Finite Group DatabasebetaFinite Group DatabasebetaOrder 4374.
8662 conjugacy classes of subgroups; only the 266 normal subgroups are shown.
This group has 8662 conjugacy classes of subgroups — too many to draw. Only its 266 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 | C3×H(3,𝔽3)2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C32×C3⋊#272 | — | 3 | 1 | no | maximal |
| 3 | C3×C3⋊(C3⋊#272) | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C32×C3⋊((C3⋊D3)⋊C3) | — | 3 | 4 | no | maximal |
| 5 | #13091501 | C3 | 1 | 3 | yes | maximal, direct product factor |
| 6 | C3×#92300 | — | 3 | 8 | no | maximal |
| 7 | C33×H(3,𝔽3) | — | 2 | 1 | no | — |
| 8 | C33×H(3,𝔽3) | D3 | 1 | 1 | yes | characteristic, complemented |
| 9 | C33×H(3,𝔽3) | D3 | 1 | 4 | yes | complemented |
| 10 | C33×H(3,𝔽3) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | H(3,𝔽3)2 | — | 2 | 24 | no | — |
| 12 | H(3,𝔽3)2 | — | 2 | 12 | no | — |
| 13 | H(3,𝔽3)2 | — | 2 | 3 | no | — |
| 14 | H(3,𝔽3)2 | C2×C3 | 1 | 3 | yes | complemented |
| 15 | C3×C32⋊H(3,𝔽3) | — | 2 | 4 | no | — |
| 16 | C3×C32⋊H(3,𝔽3) | — | 2 | 8 | no | — |
| 17 | C3×C32⋊H(3,𝔽3) | D3 | 1 | 8 | yes | complemented |
| 18 | C32×C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 19 | C33×C3⋊D3 | — | 9 | 4 | no | — |
| 20 | C3⋊(C3⋊#272) | C32 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3×C3⋊#272 | — | 3 | 1 | no | — |
| 22 | C3×C3⋊#272 | — | 3 | 3 | no | — |
| 23 | C3×C3⋊#272 | — | 3 | 8 | no | — |
| 24 | C3×C3⋊#272 | — | 9 | 9 | no | — |
| 25 | C32×#272 | — | 9 | 9 | no | — |
| 26 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 36 | no | — |
| 27 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 12 | no | — |
| 28 | C32×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 29 | C32×(C3⋊D3)⋊C3 | — | 9 | 8 | no | — |
| 30 | #92300 | — | 3 | 24 | no | — |
| 31 | C35 | — | 2 | 4 | no | — |
| 32 | C35 | C3×D3 | 1 | 4 | yes | complemented |
| 33 | C35 | C3⋊D3 | 1 | 4 | yes | complemented |
| 34 | C32×H(3,𝔽3) | — | 2 | 24 | no | — |
| 35 | C32×H(3,𝔽3) | — | 2 | 4 | no | — |
| 36 | C32×H(3,𝔽3) | — | 2 | 8 | no | — |
| 37 | C32×H(3,𝔽3) | — | 2 | 4 | no | — |
| 38 | C32×H(3,𝔽3) | — | 2 | 4 | no | — |
| 39 | C32×H(3,𝔽3) | — | 2 | 8 | no | — |
| 40 | C32×H(3,𝔽3) | — | 2 | 12 | no | — |
| 41 | C32×H(3,𝔽3) | — | 2 | 12 | no | — |
| 42 | C32×H(3,𝔽3) | — | 2 | 24 | no | — |
| 43 | C32×H(3,𝔽3) | — | 2 | 1 | no | — |
| 44 | C32×H(3,𝔽3) | — | 2 | 3 | no | — |
| 45 | C32×H(3,𝔽3) | — | 2 | 8 | no | — |
| 46 | C32×H(3,𝔽3) | — | 2 | 12 | no | — |
| 47 | C32×H(3,𝔽3) | — | 2 | 24 | no | — |
| 48 | C32×H(3,𝔽3) | — | 3 | 9 | no | — |
| 49 | C32×H(3,𝔽3) | — | 3 | 36 | no | — |
| 50 | C32×H(3,𝔽3) | — | 3 | 9 | no | — |
| 51 | C32×H(3,𝔽3) | — | 6 | 9 | no | — |
| 52 | C32×H(3,𝔽3) | — | 6 | 36 | no | — |
| 53 | C32×H(3,𝔽3) | — | 6 | 9 | no | — |
| 54 | C32×H(3,𝔽3) | — | 6 | 18 | no | — |
| 55 | C32×H(3,𝔽3) | — | 6 | 9 | no | — |
| 56 | C32×H(3,𝔽3) | C3×D3 | 1 | 1 | yes | characteristic |
| 57 | C32×H(3,𝔽3) | C3×D3 | 1 | 3 | yes | complemented |
| 58 | C32×H(3,𝔽3) | C3×D3 | 1 | 8 | yes | complemented |
| 59 | C32×H(3,𝔽3) | C3×D3 | 1 | 12 | yes | complemented |
| 60 | C32×H(3,𝔽3) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 61 | C32×H(3,𝔽3) | C3⋊D3 | 1 | 8 | yes | complemented |
| 62 | C32×H(3,𝔽3) | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 63 | C32⋊H(3,𝔽3) | — | 2 | 48 | no | — |
| 64 | C32⋊H(3,𝔽3) | — | 2 | 144 | no | — |
| 65 | C32⋊H(3,𝔽3) | — | 2 | 24 | no | — |
| 66 | C32⋊H(3,𝔽3) | — | 2 | 48 | no | — |
| 67 | C32⋊H(3,𝔽3) | — | 2 | 24 | no | — |
| 68 | C32⋊H(3,𝔽3) | — | 2 | 12 | no | — |
| 69 | C32⋊H(3,𝔽3) | — | 2 | 24 | no | — |
| 70 | C32⋊H(3,𝔽3) | — | 2 | 24 | no | — |
| 71 | C32⋊H(3,𝔽3) | — | 2 | 72 | no | — |
| 72 | C32⋊H(3,𝔽3) | C3×D3 | 1 | 24 | yes | complemented |
| 73 | C3×C3⋊(C3⋊D3) | — | 3 | 12 | no | — |
| 74 | C3×C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 75 | C32×C3⋊D3 | — | 9 | 36 | no | — |
| 76 | C32×C3⋊D3 | — | 9 | 4 | no | — |
| 77 | C32×C3⋊D3 | — | 9 | 12 | no | — |
| 78 | C32×C3⋊D3 | — | 9 | 8 | no | — |
| 79 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 80 | C32×C3⋊D3 | — | 27 | 12 | no | — |
| 81 | C33×D3 | — | 27 | 12 | no | — |
| 82 | C33×D3 | — | 27 | 1 | no | — |
| 83 | C3⋊#272 | — | 3 | 1 | no | — |
| 84 | C3⋊#272 | — | 3 | 8 | no | — |
| 85 | C3⋊#272 | — | 9 | 9 | no | — |
| 86 | C3×#272 | — | 9 | 27 | no | — |
| 87 | C3×#272 | — | 9 | 9 | no | — |
| 88 | C3×#272 | — | 27 | 24 | no | — |
| 89 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 36 | no | — |
| 90 | C3×(C3⋊D3)⋊C3 | — | 9 | 72 | no | — |
| 91 | C3×(C3⋊D3)⋊C3 | — | 9 | 9 | no | — |
| 92 | C3×(C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 93 | C3×(C3⋊D3)⋊C3 | — | 9 | 24 | no | — |
| 94 | C34 | — | 2 | 1 | no | — |
| 95 | C34 | — | 2 | 24 | no | — |
| 96 | C34 | — | 2 | 4 | no | — |
| 97 | C34 | — | 2 | 8 | no | — |
| 98 | C34 | — | 2 | 8 | no | — |
| 99 | C34 | — | 2 | 4 | no | — |
| 100 | C34 | — | 2 | 4 | no | — |
| 101 | C34 | — | 2 | 12 | no | — |
| 102 | C34 | — | 2 | 12 | no | — |
| 103 | C34 | — | 3 | 12 | no | — |
| 104 | C34 | — | 3 | 12 | no | — |
| 105 | C34 | — | 3 | 12 | no | — |
| 106 | C34 | — | 3 | 36 | no | — |
| 107 | C34 | — | 6 | 12 | no | — |
| 108 | C34 | — | 6 | 12 | no | — |
| 109 | C34 | — | 6 | 36 | no | — |
| 110 | C34 | — | 6 | 12 | no | — |
| 111 | C34 | — | 6 | 24 | no | — |
| 112 | C34 | — | 6 | 12 | no | — |
| 113 | C34 | — | 18 | 12 | no | — |
| 114 | C34 | — | 18 | 12 | no | — |
| 115 | C34 | — | 18 | 24 | no | — |
| 116 | C34 | C32×D3 | 1 | 4 | yes | complemented |
| 117 | C34 | C3×C3⋊D3 | 1 | 4 | yes | — |
| 118 | C34 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 119 | C34 | C3×C3⋊D3 | 1 | 8 | yes | — |
| 120 | C34 | C3×C3⋊D3 | 1 | 12 | yes | complemented |
| 121 | C34 | C3⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 122 | C3×H(3,𝔽3) | — | 2 | 9 | no | — |
| 123 | C3×H(3,𝔽3) | — | 2 | 4 | no | — |
| 124 | C3×H(3,𝔽3) | — | 2 | 3 | no | — |
| 125 | C3×H(3,𝔽3) | — | 2 | 9 | no | — |
| 126 | C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 127 | C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 128 | C3×H(3,𝔽3) | — | 2 | 48 | no | — |
| 129 | C3×H(3,𝔽3) | — | 2 | 48 | no | — |
| 130 | C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 131 | C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 132 | C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 133 | C3×H(3,𝔽3) | — | 2 | 12 | no | — |
| 134 | C3×H(3,𝔽3) | — | 2 | 12 | no | — |
| 135 | C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 136 | C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 137 | C3×H(3,𝔽3) | — | 2 | 144 | no | — |
| 138 | C3×H(3,𝔽3) | — | 2 | 72 | no | — |
| 139 | C3×H(3,𝔽3) | — | 3 | 9 | no | — |
| 140 | C3×H(3,𝔽3) | — | 3 | 72 | no | — |
| 141 | C3×H(3,𝔽3) | — | 3 | 36 | no | — |
| 142 | C3×H(3,𝔽3) | — | 3 | 24 | no | — |
| 143 | C3×H(3,𝔽3) | — | 3 | 27 | no | — |
| 144 | C3×H(3,𝔽3) | — | 6 | 36 | no | — |
| 145 | C3×H(3,𝔽3) | — | 6 | 72 | no | — |
| 146 | C3×H(3,𝔽3) | — | 6 | 216 | no | — |
| 147 | C3×H(3,𝔽3) | — | 6 | 36 | no | — |
| 148 | C3×H(3,𝔽3) | — | 6 | 108 | no | — |
| 149 | C3×H(3,𝔽3) | — | 6 | 108 | no | — |
| 150 | C3×H(3,𝔽3) | — | 6 | 216 | no | — |
| 151 | C3×H(3,𝔽3) | — | 6 | 72 | no | — |
| 152 | C3×H(3,𝔽3) | — | 6 | 24 | no | — |
| 153 | C3×H(3,𝔽3) | — | 6 | 72 | no | — |
| 154 | C3×H(3,𝔽3) | — | 6 | 24 | no | — |
| 155 | C3×H(3,𝔽3) | — | 6 | 24 | no | — |
| 156 | C3×H(3,𝔽3) | — | 6 | 48 | no | — |
| 157 | C3×H(3,𝔽3) | — | 6 | 12 | no | — |
| 158 | C3×H(3,𝔽3) | — | 6 | 24 | no | — |
| 159 | C3×H(3,𝔽3) | — | 6 | 12 | no | — |
| 160 | C3×H(3,𝔽3) | — | 6 | 9 | no | — |
| 161 | C3×H(3,𝔽3) | — | 6 | 27 | no | — |
| 162 | C3×H(3,𝔽3) | — | 6 | 36 | no | — |
| 163 | C3×H(3,𝔽3) | — | 18 | 72 | no | — |
| 164 | C3×H(3,𝔽3) | (C3⋊D3)⋊C3 | 1 | 9 | yes | complemented |
| 165 | C3×H(3,𝔽3) | #272 | 1 | 9 | yes | complemented |
| 166 | C3×H(3,𝔽3) | C32×D3 | 1 | 1 | yes | characteristic |
| 167 | C3×H(3,𝔽3) | C32×D3 | 1 | 8 | yes | complemented |
| 168 | C3×H(3,𝔽3) | C3×C3⋊D3 | 1 | 3 | yes | — |
| 169 | C3×H(3,𝔽3) | C3×C3⋊D3 | 1 | 24 | yes | complemented |
| 170 | C2×C33 | — | 81 | 1 | no | — |
| 171 | C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 172 | C3×C3⋊D3 | — | 9 | 36 | no | — |
| 173 | C3×C3⋊D3 | — | 9 | 12 | no | — |
| 174 | C3×C3⋊D3 | — | 9 | 4 | no | — |
| 175 | C3×C3⋊D3 | — | 9 | 24 | no | — |
| 176 | C3×C3⋊D3 | — | 9 | 3 | no | — |
| 177 | C3×C3⋊D3 | — | 9 | 8 | no | — |
| 178 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 179 | C3×C3⋊D3 | — | 27 | 12 | no | — |
| 180 | C3×C3⋊D3 | — | 27 | 36 | no | — |
| 181 | C32×D3 | — | 27 | 36 | no | — |
| 182 | C32×D3 | — | 27 | 108 | no | — |
| 183 | C32×D3 | — | 27 | 12 | no | — |
| 184 | C32×D3 | — | 27 | 9 | no | — |
| 185 | C32×D3 | — | 27 | 3 | no | — |
| 186 | C32×D3 | — | 27 | 1 | no | — |
| 187 | C32×D3 | — | 81 | 8 | no | — |
| 188 | C32×D3 | — | 81 | 1 | no | — |
| 189 | #272 | — | 9 | 9 | no | — |
| 190 | #272 | — | 27 | 24 | no | — |
| 191 | (C3⋊D3)⋊C3 | — | 9 | 72 | no | — |
| 192 | (C3⋊D3)⋊C3 | — | 9 | 9 | no | — |
| 193 | C33 | — | 2 | 12 | no | — |
| 194 | C33 | — | 2 | 3 | no | — |
| 195 | C33 | — | 2 | 9 | no | — |
| 196 | C33 | — | 2 | 4 | no | — |
| 197 | C33 | — | 2 | 1 | no | — |
| 198 | C33 | — | 2 | 3 | no | — |
| 199 | C33 | — | 2 | 8 | no | — |
| 200 | C33 | — | 2 | 12 | no | — |
| 201 | C33 | — | 2 | 24 | no | — |
| 202 | C33 | — | 3 | 1 | no | — |
| 203 | C33 | — | 3 | 1 | no | — |
| 204 | C33 | — | 3 | 12 | no | — |
| 205 | C33 | — | 3 | 4 | no | — |
| 206 | C33 | — | 3 | 12 | no | — |
| 207 | C33 | — | 3 | 36 | no | — |
| 208 | C33 | — | 3 | 8 | no | — |
| 209 | C33 | — | 3 | 36 | no | — |
| 210 | C33 | — | 3 | 24 | no | — |
| 211 | C33 | — | 6 | 1 | no | — |
| 212 | C33 | — | 6 | 12 | no | — |
| 213 | C33 | — | 6 | 3 | no | — |
| 214 | C33 | — | 6 | 4 | no | — |
| 215 | C33 | — | 6 | 1 | no | — |
| 216 | C33 | — | 6 | 3 | no | — |
| 217 | C33 | — | 6 | 36 | no | — |
| 218 | C33 | — | 6 | 36 | no | — |
| 219 | C33 | — | 6 | 12 | no | — |
| 220 | C33 | — | 6 | 24 | no | — |
| 221 | C33 | — | 6 | 12 | no | — |
| 222 | C33 | — | 6 | 24 | no | — |
| 223 | C33 | — | 6 | 8 | no | — |
| 224 | C33 | — | 6 | 2 | no | — |
| 225 | C33 | — | 6 | 6 | no | — |
| 226 | C33 | — | 6 | 24 | no | — |
| 227 | C33 | — | 6 | 8 | no | — |
| 228 | C33 | — | 6 | 16 | no | — |
| 229 | C33 | — | 6 | 72 | no | — |
| 230 | C33 | — | 6 | 8 | no | — |
| 231 | C33 | — | 6 | 72 | no | — |
| 232 | C33 | — | 6 | 24 | no | — |
| 233 | C33 | — | 6 | 48 | no | — |
| 234 | C33 | — | 6 | 1 | no | — |
| 235 | C33 | — | 6 | 12 | no | — |
| 236 | C33 | — | 6 | 36 | no | — |
| 237 | C33 | — | 6 | 4 | no | — |
| 238 | C33 | — | 6 | 4 | no | — |
| 239 | C33 | — | 6 | 8 | no | — |
| 240 | C33 | — | 6 | 24 | no | — |
| 241 | C33 | — | 6 | 12 | no | — |
| 242 | C33 | — | 6 | 36 | no | — |
| 243 | C33 | — | 9 | 108 | no | — |
| 244 | C33 | — | 9 | 36 | no | — |
| 245 | C33 | — | 18 | 36 | no | — |
| 246 | C33 | — | 18 | 108 | no | — |
| 247 | C33 | — | 18 | 12 | no | — |
| 248 | C33 | — | 18 | 4 | no | — |
| 249 | C33 | — | 18 | 8 | no | — |
| 250 | C33 | — | 18 | 24 | no | — |
| 251 | C33 | — | 18 | 24 | no | — |
| 252 | C33 | — | 18 | 8 | no | — |
| 253 | C33 | — | 18 | 16 | no | — |
| 254 | C33 | — | 18 | 48 | no | — |
| 255 | C33 | — | 18 | 108 | no | — |
| 256 | C33 | — | 18 | 36 | no | — |
| 257 | C33 | — | 18 | 72 | no | — |
| 258 | C33 | — | 18 | 216 | no | — |
| 259 | C33 | C3⋊((C3⋊D3)⋊C3) | 1 | 12 | yes | complemented |
| 260 | C33 | C3×#272 | 1 | 3 | yes | complemented |
| 261 | C33 | C3⋊#272 | 1 | 9 | yes | complemented |
| 262 | C33 | C32×C3⋊D3 | 1 | 1 | yes | characteristic |
| 263 | C33 | C32×C3⋊D3 | 1 | 8 | yes | — |
| 264 | C33 | C32×C3⋊D3 | 1 | 4 | yes | — |
| 265 | C33 | C3×C3⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 266 | C33 | C3×C3⋊(C3⋊D3) | 1 | 3 | yes | — |
| 267 | H(3,𝔽3) | — | 2 | 36 | no | — |
| 268 | H(3,𝔽3) | — | 2 | 27 | no | — |
| 269 | H(3,𝔽3) | — | 2 | 9 | no | — |
| 270 | H(3,𝔽3) | — | 3 | 24 | no | — |
| 271 | H(3,𝔽3) | — | 3 | 72 | no | — |
| 272 | H(3,𝔽3) | — | 6 | 72 | no | — |
| 273 | H(3,𝔽3) | — | 6 | 72 | no | — |
| 274 | H(3,𝔽3) | — | 6 | 72 | no | — |
| 275 | H(3,𝔽3) | — | 6 | 144 | no | — |
| 276 | H(3,𝔽3) | — | 6 | 72 | no | — |
| 277 | H(3,𝔽3) | — | 6 | 24 | no | — |
| 278 | H(3,𝔽3) | — | 6 | 144 | no | — |
| 279 | H(3,𝔽3) | — | 6 | 36 | no | — |
| 280 | H(3,𝔽3) | — | 6 | 24 | no | — |
| 281 | H(3,𝔽3) | — | 6 | 72 | no | — |
| 282 | H(3,𝔽3) | — | 6 | 12 | no | — |
| 283 | H(3,𝔽3) | — | 6 | 72 | no | — |
| 284 | H(3,𝔽3) | — | 18 | 72 | no | — |
| 285 | H(3,𝔽3) | — | 18 | 144 | no | — |
| 286 | H(3,𝔽3) | C3×(C3⋊D3)⋊C3 | 1 | 9 | yes | complemented |
| 287 | H(3,𝔽3) | C3×#272 | 1 | 9 | yes | complemented |
| 288 | C2×C32 | — | 81 | 3 | no | — |
| 289 | C2×C32 | — | 81 | 9 | no | — |
| 290 | C2×C32 | — | 81 | 1 | no | — |
| 291 | C3⋊D3 | — | 9 | 4 | no | — |
| 292 | C3⋊D3 | — | 9 | 8 | no | — |
| 293 | C3⋊D3 | — | 9 | 1 | no | — |
| 294 | C3⋊D3 | — | 27 | 12 | no | — |
| 295 | C3×D3 | — | 27 | 36 | no | — |
| 296 | C3×D3 | — | 27 | 108 | no | — |
| 297 | C3×D3 | — | 27 | 12 | no | — |
| 298 | C3×D3 | — | 27 | 3 | no | — |
| 299 | C3×D3 | — | 27 | 9 | no | — |
| 300 | C3×D3 | — | 27 | 1 | no | — |
| 301 | C3×D3 | — | 81 | 8 | no | — |
| 302 | C3×D3 | — | 81 | 1 | no | — |
| 303 | C3×D3 | — | 81 | 3 | no | — |
| 304 | C3×D3 | — | 81 | 24 | no | — |
| 305 | C32 | — | 2 | 1 | no | — |
| 306 | C32 | — | 2 | 3 | no | — |
| 307 | C32 | — | 2 | 12 | no | — |
| 308 | C32 | — | 2 | 3 | no | — |
| 309 | C32 | — | 2 | 1 | no | — |
| 310 | C32 | — | 2 | 9 | no | — |
| 311 | C32 | — | 3 | 3 | no | — |
| 312 | C32 | — | 3 | 4 | no | — |
| 313 | C32 | — | 3 | 9 | no | — |
| 314 | C32 | — | 3 | 1 | no | — |
| 315 | C32 | — | 3 | 36 | no | — |
| 316 | C32 | — | 3 | 3 | no | — |
| 317 | C32 | — | 3 | 8 | no | — |
| 318 | C32 | — | 3 | 8 | no | — |
| 319 | C32 | — | 6 | 9 | no | — |
| 320 | C32 | — | 6 | 4 | no | — |
| 321 | C32 | — | 6 | 3 | no | — |
| 322 | C32 | — | 6 | 3 | no | — |
| 323 | C32 | — | 6 | 1 | no | — |
| 324 | C32 | — | 6 | 36 | no | — |
| 325 | C32 | — | 6 | 8 | no | — |
| 326 | C32 | — | 6 | 2 | no | — |
| 327 | C32 | — | 6 | 6 | no | — |
| 328 | C32 | — | 6 | 6 | no | — |
| 329 | C32 | — | 6 | 18 | no | — |
| 330 | C32 | — | 6 | 8 | no | — |
| 331 | C32 | — | 6 | 24 | no | — |
| 332 | C32 | — | 6 | 16 | no | — |
| 333 | C32 | — | 6 | 48 | no | — |
| 334 | C32 | — | 6 | 1 | no | — |
| 335 | C32 | — | 6 | 3 | no | — |
| 336 | C32 | — | 6 | 4 | no | — |
| 337 | C32 | — | 6 | 3 | no | — |
| 338 | C32 | — | 6 | 9 | no | — |
| 339 | C32 | — | 6 | 12 | no | — |
| 340 | C32 | — | 6 | 8 | no | — |
| 341 | C32 | — | 6 | 24 | no | — |
| 342 | C32 | — | 6 | 24 | no | — |
| 343 | C32 | — | 6 | 12 | no | — |
| 344 | C32 | — | 6 | 8 | no | — |
| 345 | C32 | — | 9 | 12 | no | — |
| 346 | C32 | — | 9 | 108 | no | — |
| 347 | C32 | — | 9 | 24 | no | — |
| 348 | C32 | — | 18 | 24 | no | — |
| 349 | C32 | — | 18 | 24 | no | — |
| 350 | C32 | — | 18 | 48 | no | — |
| 351 | C32 | — | 18 | 12 | no | — |
| 352 | C32 | — | 18 | 12 | no | — |
| 353 | C32 | — | 18 | 108 | no | — |
| 354 | C32 | — | 18 | 36 | no | — |
| 355 | C32 | — | 18 | 108 | no | — |
| 356 | C32 | — | 18 | 72 | no | — |
| 357 | C32 | — | 18 | 24 | no | — |
| 358 | C32 | — | 18 | 216 | no | — |
| 359 | C32 | — | 18 | 12 | no | — |
| 360 | C32 | — | 18 | 24 | no | — |
| 361 | C32 | C3×C3⋊((C3⋊D3)⋊C3) | 1 | 12 | yes | complemented |
| 362 | C32 | C32×#272 | 1 | 1 | yes | characteristic, complemented |
| 363 | C32 | C3⋊(C3⋊((C3⋊D3)⋊C3)) | 1 | 1 | yes | characteristic |
| 364 | C32 | C3×C3⋊#272 | 1 | 3 | yes | — |
| 365 | C32 | C3×C3⋊#272 | 1 | 9 | yes | complemented |
| 366 | C32 | C32×C3⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 367 | C2×C3 | — | 81 | 9 | no | — |
| 368 | C2×C3 | — | 81 | 1 | no | — |
| 369 | C2×C3 | — | 81 | 3 | no | — |
| 370 | D3 | — | 27 | 12 | no | — |
| 371 | D3 | — | 27 | 1 | no | — |
| 372 | D3 | — | 81 | 1 | no | — |
| 373 | D3 | — | 81 | 8 | no | — |
| 374 | C3 | — | 2 | 1 | no | — |
| 375 | C3 | — | 2 | 3 | no | — |
| 376 | C3 | — | 3 | 12 | no | — |
| 377 | C3 | — | 3 | 1 | no | — |
| 378 | C3 | — | 3 | 9 | no | — |
| 379 | C3 | — | 6 | 12 | no | — |
| 380 | C3 | — | 6 | 3 | no | — |
| 381 | C3 | — | 6 | 1 | no | — |
| 382 | C3 | — | 6 | 9 | no | — |
| 383 | C3 | — | 9 | 8 | no | — |
| 384 | C3 | — | 18 | 12 | no | — |
| 385 | C3 | — | 18 | 8 | no | — |
| 386 | C3 | — | 18 | 24 | no | — |
| 387 | C3 | #13091501 | 1 | 3 | yes | direct product factor |
| 388 | C3 | C3×C3⋊(C3⋊((C3⋊D3)⋊C3)) | 1 | 1 | yes | characteristic |
| 389 | C3 | C32×C3⋊#272 | 1 | 1 | yes | characteristic |
| 390 | C2 | — | 81 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊(C3⋊((C3⋊D3)⋊C3)) |
| commutator, cosocle, hypocenter | C32×H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C32×C3⋊(C3⋊D3) |
| Fitting | C3×H(3,𝔽3)2 | C2 |
| socle | C33 | C3×C3⋊(C3⋊D3) |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×H(3,𝔽3)2 | C2 | semidirect |
| 3. C3×C3⋊(C3⋊#272) | C3 | semidirect |
| 5. #13091501 | C3 | direct (N × H) |
| 8. C33×H(3,𝔽3) | D3 | semidirect |
| 9. C33×H(3,𝔽3) | D3 | semidirect |
| 10. C33×H(3,𝔽3) | C2×C3 | semidirect |
| 14. H(3,𝔽3)2 | C2×C3 | semidirect |
| 17. C3×C32⋊H(3,𝔽3) | D3 | semidirect |
| 20. C3⋊(C3⋊#272) | C32 | semidirect |
| 32. C35 | C3×D3 | semidirect |
| 33. C35 | C3⋊D3 | semidirect |
| 57. C32×H(3,𝔽3) | C3×D3 | semidirect |
| 58. C32×H(3,𝔽3) | C3×D3 | semidirect |
| 59. C32×H(3,𝔽3) | C3×D3 | semidirect |
| 61. C32×H(3,𝔽3) | C3⋊D3 | semidirect |
| 62. C32×H(3,𝔽3) | C2×C32 | semidirect |
| 72. C32⋊H(3,𝔽3) | C3×D3 | semidirect |
| 116. C34 | C32×D3 | semidirect |
| 120. C34 | C3×C3⋊D3 | semidirect |
| 164. C3×H(3,𝔽3) | (C3⋊D3)⋊C3 | semidirect |
| 165. C3×H(3,𝔽3) | #272 | semidirect |
| 167. C3×H(3,𝔽3) | C32×D3 | semidirect |
| 169. C3×H(3,𝔽3) | C3×C3⋊D3 | semidirect |
| 259. C33 | C3⋊((C3⋊D3)⋊C3) | semidirect |
| 260. C33 | C3×#272 | semidirect |
| 261. C33 | C3⋊#272 | semidirect |
| 286. H(3,𝔽3) | C3×(C3⋊D3)⋊C3 | semidirect |
| 287. H(3,𝔽3) | C3×#272 | semidirect |
| 361. C32 | C3×C3⋊((C3⋊D3)⋊C3) | semidirect |
| 362. C32 | C32×#272 | semidirect |
| 365. C32 | C3×C3⋊#272 | semidirect |
| 387. C3 | #13091501 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)2 | 2 |
| C32×C3⋊#272 | 3 |
| C3×C3⋊(C3⋊#272) | 3 |
| C32×C3⋊((C3⋊D3)⋊C3) | 3 |
| #13091501 | 3 |
| C3×#92300 | 3 |