Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1618 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1618 conjugacy classes of subgroups — too many to draw. Only its 267 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 | C2×#11763199 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | C2×#11763196 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C2×#11763191 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C2×#11763185 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #14534890 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14528471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C17×#2657 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#63231 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×#63229 | C22 | 1 | 3 | yes | — |
| 10 | C22×#63230 | C22 | 1 | 3 | yes | — |
| 11 | C22×#63228 | C22 | 1 | 3 | yes | — |
| 12 | C22×#63228 | C22 | 1 | 6 | yes | — |
| 13 | C2×#10587560 | C22 | 1 | 3 | yes | — |
| 14 | C2×#10587561 | C22 | 1 | 3 | yes | — |
| 15 | #11763199 | — | 2 | 12 | no | — |
| 16 | #11763196 | — | 2 | 12 | no | — |
| 17 | #11763191 | — | 2 | 12 | no | — |
| 18 | #11763185 | — | 2 | 12 | no | — |
| 19 | C2×#10587474 | C22 | 1 | 3 | yes | — |
| 20 | C2×C4×#3622 | C22 | 1 | 3 | yes | — |
| 21 | #11762719 | — | 2 | 4 | no | — |
| 22 | C2×C17×#127 | C22 | 1 | 3 | yes | — |
| 23 | C2×C17×#124 | C22 | 1 | 3 | yes | — |
| 24 | C17×#392 | — | 2 | 4 | no | — |
| 25 | C17×#376 | C22 | 1 | 1 | yes | characteristic |
| 26 | C22×Q8×C17 | C23 | 1 | 1 | yes | characteristic |
| 27 | C22×D4×C17 | — | 2 | 6 | no | — |
| 28 | C22×D4×C17 | C23 | 1 | 3 | yes | — |
| 29 | C22×D68 | — | 2 | 6 | no | — |
| 30 | C22×D68 | C23 | 1 | 3 | yes | — |
| 31 | C22×Dic34 | C23 | 1 | 1 | yes | characteristic |
| 32 | C17×#127 | — | 2 | 6 | no | — |
| 33 | C17×#127 | — | 2 | 6 | no | — |
| 34 | C17×#124 | — | 2 | 6 | no | — |
| 35 | C17×#124 | — | 2 | 6 | no | — |
| 36 | C2×C22⋊C4×C17 | — | 2 | 6 | no | — |
| 37 | C2×C42×C17 | C23 | 1 | 3 | yes | — |
| 38 | C2×#63231 | — | 2 | 6 | no | — |
| 39 | C2×#63230 | — | 2 | 6 | no | — |
| 40 | C2×#63230 | — | 2 | 12 | no | — |
| 41 | C2×#63229 | — | 2 | 6 | no | — |
| 42 | C2×#63229 | — | 2 | 12 | no | — |
| 43 | C2×#63228 | — | 2 | 12 | no | — |
| 44 | C2×#63228 | — | 2 | 12 | no | — |
| 45 | C2×#63228 | — | 2 | 6 | no | — |
| 46 | C2×#63228 | — | 2 | 12 | no | — |
| 47 | C2×#63228 | — | 2 | 12 | no | — |
| 48 | C2×#63227 | — | 2 | 6 | no | — |
| 49 | C22×#3622 | C23 | 1 | 1 | yes | characteristic |
| 50 | C22×#3622 | C23 | 1 | 3 | yes | — |
| 51 | #10587561 | — | 2 | 6 | no | — |
| 52 | #10587561 | — | 2 | 6 | no | — |
| 53 | #10587560 | — | 2 | 6 | no | — |
| 54 | #10587560 | — | 2 | 6 | no | — |
| 55 | C17×#95 | D4 | 1 | 4 | yes | — |
| 56 | #10587474 | D4 | 1 | 12 | yes | complemented |
| 57 | C4×#3622 | D4 | 1 | 12 | yes | complemented |
| 58 | C24×C17 | — | 2 | 3 | no | — |
| 59 | C23×D17 | — | 2 | 3 | no | — |
| 60 | C2×Q8×C17 | — | 2 | 3 | no | — |
| 61 | C2×Q8×C17 | — | 2 | 3 | no | — |
| 62 | C2×D4×C17 | — | 2 | 3 | no | — |
| 63 | C2×D4×C17 | — | 2 | 3 | no | — |
| 64 | C2×D4×C17 | — | 2 | 6 | no | — |
| 65 | C2×D4×C17 | — | 2 | 6 | no | — |
| 66 | C2×D4×C17 | — | 4 | 12 | no | — |
| 67 | C2×D4×C17 | — | 8 | 12 | no | — |
| 68 | C22×C4×C17 | — | 2 | 1 | no | — |
| 69 | C22×C4×C17 | C2×D4 | 1 | 6 | yes | — |
| 70 | C22×C4×C17 | C24 | 1 | 1 | yes | characteristic |
| 71 | C22×Dic17 | — | 2 | 1 | no | — |
| 72 | C2×D68 | — | 2 | 6 | no | — |
| 73 | C2×D68 | — | 2 | 6 | no | — |
| 74 | C2×D68 | — | 2 | 3 | no | — |
| 75 | C2×D68 | — | 2 | 3 | no | — |
| 76 | C2×D68 | — | 4 | 12 | no | — |
| 77 | C2×D68 | — | 8 | 12 | no | — |
| 78 | C2×Dic34 | — | 2 | 3 | no | — |
| 79 | C2×Dic34 | — | 2 | 3 | no | — |
| 80 | C22⋊C4×C17 | — | 4 | 12 | no | — |
| 81 | C42×C17 | C2×D4 | 1 | 6 | yes | — |
| 82 | C42×C17 | C2×D4 | 1 | 6 | yes | — |
| 83 | #63231 | — | 4 | 4 | no | — |
| 84 | #63230 | — | 4 | 12 | no | — |
| 85 | #63229 | — | 4 | 12 | no | — |
| 86 | #63228 | — | 4 | 12 | no | — |
| 87 | #63228 | — | 4 | 24 | no | — |
| 88 | #63227 | — | 4 | 12 | no | — |
| 89 | C2×#3622 | C2×D4 | 1 | 6 | yes | — |
| 90 | C2×#3622 | C2×D4 | 1 | 6 | yes | — |
| 91 | C2×#3622 | C2×D4 | 1 | 12 | yes | — |
| 92 | #33308 | — | 17 | 1 | no | maximal, Sylow |
| 93 | C23×C17 | — | 4 | 3 | no | — |
| 94 | C23×C17 | — | 4 | 6 | no | — |
| 95 | C23×C17 | — | 4 | 12 | no | — |
| 96 | C23×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 97 | C22×D17 | — | 4 | 6 | no | — |
| 98 | C22×D17 | — | 4 | 3 | no | — |
| 99 | C22×D17 | — | 4 | 12 | no | — |
| 100 | Q8×C17 | — | 4 | 3 | no | — |
| 101 | Q8×C17 | — | 4 | 1 | no | — |
| 102 | D4×C17 | — | 4 | 6 | no | — |
| 103 | D4×C17 | — | 4 | 3 | no | — |
| 104 | D4×C17 | — | 4 | 3 | no | — |
| 105 | D4×C17 | — | 8 | 24 | no | — |
| 106 | C2×C4×C17 | — | 2 | 12 | no | — |
| 107 | C2×C4×C17 | — | 4 | 3 | no | — |
| 108 | C2×C4×C17 | #127 | 1 | 12 | yes | — |
| 109 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 110 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 111 | C2×Dic17 | — | 4 | 3 | no | — |
| 112 | D68 | — | 4 | 3 | no | — |
| 113 | D68 | — | 4 | 6 | no | — |
| 114 | D68 | — | 4 | 3 | no | — |
| 115 | D68 | — | 8 | 24 | no | — |
| 116 | Dic34 | — | 4 | 3 | no | — |
| 117 | Dic34 | — | 4 | 1 | no | — |
| 118 | #3622 | #127 | 1 | 4 | yes | — |
| 119 | #3622 | #127 | 1 | 12 | yes | — |
| 120 | C2×#496 | — | 17 | 3 | no | — |
| 121 | C2×#496 | — | 17 | 3 | no | — |
| 122 | C2×#495 | — | 17 | 3 | no | — |
| 123 | C2×#493 | — | 17 | 3 | no | — |
| 124 | #2657 | — | 17 | 1 | no | — |
| 125 | #2657 | D17 | 1 | 1 | yes | characteristic, complemented |
| 126 | #1726 | — | 17 | 1 | no | — |
| 127 | C22×C17 | — | 8 | 3 | no | — |
| 128 | C22×C17 | — | 8 | 12 | no | — |
| 129 | C22×C17 | — | 8 | 6 | no | — |
| 130 | C22×C17 | C2×#127 | 1 | 3 | yes | — |
| 131 | C22×C17 | #576 | 1 | 4 | yes | — |
| 132 | C2×D17 | — | 8 | 3 | no | — |
| 133 | C2×D17 | — | 8 | 12 | no | — |
| 134 | C2×D17 | — | 8 | 6 | no | — |
| 135 | C4×C17 | — | 2 | 12 | no | — |
| 136 | C4×C17 | — | 8 | 1 | no | — |
| 137 | C4×C17 | C2×#127 | 1 | 1 | yes | characteristic |
| 138 | C4×C17 | C2×#127 | 1 | 3 | yes | — |
| 139 | Dic17 | — | 8 | 1 | no | — |
| 140 | C22×Q16 | — | 17 | 1 | no | — |
| 141 | C22×SD16 | — | 17 | 3 | no | — |
| 142 | C22×SD16 | — | 17 | 3 | no | — |
| 143 | C22×D8 | — | 17 | 3 | no | — |
| 144 | C22×D8 | — | 17 | 6 | no | — |
| 145 | C2×#127 | — | 17 | 3 | no | — |
| 146 | C2×#127 | C2×D17 | 1 | 3 | yes | — |
| 147 | C2×#124 | — | 17 | 3 | no | — |
| 148 | C2×#124 | C2×D17 | 1 | 3 | yes | — |
| 149 | #496 | — | 34 | 12 | no | — |
| 150 | #496 | — | 34 | 12 | no | — |
| 151 | #495 | — | 34 | 12 | no | — |
| 152 | #493 | — | 34 | 12 | no | — |
| 153 | C2×#97 | — | 17 | 3 | no | — |
| 154 | C2×C4×C8 | — | 17 | 3 | no | — |
| 155 | #392 | — | 2 | 4 | no | — |
| 156 | #392 | — | 34 | 4 | no | — |
| 157 | #376 | C2×D17 | 1 | 1 | yes | characteristic |
| 158 | C2×C17 | — | 16 | 3 | no | — |
| 159 | C2×C17 | #2867 | 1 | 1 | yes | characteristic |
| 160 | C2×C17 | #3155 | 1 | 6 | yes | — |
| 161 | D17 | — | 16 | 3 | no | — |
| 162 | C22×Q8 | — | 17 | 1 | no | — |
| 163 | C22×Q8 | C22×D17 | 1 | 1 | yes | characteristic |
| 164 | C22×D4 | — | 2 | 6 | no | — |
| 165 | C22×D4 | — | 17 | 3 | no | — |
| 166 | C22×D4 | — | 34 | 6 | no | — |
| 167 | C22×D4 | C22×D17 | 1 | 3 | yes | — |
| 168 | C2×Q16 | — | 34 | 6 | no | — |
| 169 | C2×SD16 | — | 34 | 6 | no | — |
| 170 | C2×SD16 | — | 34 | 12 | no | — |
| 171 | C2×SD16 | — | 34 | 6 | no | — |
| 172 | C2×SD16 | — | 34 | 12 | no | — |
| 173 | C2×D8 | — | 34 | 12 | no | — |
| 174 | C2×D8 | — | 34 | 12 | no | — |
| 175 | C2×D8 | — | 34 | 6 | no | — |
| 176 | C2×D8 | — | 34 | 12 | no | — |
| 177 | C2×D8 | — | 34 | 12 | no | — |
| 178 | C22×C8 | — | 17 | 1 | no | — |
| 179 | C22×C8 | — | 17 | 3 | no | — |
| 180 | #127 | — | 2 | 6 | no | — |
| 181 | #127 | — | 2 | 6 | no | — |
| 182 | #127 | — | 34 | 6 | no | — |
| 183 | #127 | — | 34 | 6 | no | — |
| 184 | #124 | — | 2 | 6 | no | — |
| 185 | #124 | — | 2 | 6 | no | — |
| 186 | #124 | — | 34 | 6 | no | — |
| 187 | #124 | — | 34 | 6 | no | — |
| 188 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 189 | C2×C22⋊C4 | — | 34 | 6 | no | — |
| 190 | C2×C42 | C22×D17 | 1 | 3 | yes | — |
| 191 | #97 | — | 17 | 12 | no | — |
| 192 | C4×C8 | — | 17 | 12 | no | — |
| 193 | #95 | C22⋊D17 | 1 | 4 | yes | — |
| 194 | C17 | #33308 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 195 | C24 | — | 2 | 3 | no | — |
| 196 | C24 | — | 34 | 3 | no | — |
| 197 | C2×Q8 | — | 2 | 3 | no | — |
| 198 | C2×Q8 | — | 2 | 3 | no | — |
| 199 | C2×Q8 | — | 34 | 3 | no | — |
| 200 | C2×Q8 | — | 34 | 3 | no | — |
| 201 | C2×D4 | — | 2 | 3 | no | — |
| 202 | C2×D4 | — | 2 | 3 | no | — |
| 203 | C2×D4 | — | 2 | 6 | no | — |
| 204 | C2×D4 | — | 2 | 6 | no | — |
| 205 | C2×D4 | — | 4 | 12 | no | — |
| 206 | C2×D4 | — | 8 | 12 | no | — |
| 207 | C2×D4 | — | 34 | 3 | no | — |
| 208 | C2×D4 | — | 34 | 3 | no | — |
| 209 | C2×D4 | — | 34 | 6 | no | — |
| 210 | C2×D4 | — | 34 | 6 | no | — |
| 211 | C2×D4 | — | 68 | 12 | no | — |
| 212 | C2×D4 | — | 136 | 12 | no | — |
| 213 | C22×C4 | — | 2 | 1 | no | — |
| 214 | C22×C4 | — | 34 | 1 | no | — |
| 215 | C22×C4 | C2×C22⋊D17 | 1 | 6 | yes | — |
| 216 | C22×C4 | C23×D17 | 1 | 1 | yes | characteristic |
| 217 | Q16 | — | 68 | 4 | no | — |
| 218 | SD16 | — | 68 | 12 | no | — |
| 219 | SD16 | — | 68 | 12 | no | — |
| 220 | D8 | — | 68 | 12 | no | — |
| 221 | D8 | — | 68 | 24 | no | — |
| 222 | C2×C8 | — | 17 | 6 | no | — |
| 223 | C2×C8 | — | 17 | 6 | no | — |
| 224 | C2×C8 | — | 17 | 12 | no | — |
| 225 | C22⋊C4 | — | 4 | 12 | no | — |
| 226 | C22⋊C4 | — | 68 | 12 | no | — |
| 227 | C42 | D4×D17 | 1 | 6 | yes | — |
| 228 | C42 | D4×D17 | 1 | 6 | yes | — |
| 229 | C23 | — | 4 | 3 | no | — |
| 230 | C23 | — | 4 | 6 | no | — |
| 231 | C23 | — | 4 | 12 | no | — |
| 232 | C23 | — | 68 | 3 | no | — |
| 233 | C23 | — | 68 | 6 | no | — |
| 234 | C23 | — | 68 | 12 | no | — |
| 235 | C23 | C22×C22⋊D17 | 1 | 1 | yes | characteristic |
| 236 | Q8 | — | 4 | 3 | no | — |
| 237 | Q8 | — | 4 | 1 | no | — |
| 238 | Q8 | — | 68 | 3 | no | — |
| 239 | Q8 | — | 68 | 1 | no | — |
| 240 | D4 | — | 4 | 6 | no | — |
| 241 | D4 | — | 4 | 3 | no | — |
| 242 | D4 | — | 4 | 3 | no | — |
| 243 | D4 | — | 8 | 24 | no | — |
| 244 | D4 | — | 68 | 6 | no | — |
| 245 | D4 | — | 68 | 3 | no | — |
| 246 | D4 | — | 68 | 3 | no | — |
| 247 | D4 | — | 136 | 24 | no | — |
| 248 | C2×C4 | — | 2 | 12 | no | — |
| 249 | C2×C4 | — | 4 | 3 | no | — |
| 250 | C2×C4 | — | 68 | 3 | no | — |
| 251 | C2×C4 | #10587626 | 1 | 12 | yes | — |
| 252 | C2×C4 | C2×D4×D17 | 1 | 3 | yes | — |
| 253 | C2×C4 | C2×D4×D17 | 1 | 3 | yes | — |
| 254 | C8 | — | 17 | 4 | no | — |
| 255 | C8 | — | 17 | 12 | no | — |
| 256 | C22 | — | 8 | 12 | no | — |
| 257 | C22 | — | 8 | 6 | no | — |
| 258 | C22 | — | 8 | 3 | no | — |
| 259 | C22 | — | 136 | 12 | no | — |
| 260 | C22 | — | 136 | 6 | no | — |
| 261 | C22 | — | 136 | 3 | no | — |
| 262 | C22 | C2×#10587626 | 1 | 3 | yes | — |
| 263 | C22 | #11763612 | 1 | 4 | yes | — |
| 264 | C4 | — | 2 | 12 | no | — |
| 265 | C4 | — | 8 | 1 | no | — |
| 266 | C4 | — | 136 | 1 | no | — |
| 267 | C4 | #127×D17 | 1 | 1 | yes | characteristic |
| 268 | C4 | #127×D17 | 1 | 3 | yes | — |
| 269 | C2 | — | 16 | 3 | no | — |
| 270 | C2 | — | 272 | 3 | no | — |
| 271 | C2 | #14537178 | 1 | 1 | yes | characteristic |
| 272 | C2 | #14539267 | 1 | 6 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11763199 | C2 | semidirect |
| 2. C2×#11763196 | C2 | semidirect |
| 3. C2×#11763191 | C2 | semidirect |
| 4. C2×#11763185 | C2 | semidirect |
| 5. #14534890 | C2 | semidirect |
| 6. #14528471 | C2 | semidirect |
| 7. C17×#2657 | C2 | semidirect |
| 56. #10587474 | D4 | semidirect |
| 57. C4×#3622 | D4 | semidirect |
| 125. #2657 | D17 | semidirect |
| 194. C17 | #33308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763199 | 2 |
| C2×#11763196 | 2 |
| C2×#11763191 | 2 |
| C2×#11763185 | 2 |
| #14534890 | 2 |
| #14528471 | 2 |
| C17×#2657 | 2 |
| #33308 | 17 |