Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
620 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #14545328 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14544312 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14544205 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #14543644 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #14539231 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11763832 | C22 | 1 | 2 | yes | — |
| 7 | #11763757 | — | 2 | 4 | no | — |
| 8 | #11763757 | — | 2 | 2 | no | — |
| 9 | #11763754 | C22 | 1 | 2 | yes | — |
| 10 | #11763667 | — | 2 | 2 | no | — |
| 11 | #11763661 | — | 2 | 4 | no | — |
| 12 | C2×#10587600 | — | 2 | 2 | no | — |
| 13 | #11763360 | C22 | 1 | 1 | yes | characteristic |
| 14 | #127×D17 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11763195 | — | 2 | 2 | no | — |
| 16 | #11763186 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #11763185 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #11763183 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | C4×#63218 | C22 | 1 | 1 | yes | characteristic |
| 20 | C17×#492 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C23×#595 | — | 2 | 2 | no | — |
| 22 | C2×#63256 | — | 2 | 1 | no | — |
| 23 | C2×D4×D17 | — | 2 | 2 | no | — |
| 24 | C2×D4×D17 | D4 | 1 | 2 | yes | — |
| 25 | C2×C22⋊#595 | — | 2 | 4 | no | — |
| 26 | C2×C22⋊#595 | — | 2 | 2 | no | — |
| 27 | C2×SD16×C17 | — | 2 | 2 | no | — |
| 28 | C17×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | C17×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #10587633 | — | 2 | 1 | no | — |
| 31 | C2×#63230 | — | 2 | 2 | no | — |
| 32 | #10587626 | — | 2 | 2 | no | — |
| 33 | #10587626 | D4 | 1 | 2 | yes | — |
| 34 | C2×#63228 | — | 2 | 2 | no | — |
| 35 | #10587600 | — | 4 | 4 | no | — |
| 36 | #10587600 | — | 4 | 4 | no | — |
| 37 | C2×D136 | — | 2 | 2 | no | — |
| 38 | C2×#63218 | — | 2 | 1 | no | — |
| 39 | #10587581 | — | 2 | 2 | no | — |
| 40 | #10587579 | — | 2 | 2 | no | — |
| 41 | #10587560 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #10587560 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | C42×D17 | C23 | 1 | 1 | yes | characteristic |
| 44 | (C2×#595)⋊C4 | — | 2 | 2 | no | — |
| 45 | (C2×#595)⋊C4 | — | 2 | 2 | no | — |
| 46 | (C2×#595)⋊C4 | D4 | 1 | 4 | yes | — |
| 47 | #10587544 | — | 2 | 2 | no | — |
| 48 | #10587543 | — | 2 | 2 | no | — |
| 49 | #10587542 | — | 2 | 2 | no | — |
| 50 | C4×C8×C17 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 51 | #10587486 | — | 2 | 1 | no | — |
| 52 | C4×#3622 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 53 | C23×D17 | — | 2 | 2 | no | — |
| 54 | C22×#595 | — | 2 | 4 | no | — |
| 55 | C22×#595 | — | 8 | 4 | no | — |
| 56 | C22×#595 | — | 8 | 2 | no | — |
| 57 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 58 | C2×D4×C17 | — | 2 | 2 | no | — |
| 59 | C2×D4×C17 | C22⋊C4 | 1 | 2 | yes | — |
| 60 | C2×C22⋊D17 | — | 2 | 4 | no | — |
| 61 | C2×C22⋊D17 | — | 2 | 2 | no | — |
| 62 | #63256 | — | 4 | 2 | no | — |
| 63 | #63256 | — | 4 | 2 | no | — |
| 64 | D4×D17 | — | 4 | 2 | no | — |
| 65 | D4×D17 | — | 4 | 2 | no | — |
| 66 | D4×D17 | — | 8 | 2 | no | — |
| 67 | D4×D17 | — | 8 | 2 | no | — |
| 68 | C2×D68 | — | 2 | 1 | no | — |
| 69 | C2×D68 | — | 2 | 2 | no | — |
| 70 | C2×D68 | — | 2 | 2 | no | — |
| 71 | C2×D68 | — | 4 | 1 | no | — |
| 72 | C2×D68 | C22⋊C4 | 1 | 2 | yes | — |
| 73 | C2×C4×D17 | — | 4 | 1 | no | — |
| 74 | C2×C4×D17 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×D17 | C2×D4 | 1 | 2 | yes | — |
| 76 | C22⋊#595 | — | 8 | 4 | no | — |
| 77 | C22⋊#595 | — | 8 | 2 | no | — |
| 78 | C2×#3624 | — | 4 | 2 | no | — |
| 79 | SD16×C17 | — | 4 | 4 | no | — |
| 80 | C2×C8×C17 | — | 2 | 1 | no | — |
| 81 | C4⋊C4×C17 | — | 2 | 2 | no | — |
| 82 | C42×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 83 | #63230 | — | 4 | 4 | no | — |
| 84 | #63228 | — | 4 | 4 | no | — |
| 85 | #63227 | — | 4 | 2 | no | — |
| 86 | C4×Dic17 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C4×Dic17 | #41 | 1 | 2 | yes | — |
| 88 | C2×#3622 | — | 2 | 1 | no | — |
| 89 | D136 | — | 4 | 4 | no | — |
| 90 | #63218 | — | 2 | 4 | no | — |
| 91 | #9428 | — | 17 | 1 | no | maximal, Sylow |
| 92 | C23×C17 | — | 2 | 2 | no | — |
| 93 | C22×D17 | — | 2 | 2 | no | — |
| 94 | C22×D17 | — | 4 | 4 | no | — |
| 95 | C22×D17 | — | 4 | 4 | no | — |
| 96 | C22×D17 | — | 4 | 2 | no | — |
| 97 | C22×D17 | — | 4 | 2 | no | — |
| 98 | C22×D17 | — | 4 | 1 | no | — |
| 99 | C22×D17 | #120 | 1 | 1 | yes | characteristic |
| 100 | C2×#595 | — | 4 | 8 | no | — |
| 101 | C2×#595 | — | 4 | 4 | no | — |
| 102 | C2×#595 | — | 8 | 8 | no | — |
| 103 | Q8×C17 | — | 4 | 2 | no | — |
| 104 | D4×C17 | — | 4 | 2 | no | — |
| 105 | D4×C17 | — | 8 | 2 | no | — |
| 106 | C2×C4×C17 | — | 4 | 1 | no | — |
| 107 | C2×C4×C17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 108 | C2×C4×C17 | C4×D4 | 1 | 2 | yes | — |
| 109 | C22⋊D17 | — | 8 | 2 | no | — |
| 110 | C22⋊D17 | — | 8 | 4 | no | — |
| 111 | C2×Dic17 | #121 | 1 | 2 | yes | — |
| 112 | C2×Dic17 | #123 | 1 | 1 | yes | characteristic |
| 113 | D68 | — | 4 | 2 | no | — |
| 114 | D68 | — | 4 | 2 | no | — |
| 115 | D68 | — | 8 | 2 | no | — |
| 116 | D68 | — | 8 | 2 | no | — |
| 117 | D68 | — | 8 | 2 | no | — |
| 118 | C4×D17 | — | 2 | 2 | no | — |
| 119 | C4×D17 | — | 4 | 2 | no | — |
| 120 | C4×D17 | — | 8 | 1 | no | — |
| 121 | C4×D17 | — | 8 | 1 | no | — |
| 122 | #3624 | — | 8 | 2 | no | — |
| 123 | C8×C17 | — | 2 | 2 | no | — |
| 124 | #3622 | — | 2 | 2 | no | — |
| 125 | #3151 | — | 17 | 1 | no | — |
| 126 | #2380 | — | 17 | 1 | no | — |
| 127 | #1555 | — | 17 | 1 | no | — |
| 128 | #1514 | — | 17 | 2 | no | — |
| 129 | #1288 | — | 17 | 2 | no | — |
| 130 | C22×C17 | — | 4 | 2 | no | — |
| 131 | C22×C17 | — | 4 | 4 | no | — |
| 132 | C22×C17 | #386 | 1 | 1 | yes | characteristic |
| 133 | C2×D17 | — | 2 | 2 | no | — |
| 134 | C2×D17 | — | 4 | 2 | no | — |
| 135 | C2×D17 | — | 4 | 4 | no | — |
| 136 | C2×D17 | — | 8 | 2 | no | — |
| 137 | C2×D17 | — | 8 | 2 | no | — |
| 138 | C2×D17 | — | 8 | 4 | no | — |
| 139 | C2×D17 | — | 8 | 1 | no | — |
| 140 | C2×D17 | — | 8 | 2 | no | — |
| 141 | C2×D17 | #453 | 1 | 2 | yes | — |
| 142 | #595 | — | 8 | 4 | no | — |
| 143 | C4×C17 | — | 2 | 1 | no | — |
| 144 | C4×C17 | — | 2 | 2 | no | — |
| 145 | C4×C17 | — | 8 | 1 | no | — |
| 146 | Dic17 | — | 2 | 1 | no | — |
| 147 | Dic17 | — | 2 | 2 | no | — |
| 148 | C2×AGL(1,ℤ/8) | — | 34 | 2 | no | — |
| 149 | #532 | — | 17 | 1 | no | — |
| 150 | C2×#127 | — | 17 | 1 | no | — |
| 151 | #496 | — | 34 | 2 | no | — |
| 152 | #493 | — | 17 | 1 | no | — |
| 153 | #493 | — | 17 | 1 | no | — |
| 154 | #492 | — | 17 | 1 | no | — |
| 155 | #492 | #595 | 1 | 1 | yes | characteristic, complemented |
| 156 | #432 | — | 17 | 2 | no | — |
| 157 | C4×M16 | — | 17 | 1 | no | — |
| 158 | #386 | — | 34 | 4 | no | — |
| 159 | #386 | — | 34 | 2 | no | — |
| 160 | #383 | — | 17 | 2 | no | — |
| 161 | #331 | — | 34 | 2 | no | — |
| 162 | #327 | — | 34 | 4 | no | — |
| 163 | C2×C17 | — | 8 | 2 | no | — |
| 164 | C2×C17 | #1887 | 1 | 1 | yes | characteristic |
| 165 | C2×C17 | #1904 | 1 | 2 | yes | — |
| 166 | D17 | — | 2 | 2 | no | — |
| 167 | D17 | — | 8 | 2 | no | — |
| 168 | D17 | — | 16 | 1 | no | — |
| 169 | C2×#41 | — | 34 | 1 | no | — |
| 170 | C22×D4 | — | 17 | 2 | no | — |
| 171 | C22×D4 | — | 34 | 2 | no | — |
| 172 | C23×C4 | — | 34 | 2 | no | — |
| 173 | AGL(1,ℤ/8) | — | 68 | 4 | no | — |
| 174 | AGL(1,ℤ/8) | — | 68 | 4 | no | — |
| 175 | C2×SD16 | — | 2 | 2 | no | — |
| 176 | C2×SD16 | — | 34 | 2 | no | — |
| 177 | C2×D8 | — | 34 | 2 | no | — |
| 178 | C2×D8 | — | 34 | 2 | no | — |
| 179 | C2×M16 | — | 34 | 1 | no | — |
| 180 | C4⋊Q8 | C2×#595 | 1 | 1 | yes | characteristic, complemented |
| 181 | #127 | — | 17 | 2 | no | — |
| 182 | #127 | — | 17 | 1 | no | — |
| 183 | #127 | — | 17 | 1 | no | — |
| 184 | #127 | — | 34 | 2 | no | — |
| 185 | #127 | C2×#595 | 1 | 1 | yes | characteristic |
| 186 | #124 | — | 34 | 1 | no | — |
| 187 | #121 | — | 34 | 2 | no | — |
| 188 | C4×D4 | — | 34 | 2 | no | — |
| 189 | C2×C22⋊C4 | — | 34 | 2 | no | — |
| 190 | C2×C22⋊C4 | — | 34 | 4 | no | — |
| 191 | C2×C42 | — | 17 | 1 | no | — |
| 192 | C4⋊C8 | — | 34 | 2 | no | — |
| 193 | C22⋊C8 | — | 34 | 2 | no | — |
| 194 | #97 | — | 34 | 1 | no | — |
| 195 | #97 | — | 34 | 2 | no | — |
| 196 | C4×C8 | — | 17 | 1 | no | — |
| 197 | C4×C8 | C2×#595 | 1 | 1 | yes | characteristic, complemented |
| 198 | #95 | — | 17 | 4 | no | — |
| 199 | #95 | — | 34 | 2 | no | — |
| 200 | #95 | — | 34 | 2 | no | — |
| 201 | C17 | #9428 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 202 | C24 | — | 34 | 2 | no | — |
| 203 | #41 | — | 68 | 2 | no | — |
| 204 | #41 | — | 68 | 2 | no | — |
| 205 | C2×Q8 | — | 2 | 1 | no | — |
| 206 | C2×D4 | — | 2 | 2 | no | — |
| 207 | C2×D4 | — | 17 | 2 | no | — |
| 208 | C2×D4 | — | 34 | 4 | no | — |
| 209 | C2×D4 | — | 34 | 2 | no | — |
| 210 | C2×D4 | — | 34 | 2 | no | — |
| 211 | C2×D4 | — | 34 | 2 | no | — |
| 212 | C2×D4 | — | 34 | 1 | no | — |
| 213 | C2×D4 | — | 68 | 1 | no | — |
| 214 | C2×D4 | — | 68 | 2 | no | — |
| 215 | C2×D4 | — | 68 | 2 | no | — |
| 216 | C2×D4 | — | 136 | 2 | no | — |
| 217 | C2×D4 | — | 136 | 2 | no | — |
| 218 | C2×D4 | C22⋊#595 | 1 | 2 | yes | — |
| 219 | C22×C4 | — | 17 | 1 | no | — |
| 220 | C22×C4 | — | 17 | 2 | no | — |
| 221 | C22×C4 | — | 34 | 4 | no | — |
| 222 | C22×C4 | — | 68 | 1 | no | — |
| 223 | C22×C4 | — | 136 | 2 | no | — |
| 224 | C22×C4 | — | 136 | 4 | no | — |
| 225 | SD16 | — | 4 | 4 | no | — |
| 226 | SD16 | — | 68 | 4 | no | — |
| 227 | D8 | — | 68 | 4 | no | — |
| 228 | D8 | — | 68 | 4 | no | — |
| 229 | M16 | — | 34 | 4 | no | — |
| 230 | C2×C8 | — | 2 | 1 | no | — |
| 231 | C2×C8 | — | 34 | 1 | no | — |
| 232 | C2×C8 | — | 68 | 2 | no | — |
| 233 | C4⋊C4 | — | 2 | 2 | no | — |
| 234 | C22⋊C4 | — | 68 | 2 | no | — |
| 235 | C22⋊C4 | — | 136 | 2 | no | — |
| 236 | C22⋊C4 | — | 136 | 4 | no | — |
| 237 | C42 | — | 17 | 2 | no | — |
| 238 | C42 | — | 17 | 1 | no | — |
| 239 | C42 | C22×#595 | 1 | 1 | yes | characteristic |
| 240 | C23 | — | 2 | 2 | no | — |
| 241 | C23 | — | 17 | 1 | no | — |
| 242 | C23 | — | 34 | 2 | no | — |
| 243 | C23 | — | 68 | 2 | no | — |
| 244 | C23 | — | 68 | 2 | no | — |
| 245 | C23 | — | 68 | 4 | no | — |
| 246 | C23 | — | 68 | 4 | no | — |
| 247 | C23 | — | 68 | 1 | no | — |
| 248 | Q8 | — | 4 | 2 | no | — |
| 249 | D4 | — | 4 | 2 | no | — |
| 250 | D4 | — | 8 | 2 | no | — |
| 251 | D4 | — | 68 | 2 | no | — |
| 252 | D4 | — | 68 | 2 | no | — |
| 253 | D4 | — | 136 | 2 | no | — |
| 254 | D4 | — | 136 | 2 | no | — |
| 255 | D4 | — | 136 | 2 | no | — |
| 256 | D4 | — | 136 | 2 | no | — |
| 257 | D4 | — | 136 | 4 | no | — |
| 258 | C2×C4 | — | 4 | 1 | no | — |
| 259 | C2×C4 | — | 17 | 2 | no | — |
| 260 | C2×C4 | — | 17 | 1 | no | — |
| 261 | C2×C4 | — | 34 | 2 | no | — |
| 262 | C2×C4 | — | 68 | 2 | no | — |
| 263 | C2×C4 | — | 68 | 4 | no | — |
| 264 | C2×C4 | — | 68 | 8 | no | — |
| 265 | C2×C4 | — | 136 | 1 | no | — |
| 266 | C2×C4 | — | 136 | 1 | no | — |
| 267 | C2×C4 | — | 136 | 8 | no | — |
| 268 | C2×C4 | D4×#595 | 1 | 2 | yes | — |
| 269 | C2×C4 | C2×C22⋊#595 | 1 | 1 | yes | characteristic |
| 270 | C8 | — | 2 | 2 | no | — |
| 271 | C8 | — | 34 | 2 | no | — |
| 272 | C8 | — | 136 | 2 | no | — |
| 273 | C22 | — | 4 | 2 | no | — |
| 274 | C22 | — | 4 | 4 | no | — |
| 275 | C22 | — | 17 | 2 | no | — |
| 276 | C22 | — | 34 | 2 | no | — |
| 277 | C22 | — | 68 | 2 | no | — |
| 278 | C22 | — | 68 | 4 | no | — |
| 279 | C22 | — | 136 | 2 | no | — |
| 280 | C22 | — | 136 | 4 | no | — |
| 281 | C22 | — | 136 | 2 | no | — |
| 282 | C22 | — | 136 | 1 | no | — |
| 283 | C22 | — | 136 | 2 | no | — |
| 284 | C22 | #11763757 | 1 | 1 | yes | characteristic |
| 285 | C4 | — | 2 | 1 | no | — |
| 286 | C4 | — | 2 | 2 | no | — |
| 287 | C4 | — | 8 | 1 | no | — |
| 288 | C4 | — | 34 | 1 | no | — |
| 289 | C4 | — | 34 | 2 | no | — |
| 290 | C4 | — | 136 | 4 | no | — |
| 291 | C2 | — | 8 | 2 | no | — |
| 292 | C2 | — | 272 | 1 | no | — |
| 293 | C2 | — | 34 | 2 | no | — |
| 294 | C2 | — | 136 | 2 | no | — |
| 295 | C2 | #14544791 | 1 | 1 | yes | characteristic |
| 296 | C2 | #14544817 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545328 | C2 | semidirect |
| 2. #14544312 | C2 | semidirect |
| 3. #14544205 | C2 | semidirect |
| 4. #14543644 | C2 | semidirect |
| 16. #11763186 | C4 | semidirect |
| 17. #11763185 | C4 | semidirect |
| 18. #11763183 | C4 | semidirect |
| 20. C17×#492 | C4 | semidirect |
| 28. C17×C4⋊Q8 | C2×C4 | semidirect |
| 42. #10587560 | C2×C4 | semidirect |
| 50. C4×C8×C17 | C2×C4 | semidirect |
| 52. C4×#3622 | C2×C4 | semidirect |
| 155. #492 | #595 | semidirect |
| 180. C4⋊Q8 | C2×#595 | semidirect |
| 197. C4×C8 | C2×#595 | semidirect |
| 201. C17 | #9428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545328 | 2 |
| #14544312 | 2 |
| #14544205 | 2 |
| #14543644 | 2 |
| #14539231 | 2 |
| #9428 | 17 |