Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1782 conjugacy classes of subgroups.
The subgroup lattice has 490 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Q8×#235 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#5570 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×Q8×M16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #79983 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #79972 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #79933 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #79925 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #79068 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #79057 | C2 | 1 | 3 | yes | maximal |
| 10 | #78537 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C4×#909 | C2 | 1 | 3 | yes | maximal |
| 12 | #61322 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×C3×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 14 | Q8×#67 | — | 2 | 1 | no | — |
| 15 | C2×Q8×Dic3 | — | 2 | 1 | no | — |
| 16 | C2×#909 | C22 | 1 | 3 | yes | — |
| 17 | #5579 | C22 | 1 | 3 | yes | — |
| 18 | #5578 | — | 2 | 3 | no | — |
| 19 | Q8×D12 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×D3×Q8 | — | 2 | 1 | no | — |
| 21 | #5570 | — | 2 | 1 | no | — |
| 22 | #5570 | — | 2 | 3 | no | — |
| 23 | #5570 | C22 | 1 | 2 | yes | — |
| 24 | #5570 | C22 | 1 | 6 | yes | — |
| 25 | #5567 | C22 | 1 | 3 | yes | — |
| 26 | Q8×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 27 | #5511 | — | 2 | 3 | no | — |
| 28 | C2×#890 | — | 2 | 3 | no | — |
| 29 | C4×#235 | C22 | 1 | 3 | yes | — |
| 30 | #5470 | C22 | 1 | 3 | yes | — |
| 31 | C2×#869 | C22 | 1 | 3 | yes | — |
| 32 | C2×C4×Dic6 | C22 | 1 | 3 | yes | — |
| 33 | C3×#446 | C22 | 1 | 6 | yes | — |
| 34 | C3×C8×Q8 | C22 | 1 | 2 | yes | — |
| 35 | C3×#423 | C22 | 1 | 3 | yes | — |
| 36 | C3×C4×M16 | C22 | 1 | 3 | yes | — |
| 37 | #5133 | C22 | 1 | 1 | yes | characteristic |
| 38 | #5121 | C22 | 1 | 3 | yes | — |
| 39 | #5120 | C22 | 1 | 3 | yes | — |
| 40 | #5120 | C22 | 1 | 6 | yes | — |
| 41 | #4851 | C22 | 1 | 6 | yes | — |
| 42 | #4850 | C22 | 1 | 6 | yes | — |
| 43 | #4849 | C22 | 1 | 6 | yes | — |
| 44 | #4849 | C22 | 1 | 6 | yes | — |
| 45 | #4841 | C22 | 1 | 6 | yes | — |
| 46 | #4841 | C22 | 1 | 6 | yes | — |
| 47 | #4829 | C22 | 1 | 12 | yes | — |
| 48 | #4716 | C22 | 1 | 6 | yes | — |
| 49 | #4710 | C22 | 1 | 6 | yes | — |
| 50 | #4703 | C22 | 1 | 12 | yes | — |
| 51 | C4×Dic12 | C22 | 1 | 6 | yes | — |
| 52 | C4×#204 | C22 | 1 | 6 | yes | — |
| 53 | #4681 | C22 | 1 | 6 | yes | — |
| 54 | #4681 | C22 | 1 | 6 | yes | — |
| 55 | Q8×#41 | — | 3 | 1 | no | — |
| 56 | C2×#557 | — | 3 | 1 | no | — |
| 57 | #3374 | — | 3 | 6 | no | — |
| 58 | #3372 | — | 3 | 6 | no | — |
| 59 | #3363 | — | 3 | 2 | no | — |
| 60 | #3359 | — | 3 | 2 | no | — |
| 61 | #3139 | — | 3 | 3 | no | — |
| 62 | #3078 | — | 3 | 3 | no | — |
| 63 | #3039 | — | 3 | 3 | no | — |
| 64 | Q8×M16 | D3 | 1 | 1 | yes | characteristic, complemented |
| 65 | C4×#137 | — | 3 | 3 | no | — |
| 66 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 67 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 68 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 70 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 72 | C3×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 73 | C3×C4×Q8 | D4 | 1 | 3 | yes | — |
| 74 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 75 | C3×C4×Q8 | C23 | 1 | 3 | yes | — |
| 76 | C2×C3×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 77 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 78 | #946 | — | 2 | 3 | no | — |
| 79 | Q8×Dic3 | — | 2 | 6 | no | — |
| 80 | Q8×Dic3 | — | 2 | 2 | no | — |
| 81 | Q8×Dic3 | — | 2 | 1 | no | — |
| 82 | #944 | — | 2 | 3 | no | — |
| 83 | C4×#67 | — | 2 | 3 | no | — |
| 84 | C4×#67 | — | 2 | 3 | no | — |
| 85 | #926 | C23 | 1 | 3 | yes | — |
| 86 | C2×C4⋊Dic3 | — | 2 | 3 | no | — |
| 87 | C2×C4⋊Dic3 | — | 2 | 3 | no | — |
| 88 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 89 | #924 | — | 2 | 3 | no | — |
| 90 | #924 | — | 2 | 3 | no | — |
| 91 | C2×Dic3⋊C4 | — | 2 | 3 | no | — |
| 92 | C2×C4×Dic3 | — | 2 | 3 | no | — |
| 93 | #909 | — | 2 | 12 | no | — |
| 94 | C2×Dic12 | C23 | 1 | 6 | yes | — |
| 95 | C2×#204 | C23 | 1 | 6 | yes | — |
| 96 | #897 | — | 2 | 3 | no | — |
| 97 | #896 | — | 2 | 6 | no | — |
| 98 | D3×C4⋊C4 | — | 2 | 3 | no | — |
| 99 | #890 | — | 2 | 6 | no | — |
| 100 | #890 | — | 2 | 6 | no | — |
| 101 | #890 | — | 2 | 12 | no | — |
| 102 | #889 | — | 2 | 6 | no | — |
| 103 | #888 | — | 2 | 3 | no | — |
| 104 | #887 | — | 2 | 3 | no | — |
| 105 | C4×D12 | C23 | 1 | 3 | yes | — |
| 106 | C4×D12 | C23 | 1 | 3 | yes | — |
| 107 | #872 | — | 2 | 3 | no | — |
| 108 | C42×D3 | — | 2 | 3 | no | — |
| 109 | #870 | C23 | 1 | 6 | yes | — |
| 110 | #869 | — | 2 | 3 | no | — |
| 111 | #869 | — | 2 | 3 | no | — |
| 112 | #869 | C23 | 1 | 6 | yes | — |
| 113 | #869 | C23 | 1 | 6 | yes | — |
| 114 | #869 | C23 | 1 | 3 | yes | — |
| 115 | #869 | C23 | 1 | 3 | yes | — |
| 116 | C4×Dic6 | — | 2 | 3 | no | — |
| 117 | C4×Dic6 | — | 2 | 3 | no | — |
| 118 | C4×Dic6 | — | 2 | 3 | no | — |
| 119 | C4×Dic6 | — | 2 | 3 | no | — |
| 120 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 121 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 122 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 123 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 124 | C3×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 125 | C3×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 126 | C3×#97 | C23 | 1 | 6 | yes | — |
| 127 | C3×C4×C8 | C23 | 1 | 6 | yes | — |
| 128 | #821 | C23 | 1 | 2 | yes | — |
| 129 | #818 | C23 | 1 | 6 | yes | — |
| 130 | #817 | C23 | 1 | 6 | yes | — |
| 131 | #816 | C23 | 1 | 6 | yes | — |
| 132 | #816 | C23 | 1 | 6 | yes | — |
| 133 | #816 | C23 | 1 | 12 | yes | — |
| 134 | #816 | C23 | 1 | 12 | yes | — |
| 135 | #816 | C23 | 1 | 2 | yes | — |
| 136 | C2×#137 | — | 3 | 3 | no | — |
| 137 | Q82 | — | 3 | 1 | no | — |
| 138 | #557 | — | 3 | 3 | no | — |
| 139 | #557 | — | 3 | 2 | no | — |
| 140 | #557 | — | 3 | 6 | no | — |
| 141 | #557 | — | 6 | 1 | no | — |
| 142 | #557 | — | 6 | 3 | no | — |
| 143 | #554 | — | 3 | 3 | no | — |
| 144 | #554 | — | 6 | 3 | no | — |
| 145 | D4×Q8 | — | 3 | 1 | no | — |
| 146 | D4×Q8 | — | 6 | 1 | no | — |
| 147 | #533 | — | 3 | 3 | no | — |
| 148 | #533 | — | 6 | 3 | no | — |
| 149 | C2×C4⋊Q8 | — | 3 | 3 | no | — |
| 150 | C2×#125 | — | 6 | 3 | no | — |
| 151 | C4×#41 | — | 3 | 3 | no | — |
| 152 | C2×C4×Q8 | — | 3 | 3 | no | — |
| 153 | C2×C4×Q8 | — | 6 | 1 | no | — |
| 154 | C2×C4×Q8 | — | 6 | 1 | no | — |
| 155 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 156 | #491 | — | 3 | 12 | no | — |
| 157 | #487 | — | 3 | 6 | no | — |
| 158 | #487 | — | 3 | 6 | no | — |
| 159 | #479 | — | 3 | 12 | no | — |
| 160 | #477 | — | 3 | 6 | no | — |
| 161 | #475 | — | 3 | 6 | no | — |
| 162 | #462 | — | 3 | 6 | no | — |
| 163 | #462 | — | 3 | 6 | no | — |
| 164 | #461 | — | 3 | 6 | no | — |
| 165 | #461 | — | 3 | 6 | no | — |
| 166 | #446 | C2×D3 | 1 | 6 | yes | — |
| 167 | C8×Q8 | C2×D3 | 1 | 2 | yes | — |
| 168 | #441 | — | 3 | 6 | no | — |
| 169 | #440 | — | 3 | 6 | no | — |
| 170 | C4×Q16 | — | 3 | 6 | no | — |
| 171 | C4×SD16 | — | 3 | 6 | no | — |
| 172 | #428 | — | 3 | 3 | no | — |
| 173 | #423 | C2×D3 | 1 | 3 | yes | — |
| 174 | #419 | — | 3 | 6 | no | — |
| 175 | #419 | — | 3 | 3 | no | — |
| 176 | #417 | — | 3 | 1 | no | — |
| 177 | C4×M16 | C2×D3 | 1 | 3 | yes | — |
| 178 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 179 | C2×C3×Q8 | C2×D4 | 1 | 3 | yes | — |
| 180 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 182 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 183 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 184 | C2×#67 | — | 2 | 1 | no | — |
| 185 | C22×Dic3 | — | 2 | 1 | no | — |
| 186 | C22×Dic3 | — | 2 | 3 | no | — |
| 187 | D3×Q8 | — | 4 | 4 | no | — |
| 188 | #235 | — | 2 | 2 | no | — |
| 189 | #235 | #41 | 1 | 4 | yes | — |
| 190 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×D3 | — | 2 | 1 | no | — |
| 192 | C2×C4×D3 | — | 2 | 3 | no | — |
| 193 | C2×C4×D3 | — | 2 | 3 | no | — |
| 194 | C2×Dic6 | — | 2 | 6 | no | — |
| 195 | C2×Dic6 | — | 2 | 6 | no | — |
| 196 | C2×Dic6 | — | 2 | 3 | no | — |
| 197 | C2×Dic6 | — | 2 | 3 | no | — |
| 198 | C2×Dic6 | — | 2 | 3 | no | — |
| 199 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 200 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 201 | C3×M16 | — | 2 | 6 | no | — |
| 202 | C3×M16 | — | 2 | 2 | no | — |
| 203 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 204 | C2×C3×C8 | C24 | 1 | 6 | yes | — |
| 205 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 206 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 207 | C3×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 208 | C3×C42 | C2×D4 | 1 | 3 | yes | — |
| 209 | C3×C42 | C2×D4 | 1 | 3 | yes | — |
| 210 | C3×C42 | C24 | 1 | 3 | yes | — |
| 211 | C3×C42 | C24 | 1 | 3 | yes | — |
| 212 | #217 | — | 2 | 3 | no | — |
| 213 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 214 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 215 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 216 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 217 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 218 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 219 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 220 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 221 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 222 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 223 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 224 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 225 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 226 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 227 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 228 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 229 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 230 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 231 | C4×Dic3 | — | 2 | 3 | no | — |
| 232 | C4×Dic3 | — | 2 | 6 | no | — |
| 233 | C4×Dic3 | — | 2 | 6 | no | — |
| 234 | C4×Dic3 | — | 2 | 3 | no | — |
| 235 | C4×Dic3 | — | 2 | 3 | no | — |
| 236 | Dic12 | — | 2 | 12 | no | — |
| 237 | #204 | — | 2 | 12 | no | — |
| 238 | C2×#41 | — | 3 | 1 | no | — |
| 239 | C22×Q8 | — | 3 | 3 | no | — |
| 240 | C22×Q8 | — | 6 | 1 | no | — |
| 241 | C22×Q8 | D12 | 1 | 1 | yes | characteristic |
| 242 | #137 | — | 6 | 12 | no | — |
| 243 | C2×Q16 | — | 3 | 6 | no | — |
| 244 | C2×SD16 | — | 3 | 6 | no | — |
| 245 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 246 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 247 | C4⋊Q8 | — | 3 | 3 | no | — |
| 248 | C4⋊Q8 | — | 3 | 3 | no | — |
| 249 | C4⋊Q8 | — | 3 | 6 | no | — |
| 250 | C4⋊Q8 | — | 3 | 6 | no | — |
| 251 | C4⋊Q8 | — | 6 | 3 | no | — |
| 252 | C4⋊Q8 | — | 6 | 3 | no | — |
| 253 | C4⋊Q8 | — | 6 | 3 | no | — |
| 254 | C4⋊Q8 | — | 6 | 3 | no | — |
| 255 | #125 | — | 3 | 6 | no | — |
| 256 | #125 | — | 6 | 6 | no | — |
| 257 | #125 | — | 6 | 12 | no | — |
| 258 | #125 | — | 6 | 6 | no | — |
| 259 | #125 | — | 6 | 6 | no | — |
| 260 | C22⋊Q8 | — | 6 | 3 | no | — |
| 261 | C22⋊Q8 | — | 6 | 3 | no | — |
| 262 | C22⋊Q8 | — | 6 | 3 | no | — |
| 263 | C22⋊Q8 | — | 6 | 3 | no | — |
| 264 | C22⋊Q8 | — | 6 | 6 | no | — |
| 265 | C4×Q8 | — | 3 | 6 | no | — |
| 266 | C4×Q8 | — | 3 | 6 | no | — |
| 267 | C4×Q8 | — | 3 | 3 | no | — |
| 268 | C4×Q8 | — | 3 | 3 | no | — |
| 269 | C4×Q8 | — | 6 | 1 | no | — |
| 270 | C4×Q8 | — | 6 | 6 | no | — |
| 271 | C4×Q8 | — | 6 | 2 | no | — |
| 272 | C4×Q8 | — | 6 | 3 | no | — |
| 273 | C4×Q8 | — | 6 | 3 | no | — |
| 274 | C4×Q8 | — | 6 | 3 | no | — |
| 275 | C4×Q8 | — | 6 | 3 | no | — |
| 276 | C4×Q8 | — | 6 | 3 | no | — |
| 277 | C4×Q8 | D12 | 1 | 1 | yes | characteristic |
| 278 | C4×Q8 | D12 | 1 | 3 | yes | — |
| 279 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 280 | C4×Q8 | C22×D3 | 1 | 3 | yes | — |
| 281 | C4×D4 | — | 3 | 3 | no | — |
| 282 | C4×D4 | — | 3 | 3 | no | — |
| 283 | C4×D4 | — | 6 | 3 | no | — |
| 284 | C4×D4 | — | 6 | 3 | no | — |
| 285 | #117 | — | 3 | 3 | no | — |
| 286 | #117 | — | 6 | 3 | no | — |
| 287 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 288 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 289 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 290 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 291 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 292 | C2×C4⋊C4 | D12 | 1 | 3 | yes | — |
| 293 | C2×C42 | — | 6 | 3 | no | — |
| 294 | C2×C42 | — | 6 | 3 | no | — |
| 295 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 296 | #107 | — | 3 | 6 | no | — |
| 297 | #106 | — | 3 | 6 | no | — |
| 298 | C4⋊C8 | C22×D3 | 1 | 6 | yes | — |
| 299 | C4⋊C8 | C22×D3 | 1 | 6 | yes | — |
| 300 | #103 | — | 3 | 2 | no | — |
| 301 | #103 | — | 3 | 6 | no | — |
| 302 | #103 | — | 3 | 6 | no | — |
| 303 | #103 | — | 3 | 12 | no | — |
| 304 | #103 | — | 3 | 12 | no | — |
| 305 | #102 | — | 3 | 2 | no | — |
| 306 | #97 | C22×D3 | 1 | 6 | yes | — |
| 307 | C4×C8 | C22×D3 | 1 | 6 | yes | — |
| 308 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 309 | C22×D3 | — | 2 | 1 | no | — |
| 310 | C3×Q8 | — | 2 | 6 | no | — |
| 311 | C3×Q8 | #137 | 1 | 4 | yes | complemented |
| 312 | C2×C3×C4 | — | 2 | 6 | no | — |
| 313 | C2×C3×C4 | — | 4 | 3 | no | — |
| 314 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 315 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 316 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 317 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 318 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 319 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 320 | C2×C3×C4 | 2−1+4 | 1 | 2 | yes | — |
| 321 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 322 | #67 | — | 2 | 4 | no | — |
| 323 | C2×Dic3 | — | 2 | 1 | no | — |
| 324 | C2×Dic3 | — | 2 | 2 | no | — |
| 325 | C2×Dic3 | — | 2 | 3 | no | — |
| 326 | C2×Dic3 | — | 2 | 3 | no | — |
| 327 | C2×Dic3 | — | 2 | 6 | no | — |
| 328 | C2×Dic3 | — | 4 | 2 | no | — |
| 329 | C2×Dic3 | — | 4 | 6 | no | — |
| 330 | D12 | — | 2 | 1 | no | — |
| 331 | D12 | C2×#41 | 1 | 2 | yes | — |
| 332 | C4×D3 | — | 2 | 4 | no | — |
| 333 | C4×D3 | — | 4 | 6 | no | — |
| 334 | C4×D3 | — | 8 | 3 | no | — |
| 335 | Dic6 | — | 2 | 1 | no | — |
| 336 | Dic6 | — | 2 | 6 | no | — |
| 337 | Dic6 | — | 2 | 6 | no | — |
| 338 | Dic6 | — | 4 | 6 | no | — |
| 339 | Dic6 | — | 4 | 6 | no | — |
| 340 | Dic6 | — | 8 | 3 | no | — |
| 341 | Dic6 | C2×#41 | 1 | 2 | yes | — |
| 342 | C3×C8 | — | 2 | 6 | no | — |
| 343 | C3×C8 | — | 2 | 2 | no | — |
| 344 | #41 | — | 3 | 4 | no | — |
| 345 | #41 | — | 6 | 2 | no | — |
| 346 | C2×Q8 | — | 2 | 4 | no | — |
| 347 | C2×Q8 | — | 3 | 1 | no | — |
| 348 | C2×Q8 | — | 3 | 6 | no | — |
| 349 | C2×Q8 | — | 6 | 3 | no | — |
| 350 | C2×Q8 | — | 6 | 3 | no | — |
| 351 | C2×Q8 | — | 6 | 3 | no | — |
| 352 | C2×Q8 | — | 6 | 6 | no | — |
| 353 | C2×Q8 | — | 6 | 6 | no | — |
| 354 | C2×Q8 | — | 12 | 4 | no | — |
| 355 | C2×Q8 | C2×D12 | 1 | 3 | yes | — |
| 356 | C2×Q8 | C2×D12 | 1 | 1 | yes | characteristic |
| 357 | C2×D4 | — | 3 | 1 | no | — |
| 358 | C2×D4 | — | 6 | 1 | no | — |
| 359 | C22×C4 | — | 6 | 1 | no | — |
| 360 | C22×C4 | — | 6 | 1 | no | — |
| 361 | C22×C4 | — | 6 | 3 | no | — |
| 362 | C22×C4 | — | 6 | 3 | no | — |
| 363 | C22×C4 | — | 6 | 3 | no | — |
| 364 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 365 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 366 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 367 | Q16 | — | 6 | 12 | no | — |
| 368 | SD16 | — | 6 | 12 | no | — |
| 369 | M16 | — | 2 | 2 | no | — |
| 370 | M16 | — | 2 | 6 | no | — |
| 371 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 372 | C2×C8 | C23×D3 | 1 | 6 | yes | — |
| 373 | C4⋊C4 | — | 3 | 2 | no | — |
| 374 | C4⋊C4 | — | 3 | 3 | no | — |
| 375 | C4⋊C4 | — | 3 | 3 | no | — |
| 376 | C4⋊C4 | — | 6 | 1 | no | — |
| 377 | C4⋊C4 | — | 6 | 6 | no | — |
| 378 | C4⋊C4 | — | 6 | 6 | no | — |
| 379 | C4⋊C4 | — | 6 | 6 | no | — |
| 380 | C4⋊C4 | — | 6 | 3 | no | — |
| 381 | C4⋊C4 | — | 6 | 6 | no | — |
| 382 | C4⋊C4 | — | 6 | 6 | no | — |
| 383 | C4⋊C4 | — | 6 | 6 | no | — |
| 384 | C4⋊C4 | — | 6 | 6 | no | — |
| 385 | C4⋊C4 | — | 6 | 3 | no | — |
| 386 | C4⋊C4 | — | 6 | 3 | no | — |
| 387 | C4⋊C4 | — | 6 | 6 | no | — |
| 388 | C4⋊C4 | — | 6 | 3 | no | — |
| 389 | C4⋊C4 | C2×D12 | 1 | 3 | yes | — |
| 390 | C4⋊C4 | C2×D12 | 1 | 6 | yes | — |
| 391 | C4⋊C4 | C2×D12 | 1 | 3 | yes | — |
| 392 | C22⋊C4 | — | 6 | 3 | no | — |
| 393 | C22⋊C4 | — | 6 | 3 | no | — |
| 394 | C22⋊C4 | — | 6 | 3 | no | — |
| 395 | C42 | — | 6 | 3 | no | — |
| 396 | C42 | — | 6 | 3 | no | — |
| 397 | C42 | — | 6 | 3 | no | — |
| 398 | C42 | — | 6 | 6 | no | — |
| 399 | C42 | — | 6 | 6 | no | — |
| 400 | C42 | C2×D12 | 1 | 3 | yes | — |
| 401 | C42 | C2×D12 | 1 | 3 | yes | — |
| 402 | C42 | C23×D3 | 1 | 3 | yes | — |
| 403 | C42 | C23×D3 | 1 | 3 | yes | — |
| 404 | C22×C3 | — | 2 | 1 | no | — |
| 405 | C22×C3 | — | 2 | 1 | no | — |
| 406 | C22×C3 | #548 | 1 | 2 | yes | — |
| 407 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 408 | C2×D3 | — | 2 | 2 | no | — |
| 409 | C2×D3 | — | 4 | 1 | no | — |
| 410 | C2×D3 | — | 4 | 1 | no | — |
| 411 | C3×C4 | — | 2 | 3 | no | — |
| 412 | C3×C4 | — | 2 | 3 | no | — |
| 413 | C3×C4 | — | 2 | 3 | no | — |
| 414 | C3×C4 | #548 | 1 | 2 | yes | — |
| 415 | C3×C4 | C2×#137 | 1 | 6 | yes | — |
| 416 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 417 | C3×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 418 | Dic3 | — | 2 | 2 | no | — |
| 419 | Dic3 | — | 4 | 3 | no | — |
| 420 | Dic3 | — | 4 | 2 | no | — |
| 421 | Dic3 | — | 4 | 6 | no | — |
| 422 | Dic3 | — | 4 | 3 | no | — |
| 423 | C23 | — | 6 | 1 | no | — |
| 424 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 425 | Q8 | — | 2 | 6 | no | — |
| 426 | Q8 | — | 3 | 2 | no | — |
| 427 | Q8 | — | 6 | 1 | no | — |
| 428 | Q8 | — | 6 | 6 | no | — |
| 429 | Q8 | — | 6 | 6 | no | — |
| 430 | Q8 | — | 12 | 6 | no | — |
| 431 | Q8 | — | 12 | 6 | no | — |
| 432 | Q8 | — | 24 | 3 | no | — |
| 433 | Q8 | #909 | 1 | 4 | yes | complemented |
| 434 | D4 | — | 3 | 2 | no | — |
| 435 | D4 | — | 6 | 4 | no | — |
| 436 | D4 | — | 6 | 1 | no | — |
| 437 | C2×C4 | — | 2 | 6 | no | — |
| 438 | C2×C4 | — | 4 | 3 | no | — |
| 439 | C2×C4 | — | 6 | 1 | no | — |
| 440 | C2×C4 | — | 6 | 4 | no | — |
| 441 | C2×C4 | — | 6 | 2 | no | — |
| 442 | C2×C4 | — | 6 | 3 | no | — |
| 443 | C2×C4 | — | 6 | 3 | no | — |
| 444 | C2×C4 | — | 6 | 6 | no | — |
| 445 | C2×C4 | — | 12 | 2 | no | — |
| 446 | C2×C4 | — | 12 | 6 | no | — |
| 447 | C2×C4 | — | 12 | 6 | no | — |
| 448 | C2×C4 | — | 24 | 3 | no | — |
| 449 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 450 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 451 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 452 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 453 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 454 | C2×C4 | #1007 | 1 | 2 | yes | — |
| 455 | C2×C4 | D3×#41 | 1 | 2 | yes | — |
| 456 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 457 | C8 | — | 2 | 2 | no | — |
| 458 | C8 | — | 2 | 6 | no | — |
| 459 | C2×C3 | — | 2 | 2 | no | — |
| 460 | C2×C3 | C2×#548 | 1 | 1 | yes | characteristic |
| 461 | C2×C3 | C22×#137 | 1 | 1 | yes | characteristic |
| 462 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 463 | D3 | — | 4 | 2 | no | — |
| 464 | C22 | — | 2 | 1 | no | — |
| 465 | C22 | — | 2 | 1 | no | — |
| 466 | C22 | — | 6 | 2 | no | — |
| 467 | C22 | — | 12 | 1 | no | — |
| 468 | C22 | — | 12 | 1 | no | — |
| 469 | C22 | #5576 | 1 | 2 | yes | — |
| 470 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 471 | C4 | — | 2 | 3 | no | — |
| 472 | C4 | — | 2 | 3 | no | — |
| 473 | C4 | — | 2 | 3 | no | — |
| 474 | C4 | — | 6 | 2 | no | — |
| 475 | C4 | — | 12 | 6 | no | — |
| 476 | C4 | — | 12 | 3 | no | — |
| 477 | C4 | — | 12 | 2 | no | — |
| 478 | C4 | — | 12 | 3 | no | — |
| 479 | C4 | #5576 | 1 | 2 | yes | — |
| 480 | C4 | C2×#909 | 1 | 6 | yes | — |
| 481 | C4 | C2×#1007 | 1 | 1 | yes | characteristic |
| 482 | C4 | C2×D3×#41 | 1 | 1 | yes | characteristic |
| 483 | C3 | #61322 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 484 | C2 | — | 2 | 2 | no | — |
| 485 | C2 | — | 12 | 2 | no | — |
| 486 | C2 | C2×#5576 | 1 | 1 | yes | characteristic |
| 487 | C2 | C22×#909 | 1 | 1 | yes | characteristic |
| 488 | C2 | #87168 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#5570 | C2 | semidirect |
| 3. C3×Q8×M16 | C2 | semidirect |
| 4. #79983 | C2 | semidirect |
| 5. #79972 | C2 | semidirect |
| 6. #79933 | C2 | semidirect |
| 7. #79925 | C2 | semidirect |
| 8. #79068 | C2 | semidirect |
| 10. #78537 | C2 | semidirect |
| 64. Q8×M16 | D3 | semidirect |
| 311. C3×Q8 | #137 | semidirect |
| 433. Q8 | #909 | semidirect |
| 483. C3 | #61322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#235 | 2 |
| C2×#5570 | 2 |
| C3×Q8×M16 | 2 |
| #79983 | 2 |
| #79972 | 2 |
| #79933 | 2 |
| #79925 | 2 |
| #79068 | 2 |
| #79057 | 2 |
| #78537 | 2 |
| C4×#909 | 2 |
| #61322 | 3 |