Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
1568 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 68 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 | A4×#1113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3⋊D3×C3⋊S4 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#89101 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | D32×S4 | — | 3 | 3 | no | maximal |
| 5 | #11724440 | — | 3 | 1 | no | maximal |
| 6 | C3×A4×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 7 | C3⋊(C3⋊(C3⋊S4)) | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | C32×C3⋊S4 | C22 | 1 | 3 | yes | complemented |
| 9 | #10620215 | — | 4 | 1 | no | maximal |
| 10 | C22×#1113 | D3 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×D33 | — | 3 | 1 | no | — |
| 12 | D32×A4 | — | 3 | 3 | no | — |
| 13 | #89101 | D3 | 1 | 3 | yes | complemented |
| 14 | D3×C3⋊S4 | — | 3 | 6 | no | — |
| 15 | D3×C3⋊S4 | — | 6 | 3 | no | — |
| 16 | C3⋊D3×S4 | — | 3 | 3 | no | — |
| 17 | C3⋊D3×S4 | — | 6 | 3 | no | — |
| 18 | C3×D3×S4 | — | 3 | 6 | no | — |
| 19 | C3⋊D3×#67 | — | 3 | 3 | no | — |
| 20 | C3×#3811 | — | 3 | 3 | no | — |
| 21 | #88955 | — | 3 | 3 | no | — |
| 22 | #88953 | — | 3 | 3 | no | — |
| 23 | #88949 | — | 3 | 1 | no | — |
| 24 | C33×A4 | C23 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3⋊D32 | — | 4 | 3 | no | — |
| 26 | C3×#1113 | — | 4 | 3 | no | — |
| 27 | C3×#1113 | — | 4 | 1 | no | — |
| 28 | C2×D3×S4 | — | 9 | 3 | no | — |
| 29 | D32×D4 | — | 9 | 3 | no | — |
| 30 | C22×C3×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 31 | C2×#1113 | — | 3 | 1 | no | — |
| 32 | C2×#1113 | — | 3 | 3 | no | — |
| 33 | C2×D3×C3⋊D3 | — | 3 | 3 | no | — |
| 34 | C2×C3×D32 | — | 3 | 3 | no | — |
| 35 | A4×C3⋊D3 | — | 2 | 3 | no | — |
| 36 | A4×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 37 | C3×D3×A4 | — | 3 | 6 | no | — |
| 38 | C3×D3×A4 | — | 6 | 3 | no | — |
| 39 | C3⋊(C3⋊S4) | — | 3 | 3 | no | — |
| 40 | C3⋊(C3⋊S4) | — | 6 | 3 | no | — |
| 41 | C3⋊(C3⋊S4) | — | 6 | 3 | no | — |
| 42 | C3⋊(C3⋊S4) | — | 12 | 3 | no | — |
| 43 | C3⋊(C3⋊S4) | — | 12 | 1 | no | — |
| 44 | C3⋊(C3⋊S4) | — | 12 | 2 | no | — |
| 45 | C3×C3⋊S4 | — | 2 | 3 | no | — |
| 46 | C3×C3⋊S4 | C2×D3 | 1 | 6 | yes | complemented |
| 47 | C32×S4 | — | 3 | 3 | no | — |
| 48 | C32×S4 | — | 6 | 3 | no | — |
| 49 | D33 | — | 6 | 3 | no | — |
| 50 | D33 | — | 6 | 1 | no | — |
| 51 | D33 | — | 12 | 3 | no | — |
| 52 | #6312 | — | 3 | 1 | no | — |
| 53 | C32×#67 | — | 3 | 3 | no | — |
| 54 | #6292 | — | 3 | 3 | no | — |
| 55 | #6290 | — | 3 | 3 | no | — |
| 56 | Dic3×C3⋊D3 | — | 3 | 3 | no | — |
| 57 | C3×#626 | — | 3 | 6 | no | — |
| 58 | C3×#624 | — | 3 | 3 | no | — |
| 59 | C3⋊(C3⋊(C3⋊D3)) | — | 4 | 1 | no | — |
| 60 | C32×C3⋊D3 | — | 4 | 3 | no | — |
| 61 | C32×C3⋊D3 | — | 4 | 3 | no | — |
| 62 | C22×D32 | — | 3 | 3 | no | — |
| 63 | C22×D32 | — | 9 | 3 | no | — |
| 64 | C2×D3×A4 | — | 9 | 3 | no | — |
| 65 | C2×C3⋊S4 | — | 9 | 3 | no | — |
| 66 | C2×C3×S4 | — | 9 | 3 | no | — |
| 67 | D3×S4 | — | 3 | 6 | no | — |
| 68 | D3×S4 | — | 9 | 6 | no | — |
| 69 | D3×S4 | — | 18 | 6 | no | — |
| 70 | D3×S4 | — | 18 | 3 | no | — |
| 71 | D3×S4 | — | 18 | 6 | no | — |
| 72 | D4×C3⋊D3 | — | 9 | 3 | no | — |
| 73 | C3×D3×D4 | — | 9 | 6 | no | — |
| 74 | #3811 | — | 3 | 3 | no | — |
| 75 | #3811 | — | 9 | 3 | no | — |
| 76 | D3×#67 | — | 9 | 6 | no | — |
| 77 | D3×#67 | — | 9 | 6 | no | — |
| 78 | D3×#67 | — | 18 | 3 | no | — |
| 79 | #3802 | — | 9 | 3 | no | — |
| 80 | D3×D12 | — | 9 | 6 | no | — |
| 81 | C4×D32 | — | 9 | 3 | no | — |
| 82 | C22×C33 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 83 | C2×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 84 | C2×C3×C3⋊D3 | — | 3 | 3 | no | — |
| 85 | C2×C3×C3⋊D3 | — | 3 | 3 | no | — |
| 86 | C2×C32×D3 | — | 3 | 3 | no | — |
| 87 | C32×A4 | — | 2 | 3 | no | — |
| 88 | C32×A4 | — | 2 | 3 | no | — |
| 89 | C32×A4 | — | 4 | 2 | no | — |
| 90 | C32×A4 | — | 4 | 1 | no | — |
| 91 | C32×A4 | — | 4 | 3 | no | — |
| 92 | C32×A4 | C22×D3 | 1 | 3 | yes | complemented |
| 93 | #1113 | — | 3 | 3 | no | — |
| 94 | #1113 | — | 4 | 3 | no | — |
| 95 | #1113 | — | 6 | 1 | no | — |
| 96 | #1113 | S4 | 1 | 1 | yes | characteristic, complemented |
| 97 | D3×C3⋊D3 | — | 6 | 3 | no | — |
| 98 | D3×C3⋊D3 | — | 6 | 3 | no | — |
| 99 | D3×C3⋊D3 | — | 12 | 6 | no | — |
| 100 | D3×C3⋊D3 | — | 12 | 3 | no | — |
| 101 | D3×C3⋊D3 | — | 24 | 3 | no | — |
| 102 | D3×C3⋊D3 | — | 24 | 3 | no | — |
| 103 | C3×D32 | — | 6 | 3 | no | — |
| 104 | C3×D32 | — | 6 | 3 | no | — |
| 105 | C3×D32 | — | 12 | 3 | no | — |
| 106 | C3×D32 | — | 12 | 6 | no | — |
| 107 | C3⋊(C3⋊Dic3) | — | 3 | 1 | no | — |
| 108 | C32×Dic3 | — | 3 | 3 | no | — |
| 109 | C22×S4 | — | 27 | 1 | no | — |
| 110 | C2×D3×D4 | — | 27 | 3 | no | — |
| 111 | C34 | — | 4 | 1 | no | Sylow |
| 112 | C22×C3⋊D3 | — | 9 | 3 | no | — |
| 113 | C22×C3⋊D3 | D32 | 1 | 3 | yes | complemented |
| 114 | C22×C3×D3 | — | 3 | 6 | no | — |
| 115 | C22×C3×D3 | — | 6 | 3 | no | — |
| 116 | C22×C3×D3 | — | 9 | 6 | no | — |
| 117 | C2×C3×A4 | — | 9 | 3 | no | — |
| 118 | C2×D32 | — | 3 | 3 | no | — |
| 119 | C2×D32 | — | 9 | 3 | no | — |
| 120 | C2×D32 | — | 9 | 6 | no | — |
| 121 | C2×D32 | — | 9 | 3 | no | — |
| 122 | C2×D32 | — | 9 | 6 | no | — |
| 123 | C2×D32 | — | 18 | 3 | no | — |
| 124 | C2×D32 | — | 18 | 3 | no | — |
| 125 | C2×D32 | — | 18 | 6 | no | — |
| 126 | C2×D32 | — | 18 | 3 | no | — |
| 127 | C2×D32 | — | 36 | 3 | no | — |
| 128 | D3×A4 | — | 3 | 6 | no | — |
| 129 | D3×A4 | — | 6 | 3 | no | — |
| 130 | D3×A4 | — | 6 | 6 | no | — |
| 131 | D3×A4 | — | 6 | 6 | no | — |
| 132 | C3⋊S4 | — | 9 | 3 | no | — |
| 133 | C3⋊S4 | — | 18 | 6 | no | — |
| 134 | C3⋊S4 | — | 18 | 3 | no | — |
| 135 | C3⋊S4 | — | 18 | 6 | no | — |
| 136 | C3⋊S4 | — | 36 | 3 | no | — |
| 137 | C3⋊S4 | — | 36 | 3 | no | — |
| 138 | C3⋊S4 | — | 36 | 6 | no | — |
| 139 | C3⋊S4 | — | 36 | 1 | no | — |
| 140 | C3⋊S4 | — | 36 | 6 | no | — |
| 141 | C3⋊S4 | — | 36 | 2 | no | — |
| 142 | C3⋊S4 | D32 | 1 | 3 | yes | complemented |
| 143 | C3×S4 | — | 3 | 6 | no | — |
| 144 | C3×S4 | — | 6 | 6 | no | — |
| 145 | C3×S4 | — | 6 | 3 | no | — |
| 146 | C3×S4 | — | 6 | 6 | no | — |
| 147 | C32×D4 | — | 9 | 3 | no | — |
| 148 | #638 | — | 9 | 3 | no | — |
| 149 | #638 | — | 9 | 3 | no | — |
| 150 | #638 | — | 18 | 3 | no | — |
| 151 | #638 | — | 36 | 1 | no | — |
| 152 | C4⋊(C3⋊D3) | — | 9 | 3 | no | — |
| 153 | C4×C3⋊D3 | — | 9 | 3 | no | — |
| 154 | C3×#67 | — | 3 | 6 | no | — |
| 155 | C3×#67 | — | 6 | 3 | no | — |
| 156 | C3×#67 | — | 9 | 6 | no | — |
| 157 | C3×D12 | — | 9 | 6 | no | — |
| 158 | C3×C4×D3 | — | 9 | 6 | no | — |
| 159 | #626 | — | 3 | 6 | no | — |
| 160 | #626 | — | 9 | 6 | no | — |
| 161 | #626 | — | 18 | 3 | no | — |
| 162 | #625 | — | 9 | 6 | no | — |
| 163 | #625 | — | 18 | 3 | no | — |
| 164 | #624 | — | 3 | 3 | no | — |
| 165 | D3×Dic3 | — | 9 | 6 | no | — |
| 166 | D3×Dic3 | — | 18 | 3 | no | — |
| 167 | C2×C33 | — | 3 | 1 | no | — |
| 168 | C3⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 169 | C3⋊(C3⋊D3) | — | 12 | 3 | no | — |
| 170 | C3⋊(C3⋊D3) | — | 24 | 3 | no | — |
| 171 | C3⋊(C3⋊D3) | — | 24 | 3 | no | — |
| 172 | C3⋊(C3⋊D3) | — | 48 | 3 | no | — |
| 173 | C3⋊(C3⋊D3) | — | 48 | 1 | no | — |
| 174 | C3⋊(C3⋊D3) | — | 48 | 2 | no | — |
| 175 | C3×C3⋊D3 | — | 3 | 3 | no | — |
| 176 | C3×C3⋊D3 | — | 4 | 6 | no | — |
| 177 | C3×C3⋊D3 | — | 4 | 3 | no | — |
| 178 | C3×C3⋊D3 | — | 8 | 3 | no | — |
| 179 | C3×C3⋊D3 | — | 8 | 3 | no | — |
| 180 | C3×C3⋊D3 | C2×S4 | 1 | 3 | yes | complemented |
| 181 | C32×D3 | — | 6 | 3 | no | — |
| 182 | C32×D3 | — | 12 | 6 | no | — |
| 183 | C32×D3 | — | 12 | 3 | no | — |
| 184 | C32×D3 | — | 24 | 3 | no | — |
| 185 | C32×D3 | — | 24 | 3 | no | — |
| 186 | C23×D3 | — | 9 | 3 | no | — |
| 187 | C23×D3 | — | 27 | 3 | no | — |
| 188 | C22×A4 | — | 27 | 1 | no | — |
| 189 | C2×S4 | — | 9 | 3 | no | — |
| 190 | C2×S4 | — | 27 | 3 | no | — |
| 191 | C2×S4 | — | 54 | 3 | no | — |
| 192 | C2×C3×D4 | — | 27 | 3 | no | — |
| 193 | C2×#67 | — | 27 | 3 | no | — |
| 194 | C2×#67 | — | 27 | 3 | no | — |
| 195 | D3×D4 | — | 9 | 6 | no | — |
| 196 | D3×D4 | — | 27 | 6 | no | — |
| 197 | D3×D4 | — | 27 | 6 | no | — |
| 198 | D3×D4 | — | 27 | 6 | no | — |
| 199 | D3×D4 | — | 54 | 3 | no | — |
| 200 | C2×D12 | — | 27 | 3 | no | — |
| 201 | C2×C4×D3 | — | 27 | 3 | no | — |
| 202 | C22×C32 | — | 2 | 3 | no | — |
| 203 | C22×C32 | — | 4 | 1 | no | — |
| 204 | C22×C32 | — | 9 | 3 | no | — |
| 205 | C22×C32 | C2×D32 | 1 | 3 | yes | complemented |
| 206 | C2×C3⋊D3 | — | 3 | 3 | no | — |
| 207 | C2×C3⋊D3 | — | 3 | 3 | no | — |
| 208 | C2×C3⋊D3 | — | 9 | 3 | no | — |
| 209 | C2×C3⋊D3 | — | 18 | 3 | no | — |
| 210 | C2×C3⋊D3 | — | 18 | 3 | no | — |
| 211 | C2×C3⋊D3 | — | 18 | 3 | no | — |
| 212 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 213 | C2×C3⋊D3 | — | 36 | 3 | no | — |
| 214 | C2×C3×D3 | — | 3 | 6 | no | — |
| 215 | C2×C3×D3 | — | 6 | 3 | no | — |
| 216 | C2×C3×D3 | — | 9 | 6 | no | — |
| 217 | C2×C3×D3 | — | 9 | 6 | no | — |
| 218 | C2×C3×D3 | — | 18 | 3 | no | — |
| 219 | C2×C3×D3 | — | 18 | 3 | no | — |
| 220 | C2×C3×D3 | — | 18 | 6 | no | — |
| 221 | C2×C3×D3 | — | 18 | 6 | no | — |
| 222 | C2×C3×D3 | — | 36 | 3 | no | — |
| 223 | C2×C3×D3 | — | 36 | 3 | no | — |
| 224 | C3×A4 | — | 2 | 6 | no | — |
| 225 | C3×A4 | — | 2 | 6 | no | — |
| 226 | C3×A4 | — | 2 | 3 | no | — |
| 227 | C3×A4 | — | 4 | 3 | no | — |
| 228 | C3×A4 | — | 4 | 6 | no | — |
| 229 | C3×A4 | — | 4 | 6 | no | — |
| 230 | C3×A4 | — | 4 | 2 | no | — |
| 231 | C3×A4 | — | 4 | 3 | no | — |
| 232 | C3×A4 | — | 4 | 1 | no | — |
| 233 | C3×A4 | C2×D32 | 1 | 3 | yes | complemented |
| 234 | D32 | — | 3 | 3 | no | — |
| 235 | D32 | — | 6 | 3 | no | — |
| 236 | D32 | — | 6 | 3 | no | — |
| 237 | D32 | — | 9 | 6 | no | — |
| 238 | D32 | — | 9 | 3 | no | — |
| 239 | D32 | — | 12 | 6 | no | — |
| 240 | D32 | — | 18 | 6 | no | — |
| 241 | D32 | — | 18 | 6 | no | — |
| 242 | D32 | — | 18 | 3 | no | — |
| 243 | D32 | — | 36 | 3 | no | — |
| 244 | D32 | — | 36 | 6 | no | — |
| 245 | D32 | — | 36 | 3 | no | — |
| 246 | D32 | — | 72 | 6 | no | — |
| 247 | D32 | — | 72 | 3 | no | — |
| 248 | D32 | — | 72 | 6 | no | — |
| 249 | C32×C4 | — | 9 | 3 | no | — |
| 250 | C3⋊Dic3 | — | 9 | 3 | no | — |
| 251 | C3⋊Dic3 | — | 18 | 3 | no | — |
| 252 | C3⋊Dic3 | — | 36 | 1 | no | — |
| 253 | C3×Dic3 | — | 3 | 6 | no | — |
| 254 | C3×Dic3 | — | 6 | 3 | no | — |
| 255 | C22×D4 | — | 81 | 1 | no | Sylow |
| 256 | C33 | — | 4 | 3 | no | — |
| 257 | C33 | — | 8 | 3 | no | — |
| 258 | C33 | — | 8 | 3 | no | — |
| 259 | C33 | — | 16 | 3 | no | — |
| 260 | C33 | — | 16 | 1 | no | — |
| 261 | C33 | — | 16 | 2 | no | — |
| 262 | C33 | C22×S4 | 1 | 1 | yes | characteristic, complemented |
| 263 | C23×C3 | — | 9 | 3 | no | — |
| 264 | C23×C3 | — | 27 | 3 | no | — |
| 265 | C22×D3 | — | 3 | 6 | no | — |
| 266 | C22×D3 | — | 6 | 3 | no | — |
| 267 | C22×D3 | — | 9 | 6 | no | — |
| 268 | C22×D3 | — | 27 | 3 | no | — |
| 269 | C22×D3 | — | 27 | 3 | no | — |
| 270 | C22×D3 | — | 27 | 3 | no | — |
| 271 | C22×D3 | — | 27 | 6 | no | — |
| 272 | C22×D3 | — | 27 | 6 | no | — |
| 273 | C22×D3 | — | 54 | 3 | no | — |
| 274 | C22×D3 | — | 54 | 3 | no | — |
| 275 | C22×D3 | — | 54 | 6 | no | — |
| 276 | C22×D3 | — | 54 | 3 | no | — |
| 277 | C22×D3 | — | 108 | 1 | no | — |
| 278 | C2×A4 | — | 9 | 3 | no | — |
| 279 | C2×A4 | — | 18 | 3 | no | — |
| 280 | S4 | — | 3 | 3 | no | — |
| 281 | S4 | — | 6 | 3 | no | — |
| 282 | S4 | — | 27 | 1 | no | — |
| 283 | S4 | — | 54 | 3 | no | — |
| 284 | S4 | — | 108 | 3 | no | — |
| 285 | S4 | — | 108 | 2 | no | — |
| 286 | C3×D4 | — | 9 | 6 | no | — |
| 287 | C3×D4 | — | 18 | 3 | no | — |
| 288 | C3×D4 | — | 27 | 6 | no | — |
| 289 | C2×C3×C4 | — | 27 | 3 | no | — |
| 290 | #67 | — | 3 | 3 | no | — |
| 291 | #67 | — | 9 | 6 | no | — |
| 292 | #67 | — | 27 | 3 | no | — |
| 293 | #67 | — | 27 | 3 | no | — |
| 294 | #67 | — | 27 | 6 | no | — |
| 295 | #67 | — | 27 | 3 | no | — |
| 296 | #67 | — | 54 | 3 | no | — |
| 297 | #67 | — | 54 | 3 | no | — |
| 298 | #67 | — | 108 | 1 | no | — |
| 299 | C2×Dic3 | — | 27 | 3 | no | — |
| 300 | D12 | — | 9 | 6 | no | — |
| 301 | D12 | — | 27 | 6 | no | — |
| 302 | D12 | — | 54 | 3 | no | — |
| 303 | C4×D3 | — | 9 | 6 | no | — |
| 304 | C4×D3 | — | 27 | 6 | no | — |
| 305 | C4×D3 | — | 54 | 3 | no | — |
| 306 | C2×C32 | — | 3 | 3 | no | — |
| 307 | C2×C32 | — | 6 | 3 | no | — |
| 308 | C2×C32 | — | 12 | 1 | no | — |
| 309 | C2×C32 | — | 18 | 3 | no | — |
| 310 | C2×C32 | — | 36 | 3 | no | — |
| 311 | C3⋊D3 | — | 3 | 3 | no | — |
| 312 | C3⋊D3 | — | 4 | 3 | no | — |
| 313 | C3⋊D3 | — | 18 | 3 | no | — |
| 314 | C3⋊D3 | — | 36 | 3 | no | — |
| 315 | C3⋊D3 | — | 36 | 3 | no | — |
| 316 | C3⋊D3 | — | 72 | 6 | no | — |
| 317 | C3⋊D3 | — | 72 | 1 | no | — |
| 318 | C3⋊D3 | — | 72 | 3 | no | — |
| 319 | C3⋊D3 | — | 72 | 6 | no | — |
| 320 | C3⋊D3 | — | 144 | 3 | no | — |
| 321 | C3⋊D3 | — | 144 | 6 | no | — |
| 322 | C3⋊D3 | — | 144 | 1 | no | — |
| 323 | C3⋊D3 | — | 144 | 3 | no | — |
| 324 | C3⋊D3 | — | 144 | 2 | no | — |
| 325 | C3⋊D3 | — | 144 | 6 | no | — |
| 326 | C3⋊D3 | D3×S4 | 1 | 3 | yes | complemented |
| 327 | C3×D3 | — | 3 | 6 | no | — |
| 328 | C3×D3 | — | 6 | 3 | no | — |
| 329 | C3×D3 | — | 6 | 6 | no | — |
| 330 | C3×D3 | — | 9 | 6 | no | — |
| 331 | C3×D3 | — | 12 | 6 | no | — |
| 332 | C3×D3 | — | 12 | 3 | no | — |
| 333 | C3×D3 | — | 12 | 6 | no | — |
| 334 | C3×D3 | — | 18 | 3 | no | — |
| 335 | C3×D3 | — | 24 | 6 | no | — |
| 336 | C3×D3 | — | 24 | 3 | no | — |
| 337 | C3×D3 | — | 24 | 6 | no | — |
| 338 | C3×D3 | — | 24 | 3 | no | — |
| 339 | C3×D3 | — | 24 | 6 | no | — |
| 340 | C3×D3 | — | 24 | 6 | no | — |
| 341 | C24 | — | 27 | 1 | no | — |
| 342 | C24 | — | 81 | 1 | no | — |
| 343 | C2×D4 | — | 27 | 3 | no | — |
| 344 | C2×D4 | — | 81 | 3 | no | — |
| 345 | C2×D4 | — | 81 | 3 | no | — |
| 346 | C2×D4 | — | 81 | 3 | no | — |
| 347 | C22×C4 | — | 81 | 1 | no | — |
| 348 | C22×C3 | — | 2 | 3 | no | — |
| 349 | C22×C3 | — | 4 | 1 | no | — |
| 350 | C22×C3 | — | 9 | 6 | no | — |
| 351 | C22×C3 | — | 18 | 3 | no | — |
| 352 | C22×C3 | — | 27 | 3 | no | — |
| 353 | C22×C3 | — | 27 | 3 | no | — |
| 354 | C22×C3 | — | 54 | 3 | no | — |
| 355 | C22×C3 | — | 54 | 3 | no | — |
| 356 | C22×C3 | — | 108 | 1 | no | — |
| 357 | C22×C3 | D33 | 1 | 3 | yes | complemented |
| 358 | C2×D3 | — | 3 | 3 | no | — |
| 359 | C2×D3 | — | 9 | 3 | no | — |
| 360 | C2×D3 | — | 9 | 6 | no | — |
| 361 | C2×D3 | — | 9 | 6 | no | — |
| 362 | C2×D3 | — | 18 | 3 | no | — |
| 363 | C2×D3 | — | 18 | 3 | no | — |
| 364 | C2×D3 | — | 18 | 6 | no | — |
| 365 | C2×D3 | — | 18 | 6 | no | — |
| 366 | C2×D3 | — | 27 | 6 | no | — |
| 367 | C2×D3 | — | 27 | 3 | no | — |
| 368 | C2×D3 | — | 27 | 3 | no | — |
| 369 | C2×D3 | — | 36 | 3 | no | — |
| 370 | C2×D3 | — | 54 | 3 | no | — |
| 371 | C2×D3 | — | 54 | 6 | no | — |
| 372 | C2×D3 | — | 54 | 3 | no | — |
| 373 | C2×D3 | — | 54 | 3 | no | — |
| 374 | C2×D3 | — | 54 | 3 | no | — |
| 375 | C2×D3 | — | 54 | 6 | no | — |
| 376 | C2×D3 | — | 108 | 1 | no | — |
| 377 | C2×D3 | — | 108 | 3 | no | — |
| 378 | C2×D3 | — | 108 | 3 | no | — |
| 379 | C2×D3 | — | 108 | 3 | no | — |
| 380 | C2×D3 | — | 216 | 3 | no | — |
| 381 | A4 | — | 2 | 3 | no | — |
| 382 | A4 | — | 4 | 2 | no | — |
| 383 | A4 | — | 4 | 3 | no | — |
| 384 | A4 | D33 | 1 | 1 | yes | characteristic, complemented |
| 385 | C3×C4 | — | 9 | 6 | no | — |
| 386 | C3×C4 | — | 18 | 3 | no | — |
| 387 | Dic3 | — | 3 | 3 | no | — |
| 388 | Dic3 | — | 27 | 3 | no | — |
| 389 | Dic3 | — | 54 | 3 | no | — |
| 390 | Dic3 | — | 108 | 1 | no | — |
| 391 | C32 | — | 2 | 3 | no | — |
| 392 | C32 | — | 4 | 1 | no | — |
| 393 | C32 | — | 4 | 3 | no | — |
| 394 | C32 | — | 8 | 3 | no | — |
| 395 | C32 | — | 8 | 6 | no | — |
| 396 | C32 | — | 8 | 6 | no | — |
| 397 | C32 | — | 16 | 3 | no | — |
| 398 | C32 | — | 16 | 6 | no | — |
| 399 | C32 | — | 16 | 1 | no | — |
| 400 | C32 | — | 16 | 6 | no | — |
| 401 | C32 | — | 16 | 2 | no | — |
| 402 | C32 | — | 16 | 3 | no | — |
| 403 | C32 | C2×D3×S4 | 1 | 3 | yes | complemented |
| 404 | C23 | — | 9 | 3 | no | — |
| 405 | C23 | — | 27 | 3 | no | — |
| 406 | C23 | — | 81 | 3 | no | — |
| 407 | C23 | — | 81 | 1 | no | — |
| 408 | C23 | — | 81 | 3 | no | — |
| 409 | C23 | — | 162 | 1 | no | — |
| 410 | C23 | — | 162 | 3 | no | — |
| 411 | D4 | — | 9 | 3 | no | — |
| 412 | D4 | — | 27 | 6 | no | — |
| 413 | D4 | — | 81 | 3 | no | — |
| 414 | D4 | — | 81 | 3 | no | — |
| 415 | D4 | — | 81 | 1 | no | — |
| 416 | C2×C4 | — | 27 | 3 | no | — |
| 417 | C2×C4 | — | 81 | 3 | no | — |
| 418 | C2×C3 | — | 3 | 3 | no | — |
| 419 | C2×C3 | — | 6 | 3 | no | — |
| 420 | C2×C3 | — | 9 | 3 | no | — |
| 421 | C2×C3 | — | 12 | 1 | no | — |
| 422 | C2×C3 | — | 18 | 6 | no | — |
| 423 | C2×C3 | — | 27 | 3 | no | — |
| 424 | C2×C3 | — | 36 | 3 | no | — |
| 425 | C2×C3 | — | 36 | 3 | no | — |
| 426 | C2×C3 | — | 72 | 3 | no | — |
| 427 | D3 | — | 3 | 6 | no | — |
| 428 | D3 | — | 6 | 3 | no | — |
| 429 | D3 | — | 6 | 3 | no | — |
| 430 | D3 | — | 9 | 6 | no | — |
| 431 | D3 | — | 12 | 3 | no | — |
| 432 | D3 | — | 18 | 3 | no | — |
| 433 | D3 | — | 24 | 3 | no | — |
| 434 | D3 | — | 54 | 3 | no | — |
| 435 | D3 | — | 108 | 3 | no | — |
| 436 | D3 | — | 108 | 1 | no | — |
| 437 | D3 | — | 432 | 3 | no | — |
| 438 | D3 | — | 432 | 2 | no | — |
| 439 | D3 | — | 216 | 1 | no | — |
| 440 | D3 | — | 216 | 3 | no | — |
| 441 | C22 | — | 9 | 3 | no | — |
| 442 | C22 | — | 27 | 3 | no | — |
| 443 | C22 | — | 27 | 3 | no | — |
| 444 | C22 | — | 27 | 1 | no | — |
| 445 | C22 | — | 54 | 3 | no | — |
| 446 | C22 | — | 54 | 3 | no | — |
| 447 | C22 | — | 81 | 1 | no | — |
| 448 | C22 | — | 81 | 3 | no | — |
| 449 | C22 | — | 162 | 3 | no | — |
| 450 | C22 | — | 162 | 3 | no | — |
| 451 | C22 | — | 162 | 1 | no | — |
| 452 | C22 | #10620215 | 1 | 1 | yes | characteristic, complemented |
| 453 | C4 | — | 9 | 3 | no | — |
| 454 | C4 | — | 81 | 1 | no | — |
| 455 | C3 | — | 2 | 3 | no | — |
| 456 | C3 | — | 4 | 1 | no | — |
| 457 | C3 | — | 4 | 1 | no | — |
| 458 | C3 | — | 8 | 3 | no | — |
| 459 | C3 | — | 16 | 3 | no | — |
| 460 | C3 | — | 16 | 2 | no | — |
| 461 | C3 | D32×S4 | 1 | 3 | yes | complemented |
| 462 | C2 | — | 3 | 1 | no | — |
| 463 | C2 | — | 9 | 3 | no | — |
| 464 | C2 | — | 18 | 3 | no | — |
| 465 | C2 | — | 27 | 3 | no | — |
| 466 | C2 | — | 162 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×A4 | C23 |
| Fitting, socle | C22×C33 | C22×D3 |
| LCS | G ▷ C33×A4 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#1113 | C2 | semidirect |
| 2. C3⋊D3×C3⋊S4 | C2 | semidirect |
| 3. C3×#89101 | C2 | semidirect |
| 6. C3×A4×C3⋊D3 | C22 | semidirect |
| 7. C3⋊(C3⋊(C3⋊S4)) | C22 | semidirect |
| 8. C32×C3⋊S4 | C22 | semidirect |
| 10. C22×#1113 | D3 | semidirect |
| 13. #89101 | D3 | semidirect |
| 24. C33×A4 | C23 | semidirect |
| 30. C22×C3×C3⋊D3 | C2×D3 | semidirect |
| 36. A4×C3⋊D3 | C2×D3 | semidirect |
| 46. C3×C3⋊S4 | C2×D3 | semidirect |
| 82. C22×C33 | C22×D3 | semidirect |
| 92. C32×A4 | C22×D3 | semidirect |
| 96. #1113 | S4 | semidirect |
| 113. C22×C3⋊D3 | D32 | semidirect |
| 142. C3⋊S4 | D32 | semidirect |
| 180. C3×C3⋊D3 | C2×S4 | semidirect |
| 205. C22×C32 | C2×D32 | semidirect |
| 233. C3×A4 | C2×D32 | semidirect |
| 262. C33 | C22×S4 | semidirect |
| 326. C3⋊D3 | D3×S4 | semidirect |
| 357. C22×C3 | D33 | semidirect |
| 384. A4 | D33 | semidirect |
| 403. C32 | C2×D3×S4 | semidirect |
| 452. C22 | #10620215 | semidirect |
| 461. C3 | D32×S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#1113 | 2 |
| C3⋊D3×C3⋊S4 | 2 |
| C3×#89101 | 2 |
| D32×S4 | 3 |
| #11724440 | 3 |
| #10620215 | 4 |