Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
567 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 567 conjugacy classes of subgroups — too many to draw. Only its 52 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 | #13091656 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13091655 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13091653 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11758087 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D3×#4208 | — | 3 | 1 | no | maximal |
| 6 | D3×#4178 | — | 3 | 1 | no | maximal |
| 7 | D3×#4178 | — | 3 | 1 | no | maximal |
| 8 | D3×#4178 | — | 3 | 1 | no | maximal |
| 9 | D3×#4178 | — | 3 | 1 | no | maximal |
| 10 | #10624932 | C22 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | #92404 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3⋊#4208 | — | 3 | 1 | no | — |
| 13 | #92392 | — | 2 | 1 | no | — |
| 14 | #92392 | C2×C3 | 1 | 1 | yes | characteristic |
| 15 | #92392 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3×#4208 | D3 | 1 | 1 | yes | characteristic, complemented |
| 17 | D3×#737 | — | 3 | 1 | no | — |
| 18 | C3⋊#4178 | — | 3 | 1 | no | — |
| 19 | C3⋊#4178 | — | 3 | 1 | no | — |
| 20 | C3⋊#4178 | — | 3 | 1 | no | — |
| 21 | C3⋊#4178 | — | 3 | 1 | no | — |
| 22 | C3⋊#4178 | — | 6 | 1 | no | — |
| 23 | C3⋊#4178 | — | 6 | 1 | no | — |
| 24 | C3⋊#4178 | — | 6 | 1 | no | — |
| 25 | C3⋊#4178 | — | 6 | 1 | no | — |
| 26 | #92285 | — | 2 | 1 | no | — |
| 27 | #92285 | — | 2 | 1 | no | — |
| 28 | #92285 | — | 2 | 1 | no | — |
| 29 | #92285 | — | 2 | 1 | no | — |
| 30 | D3×#732 | — | 3 | 1 | no | — |
| 31 | D3×#732 | — | 3 | 1 | no | — |
| 32 | D3×#732 | — | 3 | 1 | no | — |
| 33 | D3×#732 | — | 3 | 1 | no | — |
| 34 | C3×#4178 | D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C3×#4178 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C3×#4178 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#4178 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×#4208 | — | 9 | 1 | no | — |
| 39 | D3×#272 | — | 3 | 1 | no | — |
| 40 | D3×#272 | — | 3 | 1 | no | — |
| 41 | D3×#272 | — | 3 | 1 | no | — |
| 42 | D3×#272 | — | 3 | 1 | no | — |
| 43 | D3×#272 | — | 3 | 1 | no | — |
| 44 | D3×#272 | — | 9 | 1 | no | — |
| 45 | D32×C9 | — | 9 | 1 | no | — |
| 46 | D32×C9 | — | 9 | 1 | no | — |
| 47 | D32×C9 | — | 9 | 1 | no | — |
| 48 | D32×C9 | — | 9 | 1 | no | — |
| 49 | C2×#4178 | — | 9 | 1 | no | — |
| 50 | H(5,𝔽3) | — | 2 | 1 | no | — |
| 51 | H(5,𝔽3) | C22×C3 | 1 | 1 | yes | characteristic |
| 52 | C3×#737 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | #6911 | — | 2 | 1 | no | — |
| 54 | #6911 | — | 2 | 1 | no | — |
| 55 | #6911 | — | 2 | 1 | no | — |
| 56 | #6911 | — | 2 | 1 | no | — |
| 57 | #6911 | — | 4 | 1 | no | — |
| 58 | #6911 | — | 4 | 1 | no | — |
| 59 | #6911 | — | 4 | 1 | no | — |
| 60 | #6911 | — | 4 | 1 | no | — |
| 61 | C3×#732 | — | 2 | 1 | no | — |
| 62 | C3×#732 | — | 2 | 1 | no | — |
| 63 | C3×#732 | — | 2 | 1 | no | — |
| 64 | C3×#732 | — | 2 | 1 | no | — |
| 65 | C3×#732 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 66 | C3×#732 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×#732 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 68 | C3×#732 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 69 | C2×#737 | — | 9 | 1 | no | — |
| 70 | C3⋊#272 | — | 3 | 1 | no | — |
| 71 | C3⋊#272 | — | 3 | 1 | no | — |
| 72 | C3⋊#272 | — | 3 | 1 | no | — |
| 73 | C3⋊#272 | — | 3 | 1 | no | — |
| 74 | C3⋊#272 | — | 3 | 1 | no | — |
| 75 | C3⋊#272 | — | 6 | 1 | no | — |
| 76 | C3⋊#272 | — | 6 | 1 | no | — |
| 77 | C3⋊#272 | — | 6 | 1 | no | — |
| 78 | C3⋊#272 | — | 6 | 1 | no | — |
| 79 | C3⋊#272 | — | 9 | 1 | no | — |
| 80 | C3⋊#272 | — | 18 | 1 | no | — |
| 81 | C3⋊#272 | — | 18 | 1 | no | — |
| 82 | C3⋊#272 | — | 18 | 1 | no | — |
| 83 | C3⋊#272 | — | 18 | 1 | no | — |
| 84 | #4208 | — | 6 | 1 | no | — |
| 85 | #4208 | — | 9 | 1 | no | — |
| 86 | #4208 | — | 18 | 1 | no | — |
| 87 | #4208 | — | 18 | 1 | no | — |
| 88 | #4208 | — | 18 | 1 | no | — |
| 89 | #4208 | — | 18 | 1 | no | — |
| 90 | C3×#272 | — | 3 | 1 | no | — |
| 91 | C3×#272 | — | 6 | 1 | no | — |
| 92 | C3×#272 | C3×D3 | 1 | 1 | yes | characteristic |
| 93 | C3×#272 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 94 | C3×#272 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | C3×#272 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 96 | C3×#272 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 97 | C9×C3⋊D3 | — | 9 | 1 | no | — |
| 98 | C9×C3⋊D3 | — | 9 | 1 | no | — |
| 99 | C9×C3⋊D3 | — | 9 | 1 | no | — |
| 100 | C9×C3⋊D3 | — | 9 | 1 | no | — |
| 101 | D3×3−1+2 | — | 6 | 1 | no | — |
| 102 | D3×3−1+2 | — | 6 | 1 | no | — |
| 103 | D3×3−1+2 | — | 6 | 1 | no | — |
| 104 | D3×3−1+2 | — | 6 | 1 | no | — |
| 105 | D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 106 | D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 107 | D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 108 | D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 109 | D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 110 | D3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 111 | D3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 112 | D3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 113 | D3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 114 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 115 | C3×D3×C9 | — | 3 | 1 | no | — |
| 116 | C3×D3×C9 | — | 3 | 1 | no | — |
| 117 | C3×D3×C9 | — | 3 | 1 | no | — |
| 118 | C3×D3×C9 | — | 3 | 1 | no | — |
| 119 | C3×D3×C9 | — | 3 | 1 | no | — |
| 120 | C3×D3×C9 | — | 3 | 1 | no | — |
| 121 | C3×D3×C9 | — | 3 | 1 | no | — |
| 122 | C3×D3×C9 | — | 3 | 1 | no | — |
| 123 | C2×#732 | — | 9 | 1 | no | — |
| 124 | #4178 | — | 2 | 1 | no | — |
| 125 | #4178 | — | 2 | 1 | no | — |
| 126 | #4178 | — | 2 | 1 | no | — |
| 127 | #4178 | — | 2 | 1 | no | — |
| 128 | #4178 | — | 9 | 1 | no | — |
| 129 | #4178 | — | 18 | 1 | no | — |
| 130 | #4178 | — | 18 | 1 | no | — |
| 131 | #4178 | — | 18 | 1 | no | — |
| 132 | #4178 | — | 18 | 1 | no | — |
| 133 | #4178 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 134 | C3×D32 | — | 9 | 1 | no | — |
| 135 | C3×D32 | — | 9 | 1 | no | — |
| 136 | C3×D32 | — | 9 | 1 | no | — |
| 137 | C3×D32 | — | 9 | 1 | no | — |
| 138 | C3×D32 | — | 27 | 1 | no | — |
| 139 | C3×D32 | — | 27 | 1 | no | — |
| 140 | C3×D32 | — | 27 | 1 | no | — |
| 141 | C3×D32 | — | 27 | 1 | no | — |
| 142 | C2×#272 | — | 9 | 1 | no | — |
| 143 | C2×#272 | — | 9 | 1 | no | — |
| 144 | C2×D3×C9 | — | 27 | 1 | no | — |
| 145 | C2×D3×C9 | — | 27 | 1 | no | — |
| 146 | C2×D3×C9 | — | 27 | 1 | no | — |
| 147 | C2×D3×C9 | — | 27 | 1 | no | — |
| 148 | C2×D3×C9 | — | 27 | 1 | no | — |
| 149 | #737 | — | 6 | 1 | no | — |
| 150 | #737 | — | 12 | 1 | no | — |
| 151 | #737 | — | 12 | 1 | no | — |
| 152 | #737 | — | 12 | 1 | no | — |
| 153 | #737 | — | 12 | 1 | no | — |
| 154 | C3×3−1+2 | — | 2 | 1 | no | — |
| 155 | C3×3−1+2 | — | 2 | 1 | no | — |
| 156 | C3×3−1+2 | — | 2 | 1 | no | — |
| 157 | C3×3−1+2 | — | 2 | 1 | no | — |
| 158 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 159 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 160 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 161 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 162 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 163 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 164 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 165 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 166 | C3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 167 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 168 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 169 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 170 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 171 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 172 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 173 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 174 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 175 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 176 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 177 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 178 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 179 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 180 | C3×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 181 | C3×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 182 | C3×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 183 | C3×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 184 | C3×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 185 | C32×C9 | D32 | 1 | 1 | yes | characteristic, complemented |
| 186 | C32×C9 | D32 | 1 | 1 | yes | characteristic, complemented |
| 187 | C32×C9 | D32 | 1 | 1 | yes | characteristic, complemented |
| 188 | C32×C9 | D32 | 1 | 1 | yes | characteristic, complemented |
| 189 | #732 | — | 2 | 1 | no | — |
| 190 | #732 | — | 2 | 1 | no | — |
| 191 | #732 | — | 2 | 1 | no | — |
| 192 | #732 | — | 2 | 1 | no | — |
| 193 | #732 | — | 2 | 1 | no | — |
| 194 | #732 | — | 2 | 1 | no | — |
| 195 | #732 | — | 2 | 1 | no | — |
| 196 | #732 | — | 2 | 1 | no | — |
| 197 | #732 | — | 4 | 1 | no | — |
| 198 | #732 | — | 4 | 1 | no | — |
| 199 | #732 | — | 4 | 1 | no | — |
| 200 | #732 | — | 4 | 1 | no | — |
| 201 | #732 | — | 4 | 1 | no | — |
| 202 | #732 | — | 4 | 1 | no | — |
| 203 | #732 | — | 4 | 1 | no | — |
| 204 | #732 | — | 4 | 1 | no | — |
| 205 | #732 | — | 4 | 1 | no | — |
| 206 | #732 | — | 4 | 1 | no | — |
| 207 | #732 | — | 4 | 1 | no | — |
| 208 | #732 | — | 4 | 1 | no | — |
| 209 | #732 | — | 4 | 1 | no | — |
| 210 | #732 | — | 4 | 1 | no | — |
| 211 | #732 | — | 4 | 1 | no | — |
| 212 | #732 | — | 4 | 1 | no | — |
| 213 | #732 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 214 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 215 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 216 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 217 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 218 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 219 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 220 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 221 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 222 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 223 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 224 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 225 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 226 | C32×D3 | — | 3 | 1 | no | — |
| 227 | C32×D3 | — | 3 | 1 | no | — |
| 228 | C32×D3 | — | 3 | 1 | no | — |
| 229 | C32×D3 | — | 3 | 1 | no | — |
| 230 | C32×D3 | — | 3 | 1 | no | — |
| 231 | C32×D3 | — | 3 | 1 | no | — |
| 232 | C32×D3 | — | 3 | 1 | no | — |
| 233 | C32×D3 | — | 3 | 1 | no | — |
| 234 | C32×D3 | — | 9 | 1 | no | — |
| 235 | C32×D3 | — | 9 | 1 | no | — |
| 236 | C32×D3 | — | 9 | 1 | no | — |
| 237 | C32×D3 | — | 9 | 1 | no | — |
| 238 | C32×D3 | — | 9 | 1 | no | — |
| 239 | C32×D3 | — | 9 | 1 | no | — |
| 240 | C32×D3 | — | 9 | 1 | no | — |
| 241 | C32×D3 | — | 9 | 1 | no | — |
| 242 | C32×D3 | — | 18 | 1 | no | — |
| 243 | C32×D3 | — | 18 | 1 | no | — |
| 244 | C32×D3 | — | 18 | 1 | no | — |
| 245 | C32×D3 | — | 18 | 1 | no | — |
| 246 | C2×3−1+2 | — | 18 | 1 | no | — |
| 247 | C2×3−1+2 | — | 18 | 1 | no | — |
| 248 | C2×3−1+2 | — | 18 | 1 | no | — |
| 249 | C2×3−1+2 | — | 18 | 1 | no | — |
| 250 | C2×H(3,𝔽3) | — | 9 | 1 | no | — |
| 251 | C2×H(3,𝔽3) | — | 9 | 1 | no | — |
| 252 | C2×H(3,𝔽3) | — | 18 | 1 | no | — |
| 253 | C2×C3×C9 | — | 9 | 1 | no | — |
| 254 | C2×C3×C9 | — | 9 | 1 | no | — |
| 255 | C2×C3×C9 | — | 9 | 1 | no | — |
| 256 | C2×C3×C9 | — | 9 | 1 | no | — |
| 257 | C2×C3×C9 | — | 9 | 1 | no | — |
| 258 | #272 | — | 9 | 1 | no | — |
| 259 | #272 | — | 9 | 1 | no | — |
| 260 | #272 | — | 18 | 1 | no | — |
| 261 | #272 | — | 18 | 1 | no | — |
| 262 | #272 | — | 18 | 1 | no | — |
| 263 | #272 | — | 18 | 1 | no | — |
| 264 | #272 | — | 18 | 1 | no | — |
| 265 | #272 | — | 18 | 1 | no | — |
| 266 | #272 | — | 18 | 1 | no | — |
| 267 | #272 | — | 18 | 1 | no | — |
| 268 | #272 | — | 54 | 1 | no | — |
| 269 | #272 | — | 54 | 1 | no | — |
| 270 | #272 | — | 54 | 1 | no | — |
| 271 | #272 | — | 54 | 1 | no | — |
| 272 | #272 | — | 54 | 1 | no | — |
| 273 | #272 | — | 54 | 1 | no | — |
| 274 | #272 | — | 54 | 1 | no | — |
| 275 | #272 | — | 54 | 1 | no | — |
| 276 | #272 | — | 54 | 1 | no | — |
| 277 | #272 | — | 54 | 1 | no | — |
| 278 | #272 | — | 54 | 1 | no | — |
| 279 | #272 | — | 54 | 1 | no | — |
| 280 | #272 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 281 | #272 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 282 | D3×C9 | — | 3 | 1 | no | — |
| 283 | D3×C9 | — | 6 | 1 | no | — |
| 284 | D3×C9 | — | 6 | 1 | no | — |
| 285 | D3×C9 | — | 6 | 1 | no | — |
| 286 | D3×C9 | — | 6 | 1 | no | — |
| 287 | D3×C9 | — | 18 | 1 | no | — |
| 288 | D3×C9 | — | 18 | 1 | no | — |
| 289 | D3×C9 | — | 18 | 1 | no | — |
| 290 | D3×C9 | — | 18 | 1 | no | — |
| 291 | D3×C9 | — | 27 | 1 | no | — |
| 292 | D3×C9 | — | 27 | 1 | no | — |
| 293 | D3×C9 | — | 27 | 1 | no | — |
| 294 | D3×C9 | — | 27 | 1 | no | — |
| 295 | D3×C9 | — | 27 | 1 | no | — |
| 296 | D3×C9 | — | 54 | 1 | no | — |
| 297 | D3×C9 | — | 54 | 1 | no | — |
| 298 | D3×C9 | — | 54 | 1 | no | — |
| 299 | D3×C9 | — | 54 | 1 | no | — |
| 300 | C2×C3×D3 | — | 27 | 1 | no | — |
| 301 | C2×C3×D3 | — | 27 | 1 | no | — |
| 302 | C2×C3×D3 | — | 27 | 1 | no | — |
| 303 | C2×C3×D3 | — | 27 | 1 | no | — |
| 304 | C2×C3×D3 | — | 27 | 1 | no | — |
| 305 | C2×C3×D3 | — | 81 | 1 | no | — |
| 306 | D32 | — | 9 | 1 | no | — |
| 307 | D32 | — | 9 | 1 | no | — |
| 308 | D32 | — | 9 | 1 | no | — |
| 309 | D32 | — | 9 | 1 | no | — |
| 310 | D32 | — | 27 | 1 | no | — |
| 311 | D32 | — | 27 | 1 | no | — |
| 312 | D32 | — | 27 | 1 | no | — |
| 313 | D32 | — | 27 | 1 | no | — |
| 314 | C22×C9 | — | 81 | 1 | no | — |
| 315 | C33 | — | 3 | 1 | no | — |
| 316 | C33 | — | 3 | 1 | no | — |
| 317 | C33 | — | 3 | 1 | no | — |
| 318 | C33 | — | 3 | 1 | no | — |
| 319 | C33 | — | 6 | 1 | no | — |
| 320 | C33 | — | 6 | 1 | no | — |
| 321 | C33 | — | 6 | 1 | no | — |
| 322 | C33 | — | 6 | 1 | no | — |
| 323 | C33 | — | 6 | 1 | no | — |
| 324 | C33 | — | 6 | 1 | no | — |
| 325 | C33 | — | 6 | 1 | no | — |
| 326 | C33 | — | 6 | 1 | no | — |
| 327 | C33 | — | 12 | 1 | no | — |
| 328 | C33 | — | 12 | 1 | no | — |
| 329 | C33 | — | 12 | 1 | no | — |
| 330 | C33 | — | 12 | 1 | no | — |
| 331 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 332 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 333 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 334 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 335 | 3−1+2 | — | 6 | 1 | no | — |
| 336 | 3−1+2 | — | 12 | 1 | no | — |
| 337 | 3−1+2 | — | 12 | 1 | no | — |
| 338 | 3−1+2 | — | 12 | 1 | no | — |
| 339 | 3−1+2 | — | 12 | 1 | no | — |
| 340 | 3−1+2 | — | 12 | 1 | no | — |
| 341 | 3−1+2 | — | 12 | 1 | no | — |
| 342 | 3−1+2 | — | 12 | 1 | no | — |
| 343 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 344 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 345 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 346 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 347 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 348 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 349 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 350 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 351 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 352 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 353 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 354 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 355 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 356 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 357 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 358 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 359 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 360 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 361 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 362 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 363 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 364 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 365 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 366 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 367 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 368 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 369 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 370 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 371 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 372 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 373 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 374 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 375 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 376 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 377 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 378 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 379 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 380 | H(3,𝔽3) | C2×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 381 | H(3,𝔽3) | C2×C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 382 | C3×C9 | — | 2 | 1 | no | — |
| 383 | C3×C9 | — | 2 | 1 | no | — |
| 384 | C3×C9 | — | 2 | 1 | no | — |
| 385 | C3×C9 | — | 2 | 1 | no | — |
| 386 | C3×C9 | — | 6 | 1 | no | — |
| 387 | C3×C9 | — | 6 | 1 | no | — |
| 388 | C3×C9 | — | 6 | 1 | no | — |
| 389 | C3×C9 | — | 6 | 1 | no | — |
| 390 | C3×C9 | — | 6 | 1 | no | — |
| 391 | C3×C9 | — | 6 | 1 | no | — |
| 392 | C3×C9 | — | 12 | 1 | no | — |
| 393 | C3×C9 | — | 12 | 1 | no | — |
| 394 | C3×C9 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 395 | C2×C32 | — | 9 | 1 | no | — |
| 396 | C2×C32 | — | 9 | 1 | no | — |
| 397 | C2×C32 | — | 9 | 1 | no | — |
| 398 | C2×C32 | — | 9 | 1 | no | — |
| 399 | C2×C32 | — | 9 | 1 | no | — |
| 400 | C2×C32 | — | 27 | 1 | no | — |
| 401 | C2×C32 | — | 54 | 1 | no | — |
| 402 | C3⋊D3 | — | 9 | 1 | no | — |
| 403 | C3⋊D3 | — | 9 | 1 | no | — |
| 404 | C3⋊D3 | — | 9 | 1 | no | — |
| 405 | C3⋊D3 | — | 9 | 1 | no | — |
| 406 | C3⋊D3 | — | 27 | 1 | no | — |
| 407 | C3⋊D3 | — | 27 | 1 | no | — |
| 408 | C3⋊D3 | — | 27 | 1 | no | — |
| 409 | C3⋊D3 | — | 27 | 1 | no | — |
| 410 | C3⋊D3 | — | 54 | 1 | no | — |
| 411 | C3⋊D3 | — | 54 | 1 | no | — |
| 412 | C3⋊D3 | — | 54 | 1 | no | — |
| 413 | C3⋊D3 | — | 54 | 1 | no | — |
| 414 | C3×D3 | — | 3 | 1 | no | — |
| 415 | C3×D3 | — | 3 | 1 | no | — |
| 416 | C3×D3 | — | 3 | 1 | no | — |
| 417 | C3×D3 | — | 3 | 1 | no | — |
| 418 | C3×D3 | — | 3 | 1 | no | — |
| 419 | C3×D3 | — | 9 | 1 | no | — |
| 420 | C3×D3 | — | 9 | 1 | no | — |
| 421 | C3×D3 | — | 9 | 1 | no | — |
| 422 | C3×D3 | — | 9 | 1 | no | — |
| 423 | C3×D3 | — | 18 | 1 | no | — |
| 424 | C3×D3 | — | 18 | 1 | no | — |
| 425 | C3×D3 | — | 18 | 1 | no | — |
| 426 | C3×D3 | — | 18 | 1 | no | — |
| 427 | C3×D3 | — | 18 | 1 | no | — |
| 428 | C3×D3 | — | 27 | 1 | no | — |
| 429 | C3×D3 | — | 27 | 1 | no | — |
| 430 | C3×D3 | — | 27 | 1 | no | — |
| 431 | C3×D3 | — | 27 | 1 | no | — |
| 432 | C3×D3 | — | 27 | 1 | no | — |
| 433 | C3×D3 | — | 27 | 1 | no | — |
| 434 | C3×D3 | — | 27 | 1 | no | — |
| 435 | C3×D3 | — | 54 | 1 | no | — |
| 436 | C3×D3 | — | 54 | 1 | no | — |
| 437 | C3×D3 | — | 54 | 1 | no | — |
| 438 | C3×D3 | — | 54 | 1 | no | — |
| 439 | C3×D3 | — | 54 | 1 | no | — |
| 440 | C3×D3 | — | 54 | 1 | no | — |
| 441 | C3×D3 | — | 54 | 1 | no | — |
| 442 | C3×D3 | — | 54 | 1 | no | — |
| 443 | C3×D3 | — | 54 | 1 | no | — |
| 444 | C3×D3 | — | 54 | 1 | no | — |
| 445 | C3×D3 | — | 54 | 1 | no | — |
| 446 | C3×D3 | — | 54 | 1 | no | — |
| 447 | C3×D3 | — | 54 | 1 | no | — |
| 448 | C3×D3 | — | 54 | 1 | no | — |
| 449 | C3×D3 | — | 81 | 1 | no | — |
| 450 | C3×D3 | — | 162 | 1 | no | — |
| 451 | C3×D3 | — | 162 | 1 | no | — |
| 452 | C3×D3 | — | 162 | 1 | no | — |
| 453 | C3×D3 | — | 162 | 1 | no | — |
| 454 | C2×C9 | — | 9 | 1 | no | — |
| 455 | C2×C9 | — | 18 | 1 | no | — |
| 456 | C2×C9 | — | 18 | 1 | no | — |
| 457 | C2×C9 | — | 18 | 1 | no | — |
| 458 | C2×C9 | — | 18 | 1 | no | — |
| 459 | C2×C9 | — | 54 | 1 | no | — |
| 460 | C2×C9 | — | 81 | 1 | no | — |
| 461 | C22×C3 | — | 81 | 1 | no | — |
| 462 | C2×D3 | — | 27 | 1 | no | — |
| 463 | C2×D3 | — | 27 | 1 | no | — |
| 464 | C2×D3 | — | 27 | 1 | no | — |
| 465 | C2×D3 | — | 27 | 1 | no | — |
| 466 | C2×D3 | — | 27 | 1 | no | — |
| 467 | C2×D3 | — | 81 | 1 | no | — |
| 468 | C32 | — | 2 | 1 | no | — |
| 469 | C32 | — | 2 | 1 | no | — |
| 470 | C32 | — | 2 | 1 | no | — |
| 471 | C32 | — | 2 | 1 | no | — |
| 472 | C32 | — | 3 | 1 | no | — |
| 473 | C32 | — | 6 | 1 | no | — |
| 474 | C32 | — | 6 | 1 | no | — |
| 475 | C32 | — | 6 | 1 | no | — |
| 476 | C32 | — | 6 | 1 | no | — |
| 477 | C32 | — | 6 | 1 | no | — |
| 478 | C32 | — | 9 | 1 | no | — |
| 479 | C32 | — | 12 | 1 | no | — |
| 480 | C32 | — | 12 | 1 | no | — |
| 481 | C32 | — | 12 | 1 | no | — |
| 482 | C32 | — | 12 | 1 | no | — |
| 483 | C32 | — | 18 | 1 | no | — |
| 484 | C32 | — | 18 | 1 | no | — |
| 485 | C32 | — | 36 | 1 | no | — |
| 486 | C32 | — | 54 | 1 | no | — |
| 487 | C32 | — | 54 | 1 | no | — |
| 488 | C32 | — | 54 | 1 | no | — |
| 489 | C32 | — | 54 | 1 | no | — |
| 490 | C32 | — | 108 | 1 | no | — |
| 491 | C32 | — | 108 | 1 | no | — |
| 492 | C32 | — | 108 | 1 | no | — |
| 493 | C32 | — | 108 | 1 | no | — |
| 494 | C32 | — | 108 | 1 | no | — |
| 495 | C32 | — | 108 | 1 | no | — |
| 496 | C32 | — | 108 | 1 | no | — |
| 497 | C32 | — | 108 | 1 | no | — |
| 498 | C32 | — | 108 | 1 | no | — |
| 499 | C32 | — | 108 | 1 | no | — |
| 500 | C32 | — | 108 | 1 | no | — |
| 501 | C32 | — | 108 | 1 | no | — |
| 502 | C32 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 503 | C32 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 504 | C32 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 505 | C32 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 506 | C32 | C3×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 507 | C9 | — | 6 | 1 | no | — |
| 508 | C9 | — | 6 | 1 | no | — |
| 509 | C9 | — | 12 | 1 | no | — |
| 510 | C9 | — | 12 | 1 | no | — |
| 511 | C9 | — | 12 | 1 | no | — |
| 512 | C2×C3 | — | 9 | 1 | no | — |
| 513 | C2×C3 | — | 9 | 1 | no | — |
| 514 | C2×C3 | — | 27 | 1 | no | — |
| 515 | C2×C3 | — | 27 | 1 | no | — |
| 516 | C2×C3 | — | 27 | 1 | no | — |
| 517 | C2×C3 | — | 54 | 1 | no | — |
| 518 | C2×C3 | — | 54 | 1 | no | — |
| 519 | C2×C3 | — | 81 | 1 | no | — |
| 520 | C2×C3 | — | 162 | 1 | no | — |
| 521 | C2×C3 | — | 162 | 1 | no | — |
| 522 | D3 | — | 3 | 1 | no | — |
| 523 | D3 | — | 3 | 1 | no | — |
| 524 | D3 | — | 3 | 1 | no | — |
| 525 | D3 | — | 3 | 1 | no | — |
| 526 | D3 | — | 3 | 1 | no | — |
| 527 | D3 | — | 9 | 1 | no | — |
| 528 | D3 | — | 27 | 1 | no | — |
| 529 | D3 | — | 27 | 1 | no | — |
| 530 | D3 | — | 27 | 1 | no | — |
| 531 | D3 | — | 27 | 1 | no | — |
| 532 | D3 | — | 27 | 1 | no | — |
| 533 | D3 | — | 54 | 1 | no | — |
| 534 | D3 | — | 54 | 1 | no | — |
| 535 | D3 | — | 54 | 1 | no | — |
| 536 | D3 | — | 54 | 1 | no | — |
| 537 | D3 | — | 81 | 1 | no | — |
| 538 | D3 | — | 162 | 1 | no | — |
| 539 | D3 | — | 162 | 1 | no | — |
| 540 | D3 | — | 162 | 1 | no | — |
| 541 | D3 | — | 162 | 1 | no | — |
| 542 | C22 | — | 81 | 1 | no | Sylow |
| 543 | C3 | — | 3 | 1 | no | — |
| 544 | C3 | — | 3 | 1 | no | — |
| 545 | C3 | — | 3 | 1 | no | — |
| 546 | C3 | — | 6 | 1 | no | — |
| 547 | C3 | — | 6 | 1 | no | — |
| 548 | C3 | — | 12 | 1 | no | — |
| 549 | C3 | — | 12 | 1 | no | — |
| 550 | C3 | — | 12 | 1 | no | — |
| 551 | C3 | — | 12 | 1 | no | — |
| 552 | C3 | — | 18 | 1 | no | — |
| 553 | C3 | — | 18 | 1 | no | — |
| 554 | C3 | — | 18 | 1 | no | — |
| 555 | C3 | — | 36 | 1 | no | — |
| 556 | C3 | — | 36 | 1 | no | — |
| 557 | C3 | — | 36 | 1 | no | — |
| 558 | C3 | — | 36 | 1 | no | — |
| 559 | C3 | — | 36 | 1 | no | — |
| 560 | C3 | — | 36 | 1 | no | — |
| 561 | C3 | — | 36 | 1 | no | — |
| 562 | C3 | C3⋊D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 563 | C2 | — | 9 | 1 | no | — |
| 564 | C2 | — | 9 | 1 | no | — |
| 565 | C2 | — | 81 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3 | C3⋊D3×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(5,𝔽3) | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | #10624932 | C22 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13091656 | C2 | semidirect |
| 2. #13091655 | C2 | semidirect |
| 3. #13091653 | C2 | semidirect |
| 4. #11758087 | C3 | semidirect |
| 10. #10624932 | C22 | semidirect |
| 11. #92404 | C2×C3 | semidirect |
| 15. #92392 | C2×C3 | semidirect |
| 16. C3×#4208 | D3 | semidirect |
| 34. C3×#4178 | D3 | semidirect |
| 35. C3×#4178 | D3 | semidirect |
| 36. C3×#4178 | D3 | semidirect |
| 37. C3×#4178 | D3 | semidirect |
| 52. C3×#737 | C2×D3 | semidirect |
| 65. C3×#732 | C2×D3 | semidirect |
| 66. C3×#732 | C2×D3 | semidirect |
| 67. C3×#732 | C2×D3 | semidirect |
| 68. C3×#732 | C2×D3 | semidirect |
| 93. C3×#272 | C3×D3 | semidirect |
| 94. C3×#272 | C3×D3 | semidirect |
| 95. C3×#272 | C3×D3 | semidirect |
| 96. C3×#272 | C3×D3 | semidirect |
| 133. #4178 | C3⋊D3 | semidirect |
| 185. C32×C9 | D32 | semidirect |
| 186. C32×C9 | D32 | semidirect |
| 187. C32×C9 | D32 | semidirect |
| 188. C32×C9 | D32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13091656 | 2 |
| #13091655 | 2 |
| #13091653 | 2 |
| #11758087 | 3 |
| D3×#4208 | 3 |
| D3×#4178 | 3 |