Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
806 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 155 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 | #14543279 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14539984 | C2 | 1 | 2 | yes | maximal |
| 3 | #14539132 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #14528113 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #14528087 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #14527400 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C17×#1537 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C17⋊#564 | C22 | 1 | 4 | yes | — |
| 9 | #11763538 | — | 2 | 2 | no | — |
| 10 | #11763537 | — | 2 | 2 | no | — |
| 11 | #11763534 | — | 2 | 2 | no | — |
| 12 | #11763421 | — | 2 | 2 | no | — |
| 13 | #11763419 | — | 2 | 4 | no | — |
| 14 | #11763366 | C22 | 1 | 2 | yes | — |
| 15 | #11763359 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11763218 | C22 | 1 | 4 | yes | — |
| 17 | #11763179 | C22 | 1 | 2 | yes | — |
| 18 | #11763175 | C22 | 1 | 2 | yes | — |
| 19 | #11763174 | C22 | 1 | 4 | yes | — |
| 20 | #11763171 | — | 2 | 2 | no | — |
| 21 | #11763134 | — | 2 | 4 | no | — |
| 22 | #11763100 | — | 2 | 2 | no | — |
| 23 | #11763090 | — | 2 | 2 | no | — |
| 24 | #11762803 | — | 2 | 2 | no | — |
| 25 | C2×#10587474 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11762550 | C22 | 1 | 8 | yes | — |
| 27 | C17×#533 | C22 | 1 | 1 | yes | characteristic |
| 28 | C17×#432 | C22 | 1 | 2 | yes | — |
| 29 | C17×#330 | C22 | 1 | 4 | yes | — |
| 30 | C2×#63252 | — | 2 | 1 | no | — |
| 31 | C17×C4⋊Q8 | D4 | 1 | 2 | yes | — |
| 32 | C17×#125 | C23 | 1 | 2 | yes | — |
| 33 | C17×C22⋊Q8 | — | 2 | 2 | no | — |
| 34 | C4×Q8×C17 | — | 2 | 2 | no | — |
| 35 | C17×#117 | D4 | 1 | 2 | yes | — |
| 36 | C2×C42×C17 | C23 | 1 | 1 | yes | characteristic |
| 37 | Q8×Dic17 | — | 2 | 4 | no | — |
| 38 | #10587630 | — | 2 | 4 | no | — |
| 39 | #10587616 | — | 2 | 2 | no | — |
| 40 | #10587612 | D4 | 1 | 4 | yes | — |
| 41 | #10587610 | — | 2 | 2 | no | — |
| 42 | #10587610 | — | 2 | 2 | no | — |
| 43 | C22×#3622 | — | 2 | 1 | no | — |
| 44 | #10587576 | — | 2 | 4 | no | — |
| 45 | #10587576 | — | 2 | 8 | no | — |
| 46 | #10587575 | — | 2 | 8 | no | — |
| 47 | #10587575 | — | 2 | 8 | no | — |
| 48 | #10587573 | — | 2 | 4 | no | — |
| 49 | #10587565 | — | 2 | 8 | no | — |
| 50 | #10587561 | — | 2 | 1 | no | — |
| 51 | #10587560 | C23 | 1 | 1 | yes | characteristic |
| 52 | C4×D68 | — | 2 | 2 | no | — |
| 53 | #10587556 | — | 2 | 2 | no | — |
| 54 | #10587556 | C23 | 1 | 4 | yes | — |
| 55 | #10587555 | — | 2 | 2 | no | — |
| 56 | #10587555 | D4 | 1 | 2 | yes | — |
| 57 | #10587555 | D4 | 1 | 2 | yes | — |
| 58 | #10587555 | C23 | 1 | 1 | yes | characteristic |
| 59 | C4×Dic34 | — | 2 | 4 | no | — |
| 60 | C4×Dic34 | — | 2 | 2 | no | — |
| 61 | C4×Dic34 | — | 2 | 2 | no | — |
| 62 | C17×C4⋊C8 | — | 2 | 2 | no | — |
| 63 | C17×C22⋊C8 | — | 2 | 2 | no | — |
| 64 | C17×#97 | C23 | 1 | 4 | yes | — |
| 65 | #10587492 | — | 2 | 4 | no | — |
| 66 | #10587492 | — | 2 | 4 | no | — |
| 67 | #10587489 | — | 2 | 4 | no | — |
| 68 | #10587488 | — | 2 | 4 | no | — |
| 69 | #10587481 | — | 2 | 4 | no | — |
| 70 | #10587480 | — | 2 | 4 | no | — |
| 71 | #10587474 | — | 2 | 1 | no | — |
| 72 | #10587474 | C23 | 1 | 2 | yes | — |
| 73 | C2×Q8×C17 | — | 2 | 2 | no | — |
| 74 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C22×C4×C17 | C2×D4 | 1 | 2 | yes | — |
| 76 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 77 | #63252 | — | 4 | 4 | no | — |
| 78 | C2×D68 | — | 2 | 1 | no | — |
| 79 | C2×D68 | — | 2 | 2 | no | — |
| 80 | C2×C4×D17 | — | 4 | 1 | no | — |
| 81 | C2×Dic34 | — | 2 | 2 | no | — |
| 82 | C2×Dic34 | — | 2 | 2 | no | — |
| 83 | C2×Dic34 | — | 2 | 1 | no | — |
| 84 | C2×C8×C17 | — | 2 | 4 | no | — |
| 85 | C4⋊C4×C17 | — | 2 | 2 | no | — |
| 86 | C4⋊C4×C17 | — | 2 | 4 | no | — |
| 87 | C4⋊C4×C17 | C2×D4 | 1 | 4 | yes | — |
| 88 | C22⋊C4×C17 | — | 2 | 2 | no | — |
| 89 | C42×C17 | — | 2 | 2 | no | — |
| 90 | C42×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C42×C17 | C2×D4 | 1 | 2 | yes | — |
| 92 | C42×C17 | C24 | 1 | 1 | yes | characteristic |
| 93 | C22⋊Dic17 | — | 2 | 4 | no | — |
| 94 | #63227 | — | 4 | 2 | no | — |
| 95 | C4⋊Dic17 | — | 2 | 8 | no | — |
| 96 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 97 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 98 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 99 | C4⋊Dic17 | C2×D4 | 1 | 4 | yes | — |
| 100 | C4⋊Dic17 | C2×D4 | 1 | 4 | yes | — |
| 101 | #63225 | — | 2 | 8 | no | — |
| 102 | #63225 | — | 2 | 8 | no | — |
| 103 | #63225 | — | 2 | 4 | no | — |
| 104 | #63225 | — | 2 | 4 | no | — |
| 105 | C4×Dic17 | — | 2 | 8 | no | — |
| 106 | C4×Dic17 | — | 2 | 4 | no | — |
| 107 | C2×#3622 | — | 2 | 2 | no | — |
| 108 | C2×#3622 | — | 4 | 2 | no | — |
| 109 | #19063 | — | 17 | 1 | no | maximal, Sylow |
| 110 | C23×C17 | #120 | 1 | 1 | yes | characteristic |
| 111 | C22×D17 | — | 4 | 1 | no | — |
| 112 | Q8×C17 | — | 4 | 4 | no | — |
| 113 | C2×C4×C17 | — | 2 | 2 | no | — |
| 114 | C2×C4×C17 | — | 2 | 4 | no | — |
| 115 | C2×C4×C17 | — | 4 | 2 | no | — |
| 116 | C2×C4×C17 | #120 | 1 | 2 | yes | — |
| 117 | C2×C4×C17 | #120 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×C17 | C22×D4 | 1 | 2 | yes | — |
| 120 | C22⋊D17 | — | 8 | 2 | no | — |
| 121 | C2×Dic17 | — | 2 | 4 | no | — |
| 122 | C2×Dic17 | — | 2 | 4 | no | — |
| 123 | C2×Dic17 | — | 4 | 1 | no | — |
| 124 | D68 | — | 4 | 4 | no | — |
| 125 | D68 | — | 4 | 2 | no | — |
| 126 | C4×D17 | — | 8 | 2 | no | — |
| 127 | Dic34 | — | 4 | 4 | no | — |
| 128 | Dic34 | — | 4 | 4 | no | — |
| 129 | Dic34 | — | 4 | 2 | no | — |
| 130 | C8×C17 | — | 4 | 4 | no | — |
| 131 | #3622 | — | 4 | 2 | no | — |
| 132 | #3556 | — | 17 | 1 | no | — |
| 133 | #3235 | — | 17 | 2 | no | — |
| 134 | #3135 | — | 17 | 1 | no | — |
| 135 | #1663 | — | 17 | 4 | no | — |
| 136 | #1658 | — | 17 | 4 | no | — |
| 137 | #1537 | D17 | 1 | 1 | yes | characteristic, complemented |
| 138 | #1531 | — | 17 | 2 | no | — |
| 139 | C22×C17 | — | 2 | 1 | no | — |
| 140 | C22×C17 | — | 2 | 2 | no | — |
| 141 | C22×C17 | C2×#120 | 1 | 1 | yes | characteristic |
| 142 | C2×D17 | — | 8 | 1 | no | — |
| 143 | C2×D17 | — | 8 | 2 | no | — |
| 144 | C4×C17 | — | 2 | 1 | no | — |
| 145 | C4×C17 | — | 2 | 2 | no | — |
| 146 | C4×C17 | — | 2 | 2 | no | — |
| 147 | C4×C17 | — | 4 | 4 | no | — |
| 148 | C4×C17 | #454 | 1 | 2 | yes | — |
| 149 | Dic17 | — | 4 | 4 | no | — |
| 150 | Dic17 | — | 4 | 4 | no | — |
| 151 | Dic17 | — | 8 | 1 | no | — |
| 152 | #564 | — | 17 | 4 | no | — |
| 153 | #557 | — | 34 | 2 | no | — |
| 154 | #557 | — | 34 | 2 | no | — |
| 155 | #557 | — | 34 | 2 | no | — |
| 156 | #541 | — | 34 | 4 | no | — |
| 157 | #541 | — | 34 | 2 | no | — |
| 158 | #533 | — | 17 | 2 | no | — |
| 159 | #533 | C2×D17 | 1 | 1 | yes | characteristic |
| 160 | #532 | — | 17 | 1 | no | — |
| 161 | #501 | — | 17 | 4 | no | — |
| 162 | #491 | — | 17 | 2 | no | — |
| 163 | #490 | — | 17 | 2 | no | — |
| 164 | #490 | — | 17 | 4 | no | — |
| 165 | #489 | — | 34 | 2 | no | — |
| 166 | #482 | — | 34 | 4 | no | — |
| 167 | #476 | — | 34 | 2 | no | — |
| 168 | #474 | — | 34 | 2 | no | — |
| 169 | #432 | C2×D17 | 1 | 2 | yes | — |
| 170 | #416 | — | 34 | 2 | no | — |
| 171 | C2×#97 | — | 17 | 1 | no | — |
| 172 | #330 | — | 17 | 8 | no | — |
| 173 | #330 | C2×D17 | 1 | 4 | yes | — |
| 174 | C2×C17 | — | 4 | 1 | no | — |
| 175 | C2×C17 | C2×#454 | 1 | 1 | yes | characteristic |
| 176 | C2×C17 | #3020 | 1 | 2 | yes | — |
| 177 | D17 | — | 16 | 1 | no | — |
| 178 | C2×#41 | — | 34 | 1 | no | — |
| 179 | C22×C8 | — | 34 | 1 | no | — |
| 180 | C4⋊Q8 | — | 17 | 2 | no | — |
| 181 | C4⋊Q8 | — | 17 | 2 | no | — |
| 182 | C4⋊Q8 | — | 17 | 1 | no | — |
| 183 | C4⋊Q8 | — | 34 | 2 | no | — |
| 184 | C4⋊Q8 | — | 34 | 4 | no | — |
| 185 | C4⋊Q8 | D68 | 1 | 2 | yes | — |
| 186 | #127 | — | 17 | 1 | no | — |
| 187 | #126 | — | 34 | 8 | no | — |
| 188 | #125 | — | 17 | 4 | no | — |
| 189 | #125 | — | 34 | 2 | no | — |
| 190 | #125 | — | 34 | 8 | no | — |
| 191 | #125 | — | 34 | 8 | no | — |
| 192 | #125 | — | 34 | 4 | no | — |
| 193 | #125 | — | 34 | 8 | no | — |
| 194 | #125 | C22×D17 | 1 | 2 | yes | — |
| 195 | #124 | — | 34 | 1 | no | — |
| 196 | C22⋊Q8 | — | 2 | 2 | no | — |
| 197 | C22⋊Q8 | — | 34 | 2 | no | — |
| 198 | C22⋊Q8 | — | 34 | 2 | no | — |
| 199 | #121 | — | 34 | 2 | no | — |
| 200 | C4×Q8 | — | 2 | 2 | no | — |
| 201 | C4×Q8 | — | 34 | 4 | no | — |
| 202 | C4×Q8 | — | 34 | 4 | no | — |
| 203 | C4×Q8 | — | 34 | 4 | no | — |
| 204 | C4×Q8 | — | 34 | 2 | no | — |
| 205 | C4×Q8 | — | 34 | 2 | no | — |
| 206 | C4×D4 | — | 34 | 2 | no | — |
| 207 | #117 | — | 17 | 4 | no | — |
| 208 | #117 | D68 | 1 | 2 | yes | — |
| 209 | C2×C42 | C22×D17 | 1 | 1 | yes | characteristic |
| 210 | #107 | — | 34 | 4 | no | — |
| 211 | #106 | — | 34 | 4 | no | — |
| 212 | C4⋊C8 | — | 2 | 2 | no | — |
| 213 | #103 | — | 34 | 4 | no | — |
| 214 | #102 | — | 34 | 4 | no | — |
| 215 | #102 | — | 34 | 4 | no | — |
| 216 | #102 | — | 34 | 4 | no | — |
| 217 | C22⋊C8 | — | 2 | 2 | no | — |
| 218 | #97 | — | 17 | 2 | no | — |
| 219 | #97 | — | 34 | 1 | no | — |
| 220 | #97 | C22×D17 | 1 | 4 | yes | — |
| 221 | C17 | #19063 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 222 | #41 | — | 68 | 4 | no | — |
| 223 | C2×Q8 | — | 2 | 2 | no | — |
| 224 | C2×Q8 | — | 34 | 2 | no | — |
| 225 | C2×Q8 | — | 34 | 2 | no | — |
| 226 | C2×Q8 | — | 34 | 1 | no | — |
| 227 | C2×D4 | — | 34 | 1 | no | — |
| 228 | C2×D4 | — | 34 | 2 | no | — |
| 229 | C2×D4 | — | 68 | 1 | no | — |
| 230 | C22×C4 | — | 68 | 1 | no | — |
| 231 | C22×C4 | C2×D68 | 1 | 1 | yes | characteristic |
| 232 | C22×C4 | D4×D17 | 1 | 2 | yes | — |
| 233 | C2×C8 | — | 2 | 4 | no | — |
| 234 | C2×C8 | — | 34 | 2 | no | — |
| 235 | C2×C8 | — | 68 | 2 | no | — |
| 236 | C4⋊C4 | — | 2 | 4 | no | — |
| 237 | C4⋊C4 | — | 2 | 2 | no | — |
| 238 | C4⋊C4 | — | 17 | 4 | no | — |
| 239 | C4⋊C4 | — | 17 | 4 | no | — |
| 240 | C4⋊C4 | — | 34 | 8 | no | — |
| 241 | C4⋊C4 | — | 34 | 8 | no | — |
| 242 | C4⋊C4 | — | 34 | 8 | no | — |
| 243 | C4⋊C4 | — | 34 | 4 | no | — |
| 244 | C4⋊C4 | — | 34 | 4 | no | — |
| 245 | C4⋊C4 | — | 34 | 2 | no | — |
| 246 | C4⋊C4 | — | 34 | 2 | no | — |
| 247 | C4⋊C4 | — | 34 | 2 | no | — |
| 248 | C4⋊C4 | C2×D68 | 1 | 4 | yes | — |
| 249 | C22⋊C4 | — | 2 | 2 | no | — |
| 250 | C22⋊C4 | — | 34 | 4 | no | — |
| 251 | C22⋊C4 | — | 68 | 2 | no | — |
| 252 | C42 | — | 2 | 2 | no | — |
| 253 | C42 | — | 34 | 8 | no | — |
| 254 | C42 | — | 34 | 4 | no | — |
| 255 | C42 | C2×D68 | 1 | 1 | yes | characteristic |
| 256 | C42 | D4×D17 | 1 | 2 | yes | — |
| 257 | C42 | C23×D17 | 1 | 1 | yes | characteristic |
| 258 | C23 | — | 68 | 1 | no | — |
| 259 | C23 | #10587568 | 1 | 1 | yes | characteristic |
| 260 | Q8 | — | 4 | 4 | no | — |
| 261 | Q8 | — | 68 | 4 | no | — |
| 262 | Q8 | — | 68 | 2 | no | — |
| 263 | Q8 | — | 68 | 4 | no | — |
| 264 | D4 | — | 68 | 2 | no | — |
| 265 | D4 | — | 68 | 4 | no | — |
| 266 | D4 | — | 136 | 2 | no | — |
| 267 | C2×C4 | — | 2 | 2 | no | — |
| 268 | C2×C4 | — | 2 | 4 | no | — |
| 269 | C2×C4 | — | 4 | 2 | no | — |
| 270 | C2×C4 | — | 34 | 4 | no | — |
| 271 | C2×C4 | — | 34 | 4 | no | — |
| 272 | C2×C4 | — | 68 | 1 | no | — |
| 273 | C2×C4 | — | 136 | 2 | no | — |
| 274 | C2×C4 | #10587568 | 1 | 2 | yes | — |
| 275 | C2×C4 | #10587568 | 1 | 1 | yes | characteristic |
| 276 | C2×C4 | C22×D68 | 1 | 1 | yes | characteristic |
| 277 | C2×C4 | C2×D4×D17 | 1 | 2 | yes | — |
| 278 | C8 | — | 4 | 4 | no | — |
| 279 | C8 | — | 68 | 2 | no | — |
| 280 | C22 | — | 2 | 1 | no | — |
| 281 | C22 | — | 2 | 2 | no | — |
| 282 | C22 | — | 136 | 1 | no | — |
| 283 | C22 | — | 136 | 2 | no | — |
| 284 | C22 | C2×#10587568 | 1 | 1 | yes | characteristic |
| 285 | C4 | — | 2 | 1 | no | — |
| 286 | C4 | — | 2 | 2 | no | — |
| 287 | C4 | — | 2 | 2 | no | — |
| 288 | C4 | — | 4 | 4 | no | — |
| 289 | C4 | — | 68 | 4 | no | — |
| 290 | C4 | — | 68 | 4 | no | — |
| 291 | C4 | — | 136 | 1 | no | — |
| 292 | C4 | #11762984 | 1 | 2 | yes | — |
| 293 | C2 | — | 4 | 1 | no | — |
| 294 | C2 | — | 272 | 1 | no | — |
| 295 | C2 | C2×#11762984 | 1 | 1 | yes | characteristic |
| 296 | C2 | #14538150 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14543279 | C2 | semidirect |
| 4. #14528113 | C2 | semidirect |
| 5. #14528087 | C2 | semidirect |
| 6. #14527400 | C2 | semidirect |
| 7. C17×#1537 | C2 | semidirect |
| 137. #1537 | D17 | semidirect |
| 221. C17 | #19063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543279 | 2 |
| #14539984 | 2 |
| #14539132 | 2 |
| #14528113 | 2 |
| #14528087 | 2 |
| #14527400 | 2 |
| C17×#1537 | 2 |
| #19063 | 17 |