Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
580 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 47 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×#92297 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | H(3,𝔽3)×C3⋊D9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C9×C3⋊((C3⋊D3)⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11758088 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | (C3⋊#1113)⋊C3 | — | 3 | 1 | no | maximal |
| 6 | C3×#66431 | — | 3 | 1 | no | maximal |
| 7 | D9×(C3⋊D3)⋊C3 | — | 3 | 1 | no | maximal |
| 8 | C3×C9×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C9×C3⋊(C3⋊D3) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C3×C3⋊(C3⋊D9) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3⋊D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 12 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 13 | C3×C3⋊((C3⋊D3)⋊C3) | D3 | 1 | 1 | yes | characteristic |
| 14 | C3×C9×C3⋊D3 | — | 3 | 1 | no | — |
| 15 | C32×C3⋊D9 | — | 2 | 1 | no | — |
| 16 | C32×C3⋊D9 | — | 3 | 1 | no | — |
| 17 | C32×C3⋊D9 | D3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C32×C3⋊D9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | #92297 | — | 2 | 1 | no | — |
| 20 | #92297 | D3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3⋊((C3⋊D3)⋊C9) | — | 2 | 1 | no | — |
| 22 | D9×H(3,𝔽3) | — | 3 | 1 | no | — |
| 23 | D9×H(3,𝔽3) | — | 6 | 1 | no | — |
| 24 | C9×(C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 25 | C9×(C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 26 | C3×#4169 | — | 6 | 1 | no | — |
| 27 | C3⋊#1113 | — | 3 | 1 | no | — |
| 28 | C3×#1113 | — | 9 | 1 | no | — |
| 29 | #66431 | — | 3 | 1 | no | — |
| 30 | #66431 | — | 9 | 1 | no | — |
| 31 | D9×C3⋊D3 | — | 3 | 1 | no | — |
| 32 | D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 33 | D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 34 | C3×D3×D9 | — | 9 | 1 | no | — |
| 35 | C3×D3×D9 | — | 9 | 1 | no | — |
| 36 | C32×H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 37 | C33×C9 | — | 2 | 1 | no | — |
| 38 | C33×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 39 | C33×C9 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 40 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 41 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 42 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 43 | C9×H(3,𝔽3) | — | 4 | 2 | no | — |
| 44 | C9×H(3,𝔽3) | — | 4 | 1 | no | — |
| 45 | C9×H(3,𝔽3) | — | 4 | 1 | no | — |
| 46 | C9×H(3,𝔽3) | — | 4 | 1 | no | — |
| 47 | C9×H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 48 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 49 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 50 | C3×C32⋊C9 | — | 4 | 1 | no | — |
| 51 | C3×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 52 | C3×C3⋊(C3⋊D3) | C3×D3 | 1 | 1 | yes | characteristic |
| 53 | C32×C3⋊D3 | — | 3 | 1 | no | — |
| 54 | C32×C3⋊D3 | — | 3 | 1 | no | — |
| 55 | C32×C3⋊D3 | — | 3 | 1 | no | — |
| 56 | C32×C3⋊D3 | — | 6 | 1 | no | — |
| 57 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 58 | C3⋊(C3⋊D9) | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 59 | C3⋊((C3⋊D3)⋊C3) | — | 2 | 1 | no | — |
| 60 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 61 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 62 | C3⋊((C3⋊D3)⋊C3) | D9 | 1 | 1 | yes | characteristic, complemented |
| 63 | C9×C3⋊D3 | — | 3 | 1 | no | — |
| 64 | C9×C3⋊D3 | — | 3 | 1 | no | — |
| 65 | C9×C3⋊D3 | — | 6 | 1 | no | — |
| 66 | C9×C3⋊D3 | — | 6 | 1 | no | — |
| 67 | C9×C3⋊D3 | — | 9 | 1 | no | — |
| 68 | C9×C3⋊D3 | — | 18 | 1 | no | — |
| 69 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 70 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 71 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 72 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 73 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 74 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 75 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 76 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 77 | C3×C3⋊D9 | — | 18 | 1 | no | — |
| 78 | C3×C3⋊D9 | C3×D3 | 1 | 1 | yes | characteristic |
| 79 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 80 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 81 | D3×H(3,𝔽3) | — | 18 | 1 | no | — |
| 82 | C3×(C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 83 | C3×(C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 84 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 85 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 86 | C3×D3×C9 | — | 9 | 1 | no | — |
| 87 | C3×D3×C9 | — | 9 | 1 | no | — |
| 88 | C3×D3×C9 | — | 18 | 1 | no | — |
| 89 | C32×D9 | — | 3 | 1 | no | — |
| 90 | C32×D9 | — | 3 | 1 | no | — |
| 91 | C32×D9 | — | 6 | 1 | no | — |
| 92 | C32×D9 | — | 6 | 1 | no | — |
| 93 | C32×D9 | — | 6 | 1 | no | — |
| 94 | C32×D9 | — | 6 | 2 | no | — |
| 95 | C32×D9 | — | 9 | 1 | no | — |
| 96 | C32×D9 | — | 18 | 1 | no | — |
| 97 | #4169 | — | 6 | 1 | no | — |
| 98 | #4169 | — | 6 | 2 | no | — |
| 99 | (C3⋊D3)⋊C9 | — | 6 | 1 | no | — |
| 100 | (C3⋊D3)⋊C9 | — | 6 | 2 | no | — |
| 101 | #1113 | — | 9 | 1 | no | — |
| 102 | #1113 | — | 27 | 1 | no | — |
| 103 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 104 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 105 | C3×D32 | — | 27 | 1 | no | — |
| 106 | C3×D32 | — | 27 | 1 | no | — |
| 107 | C3×D32 | — | 27 | 1 | no | — |
| 108 | C2×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 109 | C2×C3×D9 | — | 27 | 1 | no | — |
| 110 | D3×D9 | — | 9 | 1 | no | — |
| 111 | D3×D9 | — | 9 | 1 | no | — |
| 112 | D3×D9 | — | 27 | 1 | no | — |
| 113 | C34 | — | 2 | 1 | no | — |
| 114 | C34 | D32 | 1 | 1 | yes | characteristic |
| 115 | C34 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 116 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 117 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 118 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 119 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 120 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 121 | C3×H(3,𝔽3) | — | 4 | 2 | no | — |
| 122 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 123 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 124 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 125 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 126 | C3×H(3,𝔽3) | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 127 | C3×H(3,𝔽3) | D32 | 1 | 1 | yes | characteristic |
| 128 | C32×C9 | — | 2 | 1 | no | — |
| 129 | C32×C9 | — | 2 | 2 | no | — |
| 130 | C32×C9 | — | 2 | 1 | no | — |
| 131 | C32×C9 | — | 2 | 1 | no | — |
| 132 | C32×C9 | — | 2 | 1 | no | — |
| 133 | C32×C9 | — | 2 | 1 | no | — |
| 134 | C32×C9 | — | 2 | 1 | no | — |
| 135 | C32×C9 | — | 2 | 1 | no | — |
| 136 | C32×C9 | — | 3 | 1 | no | — |
| 137 | C32×C9 | — | 4 | 1 | no | — |
| 138 | C32×C9 | — | 4 | 1 | no | — |
| 139 | C32×C9 | — | 4 | 2 | no | — |
| 140 | C32×C9 | — | 4 | 1 | no | — |
| 141 | C32×C9 | — | 4 | 1 | no | — |
| 142 | C32×C9 | — | 6 | 1 | no | — |
| 143 | C32×C9 | — | 6 | 1 | no | — |
| 144 | C32×C9 | — | 6 | 1 | no | — |
| 145 | C32×C9 | — | 6 | 1 | no | — |
| 146 | C32×C9 | — | 12 | 1 | no | — |
| 147 | C32×C9 | — | 12 | 1 | no | — |
| 148 | C32×C9 | — | 12 | 1 | no | — |
| 149 | C32×C9 | — | 12 | 1 | no | — |
| 150 | C32×C9 | — | 12 | 1 | no | — |
| 151 | C32×C9 | — | 12 | 2 | no | — |
| 152 | C32×C9 | — | 12 | 1 | no | — |
| 153 | C32×C9 | D32 | 1 | 1 | yes | characteristic, complemented |
| 154 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 155 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 156 | C32⋊C9 | — | 2 | 2 | no | — |
| 157 | C32⋊C9 | — | 2 | 2 | no | — |
| 158 | C32⋊C9 | — | 2 | 1 | no | — |
| 159 | C32⋊C9 | — | 2 | 1 | no | — |
| 160 | C32⋊C9 | — | 4 | 1 | no | — |
| 161 | C32⋊C9 | — | 4 | 2 | no | — |
| 162 | C32⋊C9 | — | 4 | 2 | no | — |
| 163 | C32⋊C9 | — | 4 | 2 | no | — |
| 164 | C32⋊C9 | — | 4 | 2 | no | — |
| 165 | C32⋊C9 | — | 4 | 2 | no | — |
| 166 | C32⋊C9 | — | 4 | 2 | no | — |
| 167 | C32⋊C9 | — | 4 | 1 | no | — |
| 168 | C32⋊C9 | — | 4 | 1 | no | — |
| 169 | C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 170 | C3⋊(C3⋊D3) | C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 171 | C3×C3⋊D3 | — | 3 | 1 | no | — |
| 172 | C3×C3⋊D3 | — | 3 | 1 | no | — |
| 173 | C3×C3⋊D3 | — | 3 | 1 | no | — |
| 174 | C3×C3⋊D3 | — | 3 | 1 | no | — |
| 175 | C3×C3⋊D3 | — | 6 | 1 | no | — |
| 176 | C3×C3⋊D3 | — | 6 | 1 | no | — |
| 177 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 178 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 179 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 180 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 181 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 182 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 183 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 184 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 185 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 186 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 187 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 188 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 189 | C32×D3 | — | 9 | 1 | no | — |
| 190 | C32×D3 | — | 9 | 1 | no | — |
| 191 | C32×D3 | — | 9 | 1 | no | — |
| 192 | C32×D3 | — | 9 | 1 | no | — |
| 193 | C32×D3 | — | 9 | 1 | no | — |
| 194 | C32×D3 | — | 9 | 1 | no | — |
| 195 | C32×D3 | — | 18 | 1 | no | — |
| 196 | C32×D3 | — | 18 | 1 | no | — |
| 197 | C32×D3 | — | 18 | 1 | no | — |
| 198 | C32×D3 | — | 18 | 1 | no | — |
| 199 | C32×D3 | — | 18 | 1 | no | — |
| 200 | C32×D3 | — | 18 | 2 | no | — |
| 201 | C32×D3 | — | 27 | 1 | no | — |
| 202 | C32×D3 | — | 27 | 1 | no | — |
| 203 | C32×D3 | — | 54 | 1 | no | — |
| 204 | C2×H(3,𝔽3) | — | 27 | 1 | no | — |
| 205 | C2×C3×C9 | — | 27 | 1 | no | — |
| 206 | C3⋊D9 | — | 3 | 1 | no | — |
| 207 | C3⋊D9 | — | 6 | 1 | no | — |
| 208 | C3⋊D9 | — | 9 | 1 | no | — |
| 209 | C3⋊D9 | — | 18 | 1 | no | — |
| 210 | C3⋊D9 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 211 | (C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 212 | (C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 213 | (C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 214 | (C3⋊D3)⋊C3 | — | 6 | 2 | no | — |
| 215 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 216 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 217 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 218 | (C3⋊D3)⋊C3 | — | 18 | 2 | no | — |
| 219 | D3×C9 | — | 9 | 1 | no | — |
| 220 | D3×C9 | — | 9 | 1 | no | — |
| 221 | D3×C9 | — | 18 | 1 | no | — |
| 222 | D3×C9 | — | 18 | 1 | no | — |
| 223 | D3×C9 | — | 18 | 1 | no | — |
| 224 | D3×C9 | — | 18 | 2 | no | — |
| 225 | D3×C9 | — | 27 | 1 | no | — |
| 226 | D3×C9 | — | 54 | 1 | no | — |
| 227 | C3×D9 | — | 3 | 1 | no | — |
| 228 | C3×D9 | — | 6 | 1 | no | — |
| 229 | C3×D9 | — | 9 | 1 | no | — |
| 230 | C3×D9 | — | 9 | 1 | no | — |
| 231 | C3×D9 | — | 9 | 1 | no | — |
| 232 | C3×D9 | — | 9 | 1 | no | — |
| 233 | C3×D9 | — | 18 | 1 | no | — |
| 234 | C3×D9 | — | 18 | 1 | no | — |
| 235 | C3×D9 | — | 18 | 1 | no | — |
| 236 | C3×D9 | — | 18 | 2 | no | — |
| 237 | C3×D9 | — | 18 | 1 | no | — |
| 238 | C3×D9 | — | 18 | 1 | no | — |
| 239 | C3×D9 | — | 18 | 1 | no | — |
| 240 | C3×D9 | — | 18 | 2 | no | — |
| 241 | C3×D9 | — | 54 | 1 | no | — |
| 242 | C2×C3⋊D3 | — | 27 | 1 | no | — |
| 243 | C2×C3×D3 | — | 81 | 1 | no | — |
| 244 | C2×C3×D3 | — | 81 | 1 | no | — |
| 245 | C2×C3×D3 | — | 81 | 1 | no | — |
| 246 | D32 | — | 27 | 1 | no | — |
| 247 | D32 | — | 27 | 1 | no | — |
| 248 | D32 | — | 27 | 1 | no | — |
| 249 | D32 | — | 81 | 1 | no | — |
| 250 | D32 | — | 81 | 1 | no | — |
| 251 | C2×D9 | — | 27 | 1 | no | — |
| 252 | C33 | — | 2 | 2 | no | — |
| 253 | C33 | — | 2 | 1 | no | — |
| 254 | C33 | — | 2 | 1 | no | — |
| 255 | C33 | — | 2 | 1 | no | — |
| 256 | C33 | — | 2 | 1 | no | — |
| 257 | C33 | — | 2 | 1 | no | — |
| 258 | C33 | — | 2 | 1 | no | — |
| 259 | C33 | — | 2 | 1 | no | — |
| 260 | C33 | — | 2 | 1 | no | — |
| 261 | C33 | — | 3 | 1 | no | — |
| 262 | C33 | — | 4 | 1 | no | — |
| 263 | C33 | — | 4 | 1 | no | — |
| 264 | C33 | — | 4 | 2 | no | — |
| 265 | C33 | — | 4 | 1 | no | — |
| 266 | C33 | — | 4 | 1 | no | — |
| 267 | C33 | — | 6 | 1 | no | — |
| 268 | C33 | — | 6 | 1 | no | — |
| 269 | C33 | — | 6 | 1 | no | — |
| 270 | C33 | — | 6 | 1 | no | — |
| 271 | C33 | — | 12 | 1 | no | — |
| 272 | C33 | — | 12 | 1 | no | — |
| 273 | C33 | — | 12 | 1 | no | — |
| 274 | C33 | — | 12 | 1 | no | — |
| 275 | C33 | — | 12 | 1 | no | — |
| 276 | C33 | — | 12 | 1 | no | — |
| 277 | C33 | — | 12 | 2 | no | — |
| 278 | C33 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 279 | C33 | C2×C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 280 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 281 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 282 | C33 | #1113 | 1 | 1 | yes | characteristic |
| 283 | H(3,𝔽3) | — | 2 | 2 | no | — |
| 284 | H(3,𝔽3) | — | 2 | 2 | no | — |
| 285 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 286 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 287 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 288 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 289 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 290 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 291 | H(3,𝔽3) | — | 4 | 2 | no | — |
| 292 | H(3,𝔽3) | — | 4 | 2 | no | — |
| 293 | H(3,𝔽3) | — | 4 | 2 | no | — |
| 294 | H(3,𝔽3) | — | 4 | 2 | no | — |
| 295 | H(3,𝔽3) | — | 4 | 2 | no | — |
| 296 | H(3,𝔽3) | — | 4 | 2 | no | — |
| 297 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 298 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 299 | H(3,𝔽3) | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 300 | C3×C9 | — | 2 | 1 | no | — |
| 301 | C3×C9 | — | 2 | 1 | no | — |
| 302 | C3×C9 | — | 2 | 1 | no | — |
| 303 | C3×C9 | — | 2 | 1 | no | — |
| 304 | C3×C9 | — | 2 | 1 | no | — |
| 305 | C3×C9 | — | 3 | 1 | no | — |
| 306 | C3×C9 | — | 3 | 1 | no | — |
| 307 | C3×C9 | — | 4 | 1 | no | — |
| 308 | C3×C9 | — | 4 | 2 | no | — |
| 309 | C3×C9 | — | 4 | 1 | no | — |
| 310 | C3×C9 | — | 4 | 1 | no | — |
| 311 | C3×C9 | — | 4 | 1 | no | — |
| 312 | C3×C9 | — | 6 | 1 | no | — |
| 313 | C3×C9 | — | 6 | 1 | no | — |
| 314 | C3×C9 | — | 6 | 1 | no | — |
| 315 | C3×C9 | — | 6 | 2 | no | — |
| 316 | C3×C9 | — | 6 | 1 | no | — |
| 317 | C3×C9 | — | 6 | 1 | no | — |
| 318 | C3×C9 | — | 6 | 1 | no | — |
| 319 | C3×C9 | — | 6 | 1 | no | — |
| 320 | C3×C9 | — | 12 | 1 | no | — |
| 321 | C3×C9 | — | 12 | 1 | no | — |
| 322 | C3×C9 | — | 12 | 2 | no | — |
| 323 | C3×C9 | — | 12 | 2 | no | — |
| 324 | C3×C9 | — | 12 | 2 | no | — |
| 325 | C3×C9 | — | 12 | 1 | no | — |
| 326 | C3×C9 | — | 12 | 1 | no | — |
| 327 | C3×C9 | — | 12 | 1 | no | — |
| 328 | C3×C9 | — | 12 | 2 | no | — |
| 329 | C3×C9 | — | 12 | 2 | no | — |
| 330 | C3×C9 | — | 12 | 4 | no | — |
| 331 | C3×C9 | — | 12 | 1 | no | — |
| 332 | C3×C9 | — | 12 | 1 | no | — |
| 333 | C3×C9 | — | 12 | 2 | no | — |
| 334 | C3×C9 | — | 12 | 1 | no | — |
| 335 | C3×C9 | — | 12 | 2 | no | — |
| 336 | C3×C9 | — | 12 | 1 | no | — |
| 337 | C3×C9 | — | 12 | 1 | no | — |
| 338 | C3×C9 | — | 12 | 2 | no | — |
| 339 | C3×C9 | — | 12 | 1 | no | — |
| 340 | C3×C9 | C2×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 341 | C3×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 342 | C2×C32 | — | 27 | 1 | no | — |
| 343 | C2×C32 | — | 27 | 1 | no | — |
| 344 | C2×C32 | — | 27 | 1 | no | — |
| 345 | C2×C32 | — | 54 | 1 | no | — |
| 346 | C2×C32 | — | 81 | 1 | no | — |
| 347 | C3⋊D3 | — | 3 | 1 | no | — |
| 348 | C3⋊D3 | — | 3 | 1 | no | — |
| 349 | C3⋊D3 | — | 3 | 1 | no | — |
| 350 | C3⋊D3 | — | 6 | 1 | no | — |
| 351 | C3⋊D3 | — | 9 | 1 | no | — |
| 352 | C3⋊D3 | — | 9 | 1 | no | — |
| 353 | C3⋊D3 | — | 9 | 1 | no | — |
| 354 | C3⋊D3 | — | 18 | 1 | no | — |
| 355 | C3⋊D3 | — | 18 | 1 | no | — |
| 356 | C3⋊D3 | — | 27 | 1 | no | — |
| 357 | C3⋊D3 | — | 54 | 1 | no | — |
| 358 | C3×D3 | — | 9 | 1 | no | — |
| 359 | C3×D3 | — | 9 | 1 | no | — |
| 360 | C3×D3 | — | 9 | 1 | no | — |
| 361 | C3×D3 | — | 9 | 1 | no | — |
| 362 | C3×D3 | — | 9 | 1 | no | — |
| 363 | C3×D3 | — | 9 | 1 | no | — |
| 364 | C3×D3 | — | 18 | 1 | no | — |
| 365 | C3×D3 | — | 18 | 1 | no | — |
| 366 | C3×D3 | — | 18 | 1 | no | — |
| 367 | C3×D3 | — | 18 | 1 | no | — |
| 368 | C3×D3 | — | 18 | 1 | no | — |
| 369 | C3×D3 | — | 18 | 1 | no | — |
| 370 | C3×D3 | — | 18 | 1 | no | — |
| 371 | C3×D3 | — | 27 | 1 | no | — |
| 372 | C3×D3 | — | 27 | 1 | no | — |
| 373 | C3×D3 | — | 27 | 1 | no | — |
| 374 | C3×D3 | — | 27 | 1 | no | — |
| 375 | C3×D3 | — | 27 | 1 | no | — |
| 376 | C3×D3 | — | 27 | 1 | no | — |
| 377 | C3×D3 | — | 27 | 1 | no | — |
| 378 | C3×D3 | — | 54 | 1 | no | — |
| 379 | C3×D3 | — | 54 | 1 | no | — |
| 380 | C3×D3 | — | 54 | 1 | no | — |
| 381 | C3×D3 | — | 54 | 1 | no | — |
| 382 | C3×D3 | — | 54 | 1 | no | — |
| 383 | C3×D3 | — | 54 | 1 | no | — |
| 384 | C3×D3 | — | 54 | 2 | no | — |
| 385 | C3×D3 | — | 54 | 1 | no | — |
| 386 | C3×D3 | — | 54 | 1 | no | — |
| 387 | C3×D3 | — | 54 | 1 | no | — |
| 388 | C3×D3 | — | 54 | 1 | no | — |
| 389 | C3×D3 | — | 54 | 1 | no | — |
| 390 | C3×D3 | — | 54 | 2 | no | — |
| 391 | C3×D3 | — | 81 | 1 | no | — |
| 392 | C3×D3 | — | 162 | 1 | no | — |
| 393 | C2×C9 | — | 27 | 1 | no | — |
| 394 | C2×C9 | — | 54 | 1 | no | — |
| 395 | D9 | — | 3 | 1 | no | — |
| 396 | D9 | — | 6 | 1 | no | — |
| 397 | D9 | — | 9 | 1 | no | — |
| 398 | D9 | — | 18 | 1 | no | — |
| 399 | D9 | — | 54 | 1 | no | — |
| 400 | C22×C3 | — | 243 | 1 | no | — |
| 401 | C2×D3 | — | 81 | 1 | no | — |
| 402 | C2×D3 | — | 81 | 1 | no | — |
| 403 | C2×D3 | — | 81 | 1 | no | — |
| 404 | C2×D3 | — | 243 | 1 | no | — |
| 405 | C32 | — | 2 | 1 | no | — |
| 406 | C32 | — | 2 | 1 | no | — |
| 407 | C32 | — | 2 | 1 | no | — |
| 408 | C32 | — | 2 | 1 | no | — |
| 409 | C32 | — | 2 | 1 | no | — |
| 410 | C32 | — | 2 | 1 | no | — |
| 411 | C32 | — | 2 | 1 | no | — |
| 412 | C32 | — | 2 | 1 | no | — |
| 413 | C32 | — | 3 | 1 | no | — |
| 414 | C32 | — | 3 | 1 | no | — |
| 415 | C32 | — | 4 | 1 | no | — |
| 416 | C32 | — | 4 | 2 | no | — |
| 417 | C32 | — | 4 | 1 | no | — |
| 418 | C32 | — | 4 | 1 | no | — |
| 419 | C32 | — | 4 | 1 | no | — |
| 420 | C32 | — | 4 | 1 | no | — |
| 421 | C32 | — | 6 | 1 | no | — |
| 422 | C32 | — | 6 | 1 | no | — |
| 423 | C32 | — | 6 | 1 | no | — |
| 424 | C32 | — | 6 | 1 | no | — |
| 425 | C32 | — | 6 | 2 | no | — |
| 426 | C32 | — | 6 | 1 | no | — |
| 427 | C32 | — | 6 | 1 | no | — |
| 428 | C32 | — | 6 | 1 | no | — |
| 429 | C32 | — | 6 | 1 | no | — |
| 430 | C32 | — | 6 | 1 | no | — |
| 431 | C32 | — | 6 | 1 | no | — |
| 432 | C32 | — | 6 | 1 | no | — |
| 433 | C32 | — | 6 | 1 | no | — |
| 434 | C32 | — | 6 | 1 | no | — |
| 435 | C32 | — | 12 | 1 | no | — |
| 436 | C32 | — | 12 | 1 | no | — |
| 437 | C32 | — | 12 | 1 | no | — |
| 438 | C32 | — | 12 | 1 | no | — |
| 439 | C32 | — | 12 | 1 | no | — |
| 440 | C32 | — | 12 | 1 | no | — |
| 441 | C32 | — | 12 | 1 | no | — |
| 442 | C32 | — | 12 | 2 | no | — |
| 443 | C32 | — | 12 | 1 | no | — |
| 444 | C32 | — | 12 | 2 | no | — |
| 445 | C32 | — | 12 | 2 | no | — |
| 446 | C32 | — | 12 | 2 | no | — |
| 447 | C32 | — | 12 | 1 | no | — |
| 448 | C32 | — | 12 | 2 | no | — |
| 449 | C32 | — | 12 | 1 | no | — |
| 450 | C32 | — | 12 | 2 | no | — |
| 451 | C32 | — | 12 | 2 | no | — |
| 452 | C32 | — | 12 | 4 | no | — |
| 453 | C32 | — | 12 | 1 | no | — |
| 454 | C32 | — | 12 | 1 | no | — |
| 455 | C32 | — | 12 | 1 | no | — |
| 456 | C32 | C3×D3×D9 | 1 | 1 | yes | characteristic |
| 457 | C32 | C3×D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 458 | C32 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 459 | C32 | #66431 | 1 | 1 | yes | characteristic, complemented |
| 460 | C32 | C3×#1113 | 1 | 1 | yes | characteristic |
| 461 | C9 | — | 2 | 1 | no | — |
| 462 | C9 | — | 2 | 1 | no | — |
| 463 | C9 | — | 4 | 1 | no | — |
| 464 | C9 | — | 6 | 1 | no | — |
| 465 | C9 | — | 12 | 1 | no | — |
| 466 | C9 | — | 12 | 1 | no | — |
| 467 | C9 | — | 12 | 1 | no | — |
| 468 | C9 | — | 12 | 2 | no | — |
| 469 | C9 | — | 12 | 1 | no | — |
| 470 | C9 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 471 | C2×C3 | — | 27 | 1 | no | — |
| 472 | C2×C3 | — | 27 | 1 | no | — |
| 473 | C2×C3 | — | 27 | 1 | no | — |
| 474 | C2×C3 | — | 54 | 1 | no | — |
| 475 | C2×C3 | — | 81 | 1 | no | — |
| 476 | C2×C3 | — | 81 | 1 | no | — |
| 477 | C2×C3 | — | 81 | 1 | no | — |
| 478 | C2×C3 | — | 162 | 1 | no | — |
| 479 | C2×C3 | — | 162 | 1 | no | — |
| 480 | C2×C3 | — | 162 | 1 | no | — |
| 481 | D3 | — | 9 | 1 | no | — |
| 482 | D3 | — | 9 | 1 | no | — |
| 483 | D3 | — | 9 | 1 | no | — |
| 484 | D3 | — | 9 | 1 | no | — |
| 485 | D3 | — | 18 | 1 | no | — |
| 486 | D3 | — | 18 | 1 | no | — |
| 487 | D3 | — | 27 | 1 | no | — |
| 488 | D3 | — | 27 | 1 | no | — |
| 489 | D3 | — | 27 | 1 | no | — |
| 490 | D3 | — | 54 | 1 | no | — |
| 491 | D3 | — | 54 | 1 | no | — |
| 492 | D3 | — | 81 | 1 | no | — |
| 493 | D3 | — | 162 | 1 | no | — |
| 494 | C22 | — | 243 | 1 | no | Sylow |
| 495 | C3 | — | 2 | 1 | no | — |
| 496 | C3 | — | 2 | 1 | no | — |
| 497 | C3 | — | 2 | 1 | no | — |
| 498 | C3 | — | 3 | 1 | no | — |
| 499 | C3 | — | 4 | 1 | no | — |
| 500 | C3 | — | 6 | 1 | no | — |
| 501 | C3 | — | 6 | 1 | no | — |
| 502 | C3 | — | 6 | 1 | no | — |
| 503 | C3 | — | 6 | 1 | no | — |
| 504 | C3 | — | 12 | 1 | no | — |
| 505 | C3 | — | 12 | 1 | no | — |
| 506 | C3 | — | 12 | 1 | no | — |
| 507 | C3 | — | 12 | 1 | no | — |
| 508 | C3 | — | 12 | 2 | no | — |
| 509 | C3 | — | 12 | 1 | no | — |
| 510 | C3 | — | 12 | 1 | no | — |
| 511 | C3 | D9×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 512 | C3 | C3×#66431 | 1 | 1 | yes | characteristic |
| 513 | C3 | (C3⋊#1113)⋊C3 | 1 | 1 | yes | characteristic |
| 514 | C2 | — | 27 | 1 | no | — |
| 515 | C2 | — | 27 | 1 | no | — |
| 516 | C2 | — | 81 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×C9 | C22×C3 |
| Frattini | C32 | C3×#1113 |
| Fitting | C3×C9×H(3,𝔽3) | C22 |
| socle | C33 | C3×D32 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#92297 | C2 | semidirect |
| 2. H(3,𝔽3)×C3⋊D9 | C2 | semidirect |
| 3. C9×C3⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 4. #11758088 | C3 | semidirect |
| 8. C3×C9×H(3,𝔽3) | C22 | semidirect |
| 9. C9×C3⋊(C3⋊D3) | C2×C3 | semidirect |
| 10. C3×C3⋊(C3⋊D9) | C2×C3 | semidirect |
| 17. C32×C3⋊D9 | D3 | semidirect |
| 18. C32×C3⋊D9 | C2×C3 | semidirect |
| 20. #92297 | D3 | semidirect |
| 38. C33×C9 | C2×D3 | semidirect |
| 39. C33×C9 | C22×C3 | semidirect |
| 47. C9×H(3,𝔽3) | C2×D3 | semidirect |
| 58. C3⋊(C3⋊D9) | C3×D3 | semidirect |
| 62. C3⋊((C3⋊D3)⋊C3) | D9 | semidirect |
| 126. C3×H(3,𝔽3) | C2×D9 | semidirect |
| 153. C32×C9 | D32 | semidirect |
| 155. C32×C9 | C2×C3×D3 | semidirect |
| 170. C3⋊(C3⋊D3) | C3×D9 | semidirect |
| 210. C3⋊D9 | (C3⋊D3)⋊C3 | semidirect |
| 278. C33 | D3×D9 | semidirect |
| 279. C33 | C2×C3×D9 | semidirect |
| 299. H(3,𝔽3) | D3×D9 | semidirect |
| 340. C3×C9 | C2×(C3⋊D3)⋊C3 | semidirect |
| 457. C32 | C3×D3×D9 | semidirect |
| 459. C32 | #66431 | semidirect |
| 470. C9 | D3×(C3⋊D3)⋊C3 | semidirect |
| 511. C3 | D9×(C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#92297 | 2 |
| H(3,𝔽3)×C3⋊D9 | 2 |
| C9×C3⋊((C3⋊D3)⋊C3) | 2 |
| #11758088 | 3 |
| (C3⋊#1113)⋊C3 | 3 |
| C3×#66431 | 3 |
| D9×(C3⋊D3)⋊C3 | 3 |