← Q8×#1004 #11707294
Subgroups — Q8×#1004 #11707294
Order 768.
7406 conjugacy classes of subgroups.
The subgroup lattice has 590 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C3×D4×Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×Q8×#67 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #86761 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | D3×D4×Q8 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #86747 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | Q8×#237 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #86215 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #85986 | C2 | 1 | 12 | yes | maximal, complemented |
| 9 | Q8×#235 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #85766 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C4×#1004 | C2 | 1 | 3 | yes | maximal |
| 12 | Q8×H(5,𝔽2) | — | 3 | 1 | no | maximal, Sylow |
| 13 | C23×C3×Q8 | C22 | 1 | 2 | yes | complemented |
| 14 | C22×D3×Q8 | C22 | 1 | 4 | yes | complemented |
| 15 | C2×#1004 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×D4×Q8 | C22 | 1 | 4 | yes | complemented |
| 17 | C3×D4×Q8 | C22 | 1 | 12 | yes | complemented |
| 18 | C2×C3×C4⋊Q8 | C22 | 1 | 3 | yes | complemented |
| 19 | C2×C3×C22⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 20 | C2×C3×C4×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×C3×C4×D4 | C22 | 1 | 3 | yes | — |
| 22 | Q8×#67 | C22 | 1 | 4 | yes | complemented |
| 23 | Q8×#67 | C22 | 1 | 24 | yes | complemented |
| 24 | Q8×#67 | C22 | 1 | 8 | yes | complemented |
| 25 | Q8×#67 | C22 | 1 | 24 | yes | complemented |
| 26 | C2×#946 | C22 | 1 | 12 | yes | complemented |
| 27 | C2×Q8×Dic3 | C22 | 1 | 4 | yes | complemented |
| 28 | C2×#944 | C22 | 1 | 12 | yes | complemented |
| 29 | #5798 | C22 | 1 | 3 | yes | — |
| 30 | C2×C4×#67 | C22 | 1 | 12 | yes | — |
| 31 | C2×#924 | C22 | 1 | 12 | yes | complemented |
| 32 | #5730 | C22 | 1 | 12 | yes | complemented |
| 33 | #5729 | C22 | 1 | 24 | yes | complemented |
| 34 | #5728 | C22 | 1 | 12 | yes | complemented |
| 35 | #5727 | C22 | 1 | 12 | yes | complemented |
| 36 | D3×C4⋊Q8 | C22 | 1 | 12 | yes | complemented |
| 37 | #5722 | C22 | 1 | 12 | yes | complemented |
| 38 | #5721 | C22 | 1 | 12 | yes | complemented |
| 39 | #5636 | C22 | 1 | 48 | yes | complemented |
| 40 | #5635 | C22 | 1 | 24 | yes | complemented |
| 41 | #5634 | C22 | 1 | 24 | yes | complemented |
| 42 | #5632 | C22 | 1 | 24 | yes | complemented |
| 43 | D3×C22⋊Q8 | C22 | 1 | 24 | yes | complemented |
| 44 | #5623 | C22 | 1 | 24 | yes | complemented |
| 45 | #5622 | C22 | 1 | 24 | yes | complemented |
| 46 | #5579 | C22 | 1 | 6 | yes | complemented |
| 47 | #5578 | C22 | 1 | 12 | yes | complemented |
| 48 | Q8×D12 | C22 | 1 | 2 | yes | complemented |
| 49 | C4×D3×Q8 | C22 | 1 | 4 | yes | complemented |
| 50 | #5567 | C22 | 1 | 6 | yes | complemented |
| 51 | Q8×Dic6 | C22 | 1 | 2 | yes | complemented |
| 52 | #5546 | C22 | 1 | 12 | yes | — |
| 53 | #5545 | C22 | 1 | 12 | yes | — |
| 54 | C4×D3×D4 | C22 | 1 | 12 | yes | — |
| 55 | #5543 | C22 | 1 | 12 | yes | complemented |
| 56 | #5539 | C22 | 1 | 24 | yes | complemented |
| 57 | D4×Dic6 | C22 | 1 | 12 | yes | complemented |
| 58 | C4×#237 | C22 | 1 | 12 | yes | — |
| 59 | #5511 | C22 | 1 | 12 | yes | complemented |
| 60 | #5511 | C22 | 1 | 24 | yes | complemented |
| 61 | #5504 | C22 | 1 | 6 | yes | — |
| 62 | #5500 | C22 | 1 | 6 | yes | complemented |
| 63 | #5486 | C22 | 1 | 12 | yes | — |
| 64 | #5483 | C22 | 1 | 12 | yes | complemented |
| 65 | C4×#235 | C22 | 1 | 6 | yes | — |
| 66 | #5470 | C22 | 1 | 6 | yes | complemented |
| 67 | #3503 | — | 3 | 12 | no | — |
| 68 | #3503 | — | 3 | 6 | no | — |
| 69 | #3501 | — | 3 | 12 | no | — |
| 70 | #3501 | — | 3 | 12 | no | — |
| 71 | #3501 | — | 3 | 3 | no | — |
| 72 | Q8×#41 | — | 3 | 4 | no | — |
| 73 | Q8×#41 | — | 3 | 2 | no | — |
| 74 | C2×D4×Q8 | — | 3 | 4 | no | — |
| 75 | C2×D4×Q8 | — | 3 | 4 | no | — |
| 76 | C2×D4×Q8 | D3 | 1 | 1 | yes | characteristic, complemented |
| 77 | C4×H(5,𝔽2) | — | 3 | 3 | no | — |
| 78 | C22×C3×Q8 | — | 4 | 8 | no | — |
| 79 | C22×C3×Q8 | C23 | 1 | 4 | yes | — |
| 80 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×C3×Q8 | C23 | 1 | 12 | yes | — |
| 82 | C22×C3×Q8 | C23 | 1 | 6 | yes | — |
| 83 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 84 | C23×C3×C4 | C23 | 1 | 6 | yes | — |
| 85 | C22×#67 | C23 | 1 | 4 | yes | — |
| 86 | C2×D3×Q8 | — | 4 | 16 | no | — |
| 87 | C2×D3×Q8 | C23 | 1 | 4 | yes | — |
| 88 | C2×D3×Q8 | C23 | 1 | 24 | yes | — |
| 89 | #1004 | Q8 | 1 | 16 | yes | direct product factor |
| 90 | C2×#237 | C23 | 1 | 4 | yes | — |
| 91 | C2×D3×D4 | C23 | 1 | 4 | yes | — |
| 92 | C2×#235 | C23 | 1 | 2 | yes | — |
| 93 | C22×C4×D3 | C23 | 1 | 12 | yes | — |
| 94 | C22×Dic6 | C23 | 1 | 12 | yes | — |
| 95 | C3×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 96 | C3×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 97 | C3×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 98 | C3×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 99 | C3×C4×Q8 | C23 | 1 | 2 | yes | — |
| 100 | C3×C4×Q8 | C23 | 1 | 6 | yes | — |
| 101 | C3×C4×D4 | C23 | 1 | 12 | yes | — |
| 102 | C3×C4×D4 | C23 | 1 | 12 | yes | — |
| 103 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 104 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 105 | C2×C3×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 106 | C2×C3×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 107 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 108 | C2×#217 | C23 | 1 | 12 | yes | — |
| 109 | #946 | C23 | 1 | 48 | yes | — |
| 110 | #946 | C23 | 1 | 24 | yes | — |
| 111 | #946 | C23 | 1 | 12 | yes | — |
| 112 | Q8×Dic3 | C23 | 1 | 24 | yes | — |
| 113 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 114 | #944 | C23 | 1 | 24 | yes | — |
| 115 | #944 | C23 | 1 | 48 | yes | — |
| 116 | #944 | C23 | 1 | 12 | yes | — |
| 117 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 118 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 119 | C4×#67 | C23 | 1 | 24 | yes | — |
| 120 | C4×#67 | C23 | 1 | 24 | yes | — |
| 121 | C4×#67 | C23 | 1 | 12 | yes | — |
| 122 | C4×#67 | C23 | 1 | 12 | yes | — |
| 123 | C4×#67 | C23 | 1 | 24 | yes | — |
| 124 | C2×(C2×D3)⋊C4 | C23 | 1 | 12 | yes | — |
| 125 | #926 | C23 | 1 | 6 | yes | — |
| 126 | C2×C4⋊Dic3 | C23 | 1 | 12 | yes | — |
| 127 | #924 | C23 | 1 | 24 | yes | — |
| 128 | #924 | C23 | 1 | 12 | yes | — |
| 129 | #924 | C23 | 1 | 12 | yes | — |
| 130 | #924 | C23 | 1 | 24 | yes | — |
| 131 | #924 | C23 | 1 | 24 | yes | — |
| 132 | C2×Dic3⋊C4 | C23 | 1 | 24 | yes | — |
| 133 | C2×Dic3⋊C4 | C23 | 1 | 12 | yes | — |
| 134 | C2×C4×Dic3 | C23 | 1 | 12 | yes | — |
| 135 | #897 | C23 | 1 | 12 | yes | — |
| 136 | #897 | C23 | 1 | 24 | yes | — |
| 137 | #896 | C23 | 1 | 48 | yes | — |
| 138 | #896 | C23 | 1 | 24 | yes | — |
| 139 | #893 | C23 | 1 | 12 | yes | — |
| 140 | #892 | C23 | 1 | 12 | yes | — |
| 141 | D3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 142 | D3×C4⋊C4 | C23 | 1 | 24 | yes | — |
| 143 | D3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 144 | #890 | C23 | 1 | 24 | yes | — |
| 145 | #889 | C23 | 1 | 48 | yes | — |
| 146 | #889 | C23 | 1 | 24 | yes | — |
| 147 | #888 | C23 | 1 | 24 | yes | — |
| 148 | #888 | C23 | 1 | 12 | yes | — |
| 149 | #888 | C23 | 1 | 24 | yes | — |
| 150 | #887 | C23 | 1 | 12 | yes | — |
| 151 | #887 | C23 | 1 | 24 | yes | — |
| 152 | #887 | C23 | 1 | 12 | yes | — |
| 153 | #67⋊C4 | C23 | 1 | 24 | yes | — |
| 154 | #67⋊C4 | C23 | 1 | 24 | yes | — |
| 155 | D3×C22⋊C4 | C23 | 1 | 24 | yes | — |
| 156 | #878 | C23 | 1 | 48 | yes | — |
| 157 | #878 | C23 | 1 | 48 | yes | — |
| 158 | #877 | C23 | 1 | 24 | yes | — |
| 159 | C4×D12 | C23 | 1 | 6 | yes | — |
| 160 | C4×D12 | C23 | 1 | 6 | yes | — |
| 161 | #872 | C23 | 1 | 12 | yes | — |
| 162 | C42×D3 | C23 | 1 | 12 | yes | — |
| 163 | #870 | C23 | 1 | 12 | yes | — |
| 164 | #869 | C23 | 1 | 6 | yes | — |
| 165 | #869 | C23 | 1 | 6 | yes | — |
| 166 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 167 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 168 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 169 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 170 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 171 | C23×Q8 | — | 3 | 4 | no | — |
| 172 | C23×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 173 | Q82 | — | 3 | 12 | no | — |
| 174 | Q82 | — | 3 | 2 | no | — |
| 175 | #557 | — | 3 | 12 | no | — |
| 176 | #557 | — | 3 | 6 | no | — |
| 177 | #554 | — | 3 | 12 | no | — |
| 178 | #554 | — | 3 | 24 | no | — |
| 179 | #554 | — | 3 | 48 | no | — |
| 180 | #554 | — | 3 | 6 | no | — |
| 181 | #554 | — | 3 | 12 | no | — |
| 182 | #554 | — | 3 | 24 | no | — |
| 183 | #554 | — | 3 | 12 | no | — |
| 184 | #554 | — | 3 | 24 | no | — |
| 185 | D4×Q8 | — | 3 | 8 | no | — |
| 186 | D4×Q8 | — | 3 | 4 | no | — |
| 187 | D4×Q8 | — | 3 | 24 | no | — |
| 188 | D4×Q8 | — | 3 | 24 | no | — |
| 189 | D4×Q8 | — | 3 | 12 | no | — |
| 190 | D4×Q8 | — | 3 | 24 | no | — |
| 191 | D4×Q8 | — | 3 | 2 | no | — |
| 192 | D4×Q8 | — | 3 | 12 | no | — |
| 193 | D4×Q8 | C2×D3 | 1 | 4 | yes | complemented |
| 194 | D4×Q8 | C2×D3 | 1 | 12 | yes | complemented |
| 195 | #544 | — | 3 | 24 | no | — |
| 196 | #544 | — | 3 | 24 | no | — |
| 197 | #544 | — | 3 | 6 | no | — |
| 198 | #543 | — | 3 | 24 | no | — |
| 199 | #543 | — | 3 | 12 | no | — |
| 200 | #533 | — | 3 | 12 | no | — |
| 201 | #533 | — | 3 | 24 | no | — |
| 202 | #533 | — | 3 | 12 | no | — |
| 203 | #533 | — | 3 | 6 | no | — |
| 204 | C2×C4⋊Q8 | — | 3 | 12 | no | — |
| 205 | C2×C4⋊Q8 | — | 3 | 12 | no | — |
| 206 | C2×C4⋊Q8 | C2×D3 | 1 | 3 | yes | complemented |
| 207 | C2×C22⋊Q8 | — | 3 | 12 | no | — |
| 208 | C2×C22⋊Q8 | — | 3 | 12 | no | — |
| 209 | C2×C22⋊Q8 | — | 3 | 24 | no | — |
| 210 | C2×C22⋊Q8 | C2×D3 | 1 | 6 | yes | complemented |
| 211 | #520 | — | 3 | 12 | no | — |
| 212 | #520 | — | 3 | 6 | no | — |
| 213 | #518 | — | 3 | 3 | no | — |
| 214 | #518 | — | 3 | 12 | no | — |
| 215 | #518 | — | 3 | 12 | no | — |
| 216 | C4×#41 | — | 3 | 12 | no | — |
| 217 | C4×#41 | — | 3 | 6 | no | — |
| 218 | C2×C4×Q8 | — | 3 | 4 | no | — |
| 219 | C2×C4×Q8 | — | 3 | 4 | no | — |
| 220 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 221 | C2×C4×D4 | — | 3 | 12 | no | — |
| 222 | C2×C4×D4 | — | 3 | 12 | no | — |
| 223 | C2×C4×D4 | C2×D3 | 1 | 3 | yes | — |
| 224 | C24×C3 | C24 | 1 | 2 | yes | — |
| 225 | C23×D3 | C24 | 1 | 4 | yes | — |
| 226 | C2×C3×Q8 | — | 2 | 16 | no | — |
| 227 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 228 | C2×C3×Q8 | — | 4 | 24 | no | — |
| 229 | C2×C3×Q8 | — | 4 | 12 | no | — |
| 230 | C2×C3×Q8 | C24 | 1 | 3 | yes | — |
| 231 | C2×C3×Q8 | C24 | 1 | 12 | yes | — |
| 232 | C2×C3×Q8 | C24 | 1 | 12 | yes | — |
| 233 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 234 | C2×C3×D4 | C2×Q8 | 1 | 8 | yes | complemented |
| 235 | C2×C3×D4 | C24 | 1 | 4 | yes | — |
| 236 | C22×C3×C4 | — | 4 | 12 | no | — |
| 237 | C22×C3×C4 | C24 | 1 | 12 | yes | — |
| 238 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 239 | C22×C3×C4 | C24 | 1 | 12 | yes | — |
| 240 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 241 | C22×C3×C4 | C24 | 1 | 6 | yes | — |
| 242 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 243 | C2×#67 | C2×Q8 | 1 | 32 | yes | complemented |
| 244 | C2×#67 | C24 | 1 | 8 | yes | — |
| 245 | C2×#67 | C24 | 1 | 4 | yes | — |
| 246 | C22×Dic3 | C24 | 1 | 12 | yes | — |
| 247 | C22×Dic3 | C24 | 1 | 12 | yes | — |
| 248 | C22×Dic3 | C24 | 1 | 4 | yes | — |
| 249 | D3×Q8 | — | 2 | 16 | no | — |
| 250 | D3×Q8 | — | 4 | 48 | no | — |
| 251 | #237 | C2×Q8 | 1 | 32 | yes | complemented |
| 252 | D3×D4 | C2×Q8 | 1 | 32 | yes | complemented |
| 253 | #235 | C2×Q8 | 1 | 16 | yes | complemented |
| 254 | C2×D12 | C24 | 1 | 2 | yes | — |
| 255 | C2×C4×D3 | — | 4 | 24 | no | — |
| 256 | C2×C4×D3 | C24 | 1 | 12 | yes | — |
| 257 | C2×C4×D3 | C24 | 1 | 12 | yes | — |
| 258 | C2×C4×D3 | C24 | 1 | 24 | yes | — |
| 259 | C2×C4×D3 | C24 | 1 | 4 | yes | — |
| 260 | C2×Dic6 | — | 4 | 24 | no | — |
| 261 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 262 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 263 | C2×Dic6 | C24 | 1 | 24 | yes | — |
| 264 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 265 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 266 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 267 | C3×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 268 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 269 | C3×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 270 | C3×C42 | C24 | 1 | 6 | yes | — |
| 271 | C3×C42 | C24 | 1 | 6 | yes | — |
| 272 | #217 | C24 | 1 | 24 | yes | — |
| 273 | #217 | C24 | 1 | 12 | yes | — |
| 274 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 275 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 276 | (C2×D3)⋊C4 | C24 | 1 | 24 | yes | — |
| 277 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 278 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 279 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 280 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 281 | C4⋊Dic3 | C24 | 1 | 24 | yes | — |
| 282 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 283 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 284 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 285 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 286 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 287 | Dic3⋊C4 | C24 | 1 | 48 | yes | — |
| 288 | C4×Dic3 | C24 | 1 | 12 | yes | — |
| 289 | C4×Dic3 | C24 | 1 | 12 | yes | — |
| 290 | C4×Dic3 | C24 | 1 | 12 | yes | — |
| 291 | C4×Dic3 | C24 | 1 | 24 | yes | — |
| 292 | H(5,𝔽2) | — | 3 | 16 | no | — |
| 293 | C2×#41 | — | 3 | 4 | no | — |
| 294 | C2×#41 | — | 3 | 2 | no | — |
| 295 | C22×Q8 | — | 3 | 4 | no | — |
| 296 | C22×Q8 | — | 3 | 24 | no | — |
| 297 | C22×Q8 | — | 3 | 12 | no | — |
| 298 | C22×Q8 | — | 4 | 8 | no | — |
| 299 | C22×Q8 | — | 12 | 16 | no | — |
| 300 | C22×Q8 | C22×D3 | 1 | 4 | yes | — |
| 301 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 302 | C22×Q8 | C22×D3 | 1 | 12 | yes | — |
| 303 | C22×Q8 | C22×D3 | 1 | 6 | yes | — |
| 304 | C22×D4 | — | 3 | 4 | no | — |
| 305 | C22×D4 | — | 3 | 4 | no | — |
| 306 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 307 | C23×C4 | — | 3 | 12 | no | — |
| 308 | C23×C4 | C22×D3 | 1 | 6 | yes | — |
| 309 | C4⋊Q8 | — | 3 | 24 | no | — |
| 310 | C4⋊Q8 | — | 3 | 12 | no | — |
| 311 | C4⋊Q8 | — | 3 | 48 | no | — |
| 312 | C4⋊Q8 | — | 3 | 24 | no | — |
| 313 | C4⋊Q8 | — | 3 | 24 | no | — |
| 314 | C4⋊Q8 | — | 3 | 12 | no | — |
| 315 | C4⋊Q8 | — | 3 | 6 | no | — |
| 316 | C4⋊Q8 | — | 3 | 6 | no | — |
| 317 | C4⋊Q8 | C22×D3 | 1 | 12 | yes | — |
| 318 | C4⋊Q8 | C22×D3 | 1 | 12 | yes | — |
| 319 | #125 | — | 3 | 24 | no | — |
| 320 | #125 | — | 3 | 48 | no | — |
| 321 | #125 | — | 3 | 24 | no | — |
| 322 | #125 | — | 3 | 12 | no | — |
| 323 | C22⋊Q8 | — | 3 | 24 | no | — |
| 324 | C22⋊Q8 | — | 3 | 12 | no | — |
| 325 | C22⋊Q8 | — | 3 | 48 | no | — |
| 326 | C22⋊Q8 | — | 3 | 24 | no | — |
| 327 | C22⋊Q8 | — | 3 | 12 | no | — |
| 328 | C22⋊Q8 | — | 3 | 24 | no | — |
| 329 | C22⋊Q8 | — | 3 | 24 | no | — |
| 330 | C22⋊Q8 | — | 3 | 12 | no | — |
| 331 | C22⋊Q8 | — | 3 | 12 | no | — |
| 332 | C22⋊Q8 | — | 3 | 48 | no | — |
| 333 | C22⋊Q8 | — | 3 | 24 | no | — |
| 334 | C22⋊Q8 | — | 3 | 24 | no | — |
| 335 | C22⋊Q8 | — | 3 | 48 | no | — |
| 336 | C22⋊Q8 | — | 3 | 48 | no | — |
| 337 | C22⋊Q8 | C22×D3 | 1 | 24 | yes | — |
| 338 | C22⋊Q8 | C22×D3 | 1 | 24 | yes | — |
| 339 | C4×Q8 | — | 3 | 4 | no | — |
| 340 | C4×Q8 | — | 3 | 24 | no | — |
| 341 | C4×Q8 | — | 3 | 12 | no | — |
| 342 | C4×Q8 | — | 3 | 12 | no | — |
| 343 | C4×Q8 | — | 3 | 24 | no | — |
| 344 | C4×Q8 | — | 3 | 12 | no | — |
| 345 | C4×Q8 | — | 3 | 6 | no | — |
| 346 | C4×Q8 | — | 3 | 6 | no | — |
| 347 | C4×Q8 | — | 3 | 12 | no | — |
| 348 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 349 | C4×Q8 | C22×D3 | 1 | 6 | yes | — |
| 350 | C4×D4 | — | 3 | 12 | no | — |
| 351 | C4×D4 | — | 3 | 12 | no | — |
| 352 | C4×D4 | — | 3 | 24 | no | — |
| 353 | C4×D4 | — | 3 | 12 | no | — |
| 354 | C4×D4 | — | 3 | 24 | no | — |
| 355 | C4×D4 | — | 3 | 24 | no | — |
| 356 | C4×D4 | — | 3 | 12 | no | — |
| 357 | C4×D4 | — | 3 | 12 | no | — |
| 358 | C4×D4 | — | 3 | 24 | no | — |
| 359 | C4×D4 | — | 3 | 24 | no | — |
| 360 | C4×D4 | — | 3 | 6 | no | — |
| 361 | C4×D4 | — | 3 | 6 | no | — |
| 362 | C4×D4 | C22×D3 | 1 | 12 | yes | — |
| 363 | C4×D4 | C22×D3 | 1 | 12 | yes | — |
| 364 | #117 | — | 3 | 6 | no | — |
| 365 | #117 | — | 3 | 12 | no | — |
| 366 | #117 | — | 3 | 24 | no | — |
| 367 | #117 | — | 3 | 12 | no | — |
| 368 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 369 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 370 | C2×C4⋊C4 | — | 3 | 24 | no | — |
| 371 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 372 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 373 | C2×C4⋊C4 | — | 3 | 24 | no | — |
| 374 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 375 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 376 | C2×C4⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 377 | C2×C22⋊C4 | — | 3 | 12 | no | — |
| 378 | C2×C22⋊C4 | — | 3 | 12 | no | — |
| 379 | C2×C22⋊C4 | — | 3 | 24 | no | — |
| 380 | C2×C22⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 381 | C2×C42 | — | 3 | 12 | no | — |
| 382 | C2×C42 | — | 3 | 12 | no | — |
| 383 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 384 | C23×C3 | — | 4 | 2 | no | — |
| 385 | C23×C3 | — | 4 | 2 | no | — |
| 386 | C23×C3 | C22×Q8 | 1 | 8 | yes | complemented |
| 387 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 388 | C23×C3 | C25 | 1 | 4 | yes | — |
| 389 | C22×D3 | — | 4 | 4 | no | — |
| 390 | C22×D3 | — | 4 | 4 | no | — |
| 391 | C22×D3 | C22×Q8 | 1 | 16 | yes | complemented |
| 392 | C22×D3 | C25 | 1 | 4 | yes | — |
| 393 | C3×Q8 | — | 2 | 24 | no | — |
| 394 | C3×Q8 | — | 2 | 6 | no | — |
| 395 | C3×Q8 | — | 4 | 12 | no | — |
| 396 | C3×Q8 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 397 | C3×D4 | C22×Q8 | 1 | 16 | yes | complemented |
| 398 | C2×C3×C4 | — | 2 | 24 | no | — |
| 399 | C2×C3×C4 | — | 2 | 6 | no | — |
| 400 | C2×C3×C4 | — | 4 | 6 | no | — |
| 401 | C2×C3×C4 | — | 4 | 12 | no | — |
| 402 | C2×C3×C4 | — | 4 | 3 | no | — |
| 403 | C2×C3×C4 | C22×Q8 | 1 | 4 | yes | complemented |
| 404 | C2×C3×C4 | C25 | 1 | 6 | yes | — |
| 405 | C2×C3×C4 | C25 | 1 | 12 | yes | — |
| 406 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 407 | C2×C3×C4 | C25 | 1 | 2 | yes | — |
| 408 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 409 | #67 | C22×Q8 | 1 | 16 | yes | complemented |
| 410 | #67 | C22×Q8 | 1 | 32 | yes | complemented |
| 411 | C2×Dic3 | — | 4 | 12 | no | — |
| 412 | C2×Dic3 | — | 4 | 12 | no | — |
| 413 | C2×Dic3 | C22×Q8 | 1 | 16 | yes | complemented |
| 414 | C2×Dic3 | C25 | 1 | 12 | yes | — |
| 415 | C2×Dic3 | C25 | 1 | 12 | yes | — |
| 416 | C2×Dic3 | C25 | 1 | 4 | yes | — |
| 417 | D12 | C22×Q8 | 1 | 8 | yes | complemented |
| 418 | C4×D3 | — | 2 | 24 | no | — |
| 419 | C4×D3 | — | 4 | 24 | no | — |
| 420 | C4×D3 | — | 4 | 12 | no | — |
| 421 | C4×D3 | C22×Q8 | 1 | 16 | yes | complemented |
| 422 | Dic6 | — | 2 | 24 | no | — |
| 423 | Dic6 | — | 4 | 24 | no | — |
| 424 | Dic6 | — | 4 | 12 | no | — |
| 425 | Dic6 | C22×Q8 | 1 | 8 | yes | complemented |
| 426 | C24 | — | 3 | 4 | no | — |
| 427 | C24 | C23×D3 | 1 | 2 | yes | — |
| 428 | #41 | — | 3 | 32 | no | — |
| 429 | #41 | — | 3 | 16 | no | — |
| 430 | C2×Q8 | — | 2 | 4 | no | — |
| 431 | C2×Q8 | — | 2 | 16 | no | — |
| 432 | C2×Q8 | — | 3 | 2 | no | — |
| 433 | C2×Q8 | — | 3 | 12 | no | — |
| 434 | C2×Q8 | — | 3 | 12 | no | — |
| 435 | C2×Q8 | — | 3 | 24 | no | — |
| 436 | C2×Q8 | — | 4 | 12 | no | — |
| 437 | C2×Q8 | — | 4 | 24 | no | — |
| 438 | C2×Q8 | — | 6 | 16 | no | — |
| 439 | C2×Q8 | — | 12 | 24 | no | — |
| 440 | C2×Q8 | — | 12 | 48 | no | — |
| 441 | C2×Q8 | C23×D3 | 1 | 12 | yes | — |
| 442 | C2×Q8 | C23×D3 | 1 | 3 | yes | — |
| 443 | C2×Q8 | C23×D3 | 1 | 12 | yes | — |
| 444 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 445 | C2×D4 | — | 3 | 32 | no | — |
| 446 | C2×D4 | — | 3 | 4 | no | — |
| 447 | C2×D4 | — | 3 | 8 | no | — |
| 448 | C2×D4 | — | 3 | 32 | no | — |
| 449 | C2×D4 | — | 3 | 2 | no | — |
| 450 | C2×D4 | D3×Q8 | 1 | 8 | yes | complemented |
| 451 | C2×D4 | C23×D3 | 1 | 4 | yes | — |
| 452 | C22×C4 | — | 3 | 4 | no | — |
| 453 | C22×C4 | — | 3 | 4 | no | — |
| 454 | C22×C4 | — | 3 | 12 | no | — |
| 455 | C22×C4 | — | 3 | 12 | no | — |
| 456 | C22×C4 | — | 3 | 12 | no | — |
| 457 | C22×C4 | — | 3 | 12 | no | — |
| 458 | C22×C4 | — | 3 | 24 | no | — |
| 459 | C22×C4 | — | 4 | 12 | no | — |
| 460 | C22×C4 | — | 12 | 24 | no | — |
| 461 | C22×C4 | C23×D3 | 1 | 12 | yes | — |
| 462 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 463 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 464 | C22×C4 | C23×D3 | 1 | 12 | yes | — |
| 465 | C22×C4 | C23×D3 | 1 | 6 | yes | — |
| 466 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 467 | C4⋊C4 | — | 3 | 12 | no | — |
| 468 | C4⋊C4 | — | 3 | 24 | no | — |
| 469 | C4⋊C4 | — | 3 | 12 | no | — |
| 470 | C4⋊C4 | — | 3 | 6 | no | — |
| 471 | C4⋊C4 | — | 3 | 48 | no | — |
| 472 | C4⋊C4 | — | 3 | 24 | no | — |
| 473 | C4⋊C4 | — | 3 | 12 | no | — |
| 474 | C4⋊C4 | — | 3 | 24 | no | — |
| 475 | C4⋊C4 | — | 3 | 24 | no | — |
| 476 | C4⋊C4 | — | 3 | 12 | no | — |
| 477 | C4⋊C4 | — | 3 | 6 | no | — |
| 478 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 479 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 480 | C4⋊C4 | C23×D3 | 1 | 24 | yes | — |
| 481 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 482 | C22⋊C4 | — | 3 | 12 | no | — |
| 483 | C22⋊C4 | — | 3 | 24 | no | — |
| 484 | C22⋊C4 | — | 3 | 24 | no | — |
| 485 | C22⋊C4 | — | 3 | 12 | no | — |
| 486 | C22⋊C4 | — | 3 | 12 | no | — |
| 487 | C22⋊C4 | C23×D3 | 1 | 24 | yes | — |
| 488 | C42 | — | 3 | 12 | no | — |
| 489 | C42 | — | 3 | 24 | no | — |
| 490 | C42 | — | 3 | 12 | no | — |
| 491 | C42 | — | 3 | 12 | no | — |
| 492 | C42 | C23×D3 | 1 | 6 | yes | — |
| 493 | C42 | C23×D3 | 1 | 6 | yes | — |
| 494 | C22×C3 | — | 2 | 4 | no | — |
| 495 | C22×C3 | — | 2 | 1 | no | — |
| 496 | C22×C3 | — | 2 | 4 | no | — |
| 497 | C22×C3 | — | 2 | 1 | no | — |
| 498 | C22×C3 | — | 4 | 8 | no | — |
| 499 | C22×C3 | C23×Q8 | 1 | 8 | yes | — |
| 500 | C22×C3 | C23×Q8 | 1 | 2 | yes | — |
| 501 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 502 | C2×D3 | — | 2 | 4 | no | — |
| 503 | C2×D3 | — | 2 | 4 | no | — |
| 504 | C2×D3 | — | 4 | 16 | no | — |
| 505 | C2×D3 | C23×Q8 | 1 | 8 | yes | — |
| 506 | C3×C4 | — | 2 | 12 | no | — |
| 507 | C3×C4 | — | 2 | 3 | no | — |
| 508 | C3×C4 | — | 2 | 6 | no | — |
| 509 | C3×C4 | C23×Q8 | 1 | 4 | yes | — |
| 510 | C3×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 511 | Dic3 | — | 2 | 12 | no | — |
| 512 | Dic3 | — | 2 | 12 | no | — |
| 513 | Dic3 | C23×Q8 | 1 | 8 | yes | — |
| 514 | C23 | — | 3 | 4 | no | — |
| 515 | C23 | — | 3 | 16 | no | — |
| 516 | C23 | — | 4 | 2 | no | — |
| 517 | C23 | — | 4 | 2 | no | — |
| 518 | C23 | — | 12 | 4 | no | — |
| 519 | C23 | — | 12 | 4 | no | — |
| 520 | C23 | C2×D3×Q8 | 1 | 8 | yes | complemented |
| 521 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 522 | C23 | C24×D3 | 1 | 4 | yes | — |
| 523 | Q8 | — | 2 | 6 | no | — |
| 524 | Q8 | — | 2 | 24 | no | — |
| 525 | Q8 | — | 3 | 8 | no | — |
| 526 | Q8 | — | 4 | 12 | no | — |
| 527 | Q8 | — | 6 | 24 | no | — |
| 528 | Q8 | — | 12 | 24 | no | — |
| 529 | Q8 | — | 12 | 12 | no | — |
| 530 | Q8 | #1004 | 1 | 4 | yes | direct product factor |
| 531 | D4 | — | 3 | 32 | no | — |
| 532 | D4 | — | 3 | 16 | no | — |
| 533 | D4 | — | 3 | 8 | no | — |
| 534 | D4 | C2×D3×Q8 | 1 | 16 | yes | complemented |
| 535 | C2×C4 | — | 2 | 6 | no | — |
| 536 | C2×C4 | — | 2 | 24 | no | — |
| 537 | C2×C4 | — | 3 | 16 | no | — |
| 538 | C2×C4 | — | 3 | 4 | no | — |
| 539 | C2×C4 | — | 3 | 16 | no | — |
| 540 | C2×C4 | — | 3 | 12 | no | — |
| 541 | C2×C4 | — | 3 | 12 | no | — |
| 542 | C2×C4 | — | 4 | 12 | no | — |
| 543 | C2×C4 | — | 4 | 6 | no | — |
| 544 | C2×C4 | — | 4 | 3 | no | — |
| 545 | C2×C4 | — | 6 | 24 | no | — |
| 546 | C2×C4 | — | 12 | 24 | no | — |
| 547 | C2×C4 | — | 12 | 12 | no | — |
| 548 | C2×C4 | — | 12 | 12 | no | — |
| 549 | C2×C4 | — | 12 | 12 | no | — |
| 550 | C2×C4 | C2×D3×Q8 | 1 | 4 | yes | complemented |
| 551 | C2×C4 | C24×D3 | 1 | 6 | yes | — |
| 552 | C2×C4 | C24×D3 | 1 | 12 | yes | — |
| 553 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 554 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 555 | C2×C4 | C24×D3 | 1 | 2 | yes | — |
| 556 | C2×C3 | — | 2 | 8 | no | — |
| 557 | C2×C3 | — | 2 | 2 | no | — |
| 558 | C2×C3 | C24×Q8 | 1 | 1 | yes | characteristic |
| 559 | C2×C3 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 560 | C2×C3 | 2−1+6 | 1 | 1 | yes | characteristic |
| 561 | D3 | — | 2 | 8 | no | — |
| 562 | C22 | — | 2 | 1 | no | — |
| 563 | C22 | — | 2 | 4 | no | — |
| 564 | C22 | — | 2 | 1 | no | — |
| 565 | C22 | — | 2 | 4 | no | — |
| 566 | C22 | — | 3 | 8 | no | — |
| 567 | C22 | — | 4 | 8 | no | — |
| 568 | C22 | — | 6 | 4 | no | — |
| 569 | C22 | — | 6 | 4 | no | — |
| 570 | C22 | — | 12 | 16 | no | — |
| 571 | C22 | C22×D3×Q8 | 1 | 8 | yes | — |
| 572 | C22 | C22×D3×Q8 | 1 | 2 | yes | — |
| 573 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 574 | C4 | — | 2 | 3 | no | — |
| 575 | C4 | — | 2 | 12 | no | — |
| 576 | C4 | — | 2 | 6 | no | — |
| 577 | C4 | — | 3 | 8 | no | — |
| 578 | C4 | — | 6 | 12 | no | — |
| 579 | C4 | — | 6 | 12 | no | — |
| 580 | C4 | C2×#1004 | 1 | 6 | yes | — |
| 581 | C4 | C22×D3×Q8 | 1 | 4 | yes | — |
| 582 | C3 | Q8×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 583 | C2 | — | 2 | 2 | no | — |
| 584 | C2 | — | 2 | 8 | no | — |
| 585 | C2 | — | 6 | 8 | no | — |
| 586 | C2 | C22×#1004 | 1 | 1 | yes | characteristic |
| 587 | C2 | C23×D3×Q8 | 1 | 1 | yes | characteristic |
| 588 | C2 | #87571 | 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