← Q8×#1009 #11707295
Subgroups — Q8×#1009 #11707295
Order 768.
7406 conjugacy classes of subgroups.
The subgroup lattice has 516 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×Q8×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | Q8×#239 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #87018 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #86948 | C2 | 1 | 18 | yes | maximal, complemented |
| 5 | D3×D4×Q8 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #86281 | C2 | 1 | 9 | yes | maximal, complemented |
| 7 | #86280 | C2 | 1 | 9 | yes | maximal, complemented |
| 8 | C4×#1009 | C2 | 1 | 3 | yes | maximal |
| 9 | #85828 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | Q8×#235 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×Q8×D12 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | Q8×H(5,𝔽2) | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×#1009 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×D3×Q8 | C22 | 1 | 6 | yes | complemented |
| 15 | C3×Q82 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3×#557 | C22 | 1 | 3 | yes | complemented |
| 17 | C3×#554 | C22 | 1 | 9 | yes | complemented |
| 18 | C3×D4×Q8 | C22 | 1 | 3 | yes | complemented |
| 19 | C3×#533 | C22 | 1 | 9 | yes | complemented |
| 20 | C3×C4×#41 | C22 | 1 | 3 | yes | — |
| 21 | C2×C3×C4×Q8 | C22 | 1 | 3 | yes | complemented |
| 22 | #5827 | C22 | 1 | 3 | yes | — |
| 23 | Q8×#67 | C22 | 1 | 6 | yes | complemented |
| 24 | #5730 | C22 | 1 | 18 | yes | complemented |
| 25 | #5728 | C22 | 1 | 18 | yes | complemented |
| 26 | #5727 | C22 | 1 | 18 | yes | complemented |
| 27 | D3×C4⋊Q8 | C22 | 1 | 18 | yes | complemented |
| 28 | #5690 | C22 | 1 | 36 | yes | complemented |
| 29 | #5689 | C22 | 1 | 36 | yes | complemented |
| 30 | #5635 | C22 | 1 | 36 | yes | complemented |
| 31 | #5634 | C22 | 1 | 36 | yes | complemented |
| 32 | #5632 | C22 | 1 | 36 | yes | complemented |
| 33 | D3×C22⋊Q8 | C22 | 1 | 36 | yes | complemented |
| 34 | #5579 | C22 | 1 | 18 | yes | complemented |
| 35 | #5579 | C22 | 1 | 9 | yes | complemented |
| 36 | #5578 | C22 | 1 | 18 | yes | complemented |
| 37 | Q8×D12 | C22 | 1 | 18 | yes | complemented |
| 38 | Q8×D12 | C22 | 1 | 3 | yes | complemented |
| 39 | Q8×D12 | C22 | 1 | 18 | yes | complemented |
| 40 | Q8×D12 | C22 | 1 | 6 | yes | complemented |
| 41 | #5574 | C22 | 1 | 6 | yes | — |
| 42 | C4×#239 | C22 | 1 | 6 | yes | — |
| 43 | C4×D3×Q8 | C22 | 1 | 6 | yes | complemented |
| 44 | #5570 | C22 | 1 | 6 | yes | complemented |
| 45 | #5567 | C22 | 1 | 9 | yes | complemented |
| 46 | Q8×Dic6 | C22 | 1 | 6 | yes | complemented |
| 47 | Q8×Dic6 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | Q8×Dic6 | C22 | 1 | 6 | yes | complemented |
| 49 | #5545 | C22 | 1 | 18 | yes | — |
| 50 | C4×D3×D4 | C22 | 1 | 18 | yes | — |
| 51 | #5543 | C22 | 1 | 18 | yes | complemented |
| 52 | D4×Dic6 | C22 | 1 | 18 | yes | complemented |
| 53 | #5523 | C22 | 1 | 9 | yes | — |
| 54 | #5521 | C22 | 1 | 9 | yes | — |
| 55 | #5519 | C22 | 1 | 18 | yes | complemented |
| 56 | #5511 | C22 | 1 | 18 | yes | complemented |
| 57 | C2×#897 | C22 | 1 | 18 | yes | complemented |
| 58 | C4×#235 | C22 | 1 | 9 | yes | — |
| 59 | C2×C4×D12 | C22 | 1 | 9 | yes | — |
| 60 | #5470 | C22 | 1 | 9 | yes | complemented |
| 61 | C2×#869 | C22 | 1 | 9 | yes | complemented |
| 62 | #3503 | — | 3 | 6 | no | — |
| 63 | #3503 | — | 3 | 9 | no | — |
| 64 | #3503 | — | 3 | 3 | no | — |
| 65 | #3501 | — | 3 | 18 | no | — |
| 66 | #3501 | — | 3 | 9 | no | — |
| 67 | Q8×#41 | — | 3 | 2 | no | — |
| 68 | Q8×#41 | — | 3 | 3 | no | — |
| 69 | Q8×#41 | D3 | 1 | 1 | yes | characteristic, complemented |
| 70 | C2×D4×Q8 | — | 3 | 6 | no | — |
| 71 | C2×D4×Q8 | — | 3 | 3 | no | — |
| 72 | C4×H(5,𝔽2) | — | 3 | 3 | no | — |
| 73 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 74 | C22×C3×Q8 | C23 | 1 | 3 | yes | — |
| 75 | #1009 | Q8 | 1 | 16 | yes | direct product factor |
| 76 | C2×#239 | C23 | 1 | 2 | yes | — |
| 77 | C2×D3×Q8 | — | 4 | 24 | no | — |
| 78 | C2×D3×Q8 | C23 | 1 | 6 | yes | — |
| 79 | C2×D3×Q8 | C23 | 1 | 36 | yes | — |
| 80 | C2×D3×D4 | C23 | 1 | 6 | yes | — |
| 81 | C2×#235 | C23 | 1 | 3 | yes | — |
| 82 | C22×D12 | C23 | 1 | 3 | yes | — |
| 83 | C22×C4×D3 | C23 | 1 | 18 | yes | — |
| 84 | C22×Dic6 | C23 | 1 | 18 | yes | — |
| 85 | C3×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 86 | C3×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 87 | C3×#125 | C23 | 1 | 18 | yes | — |
| 88 | C3×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 89 | C3×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 90 | C3×C4×Q8 | C23 | 1 | 3 | yes | — |
| 91 | C3×C4×Q8 | C23 | 1 | 3 | yes | — |
| 92 | C3×C4×Q8 | C23 | 1 | 3 | yes | — |
| 93 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C3×C4×Q8 | C23 | 1 | 6 | yes | — |
| 95 | C3×C4×Q8 | C23 | 1 | 9 | yes | — |
| 96 | C3×C4×Q8 | C23 | 1 | 9 | yes | — |
| 97 | C3×C4×D4 | C23 | 1 | 9 | yes | — |
| 98 | C3×C4×D4 | C23 | 1 | 9 | yes | — |
| 99 | C3×#117 | C23 | 1 | 9 | yes | — |
| 100 | C2×C3×C4⋊C4 | C23 | 1 | 9 | yes | — |
| 101 | C2×C3×C42 | C23 | 1 | 9 | yes | — |
| 102 | #946 | C23 | 1 | 36 | yes | — |
| 103 | #946 | C23 | 1 | 18 | yes | — |
| 104 | Q8×Dic3 | C23 | 1 | 12 | yes | — |
| 105 | Q8×Dic3 | C23 | 1 | 2 | yes | — |
| 106 | Q8×Dic3 | C23 | 1 | 6 | yes | — |
| 107 | #944 | C23 | 1 | 18 | yes | — |
| 108 | D4×Dic3 | C23 | 1 | 18 | yes | — |
| 109 | C4×#67 | C23 | 1 | 18 | yes | — |
| 110 | C4×#67 | C23 | 1 | 18 | yes | — |
| 111 | C2×(C2×D3)⋊C4 | C23 | 1 | 18 | yes | — |
| 112 | #926 | C23 | 1 | 9 | yes | — |
| 113 | C2×C4⋊Dic3 | C23 | 1 | 18 | yes | — |
| 114 | C2×C4⋊Dic3 | C23 | 1 | 9 | yes | — |
| 115 | #924 | C23 | 1 | 18 | yes | — |
| 116 | #924 | C23 | 1 | 18 | yes | — |
| 117 | #897 | C23 | 1 | 36 | yes | — |
| 118 | #897 | C23 | 1 | 72 | yes | — |
| 119 | #897 | C23 | 1 | 18 | yes | — |
| 120 | #896 | C23 | 1 | 72 | yes | — |
| 121 | #896 | C23 | 1 | 36 | yes | — |
| 122 | #893 | C23 | 1 | 18 | yes | — |
| 123 | #893 | C23 | 1 | 18 | yes | — |
| 124 | #892 | C23 | 1 | 18 | yes | — |
| 125 | D3×C4⋊C4 | C23 | 1 | 36 | yes | — |
| 126 | D3×C4⋊C4 | C23 | 1 | 18 | yes | — |
| 127 | D3×C4⋊C4 | C23 | 1 | 18 | yes | — |
| 128 | #890 | C23 | 1 | 36 | yes | — |
| 129 | #889 | C23 | 1 | 36 | yes | — |
| 130 | #888 | C23 | 1 | 36 | yes | — |
| 131 | #888 | C23 | 1 | 36 | yes | — |
| 132 | #888 | C23 | 1 | 6 | yes | — |
| 133 | #887 | C23 | 1 | 18 | yes | — |
| 134 | #67⋊C4 | C23 | 1 | 36 | yes | — |
| 135 | D3×C22⋊C4 | C23 | 1 | 36 | yes | — |
| 136 | #878 | C23 | 1 | 72 | yes | — |
| 137 | C4×D12 | C23 | 1 | 18 | yes | — |
| 138 | C4×D12 | C23 | 1 | 18 | yes | — |
| 139 | C4×D12 | C23 | 1 | 9 | yes | — |
| 140 | C4×D12 | C23 | 1 | 18 | yes | — |
| 141 | C4×D12 | C23 | 1 | 9 | yes | — |
| 142 | #872 | C23 | 1 | 18 | yes | — |
| 143 | C42×D3 | C23 | 1 | 18 | yes | — |
| 144 | #870 | C23 | 1 | 18 | yes | — |
| 145 | #869 | C23 | 1 | 18 | yes | — |
| 146 | #869 | C23 | 1 | 18 | yes | — |
| 147 | #869 | C23 | 1 | 9 | yes | — |
| 148 | #869 | C23 | 1 | 18 | yes | — |
| 149 | #869 | C23 | 1 | 3 | yes | — |
| 150 | C4×Dic6 | C23 | 1 | 18 | yes | — |
| 151 | C4×Dic6 | C23 | 1 | 18 | yes | — |
| 152 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 153 | C4×Dic6 | C23 | 1 | 9 | yes | — |
| 154 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 155 | C23×Q8 | — | 3 | 6 | no | — |
| 156 | Q82 | — | 3 | 1 | no | — |
| 157 | Q82 | — | 3 | 6 | no | — |
| 158 | Q82 | — | 3 | 6 | no | — |
| 159 | Q82 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 160 | #557 | — | 3 | 9 | no | — |
| 161 | #557 | — | 3 | 6 | no | — |
| 162 | #557 | C2×D3 | 1 | 3 | yes | complemented |
| 163 | #554 | — | 3 | 18 | no | — |
| 164 | #554 | — | 3 | 36 | no | — |
| 165 | #554 | — | 3 | 36 | no | — |
| 166 | #554 | — | 3 | 9 | no | — |
| 167 | #554 | — | 3 | 18 | no | — |
| 168 | #554 | — | 3 | 18 | no | — |
| 169 | #554 | — | 3 | 18 | no | — |
| 170 | #554 | C2×D3 | 1 | 9 | yes | complemented |
| 171 | D4×Q8 | — | 3 | 6 | no | — |
| 172 | D4×Q8 | — | 3 | 18 | no | — |
| 173 | D4×Q8 | — | 3 | 36 | no | — |
| 174 | D4×Q8 | — | 3 | 6 | no | — |
| 175 | D4×Q8 | — | 3 | 3 | no | — |
| 176 | D4×Q8 | — | 3 | 18 | no | — |
| 177 | D4×Q8 | — | 3 | 18 | no | — |
| 178 | D4×Q8 | — | 3 | 18 | no | — |
| 179 | D4×Q8 | C2×D3 | 1 | 3 | yes | complemented |
| 180 | #544 | — | 3 | 36 | no | — |
| 181 | #544 | — | 3 | 18 | no | — |
| 182 | #543 | — | 3 | 36 | no | — |
| 183 | #533 | — | 3 | 18 | no | — |
| 184 | #533 | — | 3 | 18 | no | — |
| 185 | #533 | — | 3 | 9 | no | — |
| 186 | #533 | C2×D3 | 1 | 9 | yes | complemented |
| 187 | C2×C4⋊Q8 | — | 3 | 18 | no | — |
| 188 | C2×C4⋊Q8 | — | 3 | 9 | no | — |
| 189 | C2×C22⋊Q8 | — | 3 | 36 | no | — |
| 190 | C2×C22⋊Q8 | — | 3 | 18 | no | — |
| 191 | #520 | — | 3 | 3 | no | — |
| 192 | #520 | — | 3 | 6 | no | — |
| 193 | #520 | — | 3 | 9 | no | — |
| 194 | #518 | — | 3 | 18 | no | — |
| 195 | #518 | — | 3 | 9 | no | — |
| 196 | C4×#41 | — | 3 | 6 | no | — |
| 197 | C4×#41 | — | 3 | 9 | no | — |
| 198 | C4×#41 | C2×D3 | 1 | 3 | yes | — |
| 199 | C2×C4×Q8 | — | 3 | 6 | no | — |
| 200 | C2×C4×Q8 | C2×D3 | 1 | 3 | yes | complemented |
| 201 | C2×C4×D4 | — | 3 | 18 | no | — |
| 202 | C2×C4×D4 | — | 3 | 9 | no | — |
| 203 | C23×D3 | C24 | 1 | 6 | yes | — |
| 204 | C3×#41 | C2×Q8 | 1 | 8 | yes | complemented |
| 205 | C2×C3×Q8 | — | 2 | 12 | no | — |
| 206 | C2×C3×Q8 | C24 | 1 | 9 | yes | — |
| 207 | C2×C3×Q8 | C24 | 1 | 6 | yes | — |
| 208 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 209 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 210 | C2×C3×D4 | C24 | 1 | 3 | yes | — |
| 211 | C22×C3×C4 | C24 | 1 | 9 | yes | — |
| 212 | C22×C3×C4 | C24 | 1 | 9 | yes | — |
| 213 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 214 | C2×#67 | C24 | 1 | 6 | yes | — |
| 215 | C22×Dic3 | C24 | 1 | 18 | yes | — |
| 216 | #239 | C2×Q8 | 1 | 16 | yes | complemented |
| 217 | D3×Q8 | — | 2 | 24 | no | — |
| 218 | D3×Q8 | — | 4 | 72 | no | — |
| 219 | D3×D4 | C2×Q8 | 1 | 48 | yes | complemented |
| 220 | #235 | C2×Q8 | 1 | 24 | yes | complemented |
| 221 | C2×D12 | C2×Q8 | 1 | 24 | yes | complemented |
| 222 | C2×D12 | C24 | 1 | 3 | yes | — |
| 223 | C2×D12 | C24 | 1 | 6 | yes | — |
| 224 | C2×C4×D3 | — | 4 | 36 | no | — |
| 225 | C2×C4×D3 | C24 | 1 | 18 | yes | — |
| 226 | C2×C4×D3 | C24 | 1 | 18 | yes | — |
| 227 | C2×C4×D3 | C24 | 1 | 36 | yes | — |
| 228 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 229 | C2×Dic6 | — | 4 | 36 | no | — |
| 230 | C2×Dic6 | C24 | 1 | 18 | yes | — |
| 231 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 232 | C2×Dic6 | C24 | 1 | 36 | yes | — |
| 233 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 234 | C3×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 235 | C3×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 236 | C3×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 237 | C3×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 238 | C3×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 239 | C3×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 240 | C3×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 241 | C3×C42 | C24 | 1 | 9 | yes | — |
| 242 | C3×C42 | C24 | 1 | 9 | yes | — |
| 243 | C3×C42 | C24 | 1 | 3 | yes | — |
| 244 | C3×C42 | C24 | 1 | 9 | yes | — |
| 245 | #217 | C24 | 1 | 18 | yes | — |
| 246 | (C2×D3)⋊C4 | C24 | 1 | 18 | yes | — |
| 247 | (C2×D3)⋊C4 | C24 | 1 | 18 | yes | — |
| 248 | (C2×D3)⋊C4 | C24 | 1 | 36 | yes | — |
| 249 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 250 | C4⋊Dic3 | C24 | 1 | 9 | yes | — |
| 251 | C4⋊Dic3 | C24 | 1 | 18 | yes | — |
| 252 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 253 | C4⋊Dic3 | C24 | 1 | 18 | yes | — |
| 254 | C4⋊Dic3 | C24 | 1 | 36 | yes | — |
| 255 | Dic3⋊C4 | C24 | 1 | 36 | yes | — |
| 256 | Dic3⋊C4 | C24 | 1 | 36 | yes | — |
| 257 | Dic3⋊C4 | C24 | 1 | 6 | yes | — |
| 258 | Dic3⋊C4 | C24 | 1 | 18 | yes | — |
| 259 | C4×Dic3 | C24 | 1 | 18 | yes | — |
| 260 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 261 | C4×Dic3 | C24 | 1 | 18 | yes | — |
| 262 | H(5,𝔽2) | — | 3 | 16 | no | — |
| 263 | C2×#41 | — | 3 | 2 | no | — |
| 264 | C2×#41 | — | 3 | 3 | no | — |
| 265 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 266 | C22×Q8 | — | 3 | 6 | no | — |
| 267 | C22×Q8 | — | 3 | 36 | no | — |
| 268 | C22×Q8 | — | 3 | 18 | no | — |
| 269 | C22×Q8 | — | 12 | 24 | no | — |
| 270 | C22×Q8 | C22×D3 | 1 | 3 | yes | — |
| 271 | C22×D4 | — | 3 | 6 | no | — |
| 272 | C22×D4 | — | 3 | 3 | no | — |
| 273 | C23×C4 | — | 3 | 18 | no | — |
| 274 | C4⋊Q8 | — | 3 | 18 | no | — |
| 275 | C4⋊Q8 | — | 3 | 36 | no | — |
| 276 | C4⋊Q8 | — | 3 | 36 | no | — |
| 277 | C4⋊Q8 | — | 3 | 6 | no | — |
| 278 | C4⋊Q8 | — | 3 | 18 | no | — |
| 279 | C4⋊Q8 | — | 3 | 9 | no | — |
| 280 | C4⋊Q8 | — | 3 | 18 | no | — |
| 281 | C4⋊Q8 | — | 3 | 18 | no | — |
| 282 | C4⋊Q8 | — | 3 | 3 | no | — |
| 283 | C4⋊Q8 | C22×D3 | 1 | 9 | yes | — |
| 284 | C4⋊Q8 | C22×D3 | 1 | 9 | yes | — |
| 285 | #125 | — | 3 | 36 | no | — |
| 286 | #125 | — | 3 | 36 | no | — |
| 287 | #125 | — | 3 | 18 | no | — |
| 288 | #125 | C22×D3 | 1 | 18 | yes | — |
| 289 | C22⋊Q8 | — | 3 | 18 | no | — |
| 290 | C22⋊Q8 | — | 3 | 36 | no | — |
| 291 | C22⋊Q8 | — | 3 | 18 | no | — |
| 292 | C22⋊Q8 | — | 3 | 18 | no | — |
| 293 | C22⋊Q8 | — | 3 | 36 | no | — |
| 294 | C22⋊Q8 | — | 3 | 18 | no | — |
| 295 | C22⋊Q8 | — | 3 | 72 | no | — |
| 296 | C22⋊Q8 | — | 3 | 72 | no | — |
| 297 | C22⋊Q8 | — | 3 | 36 | no | — |
| 298 | C22⋊Q8 | — | 3 | 72 | no | — |
| 299 | C22⋊Q8 | C22×D3 | 1 | 18 | yes | — |
| 300 | C22⋊Q8 | C22×D3 | 1 | 18 | yes | — |
| 301 | C4×Q8 | — | 3 | 2 | no | — |
| 302 | C4×Q8 | — | 3 | 6 | no | — |
| 303 | C4×Q8 | — | 3 | 12 | no | — |
| 304 | C4×Q8 | — | 3 | 18 | no | — |
| 305 | C4×Q8 | — | 3 | 18 | no | — |
| 306 | C4×Q8 | — | 3 | 3 | no | — |
| 307 | C4×Q8 | — | 3 | 9 | no | — |
| 308 | C4×Q8 | — | 3 | 18 | no | — |
| 309 | C4×Q8 | C22×D3 | 1 | 3 | yes | — |
| 310 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 311 | C4×Q8 | C22×D3 | 1 | 9 | yes | — |
| 312 | C4×Q8 | C22×D3 | 1 | 9 | yes | — |
| 313 | C4×Q8 | C22×D3 | 1 | 3 | yes | — |
| 314 | C4×Q8 | C22×D3 | 1 | 3 | yes | — |
| 315 | C4×Q8 | C22×D3 | 1 | 6 | yes | — |
| 316 | C4×D4 | — | 3 | 18 | no | — |
| 317 | C4×D4 | — | 3 | 18 | no | — |
| 318 | C4×D4 | — | 3 | 18 | no | — |
| 319 | C4×D4 | — | 3 | 18 | no | — |
| 320 | C4×D4 | — | 3 | 18 | no | — |
| 321 | C4×D4 | — | 3 | 36 | no | — |
| 322 | C4×D4 | — | 3 | 18 | no | — |
| 323 | C4×D4 | — | 3 | 9 | no | — |
| 324 | C4×D4 | — | 3 | 18 | no | — |
| 325 | C4×D4 | — | 3 | 18 | no | — |
| 326 | C4×D4 | — | 3 | 9 | no | — |
| 327 | C4×D4 | C22×D3 | 1 | 9 | yes | — |
| 328 | C4×D4 | C22×D3 | 1 | 9 | yes | — |
| 329 | #117 | — | 3 | 9 | no | — |
| 330 | #117 | — | 3 | 18 | no | — |
| 331 | #117 | — | 3 | 18 | no | — |
| 332 | #117 | C22×D3 | 1 | 9 | yes | — |
| 333 | C2×C4⋊C4 | — | 3 | 9 | no | — |
| 334 | C2×C4⋊C4 | — | 3 | 18 | no | — |
| 335 | C2×C4⋊C4 | — | 3 | 18 | no | — |
| 336 | C2×C4⋊C4 | — | 3 | 18 | no | — |
| 337 | C2×C4⋊C4 | — | 3 | 36 | no | — |
| 338 | C2×C4⋊C4 | C22×D3 | 1 | 9 | yes | — |
| 339 | C2×C22⋊C4 | — | 3 | 18 | no | — |
| 340 | C2×C22⋊C4 | — | 3 | 36 | no | — |
| 341 | C2×C42 | — | 3 | 18 | no | — |
| 342 | C2×C42 | C22×D3 | 1 | 9 | yes | — |
| 343 | C23×C3 | C25 | 1 | 3 | yes | — |
| 344 | C22×D3 | — | 4 | 6 | no | — |
| 345 | C22×D3 | — | 4 | 6 | no | — |
| 346 | C22×D3 | C22×Q8 | 1 | 24 | yes | complemented |
| 347 | C22×D3 | C25 | 1 | 6 | yes | — |
| 348 | C3×Q8 | — | 2 | 18 | no | — |
| 349 | C3×Q8 | — | 4 | 6 | no | — |
| 350 | C3×Q8 | C22×Q8 | 1 | 4 | yes | complemented |
| 351 | C3×Q8 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 352 | C3×D4 | C22×Q8 | 1 | 12 | yes | complemented |
| 353 | C2×C3×C4 | — | 2 | 18 | no | — |
| 354 | C2×C3×C4 | — | 4 | 9 | no | — |
| 355 | C2×C3×C4 | C22×Q8 | 1 | 12 | yes | complemented |
| 356 | C2×C3×C4 | C25 | 1 | 9 | yes | — |
| 357 | C2×C3×C4 | C25 | 1 | 9 | yes | — |
| 358 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 359 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 360 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 361 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 362 | #67 | C22×Q8 | 1 | 24 | yes | complemented |
| 363 | C2×Dic3 | — | 4 | 18 | no | — |
| 364 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 365 | C2×Dic3 | C25 | 1 | 18 | yes | — |
| 366 | C2×Dic3 | C25 | 1 | 2 | yes | — |
| 367 | D12 | C22×Q8 | 1 | 12 | yes | complemented |
| 368 | D12 | C22×Q8 | 1 | 24 | yes | complemented |
| 369 | C4×D3 | — | 2 | 36 | no | — |
| 370 | C4×D3 | — | 4 | 36 | no | — |
| 371 | C4×D3 | — | 4 | 18 | no | — |
| 372 | C4×D3 | C22×Q8 | 1 | 24 | yes | complemented |
| 373 | Dic6 | — | 2 | 36 | no | — |
| 374 | Dic6 | — | 4 | 36 | no | — |
| 375 | Dic6 | — | 4 | 6 | no | — |
| 376 | Dic6 | C22×Q8 | 1 | 4 | yes | complemented |
| 377 | C24 | — | 3 | 6 | no | — |
| 378 | #41 | — | 3 | 16 | no | — |
| 379 | #41 | — | 3 | 24 | no | — |
| 380 | #41 | D3×Q8 | 1 | 8 | yes | complemented |
| 381 | C2×Q8 | — | 2 | 12 | no | — |
| 382 | C2×Q8 | — | 3 | 1 | no | — |
| 383 | C2×Q8 | — | 3 | 18 | no | — |
| 384 | C2×Q8 | — | 3 | 6 | no | — |
| 385 | C2×Q8 | — | 3 | 36 | no | — |
| 386 | C2×Q8 | — | 6 | 24 | no | — |
| 387 | C2×Q8 | — | 12 | 36 | no | — |
| 388 | C2×Q8 | — | 12 | 72 | no | — |
| 389 | C2×Q8 | C23×D3 | 1 | 9 | yes | — |
| 390 | C2×Q8 | C23×D3 | 1 | 6 | yes | — |
| 391 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 392 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 393 | C2×D4 | — | 3 | 6 | no | — |
| 394 | C2×D4 | — | 3 | 48 | no | — |
| 395 | C2×D4 | — | 3 | 24 | no | — |
| 396 | C2×D4 | — | 3 | 6 | no | — |
| 397 | C2×D4 | — | 3 | 3 | no | — |
| 398 | C2×D4 | C23×D3 | 1 | 3 | yes | — |
| 399 | C22×C4 | — | 3 | 6 | no | — |
| 400 | C22×C4 | — | 3 | 18 | no | — |
| 401 | C22×C4 | — | 3 | 18 | no | — |
| 402 | C22×C4 | — | 3 | 18 | no | — |
| 403 | C22×C4 | — | 3 | 36 | no | — |
| 404 | C22×C4 | — | 12 | 36 | no | — |
| 405 | C22×C4 | C23×D3 | 1 | 9 | yes | — |
| 406 | C22×C4 | C23×D3 | 1 | 9 | yes | — |
| 407 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 408 | C4⋊C4 | — | 3 | 6 | no | — |
| 409 | C4⋊C4 | — | 3 | 18 | no | — |
| 410 | C4⋊C4 | — | 3 | 18 | no | — |
| 411 | C4⋊C4 | — | 3 | 9 | no | — |
| 412 | C4⋊C4 | — | 3 | 36 | no | — |
| 413 | C4⋊C4 | — | 3 | 36 | no | — |
| 414 | C4⋊C4 | — | 3 | 18 | no | — |
| 415 | C4⋊C4 | — | 3 | 36 | no | — |
| 416 | C4⋊C4 | — | 3 | 6 | no | — |
| 417 | C4⋊C4 | — | 3 | 3 | no | — |
| 418 | C4⋊C4 | C23×D3 | 1 | 9 | yes | — |
| 419 | C4⋊C4 | C23×D3 | 1 | 9 | yes | — |
| 420 | C4⋊C4 | C23×D3 | 1 | 18 | yes | — |
| 421 | C4⋊C4 | C23×D3 | 1 | 3 | yes | — |
| 422 | C4⋊C4 | C23×D3 | 1 | 18 | yes | — |
| 423 | C4⋊C4 | C23×D3 | 1 | 9 | yes | — |
| 424 | C22⋊C4 | — | 3 | 18 | no | — |
| 425 | C22⋊C4 | — | 3 | 18 | no | — |
| 426 | C22⋊C4 | — | 3 | 36 | no | — |
| 427 | C22⋊C4 | — | 3 | 18 | no | — |
| 428 | C22⋊C4 | C23×D3 | 1 | 18 | yes | — |
| 429 | C42 | — | 3 | 6 | no | — |
| 430 | C42 | — | 3 | 18 | no | — |
| 431 | C42 | — | 3 | 18 | no | — |
| 432 | C42 | C23×D3 | 1 | 9 | yes | — |
| 433 | C42 | C23×D3 | 1 | 3 | yes | — |
| 434 | C42 | C23×D3 | 1 | 9 | yes | — |
| 435 | C42 | C23×D3 | 1 | 9 | yes | — |
| 436 | C22×C3 | — | 2 | 3 | no | — |
| 437 | C22×C3 | — | 2 | 3 | no | — |
| 438 | C22×C3 | C23×Q8 | 1 | 6 | yes | — |
| 439 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 440 | C2×D3 | — | 2 | 6 | no | — |
| 441 | C2×D3 | — | 2 | 6 | no | — |
| 442 | C2×D3 | — | 4 | 24 | no | — |
| 443 | C2×D3 | C23×Q8 | 1 | 12 | yes | — |
| 444 | C3×C4 | — | 2 | 9 | no | — |
| 445 | C3×C4 | — | 2 | 3 | no | — |
| 446 | C3×C4 | — | 2 | 9 | no | — |
| 447 | C3×C4 | C23×Q8 | 1 | 2 | yes | — |
| 448 | C3×C4 | C23×Q8 | 1 | 6 | yes | — |
| 449 | C3×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 450 | Dic3 | — | 2 | 18 | no | — |
| 451 | Dic3 | — | 2 | 6 | no | — |
| 452 | Dic3 | C23×Q8 | 1 | 4 | yes | — |
| 453 | C23 | — | 3 | 6 | no | — |
| 454 | C23 | — | 3 | 24 | no | — |
| 455 | C23 | — | 12 | 6 | no | — |
| 456 | C23 | — | 12 | 6 | no | — |
| 457 | C23 | C24×D3 | 1 | 3 | yes | — |
| 458 | Q8 | — | 2 | 18 | no | — |
| 459 | Q8 | — | 3 | 4 | no | — |
| 460 | Q8 | — | 4 | 6 | no | — |
| 461 | Q8 | — | 6 | 36 | no | — |
| 462 | Q8 | — | 12 | 36 | no | — |
| 463 | Q8 | — | 12 | 6 | no | — |
| 464 | Q8 | C2×D3×Q8 | 1 | 4 | yes | complemented |
| 465 | Q8 | #1009 | 1 | 4 | yes | direct product factor |
| 466 | D4 | — | 3 | 24 | no | — |
| 467 | D4 | — | 3 | 24 | no | — |
| 468 | D4 | — | 3 | 12 | no | — |
| 469 | D4 | C2×D3×Q8 | 1 | 12 | yes | complemented |
| 470 | C2×C4 | — | 2 | 18 | no | — |
| 471 | C2×C4 | — | 3 | 2 | no | — |
| 472 | C2×C4 | — | 3 | 24 | no | — |
| 473 | C2×C4 | — | 3 | 6 | no | — |
| 474 | C2×C4 | — | 3 | 18 | no | — |
| 475 | C2×C4 | — | 4 | 9 | no | — |
| 476 | C2×C4 | — | 6 | 36 | no | — |
| 477 | C2×C4 | — | 12 | 36 | no | — |
| 478 | C2×C4 | — | 12 | 18 | no | — |
| 479 | C2×C4 | — | 12 | 18 | no | — |
| 480 | C2×C4 | C2×D3×Q8 | 1 | 12 | yes | complemented |
| 481 | C2×C4 | C24×D3 | 1 | 9 | yes | — |
| 482 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 483 | C2×C4 | C24×D3 | 1 | 9 | yes | — |
| 484 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 485 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 486 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 487 | C2×C3 | — | 2 | 6 | no | — |
| 488 | C2×C3 | C24×Q8 | 1 | 1 | yes | characteristic |
| 489 | C2×C3 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 490 | C2×C3 | 2−1+6 | 1 | 1 | yes | characteristic |
| 491 | D3 | — | 2 | 12 | no | — |
| 492 | C22 | — | 2 | 3 | no | — |
| 493 | C22 | — | 2 | 3 | no | — |
| 494 | C22 | — | 3 | 12 | no | — |
| 495 | C22 | — | 6 | 6 | no | — |
| 496 | C22 | — | 6 | 6 | no | — |
| 497 | C22 | — | 12 | 24 | no | — |
| 498 | C22 | C22×D3×Q8 | 1 | 6 | yes | — |
| 499 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 500 | C4 | — | 2 | 9 | no | — |
| 501 | C4 | — | 2 | 3 | no | — |
| 502 | C4 | — | 2 | 9 | no | — |
| 503 | C4 | — | 3 | 4 | no | — |
| 504 | C4 | — | 6 | 18 | no | — |
| 505 | C4 | — | 6 | 6 | no | — |
| 506 | C4 | C22×D3×Q8 | 1 | 6 | yes | — |
| 507 | C4 | C22×D3×Q8 | 1 | 2 | yes | — |
| 508 | C4 | C2×#1009 | 1 | 6 | yes | — |
| 509 | C3 | Q8×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 510 | C2 | — | 2 | 6 | no | — |
| 511 | C2 | — | 6 | 12 | no | — |
| 512 | C2 | C23×D3×Q8 | 1 | 1 | yes | characteristic |
| 513 | C2 | C22×#1009 | 1 | 1 | yes | characteristic |
| 514 | C2 | #87572 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta