← #11660356
Subgroups — #11660356
Order 768.
1790 conjugacy classes of subgroups.
The subgroup lattice has 656 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #85738 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3×#424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #83756 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #83734 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #82209 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #79085 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #79084 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #79083 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #79082 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #79012 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #79008 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #79004 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #79000 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #60267 | — | 3 | 1 | no | maximal, Sylow |
| 15 | C22×C3×M16 | C22 | 1 | 1 | yes | characteristic |
| 16 | C23×C3×C8 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C3×#117 | C22 | 1 | 1 | yes | characteristic |
| 18 | #5791 | C22 | 1 | 2 | yes | — |
| 19 | C2×#901 | C22 | 1 | 2 | yes | — |
| 20 | C2×#901 | C22 | 1 | 2 | yes | — |
| 21 | #5535 | C4 | 1 | 1 | yes | characteristic |
| 22 | #5535 | C4 | 1 | 1 | yes | characteristic |
| 23 | #5534 | C4 | 1 | 2 | yes | — |
| 24 | #5534 | C4 | 1 | 2 | yes | — |
| 25 | #5528 | C22 | 1 | 4 | yes | — |
| 26 | #5528 | C22 | 1 | 4 | yes | — |
| 27 | #5518 | C4 | 1 | 1 | yes | characteristic |
| 28 | #5518 | C4 | 1 | 1 | yes | characteristic |
| 29 | #5515 | C4 | 1 | 4 | yes | — |
| 30 | #5494 | C4 | 1 | 4 | yes | — |
| 31 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×#235 | C22 | 1 | 2 | yes | — |
| 33 | #5470 | C22 | 1 | 1 | yes | characteristic |
| 34 | C3×#424 | C22 | 1 | 2 | yes | — |
| 35 | C3×#424 | C22 | 1 | 2 | yes | — |
| 36 | C3×#424 | C22 | 1 | 2 | yes | — |
| 37 | C3×#424 | C22 | 1 | 2 | yes | — |
| 38 | C2×C3×C4⋊C8 | C22 | 1 | 2 | yes | — |
| 39 | C2×C3×C4⋊C8 | C22 | 1 | 2 | yes | — |
| 40 | #5207 | C22 | 1 | 2 | yes | — |
| 41 | #5128 | C22 | 1 | 4 | yes | — |
| 42 | #5128 | C22 | 1 | 4 | yes | — |
| 43 | #5127 | C22 | 1 | 4 | yes | — |
| 44 | #5127 | C22 | 1 | 4 | yes | — |
| 45 | #5111 | C22 | 1 | 4 | yes | — |
| 46 | #5111 | C22 | 1 | 4 | yes | — |
| 47 | #5110 | C22 | 1 | 2 | yes | — |
| 48 | #5110 | C22 | 1 | 2 | yes | — |
| 49 | C8×#67 | C22 | 1 | 4 | yes | — |
| 50 | C8×#67 | C22 | 1 | 4 | yes | — |
| 51 | #5102 | C22 | 1 | 2 | yes | — |
| 52 | #5102 | C22 | 1 | 2 | yes | — |
| 53 | #5101 | C22 | 1 | 2 | yes | — |
| 54 | #5101 | C22 | 1 | 2 | yes | — |
| 55 | #5000 | C22 | 1 | 4 | yes | — |
| 56 | #5000 | C22 | 1 | 4 | yes | — |
| 57 | #4924 | C22 | 1 | 1 | yes | characteristic |
| 58 | #4924 | C22 | 1 | 1 | yes | characteristic |
| 59 | C4×#208 | C22 | 1 | 2 | yes | — |
| 60 | #4840 | C22 | 1 | 4 | yes | complemented |
| 61 | #4840 | C22 | 1 | 4 | yes | complemented |
| 62 | #4839 | C22 | 1 | 4 | yes | complemented |
| 63 | #4839 | C22 | 1 | 4 | yes | complemented |
| 64 | #4838 | C22 | 1 | 4 | yes | complemented |
| 65 | #4837 | C22 | 1 | 4 | yes | complemented |
| 66 | #4836 | C22 | 1 | 4 | yes | complemented |
| 67 | #4836 | C22 | 1 | 4 | yes | complemented |
| 68 | #4835 | C22 | 1 | 4 | yes | complemented |
| 69 | #4834 | C22 | 1 | 4 | yes | complemented |
| 70 | #4833 | C22 | 1 | 4 | yes | complemented |
| 71 | D3×C4⋊C8 | C22 | 1 | 4 | yes | complemented |
| 72 | #4831 | C22 | 1 | 4 | yes | complemented |
| 73 | #4830 | C22 | 1 | 4 | yes | complemented |
| 74 | #4828 | C22 | 1 | 4 | yes | complemented |
| 75 | #4828 | C22 | 1 | 4 | yes | complemented |
| 76 | #3455 | — | 3 | 1 | no | — |
| 77 | #2995 | — | 3 | 4 | no | — |
| 78 | #2994 | — | 3 | 4 | no | — |
| 79 | #2993 | — | 3 | 4 | no | — |
| 80 | #2992 | — | 3 | 4 | no | — |
| 81 | #2962 | — | 3 | 2 | no | — |
| 82 | #2935 | — | 3 | 2 | no | — |
| 83 | #2930 | — | 3 | 2 | no | — |
| 84 | #2929 | — | 3 | 2 | no | — |
| 85 | #2925 | — | 3 | 2 | no | — |
| 86 | #2921 | — | 3 | 1 | no | — |
| 87 | #2906 | — | 3 | 2 | no | — |
| 88 | C2×#424 | D3 | 1 | 1 | yes | characteristic, complemented |
| 89 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×#235 | C23 | 1 | 2 | yes | — |
| 91 | C2×C3×M16 | — | 4 | 2 | no | — |
| 92 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 94 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 95 | C22×C3×C8 | — | 4 | 2 | no | — |
| 96 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 97 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 98 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 99 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 100 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 101 | C3×#117 | C2×C4 | 1 | 1 | yes | characteristic |
| 102 | C3×#117 | C2×C4 | 1 | 1 | yes | characteristic |
| 103 | C3×#117 | C2×C4 | 1 | 1 | yes | characteristic |
| 104 | C3×#117 | C2×C4 | 1 | 1 | yes | characteristic |
| 105 | C3×#117 | C23 | 1 | 2 | yes | — |
| 106 | C3×#117 | C23 | 1 | 2 | yes | — |
| 107 | C2×C3×C4⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 108 | C2×C3×C22⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 109 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 111 | #953 | C2×C4 | 1 | 4 | yes | — |
| 112 | #930 | C2×C4 | 1 | 4 | yes | — |
| 113 | #930 | C2×C4 | 1 | 2 | yes | — |
| 114 | #930 | C2×C4 | 1 | 2 | yes | — |
| 115 | #929 | C2×C4 | 1 | 4 | yes | — |
| 116 | C4×#67 | C2×C4 | 1 | 4 | yes | — |
| 117 | C4×#67 | C2×C4 | 1 | 4 | yes | — |
| 118 | C4×#67 | C23 | 1 | 4 | yes | — |
| 119 | C4×#67 | C23 | 1 | 4 | yes | — |
| 120 | #926 | C23 | 1 | 2 | yes | — |
| 121 | #924 | C2×C4 | 1 | 4 | yes | — |
| 122 | #924 | C2×C4 | 1 | 2 | yes | — |
| 123 | #924 | C2×C4 | 1 | 2 | yes | — |
| 124 | C2×#208 | C23 | 1 | 2 | yes | — |
| 125 | C2×#208 | C23 | 1 | 2 | yes | — |
| 126 | #901 | — | 4 | 4 | no | — |
| 127 | #901 | — | 4 | 4 | no | — |
| 128 | C2×ΓL(1,𝔽25) | C23 | 1 | 4 | yes | — |
| 129 | C2×ΓL(1,𝔽25) | C23 | 1 | 4 | yes | — |
| 130 | C2×D3×C8 | C23 | 1 | 4 | yes | — |
| 131 | C2×D3×C8 | C23 | 1 | 4 | yes | — |
| 132 | #898 | C2×C4 | 1 | 4 | yes | — |
| 133 | #898 | C2×C4 | 1 | 4 | yes | — |
| 134 | #896 | C2×C4 | 1 | 4 | yes | — |
| 135 | #896 | C2×C4 | 1 | 4 | yes | — |
| 136 | #894 | C2×C4 | 1 | 4 | yes | — |
| 137 | #894 | C2×C4 | 1 | 4 | yes | — |
| 138 | #889 | C2×C4 | 1 | 4 | yes | — |
| 139 | #889 | C2×C4 | 1 | 4 | yes | — |
| 140 | #885 | C2×C4 | 1 | 4 | yes | — |
| 141 | #885 | C2×C4 | 1 | 4 | yes | — |
| 142 | #884 | C2×C4 | 1 | 4 | yes | — |
| 143 | #884 | C2×C4 | 1 | 4 | yes | — |
| 144 | #883 | C2×C4 | 1 | 4 | yes | — |
| 145 | #883 | C2×C4 | 1 | 4 | yes | — |
| 146 | #879 | C2×C4 | 1 | 4 | yes | — |
| 147 | #879 | C2×C4 | 1 | 4 | yes | — |
| 148 | #875 | C2×C4 | 1 | 2 | yes | — |
| 149 | #874 | C2×C4 | 1 | 1 | yes | characteristic |
| 150 | C4×D12 | C2×C4 | 1 | 2 | yes | — |
| 151 | C4×D12 | C2×C4 | 1 | 2 | yes | — |
| 152 | C4×D12 | C23 | 1 | 4 | yes | — |
| 153 | #872 | C23 | 1 | 4 | yes | — |
| 154 | C42×D3 | C23 | 1 | 4 | yes | — |
| 155 | #870 | C2×C4 | 1 | 1 | yes | characteristic |
| 156 | #870 | C2×C4 | 1 | 1 | yes | characteristic |
| 157 | #869 | C2×C4 | 1 | 2 | yes | — |
| 158 | #869 | C2×C4 | 1 | 1 | yes | characteristic |
| 159 | C4×Dic6 | C2×C4 | 1 | 2 | yes | — |
| 160 | C4×Dic6 | C2×C4 | 1 | 2 | yes | — |
| 161 | C4×Dic6 | C23 | 1 | 4 | yes | — |
| 162 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 163 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 164 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 165 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 166 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 167 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 168 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 169 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 170 | #830 | C23 | 1 | 4 | yes | — |
| 171 | #830 | C23 | 1 | 4 | yes | — |
| 172 | (C2×D3)⋊C8 | C23 | 1 | 4 | yes | — |
| 173 | (C2×D3)⋊C8 | C23 | 1 | 4 | yes | — |
| 174 | (C2×D3)⋊C8 | C23 | 1 | 4 | yes | — |
| 175 | (C2×D3)⋊C8 | C23 | 1 | 4 | yes | — |
| 176 | #815 | C23 | 1 | 4 | yes | — |
| 177 | #815 | C23 | 1 | 4 | yes | — |
| 178 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 179 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 180 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 181 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 182 | C8×Dic3 | C23 | 1 | 4 | yes | — |
| 183 | C8×Dic3 | C23 | 1 | 4 | yes | — |
| 184 | C4⋊(C3⋊C8) | C23 | 1 | 4 | yes | — |
| 185 | C4⋊(C3⋊C8) | C23 | 1 | 4 | yes | — |
| 186 | #803 | C23 | 1 | 4 | yes | — |
| 187 | C4×C3⋊C8 | C23 | 1 | 4 | yes | — |
| 188 | C2×#131 | — | 3 | 2 | no | — |
| 189 | C2×#131 | — | 3 | 2 | no | — |
| 190 | C22×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 191 | C23×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 192 | #542 | — | 3 | 2 | no | — |
| 193 | #542 | — | 3 | 2 | no | — |
| 194 | #541 | — | 3 | 1 | no | — |
| 195 | #541 | — | 3 | 1 | no | — |
| 196 | #540 | — | 3 | 1 | no | — |
| 197 | #540 | — | 3 | 1 | no | — |
| 198 | #539 | — | 3 | 4 | no | — |
| 199 | #538 | — | 3 | 4 | no | — |
| 200 | #533 | — | 3 | 1 | no | — |
| 201 | #532 | — | 3 | 1 | no | — |
| 202 | #529 | — | 3 | 4 | no | — |
| 203 | #529 | — | 3 | 4 | no | — |
| 204 | #525 | — | 3 | 2 | no | — |
| 205 | C4×#41 | — | 3 | 2 | no | — |
| 206 | C2×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 207 | #446 | — | 3 | 4 | no | — |
| 208 | #446 | — | 3 | 4 | no | — |
| 209 | #446 | — | 3 | 4 | no | — |
| 210 | C8×Q8 | — | 3 | 4 | no | — |
| 211 | #436 | — | 3 | 4 | no | — |
| 212 | #436 | — | 3 | 4 | no | — |
| 213 | #436 | — | 3 | 4 | no | — |
| 214 | #435 | — | 3 | 4 | no | — |
| 215 | #435 | — | 3 | 4 | no | — |
| 216 | #435 | — | 3 | 4 | no | — |
| 217 | #435 | — | 3 | 4 | no | — |
| 218 | #435 | — | 3 | 4 | no | — |
| 219 | #435 | — | 3 | 4 | no | — |
| 220 | C8×D4 | — | 3 | 4 | no | — |
| 221 | C8×D4 | — | 3 | 4 | no | — |
| 222 | C8×D4 | — | 3 | 4 | no | — |
| 223 | #433 | — | 3 | 4 | no | — |
| 224 | #433 | — | 3 | 4 | no | — |
| 225 | #433 | — | 3 | 4 | no | — |
| 226 | #433 | — | 3 | 4 | no | — |
| 227 | #432 | — | 3 | 4 | no | — |
| 228 | #431 | — | 3 | 4 | no | — |
| 229 | #424 | — | 3 | 2 | no | — |
| 230 | #424 | — | 3 | 2 | no | — |
| 231 | #424 | — | 3 | 4 | no | — |
| 232 | #424 | — | 3 | 4 | no | — |
| 233 | #424 | C2×D3 | 1 | 2 | yes | — |
| 234 | #424 | C2×D3 | 1 | 2 | yes | — |
| 235 | #424 | C2×D3 | 1 | 2 | yes | — |
| 236 | #424 | C2×D3 | 1 | 2 | yes | — |
| 237 | #423 | — | 3 | 1 | no | — |
| 238 | #423 | — | 3 | 1 | no | — |
| 239 | #423 | — | 3 | 4 | no | — |
| 240 | C2×C4⋊C8 | — | 3 | 4 | no | — |
| 241 | C2×C4⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 242 | C2×C4⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 243 | #408 | — | 3 | 2 | no | — |
| 244 | #408 | — | 3 | 2 | no | — |
| 245 | #407 | — | 3 | 2 | no | — |
| 246 | #405 | — | 3 | 2 | no | — |
| 247 | #405 | — | 3 | 2 | no | — |
| 248 | C4×M16 | — | 3 | 2 | no | — |
| 249 | C24×C3 | C22×C4 | 1 | 1 | yes | characteristic |
| 250 | C22×C3×C4 | — | 2 | 2 | no | — |
| 251 | C22×C3×C4 | — | 2 | 2 | no | — |
| 252 | C22×C3×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 253 | C22×C3×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 254 | C22×C3×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 255 | C22×C3×C4 | C22×C4 | 1 | 2 | yes | — |
| 256 | C22×C3×C4 | C22×C4 | 1 | 2 | yes | — |
| 257 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 258 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 259 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 260 | C2×#67 | C22×C4 | 1 | 4 | yes | — |
| 261 | C2×#67 | C22×C4 | 1 | 4 | yes | — |
| 262 | C2×#67 | C22×C4 | 1 | 4 | yes | — |
| 263 | #235 | — | 2 | 4 | no | — |
| 264 | #235 | — | 2 | 4 | no | — |
| 265 | C2×D12 | C22×C4 | 1 | 2 | yes | — |
| 266 | C2×D12 | C22×C4 | 1 | 4 | yes | — |
| 267 | C2×C4×D3 | C22×C4 | 1 | 4 | yes | — |
| 268 | C2×C4×D3 | C22×C4 | 1 | 4 | yes | — |
| 269 | C2×C4×D3 | C24 | 1 | 4 | yes | — |
| 270 | C2×Dic6 | C22×C4 | 1 | 2 | yes | — |
| 271 | C2×Dic6 | C22×C4 | 1 | 4 | yes | — |
| 272 | C3×M16 | — | 4 | 1 | no | — |
| 273 | C3×M16 | — | 4 | 2 | no | — |
| 274 | C3×M16 | — | 4 | 1 | no | — |
| 275 | C2×C3×C8 | — | 2 | 4 | no | — |
| 276 | C2×C3×C8 | — | 2 | 4 | no | — |
| 277 | C2×C3×C8 | — | 4 | 1 | no | — |
| 278 | C2×C3×C8 | — | 4 | 2 | no | — |
| 279 | C2×C3×C8 | — | 4 | 1 | no | — |
| 280 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 281 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 282 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 283 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 284 | C3×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 285 | C3×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 286 | C3×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 287 | C3×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 288 | C3×C22⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 289 | C3×C22⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 290 | C3×C22⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 291 | C3×C22⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 292 | C3×C42 | C22×C4 | 1 | 1 | yes | characteristic |
| 293 | C3×C42 | C22×C4 | 1 | 1 | yes | characteristic |
| 294 | C3×C42 | C22×C4 | 1 | 1 | yes | characteristic |
| 295 | C3×C42 | C22×C4 | 1 | 1 | yes | characteristic |
| 296 | C3×C42 | C24 | 1 | 2 | yes | — |
| 297 | C3×C42 | C24 | 1 | 2 | yes | — |
| 298 | #217 | C22×C4 | 1 | 4 | yes | — |
| 299 | #217 | C22×C4 | 1 | 4 | yes | — |
| 300 | #217 | C22×C4 | 1 | 4 | yes | — |
| 301 | (C2×D3)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 302 | (C2×D3)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 303 | (C2×D3)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 304 | (C2×D3)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 305 | (C2×D3)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 306 | (C2×D3)⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 307 | C4⋊Dic3 | C22×C4 | 1 | 2 | yes | — |
| 308 | C4⋊Dic3 | C22×C4 | 1 | 2 | yes | — |
| 309 | C4⋊Dic3 | C22×C4 | 1 | 4 | yes | — |
| 310 | C4⋊Dic3 | C22×C4 | 1 | 4 | yes | — |
| 311 | Dic3⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 312 | Dic3⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 313 | Dic3⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 314 | Dic3⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 315 | Dic3⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 316 | Dic3⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 317 | C4×Dic3 | C22×C4 | 1 | 4 | yes | — |
| 318 | C4×Dic3 | C22×C4 | 1 | 4 | yes | — |
| 319 | C4×Dic3 | C24 | 1 | 4 | yes | — |
| 320 | #208 | — | 2 | 4 | no | — |
| 321 | #208 | — | 2 | 4 | no | — |
| 322 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 323 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 324 | ΓL(1,𝔽25) | — | 4 | 4 | no | — |
| 325 | ΓL(1,𝔽25) | — | 4 | 4 | no | — |
| 326 | D3×C8 | — | 4 | 4 | no | — |
| 327 | D3×C8 | — | 4 | 4 | no | — |
| 328 | C2×#41 | — | 3 | 2 | no | — |
| 329 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 330 | #131 | — | 12 | 4 | no | — |
| 331 | #131 | — | 12 | 4 | no | — |
| 332 | C2×M16 | — | 3 | 2 | no | — |
| 333 | C2×M16 | — | 3 | 2 | no | — |
| 334 | C2×M16 | — | 3 | 4 | no | — |
| 335 | C2×M16 | — | 3 | 4 | no | — |
| 336 | C2×M16 | — | 4 | 2 | no | — |
| 337 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 338 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 339 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 340 | C22×C8 | — | 3 | 4 | no | — |
| 341 | C22×C8 | — | 3 | 4 | no | — |
| 342 | C22×C8 | — | 4 | 2 | no | — |
| 343 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 344 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 345 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 346 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 347 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 348 | C4⋊Q8 | — | 3 | 1 | no | — |
| 349 | C4⋊Q8 | — | 3 | 2 | no | — |
| 350 | #127 | — | 3 | 1 | no | — |
| 351 | #126 | — | 3 | 4 | no | — |
| 352 | #126 | — | 3 | 4 | no | — |
| 353 | #126 | — | 3 | 4 | no | — |
| 354 | #126 | — | 3 | 4 | no | — |
| 355 | #125 | — | 3 | 4 | no | — |
| 356 | #125 | — | 3 | 4 | no | — |
| 357 | #125 | — | 3 | 1 | no | — |
| 358 | #125 | — | 3 | 1 | no | — |
| 359 | #124 | — | 3 | 4 | no | — |
| 360 | #124 | — | 3 | 4 | no | — |
| 361 | #124 | — | 3 | 2 | no | — |
| 362 | #123 | — | 3 | 4 | no | — |
| 363 | #123 | — | 3 | 4 | no | — |
| 364 | #123 | — | 3 | 4 | no | — |
| 365 | #123 | — | 3 | 4 | no | — |
| 366 | #123 | — | 3 | 4 | no | — |
| 367 | C22⋊Q8 | — | 3 | 2 | no | — |
| 368 | C22⋊Q8 | — | 3 | 2 | no | — |
| 369 | C22⋊Q8 | — | 3 | 4 | no | — |
| 370 | C22⋊Q8 | — | 3 | 4 | no | — |
| 371 | C22⋊Q8 | — | 3 | 4 | no | — |
| 372 | #121 | — | 3 | 2 | no | — |
| 373 | #121 | — | 3 | 2 | no | — |
| 374 | #121 | — | 3 | 4 | no | — |
| 375 | #121 | — | 3 | 4 | no | — |
| 376 | #121 | — | 3 | 4 | no | — |
| 377 | #120 | — | 3 | 4 | no | — |
| 378 | C4×Q8 | — | 3 | 2 | no | — |
| 379 | C4×Q8 | — | 3 | 2 | no | — |
| 380 | C4×Q8 | — | 3 | 4 | no | — |
| 381 | C4×D4 | — | 3 | 4 | no | — |
| 382 | C4×D4 | — | 3 | 4 | no | — |
| 383 | C4×D4 | — | 3 | 4 | no | — |
| 384 | C4×D4 | — | 3 | 4 | no | — |
| 385 | C4×D4 | — | 3 | 2 | no | — |
| 386 | C4×D4 | — | 3 | 2 | no | — |
| 387 | C4×D4 | — | 3 | 4 | no | — |
| 388 | #117 | — | 3 | 2 | no | — |
| 389 | #117 | — | 3 | 4 | no | — |
| 390 | #117 | C4×D3 | 1 | 1 | yes | characteristic |
| 391 | #117 | C4×D3 | 1 | 1 | yes | characteristic |
| 392 | #117 | C4×D3 | 1 | 1 | yes | characteristic |
| 393 | #117 | C4×D3 | 1 | 1 | yes | characteristic |
| 394 | #117 | C22×D3 | 1 | 2 | yes | — |
| 395 | #117 | C22×D3 | 1 | 2 | yes | — |
| 396 | C2×C4⋊C4 | C4×D3 | 1 | 2 | yes | — |
| 397 | C2×C22⋊C4 | C4×D3 | 1 | 2 | yes | — |
| 398 | C2×C42 | — | 3 | 4 | no | — |
| 399 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 400 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 401 | C4⋊C8 | — | 3 | 4 | no | — |
| 402 | C4⋊C8 | — | 3 | 4 | no | — |
| 403 | C4⋊C8 | — | 3 | 4 | no | — |
| 404 | C4⋊C8 | — | 3 | 4 | no | — |
| 405 | C4⋊C8 | — | 3 | 4 | no | — |
| 406 | C4⋊C8 | — | 3 | 4 | no | — |
| 407 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 408 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 409 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 410 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 411 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 412 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 413 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 414 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 415 | C22⋊C8 | — | 3 | 4 | no | — |
| 416 | C22⋊C8 | — | 3 | 4 | no | — |
| 417 | C22⋊C8 | — | 3 | 4 | no | — |
| 418 | C22⋊C8 | — | 3 | 4 | no | — |
| 419 | C22⋊C8 | — | 3 | 4 | no | — |
| 420 | C22⋊C8 | — | 3 | 4 | no | — |
| 421 | #97 | — | 3 | 4 | no | — |
| 422 | #97 | — | 3 | 4 | no | — |
| 423 | #97 | — | 3 | 4 | no | — |
| 424 | C4×C8 | — | 3 | 4 | no | — |
| 425 | C4×C8 | — | 3 | 4 | no | — |
| 426 | C4×C8 | — | 3 | 4 | no | — |
| 427 | C23×C3 | — | 2 | 2 | no | — |
| 428 | C23×C3 | — | 4 | 2 | no | — |
| 429 | C23×C3 | C23×C4 | 1 | 1 | yes | characteristic |
| 430 | C23×C3 | C23×C4 | 1 | 1 | yes | characteristic |
| 431 | C23×C3 | C23×C4 | 1 | 1 | yes | characteristic |
| 432 | C22×D3 | C23×C4 | 1 | 4 | yes | — |
| 433 | C2×C3×C4 | — | 2 | 2 | no | — |
| 434 | C2×C3×C4 | — | 2 | 2 | no | — |
| 435 | C2×C3×C4 | — | 2 | 2 | no | — |
| 436 | C2×C3×C4 | — | 2 | 1 | no | — |
| 437 | C2×C3×C4 | — | 2 | 1 | no | — |
| 438 | C2×C3×C4 | — | 2 | 1 | no | — |
| 439 | C2×C3×C4 | — | 2 | 1 | no | — |
| 440 | C2×C3×C4 | — | 4 | 2 | no | — |
| 441 | C2×C3×C4 | — | 4 | 2 | no | — |
| 442 | C2×C3×C4 | C23×C4 | 1 | 2 | yes | — |
| 443 | C2×C3×C4 | C23×C4 | 1 | 2 | yes | — |
| 444 | C2×C3×C4 | C23×C4 | 1 | 2 | yes | — |
| 445 | C2×C3×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 446 | C2×C3×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 447 | C2×C3×C4 | C23×C4 | 1 | 2 | yes | — |
| 448 | C2×C3×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 449 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 450 | C2×C3×C4 | 2−1+4 | 1 | 2 | yes | — |
| 451 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 452 | #67 | — | 2 | 8 | no | — |
| 453 | #67 | — | 4 | 4 | no | — |
| 454 | #67 | — | 4 | 4 | no | — |
| 455 | C2×Dic3 | C23×C4 | 1 | 4 | yes | — |
| 456 | C2×Dic3 | C23×C4 | 1 | 4 | yes | — |
| 457 | C2×Dic3 | C23×C4 | 1 | 4 | yes | — |
| 458 | D12 | — | 2 | 4 | no | — |
| 459 | D12 | — | 4 | 4 | no | — |
| 460 | C4×D3 | — | 2 | 4 | no | — |
| 461 | C4×D3 | — | 2 | 4 | no | — |
| 462 | C4×D3 | — | 4 | 4 | no | — |
| 463 | C4×D3 | — | 4 | 4 | no | — |
| 464 | Dic6 | — | 2 | 4 | no | — |
| 465 | Dic6 | — | 4 | 4 | no | — |
| 466 | C3×C8 | — | 2 | 2 | no | — |
| 467 | C3×C8 | — | 2 | 2 | no | — |
| 468 | C3×C8 | — | 2 | 2 | no | — |
| 469 | C3×C8 | — | 2 | 2 | no | — |
| 470 | C3⋊C8 | — | 2 | 4 | no | — |
| 471 | C3⋊C8 | — | 2 | 4 | no | — |
| 472 | C24 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 473 | #41 | — | 6 | 4 | no | — |
| 474 | #41 | — | 6 | 4 | no | — |
| 475 | C2×Q8 | — | 3 | 2 | no | — |
| 476 | C2×Q8 | — | 3 | 4 | no | — |
| 477 | C2×D4 | — | 3 | 4 | no | — |
| 478 | C2×D4 | — | 3 | 4 | no | — |
| 479 | C2×D4 | — | 3 | 4 | no | — |
| 480 | C2×D4 | — | 3 | 2 | no | — |
| 481 | C2×D4 | — | 3 | 4 | no | — |
| 482 | C22×C4 | — | 2 | 2 | no | — |
| 483 | C22×C4 | — | 2 | 2 | no | — |
| 484 | C22×C4 | — | 3 | 4 | no | — |
| 485 | C22×C4 | — | 3 | 4 | no | — |
| 486 | C22×C4 | — | 3 | 4 | no | — |
| 487 | C22×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 488 | C22×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 489 | C22×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 490 | C22×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 491 | C22×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 492 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 493 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 494 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 495 | M16 | — | 4 | 1 | no | — |
| 496 | M16 | — | 4 | 2 | no | — |
| 497 | M16 | — | 4 | 1 | no | — |
| 498 | M16 | — | 6 | 4 | no | — |
| 499 | M16 | — | 6 | 4 | no | — |
| 500 | M16 | — | 12 | 4 | no | — |
| 501 | M16 | — | 12 | 4 | no | — |
| 502 | C2×C8 | — | 2 | 4 | no | — |
| 503 | C2×C8 | — | 2 | 4 | no | — |
| 504 | C2×C8 | — | 3 | 4 | no | — |
| 505 | C2×C8 | — | 3 | 4 | no | — |
| 506 | C2×C8 | — | 4 | 1 | no | — |
| 507 | C2×C8 | — | 4 | 2 | no | — |
| 508 | C2×C8 | — | 4 | 1 | no | — |
| 509 | C2×C8 | — | 12 | 4 | no | — |
| 510 | C2×C8 | — | 12 | 4 | no | — |
| 511 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 512 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 513 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 514 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 515 | C4⋊C4 | — | 3 | 2 | no | — |
| 516 | C4⋊C4 | — | 3 | 2 | no | — |
| 517 | C4⋊C4 | — | 3 | 4 | no | — |
| 518 | C4⋊C4 | — | 3 | 4 | no | — |
| 519 | C4⋊C4 | — | 3 | 4 | no | — |
| 520 | C4⋊C4 | — | 3 | 4 | no | — |
| 521 | C4⋊C4 | — | 3 | 4 | no | — |
| 522 | C4⋊C4 | — | 3 | 4 | no | — |
| 523 | C4⋊C4 | — | 3 | 4 | no | — |
| 524 | C4⋊C4 | — | 3 | 4 | no | — |
| 525 | C4⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 526 | C4⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 527 | C4⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 528 | C4⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 529 | C22⋊C4 | — | 3 | 4 | no | — |
| 530 | C22⋊C4 | — | 3 | 4 | no | — |
| 531 | C22⋊C4 | — | 3 | 4 | no | — |
| 532 | C22⋊C4 | — | 3 | 4 | no | — |
| 533 | C22⋊C4 | — | 3 | 4 | no | — |
| 534 | C22⋊C4 | — | 3 | 4 | no | — |
| 535 | C22⋊C4 | — | 3 | 4 | no | — |
| 536 | C22⋊C4 | — | 3 | 4 | no | — |
| 537 | C22⋊C4 | — | 3 | 4 | no | — |
| 538 | C22⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 539 | C22⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 540 | C22⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 541 | C22⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 542 | C42 | — | 3 | 4 | no | — |
| 543 | C42 | — | 3 | 4 | no | — |
| 544 | C42 | — | 3 | 4 | no | — |
| 545 | C42 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 546 | C42 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 547 | C42 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 548 | C42 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 549 | C42 | C23×D3 | 1 | 2 | yes | — |
| 550 | C42 | C23×D3 | 1 | 2 | yes | — |
| 551 | C22×C3 | — | 2 | 2 | no | — |
| 552 | C22×C3 | — | 2 | 1 | no | — |
| 553 | C22×C3 | — | 2 | 1 | no | — |
| 554 | C22×C3 | — | 2 | 2 | no | — |
| 555 | C22×C3 | — | 2 | 2 | no | — |
| 556 | C22×C3 | — | 4 | 4 | no | — |
| 557 | C22×C3 | #520 | 1 | 2 | yes | — |
| 558 | C22×C3 | C24×C4 | 1 | 1 | yes | characteristic |
| 559 | C2×D3 | — | 2 | 4 | no | — |
| 560 | C2×D3 | — | 2 | 4 | no | — |
| 561 | C2×D3 | — | 2 | 4 | no | — |
| 562 | C3×C4 | — | 2 | 1 | no | — |
| 563 | C3×C4 | — | 2 | 1 | no | — |
| 564 | C3×C4 | — | 2 | 2 | no | — |
| 565 | C3×C4 | — | 2 | 2 | no | — |
| 566 | C3×C4 | — | 2 | 2 | no | — |
| 567 | C3×C4 | — | 2 | 2 | no | — |
| 568 | C3×C4 | #520 | 1 | 2 | yes | — |
| 569 | C3×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 570 | C3×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 571 | Dic3 | — | 2 | 4 | no | — |
| 572 | Dic3 | — | 2 | 4 | no | — |
| 573 | Dic3 | — | 2 | 4 | no | — |
| 574 | C23 | — | 2 | 2 | no | — |
| 575 | C23 | — | 3 | 4 | no | — |
| 576 | C23 | — | 4 | 2 | no | — |
| 577 | C23 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 578 | C23 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 579 | C23 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 580 | Q8 | — | 6 | 4 | no | — |
| 581 | Q8 | — | 12 | 4 | no | — |
| 582 | D4 | — | 6 | 8 | no | — |
| 583 | D4 | — | 6 | 4 | no | — |
| 584 | D4 | — | 12 | 4 | no | — |
| 585 | D4 | — | 12 | 4 | no | — |
| 586 | D4 | — | 12 | 4 | no | — |
| 587 | C2×C4 | — | 2 | 2 | no | — |
| 588 | C2×C4 | — | 2 | 1 | no | — |
| 589 | C2×C4 | — | 2 | 1 | no | — |
| 590 | C2×C4 | — | 2 | 1 | no | — |
| 591 | C2×C4 | — | 2 | 1 | no | — |
| 592 | C2×C4 | — | 2 | 2 | no | — |
| 593 | C2×C4 | — | 2 | 2 | no | — |
| 594 | C2×C4 | — | 3 | 4 | no | — |
| 595 | C2×C4 | — | 3 | 4 | no | — |
| 596 | C2×C4 | — | 3 | 4 | no | — |
| 597 | C2×C4 | — | 4 | 2 | no | — |
| 598 | C2×C4 | — | 4 | 2 | no | — |
| 599 | C2×C4 | — | 6 | 4 | no | — |
| 600 | C2×C4 | — | 6 | 4 | no | — |
| 601 | C2×C4 | — | 12 | 4 | no | — |
| 602 | C2×C4 | — | 12 | 4 | no | — |
| 603 | C2×C4 | C22×C4×D3 | 1 | 2 | yes | — |
| 604 | C2×C4 | C22×C4×D3 | 1 | 2 | yes | — |
| 605 | C2×C4 | C22×C4×D3 | 1 | 2 | yes | — |
| 606 | C2×C4 | C22×C4×D3 | 1 | 2 | yes | — |
| 607 | C2×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 608 | C2×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 609 | C2×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 610 | C2×C4 | #1004 | 1 | 2 | yes | — |
| 611 | C2×C4 | #1007 | 1 | 2 | yes | — |
| 612 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 613 | C8 | — | 2 | 2 | no | — |
| 614 | C8 | — | 2 | 2 | no | — |
| 615 | C8 | — | 2 | 2 | no | — |
| 616 | C8 | — | 2 | 2 | no | — |
| 617 | C8 | — | 6 | 4 | no | — |
| 618 | C8 | — | 6 | 4 | no | — |
| 619 | C2×C3 | — | 2 | 2 | no | — |
| 620 | C2×C3 | — | 4 | 1 | no | — |
| 621 | C2×C3 | — | 4 | 1 | no | — |
| 622 | C2×C3 | C2×#520 | 1 | 1 | yes | characteristic |
| 623 | C2×C3 | #3573 | 1 | 2 | yes | — |
| 624 | D3 | — | 4 | 4 | no | — |
| 625 | C22 | — | 2 | 2 | no | — |
| 626 | C22 | — | 2 | 2 | no | — |
| 627 | C22 | — | 2 | 2 | no | — |
| 628 | C22 | — | 2 | 1 | no | — |
| 629 | C22 | — | 2 | 1 | no | — |
| 630 | C22 | — | 4 | 4 | no | — |
| 631 | C22 | — | 6 | 4 | no | — |
| 632 | C22 | — | 6 | 4 | no | — |
| 633 | C22 | — | 6 | 4 | no | — |
| 634 | C22 | #5504 | 1 | 2 | yes | — |
| 635 | C22 | C23×C4×D3 | 1 | 1 | yes | characteristic |
| 636 | C4 | — | 2 | 2 | no | — |
| 637 | C4 | — | 2 | 2 | no | — |
| 638 | C4 | — | 2 | 2 | no | — |
| 639 | C4 | — | 2 | 2 | no | — |
| 640 | C4 | — | 2 | 1 | no | — |
| 641 | C4 | — | 2 | 1 | no | — |
| 642 | C4 | — | 6 | 4 | no | — |
| 643 | C4 | — | 6 | 4 | no | — |
| 644 | C4 | — | 6 | 4 | no | — |
| 645 | C4 | #5504 | 1 | 2 | yes | — |
| 646 | C4 | C2×#1004 | 1 | 1 | yes | characteristic |
| 647 | C4 | C2×#1007 | 1 | 1 | yes | characteristic |
| 648 | C3 | #60267 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 649 | C2 | — | 2 | 2 | no | — |
| 650 | C2 | — | 4 | 1 | no | — |
| 651 | C2 | — | 4 | 1 | no | — |
| 652 | C2 | — | 12 | 4 | no | — |
| 653 | C2 | C2×#5504 | 1 | 1 | yes | characteristic |
| 654 | C2 | #87160 | 1 | 2 | yes | — |
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