Finite Group DatabasebetaFinite Group DatabasebetaOrder 3888.
1064 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 43 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 | #14518198 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14518118 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14518069 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3⋊D3×C3⋊S4 | — | 3 | 1 | no | maximal |
| 5 | #13049222 | — | 3 | 3 | no | maximal |
| 6 | #13048780 | — | 3 | 1 | no | maximal |
| 7 | (C3×A4)⋊H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | #11757731 | — | 4 | 1 | no | maximal |
| 9 | C3×A4×C3⋊D3 | — | 3 | 1 | no | — |
| 10 | C3⋊(C3⋊(C3⋊S4)) | D3 | 1 | 1 | yes | characteristic, complemented |
| 11 | C32×C3⋊S4 | — | 3 | 1 | no | — |
| 12 | C22×C3⋊((C3⋊D3)⋊C3) | D3 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×#66432 | — | 3 | 1 | no | — |
| 14 | C3⋊((C3⋊D3)⋊A4) | D3 | 1 | 3 | yes | complemented |
| 15 | C3⋊((C3⋊S4)⋊C3) | — | 3 | 3 | no | — |
| 16 | C3×#6258 | — | 3 | 3 | no | — |
| 17 | C3×#6258 | — | 6 | 1 | no | — |
| 18 | C3×#6258 | — | 6 | 3 | no | — |
| 19 | C3×#6235 | — | 3 | 1 | no | — |
| 20 | #10619977 | — | 3 | 1 | no | — |
| 21 | #10619904 | — | 3 | 1 | no | — |
| 22 | #10619902 | — | 3 | 1 | no | — |
| 23 | #10619901 | — | 3 | 1 | no | — |
| 24 | #92338 | — | 4 | 1 | no | — |
| 25 | #92301 | — | 4 | 1 | no | — |
| 26 | #92258 | — | 4 | 1 | no | — |
| 27 | D3×C3⋊S4 | — | 9 | 3 | no | — |
| 28 | D3×C3⋊S4 | — | 9 | 1 | no | — |
| 29 | C3⋊D3×S4 | — | 9 | 3 | no | — |
| 30 | #89039 | — | 9 | 1 | no | — |
| 31 | C3⋊D3×#67 | — | 9 | 1 | no | — |
| 32 | ((C3⋊S4)⋊C3)⋊C2 | — | 9 | 3 | no | — |
| 33 | #88676 | — | 9 | 1 | no | — |
| 34 | C33×A4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C3⋊D32 | — | 12 | 1 | no | — |
| 36 | C22×C3×H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×C3×#272 | — | 3 | 1 | no | — |
| 38 | C2×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 39 | C2×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 40 | C2×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 41 | C3×C22⋊H(3,𝔽3) | — | 2 | 1 | no | — |
| 42 | C3×C22⋊H(3,𝔽3) | — | 2 | 3 | no | — |
| 43 | C3×C22⋊H(3,𝔽3) | C2×D3 | 1 | 3 | yes | complemented |
| 44 | #66432 | — | 6 | 1 | no | — |
| 45 | #66432 | — | 6 | 1 | no | — |
| 46 | #66432 | — | 12 | 3 | no | — |
| 47 | C3×#1084 | — | 3 | 1 | no | — |
| 48 | C3⋊((C3⋊Dic3)⋊C3) | — | 3 | 1 | no | — |
| 49 | C32⋊H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 50 | C22×C3⋊(C3⋊D3) | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | C22×C3×C3⋊D3 | — | 3 | 1 | no | — |
| 52 | C2×D3×C3⋊D3 | — | 9 | 1 | no | — |
| 53 | C2×D3×C3⋊D3 | — | 9 | 1 | no | — |
| 54 | A4×C3⋊D3 | — | 3 | 3 | no | — |
| 55 | C3×D3×A4 | — | 9 | 1 | no | — |
| 56 | C3×D3×A4 | — | 9 | 3 | no | — |
| 57 | C3⋊(C3⋊S4) | — | 3 | 3 | no | — |
| 58 | C3⋊(C3⋊S4) | — | 9 | 1 | no | — |
| 59 | C3⋊(C3⋊S4) | — | 9 | 3 | no | — |
| 60 | C3⋊(C3⋊S4) | — | 18 | 1 | no | — |
| 61 | C3⋊(C3⋊S4) | — | 18 | 3 | no | — |
| 62 | C3×C3⋊S4 | — | 3 | 1 | no | — |
| 63 | C3×C3⋊S4 | — | 3 | 3 | no | — |
| 64 | C32×S4 | — | 9 | 3 | no | — |
| 65 | C32×S4 | — | 18 | 3 | no | — |
| 66 | #6312 | — | 3 | 1 | no | — |
| 67 | C3×#638 | — | 9 | 1 | no | — |
| 68 | C32×#67 | — | 9 | 1 | no | — |
| 69 | C32×#67 | — | 9 | 1 | no | — |
| 70 | C32×#67 | — | 18 | 1 | no | — |
| 71 | #6292 | — | 9 | 1 | no | — |
| 72 | #6292 | — | 9 | 1 | no | — |
| 73 | #6291 | — | 9 | 1 | no | — |
| 74 | #6290 | — | 9 | 1 | no | — |
| 75 | #6289 | — | 9 | 1 | no | — |
| 76 | Dic3×C3⋊D3 | — | 9 | 1 | no | — |
| 77 | C22×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 78 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 79 | (C3⋊D3)⋊A4 | — | 9 | 3 | no | — |
| 80 | #6258 | — | 3 | 3 | no | — |
| 81 | #6258 | — | 6 | 1 | no | — |
| 82 | #6258 | — | 6 | 3 | no | — |
| 83 | (C3⋊S4)⋊C3 | — | 9 | 3 | no | — |
| 84 | (C3⋊S4)⋊C3 | — | 18 | 3 | no | — |
| 85 | #6235 | — | 3 | 1 | no | — |
| 86 | #638⋊C3 | — | 9 | 1 | no | — |
| 87 | #638⋊C3 | — | 18 | 1 | no | — |
| 88 | #6200 | — | 9 | 1 | no | — |
| 89 | #6198 | — | 9 | 1 | no | — |
| 90 | ((C3⋊D3)⋊C3)⋊C4 | — | 9 | 1 | no | — |
| 91 | C3⋊(C3⋊(C3⋊D3)) | — | 4 | 1 | no | — |
| 92 | C32×C3⋊D3 | — | 12 | 1 | no | — |
| 93 | C32×C3⋊D3 | — | 12 | 1 | no | — |
| 94 | C2×C3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 95 | C3×#272 | — | 6 | 1 | no | — |
| 96 | C3×#272 | — | 12 | 3 | no | — |
| 97 | C3×#272 | — | 24 | 1 | no | — |
| 98 | C3×#272 | — | 24 | 3 | no | — |
| 99 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 100 | C3⋊((C3⋊D3)⋊C3) | — | 4 | 3 | no | — |
| 101 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 102 | C3⋊((C3⋊D3)⋊C3) | — | 12 | 3 | no | — |
| 103 | C3⋊((C3⋊D3)⋊C3) | S4 | 1 | 1 | yes | characteristic, complemented |
| 104 | C2×C3⋊S4 | — | 27 | 1 | no | — |
| 105 | D3×S4 | — | 27 | 3 | no | — |
| 106 | D3×S4 | — | 27 | 3 | no | — |
| 107 | D3×S4 | — | 27 | 6 | no | — |
| 108 | D4×C3⋊D3 | — | 27 | 1 | no | — |
| 109 | #3811 | — | 27 | 3 | no | — |
| 110 | #3811 | — | 27 | 1 | no | — |
| 111 | D3×#67 | — | 27 | 1 | no | — |
| 112 | D3×#67 | — | 27 | 3 | no | — |
| 113 | C22×C33 | — | 2 | 1 | no | — |
| 114 | C22×C33 | D32 | 1 | 1 | yes | characteristic |
| 115 | C22×C33 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 116 | C2×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 117 | C2×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 118 | C2×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 119 | C2×C3×C3⋊D3 | — | 9 | 1 | no | — |
| 120 | C2×C3×C3⋊D3 | — | 9 | 1 | no | — |
| 121 | C2×C3×C3⋊D3 | — | 9 | 1 | no | — |
| 122 | C2×C32×D3 | — | 9 | 1 | no | — |
| 123 | C2×C32×D3 | — | 9 | 1 | no | — |
| 124 | C2×C32×D3 | — | 18 | 1 | no | — |
| 125 | C32×A4 | — | 2 | 3 | no | — |
| 126 | C32×A4 | — | 3 | 1 | no | — |
| 127 | C32×A4 | — | 3 | 3 | no | — |
| 128 | C32×A4 | — | 6 | 3 | no | — |
| 129 | C32×A4 | — | 6 | 1 | no | — |
| 130 | C32×A4 | D32 | 1 | 3 | yes | — |
| 131 | D3×C3⋊D3 | — | 18 | 1 | no | — |
| 132 | D3×C3⋊D3 | — | 18 | 1 | no | — |
| 133 | D3×C3⋊D3 | — | 18 | 1 | no | — |
| 134 | D3×C3⋊D3 | — | 18 | 1 | no | — |
| 135 | D3×C3⋊D3 | — | 36 | 3 | no | — |
| 136 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 137 | D3×C3⋊D3 | — | 36 | 3 | no | — |
| 138 | C3⋊(C3⋊Dic3) | — | 3 | 1 | no | — |
| 139 | C3×C3⋊Dic3 | — | 9 | 1 | no | — |
| 140 | C32×Dic3 | — | 9 | 1 | no | — |
| 141 | C32×Dic3 | — | 9 | 1 | no | — |
| 142 | C32×Dic3 | — | 18 | 1 | no | — |
| 143 | C22×H(3,𝔽3) | — | 3 | 1 | no | — |
| 144 | C22×H(3,𝔽3) | — | 6 | 1 | no | — |
| 145 | C2×#272 | — | 3 | 1 | no | — |
| 146 | C2×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 147 | C2×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 148 | C2×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 149 | C2×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 150 | C2×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 151 | C2×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 152 | C22⋊H(3,𝔽3) | — | 3 | 3 | no | — |
| 153 | C22⋊H(3,𝔽3) | — | 6 | 3 | no | — |
| 154 | C22⋊H(3,𝔽3) | — | 6 | 1 | no | — |
| 155 | C22⋊H(3,𝔽3) | — | 6 | 3 | no | — |
| 156 | C22⋊H(3,𝔽3) | — | 12 | 3 | no | — |
| 157 | C22⋊H(3,𝔽3) | — | 12 | 1 | no | — |
| 158 | ((C3⋊D3)⋊C3)⋊C2 | — | 18 | 1 | no | — |
| 159 | ((C3⋊D3)⋊C3)⋊C2 | — | 18 | 1 | no | — |
| 160 | ((C3⋊D3)⋊C3)⋊C2 | — | 36 | 3 | no | — |
| 161 | #1084 | — | 3 | 1 | no | — |
| 162 | (C3⋊Dic3)⋊C3 | — | 9 | 1 | no | — |
| 163 | (C3⋊Dic3)⋊C3 | — | 18 | 1 | no | — |
| 164 | C34 | — | 4 | 1 | no | — |
| 165 | C3×H(3,𝔽3) | — | 4 | 3 | no | — |
| 166 | C3×H(3,𝔽3) | — | 8 | 3 | no | — |
| 167 | C3×H(3,𝔽3) | — | 8 | 1 | no | — |
| 168 | C3×H(3,𝔽3) | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 169 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 170 | C22×C3⋊D3 | — | 9 | 1 | no | — |
| 171 | C22×C3⋊D3 | — | 9 | 3 | no | — |
| 172 | C22×C3⋊D3 | — | 27 | 1 | no | — |
| 173 | C22×C3×D3 | — | 9 | 3 | no | — |
| 174 | C22×C3×D3 | — | 9 | 1 | no | — |
| 175 | C2×C3×A4 | — | 27 | 1 | no | — |
| 176 | C2×D32 | — | 27 | 1 | no | — |
| 177 | C2×D32 | — | 27 | 1 | no | — |
| 178 | C2×D32 | — | 27 | 3 | no | — |
| 179 | C2×D32 | — | 27 | 3 | no | — |
| 180 | D3×A4 | — | 9 | 6 | no | — |
| 181 | D3×A4 | — | 9 | 3 | no | — |
| 182 | D3×A4 | — | 9 | 3 | no | — |
| 183 | C3⋊S4 | — | 3 | 1 | no | — |
| 184 | C3⋊S4 | — | 9 | 3 | no | — |
| 185 | C3⋊S4 | — | 18 | 3 | no | — |
| 186 | C3⋊S4 | — | 27 | 3 | no | — |
| 187 | C3⋊S4 | — | 27 | 6 | no | — |
| 188 | C3⋊S4 | — | 27 | 1 | no | — |
| 189 | C3⋊S4 | — | 54 | 3 | no | — |
| 190 | C3⋊S4 | — | 54 | 1 | no | — |
| 191 | C3⋊S4 | — | 54 | 3 | no | — |
| 192 | C3⋊S4 | — | 54 | 3 | no | — |
| 193 | C3⋊S4 | — | 54 | 3 | no | — |
| 194 | C3×S4 | — | 9 | 6 | no | — |
| 195 | C3×S4 | — | 9 | 3 | no | — |
| 196 | C3×S4 | — | 9 | 3 | no | — |
| 197 | C3×S4 | — | 18 | 3 | no | — |
| 198 | C3×S4 | — | 18 | 3 | no | — |
| 199 | C3×S4 | — | 18 | 6 | no | — |
| 200 | C32×D4 | — | 27 | 1 | no | — |
| 201 | #638 | — | 9 | 1 | no | — |
| 202 | #638 | — | 9 | 1 | no | — |
| 203 | #638 | — | 18 | 1 | no | — |
| 204 | #638 | — | 27 | 3 | no | — |
| 205 | #638 | — | 27 | 1 | no | — |
| 206 | C4⋊(C3⋊D3) | — | 27 | 1 | no | — |
| 207 | C4×C3⋊D3 | — | 27 | 1 | no | — |
| 208 | C3×#67 | — | 9 | 1 | no | — |
| 209 | C3×#67 | — | 9 | 3 | no | — |
| 210 | C3×#67 | — | 9 | 3 | no | — |
| 211 | C3×#67 | — | 9 | 1 | no | — |
| 212 | C3×#67 | — | 18 | 1 | no | — |
| 213 | C3×#67 | — | 18 | 3 | no | — |
| 214 | C3×#67 | — | 27 | 1 | no | — |
| 215 | C3×#67 | — | 27 | 3 | no | — |
| 216 | #626 | — | 27 | 1 | no | — |
| 217 | #626 | — | 27 | 1 | no | — |
| 218 | #626 | — | 27 | 3 | no | — |
| 219 | #626 | — | 27 | 3 | no | — |
| 220 | #626 | — | 27 | 1 | no | — |
| 221 | #626 | — | 27 | 3 | no | — |
| 222 | #625 | — | 27 | 1 | no | — |
| 223 | #625 | — | 27 | 3 | no | — |
| 224 | #624 | — | 27 | 1 | no | — |
| 225 | #624 | — | 27 | 3 | no | — |
| 226 | D3×Dic3 | — | 27 | 1 | no | — |
| 227 | D3×Dic3 | — | 27 | 3 | no | — |
| 228 | C2×C33 | — | 3 | 1 | no | — |
| 229 | C2×C33 | — | 3 | 1 | no | — |
| 230 | C2×C33 | — | 6 | 1 | no | — |
| 231 | C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 232 | C3⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 233 | C3⋊(C3⋊D3) | — | 12 | 3 | no | — |
| 234 | C3⋊(C3⋊D3) | — | 36 | 1 | no | — |
| 235 | C3⋊(C3⋊D3) | — | 36 | 3 | no | — |
| 236 | C3⋊(C3⋊D3) | — | 72 | 1 | no | — |
| 237 | C3⋊(C3⋊D3) | — | 72 | 3 | no | — |
| 238 | C3⋊(C3⋊D3) | C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 239 | C3×C3⋊D3 | — | 3 | 1 | no | — |
| 240 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 241 | C3×C3⋊D3 | — | 12 | 3 | no | — |
| 242 | C3×C3⋊D3 | — | 12 | 1 | no | — |
| 243 | C3×C3⋊D3 | — | 12 | 3 | no | — |
| 244 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 245 | C32×D3 | — | 18 | 1 | no | — |
| 246 | C32×D3 | — | 18 | 1 | no | — |
| 247 | C32×D3 | — | 36 | 3 | no | — |
| 248 | C32×D3 | — | 36 | 1 | no | — |
| 249 | C32×D3 | — | 36 | 1 | no | — |
| 250 | C32×D3 | — | 36 | 3 | no | — |
| 251 | C32×D3 | — | 72 | 3 | no | — |
| 252 | C2×H(3,𝔽3) | — | 3 | 1 | no | — |
| 253 | C2×H(3,𝔽3) | — | 6 | 1 | no | — |
| 254 | C2×H(3,𝔽3) | — | 6 | 1 | no | — |
| 255 | C2×H(3,𝔽3) | — | 12 | 1 | no | — |
| 256 | #272 | — | 6 | 1 | no | — |
| 257 | #272 | — | 12 | 3 | no | — |
| 258 | #272 | — | 24 | 1 | no | — |
| 259 | #272 | — | 24 | 3 | no | — |
| 260 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 261 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 262 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 263 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 264 | (C3⋊D3)⋊C3 | — | 36 | 3 | no | — |
| 265 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 266 | (C3⋊D3)⋊C3 | — | 36 | 3 | no | — |
| 267 | (C3⋊D3)⋊C3 | — | 72 | 3 | no | — |
| 268 | C2×S4 | — | 81 | 3 | no | — |
| 269 | C2×#67 | — | 81 | 1 | no | — |
| 270 | D3×D4 | — | 81 | 1 | no | — |
| 271 | D3×D4 | — | 81 | 1 | no | — |
| 272 | D3×D4 | — | 81 | 3 | no | — |
| 273 | C22×C32 | — | 2 | 1 | no | — |
| 274 | C22×C32 | — | 3 | 3 | no | — |
| 275 | C22×C32 | — | 3 | 1 | no | — |
| 276 | C22×C32 | — | 3 | 3 | no | — |
| 277 | C22×C32 | — | 6 | 1 | no | — |
| 278 | C22×C32 | — | 6 | 3 | no | — |
| 279 | C22×C32 | — | 27 | 1 | no | — |
| 280 | C22×C32 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 281 | C22×C32 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 282 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 283 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 284 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 285 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 286 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 287 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 288 | C2×C3⋊D3 | — | 18 | 1 | no | — |
| 289 | C2×C3⋊D3 | — | 18 | 1 | no | — |
| 290 | C2×C3⋊D3 | — | 18 | 1 | no | — |
| 291 | C2×C3⋊D3 | — | 27 | 3 | no | — |
| 292 | C2×C3⋊D3 | — | 27 | 3 | no | — |
| 293 | C2×C3⋊D3 | — | 27 | 3 | no | — |
| 294 | C2×C3⋊D3 | — | 54 | 1 | no | — |
| 295 | C2×C3⋊D3 | — | 54 | 1 | no | — |
| 296 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 297 | C2×C3×D3 | — | 9 | 1 | no | — |
| 298 | C2×C3×D3 | — | 9 | 1 | no | — |
| 299 | C2×C3×D3 | — | 9 | 3 | no | — |
| 300 | C2×C3×D3 | — | 9 | 3 | no | — |
| 301 | C2×C3×D3 | — | 18 | 1 | no | — |
| 302 | C2×C3×D3 | — | 18 | 3 | no | — |
| 303 | C2×C3×D3 | — | 27 | 1 | no | — |
| 304 | C2×C3×D3 | — | 27 | 3 | no | — |
| 305 | C2×C3×D3 | — | 27 | 1 | no | — |
| 306 | C2×C3×D3 | — | 27 | 3 | no | — |
| 307 | C2×C3×D3 | — | 27 | 1 | no | — |
| 308 | C2×C3×D3 | — | 27 | 3 | no | — |
| 309 | C3×A4 | — | 2 | 3 | no | — |
| 310 | C3×A4 | — | 3 | 1 | no | — |
| 311 | C3×A4 | — | 3 | 6 | no | — |
| 312 | C3×A4 | — | 3 | 3 | no | — |
| 313 | C3×A4 | — | 6 | 3 | no | — |
| 314 | C3×A4 | — | 6 | 3 | no | — |
| 315 | C3×A4 | — | 6 | 3 | no | — |
| 316 | C3×A4 | — | 6 | 1 | no | — |
| 317 | C3×A4 | — | 6 | 3 | no | — |
| 318 | C3×A4 | — | 6 | 3 | no | — |
| 319 | C3×A4 | — | 6 | 6 | no | — |
| 320 | C3×A4 | — | 6 | 3 | no | — |
| 321 | C3×A4 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | complemented |
| 322 | D32 | — | 54 | 1 | no | — |
| 323 | D32 | — | 54 | 3 | no | — |
| 324 | D32 | — | 54 | 1 | no | — |
| 325 | D32 | — | 54 | 3 | no | — |
| 326 | D32 | — | 54 | 1 | no | — |
| 327 | D32 | — | 54 | 1 | no | — |
| 328 | D32 | — | 54 | 3 | no | — |
| 329 | D32 | — | 54 | 3 | no | — |
| 330 | D32 | — | 108 | 3 | no | — |
| 331 | D32 | — | 108 | 6 | no | — |
| 332 | D32 | — | 108 | 3 | no | — |
| 333 | C32×C4 | — | 27 | 1 | no | — |
| 334 | C3⋊Dic3 | — | 9 | 1 | no | — |
| 335 | C3⋊Dic3 | — | 9 | 1 | no | — |
| 336 | C3⋊Dic3 | — | 18 | 1 | no | — |
| 337 | C3⋊Dic3 | — | 27 | 3 | no | — |
| 338 | C3×Dic3 | — | 9 | 1 | no | — |
| 339 | C3×Dic3 | — | 9 | 1 | no | — |
| 340 | C3×Dic3 | — | 9 | 3 | no | — |
| 341 | C3×Dic3 | — | 9 | 3 | no | — |
| 342 | C3×Dic3 | — | 18 | 1 | no | — |
| 343 | C3×Dic3 | — | 18 | 3 | no | — |
| 344 | C3×Dic3 | — | 27 | 1 | no | — |
| 345 | C3×Dic3 | — | 27 | 3 | no | — |
| 346 | C33 | — | 2 | 1 | no | — |
| 347 | C33 | — | 4 | 3 | no | — |
| 348 | C33 | — | 8 | 3 | no | — |
| 349 | C33 | — | 12 | 3 | no | — |
| 350 | C33 | — | 12 | 1 | no | — |
| 351 | C33 | — | 24 | 1 | no | — |
| 352 | C33 | — | 24 | 3 | no | — |
| 353 | C33 | D3×S4 | 1 | 1 | yes | characteristic |
| 354 | C33 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 355 | H(3,𝔽3) | — | 3 | 1 | no | — |
| 356 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 357 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 358 | H(3,𝔽3) | — | 24 | 3 | no | — |
| 359 | H(3,𝔽3) | — | 24 | 3 | no | — |
| 360 | H(3,𝔽3) | — | 24 | 1 | no | — |
| 361 | H(3,𝔽3) | — | 48 | 1 | no | — |
| 362 | H(3,𝔽3) | — | 48 | 3 | no | — |
| 363 | C23×C3 | — | 27 | 1 | no | — |
| 364 | C22×D3 | — | 9 | 1 | no | — |
| 365 | C22×D3 | — | 9 | 3 | no | — |
| 366 | C22×D3 | — | 81 | 1 | no | — |
| 367 | C22×D3 | — | 81 | 1 | no | — |
| 368 | C22×D3 | — | 81 | 1 | no | — |
| 369 | C22×D3 | — | 81 | 1 | no | — |
| 370 | C22×D3 | — | 81 | 3 | no | — |
| 371 | C2×A4 | — | 27 | 3 | no | — |
| 372 | S4 | — | 9 | 3 | no | — |
| 373 | S4 | — | 18 | 3 | no | — |
| 374 | S4 | — | 81 | 3 | no | — |
| 375 | S4 | — | 162 | 3 | no | — |
| 376 | C3×D4 | — | 27 | 3 | no | — |
| 377 | C3×D4 | — | 27 | 1 | no | — |
| 378 | C3×D4 | — | 81 | 1 | no | — |
| 379 | #67 | — | 9 | 1 | no | — |
| 380 | #67 | — | 9 | 1 | no | — |
| 381 | #67 | — | 18 | 1 | no | — |
| 382 | #67 | — | 27 | 1 | no | — |
| 383 | #67 | — | 27 | 3 | no | — |
| 384 | #67 | — | 81 | 1 | no | — |
| 385 | #67 | — | 81 | 1 | no | — |
| 386 | #67 | — | 81 | 1 | no | — |
| 387 | #67 | — | 81 | 1 | no | — |
| 388 | #67 | — | 81 | 3 | no | — |
| 389 | #67 | — | 81 | 1 | no | — |
| 390 | #67 | — | 162 | 1 | no | — |
| 391 | C2×Dic3 | — | 81 | 1 | no | — |
| 392 | D12 | — | 81 | 1 | no | — |
| 393 | D12 | — | 81 | 3 | no | — |
| 394 | D12 | — | 81 | 1 | no | — |
| 395 | C4×D3 | — | 81 | 1 | no | — |
| 396 | C4×D3 | — | 81 | 1 | no | — |
| 397 | C4×D3 | — | 81 | 3 | no | — |
| 398 | C2×C32 | — | 3 | 1 | no | — |
| 399 | C2×C32 | — | 3 | 1 | no | — |
| 400 | C2×C32 | — | 3 | 1 | no | — |
| 401 | C2×C32 | — | 6 | 1 | no | — |
| 402 | C2×C32 | — | 6 | 1 | no | — |
| 403 | C2×C32 | — | 6 | 1 | no | — |
| 404 | C2×C32 | — | 9 | 3 | no | — |
| 405 | C2×C32 | — | 9 | 3 | no | — |
| 406 | C2×C32 | — | 12 | 1 | no | — |
| 407 | C2×C32 | — | 18 | 3 | no | — |
| 408 | C2×C32 | — | 54 | 1 | no | — |
| 409 | C2×C32 | — | 108 | 1 | no | — |
| 410 | C3⋊D3 | — | 3 | 1 | no | — |
| 411 | C3⋊D3 | — | 9 | 1 | no | — |
| 412 | C3⋊D3 | — | 9 | 3 | no | — |
| 413 | C3⋊D3 | — | 9 | 1 | no | — |
| 414 | C3⋊D3 | — | 9 | 1 | no | — |
| 415 | C3⋊D3 | — | 12 | 1 | no | — |
| 416 | C3⋊D3 | — | 18 | 1 | no | — |
| 417 | C3⋊D3 | — | 18 | 1 | no | — |
| 418 | C3⋊D3 | — | 18 | 1 | no | — |
| 419 | C3⋊D3 | — | 27 | 3 | no | — |
| 420 | C3⋊D3 | — | 36 | 1 | no | — |
| 421 | C3⋊D3 | — | 36 | 3 | no | — |
| 422 | C3⋊D3 | — | 54 | 3 | no | — |
| 423 | C3⋊D3 | — | 72 | 3 | no | — |
| 424 | C3⋊D3 | — | 108 | 6 | no | — |
| 425 | C3⋊D3 | — | 108 | 3 | no | — |
| 426 | C3⋊D3 | — | 108 | 1 | no | — |
| 427 | C3⋊D3 | — | 216 | 3 | no | — |
| 428 | C3⋊D3 | — | 216 | 3 | no | — |
| 429 | C3⋊D3 | — | 216 | 3 | no | — |
| 430 | C3⋊D3 | — | 216 | 3 | no | — |
| 431 | C3⋊D3 | — | 216 | 1 | no | — |
| 432 | C3×D3 | — | 9 | 3 | no | — |
| 433 | C3×D3 | — | 9 | 1 | no | — |
| 434 | C3×D3 | — | 18 | 1 | no | — |
| 435 | C3×D3 | — | 18 | 3 | no | — |
| 436 | C3×D3 | — | 18 | 3 | no | — |
| 437 | C3×D3 | — | 18 | 1 | no | — |
| 438 | C3×D3 | — | 27 | 3 | no | — |
| 439 | C3×D3 | — | 27 | 1 | no | — |
| 440 | C3×D3 | — | 36 | 3 | no | — |
| 441 | C3×D3 | — | 36 | 6 | no | — |
| 442 | C3×D3 | — | 36 | 3 | no | — |
| 443 | C3×D3 | — | 36 | 3 | no | — |
| 444 | C3×D3 | — | 36 | 1 | no | — |
| 445 | C3×D3 | — | 36 | 3 | no | — |
| 446 | C3×D3 | — | 36 | 6 | no | — |
| 447 | C3×D3 | — | 36 | 3 | no | — |
| 448 | C3×D3 | — | 54 | 1 | no | — |
| 449 | C3×D3 | — | 54 | 3 | no | — |
| 450 | C3×D3 | — | 72 | 3 | no | — |
| 451 | C3×D3 | — | 72 | 6 | no | — |
| 452 | C3×D3 | — | 72 | 3 | no | — |
| 453 | C2×D4 | — | 243 | 1 | no | Sylow |
| 454 | C22×C3 | — | 3 | 1 | no | — |
| 455 | C22×C3 | — | 6 | 1 | no | — |
| 456 | C22×C3 | — | 9 | 1 | no | — |
| 457 | C22×C3 | — | 18 | 1 | no | — |
| 458 | C22×C3 | — | 27 | 3 | no | — |
| 459 | C22×C3 | — | 27 | 1 | no | — |
| 460 | C22×C3 | — | 81 | 1 | no | — |
| 461 | C22×C3 | — | 81 | 1 | no | — |
| 462 | C22×C3 | — | 81 | 1 | no | — |
| 463 | C22×C3 | ((C3⋊D3)⋊C3)⋊D3 | 1 | 3 | yes | — |
| 464 | C22×C3 | ((C3⋊D3)⋊C3)⋊D3 | 1 | 1 | yes | characteristic |
| 465 | C2×D3 | — | 9 | 1 | no | — |
| 466 | C2×D3 | — | 9 | 1 | no | — |
| 467 | C2×D3 | — | 18 | 1 | no | — |
| 468 | C2×D3 | — | 27 | 1 | no | — |
| 469 | C2×D3 | — | 27 | 3 | no | — |
| 470 | C2×D3 | — | 27 | 1 | no | — |
| 471 | C2×D3 | — | 27 | 3 | no | — |
| 472 | C2×D3 | — | 27 | 1 | no | — |
| 473 | C2×D3 | — | 27 | 3 | no | — |
| 474 | C2×D3 | — | 324 | 3 | no | — |
| 475 | C2×D3 | — | 81 | 1 | no | — |
| 476 | C2×D3 | — | 81 | 1 | no | — |
| 477 | C2×D3 | — | 81 | 1 | no | — |
| 478 | C2×D3 | — | 162 | 1 | no | — |
| 479 | C2×D3 | — | 162 | 1 | no | — |
| 480 | C2×D3 | — | 162 | 1 | no | — |
| 481 | C2×D3 | — | 162 | 3 | no | — |
| 482 | C2×D3 | — | 162 | 1 | no | — |
| 483 | C2×D3 | — | 162 | 1 | no | — |
| 484 | C2×D3 | — | 162 | 1 | no | — |
| 485 | C2×D3 | — | 162 | 1 | no | — |
| 486 | C2×D3 | — | 162 | 1 | no | — |
| 487 | C2×D3 | — | 162 | 3 | no | — |
| 488 | C2×D3 | — | 162 | 1 | no | — |
| 489 | A4 | — | 3 | 3 | no | — |
| 490 | A4 | — | 6 | 3 | no | — |
| 491 | A4 | — | 18 | 3 | no | — |
| 492 | C3×C4 | — | 27 | 3 | no | — |
| 493 | C3×C4 | — | 27 | 1 | no | — |
| 494 | C3×C4 | — | 81 | 1 | no | — |
| 495 | Dic3 | — | 9 | 1 | no | — |
| 496 | Dic3 | — | 9 | 1 | no | — |
| 497 | Dic3 | — | 18 | 1 | no | — |
| 498 | Dic3 | — | 27 | 1 | no | — |
| 499 | Dic3 | — | 27 | 3 | no | — |
| 500 | Dic3 | — | 81 | 1 | no | — |
| 501 | Dic3 | — | 162 | 1 | no | — |
| 502 | C32 | — | 2 | 1 | no | — |
| 503 | C32 | — | 3 | 3 | no | — |
| 504 | C32 | — | 3 | 3 | no | — |
| 505 | C32 | — | 3 | 1 | no | — |
| 506 | C32 | — | 4 | 3 | no | — |
| 507 | C32 | — | 6 | 3 | no | — |
| 508 | C32 | — | 6 | 1 | no | — |
| 509 | C32 | — | 8 | 3 | no | — |
| 510 | C32 | — | 12 | 1 | no | — |
| 511 | C32 | — | 12 | 6 | no | — |
| 512 | C32 | — | 12 | 3 | no | — |
| 513 | C32 | — | 24 | 3 | no | — |
| 514 | C32 | — | 24 | 1 | no | — |
| 515 | C32 | — | 24 | 3 | no | — |
| 516 | C32 | — | 24 | 3 | no | — |
| 517 | C32 | — | 24 | 3 | no | — |
| 518 | C32 | — | 24 | 3 | no | — |
| 519 | C32 | — | 24 | 6 | no | — |
| 520 | C32 | — | 24 | 3 | no | — |
| 521 | C32 | ((C3⋊S4)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 522 | C32 | D3×C3⋊S4 | 1 | 1 | yes | characteristic |
| 523 | C23 | — | 27 | 1 | no | — |
| 524 | C23 | — | 243 | 1 | no | — |
| 525 | D4 | — | 27 | 1 | no | — |
| 526 | D4 | — | 81 | 1 | no | — |
| 527 | D4 | — | 243 | 1 | no | — |
| 528 | D4 | — | 243 | 1 | no | — |
| 529 | C2×C4 | — | 243 | 1 | no | — |
| 530 | C2×C3 | — | 3 | 3 | no | — |
| 531 | C2×C3 | — | 3 | 1 | no | — |
| 532 | C2×C3 | — | 9 | 1 | no | — |
| 533 | C2×C3 | — | 9 | 1 | no | — |
| 534 | C2×C3 | — | 18 | 1 | no | — |
| 535 | C2×C3 | — | 18 | 1 | no | — |
| 536 | C2×C3 | — | 18 | 1 | no | — |
| 537 | C2×C3 | — | 27 | 1 | no | — |
| 538 | C2×C3 | — | 36 | 1 | no | — |
| 539 | C2×C3 | — | 54 | 3 | no | — |
| 540 | C2×C3 | — | 54 | 1 | no | — |
| 541 | C2×C3 | — | 81 | 1 | no | — |
| 542 | C2×C3 | — | 108 | 3 | no | — |
| 543 | C2×C3 | — | 162 | 1 | no | — |
| 544 | D3 | — | 9 | 3 | no | — |
| 545 | D3 | — | 9 | 1 | no | — |
| 546 | D3 | — | 18 | 1 | no | — |
| 547 | D3 | — | 18 | 1 | no | — |
| 548 | D3 | — | 27 | 3 | no | — |
| 549 | D3 | — | 27 | 1 | no | — |
| 550 | D3 | — | 36 | 3 | no | — |
| 551 | D3 | — | 36 | 1 | no | — |
| 552 | D3 | — | 54 | 3 | no | — |
| 553 | D3 | — | 54 | 1 | no | — |
| 554 | D3 | — | 324 | 1 | no | — |
| 555 | D3 | — | 324 | 3 | no | — |
| 556 | D3 | — | 72 | 3 | no | — |
| 557 | D3 | — | 81 | 1 | no | — |
| 558 | D3 | — | 81 | 1 | no | — |
| 559 | D3 | — | 648 | 3 | no | — |
| 560 | D3 | — | 162 | 1 | no | — |
| 561 | D3 | — | 162 | 1 | no | — |
| 562 | C22 | — | 27 | 1 | no | — |
| 563 | C22 | — | 81 | 1 | no | — |
| 564 | C22 | — | 81 | 1 | no | — |
| 565 | C22 | — | 81 | 1 | no | — |
| 566 | C22 | — | 486 | 1 | no | — |
| 567 | C22 | — | 486 | 1 | no | — |
| 568 | C22 | #11757731 | 1 | 1 | yes | characteristic, complemented |
| 569 | C4 | — | 27 | 1 | no | — |
| 570 | C4 | — | 81 | 1 | no | — |
| 571 | C3 | — | 3 | 1 | no | — |
| 572 | C3 | — | 6 | 1 | no | — |
| 573 | C3 | — | 9 | 1 | no | — |
| 574 | C3 | — | 12 | 3 | no | — |
| 575 | C3 | — | 18 | 1 | no | — |
| 576 | C3 | — | 24 | 3 | no | — |
| 577 | C3 | — | 72 | 3 | no | — |
| 578 | C3 | ((C3⋊D3)⋊C3)⋊S4 | 1 | 3 | yes | — |
| 579 | C3 | #13049215 | 1 | 1 | yes | characteristic |
| 580 | C2 | — | 3 | 1 | no | — |
| 581 | C2 | — | 27 | 1 | no | — |
| 582 | C2 | — | 54 | 1 | no | — |
| 583 | C2 | — | 81 | 1 | no | — |
| 584 | C2 | — | 162 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | (C3×A4)⋊H(3,𝔽3) | C22 |
| Frattini | C32 | D3×C3⋊S4 |
| Fitting | C22×C3×H(3,𝔽3) | C2×D3 |
| socle | C22×C32 | D3×C3⋊D3 |
| LCS | G ▷ (C3×A4)⋊H(3,𝔽3) | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14518198 | C2 | semidirect |
| 2. #14518118 | C2 | semidirect |
| 3. #14518069 | C2 | semidirect |
| 7. (C3×A4)⋊H(3,𝔽3) | C22 | semidirect |
| 10. C3⋊(C3⋊(C3⋊S4)) | D3 | semidirect |
| 12. C22×C3⋊((C3⋊D3)⋊C3) | D3 | semidirect |
| 14. C3⋊((C3⋊D3)⋊A4) | D3 | semidirect |
| 34. C33×A4 | C2×D3 | semidirect |
| 36. C22×C3×H(3,𝔽3) | C2×D3 | semidirect |
| 43. C3×C22⋊H(3,𝔽3) | C2×D3 | semidirect |
| 50. C22×C3⋊(C3⋊D3) | C3⋊D3 | semidirect |
| 103. C3⋊((C3⋊D3)⋊C3) | S4 | semidirect |
| 115. C22×C33 | C2×C3⋊D3 | semidirect |
| 168. C3×H(3,𝔽3) | C2×S4 | semidirect |
| 238. C3⋊(C3⋊D3) | C3⋊S4 | semidirect |
| 280. C22×C32 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 321. C3×A4 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 354. C33 | C2×C3⋊S4 | semidirect |
| 521. C32 | ((C3⋊S4)⋊C3)⋊C2 | semidirect |
| 568. C22 | #11757731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14518198 | 2 |
| #14518118 | 2 |
| #14518069 | 2 |
| C3⋊D3×C3⋊S4 | 3 |
| #13049222 | 3 |
| #13048780 | 3 |
| #11757731 | 4 |