Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
927 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 927 conjugacy classes of subgroups — too many to draw. Only its 90 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⋊D3×#41⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#1010⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | D32×SL(2,𝔽3) | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #64316⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10596694 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D3×2−1+4⋊C3 | — | 3 | 2 | no | maximal |
| 7 | C32×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | C3×#3802 | — | 4 | 1 | no | maximal |
| 9 | C3⋊D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 10 | C3⋊(C3⋊(#41⋊C3)) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3×D3×SL(2,𝔽3) | C22 | 1 | 4 | yes | complemented |
| 12 | #41×C3⋊D3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 13 | C3×#1010 | C2×C3 | 1 | 2 | yes | complemented |
| 14 | C3×2−1+4⋊C3 | — | 3 | 2 | no | — |
| 15 | D32×Q8 | C2×C3 | 1 | 2 | yes | complemented |
| 16 | #64316 | C2×C3 | 1 | 2 | yes | complemented |
| 17 | #64312 | — | 3 | 2 | no | — |
| 18 | #64309 | — | 3 | 2 | no | — |
| 19 | #64306 | — | 3 | 1 | no | — |
| 20 | C2×#3797 | — | 3 | 1 | no | — |
| 21 | #64297 | — | 3 | 2 | no | — |
| 22 | #1010⋊C3 | — | 2 | 2 | no | — |
| 23 | #1010⋊C3 | D3 | 1 | 2 | yes | complemented |
| 24 | D3×#41⋊C3 | — | 3 | 2 | no | — |
| 25 | D3×#41⋊C3 | — | 6 | 1 | no | — |
| 26 | #1007⋊C3 | — | 3 | 4 | no | — |
| 27 | C2×D3×SL(2,𝔽3) | — | 3 | 4 | no | — |
| 28 | C2×C3×D32 | — | 4 | 2 | no | — |
| 29 | C3×C4×C3⋊D3 | — | 4 | 1 | no | — |
| 30 | C32×D12 | — | 4 | 2 | no | — |
| 31 | C32×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 32 | C3×#625 | — | 4 | 2 | no | — |
| 33 | D3×2−1+4 | — | 3 | 2 | no | — |
| 34 | C2×2−1+4⋊C3 | — | 9 | 1 | no | — |
| 35 | C32×#41 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 36 | #3832 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 37 | Q8×C3⋊D3 | C22×C3 | 1 | 1 | yes | characteristic |
| 38 | #3830 | — | 3 | 1 | no | — |
| 39 | D4×C3⋊D3 | — | 3 | 1 | no | — |
| 40 | #3828 | — | 3 | 1 | no | — |
| 41 | C2×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 42 | C3×D3×Q8 | C22×C3 | 1 | 4 | yes | complemented |
| 43 | C3×#237 | — | 3 | 4 | no | — |
| 44 | C3×D3×D4 | — | 12 | 2 | no | — |
| 45 | C3×#235 | — | 3 | 2 | no | — |
| 46 | C2×C3×Dic6 | — | 3 | 2 | no | — |
| 47 | C3×#41⋊C3 | — | 2 | 2 | no | — |
| 48 | C3×#41⋊C3 | — | 2 | 1 | no | — |
| 49 | C3×#41⋊C3 | — | 4 | 1 | no | — |
| 50 | C3×#41⋊C3 | C2×D3 | 1 | 2 | yes | complemented |
| 51 | C2×C3×SL(2,𝔽3) | — | 3 | 4 | no | — |
| 52 | #3811 | — | 3 | 2 | no | — |
| 53 | C2×#627 | — | 3 | 2 | no | — |
| 54 | C2×#624 | — | 3 | 2 | no | — |
| 55 | #3805 | — | 3 | 2 | no | — |
| 56 | #3804 | — | 3 | 8 | no | — |
| 57 | #3802 | A4 | 1 | 1 | yes | characteristic |
| 58 | C4×D32 | — | 3 | 2 | no | — |
| 59 | #3799 | — | 3 | 4 | no | — |
| 60 | #3798 | — | 3 | 2 | no | — |
| 61 | #3797 | — | 3 | 2 | no | — |
| 62 | #3797 | — | 3 | 1 | no | — |
| 63 | #3797 | — | 3 | 2 | no | — |
| 64 | #3797 | — | 3 | 2 | no | — |
| 65 | #3796 | — | 3 | 2 | no | — |
| 66 | D3×Dic6 | — | 3 | 4 | no | — |
| 67 | D3×SL(2,𝔽3) | — | 2 | 4 | no | — |
| 68 | D3×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 69 | D3×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 70 | D3×SL(2,𝔽3) | C2×D3 | 1 | 4 | yes | complemented |
| 71 | C3⋊(#41⋊C3) | — | 3 | 2 | no | — |
| 72 | C3⋊(#41⋊C3) | — | 6 | 1 | no | — |
| 73 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 74 | C2×C32×D3 | — | 4 | 4 | no | — |
| 75 | C3×D32 | — | 8 | 4 | no | — |
| 76 | C33×C4 | — | 4 | 1 | no | — |
| 77 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 78 | C3×2−1+4 | — | 3 | 2 | no | — |
| 79 | #1010 | — | 9 | 2 | no | — |
| 80 | #1010 | — | 9 | 4 | no | — |
| 81 | #1010 | C3×D3 | 1 | 2 | yes | complemented |
| 82 | D3×#41 | — | 3 | 2 | no | — |
| 83 | D3×#41 | — | 6 | 1 | no | — |
| 84 | D3×#41 | — | 9 | 2 | no | — |
| 85 | D3×#41 | — | 9 | 4 | no | — |
| 86 | #1007 | — | 3 | 4 | no | — |
| 87 | #1007 | — | 9 | 2 | no | — |
| 88 | C2×D3×Q8 | — | 3 | 4 | no | — |
| 89 | C2×D3×Q8 | — | 9 | 2 | no | — |
| 90 | 2−1+4⋊C3 | — | 3 | 2 | no | — |
| 91 | 2−1+4⋊C3 | — | 6 | 2 | no | — |
| 92 | 2−1+4⋊C3 | — | 9 | 2 | no | — |
| 93 | C2×#41⋊C3 | — | 9 | 1 | no | — |
| 94 | C22×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 95 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 96 | C22×C3×D3 | — | 12 | 4 | no | — |
| 97 | C2×D32 | C2×A4 | 1 | 2 | yes | — |
| 98 | C32×Q8 | C23×C3 | 1 | 1 | yes | characteristic |
| 99 | C32×D4 | — | 3 | 1 | no | — |
| 100 | C32×D4 | — | 12 | 2 | no | — |
| 101 | C2×C32×C4 | — | 3 | 1 | no | — |
| 102 | #638 | — | 3 | 2 | no | — |
| 103 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 104 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 105 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 106 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 107 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 108 | C4×C3⋊D3 | C2×A4 | 1 | 1 | yes | characteristic |
| 109 | #634 | — | 3 | 1 | no | — |
| 110 | C3×#67 | — | 3 | 4 | no | — |
| 111 | C3×#67 | — | 12 | 4 | no | — |
| 112 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 113 | C3×D12 | — | 4 | 2 | no | — |
| 114 | C3×D12 | — | 8 | 2 | no | — |
| 115 | C3×D12 | C2×A4 | 1 | 2 | yes | — |
| 116 | C3×C4×D3 | — | 3 | 4 | no | — |
| 117 | C3×C4×D3 | — | 12 | 2 | no | — |
| 118 | C3×C4×D3 | — | 24 | 1 | no | — |
| 119 | C3×Dic6 | — | 3 | 2 | no | — |
| 120 | C3×Dic6 | — | 3 | 4 | no | — |
| 121 | C3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 122 | C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 123 | C3×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 124 | C3×SL(2,𝔽3) | C22×D3 | 1 | 2 | yes | — |
| 125 | #627 | — | 3 | 4 | no | — |
| 126 | #627 | — | 3 | 2 | no | — |
| 127 | #626 | — | 3 | 4 | no | — |
| 128 | #625 | C2×A4 | 1 | 2 | yes | — |
| 129 | #624 | — | 3 | 4 | no | — |
| 130 | #624 | — | 3 | 2 | no | — |
| 131 | D3×Dic3 | — | 3 | 4 | no | — |
| 132 | C2×2−1+4 | — | 9 | 1 | no | Sylow |
| 133 | C2×C33 | — | 4 | 1 | no | — |
| 134 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 135 | C32×D3 | — | 8 | 4 | no | — |
| 136 | C3×#41 | — | 2 | 1 | no | — |
| 137 | C3×#41 | — | 9 | 2 | no | — |
| 138 | C3×#41 | — | 9 | 4 | no | — |
| 139 | C3×#41 | C2×C3×D3 | 1 | 2 | yes | complemented |
| 140 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 141 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 142 | C2×C3×D4 | — | 36 | 1 | no | — |
| 143 | #239 | — | 3 | 2 | no | — |
| 144 | #239 | — | 6 | 1 | no | — |
| 145 | #239 | — | 9 | 4 | no | — |
| 146 | #239 | — | 9 | 2 | no | — |
| 147 | D3×Q8 | — | 3 | 2 | no | — |
| 148 | D3×Q8 | — | 6 | 1 | no | — |
| 149 | D3×Q8 | — | 9 | 2 | no | — |
| 150 | D3×Q8 | — | 9 | 4 | no | — |
| 151 | D3×Q8 | — | 9 | 4 | no | — |
| 152 | D3×Q8 | — | 9 | 4 | no | — |
| 153 | D3×Q8 | — | 9 | 4 | no | — |
| 154 | D3×Q8 | C2×C3×D3 | 1 | 4 | yes | complemented |
| 155 | #237 | — | 3 | 4 | no | — |
| 156 | #237 | — | 9 | 2 | no | — |
| 157 | #237 | — | 9 | 8 | no | — |
| 158 | #237 | — | 9 | 4 | no | — |
| 159 | #237 | — | 9 | 2 | no | — |
| 160 | #237 | — | 18 | 1 | no | — |
| 161 | D3×D4 | — | 3 | 2 | no | — |
| 162 | D3×D4 | — | 9 | 4 | no | — |
| 163 | D3×D4 | — | 9 | 2 | no | — |
| 164 | D3×D4 | — | 18 | 1 | no | — |
| 165 | #235 | — | 3 | 2 | no | — |
| 166 | #235 | — | 9 | 4 | no | — |
| 167 | #235 | — | 9 | 4 | no | — |
| 168 | #235 | — | 9 | 8 | no | — |
| 169 | #235 | — | 9 | 2 | no | — |
| 170 | #235 | — | 18 | 1 | no | — |
| 171 | C2×C4×D3 | — | 9 | 2 | no | — |
| 172 | C2×C4×D3 | — | 9 | 4 | no | — |
| 173 | C2×C4×D3 | — | 9 | 4 | no | — |
| 174 | C2×C4×D3 | — | 18 | 1 | no | — |
| 175 | C2×Dic6 | — | 3 | 2 | no | — |
| 176 | C2×Dic6 | — | 9 | 4 | no | — |
| 177 | C2×Dic6 | — | 9 | 4 | no | — |
| 178 | #41⋊C3 | — | 2 | 2 | no | — |
| 179 | #41⋊C3 | — | 4 | 1 | no | — |
| 180 | #41⋊C3 | — | 9 | 1 | no | — |
| 181 | #41⋊C3 | D32 | 1 | 1 | yes | characteristic, complemented |
| 182 | C2×SL(2,𝔽3) | — | 3 | 4 | no | — |
| 183 | C2×SL(2,𝔽3) | — | 6 | 4 | no | — |
| 184 | C2×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 185 | C22×C32 | — | 3 | 1 | no | — |
| 186 | C22×C32 | — | 12 | 4 | no | — |
| 187 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 188 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 189 | C2×C3⋊D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 190 | C2×C3×D3 | — | 4 | 4 | no | — |
| 191 | C2×C3×D3 | — | 8 | 4 | no | — |
| 192 | C2×C3×D3 | — | 12 | 2 | no | — |
| 193 | C2×C3×D3 | — | 24 | 1 | no | — |
| 194 | C2×C3×D3 | — | 24 | 8 | no | — |
| 195 | C2×C3×D3 | C22×A4 | 1 | 4 | yes | — |
| 196 | D32 | — | 2 | 4 | no | — |
| 197 | C32×C4 | — | 3 | 1 | no | — |
| 198 | C32×C4 | — | 4 | 2 | no | — |
| 199 | C32×C4 | — | 8 | 1 | no | — |
| 200 | C32×C4 | — | 8 | 2 | no | — |
| 201 | C32×C4 | — | 16 | 1 | no | — |
| 202 | C32×C4 | C22×A4 | 1 | 1 | yes | characteristic |
| 203 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 204 | C3⋊Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 205 | C3×Dic3 | — | 3 | 4 | no | — |
| 206 | C3×Dic3 | — | 12 | 2 | no | — |
| 207 | C3×Dic3 | — | 24 | 1 | no | — |
| 208 | 2−1+4 | — | 3 | 2 | no | — |
| 209 | 2−1+4 | — | 9 | 2 | no | — |
| 210 | 2−1+4 | — | 27 | 2 | no | — |
| 211 | 2−1+4 | — | 27 | 2 | no | — |
| 212 | C2×#41 | — | 9 | 1 | no | — |
| 213 | C2×#41 | — | 27 | 1 | no | — |
| 214 | C2×#41 | — | 27 | 2 | no | — |
| 215 | C22×Q8 | — | 9 | 2 | no | — |
| 216 | C22×Q8 | — | 27 | 1 | no | — |
| 217 | C33 | — | 4 | 1 | no | Sylow |
| 218 | C23×C3 | — | 36 | 2 | no | — |
| 219 | C22×D3 | — | 3 | 4 | no | — |
| 220 | C22×D3 | — | 9 | 2 | no | — |
| 221 | C22×D3 | — | 18 | 1 | no | — |
| 222 | C3×Q8 | — | 2 | 1 | no | — |
| 223 | C3×Q8 | — | 9 | 4 | no | — |
| 224 | C3×Q8 | — | 9 | 2 | no | — |
| 225 | C3×Q8 | C22×C3×D3 | 1 | 2 | yes | — |
| 226 | C3×D4 | — | 3 | 2 | no | — |
| 227 | C3×D4 | — | 3 | 2 | no | — |
| 228 | C3×D4 | — | 6 | 1 | no | — |
| 229 | C3×D4 | — | 9 | 4 | no | — |
| 230 | C3×D4 | — | 12 | 2 | no | — |
| 231 | C3×D4 | — | 24 | 2 | no | — |
| 232 | C3×D4 | — | 36 | 2 | no | — |
| 233 | C2×C3×C4 | — | 3 | 2 | no | — |
| 234 | C2×C3×C4 | — | 6 | 1 | no | — |
| 235 | C2×C3×C4 | — | 9 | 4 | no | — |
| 236 | C2×C3×C4 | — | 9 | 4 | no | — |
| 237 | C2×C3×C4 | — | 36 | 1 | no | — |
| 238 | #67 | — | 3 | 4 | no | — |
| 239 | #67 | — | 3 | 4 | no | — |
| 240 | #67 | — | 9 | 4 | no | — |
| 241 | #67 | — | 9 | 4 | no | — |
| 242 | #67 | — | 18 | 2 | no | — |
| 243 | C2×Dic3 | — | 3 | 4 | no | — |
| 244 | C2×Dic3 | — | 9 | 4 | no | — |
| 245 | C2×Dic3 | — | 9 | 2 | no | — |
| 246 | C2×Dic3 | — | 18 | 1 | no | — |
| 247 | D12 | — | 9 | 2 | no | — |
| 248 | D12 | — | 9 | 4 | no | — |
| 249 | D12 | — | 18 | 1 | no | — |
| 250 | D12 | D3×A4 | 1 | 2 | yes | — |
| 251 | C4×D3 | — | 3 | 4 | no | — |
| 252 | C4×D3 | — | 3 | 2 | no | — |
| 253 | C4×D3 | — | 6 | 1 | no | — |
| 254 | C4×D3 | — | 9 | 2 | no | — |
| 255 | C4×D3 | — | 9 | 4 | no | — |
| 256 | C4×D3 | — | 9 | 8 | no | — |
| 257 | C4×D3 | — | 9 | 2 | no | — |
| 258 | C4×D3 | — | 9 | 4 | no | — |
| 259 | C4×D3 | — | 9 | 2 | no | — |
| 260 | C4×D3 | — | 18 | 1 | no | — |
| 261 | C4×D3 | — | 18 | 1 | no | — |
| 262 | C4×D3 | — | 18 | 1 | no | — |
| 263 | Dic6 | — | 3 | 2 | no | — |
| 264 | Dic6 | — | 3 | 4 | no | — |
| 265 | Dic6 | — | 9 | 4 | no | — |
| 266 | Dic6 | — | 9 | 8 | no | — |
| 267 | Dic6 | — | 9 | 2 | no | — |
| 268 | Dic6 | — | 18 | 1 | no | — |
| 269 | SL(2,𝔽3) | — | 2 | 2 | no | — |
| 270 | SL(2,𝔽3) | — | 4 | 1 | no | — |
| 271 | SL(2,𝔽3) | C2×D32 | 1 | 1 | yes | characteristic |
| 272 | C2×C32 | — | 4 | 2 | no | — |
| 273 | C2×C32 | — | 6 | 1 | no | — |
| 274 | C2×C32 | — | 8 | 1 | no | — |
| 275 | C2×C32 | — | 8 | 2 | no | — |
| 276 | C2×C32 | — | 16 | 1 | no | — |
| 277 | C2×C32 | — | 24 | 4 | no | — |
| 278 | C2×C32 | C23×A4 | 1 | 1 | yes | characteristic |
| 279 | C3⋊D3 | — | 6 | 1 | no | — |
| 280 | C3⋊D3 | 2−1+4⋊C3 | 1 | 2 | yes | complemented |
| 281 | C3×D3 | — | 2 | 4 | no | — |
| 282 | C3×D3 | — | 8 | 4 | no | — |
| 283 | C3×D3 | — | 12 | 4 | no | — |
| 284 | C3×D3 | — | 16 | 4 | no | — |
| 285 | C3×D3 | — | 24 | 2 | no | — |
| 286 | #41 | — | 9 | 2 | no | — |
| 287 | #41 | — | 9 | 4 | no | — |
| 288 | #41 | — | 9 | 1 | no | — |
| 289 | #41 | — | 27 | 1 | no | — |
| 290 | #41 | — | 27 | 2 | no | — |
| 291 | #41 | — | 27 | 8 | no | — |
| 292 | #41 | — | 27 | 4 | no | — |
| 293 | #41 | — | 27 | 2 | no | — |
| 294 | #41 | — | 27 | 2 | no | — |
| 295 | #41 | — | 27 | 1 | no | — |
| 296 | #41 | C3×D32 | 1 | 1 | yes | characteristic, complemented |
| 297 | C2×Q8 | — | 3 | 4 | no | — |
| 298 | C2×Q8 | — | 9 | 2 | no | — |
| 299 | C2×Q8 | — | 9 | 1 | no | — |
| 300 | C2×Q8 | — | 27 | 2 | no | — |
| 301 | C2×Q8 | — | 27 | 1 | no | — |
| 302 | C2×Q8 | — | 27 | 4 | no | — |
| 303 | C2×Q8 | — | 27 | 2 | no | — |
| 304 | C2×Q8 | — | 27 | 2 | no | — |
| 305 | C2×Q8 | — | 27 | 2 | no | — |
| 306 | C2×D4 | — | 9 | 1 | no | — |
| 307 | C2×D4 | — | 27 | 1 | no | — |
| 308 | C2×D4 | — | 27 | 2 | no | — |
| 309 | C22×C4 | — | 27 | 1 | no | — |
| 310 | C22×C4 | — | 27 | 2 | no | — |
| 311 | C22×C4 | — | 27 | 2 | no | — |
| 312 | C22×C3 | — | 3 | 2 | no | — |
| 313 | C22×C3 | — | 3 | 4 | no | — |
| 314 | C22×C3 | — | 6 | 1 | no | — |
| 315 | C22×C3 | — | 12 | 4 | no | — |
| 316 | C22×C3 | — | 24 | 4 | no | — |
| 317 | C22×C3 | — | 36 | 1 | no | — |
| 318 | C22×C3 | — | 72 | 4 | no | — |
| 319 | C2×D3 | — | 3 | 2 | no | — |
| 320 | C2×D3 | — | 6 | 1 | no | — |
| 321 | C2×D3 | — | 6 | 8 | no | — |
| 322 | C2×D3 | — | 9 | 2 | no | — |
| 323 | C2×D3 | — | 18 | 1 | no | — |
| 324 | C2×D3 | — | 18 | 4 | no | — |
| 325 | C2×D3 | — | 36 | 2 | no | — |
| 326 | C2×D3 | C2×D3×A4 | 1 | 4 | yes | — |
| 327 | C3×C4 | — | 2 | 1 | no | — |
| 328 | C3×C4 | — | 3 | 2 | no | — |
| 329 | C3×C4 | — | 4 | 1 | no | — |
| 330 | C3×C4 | — | 6 | 1 | no | — |
| 331 | C3×C4 | — | 8 | 2 | no | — |
| 332 | C3×C4 | — | 9 | 4 | no | — |
| 333 | C3×C4 | — | 16 | 1 | no | — |
| 334 | C3×C4 | — | 36 | 1 | no | — |
| 335 | C3×C4 | C2×D3×A4 | 1 | 2 | yes | — |
| 336 | Dic3 | — | 3 | 4 | no | — |
| 337 | Dic3 | — | 3 | 2 | no | — |
| 338 | Dic3 | — | 6 | 1 | no | — |
| 339 | Dic3 | — | 9 | 2 | no | — |
| 340 | Dic3 | — | 18 | 1 | no | — |
| 341 | C32 | — | 4 | 2 | no | — |
| 342 | C32 | — | 8 | 1 | no | — |
| 343 | C32 | — | 8 | 2 | no | — |
| 344 | C32 | — | 16 | 1 | no | — |
| 345 | C32 | C2×2−1+4⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 346 | C23 | — | 9 | 2 | no | — |
| 347 | C23 | — | 27 | 1 | no | — |
| 348 | Q8 | — | 9 | 4 | no | — |
| 349 | Q8 | — | 9 | 2 | no | — |
| 350 | Q8 | — | 27 | 1 | no | — |
| 351 | Q8 | — | 27 | 2 | no | — |
| 352 | Q8 | — | 27 | 4 | no | — |
| 353 | Q8 | C2×C3×D32 | 1 | 1 | yes | characteristic |
| 354 | D4 | — | 3 | 1 | no | — |
| 355 | D4 | — | 3 | 2 | no | — |
| 356 | D4 | — | 9 | 2 | no | — |
| 357 | D4 | — | 9 | 4 | no | — |
| 358 | D4 | — | 27 | 1 | no | — |
| 359 | D4 | — | 27 | 4 | no | — |
| 360 | D4 | — | 27 | 2 | no | — |
| 361 | C2×C4 | — | 3 | 1 | no | — |
| 362 | C2×C4 | — | 9 | 4 | no | — |
| 363 | C2×C4 | — | 9 | 4 | no | — |
| 364 | C2×C4 | — | 9 | 1 | no | — |
| 365 | C2×C4 | — | 27 | 1 | no | — |
| 366 | C2×C4 | — | 27 | 1 | no | — |
| 367 | C2×C4 | — | 27 | 2 | no | — |
| 368 | C2×C4 | — | 27 | 4 | no | — |
| 369 | C2×C4 | — | 27 | 1 | no | — |
| 370 | C2×C4 | — | 27 | 4 | no | — |
| 371 | C2×C4 | — | 27 | 1 | no | — |
| 372 | C2×C3 | — | 2 | 1 | no | — |
| 373 | C2×C3 | — | 4 | 1 | no | — |
| 374 | C2×C3 | — | 6 | 4 | no | — |
| 375 | C2×C3 | — | 6 | 2 | no | — |
| 376 | C2×C3 | — | 8 | 2 | no | — |
| 377 | C2×C3 | — | 12 | 1 | no | — |
| 378 | C2×C3 | — | 16 | 1 | no | — |
| 379 | C2×C3 | — | 24 | 4 | no | — |
| 380 | C2×C3 | — | 36 | 2 | no | — |
| 381 | C2×C3 | — | 48 | 4 | no | — |
| 382 | C2×C3 | C22×D3×A4 | 1 | 2 | yes | — |
| 383 | D3 | — | 2 | 4 | no | — |
| 384 | D3 | — | 3 | 4 | no | — |
| 385 | D3 | — | 6 | 2 | no | — |
| 386 | D3 | — | 18 | 2 | no | — |
| 387 | D3 | — | 36 | 1 | no | — |
| 388 | C22 | — | 3 | 1 | no | — |
| 389 | C22 | — | 3 | 4 | no | — |
| 390 | C22 | — | 9 | 1 | no | — |
| 391 | C22 | — | 18 | 4 | no | — |
| 392 | C22 | — | 27 | 1 | no | — |
| 393 | C22 | — | 54 | 2 | no | — |
| 394 | C4 | — | 3 | 1 | no | — |
| 395 | C4 | — | 9 | 4 | no | — |
| 396 | C4 | — | 9 | 1 | no | — |
| 397 | C4 | — | 27 | 1 | no | — |
| 398 | C4 | D32×A4 | 1 | 1 | yes | characteristic |
| 399 | C3 | — | 2 | 1 | no | — |
| 400 | C3 | — | 4 | 1 | no | — |
| 401 | C3 | — | 8 | 2 | no | — |
| 402 | C3 | — | 16 | 1 | no | — |
| 403 | C3 | D3×2−1+4⋊C3 | 1 | 2 | yes | complemented |
| 404 | C2 | — | 6 | 4 | no | — |
| 405 | C2 | — | 6 | 1 | no | — |
| 406 | C2 | — | 9 | 2 | no | — |
| 407 | C2 | — | 54 | 1 | no | — |
| 408 | C2 | C2×D32×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×A4 |
| commutator, cosocle, hypocenter | C32×Q8 | C23×C3 |
| Fitting | C32×#41 | C22×C3 |
| socle | C2×C32 | C23×A4 |
| hypercenter | C4 | D32×A4 |
| LCS | G ▷ C32×Q8 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊D3×#41⋊C3 | C2 | semidirect |
| 2. C3×#1010⋊C3 | C2 | semidirect |
| 3. D32×SL(2,𝔽3) | C2 | semidirect |
| 4. #64316⋊C3 | C2 | semidirect |
| 5. #10596694 | C3 | semidirect |
| 7. C32×#41⋊C3 | C22 | semidirect |
| 10. C3⋊(C3⋊(#41⋊C3)) | C22 | semidirect |
| 11. C3×D3×SL(2,𝔽3) | C22 | semidirect |
| 12. #41×C3⋊D3 | C2×C3 | semidirect |
| 13. C3×#1010 | C2×C3 | semidirect |
| 15. D32×Q8 | C2×C3 | semidirect |
| 16. #64316 | C2×C3 | semidirect |
| 23. #1010⋊C3 | D3 | semidirect |
| 35. C32×#41 | C22×C3 | semidirect |
| 36. #3832 | C22×C3 | semidirect |
| 42. C3×D3×Q8 | C22×C3 | semidirect |
| 50. C3×#41⋊C3 | C2×D3 | semidirect |
| 70. D3×SL(2,𝔽3) | C2×D3 | semidirect |
| 81. #1010 | C3×D3 | semidirect |
| 139. C3×#41 | C2×C3×D3 | semidirect |
| 154. D3×Q8 | C2×C3×D3 | semidirect |
| 181. #41⋊C3 | D32 | semidirect |
| 280. C3⋊D3 | 2−1+4⋊C3 | semidirect |
| 296. #41 | C3×D32 | semidirect |
| 345. C32 | C2×2−1+4⋊C3 | semidirect |
| 403. C3 | D3×2−1+4⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#41⋊C3 | 2 |
| C3×#1010⋊C3 | 2 |
| D32×SL(2,𝔽3) | 2 |
| #64316⋊C3 | 2 |
| #10596694 | 3 |
| D3×2−1+4⋊C3 | 3 |
| C3×#3802 | 4 |