Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
962 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 962 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #11723697 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11723524 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#88791 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×C3×#3714 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#63553 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10591484 | — | 3 | 1 | no | maximal |
| 7 | #10590880 | — | 3 | 2 | no | maximal |
| 8 | C2×C4⋊(C3⋊(C3⋊D3)) | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×C3×C4⋊(C3⋊D3) | C22 | 1 | 2 | yes | — |
| 10 | C2×C32×D12 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#6295 | — | 2 | 2 | no | — |
| 12 | C2×#6291 | — | 2 | 2 | no | — |
| 13 | C3×C4×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C32×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 15 | #88791 | — | 2 | 4 | no | — |
| 16 | C3×#3714 | — | 2 | 4 | no | — |
| 17 | #64149 | — | 3 | 1 | no | — |
| 18 | C2×#3745 | — | 3 | 2 | no | — |
| 19 | C2×C3×#213 | — | 3 | 2 | no | — |
| 20 | C2×C3×D24 | — | 3 | 2 | no | — |
| 21 | #63914 | — | 3 | 1 | no | — |
| 22 | #63911 | — | 3 | 2 | no | — |
| 23 | #63911 | — | 3 | 2 | no | — |
| 24 | #63911 | — | 6 | 1 | no | — |
| 25 | C2×#3714 | — | 3 | 2 | no | — |
| 26 | C2×#3714 | — | 3 | 2 | no | — |
| 27 | C2×#3714 | — | 6 | 2 | no | — |
| 28 | C2×#3714 | D3 | 1 | 2 | yes | complemented |
| 29 | C3×C8×Dic3 | — | 3 | 2 | no | — |
| 30 | #63553 | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | C22×C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 32 | C22×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 33 | C22×C32×D3 | — | 2 | 1 | no | — |
| 34 | C2×C33×C4 | C23 | 1 | 1 | yes | characteristic |
| 35 | C4⋊(C3⋊(C3⋊D3)) | — | 2 | 2 | no | — |
| 36 | C2×C3×C3⋊Dic3 | D4 | 1 | 2 | yes | — |
| 37 | C3×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 38 | C3×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 39 | C32×D12 | — | 2 | 2 | no | — |
| 40 | #6295 | — | 4 | 4 | no | — |
| 41 | #6291 | — | 4 | 4 | no | — |
| 42 | C32×C3⋊C8 | D4 | 1 | 4 | yes | complemented |
| 43 | #5151 | — | 9 | 2 | no | — |
| 44 | #4695 | — | 9 | 1 | no | — |
| 45 | C2×C32×D4 | — | 3 | 1 | no | — |
| 46 | C2×#638 | — | 6 | 2 | no | — |
| 47 | C2×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 48 | C2×C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 49 | C2×C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 50 | C2×C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 51 | C2×C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 52 | C2×C4⋊(C3⋊D3) | C2×D3 | 1 | 2 | yes | — |
| 53 | C2×C3×D12 | — | 2 | 1 | no | — |
| 54 | C2×C3×D12 | — | 3 | 2 | no | — |
| 55 | C2×C3×D12 | — | 3 | 2 | no | — |
| 56 | C2×C3×D12 | — | 6 | 2 | no | — |
| 57 | C2×C3×D12 | C2×D3 | 1 | 2 | yes | — |
| 58 | C2×#626 | — | 6 | 4 | no | — |
| 59 | C2×#626 | — | 6 | 4 | no | — |
| 60 | C2×#626 | — | 6 | 4 | no | — |
| 61 | C2×#625 | — | 6 | 2 | no | — |
| 62 | C2×C32×C8 | — | 3 | 2 | no | — |
| 63 | C4×C3⋊Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 64 | #3745 | — | 6 | 4 | no | — |
| 65 | C3×#213 | — | 6 | 4 | no | — |
| 66 | C3×C4×Dic3 | — | 3 | 2 | no | — |
| 67 | C3×C4×Dic3 | — | 6 | 1 | no | — |
| 68 | C2×C3×C3⋊C8 | — | 2 | 2 | no | — |
| 69 | C2×C3×C3⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 70 | C2×C3×C3⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 71 | C3×D24 | — | 6 | 4 | no | — |
| 72 | #3714 | — | 2 | 4 | no | — |
| 73 | #3714 | — | 6 | 8 | no | — |
| 74 | #3714 | — | 6 | 4 | no | — |
| 75 | #3714 | — | 6 | 4 | no | — |
| 76 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C2×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 78 | C2×C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 79 | C2×C3×C3⋊D3 | — | 4 | 2 | no | — |
| 80 | C2×C3×C3⋊D3 | — | 4 | 4 | no | — |
| 81 | C2×C32×D3 | — | 4 | 1 | no | — |
| 82 | C2×C32×D3 | — | 4 | 2 | no | — |
| 83 | C33×C4 | C2×D4 | 1 | 2 | yes | — |
| 84 | C3×C3⋊Dic3 | D8 | 1 | 4 | yes | complemented |
| 85 | C2×C3×D8 | — | 9 | 2 | no | — |
| 86 | #940 | — | 9 | 2 | no | — |
| 87 | #940 | — | 9 | 2 | no | — |
| 88 | #940 | — | 18 | 1 | no | — |
| 89 | C2×#213 | — | 3 | 2 | no | — |
| 90 | C2×#213 | — | 9 | 2 | no | — |
| 91 | C2×D24 | — | 3 | 2 | no | — |
| 92 | C2×D24 | — | 9 | 2 | no | — |
| 93 | C2×D24 | — | 9 | 2 | no | — |
| 94 | C2×D24 | — | 18 | 2 | no | — |
| 95 | #874 | — | 9 | 1 | no | — |
| 96 | #874 | — | 9 | 1 | no | — |
| 97 | C3×C4×C8 | — | 9 | 1 | no | — |
| 98 | C8×Dic3 | — | 3 | 2 | no | — |
| 99 | C23×C32 | — | 6 | 1 | no | — |
| 100 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 101 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 102 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 103 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 104 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 105 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 106 | C22×C3×D3 | — | 2 | 2 | no | — |
| 107 | C22×C3×D3 | — | 2 | 2 | no | — |
| 108 | C22×C3×D3 | — | 6 | 2 | no | — |
| 109 | C22×C3×D3 | — | 6 | 2 | no | — |
| 110 | C22×C3×D3 | — | 12 | 2 | no | — |
| 111 | C32×D4 | — | 6 | 2 | no | — |
| 112 | C2×C32×C4 | — | 2 | 2 | no | — |
| 113 | C2×C32×C4 | — | 2 | 1 | no | — |
| 114 | C2×C32×C4 | — | 4 | 1 | no | — |
| 115 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 116 | C2×C32×C4 | C22×D3 | 1 | 2 | yes | — |
| 117 | #638 | — | 12 | 4 | no | — |
| 118 | C2×C3⋊Dic3 | D12 | 1 | 2 | yes | — |
| 119 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 120 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 121 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 122 | C4⋊(C3⋊D3) | — | 6 | 4 | no | — |
| 123 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 124 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 125 | C4⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 126 | C4⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 127 | C4⋊(C3⋊D3) | — | 12 | 4 | no | — |
| 128 | C2×C3×Dic3 | — | 3 | 4 | no | — |
| 129 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 130 | C3×D12 | — | 2 | 2 | no | — |
| 131 | C3×D12 | — | 2 | 2 | no | — |
| 132 | C3×D12 | — | 4 | 2 | no | — |
| 133 | C3×D12 | — | 6 | 4 | no | — |
| 134 | C3×D12 | — | 6 | 2 | no | — |
| 135 | C3×D12 | — | 6 | 2 | no | — |
| 136 | C3×D12 | — | 6 | 2 | no | — |
| 137 | C3×D12 | — | 6 | 2 | no | — |
| 138 | C3×D12 | — | 12 | 2 | no | — |
| 139 | #626 | — | 12 | 8 | no | — |
| 140 | #626 | — | 12 | 8 | no | — |
| 141 | #626 | — | 12 | 8 | no | — |
| 142 | #625 | — | 12 | 4 | no | — |
| 143 | C32×C8 | — | 3 | 4 | no | — |
| 144 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 145 | C3×C3⋊C8 | D12 | 1 | 4 | yes | complemented |
| 146 | C3×C3⋊C8 | #67 | 1 | 4 | yes | complemented |
| 147 | #493 | — | 27 | 1 | no | Sylow |
| 148 | C2×C33 | #127 | 1 | 1 | yes | characteristic |
| 149 | C2×C33 | C2×D8 | 1 | 2 | yes | — |
| 150 | C3⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 151 | C3×C3⋊D3 | — | 8 | 2 | no | — |
| 152 | C32×D3 | — | 8 | 1 | no | — |
| 153 | C2×C3×D4 | — | 3 | 2 | no | — |
| 154 | C2×C3×D4 | — | 6 | 1 | no | — |
| 155 | C2×C3×D4 | — | 9 | 2 | no | — |
| 156 | C2×#67 | — | 18 | 4 | no | — |
| 157 | C2×#67 | — | 18 | 4 | no | — |
| 158 | C2×#67 | — | 18 | 4 | no | — |
| 159 | C2×D12 | — | 3 | 2 | no | — |
| 160 | C2×D12 | — | 3 | 2 | no | — |
| 161 | C2×D12 | — | 6 | 2 | no | — |
| 162 | C2×D12 | — | 9 | 1 | no | — |
| 163 | C2×D12 | — | 9 | 2 | no | — |
| 164 | C2×D12 | — | 18 | 2 | no | — |
| 165 | C2×D12 | — | 18 | 1 | no | — |
| 166 | C2×D12 | — | 18 | 2 | no | — |
| 167 | C2×D12 | — | 18 | 2 | no | — |
| 168 | C2×D12 | — | 36 | 1 | no | — |
| 169 | C2×D12 | D32 | 1 | 1 | yes | characteristic |
| 170 | C3×D8 | — | 18 | 4 | no | — |
| 171 | C2×C3×C8 | — | 3 | 2 | no | — |
| 172 | C2×C3×C8 | — | 3 | 2 | no | — |
| 173 | C2×C3×C8 | — | 6 | 2 | no | — |
| 174 | C3×C42 | — | 9 | 1 | no | — |
| 175 | #213 | — | 6 | 4 | no | — |
| 176 | #213 | — | 18 | 4 | no | — |
| 177 | C4×Dic3 | — | 3 | 2 | no | — |
| 178 | C4×Dic3 | — | 6 | 1 | no | — |
| 179 | C2×C3⋊C8 | D32 | 1 | 2 | yes | — |
| 180 | D24 | — | 6 | 4 | no | — |
| 181 | D24 | — | 18 | 4 | no | — |
| 182 | D24 | — | 18 | 4 | no | — |
| 183 | D24 | — | 18 | 8 | no | — |
| 184 | C22×C32 | — | 2 | 2 | no | — |
| 185 | C22×C32 | — | 2 | 1 | no | — |
| 186 | C22×C32 | — | 4 | 1 | no | — |
| 187 | C22×C32 | — | 12 | 1 | no | — |
| 188 | C22×C32 | — | 12 | 2 | no | — |
| 189 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 190 | C22×C32 | D3×D4 | 1 | 2 | yes | — |
| 191 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 192 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 193 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 194 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 195 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 196 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 197 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 198 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 199 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 200 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 201 | C2×C3⋊D3 | — | 24 | 4 | no | — |
| 202 | C2×C3⋊D3 | — | 24 | 4 | no | — |
| 203 | C2×C3×D3 | — | 4 | 4 | no | — |
| 204 | C2×C3×D3 | — | 4 | 2 | no | — |
| 205 | C2×C3×D3 | — | 4 | 4 | no | — |
| 206 | C2×C3×D3 | — | 4 | 2 | no | — |
| 207 | C2×C3×D3 | — | 12 | 4 | no | — |
| 208 | C2×C3×D3 | — | 12 | 2 | no | — |
| 209 | C2×C3×D3 | — | 12 | 4 | no | — |
| 210 | C2×C3×D3 | — | 12 | 4 | no | — |
| 211 | C2×C3×D3 | — | 12 | 2 | no | — |
| 212 | C2×C3×D3 | — | 24 | 4 | no | — |
| 213 | C32×C4 | — | 2 | 2 | no | — |
| 214 | C32×C4 | — | 2 | 2 | no | — |
| 215 | C32×C4 | — | 2 | 2 | no | — |
| 216 | C32×C4 | — | 4 | 2 | no | — |
| 217 | C32×C4 | C2×D12 | 1 | 2 | yes | — |
| 218 | C32×C4 | D3×D4 | 1 | 2 | yes | — |
| 219 | C32×C4 | C2×#67 | 1 | 2 | yes | — |
| 220 | C3⋊Dic3 | D24 | 1 | 4 | yes | complemented |
| 221 | C3×Dic3 | — | 3 | 8 | no | — |
| 222 | C3×Dic3 | — | 6 | 4 | no | — |
| 223 | C2×D8 | — | 9 | 2 | no | — |
| 224 | C2×D8 | — | 27 | 2 | no | — |
| 225 | #127 | — | 27 | 1 | no | — |
| 226 | #127 | — | 27 | 1 | no | — |
| 227 | C4×C8 | — | 9 | 1 | no | — |
| 228 | C33 | #493 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 229 | C23×C3 | — | 6 | 2 | no | — |
| 230 | C23×C3 | — | 6 | 2 | no | — |
| 231 | C23×C3 | — | 18 | 2 | no | — |
| 232 | C22×D3 | — | 2 | 1 | no | — |
| 233 | C22×D3 | — | 6 | 2 | no | — |
| 234 | C22×D3 | — | 6 | 2 | no | — |
| 235 | C22×D3 | — | 12 | 2 | no | — |
| 236 | C22×D3 | — | 18 | 2 | no | — |
| 237 | C22×D3 | — | 18 | 2 | no | — |
| 238 | C22×D3 | — | 18 | 1 | no | — |
| 239 | C22×D3 | — | 36 | 2 | no | — |
| 240 | C22×D3 | — | 36 | 2 | no | — |
| 241 | C3×D4 | — | 6 | 2 | no | — |
| 242 | C3×D4 | — | 6 | 2 | no | — |
| 243 | C3×D4 | — | 12 | 2 | no | — |
| 244 | C3×D4 | — | 18 | 2 | no | — |
| 245 | C3×D4 | — | 18 | 2 | no | — |
| 246 | C2×C3×C4 | — | 2 | 1 | no | — |
| 247 | C2×C3×C4 | — | 2 | 2 | no | — |
| 248 | C2×C3×C4 | — | 4 | 1 | no | — |
| 249 | C2×C3×C4 | — | 9 | 2 | no | — |
| 250 | C2×C3×C4 | C2×D32 | 1 | 2 | yes | — |
| 251 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 252 | #67 | — | 36 | 8 | no | — |
| 253 | #67 | — | 36 | 8 | no | — |
| 254 | #67 | — | 36 | 8 | no | — |
| 255 | C2×Dic3 | — | 3 | 4 | no | — |
| 256 | C2×Dic3 | — | 6 | 2 | no | — |
| 257 | D12 | — | 2 | 2 | no | — |
| 258 | D12 | — | 6 | 4 | no | — |
| 259 | D12 | — | 6 | 2 | no | — |
| 260 | D12 | — | 6 | 2 | no | — |
| 261 | D12 | — | 6 | 2 | no | — |
| 262 | D12 | — | 6 | 2 | no | — |
| 263 | D12 | — | 12 | 2 | no | — |
| 264 | D12 | — | 18 | 4 | no | — |
| 265 | D12 | — | 18 | 2 | no | — |
| 266 | D12 | — | 18 | 2 | no | — |
| 267 | D12 | — | 18 | 2 | no | — |
| 268 | D12 | — | 36 | 2 | no | — |
| 269 | D12 | — | 36 | 2 | no | — |
| 270 | D12 | — | 36 | 4 | no | — |
| 271 | D12 | — | 36 | 4 | no | — |
| 272 | D12 | — | 36 | 4 | no | — |
| 273 | C3×C8 | — | 3 | 4 | no | — |
| 274 | C3×C8 | — | 3 | 4 | no | — |
| 275 | C3×C8 | — | 6 | 4 | no | — |
| 276 | C3⋊C8 | #626 | 1 | 4 | yes | complemented |
| 277 | C2×C32 | — | 2 | 4 | no | — |
| 278 | C2×C32 | — | 2 | 2 | no | — |
| 279 | C2×C32 | — | 2 | 2 | no | — |
| 280 | C2×C32 | — | 2 | 1 | no | — |
| 281 | C2×C32 | — | 4 | 1 | no | — |
| 282 | C2×C32 | — | 4 | 2 | no | — |
| 283 | C2×C32 | — | 24 | 1 | no | — |
| 284 | C2×C32 | #874 | 1 | 1 | yes | characteristic |
| 285 | C2×C32 | C2×D24 | 1 | 2 | yes | — |
| 286 | C2×C32 | D3×D8 | 1 | 4 | yes | — |
| 287 | C2×C32 | #940 | 1 | 2 | yes | — |
| 288 | C3⋊D3 | — | 8 | 2 | no | — |
| 289 | C3⋊D3 | — | 24 | 2 | no | — |
| 290 | C3⋊D3 | — | 24 | 4 | no | — |
| 291 | C3⋊D3 | — | 24 | 4 | no | — |
| 292 | C3⋊D3 | — | 24 | 2 | no | — |
| 293 | C3⋊D3 | — | 24 | 1 | no | — |
| 294 | C3×D3 | — | 8 | 2 | no | — |
| 295 | C3×D3 | — | 8 | 2 | no | — |
| 296 | C3×D3 | — | 24 | 4 | no | — |
| 297 | C3×D3 | — | 24 | 2 | no | — |
| 298 | C3×D3 | — | 24 | 2 | no | — |
| 299 | C2×D4 | — | 3 | 1 | no | — |
| 300 | C2×D4 | — | 9 | 2 | no | — |
| 301 | C2×D4 | — | 27 | 1 | no | — |
| 302 | C2×D4 | — | 54 | 2 | no | — |
| 303 | C2×D4 | — | 54 | 2 | no | — |
| 304 | D8 | — | 18 | 4 | no | — |
| 305 | D8 | — | 54 | 4 | no | — |
| 306 | C2×C8 | — | 3 | 2 | no | — |
| 307 | C42 | — | 9 | 1 | no | — |
| 308 | C22×C3 | — | 2 | 1 | no | — |
| 309 | C22×C3 | — | 2 | 2 | no | — |
| 310 | C22×C3 | — | 4 | 1 | no | — |
| 311 | C22×C3 | — | 12 | 4 | no | — |
| 312 | C22×C3 | — | 12 | 2 | no | — |
| 313 | C22×C3 | — | 12 | 4 | no | — |
| 314 | C22×C3 | — | 12 | 2 | no | — |
| 315 | C22×C3 | — | 36 | 4 | no | — |
| 316 | C22×C3 | — | 36 | 2 | no | — |
| 317 | C22×C3 | D3×D12 | 1 | 2 | yes | — |
| 318 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 319 | C2×D3 | — | 4 | 2 | no | — |
| 320 | C2×D3 | — | 4 | 1 | no | — |
| 321 | C2×D3 | — | 12 | 4 | no | — |
| 322 | C2×D3 | — | 12 | 4 | no | — |
| 323 | C2×D3 | — | 12 | 2 | no | — |
| 324 | C2×D3 | — | 12 | 4 | no | — |
| 325 | C2×D3 | — | 12 | 2 | no | — |
| 326 | C2×D3 | — | 24 | 4 | no | — |
| 327 | C2×D3 | — | 36 | 4 | no | — |
| 328 | C2×D3 | — | 36 | 2 | no | — |
| 329 | C2×D3 | — | 36 | 4 | no | — |
| 330 | C2×D3 | — | 36 | 4 | no | — |
| 331 | C2×D3 | — | 36 | 4 | no | — |
| 332 | C2×D3 | — | 36 | 2 | no | — |
| 333 | C2×D3 | — | 36 | 2 | no | — |
| 334 | C2×D3 | — | 36 | 1 | no | — |
| 335 | C2×D3 | — | 72 | 4 | no | — |
| 336 | C2×D3 | — | 72 | 4 | no | — |
| 337 | C3×C4 | — | 2 | 2 | no | — |
| 338 | C3×C4 | — | 2 | 2 | no | — |
| 339 | C3×C4 | — | 2 | 2 | no | — |
| 340 | C3×C4 | — | 4 | 2 | no | — |
| 341 | C3×C4 | — | 9 | 4 | no | — |
| 342 | C3×C4 | D3×D12 | 1 | 2 | yes | — |
| 343 | C3×C4 | C2×#626 | 1 | 2 | yes | — |
| 344 | C3×C4 | D3×#67 | 1 | 2 | yes | — |
| 345 | Dic3 | — | 3 | 8 | no | — |
| 346 | Dic3 | — | 6 | 4 | no | — |
| 347 | C32 | — | 2 | 2 | no | — |
| 348 | C32 | — | 2 | 1 | no | — |
| 349 | C32 | — | 4 | 1 | no | — |
| 350 | C32 | #4695 | 1 | 1 | yes | characteristic, complemented |
| 351 | C32 | #5151 | 1 | 2 | yes | complemented |
| 352 | C23 | — | 6 | 1 | no | — |
| 353 | C23 | — | 18 | 2 | no | — |
| 354 | C23 | — | 54 | 1 | no | — |
| 355 | D4 | — | 6 | 2 | no | — |
| 356 | D4 | — | 18 | 2 | no | — |
| 357 | D4 | — | 18 | 2 | no | — |
| 358 | D4 | — | 54 | 2 | no | — |
| 359 | D4 | — | 108 | 4 | no | — |
| 360 | D4 | — | 108 | 4 | no | — |
| 361 | C2×C4 | — | 9 | 2 | no | — |
| 362 | C2×C4 | D33 | 1 | 1 | yes | characteristic |
| 363 | C8 | — | 3 | 4 | no | — |
| 364 | C2×C3 | — | 2 | 2 | no | — |
| 365 | C2×C3 | — | 2 | 1 | no | — |
| 366 | C2×C3 | — | 2 | 2 | no | — |
| 367 | C2×C3 | — | 2 | 4 | no | — |
| 368 | C2×C3 | — | 4 | 1 | no | — |
| 369 | C2×C3 | — | 4 | 2 | no | — |
| 370 | C2×C3 | — | 24 | 2 | no | — |
| 371 | C2×C3 | — | 24 | 2 | no | — |
| 372 | C2×C3 | — | 72 | 2 | no | — |
| 373 | C2×C3 | D3×D24 | 1 | 4 | yes | — |
| 374 | C2×C3 | #63911 | 1 | 2 | yes | — |
| 375 | C2×C3 | #63926 | 1 | 2 | yes | — |
| 376 | C2×C3 | #63979 | 1 | 1 | yes | characteristic |
| 377 | D3 | — | 8 | 1 | no | — |
| 378 | D3 | — | 24 | 4 | no | — |
| 379 | D3 | — | 24 | 2 | no | — |
| 380 | D3 | — | 24 | 2 | no | — |
| 381 | D3 | — | 72 | 2 | no | — |
| 382 | D3 | — | 72 | 4 | no | — |
| 383 | D3 | — | 72 | 4 | no | — |
| 384 | D3 | — | 72 | 2 | no | — |
| 385 | D3 | — | 72 | 1 | no | — |
| 386 | C22 | — | 12 | 1 | no | — |
| 387 | C22 | — | 12 | 2 | no | — |
| 388 | C22 | — | 36 | 2 | no | — |
| 389 | C22 | — | 36 | 4 | no | — |
| 390 | C22 | — | 108 | 1 | no | — |
| 391 | C22 | — | 108 | 2 | no | — |
| 392 | C22 | #88955 | 1 | 1 | yes | characteristic |
| 393 | C4 | — | 9 | 4 | no | — |
| 394 | C4 | D3×#626 | 1 | 2 | yes | — |
| 395 | C3 | — | 2 | 2 | no | — |
| 396 | C3 | — | 2 | 1 | no | — |
| 397 | C3 | — | 4 | 1 | no | — |
| 398 | C3 | #10590880 | 1 | 2 | yes | complemented |
| 399 | C3 | #10591484 | 1 | 1 | yes | characteristic, complemented |
| 400 | C2 | — | 24 | 1 | no | — |
| 401 | C2 | — | 72 | 2 | no | — |
| 402 | C2 | — | 216 | 1 | no | — |
| 403 | C2 | #11722833 | 1 | 2 | yes | — |
| 404 | C2 | #11723030 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #88955 |
| commutator, Fitting, cosocle | C2×C33×C4 | C23 |
| Frattini, hypercenter | C2×C4 | D33 |
| socle | C22×C33 | C2×D4 |
| hypocenter | C33 | #493 |
| LCS | G ▷ C2×C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11723697 | C2 | semidirect |
| 2. #11723524 | C2 | semidirect |
| 3. C2×#88791 | C2 | semidirect |
| 4. C2×C3×#3714 | C2 | semidirect |
| 5. C3×#63553 | C2 | semidirect |
| 28. C2×#3714 | D3 | semidirect |
| 30. #63553 | D3 | semidirect |
| 42. C32×C3⋊C8 | D4 | semidirect |
| 84. C3×C3⋊Dic3 | D8 | semidirect |
| 145. C3×C3⋊C8 | D12 | semidirect |
| 146. C3×C3⋊C8 | #67 | semidirect |
| 220. C3⋊Dic3 | D24 | semidirect |
| 228. C33 | #493 | semidirect |
| 276. C3⋊C8 | #626 | semidirect |
| 350. C32 | #4695 | semidirect |
| 351. C32 | #5151 | semidirect |
| 398. C3 | #10590880 | semidirect |
| 399. C3 | #10591484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723697 | 2 |
| #11723524 | 2 |
| C2×#88791 | 2 |
| C2×C3×#3714 | 2 |
| C3×#63553 | 2 |
| #10591484 | 3 |
| #10590880 | 3 |