Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
1894 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 1894 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×#63703 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3⋊#10593110 | C2 | 1 | 2 | yes | maximal, direct product factor |
| 3 | C2×#10593110 | — | 3 | 3 | no | maximal |
| 4 | C2×#10592940 | — | 3 | 1 | no | maximal |
| 5 | C22×C3⋊((C22⋊C9)⋊C2) | — | 4 | 1 | no | maximal |
| 6 | C3×#63703 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×C3⋊#3689 | — | 4 | 2 | no | maximal |
| 8 | C2×C32×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 9 | C2×#64158 | — | 3 | 2 | no | — |
| 10 | C2×#64149 | — | 3 | 1 | no | — |
| 11 | C2×#63703 | D3 | 1 | 3 | yes | complemented |
| 12 | #10593110 | — | 3 | 6 | no | — |
| 13 | #10592940 | — | 3 | 2 | no | — |
| 14 | #10592940 | — | 3 | 4 | no | — |
| 15 | #10592940 | — | 3 | 2 | no | — |
| 16 | C2×#63664 | — | 3 | 2 | no | — |
| 17 | C2×#63660 | — | 3 | 1 | no | — |
| 18 | C22×C3×C22⋊C9 | — | 4 | 1 | no | — |
| 19 | C22×C3×C22⋊C9 | — | 8 | 1 | no | — |
| 20 | C2×C3⋊((C22⋊C9)⋊C2) | — | 4 | 2 | no | — |
| 21 | C2×C3⋊((C22⋊C9)⋊C2) | — | 4 | 4 | no | — |
| 22 | C2×C3×Q8⋊C9 | — | 4 | 2 | no | — |
| 23 | C3⋊#3689 | — | 4 | 4 | no | — |
| 24 | C2×#5241 | — | 9 | 3 | no | — |
| 25 | C2×#5241 | — | 9 | 1 | no | — |
| 26 | C32×H(5,𝔽2) | — | 3 | 1 | no | — |
| 27 | C32×H(5,𝔽2) | — | 3 | 2 | no | — |
| 28 | C32×H(5,𝔽2) | — | 6 | 1 | no | — |
| 29 | C32×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 30 | C2×C32×#41 | — | 3 | 2 | no | — |
| 31 | C22×C32×D4 | — | 3 | 1 | no | — |
| 32 | C22×C32×D4 | — | 6 | 1 | no | — |
| 33 | C22×#638 | — | 6 | 1 | no | — |
| 34 | C22×#638 | — | 6 | 1 | no | — |
| 35 | C22×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 36 | C22×(C22⋊C9)⋊C2 | — | 12 | 3 | no | — |
| 37 | #64158 | — | 3 | 4 | no | — |
| 38 | #64158 | — | 3 | 4 | no | — |
| 39 | #64158 | — | 6 | 2 | no | — |
| 40 | #64158 | — | 6 | 2 | no | — |
| 41 | C2×#3755 | — | 6 | 2 | no | — |
| 42 | #64149 | — | 3 | 2 | no | — |
| 43 | #64149 | — | 3 | 2 | no | — |
| 44 | #64149 | — | 6 | 1 | no | — |
| 45 | #64149 | — | 6 | 1 | no | — |
| 46 | C2×#3753 | — | 6 | 2 | no | — |
| 47 | C2×C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 48 | C2×#3748 | — | 3 | 2 | no | — |
| 49 | #63703 | C2×D3 | 1 | 3 | yes | complemented |
| 50 | C2×#3689 | — | 12 | 6 | no | — |
| 51 | #63664 | — | 3 | 4 | no | — |
| 52 | #63664 | — | 3 | 4 | no | — |
| 53 | #63660 | — | 3 | 2 | no | — |
| 54 | #63660 | — | 3 | 2 | no | — |
| 55 | C22×C3⋊D9 | — | 16 | 1 | no | — |
| 56 | C2×C3×C22⋊C9 | — | 4 | 2 | no | — |
| 57 | C2×C3×C22⋊C9 | — | 4 | 1 | no | — |
| 58 | C2×C3×C22⋊C9 | — | 8 | 1 | no | — |
| 59 | C2×C3×C22⋊C9 | — | 8 | 2 | no | — |
| 60 | C3⋊((C22⋊C9)⋊C2) | — | 4 | 4 | no | — |
| 61 | C3×Q8⋊C9 | — | 4 | 2 | no | — |
| 62 | C2×C3×H(5,𝔽2) | D9 | 1 | 3 | yes | complemented |
| 63 | C2×C3×H(5,𝔽2) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 64 | C2×#949 | — | 9 | 6 | no | — |
| 65 | C2×#949 | — | 9 | 2 | no | — |
| 66 | C2×#940 | — | 9 | 3 | no | — |
| 67 | C2×#940 | — | 9 | 1 | no | — |
| 68 | #5241 | — | 9 | 6 | no | — |
| 69 | #5241 | — | 9 | 2 | no | — |
| 70 | #5241 | — | 9 | 12 | no | — |
| 71 | #5241 | — | 9 | 4 | no | — |
| 72 | #5241 | — | 9 | 6 | no | — |
| 73 | #5241 | — | 9 | 2 | no | — |
| 74 | C2×#837 | — | 9 | 6 | no | — |
| 75 | C2×#837 | — | 9 | 2 | no | — |
| 76 | C2×#833 | — | 9 | 3 | no | — |
| 77 | C2×#833 | — | 9 | 1 | no | — |
| 78 | C24×C32 | — | 2 | 1 | no | — |
| 79 | C24×C32 | — | 3 | 1 | no | — |
| 80 | C24×C32 | S4 | 1 | 1 | yes | characteristic |
| 81 | C23×C3⋊D3 | — | 6 | 1 | no | — |
| 82 | C32×#41 | — | 3 | 2 | no | — |
| 83 | C32×#41 | — | 3 | 2 | no | — |
| 84 | C32×#41 | — | 3 | 2 | no | — |
| 85 | C32×#41 | — | 3 | 2 | no | — |
| 86 | C32×#41 | — | 6 | 2 | no | — |
| 87 | C32×#41 | — | 6 | 2 | no | — |
| 88 | C2×C32×Q8 | S4 | 1 | 2 | yes | — |
| 89 | C2×C32×D4 | — | 3 | 2 | no | — |
| 90 | C2×C32×D4 | — | 3 | 1 | no | — |
| 91 | C2×C32×D4 | — | 3 | 1 | no | — |
| 92 | C2×C32×D4 | — | 3 | 1 | no | — |
| 93 | C2×C32×D4 | — | 3 | 1 | no | — |
| 94 | C2×C32×D4 | — | 6 | 2 | no | — |
| 95 | C2×C32×D4 | — | 6 | 2 | no | — |
| 96 | C2×C32×D4 | — | 6 | 1 | no | — |
| 97 | C2×C32×D4 | — | 6 | 1 | no | — |
| 98 | C2×C32×D4 | — | 6 | 2 | no | — |
| 99 | C2×C32×D4 | — | 6 | 2 | no | — |
| 100 | C2×C32×D4 | — | 6 | 1 | no | — |
| 101 | C2×C32×D4 | — | 6 | 1 | no | — |
| 102 | C22×C32×C4 | — | 3 | 1 | no | — |
| 103 | C22×C32×C4 | — | 6 | 1 | no | — |
| 104 | C2×#638 | — | 6 | 2 | no | — |
| 105 | C2×#638 | — | 6 | 2 | no | — |
| 106 | C2×#638 | — | 6 | 2 | no | — |
| 107 | C2×#638 | — | 6 | 2 | no | — |
| 108 | C2×#638 | — | 12 | 4 | no | — |
| 109 | C2×#638 | — | 12 | 4 | no | — |
| 110 | C22×C3⋊Dic3 | — | 6 | 1 | no | — |
| 111 | C2×C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 112 | C2×C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 113 | C2×C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 114 | C2×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 115 | C22×C22⋊C9 | — | 4 | 3 | no | — |
| 116 | C22×C22⋊C9 | — | 8 | 3 | no | — |
| 117 | C2×(C22⋊C9)⋊C2 | — | 12 | 6 | no | — |
| 118 | C2×(C22⋊C9)⋊C2 | — | 12 | 12 | no | — |
| 119 | #3755 | — | 6 | 4 | no | — |
| 120 | #3755 | — | 6 | 4 | no | — |
| 121 | #3753 | — | 6 | 4 | no | — |
| 122 | #3753 | — | 6 | 4 | no | — |
| 123 | C4×C3⋊Dic3 | — | 3 | 2 | no | — |
| 124 | C4×C3⋊Dic3 | — | 6 | 1 | no | — |
| 125 | #3748 | — | 3 | 4 | no | — |
| 126 | #3748 | — | 6 | 2 | no | — |
| 127 | C2×C3⋊(C3⋊C8) | — | 6 | 2 | no | — |
| 128 | C2×Q8⋊C9 | — | 4 | 6 | no | — |
| 129 | #3689 | — | 12 | 12 | no | — |
| 130 | C2×#453 | — | 27 | 1 | no | Sylow |
| 131 | C22×C3×C9 | — | 16 | 1 | no | — |
| 132 | C2×C3⋊D9 | — | 16 | 2 | no | — |
| 133 | C2×C3⋊D9 | — | 16 | 4 | no | — |
| 134 | C3×C22⋊C9 | — | 4 | 1 | no | — |
| 135 | C3×C22⋊C9 | — | 8 | 1 | no | — |
| 136 | C3×H(5,𝔽2) | — | 3 | 3 | no | — |
| 137 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 138 | C3×H(5,𝔽2) | — | 3 | 6 | no | — |
| 139 | C3×H(5,𝔽2) | — | 3 | 2 | no | — |
| 140 | C3×H(5,𝔽2) | — | 6 | 3 | no | — |
| 141 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 142 | C3×H(5,𝔽2) | C2×D9 | 1 | 3 | yes | complemented |
| 143 | C3×H(5,𝔽2) | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 144 | C2×C3×#41 | — | 3 | 6 | no | — |
| 145 | C2×C3×#41 | — | 3 | 2 | no | — |
| 146 | C22×C3×D4 | — | 3 | 3 | no | — |
| 147 | C22×C3×D4 | — | 3 | 1 | no | — |
| 148 | C22×C3×D4 | — | 6 | 3 | no | — |
| 149 | C22×C3×D4 | — | 6 | 1 | no | — |
| 150 | C22×#67 | — | 18 | 1 | no | — |
| 151 | C22×#67 | — | 18 | 3 | no | — |
| 152 | C22×#67 | — | 18 | 3 | no | — |
| 153 | C22×#67 | — | 18 | 1 | no | — |
| 154 | C22×D12 | — | 9 | 1 | no | — |
| 155 | C22×D12 | — | 9 | 3 | no | — |
| 156 | #949 | — | 9 | 12 | no | — |
| 157 | #949 | — | 9 | 4 | no | — |
| 158 | #949 | — | 9 | 4 | no | — |
| 159 | #949 | — | 9 | 12 | no | — |
| 160 | #949 | — | 18 | 6 | no | — |
| 161 | #949 | — | 18 | 2 | no | — |
| 162 | #949 | — | 18 | 2 | no | — |
| 163 | #949 | — | 18 | 6 | no | — |
| 164 | C2×#215 | — | 18 | 6 | no | — |
| 165 | C2×#215 | — | 18 | 2 | no | — |
| 166 | #940 | — | 9 | 6 | no | — |
| 167 | #940 | — | 9 | 2 | no | — |
| 168 | #940 | — | 9 | 2 | no | — |
| 169 | #940 | — | 9 | 6 | no | — |
| 170 | #940 | — | 18 | 3 | no | — |
| 171 | #940 | — | 18 | 1 | no | — |
| 172 | #940 | — | 18 | 1 | no | — |
| 173 | #940 | — | 18 | 3 | no | — |
| 174 | C2×#213 | — | 18 | 2 | no | — |
| 175 | C2×#213 | — | 18 | 6 | no | — |
| 176 | C2×C4×Dic3 | — | 9 | 1 | no | — |
| 177 | C2×C4×Dic3 | — | 9 | 3 | no | — |
| 178 | C2×#208 | — | 9 | 2 | no | — |
| 179 | C2×#208 | — | 9 | 6 | no | — |
| 180 | #837 | — | 9 | 12 | no | — |
| 181 | #837 | — | 9 | 4 | no | — |
| 182 | #837 | — | 9 | 4 | no | — |
| 183 | #837 | — | 9 | 12 | no | — |
| 184 | #833 | — | 9 | 6 | no | — |
| 185 | #833 | — | 9 | 2 | no | — |
| 186 | #833 | — | 9 | 2 | no | — |
| 187 | #833 | — | 9 | 6 | no | — |
| 188 | C23×C32 | — | 2 | 1 | no | — |
| 189 | C23×C32 | — | 3 | 1 | no | — |
| 190 | C23×C32 | — | 3 | 1 | no | — |
| 191 | C23×C32 | — | 3 | 1 | no | — |
| 192 | C23×C32 | — | 3 | 1 | no | — |
| 193 | C23×C32 | — | 4 | 2 | no | — |
| 194 | C23×C32 | — | 6 | 1 | no | — |
| 195 | C23×C32 | — | 6 | 1 | no | — |
| 196 | C23×C32 | — | 6 | 1 | no | — |
| 197 | C23×C32 | — | 8 | 2 | no | — |
| 198 | C23×C32 | — | 12 | 2 | no | — |
| 199 | C23×C32 | C2×S4 | 1 | 1 | yes | characteristic |
| 200 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 201 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 202 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 203 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 204 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 205 | C32×Q8 | — | 3 | 2 | no | — |
| 206 | C32×Q8 | C2×S4 | 1 | 2 | yes | — |
| 207 | C32×D4 | — | 3 | 2 | no | — |
| 208 | C32×D4 | — | 3 | 2 | no | — |
| 209 | C32×D4 | — | 6 | 2 | no | — |
| 210 | C32×D4 | — | 6 | 2 | no | — |
| 211 | C32×D4 | — | 6 | 2 | no | — |
| 212 | C32×D4 | — | 6 | 2 | no | — |
| 213 | C32×D4 | — | 6 | 2 | no | — |
| 214 | C2×C32×C4 | — | 3 | 1 | no | — |
| 215 | C2×C32×C4 | — | 3 | 2 | no | — |
| 216 | C2×C32×C4 | — | 3 | 1 | no | — |
| 217 | C2×C32×C4 | — | 3 | 2 | no | — |
| 218 | C2×C32×C4 | — | 6 | 1 | no | — |
| 219 | C2×C32×C4 | — | 6 | 2 | no | — |
| 220 | C2×C32×C4 | — | 6 | 1 | no | — |
| 221 | #638 | — | 12 | 4 | no | — |
| 222 | #638 | — | 12 | 4 | no | — |
| 223 | #638 | — | 12 | 4 | no | — |
| 224 | #638 | — | 12 | 4 | no | — |
| 225 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 226 | C2×C3⋊Dic3 | — | 6 | 4 | no | — |
| 227 | C4⋊(C3⋊D3) | — | 6 | 4 | no | — |
| 228 | C4⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 229 | C22×D9 | — | 48 | 3 | no | — |
| 230 | C2×C22⋊C9 | — | 4 | 6 | no | — |
| 231 | C2×C22⋊C9 | — | 4 | 3 | no | — |
| 232 | C2×C22⋊C9 | — | 8 | 3 | no | — |
| 233 | C2×C22⋊C9 | — | 8 | 6 | no | — |
| 234 | (C22⋊C9)⋊C2 | — | 12 | 12 | no | — |
| 235 | C3⋊(C3⋊C8) | — | 6 | 4 | no | — |
| 236 | Q8⋊C9 | — | 4 | 6 | no | — |
| 237 | C2×H(5,𝔽2) | C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 238 | C2×AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 239 | C2×#127 | — | 27 | 1 | no | — |
| 240 | #453 | — | 27 | 2 | no | — |
| 241 | #453 | — | 27 | 4 | no | — |
| 242 | #453 | — | 27 | 2 | no | — |
| 243 | C2×#104 | — | 27 | 2 | no | — |
| 244 | C2×#100 | — | 27 | 1 | no | — |
| 245 | C2×C3×C9 | — | 16 | 2 | no | — |
| 246 | C2×C3×C9 | — | 16 | 1 | no | — |
| 247 | C3⋊D9 | — | 16 | 4 | no | — |
| 248 | C24×C3 | — | 2 | 1 | no | — |
| 249 | C24×C3 | — | 2 | 3 | no | — |
| 250 | C24×C3 | — | 3 | 1 | no | — |
| 251 | C24×C3 | — | 3 | 3 | no | — |
| 252 | C24×C3 | (C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 253 | C24×C3 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 254 | C23×D3 | — | 18 | 1 | no | — |
| 255 | C23×D3 | — | 18 | 3 | no | — |
| 256 | C3×#41 | — | 3 | 6 | no | — |
| 257 | C3×#41 | — | 3 | 2 | no | — |
| 258 | C3×#41 | — | 3 | 6 | no | — |
| 259 | C3×#41 | — | 3 | 2 | no | — |
| 260 | C3×#41 | — | 3 | 2 | no | — |
| 261 | C3×#41 | — | 3 | 2 | no | — |
| 262 | C3×#41 | — | 3 | 6 | no | — |
| 263 | C3×#41 | — | 3 | 6 | no | — |
| 264 | C3×#41 | — | 6 | 6 | no | — |
| 265 | C3×#41 | — | 6 | 2 | no | — |
| 266 | C3×#41 | — | 6 | 6 | no | — |
| 267 | C3×#41 | — | 6 | 2 | no | — |
| 268 | C2×C3×Q8 | (C22⋊C9)⋊C2 | 1 | 6 | yes | complemented |
| 269 | C2×C3×Q8 | C3⋊S4 | 1 | 2 | yes | — |
| 270 | C2×C3×D4 | — | 3 | 2 | no | — |
| 271 | C2×C3×D4 | — | 3 | 6 | no | — |
| 272 | C2×C3×D4 | — | 3 | 3 | no | — |
| 273 | C2×C3×D4 | — | 3 | 1 | no | — |
| 274 | C2×C3×D4 | — | 3 | 3 | no | — |
| 275 | C2×C3×D4 | — | 3 | 1 | no | — |
| 276 | C2×C3×D4 | — | 3 | 1 | no | — |
| 277 | C2×C3×D4 | — | 3 | 1 | no | — |
| 278 | C2×C3×D4 | — | 3 | 3 | no | — |
| 279 | C2×C3×D4 | — | 3 | 3 | no | — |
| 280 | C2×C3×D4 | — | 6 | 2 | no | — |
| 281 | C2×C3×D4 | — | 6 | 6 | no | — |
| 282 | C2×C3×D4 | — | 6 | 6 | no | — |
| 283 | C2×C3×D4 | — | 6 | 2 | no | — |
| 284 | C2×C3×D4 | — | 6 | 3 | no | — |
| 285 | C2×C3×D4 | — | 6 | 1 | no | — |
| 286 | C2×C3×D4 | — | 6 | 3 | no | — |
| 287 | C2×C3×D4 | — | 6 | 1 | no | — |
| 288 | C2×C3×D4 | — | 6 | 6 | no | — |
| 289 | C2×C3×D4 | — | 6 | 2 | no | — |
| 290 | C2×C3×D4 | — | 6 | 6 | no | — |
| 291 | C2×C3×D4 | — | 6 | 2 | no | — |
| 292 | C2×C3×D4 | — | 6 | 1 | no | — |
| 293 | C2×C3×D4 | — | 6 | 3 | no | — |
| 294 | C2×C3×D4 | — | 6 | 3 | no | — |
| 295 | C2×C3×D4 | — | 6 | 1 | no | — |
| 296 | C22×C3×C4 | — | 3 | 1 | no | — |
| 297 | C22×C3×C4 | — | 3 | 3 | no | — |
| 298 | C22×C3×C4 | — | 6 | 1 | no | — |
| 299 | C22×C3×C4 | — | 6 | 3 | no | — |
| 300 | C2×#67 | — | 18 | 6 | no | — |
| 301 | C2×#67 | — | 18 | 2 | no | — |
| 302 | C2×#67 | — | 18 | 6 | no | — |
| 303 | C2×#67 | — | 18 | 6 | no | — |
| 304 | C2×#67 | — | 18 | 2 | no | — |
| 305 | C2×#67 | — | 18 | 2 | no | — |
| 306 | C2×#67 | — | 18 | 2 | no | — |
| 307 | C2×#67 | — | 18 | 6 | no | — |
| 308 | C2×#67 | — | 36 | 4 | no | — |
| 309 | C2×#67 | — | 36 | 12 | no | — |
| 310 | C2×#67 | — | 36 | 12 | no | — |
| 311 | C2×#67 | — | 36 | 4 | no | — |
| 312 | C22×Dic3 | — | 18 | 1 | no | — |
| 313 | C22×Dic3 | — | 18 | 3 | no | — |
| 314 | C2×D12 | — | 9 | 6 | no | — |
| 315 | C2×D12 | — | 9 | 2 | no | — |
| 316 | C2×D12 | — | 18 | 2 | no | — |
| 317 | C2×D12 | — | 18 | 6 | no | — |
| 318 | C2×D12 | — | 18 | 6 | no | — |
| 319 | C2×D12 | — | 18 | 2 | no | — |
| 320 | C2×D12 | — | 18 | 3 | no | — |
| 321 | C2×D12 | — | 18 | 1 | no | — |
| 322 | #215 | — | 18 | 12 | no | — |
| 323 | #215 | — | 18 | 4 | no | — |
| 324 | #215 | — | 18 | 4 | no | — |
| 325 | #215 | — | 18 | 12 | no | — |
| 326 | #213 | — | 18 | 12 | no | — |
| 327 | #213 | — | 18 | 12 | no | — |
| 328 | #213 | — | 18 | 4 | no | — |
| 329 | #213 | — | 18 | 4 | no | — |
| 330 | C4×Dic3 | — | 9 | 6 | no | — |
| 331 | C4×Dic3 | — | 9 | 2 | no | — |
| 332 | C4×Dic3 | — | 18 | 3 | no | — |
| 333 | C4×Dic3 | — | 18 | 1 | no | — |
| 334 | #208 | — | 9 | 12 | no | — |
| 335 | #208 | — | 9 | 4 | no | — |
| 336 | #208 | — | 18 | 6 | no | — |
| 337 | #208 | — | 18 | 2 | no | — |
| 338 | C2×C3⋊C8 | — | 18 | 2 | no | — |
| 339 | C2×C3⋊C8 | — | 18 | 6 | no | — |
| 340 | C22×C32 | — | 3 | 1 | no | — |
| 341 | C22×C32 | — | 3 | 1 | no | — |
| 342 | C22×C32 | — | 4 | 1 | no | — |
| 343 | C22×C32 | — | 6 | 2 | no | — |
| 344 | C22×C32 | — | 6 | 1 | no | — |
| 345 | C22×C32 | — | 6 | 1 | no | — |
| 346 | C22×C32 | — | 8 | 1 | no | — |
| 347 | C22×C32 | — | 12 | 1 | no | — |
| 348 | C22×C32 | — | 12 | 1 | no | — |
| 349 | C22×C32 | — | 12 | 1 | no | — |
| 350 | C22×C32 | — | 12 | 2 | no | — |
| 351 | C22×C32 | — | 24 | 1 | no | — |
| 352 | C22×C32 | — | 24 | 1 | no | — |
| 353 | C22×C32 | #1020 | 1 | 1 | yes | characteristic |
| 354 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 355 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 356 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 357 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 358 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 359 | C32×C4 | — | 3 | 2 | no | — |
| 360 | C32×C4 | — | 3 | 2 | no | — |
| 361 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 362 | C22×C9 | — | 16 | 3 | no | — |
| 363 | C2×D9 | — | 48 | 6 | no | — |
| 364 | C2×D9 | — | 48 | 12 | no | — |
| 365 | C22⋊C9 | — | 4 | 3 | no | — |
| 366 | C22⋊C9 | — | 8 | 3 | no | — |
| 367 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 368 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 369 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 370 | H(5,𝔽2) | C2×C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 371 | C2×#41 | — | 3 | 2 | no | — |
| 372 | C22×D4 | — | 3 | 1 | no | — |
| 373 | C22×D4 | — | 6 | 1 | no | — |
| 374 | C22×D4 | — | 27 | 1 | no | — |
| 375 | C22×D4 | — | 54 | 1 | no | — |
| 376 | C22×D4 | — | 54 | 1 | no | — |
| 377 | AGL(1,ℤ/8) | — | 27 | 4 | no | — |
| 378 | AGL(1,ℤ/8) | — | 27 | 4 | no | — |
| 379 | AGL(1,ℤ/8) | — | 54 | 2 | no | — |
| 380 | AGL(1,ℤ/8) | — | 54 | 2 | no | — |
| 381 | C2×SD16 | — | 54 | 2 | no | — |
| 382 | C2×D8 | — | 54 | 2 | no | — |
| 383 | C2×M16 | — | 27 | 2 | no | — |
| 384 | #127 | — | 27 | 2 | no | — |
| 385 | #127 | — | 27 | 2 | no | — |
| 386 | #127 | — | 54 | 1 | no | — |
| 387 | #127 | — | 54 | 1 | no | — |
| 388 | C2×C42 | — | 27 | 1 | no | — |
| 389 | #104 | — | 27 | 4 | no | — |
| 390 | #104 | — | 27 | 4 | no | — |
| 391 | #100 | — | 27 | 2 | no | — |
| 392 | #100 | — | 27 | 2 | no | — |
| 393 | C3×C9 | — | 16 | 1 | no | Sylow |
| 394 | C23×C3 | — | 2 | 1 | no | — |
| 395 | C23×C3 | — | 2 | 3 | no | — |
| 396 | C23×C3 | — | 3 | 1 | no | — |
| 397 | C23×C3 | — | 3 | 3 | no | — |
| 398 | C23×C3 | — | 3 | 3 | no | — |
| 399 | C23×C3 | — | 3 | 1 | no | — |
| 400 | C23×C3 | — | 3 | 3 | no | — |
| 401 | C23×C3 | — | 3 | 3 | no | — |
| 402 | C23×C3 | — | 3 | 1 | no | — |
| 403 | C23×C3 | — | 3 | 1 | no | — |
| 404 | C23×C3 | — | 4 | 2 | no | — |
| 405 | C23×C3 | — | 4 | 6 | no | — |
| 406 | C23×C3 | — | 6 | 3 | no | — |
| 407 | C23×C3 | — | 6 | 1 | no | — |
| 408 | C23×C3 | — | 6 | 1 | no | — |
| 409 | C23×C3 | — | 6 | 3 | no | — |
| 410 | C23×C3 | — | 6 | 3 | no | — |
| 411 | C23×C3 | — | 6 | 1 | no | — |
| 412 | C23×C3 | — | 8 | 2 | no | — |
| 413 | C23×C3 | — | 8 | 6 | no | — |
| 414 | C23×C3 | — | 12 | 6 | no | — |
| 415 | C23×C3 | — | 12 | 2 | no | — |
| 416 | C23×C3 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 417 | C23×C3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 418 | C22×D3 | — | 18 | 6 | no | — |
| 419 | C22×D3 | — | 18 | 2 | no | — |
| 420 | C22×D3 | — | 36 | 3 | no | — |
| 421 | C22×D3 | — | 36 | 1 | no | — |
| 422 | C22×D3 | — | 36 | 6 | no | — |
| 423 | C22×D3 | — | 36 | 6 | no | — |
| 424 | C22×D3 | — | 36 | 2 | no | — |
| 425 | C22×D3 | — | 36 | 2 | no | — |
| 426 | C22×D3 | — | 36 | 1 | no | — |
| 427 | C22×D3 | — | 36 | 3 | no | — |
| 428 | C3×Q8 | — | 3 | 6 | no | — |
| 429 | C3×Q8 | — | 3 | 2 | no | — |
| 430 | C3×Q8 | C2×(C22⋊C9)⋊C2 | 1 | 6 | yes | complemented |
| 431 | C3×Q8 | C2×C3⋊S4 | 1 | 2 | yes | — |
| 432 | C3×D4 | — | 3 | 6 | no | — |
| 433 | C3×D4 | — | 3 | 6 | no | — |
| 434 | C3×D4 | — | 3 | 2 | no | — |
| 435 | C3×D4 | — | 3 | 2 | no | — |
| 436 | C3×D4 | — | 6 | 6 | no | — |
| 437 | C3×D4 | — | 6 | 6 | no | — |
| 438 | C3×D4 | — | 6 | 6 | no | — |
| 439 | C3×D4 | — | 6 | 6 | no | — |
| 440 | C3×D4 | — | 6 | 2 | no | — |
| 441 | C3×D4 | — | 6 | 2 | no | — |
| 442 | C3×D4 | — | 6 | 2 | no | — |
| 443 | C3×D4 | — | 6 | 2 | no | — |
| 444 | C3×D4 | — | 6 | 6 | no | — |
| 445 | C3×D4 | — | 6 | 2 | no | — |
| 446 | C2×C3×C4 | — | 3 | 3 | no | — |
| 447 | C2×C3×C4 | — | 3 | 1 | no | — |
| 448 | C2×C3×C4 | — | 3 | 6 | no | — |
| 449 | C2×C3×C4 | — | 3 | 2 | no | — |
| 450 | C2×C3×C4 | — | 3 | 3 | no | — |
| 451 | C2×C3×C4 | — | 3 | 1 | no | — |
| 452 | C2×C3×C4 | — | 3 | 2 | no | — |
| 453 | C2×C3×C4 | — | 3 | 6 | no | — |
| 454 | C2×C3×C4 | — | 6 | 3 | no | — |
| 455 | C2×C3×C4 | — | 6 | 6 | no | — |
| 456 | C2×C3×C4 | — | 6 | 3 | no | — |
| 457 | C2×C3×C4 | — | 6 | 1 | no | — |
| 458 | C2×C3×C4 | — | 6 | 2 | no | — |
| 459 | C2×C3×C4 | — | 6 | 1 | no | — |
| 460 | #67 | — | 36 | 4 | no | — |
| 461 | #67 | — | 36 | 12 | no | — |
| 462 | #67 | — | 36 | 4 | no | — |
| 463 | #67 | — | 36 | 12 | no | — |
| 464 | #67 | — | 36 | 12 | no | — |
| 465 | #67 | — | 36 | 12 | no | — |
| 466 | #67 | — | 36 | 4 | no | — |
| 467 | #67 | — | 36 | 4 | no | — |
| 468 | C2×Dic3 | — | 18 | 6 | no | — |
| 469 | C2×Dic3 | — | 18 | 2 | no | — |
| 470 | C2×Dic3 | — | 18 | 12 | no | — |
| 471 | C2×Dic3 | — | 18 | 4 | no | — |
| 472 | D12 | — | 18 | 12 | no | — |
| 473 | D12 | — | 18 | 4 | no | — |
| 474 | D12 | — | 36 | 6 | no | — |
| 475 | D12 | — | 36 | 2 | no | — |
| 476 | C3⋊C8 | — | 18 | 12 | no | — |
| 477 | C3⋊C8 | — | 18 | 4 | no | — |
| 478 | C2×C32 | — | 6 | 1 | no | — |
| 479 | C2×C32 | — | 6 | 1 | no | — |
| 480 | C2×C32 | — | 12 | 1 | no | — |
| 481 | C2×C32 | — | 12 | 1 | no | — |
| 482 | C2×C32 | #5935 | 1 | 2 | yes | — |
| 483 | C2×C32 | C2×#1020 | 1 | 1 | yes | characteristic |
| 484 | C3⋊D3 | — | 24 | 2 | no | — |
| 485 | C2×C9 | — | 16 | 3 | no | — |
| 486 | C2×C9 | — | 16 | 6 | no | — |
| 487 | D9 | — | 48 | 12 | no | — |
| 488 | C24 | — | 2 | 1 | no | — |
| 489 | C24 | — | 3 | 1 | no | — |
| 490 | C24 | — | 54 | 1 | no | — |
| 491 | C24 | C3⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic |
| 492 | #41 | — | 3 | 2 | no | — |
| 493 | #41 | — | 3 | 2 | no | — |
| 494 | #41 | — | 3 | 2 | no | — |
| 495 | #41 | — | 3 | 2 | no | — |
| 496 | #41 | — | 6 | 2 | no | — |
| 497 | #41 | — | 6 | 2 | no | — |
| 498 | C2×Q8 | C3⋊((C22⋊C9)⋊C2) | 1 | 2 | yes | complemented |
| 499 | C2×D4 | — | 3 | 2 | no | — |
| 500 | C2×D4 | — | 3 | 1 | no | — |
| 501 | C2×D4 | — | 3 | 1 | no | — |
| 502 | C2×D4 | — | 3 | 1 | no | — |
| 503 | C2×D4 | — | 3 | 1 | no | — |
| 504 | C2×D4 | — | 6 | 2 | no | — |
| 505 | C2×D4 | — | 6 | 2 | no | — |
| 506 | C2×D4 | — | 6 | 1 | no | — |
| 507 | C2×D4 | — | 6 | 1 | no | — |
| 508 | C2×D4 | — | 6 | 2 | no | — |
| 509 | C2×D4 | — | 6 | 2 | no | — |
| 510 | C2×D4 | — | 6 | 1 | no | — |
| 511 | C2×D4 | — | 6 | 1 | no | — |
| 512 | C2×D4 | — | 27 | 2 | no | — |
| 513 | C2×D4 | — | 54 | 2 | no | — |
| 514 | C2×D4 | — | 54 | 2 | no | — |
| 515 | C2×D4 | — | 54 | 1 | no | — |
| 516 | C2×D4 | — | 54 | 2 | no | — |
| 517 | C2×D4 | — | 54 | 2 | no | — |
| 518 | C2×D4 | — | 54 | 2 | no | — |
| 519 | C2×D4 | — | 54 | 2 | no | — |
| 520 | C2×D4 | — | 108 | 4 | no | — |
| 521 | C2×D4 | — | 108 | 4 | no | — |
| 522 | C22×C4 | — | 3 | 1 | no | — |
| 523 | C22×C4 | — | 6 | 1 | no | — |
| 524 | C22×C4 | — | 54 | 1 | no | — |
| 525 | SD16 | — | 54 | 4 | no | — |
| 526 | SD16 | — | 54 | 4 | no | — |
| 527 | D8 | — | 54 | 4 | no | — |
| 528 | D8 | — | 54 | 4 | no | — |
| 529 | M16 | — | 27 | 4 | no | — |
| 530 | M16 | — | 54 | 2 | no | — |
| 531 | C2×C8 | — | 54 | 2 | no | — |
| 532 | C42 | — | 27 | 2 | no | — |
| 533 | C42 | — | 54 | 1 | no | — |
| 534 | C22×C3 | — | 3 | 3 | no | — |
| 535 | C22×C3 | — | 3 | 3 | no | — |
| 536 | C22×C3 | — | 3 | 1 | no | — |
| 537 | C22×C3 | — | 3 | 1 | no | — |
| 538 | C22×C3 | — | 4 | 1 | no | — |
| 539 | C22×C3 | — | 4 | 3 | no | — |
| 540 | C22×C3 | — | 6 | 6 | no | — |
| 541 | C22×C3 | — | 6 | 2 | no | — |
| 542 | C22×C3 | — | 6 | 3 | no | — |
| 543 | C22×C3 | — | 6 | 3 | no | — |
| 544 | C22×C3 | — | 6 | 1 | no | — |
| 545 | C22×C3 | — | 6 | 1 | no | — |
| 546 | C22×C3 | — | 8 | 1 | no | — |
| 547 | C22×C3 | — | 8 | 3 | no | — |
| 548 | C22×C3 | — | 12 | 3 | no | — |
| 549 | C22×C3 | — | 12 | 1 | no | — |
| 550 | C22×C3 | — | 12 | 3 | no | — |
| 551 | C22×C3 | — | 12 | 3 | no | — |
| 552 | C22×C3 | — | 12 | 1 | no | — |
| 553 | C22×C3 | — | 12 | 1 | no | — |
| 554 | C22×C3 | — | 12 | 6 | no | — |
| 555 | C22×C3 | — | 12 | 2 | no | — |
| 556 | C22×C3 | — | 24 | 3 | no | — |
| 557 | C22×C3 | — | 24 | 1 | no | — |
| 558 | C22×C3 | — | 24 | 3 | no | — |
| 559 | C22×C3 | — | 24 | 1 | no | — |
| 560 | C22×C3 | #64188 | 1 | 3 | yes | — |
| 561 | C22×C3 | C3⋊#1020 | 1 | 1 | yes | characteristic |
| 562 | C2×D3 | — | 36 | 6 | no | — |
| 563 | C2×D3 | — | 36 | 6 | no | — |
| 564 | C2×D3 | — | 36 | 2 | no | — |
| 565 | C2×D3 | — | 36 | 2 | no | — |
| 566 | C2×D3 | — | 36 | 6 | no | — |
| 567 | C2×D3 | — | 36 | 2 | no | — |
| 568 | C2×D3 | — | 72 | 6 | no | — |
| 569 | C2×D3 | — | 72 | 2 | no | — |
| 570 | C2×D3 | — | 72 | 6 | no | — |
| 571 | C2×D3 | — | 72 | 2 | no | — |
| 572 | C3×C4 | — | 3 | 6 | no | — |
| 573 | C3×C4 | — | 3 | 6 | no | — |
| 574 | C3×C4 | — | 3 | 2 | no | — |
| 575 | C3×C4 | — | 3 | 2 | no | — |
| 576 | Dic3 | — | 18 | 12 | no | — |
| 577 | Dic3 | — | 18 | 4 | no | — |
| 578 | C32 | C2×#5935 | 1 | 1 | yes | characteristic |
| 579 | C9 | — | 16 | 3 | no | — |
| 580 | C23 | — | 2 | 1 | no | — |
| 581 | C23 | — | 3 | 1 | no | — |
| 582 | C23 | — | 3 | 1 | no | — |
| 583 | C23 | — | 3 | 1 | no | — |
| 584 | C23 | — | 3 | 1 | no | — |
| 585 | C23 | — | 4 | 2 | no | — |
| 586 | C23 | — | 6 | 1 | no | — |
| 587 | C23 | — | 6 | 1 | no | — |
| 588 | C23 | — | 6 | 1 | no | — |
| 589 | C23 | — | 8 | 2 | no | — |
| 590 | C23 | — | 12 | 2 | no | — |
| 591 | C23 | — | 54 | 2 | no | — |
| 592 | C23 | — | 108 | 1 | no | — |
| 593 | C23 | — | 108 | 2 | no | — |
| 594 | C23 | — | 108 | 2 | no | — |
| 595 | C23 | — | 108 | 1 | no | — |
| 596 | C23 | C2×C3⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic |
| 597 | Q8 | — | 3 | 2 | no | — |
| 598 | Q8 | C2×C3⋊((C22⋊C9)⋊C2) | 1 | 2 | yes | complemented |
| 599 | D4 | — | 3 | 2 | no | — |
| 600 | D4 | — | 3 | 2 | no | — |
| 601 | D4 | — | 6 | 2 | no | — |
| 602 | D4 | — | 6 | 2 | no | — |
| 603 | D4 | — | 6 | 2 | no | — |
| 604 | D4 | — | 6 | 2 | no | — |
| 605 | D4 | — | 6 | 2 | no | — |
| 606 | D4 | — | 54 | 4 | no | — |
| 607 | D4 | — | 108 | 2 | no | — |
| 608 | D4 | — | 108 | 4 | no | — |
| 609 | D4 | — | 108 | 4 | no | — |
| 610 | D4 | — | 108 | 4 | no | — |
| 611 | D4 | — | 108 | 4 | no | — |
| 612 | C2×C4 | — | 3 | 1 | no | — |
| 613 | C2×C4 | — | 3 | 1 | no | — |
| 614 | C2×C4 | — | 3 | 2 | no | — |
| 615 | C2×C4 | — | 3 | 2 | no | — |
| 616 | C2×C4 | — | 6 | 1 | no | — |
| 617 | C2×C4 | — | 6 | 2 | no | — |
| 618 | C2×C4 | — | 6 | 1 | no | — |
| 619 | C2×C4 | — | 54 | 2 | no | — |
| 620 | C2×C4 | — | 54 | 4 | no | — |
| 621 | C8 | — | 54 | 4 | no | — |
| 622 | C2×C3 | — | 6 | 3 | no | — |
| 623 | C2×C3 | — | 6 | 3 | no | — |
| 624 | C2×C3 | — | 6 | 1 | no | — |
| 625 | C2×C3 | — | 6 | 1 | no | — |
| 626 | C2×C3 | — | 12 | 3 | no | — |
| 627 | C2×C3 | — | 12 | 3 | no | — |
| 628 | C2×C3 | — | 12 | 1 | no | — |
| 629 | C2×C3 | — | 12 | 1 | no | — |
| 630 | C2×C3 | #10593110 | 1 | 6 | yes | complemented |
| 631 | C2×C3 | C2×#64188 | 1 | 3 | yes | — |
| 632 | C2×C3 | C3⋊#5935 | 1 | 2 | yes | — |
| 633 | C2×C3 | C2×C3⋊#1020 | 1 | 1 | yes | characteristic |
| 634 | D3 | — | 72 | 6 | no | — |
| 635 | D3 | — | 72 | 2 | no | — |
| 636 | C22 | — | 3 | 1 | no | — |
| 637 | C22 | — | 3 | 1 | no | — |
| 638 | C22 | — | 4 | 1 | no | — |
| 639 | C22 | — | 6 | 2 | no | — |
| 640 | C22 | — | 6 | 1 | no | — |
| 641 | C22 | — | 6 | 1 | no | — |
| 642 | C22 | — | 8 | 1 | no | — |
| 643 | C22 | — | 12 | 1 | no | — |
| 644 | C22 | — | 12 | 1 | no | — |
| 645 | C22 | — | 12 | 1 | no | — |
| 646 | C22 | — | 12 | 2 | no | — |
| 647 | C22 | — | 24 | 1 | no | — |
| 648 | C22 | — | 24 | 1 | no | — |
| 649 | C22 | — | 108 | 2 | no | — |
| 650 | C22 | — | 108 | 2 | no | — |
| 651 | C22 | — | 108 | 2 | no | — |
| 652 | C22 | — | 216 | 2 | no | — |
| 653 | C22 | — | 216 | 2 | no | — |
| 654 | C22 | C3⋊#64188 | 1 | 1 | yes | characteristic |
| 655 | C4 | — | 3 | 2 | no | — |
| 656 | C4 | — | 3 | 2 | no | — |
| 657 | C4 | — | 54 | 4 | no | — |
| 658 | C3 | C2×#10593110 | 1 | 3 | yes | complemented |
| 659 | C3 | C2×C3⋊#5935 | 1 | 1 | yes | characteristic |
| 660 | C2 | — | 6 | 1 | no | — |
| 661 | C2 | — | 6 | 1 | no | — |
| 662 | C2 | — | 12 | 1 | no | — |
| 663 | C2 | — | 12 | 1 | no | — |
| 664 | C2 | — | 216 | 2 | no | — |
| 665 | C2 | C3⋊#10593110 | 1 | 2 | yes | direct product factor |
| 666 | C2 | C2×C3⋊#64188 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#64188 |
| commutator, cosocle, hypocenter | C3×#63703 | C22 |
| Frattini | C2×C3 | C2×C3⋊#1020 |
| Fitting | C2×C32×H(5,𝔽2) | D3 |
| socle | C22×C32 | #1020 |
| LCS | G ▷ C3×#63703 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#63703 | C2 | semidirect |
| 2. C3⋊#10593110 | C2 | direct (N × H) |
| 6. C3×#63703 | C22 | semidirect |
| 11. C2×#63703 | D3 | semidirect |
| 49. #63703 | C2×D3 | semidirect |
| 62. C2×C3×H(5,𝔽2) | D9 | semidirect |
| 142. C3×H(5,𝔽2) | C2×D9 | semidirect |
| 237. C2×H(5,𝔽2) | C3⋊D9 | semidirect |
| 268. C2×C3×Q8 | (C22⋊C9)⋊C2 | semidirect |
| 370. H(5,𝔽2) | C2×C3⋊D9 | semidirect |
| 430. C3×Q8 | C2×(C22⋊C9)⋊C2 | semidirect |
| 498. C2×Q8 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 598. Q8 | C2×C3⋊((C22⋊C9)⋊C2) | semidirect |
| 630. C2×C3 | #10593110 | semidirect |
| 658. C3 | C2×#10593110 | semidirect |
| 665. C2 | C3⋊#10593110 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#63703 | 2 |
| C3⋊#10593110 | 2 |
| C2×#10593110 | 3 |
| C2×#10592940 | 3 |
| C22×C3⋊((C22⋊C9)⋊C2) | 4 |
| C2×C3⋊#3689 | 4 |