Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
384 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #14540165 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14530730 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #14526774 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #14526735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C17×#2050 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11763359 | — | 2 | 1 | no | — |
| 7 | #11763244 | — | 2 | 2 | no | — |
| 8 | #11763100 | — | 2 | 2 | no | — |
| 9 | #11763062 | — | 2 | 1 | no | — |
| 10 | #11763062 | C22 | 1 | 2 | yes | — |
| 11 | #11763005 | — | 2 | 2 | no | — |
| 12 | #11762619 | — | 2 | 2 | no | — |
| 13 | #11762591 | C22 | 1 | 2 | yes | — |
| 14 | C17×#575 | C22 | 1 | 1 | yes | characteristic |
| 15 | C17×#423 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C17×#104 | — | 2 | 1 | no | — |
| 17 | C17×#413 | — | 2 | 1 | no | — |
| 18 | C17×#338 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#41×C17 | — | 2 | 1 | no | — |
| 20 | C2×#63252 | — | 4 | 1 | no | — |
| 21 | C17×#137 | — | 4 | 1 | no | — |
| 22 | C17×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 23 | C17×#135 | — | 2 | 2 | no | — |
| 24 | C2×M16×C17 | — | 2 | 1 | no | — |
| 25 | C2×M16×C17 | D4 | 1 | 1 | yes | characteristic |
| 26 | C2×M16×C17 | C23 | 1 | 1 | yes | characteristic |
| 27 | C2×C42×C17 | D4 | 1 | 1 | yes | characteristic |
| 28 | #10587616 | — | 2 | 2 | no | — |
| 29 | #10587616 | — | 4 | 1 | no | — |
| 30 | C2×D136 | — | 2 | 1 | no | — |
| 31 | C2×D136 | D4 | 1 | 2 | yes | — |
| 32 | #10587561 | — | 4 | 1 | no | — |
| 33 | #10587560 | — | 2 | 1 | no | — |
| 34 | C4×D68 | — | 2 | 2 | no | — |
| 35 | C4×D68 | — | 4 | 1 | no | — |
| 36 | #10587555 | — | 2 | 1 | no | — |
| 37 | C17×C4⋊C8 | — | 2 | 2 | no | — |
| 38 | C17×#104 | — | 4 | 1 | no | — |
| 39 | C17×#104 | — | 4 | 1 | no | — |
| 40 | C17×#101 | — | 4 | 1 | no | — |
| 41 | C17×#100 | — | 4 | 1 | no | — |
| 42 | #10587499 | — | 4 | 2 | no | — |
| 43 | #10587497 | — | 4 | 2 | no | — |
| 44 | #10587492 | — | 2 | 2 | no | — |
| 45 | #10587492 | — | 2 | 2 | no | — |
| 46 | #10587488 | — | 2 | 1 | no | — |
| 47 | #10587488 | D4 | 1 | 2 | yes | — |
| 48 | #10587483 | — | 2 | 2 | no | — |
| 49 | #41×C17 | — | 4 | 1 | no | — |
| 50 | #41×C17 | — | 4 | 1 | no | — |
| 51 | #41×C17 | — | 4 | 1 | no | — |
| 52 | #41×C17 | — | 4 | 1 | no | — |
| 53 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 54 | C2×D4×C17 | — | 2 | 1 | no | — |
| 55 | C2×D4×C17 | — | 4 | 1 | no | — |
| 56 | C22×C4×C17 | — | 2 | 1 | no | — |
| 57 | C22×C4×C17 | — | 4 | 1 | no | — |
| 58 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C22⋊D17 | — | 4 | 2 | no | — |
| 60 | #63252 | — | 8 | 4 | no | — |
| 61 | C2×D68 | — | 2 | 2 | no | — |
| 62 | C2×D68 | — | 4 | 1 | no | — |
| 63 | C2×D68 | — | 4 | 1 | no | — |
| 64 | C2×C4×D17 | — | 4 | 2 | no | — |
| 65 | C2×Dic34 | — | 4 | 1 | no | — |
| 66 | Q16×C17 | — | 2 | 2 | no | — |
| 67 | SD16×C17 | — | 4 | 2 | no | — |
| 68 | D8×C17 | — | 2 | 2 | no | — |
| 69 | M16×C17 | — | 4 | 1 | no | — |
| 70 | M16×C17 | — | 4 | 1 | no | — |
| 71 | M16×C17 | — | 4 | 1 | no | — |
| 72 | M16×C17 | — | 4 | 1 | no | — |
| 73 | C2×C8×C17 | — | 2 | 1 | no | — |
| 74 | C2×C8×C17 | — | 4 | 1 | no | — |
| 75 | C2×C8×C17 | C2×D4 | 1 | 2 | yes | — |
| 76 | C42×C17 | — | 2 | 1 | no | — |
| 77 | C42×C17 | D8 | 1 | 1 | yes | characteristic |
| 78 | C42×C17 | D8 | 1 | 1 | yes | characteristic |
| 79 | #63227 | — | 4 | 2 | no | — |
| 80 | #63227 | — | 4 | 2 | no | — |
| 81 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 82 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 83 | D136 | — | 4 | 2 | no | — |
| 84 | D136 | — | 8 | 1 | no | — |
| 85 | #63214 | — | 4 | 2 | no | — |
| 86 | #12173 | — | 17 | 1 | no | maximal, Sylow |
| 87 | C23×C17 | — | 4 | 1 | no | — |
| 88 | C23×C17 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 89 | C22×D17 | — | 4 | 2 | no | — |
| 90 | Q8×C17 | — | 4 | 1 | no | — |
| 91 | Q8×C17 | — | 4 | 1 | no | — |
| 92 | D4×C17 | — | 4 | 1 | no | — |
| 93 | D4×C17 | — | 4 | 1 | no | — |
| 94 | D4×C17 | — | 8 | 1 | no | — |
| 95 | D4×C17 | — | 8 | 1 | no | — |
| 96 | C2×C4×C17 | — | 2 | 1 | no | — |
| 97 | C2×C4×C17 | — | 2 | 1 | no | — |
| 98 | C2×C4×C17 | — | 2 | 1 | no | — |
| 99 | C2×C4×C17 | — | 2 | 1 | no | — |
| 100 | C2×C4×C17 | — | 4 | 2 | no | — |
| 101 | C2×C4×C17 | — | 4 | 1 | no | — |
| 102 | C2×C4×C17 | — | 8 | 1 | no | — |
| 103 | C2×C4×C17 | — | 8 | 1 | no | — |
| 104 | C2×C4×C17 | #120 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C17 | C2×D8 | 1 | 1 | yes | characteristic |
| 106 | C22⋊D17 | — | 8 | 4 | no | — |
| 107 | C2×Dic17 | — | 4 | 2 | no | — |
| 108 | D68 | — | 4 | 2 | no | — |
| 109 | D68 | — | 4 | 2 | no | — |
| 110 | D68 | — | 8 | 2 | no | — |
| 111 | D68 | — | 8 | 2 | no | — |
| 112 | C4×D17 | — | 8 | 4 | no | — |
| 113 | Dic34 | — | 8 | 2 | no | — |
| 114 | C8×C17 | — | 2 | 2 | no | — |
| 115 | C8×C17 | — | 4 | 1 | no | — |
| 116 | C8×C17 | — | 8 | 1 | no | — |
| 117 | #3253 | — | 17 | 1 | no | — |
| 118 | #2190 | — | 17 | 2 | no | — |
| 119 | #2050 | D17 | 1 | 1 | yes | characteristic, complemented |
| 120 | #1341 | — | 17 | 2 | no | — |
| 121 | #1327 | — | 17 | 1 | no | — |
| 122 | C22×C17 | — | 2 | 1 | no | — |
| 123 | C22×C17 | — | 4 | 1 | no | — |
| 124 | C22×C17 | — | 8 | 1 | no | — |
| 125 | C22×C17 | — | 16 | 1 | no | — |
| 126 | C22×C17 | #447 | 1 | 1 | yes | characteristic |
| 127 | C2×D17 | — | 8 | 2 | no | — |
| 128 | C2×D17 | — | 8 | 2 | no | — |
| 129 | C2×D17 | — | 8 | 2 | no | — |
| 130 | C4×C17 | — | 2 | 2 | no | — |
| 131 | C4×C17 | — | 2 | 1 | no | — |
| 132 | C4×C17 | — | 4 | 1 | no | — |
| 133 | C4×C17 | — | 8 | 1 | no | — |
| 134 | C4×C17 | #454 | 1 | 1 | yes | characteristic |
| 135 | C4×C17 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 136 | Dic17 | — | 8 | 2 | no | — |
| 137 | #575 | C2×D17 | 1 | 1 | yes | characteristic |
| 138 | #532 | — | 34 | 1 | no | — |
| 139 | #509 | — | 34 | 2 | no | — |
| 140 | #476 | — | 34 | 2 | no | — |
| 141 | #469 | — | 17 | 2 | no | — |
| 142 | #469 | — | 34 | 1 | no | — |
| 143 | #459 | — | 34 | 2 | no | — |
| 144 | #423 | C2×D17 | 1 | 1 | yes | characteristic |
| 145 | C2×#104 | — | 2 | 1 | no | — |
| 146 | #413 | — | 2 | 1 | no | — |
| 147 | #360 | — | 34 | 2 | no | — |
| 148 | #349 | — | 17 | 2 | no | — |
| 149 | #338 | C2×D17 | 1 | 1 | yes | characteristic |
| 150 | C2×C17 | — | 2 | 1 | no | — |
| 151 | C2×C17 | — | 4 | 1 | no | — |
| 152 | C2×C17 | — | 16 | 1 | no | — |
| 153 | C2×C17 | #1598 | 1 | 1 | yes | characteristic |
| 154 | D17 | — | 16 | 2 | no | — |
| 155 | C2×#41 | — | 2 | 1 | no | — |
| 156 | C2×#41 | — | 68 | 1 | no | — |
| 157 | #137 | — | 4 | 1 | no | — |
| 158 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 159 | #135 | — | 2 | 2 | no | — |
| 160 | C2×D8 | — | 17 | 2 | no | — |
| 161 | C2×D8 | — | 34 | 1 | no | — |
| 162 | C2×M16 | — | 2 | 1 | no | — |
| 163 | C2×M16 | C22⋊D17 | 1 | 1 | yes | characteristic |
| 164 | C2×M16 | C22×D17 | 1 | 1 | yes | characteristic |
| 165 | C4⋊Q8 | — | 34 | 1 | no | — |
| 166 | #127 | — | 34 | 1 | no | — |
| 167 | #124 | — | 68 | 1 | no | — |
| 168 | #121 | — | 34 | 2 | no | — |
| 169 | #121 | — | 68 | 1 | no | — |
| 170 | C4×D4 | — | 34 | 2 | no | — |
| 171 | C4×D4 | — | 68 | 1 | no | — |
| 172 | C2×C42 | C22⋊D17 | 1 | 1 | yes | characteristic |
| 173 | SD32 | — | 68 | 2 | no | — |
| 174 | D16 | — | 68 | 2 | no | — |
| 175 | M32 | — | 34 | 2 | no | — |
| 176 | #106 | — | 17 | 2 | no | — |
| 177 | #106 | — | 34 | 1 | no | — |
| 178 | C4⋊C8 | — | 2 | 2 | no | — |
| 179 | #104 | — | 4 | 1 | no | — |
| 180 | #104 | — | 4 | 1 | no | — |
| 181 | #102 | — | 34 | 2 | no | — |
| 182 | #102 | — | 34 | 2 | no | — |
| 183 | #101 | — | 4 | 1 | no | — |
| 184 | #100 | — | 4 | 1 | no | — |
| 185 | C17 | #12173 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 186 | #41 | — | 4 | 1 | no | — |
| 187 | #41 | — | 4 | 1 | no | — |
| 188 | #41 | — | 4 | 1 | no | — |
| 189 | #41 | — | 4 | 1 | no | — |
| 190 | #41 | — | 136 | 4 | no | — |
| 191 | C2×Q8 | — | 2 | 1 | no | — |
| 192 | C2×Q8 | — | 68 | 1 | no | — |
| 193 | C2×D4 | — | 2 | 1 | no | — |
| 194 | C2×D4 | — | 4 | 1 | no | — |
| 195 | C2×D4 | — | 34 | 2 | no | — |
| 196 | C2×D4 | — | 68 | 1 | no | — |
| 197 | C2×D4 | — | 68 | 1 | no | — |
| 198 | C2×D4 | — | 68 | 2 | no | — |
| 199 | C22×C4 | — | 2 | 1 | no | — |
| 200 | C22×C4 | — | 4 | 1 | no | — |
| 201 | C22×C4 | — | 68 | 2 | no | — |
| 202 | C22×C4 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 203 | Q16 | — | 2 | 2 | no | — |
| 204 | SD16 | — | 4 | 2 | no | — |
| 205 | D8 | — | 2 | 2 | no | — |
| 206 | D8 | — | 68 | 2 | no | — |
| 207 | D8 | — | 136 | 1 | no | — |
| 208 | M16 | — | 4 | 1 | no | — |
| 209 | M16 | — | 4 | 1 | no | — |
| 210 | M16 | — | 4 | 1 | no | — |
| 211 | M16 | — | 4 | 1 | no | — |
| 212 | C2×C8 | — | 2 | 1 | no | — |
| 213 | C2×C8 | — | 4 | 1 | no | — |
| 214 | C2×C8 | D4×D17 | 1 | 2 | yes | — |
| 215 | C4⋊C4 | — | 34 | 2 | no | — |
| 216 | C4⋊C4 | — | 68 | 1 | no | — |
| 217 | C22⋊C4 | — | 68 | 2 | no | — |
| 218 | C22⋊C4 | — | 68 | 2 | no | — |
| 219 | C42 | — | 2 | 1 | no | — |
| 220 | C42 | #63228 | 1 | 1 | yes | characteristic |
| 221 | C42 | #63228 | 1 | 1 | yes | characteristic |
| 222 | C16 | — | 68 | 2 | no | — |
| 223 | C23 | — | 4 | 1 | no | — |
| 224 | C23 | — | 68 | 2 | no | — |
| 225 | C23 | #10587635 | 1 | 1 | yes | characteristic |
| 226 | Q8 | — | 4 | 1 | no | — |
| 227 | Q8 | — | 4 | 1 | no | — |
| 228 | Q8 | — | 136 | 2 | no | — |
| 229 | D4 | — | 4 | 1 | no | — |
| 230 | D4 | — | 4 | 1 | no | — |
| 231 | D4 | — | 8 | 1 | no | — |
| 232 | D4 | — | 8 | 1 | no | — |
| 233 | D4 | — | 68 | 2 | no | — |
| 234 | D4 | — | 68 | 2 | no | — |
| 235 | D4 | — | 136 | 2 | no | — |
| 236 | D4 | — | 136 | 2 | no | — |
| 237 | D4 | — | 136 | 4 | no | — |
| 238 | C2×C4 | — | 2 | 1 | no | — |
| 239 | C2×C4 | — | 2 | 1 | no | — |
| 240 | C2×C4 | — | 2 | 1 | no | — |
| 241 | C2×C4 | — | 2 | 1 | no | — |
| 242 | C2×C4 | — | 4 | 2 | no | — |
| 243 | C2×C4 | — | 4 | 1 | no | — |
| 244 | C2×C4 | — | 8 | 1 | no | — |
| 245 | C2×C4 | — | 8 | 1 | no | — |
| 246 | C2×C4 | — | 68 | 2 | no | — |
| 247 | C2×C4 | — | 136 | 4 | no | — |
| 248 | C2×C4 | C2×#63228 | 1 | 1 | yes | characteristic |
| 249 | C2×C4 | #10587623 | 1 | 1 | yes | characteristic |
| 250 | C8 | — | 2 | 2 | no | — |
| 251 | C8 | — | 4 | 1 | no | — |
| 252 | C8 | — | 8 | 1 | no | — |
| 253 | C22 | — | 2 | 1 | no | — |
| 254 | C22 | — | 4 | 1 | no | — |
| 255 | C22 | — | 8 | 1 | no | — |
| 256 | C22 | — | 16 | 1 | no | — |
| 257 | C22 | — | 136 | 2 | no | — |
| 258 | C22 | — | 136 | 2 | no | — |
| 259 | C22 | — | 136 | 2 | no | — |
| 260 | C22 | #11762942 | 1 | 1 | yes | characteristic |
| 261 | C4 | — | 2 | 2 | no | — |
| 262 | C4 | — | 2 | 1 | no | — |
| 263 | C4 | — | 4 | 1 | no | — |
| 264 | C4 | — | 8 | 1 | no | — |
| 265 | C4 | — | 136 | 2 | no | — |
| 266 | C4 | #11762981 | 1 | 1 | yes | characteristic |
| 267 | C4 | #11762995 | 1 | 1 | yes | characteristic |
| 268 | C2 | — | 2 | 1 | no | — |
| 269 | C2 | — | 4 | 1 | no | — |
| 270 | C2 | — | 16 | 1 | no | — |
| 271 | C2 | — | 272 | 2 | no | — |
| 272 | C2 | #14527718 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14540165 | C2 | semidirect |
| 2. #14530730 | C2 | semidirect |
| 3. #14526774 | C2 | semidirect |
| 4. #14526735 | C2 | semidirect |
| 5. C17×#2050 | C2 | semidirect |
| 119. #2050 | D17 | semidirect |
| 185. C17 | #12173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540165 | 2 |
| #14530730 | 2 |
| #14526774 | 2 |
| #14526735 | 2 |
| C17×#2050 | 2 |
| #12173 | 17 |