 20 | yes | — |
| 97 | #926 | C23 | 1 | 10 | yes | — |
| 98 | #926 | C23 | 1 | 5 | yes | — |
| 99 | #924 | C23 | 1 | 20 | yes | — |
| 100 | #924 | C23 | 1 | 10 | yes | — |
| 101 | #898 | C23 | 1 | 20 | yes | — |
| 102 | #898 | C23 | 1 | 20 | yes | — |
| 103 | #898 | C23 | 1 | 20 | yes | — |
| 104 | #898 | C23 | 1 | 20 | yes | — |
| 105 | #898 | C23 | 1 | 20 | yes | — |
| 106 | #898 | C23 | 1 | 20 | yes | — |
| 107 | #897 | C23 | 1 | 10 | yes | — |
| 108 | #897 | C23 | 1 | 10 | yes | — |
| 109 | #897 | C23 | 1 | 20 | yes | — |
| 110 | #897 | C23 | 1 | 20 | yes | — |
| 111 | #896 | C23 | 1 | 20 | yes | — |
| 112 | #896 | C23 | 1 | 20 | yes | — |
| 113 | #896 | C23 | 1 | 20 | yes | — |
| 114 | #896 | C23 | 1 | 20 | yes | — |
| 115 | #896 | C23 | 1 | 20 | yes | — |
| 116 | #896 | C23 | 1 | 20 | yes | — |
| 117 | #895 | C23 | 1 | 10 | yes | — |
| 118 | #895 | C23 | 1 | 10 | yes | — |
| 119 | #894 | C23 | 1 | 20 | yes | — |
| 120 | #894 | C23 | 1 | 20 | yes | — |
| 121 | #894 | C23 | 1 | 20 | yes | — |
| 122 | #894 | C23 | 1 | 20 | yes | — |
| 123 | #893 | C23 | 1 | 20 | yes | — |
| 124 | #893 | C23 | 1 | 10 | yes | — |
| 125 | #893 | C23 | 1 | 10 | yes | — |
| 126 | #892 | C23 | 1 | 10 | yes | — |
| 127 | #892 | C23 | 1 | 10 | yes | — |
| 128 | #892 | C23 | 1 | 10 | yes | — |
| 129 | #892 | C23 | 1 | 10 | yes | — |
| 130 | #892 | C23 | 1 | 20 | yes | — |
| 131 | D3×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 132 | D3×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 133 | D3×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 134 | D3×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 135 | D3×C4⋊C4 | C23 | 1 | 20 | yes | — |
| 136 | #890 | C23 | 1 | 10 | yes | — |
| 137 | #890 | C23 | 1 | 20 | yes | — |
| 138 | #890 | C23 | 1 | 20 | yes | — |
| 139 | #890 | C23 | 1 | 10 | yes | — |
| 140 | #890 | C23 | 1 | 10 | yes | — |
| 141 | #890 | C23 | 1 | 10 | yes | — |
| 142 | #889 | C23 | 1 | 20 | yes | — |
| 143 | #889 | C23 | 1 | 20 | yes | — |
| 144 | #889 | C23 | 1 | 20 | yes | — |
| 145 | #889 | C23 | 1 | 20 | yes | — |
| 146 | #889 | C23 | 1 | 20 | yes | — |
| 147 | #889 | C23 | 1 | 20 | yes | — |
| 148 | #889 | C23 | 1 | 20 | yes | — |
| 149 | #889 | C23 | 1 | 20 | yes | — |
| 150 | #888 | C23 | 1 | 10 | yes | — |
| 151 | #888 | C23 | 1 | 10 | yes | — |
| 152 | #888 | C23 | 1 | 10 | yes | — |
| 153 | #888 | C23 | 1 | 20 | yes | — |
| 154 | #888 | C23 | 1 | 20 | yes | — |
| 155 | #888 | C23 | 1 | 10 | yes | — |
| 156 | #887 | C23 | 1 | 10 | yes | — |
| 157 | #887 | C23 | 1 | 20 | yes | — |
| 158 | #887 | C23 | 1 | 10 | yes | — |
| 159 | #887 | C23 | 1 | 20 | yes | — |
| 160 | #887 | C23 | 1 | 20 | yes | — |
| 161 | #876 | C23 | 1 | 20 | yes | — |
| 162 | #875 | C23 | 1 | 10 | yes | — |
| 163 | C4×D12 | C23 | 1 | 10 | yes | — |
| 164 | C4×D12 | C23 | 1 | 10 | yes | — |
| 165 | #872 | C23 | 1 | 5 | yes | — |
| 166 | #872 | C23 | 1 | 5 | yes | — |
| 167 | #872 | C23 | 1 | 20 | yes | — |
| 168 | C42×D3 | C23 | 1 | 5 | yes | — |
| 169 | C42×D3 | C23 | 1 | 5 | yes | — |
| 170 | #870 | C23 | 1 | 10 | yes | — |
| 171 | #870 | C23 | 1 | 5 | yes | — |
| 172 | #870 | C23 | 1 | 5 | yes | — |
| 173 | #869 | C23 | 1 | 10 | yes | — |
| 174 | C4×Dic6 | C23 | 1 | 10 | yes | — |
| 175 | C4×Dic6 | C23 | 1 | 10 | yes | — |
| 176 | C4×Dic6 | C23 | 1 | 20 | yes | — |
| 177 | #564 | — | 3 | 5 | no | — |
| 178 | #564 | — | 3 | 10 | no | — |
| 179 | #564 | — | 3 | 10 | no | — |
| 180 | #564 | C2×D3 | 1 | 1 | yes | characteristic |
| 181 | #564 | C2×D3 | 1 | 5 | yes | — |
| 182 | #564 | C2×D3 | 1 | 10 | yes | — |
| 183 | #563 | — | 3 | 10 | no | — |
| 184 | #563 | — | 3 | 10 | no | — |
| 185 | #563 | — | 3 | 10 | no | — |
| 186 | #562 | — | 3 | 5 | no | — |
| 187 | #557 | — | 3 | 20 | no | — |
| 188 | #557 | — | 3 | 10 | no | — |
| 189 | #557 | — | 3 | 20 | no | — |
| 190 | #554 | — | 3 | 20 | no | — |
| 191 | #554 | — | 3 | 10 | no | — |
| 192 | #554 | — | 3 | 10 | no | — |
| 193 | #554 | — | 3 | 20 | no | — |
| 194 | #553 | — | 3 | 10 | no | — |
| 195 | #553 | — | 3 | 10 | no | — |
| 196 | #552 | — | 3 | 20 | no | — |
| 197 | #552 | — | 3 | 20 | no | — |
| 198 | #552 | — | 3 | 20 | no | — |
| 199 | #552 | — | 3 | 10 | no | — |
| 200 | #552 | — | 3 | 20 | no | — |
| 201 | #552 | — | 3 | 20 | no | — |
| 202 | #552 | — | 3 | 10 | no | — |
| 203 | #547 | — | 3 | 10 | no | — |
| 204 | #544 | — | 3 | 10 | no | — |
| 205 | #544 | — | 3 | 10 | no | — |
| 206 | #544 | — | 3 | 20 | no | — |
| 207 | #544 | — | 3 | 10 | no | — |
| 208 | #541 | — | 3 | 20 | no | — |
| 209 | #541 | — | 3 | 20 | no | — |
| 210 | #541 | — | 3 | 20 | no | — |
| 211 | #541 | — | 3 | 20 | no | — |
| 212 | #541 | — | 3 | 20 | no | — |
| 213 | #539 | — | 3 | 20 | no | — |
| 214 | #539 | — | 3 | 20 | no | — |
| 215 | #539 | — | 3 | 20 | no | — |
| 216 | #533 | — | 3 | 5 | no | — |
| 217 | #533 | — | 3 | 5 | no | — |
| 218 | #533 | — | 3 | 10 | no | — |
| 219 | #533 | — | 3 | 5 | no | — |
| 220 | #529 | — | 3 | 10 | no | — |
| 221 | #529 | — | 3 | 10 | no | — |
| 222 | #529 | — | 3 | 10 | no | — |
| 223 | C2×#125 | — | 3 | 5 | no | — |
| 224 | C2×#125 | — | 3 | 5 | no | — |
| 225 | C2×#125 | — | 3 | 10 | no | — |
| 226 | C2×#125 | C2×D3 | 1 | 5 | yes | — |
| 227 | C2×#125 | C2×D3 | 1 | 10 | yes | — |
| 228 | #520 | — | 3 | 10 | no | — |
| 229 | C4×#41 | — | 3 | 5 | no | — |
| 230 | C22×C3×C4 | C24 | 1 | 5 | yes | — |
| 231 | C22×C3×C4 | C24 | 1 | 10 | yes | — |
| 232 | C2×#67 | C24 | 1 | 5 | yes | — |
| 233 | C2×#67 | C24 | 1 | 1 | yes | characteristic |
| 234 | #235 | — | 2 | 20 | no | — |
| 235 | C2×D12 | C24 | 1 | 5 | yes | — |
| 236 | C2×D12 | C24 | 1 | 10 | yes | — |
| 237 | C2×C4×D3 | C24 | 1 | 5 | yes | — |
| 238 | C2×C4×D3 | C24 | 1 | 5 | yes | — |
| 239 | C2×C4×D3 | C24 | 1 | 10 | yes | — |
| 240 | C2×C4×D3 | C24 | 1 | 10 | yes | — |
| 241 | C2×C4×D3 | C24 | 1 | 20 | yes | — |
| 242 | C2×Dic6 | C24 | 1 | 5 | yes | — |
| 243 | C2×Dic6 | C24 | 1 | 20 | yes | — |
| 244 | C2×Dic6 | C24 | 1 | 10 | yes | — |
| 245 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 246 | C3×C4⋊C4 | C24 | 1 | 20 | yes | — |
| 247 | C3×C4⋊C4 | C24 | 1 | 20 | yes | — |
| 248 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 249 | C3×C4⋊C4 | C24 | 1 | 20 | yes | — |
| 250 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 251 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 252 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 253 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 254 | C3×C42 | C24 | 1 | 10 | yes | — |
| 255 | C3×C42 | C24 | 1 | 5 | yes | — |
| 256 | C3×C42 | C24 | 1 | 5 | yes | — |
| 257 | #217 | C24 | 1 | 10 | yes | — |
| 258 | (C2×D3)⋊C4 | C24 | 1 | 10 | yes | — |
| 259 | (C2×D3)⋊C4 | C24 | 1 | 10 | yes | — |
| 260 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 261 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 262 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 263 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 264 | C4⋊Dic3 | C24 | 1 | 20 | yes | — |
| 265 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 266 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 267 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 268 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 269 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 270 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 271 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 272 | Dic3⋊C4 | C24 | 1 | 10 | yes | — |
| 273 | Dic3⋊C4 | C24 | 1 | 10 | yes | — |
| 274 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 275 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 276 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 277 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 278 | C4×Dic3 | C24 | 1 | 20 | yes | — |
| 279 | C4×Dic3 | C24 | 1 | 10 | yes | — |
| 280 | C4×Dic3 | C24 | 1 | 10 | yes | — |
| 281 | C4×Dic3 | C24 | 1 | 20 | yes | — |
| 282 | C4×Dic3 | C24 | 1 | 5 | yes | — |
| 283 | C4×Dic3 | C24 | 1 | 5 | yes | — |
| 284 | C2×#41 | — | 3 | 5 | no | — |
| 285 | C4⋊Q8 | — | 3 | 10 | no | — |
| 286 | C4⋊Q8 | — | 3 | 10 | no | — |
| 287 | C4⋊Q8 | — | 3 | 10 | no | — |
| 288 | C4⋊Q8 | — | 3 | 10 | no | — |
| 289 | C4⋊Q8 | — | 3 | 20 | no | — |
| 290 | C4⋊Q8 | — | 3 | 20 | no | — |
| 291 | C4⋊Q8 | — | 3 | 10 | no | — |
| 292 | #126 | — | 3 | 20 | no | — |
| 293 | #126 | — | 3 | 20 | no | — |
| 294 | #126 | — | 3 | 20 | no | — |
| 295 | #126 | — | 3 | 20 | no | — |
| 296 | #126 | — | 3 | 20 | no | — |
| 297 | #126 | — | 3 | 20 | no | — |
| 298 | #126 | — | 3 | 20 | no | — |
| 299 | #125 | — | 3 | 20 | no | — |
| 300 | #125 | — | 3 | 20 | no | — |
| 301 | #125 | — | 3 | 10 | no | — |
| 302 | #125 | — | 3 | 10 | no | — |
| 303 | #125 | — | 3 | 10 | no | — |
| 304 | #125 | — | 3 | 20 | no | — |
| 305 | #125 | — | 3 | 20 | no | — |
| 306 | #125 | — | 3 | 10 | no | — |
| 307 | #125 | — | 3 | 20 | no | — |
| 308 | #125 | — | 3 | 20 | no | — |
| 309 | #125 | — | 3 | 20 | no | — |
| 310 | #125 | — | 3 | 20 | no | — |
| 311 | #125 | — | 3 | 20 | no | — |
| 312 | #125 | — | 3 | 20 | no | — |
| 313 | #125 | — | 3 | 5 | no | — |
| 314 | #125 | — | 3 | 10 | no | — |
| 315 | #125 | — | 3 | 5 | no | — |
| 316 | #125 | C22×D3 | 1 | 10 | yes | — |
| 317 | #125 | C22×D3 | 1 | 5 | yes | — |
| 318 | #125 | C22×D3 | 1 | 5 | yes | — |
| 319 | #125 | C22×D3 | 1 | 10 | yes | — |
| 320 | #125 | C22×D3 | 1 | 20 | yes | — |
| 321 | #125 | C22×D3 | 1 | 20 | yes | — |
| 322 | #125 | C22×D3 | 1 | 10 | yes | — |
| 323 | #125 | C22×D3 | 1 | 10 | yes | — |
| 324 | #125 | C22×D3 | 1 | 20 | yes | — |
| 325 | #125 | C22×D3 | 1 | 10 | yes | — |
| 326 | #124 | — | 3 | 10 | no | — |
| 327 | #123 | — | 3 | 20 | no | — |
| 328 | #123 | — | 3 | 20 | no | — |
| 329 | #123 | — | 3 | 20 | no | — |
| 330 | #123 | — | 3 | 20 | no | — |
| 331 | #123 | — | 3 | 20 | no | — |
| 332 | C22⋊Q8 | — | 3 | 10 | no | — |
| 333 | C22⋊Q8 | — | 3 | 20 | no | — |
| 334 | C22⋊Q8 | — | 3 | 10 | no | — |
| 335 | C22⋊Q8 | — | 3 | 10 | no | — |
| 336 | C22⋊Q8 | — | 3 | 20 | no | — |
| 337 | C22⋊Q8 | — | 3 | 20 | no | — |
| 338 | C22⋊Q8 | — | 3 | 20 | no | — |
| 339 | C22⋊Q8 | — | 3 | 20 | no | — |
| 340 | C22⋊Q8 | — | 3 | 20 | no | — |
| 341 | C22⋊Q8 | — | 3 | 20 | no | — |
| 342 | C22⋊Q8 | — | 3 | 20 | no | — |
| 343 | C22⋊Q8 | — | 3 | 20 | no | — |
| 344 | #121 | — | 3 | 10 | no | — |
| 345 | #121 | — | 3 | 10 | no | — |
| 346 | #121 | — | 3 | 10 | no | — |
| 347 | C4×Q8 | — | 3 | 20 | no | — |
| 348 | C4×Q8 | — | 3 | 10 | no | — |
| 349 | C4×Q8 | — | 3 | 10 | no | — |
| 350 | C4×Q8 | — | 3 | 20 | no | — |
| 351 | C4×Q8 | — | 3 | 20 | no | — |
| 352 | C4×Q8 | — | 3 | 10 | no | — |
| 353 | C4×Q8 | — | 3 | 10 | no | — |
| 354 | C4×Q8 | — | 3 | 20 | no | — |
| 355 | C4×D4 | — | 3 | 10 | no | — |
| 356 | C4×D4 | — | 3 | 10 | no | — |
| 357 | C4×D4 | — | 3 | 20 | no | — |
| 358 | C4×D4 | — | 3 | 20 | no | — |
| 359 | C4×D4 | — | 3 | 10 | no | — |
| 360 | C4×D4 | — | 3 | 10 | no | — |
| 361 | C4×D4 | — | 3 | 10 | no | — |
| 362 | C4×D4 | — | 3 | 10 | no | — |
| 363 | #117 | — | 3 | 5 | no | — |
| 364 | #117 | — | 3 | 10 | no | — |
| 365 | #117 | — | 3 | 10 | no | — |
| 366 | #117 | — | 3 | 10 | no | — |
| 367 | #117 | — | 3 | 20 | no | — |
| 368 | #117 | — | 3 | 10 | no | — |
| 369 | #117 | — | 3 | 10 | no | — |
| 370 | #117 | — | 3 | 5 | no | — |
| 371 | #117 | — | 3 | 5 | no | — |
| 372 | #117 | — | 3 | 20 | no | — |
| 373 | C2×C4⋊C4 | — | 3 | 10 | no | — |
| 374 | C2×C4⋊C4 | — | 3 | 10 | no | — |
| 375 | C2×C4⋊C4 | — | 3 | 10 | no | — |
| 376 | C2×C4⋊C4 | — | 3 | 10 | no | — |
| 377 | C2×C4⋊C4 | — | 3 | 20 | no | — |
| 378 | C2×C4⋊C4 | C22×D3 | 1 | 10 | yes | — |
| 379 | C2×C4⋊C4 | C22×D3 | 1 | 10 | yes | — |
| 380 | C2×C4⋊C4 | C22×D3 | 1 | 10 | yes | — |
| 381 | C2×C42 | — | 3 | 5 | no | — |
| 382 | C2×C42 | — | 3 | 5 | no | — |
| 383 | C2×C42 | C22×D3 | 1 | 5 | yes | — |
| 384 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 385 | C22×D3 | C25 | 1 | 5 | yes | — |
| 386 | C22×D3 | C25 | 1 | 1 | yes | characteristic |
| 387 | C2×C3×C4 | — | 2 | 10 | no | — |
| 388 | C2×C3×C4 | — | 4 | 10 | no | — |
| 389 | C2×C3×C4 | C25 | 1 | 5 | yes | — |
| 390 | C2×C3×C4 | C25 | 1 | 10 | yes | — |
| 391 | C2×C3×C4 | C25 | 1 | 5 | yes | — |
| 392 | C2×C3×C4 | C25 | 1 | 10 | yes | — |
| 393 | #67 | — | 2 | 10 | no | — |
| 394 | #67 | 2−1+4 | 1 | 4 | yes | — |
| 395 | C2×Dic3 | C25 | 1 | 5 | yes | — |
| 396 | C2×Dic3 | C25 | 1 | 10 | yes | — |
| 397 | C2×Dic3 | C25 | 1 | 10 | yes | — |
| 398 | C2×Dic3 | C25 | 1 | 1 | yes | characteristic |
| 399 | D12 | — | 2 | 10 | no | — |
| 400 | D12 | — | 4 | 10 | no | — |
| 401 | C4×D3 | — | 2 | 10 | no | — |
| 402 | C4×D3 | — | 2 | 10 | no | — |
| 403 | C4×D3 | — | 4 | 10 | no | — |
| 404 | C4×D3 | — | 4 | 20 | no | — |
| 405 | C4×D3 | — | 4 | 10 | no | — |
| 406 | Dic6 | — | 2 | 10 | no | — |
| 407 | Dic6 | — | 4 | 10 | no | — |
| 408 | Dic6 | — | 4 | 20 | no | — |
| 409 | #41 | — | 6 | 20 | no | — |
| 410 | C2×Q8 | — | 3 | 5 | no | — |
| 411 | C2×Q8 | — | 3 | 20 | no | — |
| 412 | C2×Q8 | — | 3 | 10 | no | — |
| 413 | C2×D4 | — | 3 | 1 | no | — |
| 414 | C2×D4 | — | 3 | 5 | no | — |
| 415 | C2×D4 | — | 3 | 5 | no | — |
| 416 | C2×D4 | — | 3 | 10 | no | — |
| 417 | C22×C4 | — | 3 | 5 | no | — |
| 418 | C22×C4 | — | 3 | 5 | no | — |
| 419 | C22×C4 | — | 3 | 10 | no | — |
| 420 | C22×C4 | — | 3 | 10 | no | — |
| 421 | C22×C4 | — | 3 | 20 | no | — |
| 422 | C22×C4 | C23×D3 | 1 | 5 | yes | — |
| 423 | C22×C4 | C23×D3 | 1 | 10 | yes | — |
| 424 | C4⋊C4 | — | 3 | 10 | no | — |
| 425 | C4⋊C4 | — | 3 | 10 | no | — |
| 426 | C4⋊C4 | — | 3 | 20 | no | — |
| 427 | C4⋊C4 | — | 3 | 10 | no | — |
| 428 | C4⋊C4 | — | 3 | 10 | no | — |
| 429 | C4⋊C4 | — | 3 | 20 | no | — |
| 430 | C4⋊C4 | — | 3 | 20 | no | — |
| 431 | C4⋊C4 | — | 3 | 20 | no | — |
| 432 | C4⋊C4 | — | 3 | 20 | no | — |
| 433 | C4⋊C4 | — | 3 | 10 | no | — |
| 434 | C4⋊C4 | — | 3 | 10 | no | — |
| 435 | C4⋊C4 | — | 3 | 10 | no | — |
| 436 | C4⋊C4 | — | 3 | 20 | no | — |
| 437 | C4⋊C4 | — | 3 | 20 | no | — |
| 438 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 439 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 440 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 441 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 442 | C4⋊C4 | C23×D3 | 1 | 20 | yes | — |
| 443 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 444 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 445 | C4⋊C4 | C23×D3 | 1 | 20 | yes | — |
| 446 | C4⋊C4 | C23×D3 | 1 | 20 | yes | — |
| 447 | C22⋊C4 | — | 3 | 10 | no | — |
| 448 | C22⋊C4 | — | 3 | 10 | no | — |
| 449 | C22⋊C4 | — | 3 | 20 | no | — |
| 450 | C22⋊C4 | — | 3 | 20 | no | — |
| 451 | C22⋊C4 | — | 3 | 20 | no | — |
| 452 | C22⋊C4 | — | 3 | 20 | no | — |
| 453 | C22⋊C4 | — | 3 | 10 | no | — |
| 454 | C42 | — | 3 | 5 | no | — |
| 455 | C42 | — | 3 | 10 | no | — |
| 456 | C42 | — | 3 | 5 | no | — |
| 457 | C42 | — | 3 | 10 | no | — |
| 458 | C42 | — | 3 | 20 | no | — |
| 459 | C42 | — | 3 | 20 | no | — |
| 460 | C42 | C23×D3 | 1 | 5 | yes | — |
| 461 | C42 | C23×D3 | 1 | 5 | yes | — |
| 462 | C42 | C23×D3 | 1 | 10 | yes | — |
| 463 | C22×C3 | — | 2 | 2 | no | — |
| 464 | C22×C3 | C2×2−1+4 | 1 | 2 | yes | — |
| 465 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 466 | C2×D3 | — | 2 | 2 | no | — |
| 467 | C2×D3 | — | 2 | 5 | no | — |
| 468 | C2×D3 | — | 2 | 10 | no | — |
| 469 | C2×D3 | C2×2−1+4 | 1 | 2 | yes | — |
| 470 | C3×C4 | — | 2 | 5 | no | — |
| 471 | C3×C4 | — | 2 | 5 | no | — |
| 472 | C3×C4 | — | 2 | 10 | no | — |
| 473 | C3×C4 | — | 2 | 10 | no | — |
| 474 | Dic3 | — | 2 | 5 | no | — |
| 475 | Dic3 | — | 2 | 10 | no | — |
| 476 | Dic3 | — | 2 | 10 | no | — |
| 477 | Dic3 | C2×2−1+4 | 1 | 2 | yes | — |
| 478 | C23 | — | 3 | 1 | no | — |
| 479 | C23 | — | 3 | 5 | no | — |
| 480 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 481 | Q8 | — | 6 | 10 | no | — |
| 482 | Q8 | — | 12 | 10 | no | — |
| 483 | Q8 | — | 12 | 20 | no | — |
| 484 | D4 | — | 3 | 4 | no | — |
| 485 | D4 | — | 6 | 10 | no | — |
| 486 | D4 | — | 6 | 10 | no | — |
| 487 | D4 | — | 12 | 10 | no | — |
| 488 | C2×C4 | — | 2 | 10 | no | — |
| 489 | C2×C4 | — | 3 | 1 | no | — |
| 490 | C2×C4 | — | 3 | 10 | no | — |
| 491 | C2×C4 | — | 3 | 5 | no | — |
| 492 | C2×C4 | — | 3 | 10 | no | — |
| 493 | C2×C4 | — | 4 | 10 | no | — |
| 494 | C2×C4 | — | 6 | 10 | no | — |
| 495 | C2×C4 | — | 6 | 10 | no | — |
| 496 | C2×C4 | — | 12 | 10 | no | — |
| 497 | C2×C4 | — | 12 | 10 | no | — |
| 498 | C2×C4 | — | 12 | 20 | no | — |
| 499 | C2×C4 | C24×D3 | 1 | 5 | yes | — |
| 500 | C2×C4 | C24×D3 | 1 | 5 | yes | — |
| 501 | C2×C4 | C24×D3 | 1 | 10 | yes | — |
| 502 | C2×C4 | C24×D3 | 1 | 10 | yes | — |
| 503 | C2×C3 | — | 2 | 2 | no | — |
| 504 | C2×C3 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 505 | C2×C3 | 2−1+6 | 1 | 2 | yes | — |
| 506 | D3 | — | 2 | 2 | no | — |
| 507 | D3 | — | 4 | 5 | no | — |
| 508 | C22 | — | 2 | 2 | no | — |
| 509 | C22 | — | 3 | 2 | no | — |
| 510 | C22 | — | 6 | 2 | no | — |
| 511 | C22 | — | 6 | 5 | no | — |
| 512 | C22 | — | 6 | 10 | no | — |
| 513 | C22 | D3×2−1+4 | 1 | 2 | yes | — |
| 514 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 515 | C4 | — | 2 | 5 | no | — |
| 516 | C4 | — | 2 | 5 | no | — |
| 517 | C4 | — | 2 | 10 | no | — |
| 518 | C4 | — | 2 | 10 | no | — |
| 519 | C4 | — | 3 | 2 | no | — |
| 520 | C4 | — | 6 | 5 | no | — |
| 521 | C4 | — | 6 | 10 | no | — |
| 522 | C4 | — | 6 | 10 | no | — |
| 523 | C3 | #63067 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 524 | C2 | — | 2 | 2 | no | — |
| 525 | C2 | — | 6 | 2 | no | — |
| 526 | C2 | — | 12 | 5 | no | — |
| 527 | C2 | C2×D3×2−1+4 | 1 | 1 | yes | characteristic |
| 528 | C2 | #87571 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Fitting | C2×C3×#564 | C2 |
| hypercenter | C2×#564 | D3 |
| hypocenter | C3 | #63067 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×#564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#564 | C2 | semidirect |
| 2. #87144 | C2 | semidirect |
| 3. #87144 | C2 | semidirect |
| 4. #87143 | C2 | semidirect |
| 5. D3×#564 | C2 | semidirect |
| 6. #87140 | C2 | semidirect |
| 7. #87139 | C2 | semidirect |
| 8. #86102 | C2 | semidirect |
| 9. #86099 | C2 | semidirect |
| 10. #86098 | C2 | semidirect |
| 11. #86089 | C2 | semidirect |
| 74. C2×#564 | D3 | semidirect |
| 523. C3 | #63067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#564 | 2 |
| #87144 | 2 |
| #87143 | 2 |
| D3×#564 | 2 |
| #87140 | 2 |
| #87139 | 2 |
| #86102 | 2 |
| #86099 | 2 |
| #86098 | 2 |
| #86089 | 2 |
| #63067 | 3 |