← #11906367
Subgroups — #11906367
Order 1152.
2231 conjugacy classes of subgroups.
The subgroup lattice has 637 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10596199 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×D3×C4⋊Q8 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | Q8×#625 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595403 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10595338 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10594537 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10594531 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10594509 | C2 | 1 | 2 | yes | maximal |
| 9 | #10594351 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10594342 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #10594313 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C4×#3798 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #10593909 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10593859 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #86215 | — | 3 | 2 | no | maximal |
| 16 | C2×C3×D3×Q8 | C22 | 1 | 4 | yes | — |
| 17 | C2×#3798 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#3797 | C22 | 1 | 2 | yes | — |
| 19 | C32×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 20 | #64155 | C22 | 1 | 2 | yes | — |
| 21 | Q8×C3⋊Dic3 | C22 | 1 | 2 | yes | — |
| 22 | #64106 | C22 | 1 | 2 | yes | — |
| 23 | #64101 | C22 | 1 | 2 | yes | — |
| 24 | #64099 | C22 | 1 | 2 | yes | — |
| 25 | #64096 | C22 | 1 | 2 | yes | — |
| 26 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 27 | #64078 | C22 | 1 | 1 | yes | characteristic |
| 28 | C3×#944 | C22 | 1 | 4 | yes | — |
| 29 | C3×D3×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 30 | C3×D3×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 31 | C3×#888 | C22 | 1 | 4 | yes | — |
| 32 | C3×#888 | C22 | 1 | 4 | yes | — |
| 33 | C3×C42×D3 | C22 | 1 | 2 | yes | — |
| 34 | C3×#869 | C22 | 1 | 2 | yes | — |
| 35 | #63919 | C22 | 1 | 2 | yes | — |
| 36 | #63919 | C22 | 1 | 2 | yes | — |
| 37 | C4×#627 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4×#627 | C22 | 1 | 1 | yes | characteristic |
| 39 | #63904 | C22 | 1 | 8 | yes | — |
| 40 | C4×#626 | C22 | 1 | 2 | yes | — |
| 41 | C4×#626 | C22 | 1 | 2 | yes | — |
| 42 | C4×#625 | C22 | 1 | 1 | yes | characteristic |
| 43 | C4×#625 | C22 | 1 | 4 | yes | — |
| 44 | C4×#625 | C22 | 1 | 1 | yes | characteristic |
| 45 | #63900 | C22 | 1 | 2 | yes | — |
| 46 | #63900 | C22 | 1 | 2 | yes | — |
| 47 | #63888 | C22 | 1 | 8 | yes | — |
| 48 | #63874 | C22 | 1 | 1 | yes | characteristic |
| 49 | #63873 | C22 | 1 | 4 | yes | — |
| 50 | #63873 | C22 | 1 | 2 | yes | — |
| 51 | #63870 | C22 | 1 | 4 | yes | — |
| 52 | #63869 | C22 | 1 | 4 | yes | — |
| 53 | #63857 | C22 | 1 | 4 | yes | — |
| 54 | #63856 | C22 | 1 | 8 | yes | — |
| 55 | #63856 | C22 | 1 | 4 | yes | — |
| 56 | #63855 | C22 | 1 | 2 | yes | — |
| 57 | #63851 | C22 | 1 | 8 | yes | — |
| 58 | #63845 | C22 | 1 | 8 | yes | — |
| 59 | #63844 | C22 | 1 | 4 | yes | — |
| 60 | Dic3×Dic6 | C22 | 1 | 4 | yes | — |
| 61 | #63841 | C22 | 1 | 4 | yes | — |
| 62 | #63839 | C22 | 1 | 8 | yes | — |
| 63 | #63838 | C22 | 1 | 4 | yes | — |
| 64 | C2×C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 65 | Q8×#67 | — | 3 | 4 | no | — |
| 66 | Q8×#67 | — | 3 | 4 | no | — |
| 67 | #5730 | — | 3 | 4 | no | — |
| 68 | #5729 | — | 3 | 4 | no | — |
| 69 | #5729 | — | 3 | 4 | no | — |
| 70 | #5728 | — | 3 | 2 | no | — |
| 71 | #5728 | — | 3 | 2 | no | — |
| 72 | #5728 | — | 6 | 1 | no | — |
| 73 | #5727 | — | 3 | 4 | no | — |
| 74 | D3×C4⋊Q8 | — | 3 | 2 | no | — |
| 75 | D3×C4⋊Q8 | D3 | 1 | 2 | yes | complemented |
| 76 | #5722 | — | 3 | 4 | no | — |
| 77 | #5721 | — | 3 | 4 | no | — |
| 78 | #5511 | — | 3 | 4 | no | — |
| 79 | #5511 | — | 3 | 4 | no | — |
| 80 | #5504 | — | 3 | 4 | no | — |
| 81 | #5500 | — | 3 | 4 | no | — |
| 82 | C4×#235 | — | 3 | 2 | no | — |
| 83 | #5470 | — | 3 | 2 | no | — |
| 84 | C2×C32×Q8 | C23 | 1 | 2 | yes | — |
| 85 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#634 | C23 | 1 | 2 | yes | — |
| 89 | C3×D3×Q8 | — | 4 | 8 | no | — |
| 90 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 91 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 92 | C2×C3×C4×D3 | C23 | 1 | 8 | yes | — |
| 93 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 94 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 95 | C2×C3×Dic6 | C23 | 1 | 8 | yes | — |
| 96 | C2×#627 | C23 | 1 | 4 | yes | — |
| 97 | C2×#627 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×#626 | C23 | 1 | 2 | yes | — |
| 99 | C2×#625 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×#624 | C23 | 1 | 4 | yes | — |
| 101 | #3798 | Q8 | 1 | 8 | yes | complemented |
| 102 | #3797 | — | 4 | 4 | no | — |
| 103 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 104 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 105 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 106 | #3752 | C23 | 1 | 4 | yes | — |
| 107 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 108 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 109 | C4⋊(C3⋊Dic3) | C23 | 1 | 4 | yes | — |
| 110 | #3750 | C23 | 1 | 4 | yes | — |
| 111 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 112 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 113 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 114 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 115 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 116 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 117 | C3×Dic3⋊C4 | C23 | 1 | 8 | yes | — |
| 118 | C3×Dic3⋊C4 | C23 | 1 | 8 | yes | — |
| 119 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 120 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 121 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 122 | #3724 | C23 | 1 | 4 | yes | — |
| 123 | #3724 | C23 | 1 | 8 | yes | — |
| 124 | #3724 | C23 | 1 | 4 | yes | — |
| 125 | #3724 | C23 | 1 | 1 | yes | characteristic |
| 126 | #3724 | C23 | 1 | 1 | yes | characteristic |
| 127 | Dic3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 128 | Dic3⋊Dic3 | C23 | 1 | 8 | yes | — |
| 129 | Dic3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 130 | #3722 | C23 | 1 | 2 | yes | — |
| 131 | (C2×D3)⋊Dic3 | C23 | 1 | 8 | yes | — |
| 132 | (C2×D3)⋊Dic3 | C23 | 1 | 2 | yes | — |
| 133 | (C2×D3)⋊Dic3 | C23 | 1 | 2 | yes | — |
| 134 | Dic32 | C23 | 1 | 8 | yes | — |
| 135 | #3503 | — | 9 | 1 | no | Sylow |
| 136 | C22×C3×Q8 | — | 3 | 4 | no | — |
| 137 | C2×D3×Q8 | — | 3 | 4 | no | — |
| 138 | C2×D3×Q8 | C2×D3 | 1 | 4 | yes | — |
| 139 | C2×#235 | — | 3 | 2 | no | — |
| 140 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 141 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 142 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 143 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 144 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 145 | C3×C4⋊Q8 | C2×D3 | 1 | 2 | yes | — |
| 146 | C2×C3×C4⋊C4 | — | 3 | 4 | no | — |
| 147 | C2×C3×C4⋊C4 | — | 3 | 4 | no | — |
| 148 | C2×C3×C42 | — | 3 | 2 | no | — |
| 149 | #946 | — | 3 | 4 | no | — |
| 150 | #946 | — | 3 | 4 | no | — |
| 151 | #946 | — | 3 | 8 | no | — |
| 152 | #946 | — | 3 | 8 | no | — |
| 153 | #946 | — | 6 | 2 | no | — |
| 154 | Q8×Dic3 | — | 3 | 4 | no | — |
| 155 | Q8×Dic3 | — | 3 | 4 | no | — |
| 156 | Q8×Dic3 | — | 6 | 2 | no | — |
| 157 | #944 | — | 3 | 4 | no | — |
| 158 | #944 | — | 3 | 8 | no | — |
| 159 | #944 | — | 3 | 8 | no | — |
| 160 | #944 | C2×D3 | 1 | 4 | yes | — |
| 161 | C4×#67 | — | 3 | 2 | no | — |
| 162 | C4×#67 | — | 3 | 2 | no | — |
| 163 | C4×#67 | — | 3 | 8 | no | — |
| 164 | C4×#67 | — | 3 | 8 | no | — |
| 165 | C4×#67 | — | 3 | 2 | no | — |
| 166 | C4×#67 | — | 3 | 2 | no | — |
| 167 | #926 | — | 3 | 4 | no | — |
| 168 | #926 | — | 3 | 2 | no | — |
| 169 | #924 | — | 3 | 4 | no | — |
| 170 | #924 | — | 3 | 8 | no | — |
| 171 | #924 | — | 3 | 4 | no | — |
| 172 | #924 | — | 3 | 8 | no | — |
| 173 | #897 | — | 3 | 4 | no | — |
| 174 | #897 | — | 3 | 4 | no | — |
| 175 | #897 | — | 6 | 2 | no | — |
| 176 | #896 | — | 3 | 8 | no | — |
| 177 | #896 | — | 3 | 8 | no | — |
| 178 | #893 | — | 3 | 8 | no | — |
| 179 | #892 | — | 3 | 4 | no | — |
| 180 | #892 | — | 3 | 4 | no | — |
| 181 | #892 | — | 6 | 2 | no | — |
| 182 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 183 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 184 | D3×C4⋊C4 | C2×D3 | 1 | 4 | yes | — |
| 185 | D3×C4⋊C4 | C2×D3 | 1 | 4 | yes | — |
| 186 | #890 | — | 3 | 4 | no | — |
| 187 | #890 | — | 3 | 8 | no | — |
| 188 | #890 | — | 3 | 4 | no | — |
| 189 | #890 | — | 6 | 2 | no | — |
| 190 | #889 | — | 3 | 8 | no | — |
| 191 | #889 | — | 3 | 8 | no | — |
| 192 | #888 | — | 3 | 8 | no | — |
| 193 | #888 | — | 3 | 4 | no | — |
| 194 | #888 | — | 3 | 4 | no | — |
| 195 | #888 | C2×D3 | 1 | 4 | yes | — |
| 196 | #888 | C2×D3 | 1 | 4 | yes | — |
| 197 | #887 | — | 3 | 4 | no | — |
| 198 | #887 | — | 3 | 8 | no | — |
| 199 | #887 | — | 3 | 4 | no | — |
| 200 | #887 | — | 6 | 2 | no | — |
| 201 | C4×D12 | — | 3 | 2 | no | — |
| 202 | C4×D12 | — | 3 | 2 | no | — |
| 203 | #872 | — | 3 | 2 | no | — |
| 204 | #872 | — | 3 | 2 | no | — |
| 205 | C42×D3 | — | 3 | 2 | no | — |
| 206 | C42×D3 | — | 6 | 1 | no | — |
| 207 | C42×D3 | C2×D3 | 1 | 2 | yes | — |
| 208 | #870 | — | 3 | 4 | no | — |
| 209 | #869 | — | 3 | 2 | no | — |
| 210 | #869 | — | 6 | 1 | no | — |
| 211 | #869 | C2×D3 | 1 | 2 | yes | — |
| 212 | C4×Dic6 | — | 3 | 4 | no | — |
| 213 | C4×Dic6 | — | 3 | 4 | no | — |
| 214 | C4×Dic6 | — | 3 | 2 | no | — |
| 215 | C4×Dic6 | — | 3 | 2 | no | — |
| 216 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 217 | C22×C3×D3 | C24 | 1 | 2 | yes | — |
| 218 | C32×Q8 | — | 2 | 4 | no | — |
| 219 | C2×C32×C4 | C24 | 1 | 4 | yes | — |
| 220 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 221 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 222 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 223 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 224 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 225 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 226 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 227 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 228 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 229 | C4×C3⋊D3 | C2×Q8 | 1 | 4 | yes | complemented |
| 230 | #634 | — | 2 | 4 | no | — |
| 231 | C2×C3×Dic3 | C24 | 1 | 8 | yes | — |
| 232 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 233 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 234 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 235 | C3×C4×D3 | — | 2 | 4 | no | — |
| 236 | C3×C4×D3 | — | 2 | 4 | no | — |
| 237 | C3×C4×D3 | — | 4 | 8 | no | — |
| 238 | C3×C4×D3 | C2×Q8 | 1 | 8 | yes | complemented |
| 239 | C3×Dic6 | — | 2 | 8 | no | — |
| 240 | C3×Dic6 | — | 4 | 8 | no | — |
| 241 | #627 | — | 4 | 4 | no | — |
| 242 | #627 | C2×Q8 | 1 | 4 | yes | complemented |
| 243 | #626 | C2×Q8 | 1 | 8 | yes | complemented |
| 244 | #625 | C2×Q8 | 1 | 4 | yes | complemented |
| 245 | #624 | — | 4 | 4 | no | — |
| 246 | Q82 | — | 9 | 2 | no | — |
| 247 | #557 | — | 9 | 2 | no | — |
| 248 | #554 | — | 9 | 2 | no | — |
| 249 | #554 | — | 9 | 4 | no | — |
| 250 | D4×Q8 | — | 9 | 4 | no | — |
| 251 | D4×Q8 | — | 9 | 2 | no | — |
| 252 | #544 | — | 9 | 4 | no | — |
| 253 | #544 | — | 9 | 2 | no | — |
| 254 | #533 | — | 9 | 2 | no | — |
| 255 | #533 | — | 9 | 1 | no | — |
| 256 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 257 | C2×C4⋊Q8 | — | 9 | 1 | no | — |
| 258 | #520 | — | 9 | 2 | no | — |
| 259 | C4×#41 | — | 9 | 1 | no | — |
| 260 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 261 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 262 | C2×C3×Q8 | — | 3 | 8 | no | — |
| 263 | C2×C3×Q8 | — | 12 | 8 | no | — |
| 264 | C2×C3×Q8 | C22×D3 | 1 | 4 | yes | — |
| 265 | C22×C3×C4 | — | 3 | 2 | no | — |
| 266 | C22×C3×C4 | — | 3 | 2 | no | — |
| 267 | C22×C3×C4 | — | 3 | 2 | no | — |
| 268 | C22×C3×C4 | — | 3 | 8 | no | — |
| 269 | C2×#67 | — | 3 | 2 | no | — |
| 270 | C2×#67 | — | 3 | 2 | no | — |
| 271 | D3×Q8 | — | 4 | 8 | no | — |
| 272 | D3×Q8 | — | 12 | 8 | no | — |
| 273 | #235 | — | 3 | 16 | no | — |
| 274 | C2×D12 | — | 3 | 2 | no | — |
| 275 | C2×C4×D3 | — | 3 | 2 | no | — |
| 276 | C2×C4×D3 | — | 3 | 2 | no | — |
| 277 | C2×C4×D3 | — | 3 | 2 | no | — |
| 278 | C2×C4×D3 | — | 3 | 8 | no | — |
| 279 | C2×C4×D3 | — | 6 | 1 | no | — |
| 280 | C2×C4×D3 | — | 6 | 1 | no | — |
| 281 | C2×C4×D3 | — | 6 | 1 | no | — |
| 282 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 283 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 284 | C2×C4×D3 | C22×D3 | 1 | 8 | yes | — |
| 285 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 286 | C2×Dic6 | — | 3 | 2 | no | — |
| 287 | C2×Dic6 | — | 3 | 4 | no | — |
| 288 | C2×Dic6 | — | 3 | 8 | no | — |
| 289 | C2×Dic6 | — | 6 | 2 | no | — |
| 290 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 291 | C2×Dic6 | C22×D3 | 1 | 8 | yes | — |
| 292 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 293 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 294 | C3×C4⋊C4 | — | 3 | 8 | no | — |
| 295 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 296 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 297 | C3×C4⋊C4 | — | 3 | 8 | no | — |
| 298 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 299 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 300 | C3×C42 | — | 2 | 1 | no | — |
| 301 | C3×C42 | — | 3 | 2 | no | — |
| 302 | C3×C42 | — | 3 | 2 | no | — |
| 303 | C3×C42 | — | 3 | 2 | no | — |
| 304 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 305 | #217 | — | 3 | 8 | no | — |
| 306 | #217 | — | 3 | 2 | no | — |
| 307 | #217 | — | 3 | 2 | no | — |
| 308 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 309 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 310 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 311 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 312 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 313 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 314 | (C2×D3)⋊C4 | — | 6 | 4 | no | — |
| 315 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 316 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 317 | C4⋊Dic3 | — | 3 | 8 | no | — |
| 318 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 319 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 320 | C4⋊Dic3 | — | 3 | 8 | no | — |
| 321 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 322 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 323 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 324 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 325 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 326 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 327 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 328 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 329 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 330 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 331 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 332 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 333 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 334 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 335 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 336 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 337 | Dic3⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 338 | Dic3⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 339 | C4×Dic3 | — | 3 | 2 | no | — |
| 340 | C4×Dic3 | — | 3 | 2 | no | — |
| 341 | C4×Dic3 | — | 3 | 2 | no | — |
| 342 | C4×Dic3 | — | 3 | 8 | no | — |
| 343 | C4×Dic3 | — | 3 | 8 | no | — |
| 344 | C4×Dic3 | — | 3 | 8 | no | — |
| 345 | C4×Dic3 | — | 6 | 1 | no | — |
| 346 | C4×Dic3 | — | 6 | 1 | no | — |
| 347 | C4×Dic3 | — | 6 | 1 | no | — |
| 348 | C4×Dic3 | — | 6 | 4 | no | — |
| 349 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 350 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 351 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 352 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 353 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 354 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 355 | C2×C3⋊D3 | C22×Q8 | 1 | 2 | yes | — |
| 356 | C2×C3×D3 | — | 2 | 2 | no | — |
| 357 | C2×C3×D3 | — | 2 | 2 | no | — |
| 358 | C2×C3×D3 | C22×Q8 | 1 | 4 | yes | — |
| 359 | C32×C4 | — | 2 | 4 | no | — |
| 360 | C32×C4 | C22×Q8 | 1 | 2 | yes | — |
| 361 | C32×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 362 | C32×C4 | 2−1+4 | 1 | 2 | yes | — |
| 363 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 364 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 365 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 366 | C3⋊Dic3 | C22×Q8 | 1 | 2 | yes | — |
| 367 | C3×Dic3 | — | 2 | 8 | no | — |
| 368 | C3×Dic3 | — | 2 | 2 | no | — |
| 369 | C3×Dic3 | — | 2 | 2 | no | — |
| 370 | C3×Dic3 | C22×Q8 | 1 | 4 | yes | — |
| 371 | C2×#41 | — | 9 | 1 | no | — |
| 372 | C22×Q8 | — | 3 | 4 | no | — |
| 373 | C22×Q8 | — | 9 | 2 | no | — |
| 374 | C4⋊Q8 | — | 3 | 4 | no | — |
| 375 | C4⋊Q8 | — | 3 | 4 | no | — |
| 376 | C4⋊Q8 | — | 3 | 4 | no | — |
| 377 | C4⋊Q8 | — | 3 | 2 | no | — |
| 378 | C4⋊Q8 | — | 9 | 2 | no | — |
| 379 | C4⋊Q8 | — | 9 | 2 | no | — |
| 380 | C4⋊Q8 | — | 9 | 8 | no | — |
| 381 | C4⋊Q8 | — | 9 | 2 | no | — |
| 382 | C4⋊Q8 | — | 9 | 4 | no | — |
| 383 | C4⋊Q8 | — | 9 | 1 | no | — |
| 384 | C4⋊Q8 | D32 | 1 | 1 | yes | characteristic |
| 385 | #125 | — | 9 | 4 | no | — |
| 386 | #125 | — | 9 | 4 | no | — |
| 387 | #125 | — | 9 | 8 | no | — |
| 388 | #125 | — | 9 | 2 | no | — |
| 389 | C22⋊Q8 | — | 9 | 4 | no | — |
| 390 | C22⋊Q8 | — | 9 | 8 | no | — |
| 391 | C22⋊Q8 | — | 9 | 8 | no | — |
| 392 | C22⋊Q8 | — | 9 | 4 | no | — |
| 393 | C22⋊Q8 | — | 9 | 8 | no | — |
| 394 | C22⋊Q8 | — | 9 | 2 | no | — |
| 395 | C22⋊Q8 | — | 9 | 2 | no | — |
| 396 | C4×Q8 | — | 9 | 1 | no | — |
| 397 | C4×Q8 | — | 9 | 1 | no | — |
| 398 | C4×Q8 | — | 9 | 4 | no | — |
| 399 | C4×Q8 | — | 9 | 4 | no | — |
| 400 | C4×Q8 | — | 9 | 4 | no | — |
| 401 | C4×Q8 | — | 9 | 2 | no | — |
| 402 | C4×Q8 | — | 9 | 2 | no | — |
| 403 | C4×D4 | — | 9 | 2 | no | — |
| 404 | C4×D4 | — | 9 | 2 | no | — |
| 405 | C4×D4 | — | 9 | 8 | no | — |
| 406 | C4×D4 | — | 9 | 1 | no | — |
| 407 | C4×D4 | — | 9 | 1 | no | — |
| 408 | C4×D4 | — | 9 | 4 | no | — |
| 409 | #117 | — | 9 | 1 | no | — |
| 410 | #117 | — | 9 | 2 | no | — |
| 411 | #117 | — | 9 | 4 | no | — |
| 412 | #117 | — | 9 | 2 | no | — |
| 413 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 414 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 415 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 416 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 417 | C2×C42 | — | 3 | 2 | no | — |
| 418 | C2×C42 | — | 9 | 1 | no | — |
| 419 | C23×C3 | — | 3 | 2 | no | — |
| 420 | C22×D3 | — | 3 | 2 | no | — |
| 421 | C22×D3 | — | 6 | 1 | no | — |
| 422 | C22×D3 | C23×D3 | 1 | 2 | yes | — |
| 423 | C3×Q8 | — | 2 | 8 | no | — |
| 424 | C3×Q8 | — | 4 | 4 | no | — |
| 425 | C3×Q8 | — | 6 | 8 | no | — |
| 426 | C3×Q8 | — | 12 | 8 | no | — |
| 427 | C2×C3×C4 | — | 2 | 1 | no | — |
| 428 | C2×C3×C4 | — | 2 | 1 | no | — |
| 429 | C2×C3×C4 | — | 2 | 1 | no | — |
| 430 | C2×C3×C4 | — | 2 | 4 | no | — |
| 431 | C2×C3×C4 | — | 3 | 2 | no | — |
| 432 | C2×C3×C4 | — | 3 | 8 | no | — |
| 433 | C2×C3×C4 | — | 3 | 8 | no | — |
| 434 | C2×C3×C4 | — | 3 | 2 | no | — |
| 435 | C2×C3×C4 | — | 3 | 2 | no | — |
| 436 | C2×C3×C4 | — | 6 | 4 | no | — |
| 437 | C2×C3×C4 | — | 6 | 4 | no | — |
| 438 | C2×C3×C4 | — | 12 | 8 | no | — |
| 439 | C2×C3×C4 | C23×D3 | 1 | 8 | yes | — |
| 440 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 441 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 442 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 443 | #67 | — | 3 | 8 | no | — |
| 444 | #67 | — | 3 | 8 | no | — |
| 445 | C2×Dic3 | — | 3 | 2 | no | — |
| 446 | C2×Dic3 | — | 3 | 8 | no | — |
| 447 | C2×Dic3 | — | 3 | 2 | no | — |
| 448 | C2×Dic3 | — | 3 | 2 | no | — |
| 449 | C2×Dic3 | — | 6 | 1 | no | — |
| 450 | C2×Dic3 | — | 6 | 1 | no | — |
| 451 | C2×Dic3 | — | 6 | 1 | no | — |
| 452 | C2×Dic3 | — | 6 | 4 | no | — |
| 453 | C2×Dic3 | C23×D3 | 1 | 8 | yes | — |
| 454 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 455 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 456 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 457 | D12 | — | 3 | 8 | no | — |
| 458 | C4×D3 | — | 2 | 4 | no | — |
| 459 | C4×D3 | — | 2 | 4 | no | — |
| 460 | C4×D3 | — | 3 | 8 | no | — |
| 461 | C4×D3 | — | 4 | 8 | no | — |
| 462 | C4×D3 | — | 6 | 4 | no | — |
| 463 | C4×D3 | — | 6 | 4 | no | — |
| 464 | C4×D3 | — | 6 | 4 | no | — |
| 465 | C4×D3 | — | 12 | 2 | no | — |
| 466 | C4×D3 | — | 12 | 2 | no | — |
| 467 | C4×D3 | — | 12 | 8 | no | — |
| 468 | C4×D3 | D3×Q8 | 1 | 8 | yes | complemented |
| 469 | Dic6 | — | 2 | 8 | no | — |
| 470 | Dic6 | — | 3 | 8 | no | — |
| 471 | Dic6 | — | 4 | 8 | no | — |
| 472 | Dic6 | — | 6 | 8 | no | — |
| 473 | Dic6 | — | 12 | 4 | no | — |
| 474 | Dic6 | — | 12 | 8 | no | — |
| 475 | C2×C32 | C23×Q8 | 1 | 1 | yes | characteristic |
| 476 | C2×C32 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 477 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 478 | C3⋊D3 | — | 2 | 2 | no | — |
| 479 | C3×D3 | — | 2 | 4 | no | — |
| 480 | #41 | — | 9 | 8 | no | — |
| 481 | C2×Q8 | — | 3 | 4 | no | — |
| 482 | C2×Q8 | — | 3 | 8 | no | — |
| 483 | C2×Q8 | — | 9 | 1 | no | — |
| 484 | C2×Q8 | — | 9 | 4 | no | — |
| 485 | C2×Q8 | — | 9 | 2 | no | — |
| 486 | C2×Q8 | — | 12 | 8 | no | — |
| 487 | C2×Q8 | — | 36 | 4 | no | — |
| 488 | C2×Q8 | C2×D32 | 1 | 2 | yes | — |
| 489 | C2×D4 | — | 9 | 2 | no | — |
| 490 | C2×D4 | — | 9 | 1 | no | — |
| 491 | C22×C4 | — | 3 | 2 | no | — |
| 492 | C22×C4 | — | 3 | 2 | no | — |
| 493 | C22×C4 | — | 3 | 2 | no | — |
| 494 | C22×C4 | — | 3 | 8 | no | — |
| 495 | C22×C4 | — | 9 | 4 | no | — |
| 496 | C22×C4 | — | 9 | 1 | no | — |
| 497 | C22×C4 | — | 9 | 1 | no | — |
| 498 | C22×C4 | — | 9 | 1 | no | — |
| 499 | C4⋊C4 | — | 3 | 4 | no | — |
| 500 | C4⋊C4 | — | 3 | 4 | no | — |
| 501 | C4⋊C4 | — | 3 | 8 | no | — |
| 502 | C4⋊C4 | — | 3 | 8 | no | — |
| 503 | C4⋊C4 | — | 9 | 4 | no | — |
| 504 | C4⋊C4 | — | 9 | 4 | no | — |
| 505 | C4⋊C4 | — | 9 | 1 | no | — |
| 506 | C4⋊C4 | — | 9 | 2 | no | — |
| 507 | C4⋊C4 | — | 9 | 1 | no | — |
| 508 | C4⋊C4 | — | 9 | 2 | no | — |
| 509 | C4⋊C4 | — | 9 | 8 | no | — |
| 510 | C4⋊C4 | — | 9 | 8 | no | — |
| 511 | C4⋊C4 | — | 9 | 2 | no | — |
| 512 | C4⋊C4 | — | 9 | 2 | no | — |
| 513 | C4⋊C4 | — | 9 | 4 | no | — |
| 514 | C4⋊C4 | — | 9 | 4 | no | — |
| 515 | C4⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 516 | C4⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 517 | C22⋊C4 | — | 9 | 2 | no | — |
| 518 | C22⋊C4 | — | 9 | 2 | no | — |
| 519 | C22⋊C4 | — | 9 | 2 | no | — |
| 520 | C22⋊C4 | — | 9 | 8 | no | — |
| 521 | C22⋊C4 | — | 9 | 4 | no | — |
| 522 | C42 | — | 3 | 2 | no | — |
| 523 | C42 | — | 3 | 2 | no | — |
| 524 | C42 | — | 3 | 2 | no | — |
| 525 | C42 | — | 9 | 8 | no | — |
| 526 | C42 | — | 9 | 1 | no | — |
| 527 | C42 | — | 9 | 1 | no | — |
| 528 | C42 | — | 9 | 1 | no | — |
| 529 | C42 | — | 9 | 4 | no | — |
| 530 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 531 | C22×C3 | — | 2 | 1 | no | — |
| 532 | C22×C3 | — | 3 | 4 | no | — |
| 533 | C22×C3 | — | 6 | 2 | no | — |
| 534 | C22×C3 | — | 6 | 2 | no | — |
| 535 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 536 | C2×D3 | — | 2 | 2 | no | — |
| 537 | C2×D3 | — | 2 | 2 | no | — |
| 538 | C2×D3 | — | 3 | 4 | no | — |
| 539 | C2×D3 | — | 6 | 2 | no | — |
| 540 | C2×D3 | — | 6 | 2 | no | — |
| 541 | C2×D3 | — | 6 | 2 | no | — |
| 542 | C2×D3 | — | 12 | 1 | no | — |
| 543 | C2×D3 | — | 12 | 1 | no | — |
| 544 | C2×D3 | C2×D3×Q8 | 1 | 4 | yes | — |
| 545 | C3×C4 | — | 2 | 8 | no | — |
| 546 | C3×C4 | — | 2 | 2 | no | — |
| 547 | C3×C4 | — | 2 | 2 | no | — |
| 548 | C3×C4 | — | 2 | 2 | no | — |
| 549 | C3×C4 | — | 3 | 4 | no | — |
| 550 | C3×C4 | — | 4 | 4 | no | — |
| 551 | C3×C4 | — | 6 | 8 | no | — |
| 552 | C3×C4 | — | 6 | 2 | no | — |
| 553 | C3×C4 | — | 6 | 2 | no | — |
| 554 | C3×C4 | #1004 | 1 | 4 | yes | — |
| 555 | C3×C4 | C2×D3×Q8 | 1 | 4 | yes | — |
| 556 | C3×C4 | #1007 | 1 | 4 | yes | — |
| 557 | Dic3 | — | 2 | 8 | no | — |
| 558 | Dic3 | — | 2 | 2 | no | — |
| 559 | Dic3 | — | 2 | 2 | no | — |
| 560 | Dic3 | — | 3 | 4 | no | — |
| 561 | Dic3 | — | 6 | 2 | no | — |
| 562 | Dic3 | — | 6 | 2 | no | — |
| 563 | Dic3 | — | 6 | 8 | no | — |
| 564 | Dic3 | — | 6 | 2 | no | — |
| 565 | Dic3 | — | 12 | 4 | no | — |
| 566 | Dic3 | — | 12 | 1 | no | — |
| 567 | Dic3 | — | 12 | 1 | no | — |
| 568 | Dic3 | C2×D3×Q8 | 1 | 4 | yes | — |
| 569 | C32 | #3503 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 570 | C23 | — | 3 | 2 | no | — |
| 571 | C23 | — | 9 | 1 | no | — |
| 572 | Q8 | — | 2 | 4 | no | — |
| 573 | Q8 | — | 6 | 8 | no | — |
| 574 | Q8 | — | 9 | 4 | no | — |
| 575 | Q8 | — | 12 | 8 | no | — |
| 576 | Q8 | — | 18 | 4 | no | — |
| 577 | Q8 | — | 36 | 4 | no | — |
| 578 | D4 | — | 9 | 8 | no | — |
| 579 | D4 | — | 9 | 4 | no | — |
| 580 | C2×C4 | — | 3 | 2 | no | — |
| 581 | C2×C4 | — | 3 | 8 | no | — |
| 582 | C2×C4 | — | 3 | 2 | no | — |
| 583 | C2×C4 | — | 3 | 2 | no | — |
| 584 | C2×C4 | — | 3 | 8 | no | — |
| 585 | C2×C4 | — | 6 | 4 | no | — |
| 586 | C2×C4 | — | 6 | 4 | no | — |
| 587 | C2×C4 | — | 9 | 1 | no | — |
| 588 | C2×C4 | — | 9 | 4 | no | — |
| 589 | C2×C4 | — | 9 | 4 | no | — |
| 590 | C2×C4 | — | 9 | 1 | no | — |
| 591 | C2×C4 | — | 9 | 1 | no | — |
| 592 | C2×C4 | — | 12 | 8 | no | — |
| 593 | C2×C4 | — | 18 | 2 | no | — |
| 594 | C2×C4 | — | 18 | 2 | no | — |
| 595 | C2×C4 | — | 36 | 4 | no | — |
| 596 | C2×C4 | C22×D32 | 1 | 4 | yes | — |
| 597 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 598 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 599 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 600 | C2×C3 | — | 2 | 1 | no | — |
| 601 | C2×C3 | — | 2 | 1 | no | — |
| 602 | C2×C3 | — | 2 | 1 | no | — |
| 603 | C2×C3 | — | 6 | 4 | no | — |
| 604 | C2×C3 | C2×#1004 | 1 | 2 | yes | — |
| 605 | C2×C3 | C22×D3×Q8 | 1 | 2 | yes | — |
| 606 | C2×C3 | C2×#1007 | 1 | 2 | yes | — |
| 607 | D3 | — | 2 | 4 | no | — |
| 608 | D3 | — | 6 | 4 | no | — |
| 609 | D3 | — | 12 | 2 | no | — |
| 610 | C22 | — | 3 | 4 | no | — |
| 611 | C22 | — | 6 | 2 | no | — |
| 612 | C22 | — | 6 | 2 | no | — |
| 613 | C22 | — | 9 | 2 | no | — |
| 614 | C22 | — | 18 | 1 | no | — |
| 615 | C22 | — | 18 | 1 | no | — |
| 616 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 617 | C4 | — | 2 | 4 | no | — |
| 618 | C4 | — | 3 | 4 | no | — |
| 619 | C4 | — | 6 | 2 | no | — |
| 620 | C4 | — | 6 | 8 | no | — |
| 621 | C4 | — | 6 | 2 | no | — |
| 622 | C4 | — | 9 | 2 | no | — |
| 623 | C4 | — | 18 | 1 | no | — |
| 624 | C4 | — | 18 | 1 | no | — |
| 625 | C4 | — | 18 | 4 | no | — |
| 626 | C4 | #64313 | 1 | 2 | yes | — |
| 627 | C4 | #64316 | 1 | 2 | yes | — |
| 628 | C4 | D32×Q8 | 1 | 2 | yes | — |
| 629 | C3 | — | 2 | 1 | no | — |
| 630 | C3 | #86215 | 1 | 2 | yes | complemented |
| 631 | C2 | — | 6 | 4 | no | — |
| 632 | C2 | — | 18 | 2 | no | — |
| 633 | C2 | C2×#64313 | 1 | 1 | yes | characteristic |
| 634 | C2 | C2×#64316 | 1 | 1 | yes | characteristic |
| 635 | C2 | C2×D32×Q8 | 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