Finite Group DatabasebetaFinite Group DatabasebetaOrder 5184.
1155 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 1155 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #72252951 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72252949 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#11722576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#10592940 | — | 3 | 1 | no | maximal |
| 5 | #13147076 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10589531⋊C3 | — | 3 | 3 | no | maximal |
| 7 | C3×#88691 | — | 2 | 1 | no | — |
| 8 | C3×#88691 | C22 | 1 | 1 | yes | characteristic |
| 9 | C3⋊(#3689⋊C3) | — | 2 | 1 | no | — |
| 10 | #13047985 | — | 4 | 1 | no | maximal |
| 11 | C33×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 12 | C3×#64158 | — | 3 | 1 | no | — |
| 13 | C3×#64158 | — | 3 | 1 | no | — |
| 14 | C3×#64149 | — | 3 | 1 | no | — |
| 15 | #11722576 | — | 2 | 3 | no | — |
| 16 | #11722576 | D3 | 1 | 3 | yes | complemented |
| 17 | C3×#63700 | — | 2 | 1 | no | — |
| 18 | C3×#63700 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | #11722391 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | #63692⋊C3 | — | 3 | 3 | no | — |
| 21 | C3×#63664 | — | 3 | 1 | no | — |
| 22 | C3×#63664 | — | 3 | 1 | no | — |
| 23 | C3×#63660 | — | 3 | 1 | no | — |
| 24 | C3⋊#63422 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #63422⋊C3 | — | 3 | 3 | no | — |
| 26 | C3×Q8×3−1+2 | — | 4 | 1 | no | — |
| 27 | C4⋊(C3⋊AGL(1,ℤ/9)) | — | 4 | 1 | no | — |
| 28 | C3×#6204 | D4 | 1 | 1 | yes | characteristic, complemented |
| 29 | C3⋊(3−1+2⋊C8) | — | 4 | 1 | no | — |
| 30 | #10592940 | — | 3 | 1 | no | — |
| 31 | C3×#5241 | — | 9 | 3 | no | — |
| 32 | C3×#5241 | — | 9 | 1 | no | — |
| 33 | #10589531 | — | 3 | 3 | no | — |
| 34 | C33×#41 | — | 2 | 1 | no | — |
| 35 | C33×#41 | — | 3 | 1 | no | — |
| 36 | C33×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 37 | C2×C33×D4 | — | 3 | 1 | no | — |
| 38 | C2×C33×D4 | — | 6 | 1 | no | — |
| 39 | C2×C3×#638 | — | 6 | 2 | no | — |
| 40 | C2×C3×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 41 | C3×#3755 | — | 6 | 1 | no | — |
| 42 | C3×#3755 | — | 6 | 1 | no | — |
| 43 | C3×#3753 | — | 6 | 1 | no | — |
| 44 | C3×#3753 | — | 6 | 1 | no | — |
| 45 | C3×C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 46 | C3×#3748 | — | 3 | 1 | no | — |
| 47 | C3×#3748 | — | 3 | 1 | no | — |
| 48 | #88691 | — | 2 | 6 | no | — |
| 49 | #88691 | — | 2 | 3 | no | — |
| 50 | #88691 | — | 2 | 3 | no | — |
| 51 | #88691 | C2×D3 | 1 | 3 | yes | — |
| 52 | C3×#41⋊C9 | — | 2 | 2 | no | — |
| 53 | C3×#41⋊C9 | — | 2 | 1 | no | — |
| 54 | C3×#41⋊C9 | — | 2 | 1 | no | — |
| 55 | C3×#41⋊C9 | C22×C3 | 1 | 1 | yes | characteristic |
| 56 | C3⋊#3689 | — | 2 | 1 | no | — |
| 57 | #3689⋊C3 | — | 6 | 3 | no | — |
| 58 | #88548 | — | 4 | 1 | no | — |
| 59 | #3675⋊C3 | — | 12 | 3 | no | — |
| 60 | C2×C3⋊AGL(1,ℤ/9) | — | 8 | 1 | no | — |
| 61 | C3×C4×3−1+2 | — | 4 | 1 | no | — |
| 62 | C3×C4×3−1+2 | — | 8 | 1 | no | — |
| 63 | C32×H(5,𝔽2) | — | 2 | 1 | no | — |
| 64 | C32×H(5,𝔽2) | — | 3 | 3 | no | — |
| 65 | C32×H(5,𝔽2) | C3×D3 | 1 | 1 | yes | characteristic |
| 66 | C32×H(5,𝔽2) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 67 | #64158 | — | 3 | 1 | no | — |
| 68 | #64158 | — | 3 | 1 | no | — |
| 69 | #64149 | — | 3 | 1 | no | — |
| 70 | C3×#949 | — | 9 | 3 | no | — |
| 71 | C3×#949 | — | 9 | 3 | no | — |
| 72 | C3×#949 | — | 9 | 1 | no | — |
| 73 | C3×#949 | — | 9 | 1 | no | — |
| 74 | C3×#940 | — | 9 | 1 | no | — |
| 75 | C3×#940 | — | 9 | 3 | no | — |
| 76 | #63700 | — | 2 | 3 | no | — |
| 77 | #63700 | C3×D3 | 1 | 3 | yes | complemented |
| 78 | #63692 | — | 3 | 3 | no | — |
| 79 | #63664 | — | 3 | 1 | no | — |
| 80 | #63664 | — | 3 | 1 | no | — |
| 81 | #63660 | — | 3 | 1 | no | — |
| 82 | C3×#837 | — | 9 | 3 | no | — |
| 83 | C3×#837 | — | 9 | 1 | no | — |
| 84 | C3×#837 | — | 9 | 3 | no | — |
| 85 | C3×#837 | — | 9 | 1 | no | — |
| 86 | C3×#833 | — | 9 | 1 | no | — |
| 87 | C3×#833 | — | 9 | 3 | no | — |
| 88 | #63422 | — | 3 | 3 | no | — |
| 89 | C23×C33 | — | 3 | 2 | no | — |
| 90 | C22×C3×C3⋊D3 | — | 6 | 1 | no | — |
| 91 | C33×Q8 | #67 | 1 | 1 | yes | characteristic |
| 92 | C33×Q8 | S4 | 1 | 1 | yes | characteristic |
| 93 | C33×D4 | — | 3 | 1 | no | — |
| 94 | C33×D4 | — | 3 | 1 | no | — |
| 95 | C33×D4 | — | 6 | 1 | no | — |
| 96 | C33×D4 | — | 6 | 1 | no | — |
| 97 | C2×C33×C4 | — | 3 | 1 | no | — |
| 98 | C2×C33×C4 | — | 6 | 1 | no | — |
| 99 | C3×#638 | — | 12 | 4 | no | — |
| 100 | C2×C3×C3⋊Dic3 | — | 6 | 1 | no | — |
| 101 | C3×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 102 | C3×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 103 | C3×C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 104 | C3×C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 105 | Q8×3−1+2 | — | 4 | 3 | no | — |
| 106 | Q8×3−1+2 | — | 8 | 3 | no | — |
| 107 | C3×Q8×C9 | — | 4 | 1 | no | — |
| 108 | C3×Q8×C9 | — | 8 | 1 | no | — |
| 109 | C4⋊(C3⋊D9) | — | 4 | 1 | no | — |
| 110 | C4⋊AGL(1,ℤ/9) | — | 12 | 3 | no | — |
| 111 | #6204 | — | 2 | 3 | no | — |
| 112 | #6204 | #67 | 1 | 3 | yes | complemented |
| 113 | C3×Q8⋊C9 | — | 2 | 1 | no | — |
| 114 | C3×Q8⋊C9 | C3×D4 | 1 | 1 | yes | characteristic, complemented |
| 115 | C3⋊(C9⋊C8) | — | 4 | 1 | no | — |
| 116 | 3−1+2⋊C8 | — | 12 | 3 | no | — |
| 117 | C3×#453 | — | 27 | 1 | no | — |
| 118 | #5241 | — | 9 | 3 | no | — |
| 119 | #5241 | — | 9 | 1 | no | — |
| 120 | C2×C3×3−1+2 | — | 4 | 1 | no | — |
| 121 | C3⋊AGL(1,ℤ/9) | — | 16 | 1 | no | — |
| 122 | C32×#41 | — | 2 | 2 | no | — |
| 123 | C32×#41 | — | 2 | 1 | no | — |
| 124 | C32×#41 | — | 2 | 1 | no | — |
| 125 | C32×#41 | — | 2 | 1 | no | — |
| 126 | C32×#41 | — | 3 | 3 | no | — |
| 127 | C32×#41 | — | 3 | 3 | no | — |
| 128 | C32×#41 | — | 3 | 1 | no | — |
| 129 | C32×#41 | — | 3 | 1 | no | — |
| 130 | C32×#41 | — | 6 | 1 | no | — |
| 131 | C32×#41 | — | 6 | 3 | no | — |
| 132 | C32×#41 | — | 6 | 3 | no | — |
| 133 | C32×#41 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 134 | C32×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 135 | C2×C32×D4 | — | 3 | 1 | no | — |
| 136 | C2×C32×D4 | — | 3 | 1 | no | — |
| 137 | C2×C32×D4 | — | 3 | 3 | no | — |
| 138 | C2×C32×D4 | — | 6 | 3 | no | — |
| 139 | C2×C32×D4 | — | 6 | 3 | no | — |
| 140 | C2×C32×D4 | — | 6 | 1 | no | — |
| 141 | C2×C32×D4 | — | 6 | 1 | no | — |
| 142 | C2×C32×D4 | — | 6 | 6 | no | — |
| 143 | C2×C32×D4 | — | 6 | 1 | no | — |
| 144 | C2×C32×D4 | — | 6 | 2 | no | — |
| 145 | C2×#638 | — | 6 | 2 | no | — |
| 146 | C2×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 147 | C2×C3×#67 | — | 18 | 6 | no | — |
| 148 | C2×C3×#67 | — | 18 | 2 | no | — |
| 149 | C2×C3×D12 | — | 9 | 3 | no | — |
| 150 | C2×C3×D12 | — | 9 | 1 | no | — |
| 151 | #3755 | — | 6 | 1 | no | — |
| 152 | #3755 | — | 6 | 1 | no | — |
| 153 | #3753 | — | 6 | 1 | no | — |
| 154 | #3753 | — | 6 | 1 | no | — |
| 155 | C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 156 | #3748 | — | 3 | 1 | no | — |
| 157 | #3748 | — | 3 | 1 | no | — |
| 158 | C3×#215 | — | 18 | 3 | no | — |
| 159 | C3×#215 | — | 18 | 3 | no | — |
| 160 | C3×#215 | — | 18 | 1 | no | — |
| 161 | C3×#215 | — | 18 | 1 | no | — |
| 162 | C3×#213 | — | 18 | 1 | no | — |
| 163 | C3×#213 | — | 18 | 3 | no | — |
| 164 | C3×#213 | — | 18 | 3 | no | — |
| 165 | C3×#213 | — | 18 | 1 | no | — |
| 166 | C3×C4×Dic3 | — | 9 | 3 | no | — |
| 167 | C3×C4×Dic3 | — | 9 | 1 | no | — |
| 168 | C3×#208 | — | 9 | 3 | no | — |
| 169 | C3×#208 | — | 9 | 3 | no | — |
| 170 | C3×#208 | — | 9 | 1 | no | — |
| 171 | C3×#208 | — | 9 | 1 | no | — |
| 172 | #41⋊C9 | — | 2 | 6 | no | — |
| 173 | #41⋊C9 | — | 2 | 3 | no | — |
| 174 | #41⋊C9 | — | 2 | 3 | no | — |
| 175 | #41⋊C9 | C2×C3×D3 | 1 | 3 | yes | — |
| 176 | #3689 | — | 6 | 3 | no | — |
| 177 | #3675 | — | 12 | 3 | no | — |
| 178 | C22×C33 | — | 3 | 1 | no | — |
| 179 | C22×C33 | — | 6 | 1 | no | — |
| 180 | C22×C33 | — | 12 | 2 | no | — |
| 181 | C2×C3×C3⋊D3 | — | 12 | 2 | no | — |
| 182 | C2×C3×C3⋊D3 | — | 12 | 1 | no | — |
| 183 | C33×C4 | — | 2 | 1 | no | — |
| 184 | C33×C4 | — | 3 | 1 | no | — |
| 185 | C33×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 186 | C3×C3⋊Dic3 | — | 6 | 2 | no | — |
| 187 | C2×C3⋊D9 | — | 8 | 1 | no | — |
| 188 | C2×AGL(1,ℤ/9) | — | 24 | 3 | no | — |
| 189 | C4×3−1+2 | — | 4 | 3 | no | — |
| 190 | C4×3−1+2 | — | 8 | 3 | no | — |
| 191 | C4×3−1+2 | — | 8 | 3 | no | — |
| 192 | C4×3−1+2 | — | 8 | 6 | no | — |
| 193 | C3×C4×C9 | — | 4 | 1 | no | — |
| 194 | C3×C4×C9 | — | 8 | 1 | no | — |
| 195 | C3×C4×C9 | — | 8 | 2 | no | — |
| 196 | C3×C4×C9 | — | 8 | 1 | no | — |
| 197 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 198 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 199 | C3×H(5,𝔽2) | AGL(1,ℤ/9) | 1 | 3 | yes | complemented |
| 200 | C3×H(5,𝔽2) | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 201 | C3×AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 202 | C3×AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 203 | C3×#127 | — | 27 | 1 | no | — |
| 204 | #949 | — | 9 | 3 | no | — |
| 205 | #949 | — | 9 | 1 | no | — |
| 206 | #949 | — | 9 | 3 | no | — |
| 207 | #949 | — | 9 | 1 | no | — |
| 208 | #940 | — | 9 | 3 | no | — |
| 209 | #940 | — | 9 | 1 | no | — |
| 210 | C3×#104 | — | 27 | 1 | no | — |
| 211 | C3×#104 | — | 27 | 1 | no | — |
| 212 | C3×#100 | — | 27 | 1 | no | — |
| 213 | #837 | — | 9 | 3 | no | — |
| 214 | #837 | — | 9 | 1 | no | — |
| 215 | #837 | — | 9 | 3 | no | — |
| 216 | #837 | — | 9 | 1 | no | — |
| 217 | #833 | — | 9 | 3 | no | — |
| 218 | #833 | — | 9 | 1 | no | — |
| 219 | C3×3−1+2 | — | 4 | 1 | no | Sylow |
| 220 | C23×C32 | — | 3 | 2 | no | — |
| 221 | C23×C32 | — | 3 | 6 | no | — |
| 222 | C23×C32 | — | 3 | 2 | no | — |
| 223 | C23×C32 | — | 6 | 2 | no | — |
| 224 | C23×C32 | — | 6 | 6 | no | — |
| 225 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 226 | C22×C3×D3 | — | 18 | 3 | no | — |
| 227 | C22×C3×D3 | — | 18 | 1 | no | — |
| 228 | C32×Q8 | — | 2 | 1 | no | — |
| 229 | C32×Q8 | — | 2 | 1 | no | — |
| 230 | C32×Q8 | — | 3 | 3 | no | — |
| 231 | C32×Q8 | — | 3 | 3 | no | — |
| 232 | C32×Q8 | C3×#67 | 1 | 1 | yes | characteristic |
| 233 | C32×Q8 | #638 | 1 | 1 | yes | characteristic |
| 234 | C32×Q8 | C3×S4 | 1 | 1 | yes | characteristic |
| 235 | C32×Q8 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 236 | C32×D4 | — | 3 | 1 | no | — |
| 237 | C32×D4 | — | 3 | 1 | no | — |
| 238 | C32×D4 | — | 3 | 1 | no | — |
| 239 | C32×D4 | — | 3 | 3 | no | — |
| 240 | C32×D4 | — | 3 | 3 | no | — |
| 241 | C32×D4 | — | 3 | 1 | no | — |
| 242 | C32×D4 | — | 6 | 1 | no | — |
| 243 | C32×D4 | — | 6 | 3 | no | — |
| 244 | C32×D4 | — | 6 | 3 | no | — |
| 245 | C32×D4 | — | 6 | 1 | no | — |
| 246 | C32×D4 | — | 6 | 1 | no | — |
| 247 | C32×D4 | — | 6 | 1 | no | — |
| 248 | C32×D4 | — | 6 | 2 | no | — |
| 249 | C32×D4 | — | 6 | 1 | no | — |
| 250 | C32×D4 | — | 6 | 1 | no | — |
| 251 | C32×D4 | — | 6 | 3 | no | — |
| 252 | C32×D4 | — | 6 | 3 | no | — |
| 253 | C32×D4 | — | 6 | 2 | no | — |
| 254 | C32×D4 | — | 6 | 6 | no | — |
| 255 | C32×D4 | — | 6 | 6 | no | — |
| 256 | C2×C32×C4 | — | 3 | 1 | no | — |
| 257 | C2×C32×C4 | — | 3 | 3 | no | — |
| 258 | C2×C32×C4 | — | 3 | 1 | no | — |
| 259 | C2×C32×C4 | — | 6 | 1 | no | — |
| 260 | C2×C32×C4 | — | 6 | 3 | no | — |
| 261 | C2×C32×C4 | — | 6 | 1 | no | — |
| 262 | C2×C32×C4 | — | 6 | 1 | no | — |
| 263 | C2×C32×C4 | — | 6 | 2 | no | — |
| 264 | C2×C32×C4 | — | 6 | 3 | no | — |
| 265 | C2×C32×C4 | — | 6 | 6 | no | — |
| 266 | #638 | — | 12 | 4 | no | — |
| 267 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 268 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 269 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 270 | C3×#67 | — | 36 | 12 | no | — |
| 271 | C3×#67 | — | 36 | 4 | no | — |
| 272 | C2×C3×Dic3 | — | 18 | 3 | no | — |
| 273 | C2×C3×Dic3 | — | 18 | 1 | no | — |
| 274 | C3×D12 | — | 18 | 3 | no | — |
| 275 | C3×D12 | — | 18 | 1 | no | — |
| 276 | C3×D12 | — | 18 | 3 | no | — |
| 277 | C3×D12 | — | 18 | 1 | no | — |
| 278 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 279 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 280 | C3×C3⋊C8 | — | 18 | 3 | no | — |
| 281 | C3×C3⋊C8 | — | 18 | 1 | no | — |
| 282 | C3×C3⋊C8 | — | 18 | 3 | no | — |
| 283 | C3×C3⋊C8 | — | 18 | 1 | no | — |
| 284 | Q8×C9 | — | 4 | 3 | no | — |
| 285 | Q8×C9 | — | 8 | 3 | no | — |
| 286 | D36 | — | 12 | 3 | no | — |
| 287 | Q8⋊C9 | — | 2 | 3 | no | — |
| 288 | Q8⋊C9 | C3×#67 | 1 | 3 | yes | complemented |
| 289 | C9⋊C8 | — | 12 | 3 | no | — |
| 290 | #453 | — | 27 | 1 | no | Sylow |
| 291 | C2×C33 | — | 6 | 1 | no | — |
| 292 | C2×C33 | — | 12 | 1 | no | — |
| 293 | C2×C33 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 294 | C3×C3⋊D3 | — | 24 | 1 | no | — |
| 295 | C2×3−1+2 | — | 4 | 3 | no | — |
| 296 | C2×3−1+2 | — | 8 | 3 | no | — |
| 297 | C2×C3×C9 | — | 4 | 1 | no | — |
| 298 | C2×C3×C9 | — | 8 | 1 | no | — |
| 299 | C3⋊D9 | — | 16 | 1 | no | — |
| 300 | AGL(1,ℤ/9) | — | 48 | 3 | no | — |
| 301 | C3×#41 | — | 2 | 3 | no | — |
| 302 | C3×#41 | — | 2 | 1 | no | — |
| 303 | C3×#41 | — | 3 | 1 | no | — |
| 304 | C3×#41 | — | 3 | 3 | no | — |
| 305 | C3×#41 | — | 3 | 1 | no | — |
| 306 | C3×#41 | — | 3 | 1 | no | — |
| 307 | C3×#41 | — | 6 | 1 | no | — |
| 308 | C3×#41 | — | 6 | 2 | no | — |
| 309 | C3×#41 | — | 6 | 1 | no | — |
| 310 | C3×#41 | — | 6 | 3 | no | — |
| 311 | C3×#41 | — | 6 | 1 | no | — |
| 312 | C3×#41 | C2×AGL(1,ℤ/9) | 1 | 3 | yes | — |
| 313 | C3×#41 | C2×C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 314 | C2×C3×D4 | — | 3 | 3 | no | — |
| 315 | C2×C3×D4 | — | 3 | 1 | no | — |
| 316 | C2×C3×D4 | — | 3 | 1 | no | — |
| 317 | C2×C3×D4 | — | 6 | 1 | no | — |
| 318 | C2×C3×D4 | — | 6 | 3 | no | — |
| 319 | C2×C3×D4 | — | 6 | 1 | no | — |
| 320 | C2×C3×D4 | — | 6 | 3 | no | — |
| 321 | C2×C3×D4 | — | 6 | 1 | no | — |
| 322 | C2×C3×D4 | — | 6 | 2 | no | — |
| 323 | C2×C3×D4 | — | 6 | 6 | no | — |
| 324 | C2×C3×D4 | — | 27 | 1 | no | — |
| 325 | C2×C3×D4 | — | 54 | 2 | no | — |
| 326 | C2×#67 | — | 18 | 6 | no | — |
| 327 | C2×#67 | — | 18 | 2 | no | — |
| 328 | C2×D12 | — | 9 | 1 | no | — |
| 329 | C2×D12 | — | 9 | 3 | no | — |
| 330 | C3×SD16 | — | 54 | 1 | no | — |
| 331 | C3×SD16 | — | 54 | 1 | no | — |
| 332 | C3×D8 | — | 54 | 1 | no | — |
| 333 | C3×D8 | — | 54 | 1 | no | — |
| 334 | C3×M16 | — | 27 | 1 | no | — |
| 335 | C3×M16 | — | 27 | 1 | no | — |
| 336 | C3×C42 | — | 27 | 1 | no | — |
| 337 | #215 | — | 18 | 3 | no | — |
| 338 | #215 | — | 18 | 3 | no | — |
| 339 | #215 | — | 18 | 1 | no | — |
| 340 | #215 | — | 18 | 1 | no | — |
| 341 | #213 | — | 18 | 3 | no | — |
| 342 | #213 | — | 18 | 1 | no | — |
| 343 | #213 | — | 18 | 1 | no | — |
| 344 | #213 | — | 18 | 3 | no | — |
| 345 | C4×Dic3 | — | 9 | 1 | no | — |
| 346 | C4×Dic3 | — | 9 | 3 | no | — |
| 347 | #208 | — | 9 | 1 | no | — |
| 348 | #208 | — | 9 | 3 | no | — |
| 349 | #208 | — | 9 | 1 | no | — |
| 350 | #208 | — | 9 | 3 | no | — |
| 351 | C22×C32 | — | 3 | 1 | no | — |
| 352 | C22×C32 | — | 3 | 3 | no | — |
| 353 | C22×C32 | — | 3 | 1 | no | — |
| 354 | C22×C32 | — | 6 | 1 | no | — |
| 355 | C22×C32 | — | 6 | 3 | no | — |
| 356 | C22×C32 | — | 6 | 2 | no | — |
| 357 | C22×C32 | — | 6 | 3 | no | — |
| 358 | C22×C32 | — | 6 | 6 | no | — |
| 359 | C22×C32 | — | 6 | 1 | no | — |
| 360 | C22×C32 | — | 6 | 1 | no | — |
| 361 | C22×C32 | — | 12 | 2 | no | — |
| 362 | C22×C32 | — | 12 | 6 | no | — |
| 363 | C22×C32 | — | 12 | 2 | no | — |
| 364 | C22×C32 | — | 24 | 2 | no | — |
| 365 | C22×C32 | — | 24 | 6 | no | — |
| 366 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 367 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 368 | C2×C3×D3 | — | 36 | 3 | no | — |
| 369 | C2×C3×D3 | — | 36 | 6 | no | — |
| 370 | C2×C3×D3 | — | 36 | 2 | no | — |
| 371 | C2×C3×D3 | — | 36 | 1 | no | — |
| 372 | C32×C4 | — | 2 | 1 | no | — |
| 373 | C32×C4 | — | 2 | 2 | no | — |
| 374 | C32×C4 | — | 2 | 1 | no | — |
| 375 | C32×C4 | — | 2 | 1 | no | — |
| 376 | C32×C4 | — | 3 | 1 | no | — |
| 377 | C32×C4 | — | 3 | 3 | no | — |
| 378 | C32×C4 | — | 3 | 1 | no | — |
| 379 | C32×C4 | — | 3 | 3 | no | — |
| 380 | C32×C4 | — | 6 | 3 | no | — |
| 381 | C32×C4 | — | 6 | 1 | no | — |
| 382 | C32×C4 | — | 6 | 3 | no | — |
| 383 | C32×C4 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 384 | C32×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 385 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 386 | C3×Dic3 | — | 18 | 6 | no | — |
| 387 | C3×Dic3 | — | 18 | 2 | no | — |
| 388 | C2×D9 | — | 24 | 3 | no | — |
| 389 | C4×C9 | — | 4 | 3 | no | — |
| 390 | C4×C9 | — | 8 | 3 | no | — |
| 391 | C4×C9 | — | 8 | 6 | no | — |
| 392 | C4×C9 | — | 8 | 3 | no | — |
| 393 | H(5,𝔽2) | C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 394 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 395 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 396 | #127 | — | 27 | 1 | no | — |
| 397 | #104 | — | 27 | 1 | no | — |
| 398 | #104 | — | 27 | 1 | no | — |
| 399 | #100 | — | 27 | 1 | no | — |
| 400 | C33 | #5429 | 1 | 1 | yes | characteristic |
| 401 | 3−1+2 | — | 4 | 3 | no | — |
| 402 | 3−1+2 | — | 8 | 3 | no | — |
| 403 | C3×C9 | — | 4 | 1 | no | — |
| 404 | C3×C9 | — | 8 | 1 | no | — |
| 405 | C23×C3 | — | 3 | 2 | no | — |
| 406 | C23×C3 | — | 3 | 6 | no | — |
| 407 | C23×C3 | — | 3 | 2 | no | — |
| 408 | C23×C3 | — | 6 | 2 | no | — |
| 409 | C23×C3 | — | 6 | 6 | no | — |
| 410 | C23×C3 | — | 54 | 1 | no | — |
| 411 | C22×D3 | — | 18 | 3 | no | — |
| 412 | C22×D3 | — | 18 | 1 | no | — |
| 413 | C3×Q8 | — | 3 | 1 | no | — |
| 414 | C3×Q8 | — | 3 | 1 | no | — |
| 415 | C3×Q8 | — | 6 | 1 | no | — |
| 416 | C3×Q8 | — | 6 | 1 | no | — |
| 417 | C3×Q8 | #611⋊C3 | 1 | 3 | yes | — |
| 418 | C3×Q8 | ((C22⋊C9)⋊C2)⋊C3 | 1 | 3 | yes | — |
| 419 | C3×Q8 | C3×#638 | 1 | 1 | yes | characteristic |
| 420 | C3×Q8 | C3×C3⋊S4 | 1 | 1 | yes | characteristic |
| 421 | C3×D4 | — | 3 | 3 | no | — |
| 422 | C3×D4 | — | 3 | 1 | no | — |
| 423 | C3×D4 | — | 3 | 1 | no | — |
| 424 | C3×D4 | — | 3 | 1 | no | — |
| 425 | C3×D4 | — | 3 | 1 | no | — |
| 426 | C3×D4 | — | 3 | 3 | no | — |
| 427 | C3×D4 | — | 6 | 1 | no | — |
| 428 | C3×D4 | — | 6 | 1 | no | — |
| 429 | C3×D4 | — | 6 | 3 | no | — |
| 430 | C3×D4 | — | 6 | 3 | no | — |
| 431 | C3×D4 | — | 6 | 3 | no | — |
| 432 | C3×D4 | — | 6 | 1 | no | — |
| 433 | C3×D4 | — | 6 | 3 | no | — |
| 434 | C3×D4 | — | 6 | 1 | no | — |
| 435 | C3×D4 | — | 6 | 1 | no | — |
| 436 | C3×D4 | — | 6 | 1 | no | — |
| 437 | C3×D4 | — | 6 | 2 | no | — |
| 438 | C3×D4 | — | 6 | 6 | no | — |
| 439 | C3×D4 | — | 6 | 2 | no | — |
| 440 | C3×D4 | — | 6 | 6 | no | — |
| 441 | C3×D4 | — | 54 | 1 | no | — |
| 442 | C3×D4 | — | 54 | 1 | no | — |
| 443 | C3×D4 | — | 108 | 4 | no | — |
| 444 | C2×C3×C4 | — | 3 | 1 | no | — |
| 445 | C2×C3×C4 | — | 3 | 1 | no | — |
| 446 | C2×C3×C4 | — | 3 | 3 | no | — |
| 447 | C2×C3×C4 | — | 6 | 1 | no | — |
| 448 | C2×C3×C4 | — | 6 | 3 | no | — |
| 449 | C2×C3×C4 | — | 6 | 3 | no | — |
| 450 | C2×C3×C4 | — | 6 | 1 | no | — |
| 451 | C2×C3×C4 | — | 6 | 1 | no | — |
| 452 | C2×C3×C4 | — | 6 | 2 | no | — |
| 453 | C2×C3×C4 | — | 6 | 6 | no | — |
| 454 | C2×C3×C4 | — | 54 | 1 | no | — |
| 455 | #67 | — | 36 | 4 | no | — |
| 456 | #67 | — | 36 | 12 | no | — |
| 457 | C2×Dic3 | — | 18 | 3 | no | — |
| 458 | C2×Dic3 | — | 18 | 1 | no | — |
| 459 | D12 | — | 18 | 3 | no | — |
| 460 | D12 | — | 18 | 1 | no | — |
| 461 | D12 | — | 18 | 1 | no | — |
| 462 | D12 | — | 18 | 3 | no | — |
| 463 | C3×C8 | — | 54 | 1 | no | — |
| 464 | C3×C8 | — | 54 | 1 | no | — |
| 465 | C3⋊C8 | — | 18 | 3 | no | — |
| 466 | C3⋊C8 | — | 18 | 1 | no | — |
| 467 | C3⋊C8 | — | 18 | 1 | no | — |
| 468 | C3⋊C8 | — | 18 | 3 | no | — |
| 469 | C2×C32 | — | 2 | 1 | no | — |
| 470 | C2×C32 | — | 3 | 3 | no | — |
| 471 | C2×C32 | — | 6 | 1 | no | — |
| 472 | C2×C32 | — | 6 | 3 | no | — |
| 473 | C2×C32 | — | 6 | 1 | no | — |
| 474 | C2×C32 | — | 12 | 1 | no | — |
| 475 | C2×C32 | — | 12 | 3 | no | — |
| 476 | C2×C32 | — | 12 | 2 | no | — |
| 477 | C2×C32 | — | 12 | 6 | no | — |
| 478 | C2×C32 | — | 12 | 3 | no | — |
| 479 | C2×C32 | — | 12 | 1 | no | — |
| 480 | C2×C32 | — | 12 | 1 | no | — |
| 481 | C2×C32 | C3×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 482 | C2×C32 | #64269 | 1 | 1 | yes | characteristic |
| 483 | C3⋊D3 | — | 24 | 1 | no | — |
| 484 | C3×D3 | — | 72 | 3 | no | — |
| 485 | C3×D3 | — | 72 | 1 | no | — |
| 486 | C2×C9 | — | 4 | 3 | no | — |
| 487 | C2×C9 | — | 8 | 3 | no | — |
| 488 | D9 | — | 48 | 3 | no | — |
| 489 | #41 | — | 2 | 1 | no | — |
| 490 | #41 | — | 3 | 1 | no | — |
| 491 | #41 | C2×C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 492 | C2×D4 | — | 3 | 1 | no | — |
| 493 | C2×D4 | — | 6 | 1 | no | — |
| 494 | C2×D4 | — | 27 | 1 | no | — |
| 495 | C2×D4 | — | 54 | 2 | no | — |
| 496 | SD16 | — | 54 | 1 | no | — |
| 497 | SD16 | — | 54 | 1 | no | — |
| 498 | D8 | — | 54 | 1 | no | — |
| 499 | D8 | — | 54 | 1 | no | — |
| 500 | M16 | — | 27 | 1 | no | — |
| 501 | M16 | — | 27 | 1 | no | — |
| 502 | C42 | — | 27 | 1 | no | — |
| 503 | C22×C3 | — | 3 | 1 | no | — |
| 504 | C22×C3 | — | 3 | 3 | no | — |
| 505 | C22×C3 | — | 3 | 1 | no | — |
| 506 | C22×C3 | — | 6 | 1 | no | — |
| 507 | C22×C3 | — | 6 | 3 | no | — |
| 508 | C22×C3 | — | 6 | 1 | no | — |
| 509 | C22×C3 | — | 6 | 2 | no | — |
| 510 | C22×C3 | — | 6 | 6 | no | — |
| 511 | C22×C3 | — | 6 | 3 | no | — |
| 512 | C22×C3 | — | 6 | 1 | no | — |
| 513 | C22×C3 | — | 12 | 2 | no | — |
| 514 | C22×C3 | — | 12 | 6 | no | — |
| 515 | C22×C3 | — | 12 | 2 | no | — |
| 516 | C22×C3 | — | 24 | 2 | no | — |
| 517 | C22×C3 | — | 24 | 6 | no | — |
| 518 | C22×C3 | — | 108 | 1 | no | — |
| 519 | C22×C3 | — | 108 | 2 | no | — |
| 520 | C2×D3 | — | 36 | 2 | no | — |
| 521 | C2×D3 | — | 36 | 6 | no | — |
| 522 | C2×D3 | — | 36 | 3 | no | — |
| 523 | C2×D3 | — | 36 | 1 | no | — |
| 524 | C3×C4 | — | 2 | 3 | no | — |
| 525 | C3×C4 | — | 2 | 1 | no | — |
| 526 | C3×C4 | — | 3 | 1 | no | — |
| 527 | C3×C4 | — | 3 | 3 | no | — |
| 528 | C3×C4 | — | 3 | 1 | no | — |
| 529 | C3×C4 | — | 3 | 1 | no | — |
| 530 | C3×C4 | — | 6 | 1 | no | — |
| 531 | C3×C4 | — | 6 | 2 | no | — |
| 532 | C3×C4 | — | 6 | 1 | no | — |
| 533 | C3×C4 | — | 6 | 3 | no | — |
| 534 | C3×C4 | — | 6 | 1 | no | — |
| 535 | C3×C4 | — | 54 | 2 | no | — |
| 536 | C3×C4 | C2×((C22⋊C9)⋊C2)⋊C3 | 1 | 3 | yes | — |
| 537 | C3×C4 | C2×C3×C3⋊S4 | 1 | 1 | yes | characteristic |
| 538 | Dic3 | — | 18 | 2 | no | — |
| 539 | Dic3 | — | 18 | 6 | no | — |
| 540 | C32 | — | 2 | 1 | no | — |
| 541 | C32 | — | 3 | 3 | no | — |
| 542 | C32 | C3×#5429 | 1 | 1 | yes | characteristic |
| 543 | C32 | #10593663 | 1 | 1 | yes | characteristic |
| 544 | C9 | — | 4 | 3 | no | — |
| 545 | C9 | — | 8 | 3 | no | — |
| 546 | C23 | — | 3 | 2 | no | — |
| 547 | C23 | — | 54 | 1 | no | — |
| 548 | Q8 | #10619980 | 1 | 1 | yes | characteristic |
| 549 | Q8 | C3⋊(((C22⋊C9)⋊C2)⋊C3) | 1 | 1 | yes | characteristic |
| 550 | D4 | — | 3 | 1 | no | — |
| 551 | D4 | — | 3 | 1 | no | — |
| 552 | D4 | — | 6 | 1 | no | — |
| 553 | D4 | — | 6 | 1 | no | — |
| 554 | D4 | — | 54 | 1 | no | — |
| 555 | D4 | — | 54 | 1 | no | — |
| 556 | D4 | — | 108 | 4 | no | — |
| 557 | C2×C4 | — | 3 | 1 | no | — |
| 558 | C2×C4 | — | 6 | 1 | no | — |
| 559 | C2×C4 | — | 54 | 1 | no | — |
| 560 | C8 | — | 54 | 1 | no | — |
| 561 | C8 | — | 54 | 1 | no | — |
| 562 | C2×C3 | — | 3 | 1 | no | — |
| 563 | C2×C3 | — | 6 | 1 | no | — |
| 564 | C2×C3 | — | 6 | 1 | no | — |
| 565 | C2×C3 | — | 6 | 3 | no | — |
| 566 | C2×C3 | — | 6 | 1 | no | — |
| 567 | C2×C3 | — | 12 | 1 | no | — |
| 568 | C2×C3 | — | 12 | 3 | no | — |
| 569 | C2×C3 | — | 12 | 2 | no | — |
| 570 | C2×C3 | — | 12 | 1 | no | — |
| 571 | C2×C3 | — | 12 | 6 | no | — |
| 572 | C2×C3 | — | 12 | 1 | no | — |
| 573 | C2×C3 | — | 12 | 3 | no | — |
| 574 | C2×C3 | — | 216 | 1 | no | — |
| 575 | C2×C3 | #63694⋊C3 | 1 | 3 | yes | — |
| 576 | C2×C3 | C3×#64269 | 1 | 1 | yes | characteristic |
| 577 | D3 | — | 72 | 1 | no | — |
| 578 | D3 | — | 72 | 3 | no | — |
| 579 | C22 | — | 3 | 1 | no | — |
| 580 | C22 | — | 6 | 1 | no | — |
| 581 | C22 | — | 12 | 2 | no | — |
| 582 | C22 | — | 108 | 2 | no | — |
| 583 | C22 | — | 108 | 1 | no | — |
| 584 | C4 | — | 2 | 1 | no | — |
| 585 | C4 | — | 3 | 1 | no | — |
| 586 | C4 | — | 54 | 2 | no | — |
| 587 | C4 | C2×C3⋊(((C22⋊C9)⋊C2)⋊C3) | 1 | 1 | yes | characteristic |
| 588 | C3 | — | 3 | 1 | no | — |
| 589 | C3 | — | 6 | 1 | no | — |
| 590 | C3 | #10589531⋊C3 | 1 | 3 | yes | complemented |
| 591 | C3 | C3×#10593663 | 1 | 1 | yes | characteristic |
| 592 | C2 | — | 6 | 1 | no | — |
| 593 | C2 | — | 12 | 1 | no | — |
| 594 | C2 | — | 216 | 1 | no | — |
| 595 | C2 | #72220152 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72252951 | C2 | semidirect |
| 2. #72252949 | C2 | semidirect |
| 3. C3×#11722576 | C2 | semidirect |
| 5. #13147076 | C3 | semidirect |
| 16. #11722576 | D3 | semidirect |
| 18. C3×#63700 | C2×C3 | semidirect |
| 19. #11722391 | C2×C3 | semidirect |
| 24. C3⋊#63422 | C2×C3 | semidirect |
| 28. C3×#6204 | D4 | semidirect |
| 77. #63700 | C3×D3 | semidirect |
| 112. #6204 | #67 | semidirect |
| 114. C3×Q8⋊C9 | C3×D4 | semidirect |
| 199. C3×H(5,𝔽2) | AGL(1,ℤ/9) | semidirect |
| 288. Q8⋊C9 | C3×#67 | semidirect |
| 393. H(5,𝔽2) | C3⋊AGL(1,ℤ/9) | semidirect |
| 590. C3 | #10589531⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72252951 | 2 |
| #72252949 | 2 |
| C3×#11722576 | 2 |
| C3×#10592940 | 3 |
| #13147076 | 3 |
| #10589531⋊C3 | 3 |
| #13047985 | 4 |