Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3772 conjugacy classes of subgroups; only the 636 normal subgroups are shown.
This group has 3772 conjugacy classes of subgroups — too many to draw. Only its 636 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 | #11724627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D3×#3832 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#64316 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #11724399 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11724398 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11724391 | C2 | 1 | 9 | yes | maximal, complemented |
| 7 | #11724390 | C2 | 1 | 9 | yes | maximal, complemented |
| 8 | #10596689 | — | 3 | 3 | no | maximal |
| 9 | #89080 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C3×#3832 | C22 | 1 | 3 | yes | complemented |
| 11 | C32×D3×Q8 | C22 | 1 | 3 | yes | complemented |
| 12 | C4⋊#1113 | C22 | 1 | 9 | yes | complemented |
| 13 | #89042 | C22 | 1 | 3 | yes | complemented |
| 14 | D3×C4⋊(C3⋊D3) | C22 | 1 | 9 | yes | complemented |
| 15 | C4×D3×C3⋊D3 | C22 | 1 | 9 | yes | complemented |
| 16 | #89018 | C22 | 1 | 9 | yes | complemented |
| 17 | #89017 | C22 | 1 | 9 | yes | complemented |
| 18 | C3×#3799 | C22 | 1 | 18 | yes | complemented |
| 19 | C3×#3798 | C22 | 1 | 9 | yes | complemented |
| 20 | C3×#3797 | C22 | 1 | 9 | yes | complemented |
| 21 | #88965 | C22 | 1 | 18 | yes | complemented |
| 22 | #88964 | C22 | 1 | 9 | yes | complemented |
| 23 | #88963 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #88958 | C22 | 1 | 3 | yes | complemented |
| 25 | #88955 | C22 | 1 | 18 | yes | complemented |
| 26 | #88954 | C22 | 1 | 9 | yes | complemented |
| 27 | #88949 | C22 | 1 | 6 | yes | complemented |
| 28 | C2×#3832 | — | 3 | 3 | no | — |
| 29 | C3×#1007 | — | 3 | 6 | no | — |
| 30 | #64320 | — | 3 | 3 | no | — |
| 31 | #64320 | — | 3 | 9 | no | — |
| 32 | D3×#239 | — | 3 | 6 | no | — |
| 33 | D3×#239 | — | 3 | 18 | no | — |
| 34 | D3×#239 | — | 6 | 3 | no | — |
| 35 | #64316 | — | 3 | 9 | no | — |
| 36 | #64316 | D3 | 1 | 3 | yes | complemented |
| 37 | #64308 | — | 3 | 18 | no | — |
| 38 | #64306 | — | 3 | 9 | no | — |
| 39 | #64306 | — | 3 | 9 | no | — |
| 40 | C2×#1113 | C23 | 1 | 6 | yes | — |
| 41 | C2×D3×C3⋊D3 | C23 | 1 | 9 | yes | — |
| 42 | C33×Q8 | C23 | 1 | 1 | yes | characteristic |
| 43 | C4⋊(C3⋊(C3⋊D3)) | C23 | 1 | 3 | yes | — |
| 44 | C4×C3⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 45 | C3×C4⋊(C3⋊D3) | C23 | 1 | 9 | yes | — |
| 46 | C3×C4×C3⋊D3 | C23 | 1 | 9 | yes | — |
| 47 | C32×C4×D3 | C23 | 1 | 9 | yes | — |
| 48 | C32×Dic6 | C23 | 1 | 9 | yes | — |
| 49 | #6296 | C23 | 1 | 1 | yes | characteristic |
| 50 | #6295 | C23 | 1 | 9 | yes | — |
| 51 | #6292 | C23 | 1 | 18 | yes | — |
| 52 | #6289 | C23 | 1 | 9 | yes | — |
| 53 | Dic3×C3⋊D3 | C23 | 1 | 9 | yes | — |
| 54 | D3×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 55 | C3×#627 | C23 | 1 | 9 | yes | — |
| 56 | C3×#626 | C23 | 1 | 18 | yes | — |
| 57 | C3×#625 | C23 | 1 | 3 | yes | — |
| 58 | C3×#624 | C23 | 1 | 18 | yes | — |
| 59 | #5968 | — | 9 | 3 | no | — |
| 60 | C2×C32×Q8 | — | 3 | 3 | no | — |
| 61 | #3832 | — | 3 | 3 | no | — |
| 62 | #3832 | — | 3 | 9 | no | — |
| 63 | #3832 | — | 3 | 9 | no | — |
| 64 | #3832 | — | 6 | 3 | no | — |
| 65 | #3832 | — | 12 | 1 | no | — |
| 66 | #3832 | C2×D3 | 1 | 3 | yes | complemented |
| 67 | C2×C4⋊(C3⋊D3) | — | 3 | 9 | no | — |
| 68 | C2×C4×C3⋊D3 | — | 3 | 9 | no | — |
| 69 | C3×#239 | — | 3 | 6 | no | — |
| 70 | C3×#239 | — | 3 | 18 | no | — |
| 71 | C3×#239 | — | 6 | 3 | no | — |
| 72 | C3×D3×Q8 | — | 2 | 3 | no | — |
| 73 | C3×D3×Q8 | — | 3 | 18 | no | — |
| 74 | C3×D3×Q8 | C2×D3 | 1 | 6 | yes | complemented |
| 75 | C3×#235 | — | 3 | 18 | no | — |
| 76 | C3×#235 | — | 3 | 18 | no | — |
| 77 | #3811 | — | 3 | 18 | no | — |
| 78 | #3811 | — | 3 | 18 | no | — |
| 79 | #3805 | — | 3 | 9 | no | — |
| 80 | #3805 | — | 3 | 3 | no | — |
| 81 | #3802 | — | 3 | 9 | no | — |
| 82 | #3802 | — | 3 | 9 | no | — |
| 83 | D3×D12 | — | 3 | 18 | no | — |
| 84 | D3×D12 | — | 3 | 18 | no | — |
| 85 | D3×D12 | — | 3 | 36 | no | — |
| 86 | D3×D12 | — | 6 | 9 | no | — |
| 87 | C4×D32 | — | 3 | 18 | no | — |
| 88 | C4×D32 | — | 3 | 18 | no | — |
| 89 | C4×D32 | — | 6 | 9 | no | — |
| 90 | #3799 | — | 3 | 18 | no | — |
| 91 | #3799 | — | 3 | 36 | no | — |
| 92 | #3799 | — | 6 | 9 | no | — |
| 93 | #3799 | C2×D3 | 1 | 18 | yes | complemented |
| 94 | #3798 | — | 3 | 9 | no | — |
| 95 | #3798 | — | 3 | 18 | no | — |
| 96 | #3798 | C2×D3 | 1 | 9 | yes | complemented |
| 97 | #3797 | — | 3 | 9 | no | — |
| 98 | #3797 | C2×D3 | 1 | 9 | yes | complemented |
| 99 | #3796 | — | 3 | 18 | no | — |
| 100 | #3796 | — | 3 | 18 | no | — |
| 101 | #3796 | — | 6 | 9 | no | — |
| 102 | C2×C3⋊(C3⋊D3) | C24 | 1 | 3 | yes | — |
| 103 | C2×C3×C3⋊D3 | C24 | 1 | 9 | yes | — |
| 104 | C2×C32×D3 | C24 | 1 | 3 | yes | — |
| 105 | #1113 | — | 4 | 6 | no | — |
| 106 | D3×C3⋊D3 | — | 4 | 9 | no | — |
| 107 | C33×C4 | C24 | 1 | 3 | yes | — |
| 108 | C3⋊(C3⋊Dic3) | C24 | 1 | 1 | yes | characteristic |
| 109 | C3×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 110 | C32×Dic3 | C24 | 1 | 9 | yes | — |
| 111 | C3×2−1+4 | — | 9 | 3 | no | — |
| 112 | #1009 | — | 9 | 9 | no | — |
| 113 | #1009 | — | 9 | 18 | no | — |
| 114 | #1009 | — | 9 | 3 | no | — |
| 115 | D3×#41 | — | 9 | 9 | no | — |
| 116 | D3×#41 | — | 9 | 18 | no | — |
| 117 | D3×#41 | — | 9 | 3 | no | — |
| 118 | #1007 | — | 3 | 6 | no | — |
| 119 | #1007 | — | 9 | 9 | no | — |
| 120 | C2×#239 | — | 9 | 9 | no | — |
| 121 | C2×#239 | — | 9 | 6 | no | — |
| 122 | C2×#239 | — | 18 | 3 | no | — |
| 123 | C22×C3⋊D3 | — | 3 | 9 | no | — |
| 124 | C2×D32 | — | 3 | 18 | no | — |
| 125 | C2×D32 | — | 3 | 18 | no | — |
| 126 | C2×D32 | — | 6 | 9 | no | — |
| 127 | C32×Q8 | — | 2 | 3 | no | — |
| 128 | C32×Q8 | — | 3 | 9 | no | — |
| 129 | C32×Q8 | — | 4 | 1 | no | — |
| 130 | C32×Q8 | C22×D3 | 1 | 3 | yes | — |
| 131 | C2×C32×C4 | — | 3 | 9 | no | — |
| 132 | C2×C3⋊Dic3 | — | 3 | 3 | no | — |
| 133 | C4⋊(C3⋊D3) | — | 3 | 18 | no | — |
| 134 | C4⋊(C3⋊D3) | — | 3 | 9 | no | — |
| 135 | C4⋊(C3⋊D3) | — | 6 | 9 | no | — |
| 136 | C4⋊(C3⋊D3) | — | 12 | 3 | no | — |
| 137 | C4⋊(C3⋊D3) | C22×D3 | 1 | 9 | yes | — |
| 138 | C4×C3⋊D3 | — | 3 | 9 | no | — |
| 139 | C4×C3⋊D3 | — | 3 | 9 | no | — |
| 140 | C4×C3⋊D3 | — | 3 | 9 | no | — |
| 141 | C4×C3⋊D3 | — | 6 | 9 | no | — |
| 142 | C4×C3⋊D3 | — | 12 | 3 | no | — |
| 143 | C4×C3⋊D3 | C22×D3 | 1 | 9 | yes | — |
| 144 | C3×#67 | — | 3 | 6 | no | — |
| 145 | C3×#67 | — | 3 | 18 | no | — |
| 146 | C3×D12 | — | 3 | 18 | no | — |
| 147 | C3×D12 | — | 3 | 18 | no | — |
| 148 | C3×D12 | — | 6 | 9 | no | — |
| 149 | C3×C4×D3 | — | 2 | 9 | no | — |
| 150 | C3×C4×D3 | — | 3 | 18 | no | — |
| 151 | C3×C4×D3 | — | 3 | 36 | no | — |
| 152 | C3×C4×D3 | — | 6 | 9 | no | — |
| 153 | C3×C4×D3 | C22×D3 | 1 | 18 | yes | — |
| 154 | C3×Dic6 | — | 2 | 9 | no | — |
| 155 | C3×Dic6 | — | 3 | 18 | no | — |
| 156 | C3×Dic6 | C22×D3 | 1 | 18 | yes | — |
| 157 | #627 | — | 3 | 3 | no | — |
| 158 | #627 | C22×D3 | 1 | 9 | yes | — |
| 159 | #626 | — | 3 | 18 | no | — |
| 160 | #626 | — | 3 | 36 | no | — |
| 161 | #626 | — | 6 | 18 | no | — |
| 162 | #626 | C22×D3 | 1 | 18 | yes | — |
| 163 | #625 | — | 3 | 9 | no | — |
| 164 | #625 | C22×D3 | 1 | 3 | yes | — |
| 165 | #624 | — | 3 | 18 | no | — |
| 166 | #624 | — | 6 | 9 | no | — |
| 167 | #624 | C22×D3 | 1 | 18 | yes | — |
| 168 | D3×Dic3 | — | 3 | 6 | no | — |
| 169 | D3×Dic3 | — | 3 | 18 | no | — |
| 170 | D3×Dic3 | — | 6 | 3 | no | — |
| 171 | D3×Dic3 | — | 6 | 9 | no | — |
| 172 | #585 | — | 27 | 1 | no | Sylow |
| 173 | C2×C33 | C25 | 1 | 1 | yes | characteristic |
| 174 | C3⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 175 | C3×C3⋊D3 | — | 2 | 9 | no | — |
| 176 | C32×D3 | — | 2 | 3 | no | — |
| 177 | C3×#41 | — | 9 | 9 | no | — |
| 178 | C3×#41 | — | 9 | 18 | no | — |
| 179 | C3×#41 | — | 9 | 3 | no | — |
| 180 | C2×C3×Q8 | — | 3 | 6 | no | — |
| 181 | C2×C3×Q8 | — | 6 | 3 | no | — |
| 182 | C2×C3×Q8 | — | 9 | 9 | no | — |
| 183 | #239 | — | 3 | 6 | no | — |
| 184 | #239 | — | 3 | 18 | no | — |
| 185 | #239 | — | 6 | 3 | no | — |
| 186 | #239 | — | 9 | 18 | no | — |
| 187 | #239 | — | 9 | 18 | no | — |
| 188 | #239 | — | 9 | 9 | no | — |
| 189 | #239 | — | 9 | 18 | no | — |
| 190 | #239 | — | 9 | 3 | no | — |
| 191 | #239 | — | 18 | 9 | no | — |
| 192 | #239 | — | 18 | 9 | no | — |
| 193 | #239 | — | 18 | 3 | no | — |
| 194 | #239 | — | 36 | 1 | no | — |
| 195 | D3×Q8 | — | 3 | 18 | no | — |
| 196 | D3×Q8 | — | 9 | 9 | no | — |
| 197 | D3×Q8 | D32 | 1 | 3 | yes | complemented |
| 198 | #237 | — | 9 | 18 | no | — |
| 199 | #237 | — | 9 | 3 | no | — |
| 200 | #237 | — | 9 | 9 | no | — |
| 201 | D3×D4 | — | 9 | 18 | no | — |
| 202 | D3×D4 | — | 9 | 36 | no | — |
| 203 | D3×D4 | — | 9 | 18 | no | — |
| 204 | D3×D4 | — | 9 | 9 | no | — |
| 205 | D3×D4 | — | 9 | 9 | no | — |
| 206 | #235 | — | 3 | 18 | no | — |
| 207 | #235 | — | 3 | 18 | no | — |
| 208 | #235 | — | 9 | 36 | no | — |
| 209 | #235 | — | 9 | 9 | no | — |
| 210 | #235 | — | 9 | 9 | no | — |
| 211 | C2×D12 | — | 9 | 18 | no | — |
| 212 | C2×D12 | — | 9 | 9 | no | — |
| 213 | C2×D12 | — | 9 | 18 | no | — |
| 214 | C2×D12 | — | 18 | 9 | no | — |
| 215 | C2×C4×D3 | — | 9 | 18 | no | — |
| 216 | C2×C4×D3 | — | 9 | 18 | no | — |
| 217 | C2×C4×D3 | — | 9 | 9 | no | — |
| 218 | C2×C4×D3 | — | 18 | 9 | no | — |
| 219 | C22×C32 | — | 3 | 3 | no | — |
| 220 | C2×C3⋊D3 | — | 3 | 9 | no | — |
| 221 | C2×C3⋊D3 | — | 6 | 9 | no | — |
| 222 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 223 | C2×C3⋊D3 | — | 12 | 9 | no | — |
| 224 | C2×C3⋊D3 | C23×D3 | 1 | 9 | yes | — |
| 225 | C2×C3×D3 | — | 2 | 3 | no | — |
| 226 | C2×C3×D3 | — | 3 | 18 | no | — |
| 227 | C2×C3×D3 | — | 6 | 9 | no | — |
| 228 | C2×C3×D3 | C23×D3 | 1 | 6 | yes | — |
| 229 | D32 | — | 12 | 18 | no | — |
| 230 | D32 | — | 12 | 18 | no | — |
| 231 | D32 | — | 12 | 18 | no | — |
| 232 | C32×C4 | — | 2 | 9 | no | — |
| 233 | C32×C4 | — | 3 | 9 | no | — |
| 234 | C32×C4 | — | 4 | 3 | no | — |
| 235 | C32×C4 | C23×D3 | 1 | 9 | yes | — |
| 236 | C3⋊Dic3 | — | 3 | 3 | no | — |
| 237 | C3⋊Dic3 | — | 6 | 3 | no | — |
| 238 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 239 | C3⋊Dic3 | C23×D3 | 1 | 3 | yes | — |
| 240 | C3×Dic3 | — | 2 | 9 | no | — |
| 241 | C3×Dic3 | — | 3 | 6 | no | — |
| 242 | C3×Dic3 | — | 6 | 3 | no | — |
| 243 | C3×Dic3 | C23×D3 | 1 | 18 | yes | — |
| 244 | 2−1+4 | — | 9 | 3 | no | — |
| 245 | 2−1+4 | — | 27 | 3 | no | — |
| 246 | H(5,𝔽2) | — | 27 | 9 | no | — |
| 247 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 248 | C2×#41 | — | 27 | 3 | no | — |
| 249 | C2×#41 | — | 27 | 9 | no | — |
| 250 | C2×#41 | — | 27 | 3 | no | — |
| 251 | C33 | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 252 | C22×D3 | — | 9 | 18 | no | — |
| 253 | C22×D3 | — | 9 | 18 | no | — |
| 254 | C22×D3 | — | 9 | 9 | no | — |
| 255 | C22×D3 | — | 18 | 9 | no | — |
| 256 | C3×Q8 | — | 2 | 3 | no | — |
| 257 | C3×Q8 | — | 3 | 18 | no | — |
| 258 | C3×Q8 | — | 4 | 1 | no | — |
| 259 | C3×Q8 | — | 6 | 9 | no | — |
| 260 | C3×Q8 | — | 9 | 9 | no | — |
| 261 | C3×Q8 | C2×D32 | 1 | 3 | yes | — |
| 262 | C3×D4 | — | 9 | 18 | no | — |
| 263 | C3×D4 | — | 9 | 3 | no | — |
| 264 | C3×D4 | — | 9 | 9 | no | — |
| 265 | C2×C3×C4 | — | 3 | 18 | no | — |
| 266 | C2×C3×C4 | — | 6 | 9 | no | — |
| 267 | C2×C3×C4 | — | 9 | 18 | no | — |
| 268 | C2×C3×C4 | — | 9 | 9 | no | — |
| 269 | #67 | — | 3 | 6 | no | — |
| 270 | #67 | — | 3 | 18 | no | — |
| 271 | #67 | — | 9 | 18 | no | — |
| 272 | #67 | — | 9 | 18 | no | — |
| 273 | C2×Dic3 | — | 9 | 6 | no | — |
| 274 | C2×Dic3 | — | 9 | 9 | no | — |
| 275 | C2×Dic3 | — | 18 | 3 | no | — |
| 276 | D12 | — | 3 | 18 | no | — |
| 277 | D12 | — | 3 | 18 | no | — |
| 278 | D12 | — | 6 | 9 | no | — |
| 279 | D12 | — | 9 | 36 | no | — |
| 280 | D12 | — | 9 | 9 | no | — |
| 281 | D12 | — | 9 | 9 | no | — |
| 282 | D12 | — | 18 | 9 | no | — |
| 283 | D12 | — | 18 | 18 | no | — |
| 284 | D12 | — | 36 | 3 | no | — |
| 285 | C4×D3 | — | 3 | 18 | no | — |
| 286 | C4×D3 | — | 3 | 36 | no | — |
| 287 | C4×D3 | — | 6 | 9 | no | — |
| 288 | C4×D3 | — | 9 | 18 | no | — |
| 289 | C4×D3 | — | 9 | 18 | no | — |
| 290 | C4×D3 | — | 9 | 3 | no | — |
| 291 | C4×D3 | — | 9 | 9 | no | — |
| 292 | C4×D3 | — | 9 | 9 | no | — |
| 293 | C4×D3 | — | 18 | 9 | no | — |
| 294 | C4×D3 | — | 18 | 9 | no | — |
| 295 | C4×D3 | — | 18 | 9 | no | — |
| 296 | C4×D3 | — | 36 | 3 | no | — |
| 297 | C4×D3 | C2×D32 | 1 | 9 | yes | — |
| 298 | Dic6 | — | 3 | 18 | no | — |
| 299 | Dic6 | — | 9 | 3 | no | — |
| 300 | Dic6 | C2×D32 | 1 | 9 | yes | — |
| 301 | C2×C32 | — | 2 | 3 | no | — |
| 302 | C2×C32 | — | 4 | 1 | no | — |
| 303 | C2×C32 | — | 6 | 3 | no | — |
| 304 | C2×C32 | C24×D3 | 1 | 3 | yes | — |
| 305 | C3⋊D3 | — | 2 | 9 | no | — |
| 306 | C3⋊D3 | — | 6 | 9 | no | — |
| 307 | C3⋊D3 | — | 12 | 9 | no | — |
| 308 | C3⋊D3 | — | 24 | 3 | no | — |
| 309 | C3×D3 | — | 2 | 6 | no | — |
| 310 | C3×D3 | — | 2 | 6 | no | — |
| 311 | C3×D3 | — | 6 | 18 | no | — |
| 312 | C3×D3 | — | 12 | 9 | no | — |
| 313 | #41 | — | 9 | 9 | no | — |
| 314 | #41 | — | 9 | 18 | no | — |
| 315 | #41 | — | 9 | 3 | no | — |
| 316 | #41 | — | 27 | 3 | no | — |
| 317 | #41 | — | 27 | 18 | no | — |
| 318 | #41 | — | 27 | 9 | no | — |
| 319 | #41 | — | 27 | 1 | no | — |
| 320 | #41 | — | 27 | 9 | no | — |
| 321 | #41 | — | 27 | 9 | no | — |
| 322 | #41 | — | 27 | 1 | no | — |
| 323 | C2×Q8 | — | 3 | 3 | no | — |
| 324 | C2×Q8 | — | 9 | 9 | no | — |
| 325 | C2×Q8 | — | 27 | 3 | no | — |
| 326 | C2×D4 | — | 27 | 9 | no | — |
| 327 | C2×D4 | — | 27 | 18 | no | — |
| 328 | C2×D4 | — | 27 | 9 | no | — |
| 329 | C2×D4 | — | 27 | 9 | no | — |
| 330 | C22×C4 | — | 27 | 9 | no | — |
| 331 | C22×C4 | — | 27 | 6 | no | — |
| 332 | C22×C3 | — | 3 | 6 | no | — |
| 333 | C22×C3 | — | 6 | 3 | no | — |
| 334 | C22×C3 | — | 9 | 9 | no | — |
| 335 | C2×D3 | — | 3 | 18 | no | — |
| 336 | C2×D3 | — | 6 | 9 | no | — |
| 337 | C2×D3 | — | 9 | 9 | no | — |
| 338 | C2×D3 | — | 18 | 9 | no | — |
| 339 | C2×D3 | — | 36 | 3 | no | — |
| 340 | C2×D3 | — | 36 | 9 | no | — |
| 341 | C2×D3 | — | 36 | 18 | no | — |
| 342 | C2×D3 | — | 36 | 18 | no | — |
| 343 | C2×D3 | — | 36 | 18 | no | — |
| 344 | C2×D3 | C22×D32 | 1 | 3 | yes | — |
| 345 | C3×C4 | — | 2 | 9 | no | — |
| 346 | C3×C4 | — | 3 | 18 | no | — |
| 347 | C3×C4 | — | 4 | 3 | no | — |
| 348 | C3×C4 | — | 6 | 9 | no | — |
| 349 | C3×C4 | — | 9 | 3 | no | — |
| 350 | C3×C4 | C22×D32 | 1 | 9 | yes | — |
| 351 | Dic3 | — | 3 | 6 | no | — |
| 352 | Dic3 | — | 6 | 3 | no | — |
| 353 | Dic3 | — | 9 | 3 | no | — |
| 354 | Dic3 | — | 18 | 3 | no | — |
| 355 | Dic3 | — | 36 | 1 | no | — |
| 356 | Dic3 | C22×D32 | 1 | 9 | yes | — |
| 357 | C32 | — | 2 | 3 | no | — |
| 358 | C32 | — | 4 | 1 | no | — |
| 359 | C32 | #5968 | 1 | 3 | yes | complemented |
| 360 | C23 | — | 27 | 9 | no | — |
| 361 | C23 | — | 27 | 6 | no | — |
| 362 | Q8 | — | 3 | 9 | no | — |
| 363 | Q8 | — | 9 | 9 | no | — |
| 364 | Q8 | — | 27 | 1 | no | — |
| 365 | Q8 | D33 | 1 | 1 | yes | characteristic |
| 366 | D4 | — | 9 | 18 | no | — |
| 367 | D4 | — | 9 | 3 | no | — |
| 368 | D4 | — | 9 | 9 | no | — |
| 369 | D4 | — | 27 | 18 | no | — |
| 370 | D4 | — | 27 | 9 | no | — |
| 371 | D4 | — | 27 | 3 | no | — |
| 372 | C2×C4 | — | 3 | 9 | no | — |
| 373 | C2×C4 | — | 9 | 18 | no | — |
| 374 | C2×C4 | — | 9 | 9 | no | — |
| 375 | C2×C4 | — | 27 | 9 | no | — |
| 376 | C2×C4 | — | 27 | 9 | no | — |
| 377 | C2×C4 | — | 27 | 3 | no | — |
| 378 | C2×C4 | — | 27 | 3 | no | — |
| 379 | C2×C3 | — | 2 | 3 | no | — |
| 380 | C2×C3 | — | 4 | 1 | no | — |
| 381 | C2×C3 | — | 6 | 6 | no | — |
| 382 | C2×C3 | — | 6 | 6 | no | — |
| 383 | C2×C3 | — | 18 | 9 | no | — |
| 384 | C2×C3 | C23×D32 | 1 | 3 | yes | — |
| 385 | D3 | — | 2 | 3 | no | — |
| 386 | D3 | — | 6 | 18 | no | — |
| 387 | D3 | — | 12 | 9 | no | — |
| 388 | D3 | — | 18 | 9 | no | — |
| 389 | D3 | — | 36 | 9 | no | — |
| 390 | D3 | — | 72 | 3 | no | — |
| 391 | C22 | — | 3 | 3 | no | — |
| 392 | C22 | — | 9 | 9 | no | — |
| 393 | C22 | — | 27 | 3 | no | — |
| 394 | C22 | — | 108 | 9 | no | — |
| 395 | C22 | — | 108 | 6 | no | — |
| 396 | C4 | — | 3 | 9 | no | — |
| 397 | C4 | — | 9 | 3 | no | — |
| 398 | C4 | — | 27 | 1 | no | — |
| 399 | C4 | C2×D33 | 1 | 3 | yes | — |
| 400 | C3 | — | 2 | 3 | no | — |
| 401 | C3 | — | 4 | 1 | no | — |
| 402 | C3 | #10596689 | 1 | 3 | yes | complemented |
| 403 | C2 | — | 6 | 3 | no | — |
| 404 | C2 | — | 18 | 9 | no | — |
| 405 | C2 | — | 54 | 3 | no | — |
| 406 | C2 | C22×D33 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D33 |
| commutator, socle, cosocle | C2×C33 | C25 |
| Fitting | C33×Q8 | C23 |
| hypercenter | Q8 | D33 |
| hypocenter | C33 | #585 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724627 | C2 | semidirect |
| 2. D3×#3832 | C2 | semidirect |
| 3. C3×#64316 | C2 | semidirect |
| 4. #11724399 | C2 | semidirect |
| 5. #11724398 | C2 | semidirect |
| 6. #11724391 | C2 | semidirect |
| 7. #11724390 | C2 | semidirect |
| 9. #89080 | C22 | semidirect |
| 10. C3×#3832 | C22 | semidirect |
| 11. C32×D3×Q8 | C22 | semidirect |
| 12. C4⋊#1113 | C22 | semidirect |
| 13. #89042 | C22 | semidirect |
| 14. D3×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C4×D3×C3⋊D3 | C22 | semidirect |
| 16. #89018 | C22 | semidirect |
| 17. #89017 | C22 | semidirect |
| 18. C3×#3799 | C22 | semidirect |
| 19. C3×#3798 | C22 | semidirect |
| 20. C3×#3797 | C22 | semidirect |
| 21. #88965 | C22 | semidirect |
| 22. #88964 | C22 | semidirect |
| 23. #88963 | C22 | semidirect |
| 24. #88958 | C22 | semidirect |
| 25. #88955 | C22 | semidirect |
| 26. #88954 | C22 | semidirect |
| 27. #88949 | C22 | semidirect |
| 36. #64316 | D3 | semidirect |
| 66. #3832 | C2×D3 | semidirect |
| 74. C3×D3×Q8 | C2×D3 | semidirect |
| 93. #3799 | C2×D3 | semidirect |
| 96. #3798 | C2×D3 | semidirect |
| 98. #3797 | C2×D3 | semidirect |
| 197. D3×Q8 | D32 | semidirect |
| 251. C33 | #585 | semidirect |
| 359. C32 | #5968 | semidirect |
| 402. C3 | #10596689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724627 | 2 |
| D3×#3832 | 2 |
| C3×#64316 | 2 |
| #11724399 | 2 |
| #11724398 | 2 |
| #11724391 | 2 |
| #11724390 | 2 |
| #10596689 | 3 |