Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
298 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 36 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 | #14543879 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14543601 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14529826 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#10587539 | — | 2 | 1 | no | — |
| 5 | #11763675 | — | 2 | 1 | no | — |
| 6 | C2×#10587635 | — | 2 | 1 | no | — |
| 7 | C2×#10587508 | — | 2 | 1 | no | — |
| 8 | #11762710 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11762578 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C17×#537 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#41×C17 | — | 2 | 1 | no | — |
| 12 | C22×D68 | D4 | 1 | 1 | yes | characteristic |
| 13 | C2×C22⋊#595 | — | 4 | 1 | no | — |
| 14 | C22×#3624 | — | 4 | 1 | no | — |
| 15 | C17×C22⋊Q8 | — | 4 | 1 | no | — |
| 16 | C17×#121 | — | 4 | 1 | no | — |
| 17 | C17×#121 | — | 4 | 1 | no | — |
| 18 | C2×C4⋊C4×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 19 | #10587635 | — | 4 | 2 | no | — |
| 20 | #10587635 | — | 4 | 1 | no | — |
| 21 | #10587635 | — | 4 | 1 | no | — |
| 22 | C2×#63230 | — | 4 | 1 | no | — |
| 23 | C2×#63228 | — | 4 | 1 | no | — |
| 24 | C2×#63227 | — | 4 | 1 | no | — |
| 25 | C2×C4×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 26 | C2×#63223 | — | 2 | 1 | no | — |
| 27 | #10587539 | — | 2 | 2 | no | — |
| 28 | #10587539 | — | 4 | 1 | no | — |
| 29 | #10587508 | — | 4 | 2 | no | — |
| 30 | C23×D17 | — | 2 | 1 | no | — |
| 31 | C22×#595 | — | 8 | 1 | no | — |
| 32 | #41×C17 | — | 4 | 1 | no | — |
| 33 | #41×C17 | — | 4 | 1 | no | — |
| 34 | #41×C17 | — | 4 | 1 | no | — |
| 35 | #41×C17 | — | 4 | 1 | no | — |
| 36 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 37 | C2×D4×C17 | — | 2 | 1 | no | — |
| 38 | C2×D4×C17 | — | 4 | 1 | no | — |
| 39 | C2×D4×C17 | — | 4 | 1 | no | — |
| 40 | C22×C4×C17 | — | 2 | 1 | no | — |
| 41 | C22×C4×C17 | — | 4 | 1 | no | — |
| 42 | C22×C4×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 43 | C22×Dic17 | — | 2 | 1 | no | — |
| 44 | C2×D68 | — | 2 | 1 | no | — |
| 45 | C2×D68 | — | 4 | 1 | no | — |
| 46 | C2×D68 | — | 4 | 1 | no | — |
| 47 | C2×D68 | D8 | 1 | 1 | yes | characteristic |
| 48 | C2×D68 | SD16 | 1 | 1 | yes | characteristic |
| 49 | C22⋊#595 | — | 4 | 2 | no | — |
| 50 | C22⋊#595 | — | 8 | 1 | no | — |
| 51 | C2×#3624 | — | 4 | 2 | no | — |
| 52 | C2×#3624 | — | 8 | 1 | no | — |
| 53 | C2×#3624 | — | 8 | 1 | no | — |
| 54 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 55 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 56 | C22⋊C4×C17 | — | 4 | 2 | no | — |
| 57 | #63230 | — | 4 | 2 | no | — |
| 58 | #63230 | — | 4 | 2 | no | — |
| 59 | #63228 | — | 4 | 2 | no | — |
| 60 | #63228 | — | 4 | 2 | no | — |
| 61 | #63227 | — | 8 | 1 | no | — |
| 62 | #63227 | — | 8 | 1 | no | — |
| 63 | C4×Dic17 | — | 4 | 1 | no | — |
| 64 | #63223 | — | 2 | 2 | no | — |
| 65 | #63223 | — | 4 | 1 | no | — |
| 66 | C2×#3622 | — | 4 | 1 | no | — |
| 67 | #7408 | — | 17 | 1 | no | maximal, Sylow |
| 68 | C23×C17 | — | 4 | 1 | no | — |
| 69 | C23×C17 | #99 | 1 | 1 | yes | characteristic |
| 70 | C22×D17 | — | 2 | 1 | no | — |
| 71 | C22×D17 | — | 2 | 1 | no | — |
| 72 | C22×D17 | — | 4 | 1 | no | — |
| 73 | C22×D17 | — | 4 | 1 | no | — |
| 74 | C22×D17 | — | 8 | 1 | no | — |
| 75 | C22×D17 | — | 8 | 1 | no | — |
| 76 | C2×#595 | — | 8 | 2 | no | — |
| 77 | C2×#595 | — | 16 | 1 | no | — |
| 78 | C2×#595 | — | 16 | 1 | no | — |
| 79 | Q8×C17 | — | 4 | 1 | no | — |
| 80 | Q8×C17 | — | 4 | 1 | no | — |
| 81 | D4×C17 | — | 4 | 1 | no | — |
| 82 | D4×C17 | — | 4 | 1 | no | — |
| 83 | D4×C17 | — | 8 | 1 | no | — |
| 84 | D4×C17 | — | 8 | 1 | no | — |
| 85 | D4×C17 | — | 16 | 1 | no | — |
| 86 | C2×C4×C17 | — | 2 | 1 | no | — |
| 87 | C2×C4×C17 | — | 2 | 1 | no | — |
| 88 | C2×C4×C17 | — | 4 | 1 | no | — |
| 89 | C2×C4×C17 | — | 4 | 1 | no | — |
| 90 | C2×C4×C17 | — | 8 | 1 | no | — |
| 91 | C2×C4×C17 | — | 8 | 1 | no | — |
| 92 | C2×C4×C17 | — | 8 | 1 | no | — |
| 93 | C2×C4×C17 | #102 | 1 | 1 | yes | characteristic |
| 94 | C2×C4×C17 | #104 | 1 | 1 | yes | characteristic |
| 95 | C2×Dic17 | — | 2 | 1 | no | — |
| 96 | C2×Dic17 | — | 2 | 1 | no | — |
| 97 | C2×Dic17 | — | 4 | 1 | no | — |
| 98 | C2×Dic17 | — | 4 | 1 | no | — |
| 99 | D68 | — | 4 | 1 | no | — |
| 100 | D68 | — | 4 | 1 | no | — |
| 101 | D68 | — | 8 | 1 | no | — |
| 102 | #3624 | — | 8 | 2 | no | — |
| 103 | #3622 | — | 4 | 2 | no | — |
| 104 | #2006 | — | 17 | 1 | no | — |
| 105 | #1393 | — | 17 | 1 | no | — |
| 106 | #1270 | — | 17 | 1 | no | — |
| 107 | C22×C17 | — | 2 | 1 | no | — |
| 108 | C22×C17 | — | 2 | 1 | no | — |
| 109 | C22×C17 | — | 8 | 1 | no | — |
| 110 | C22×C17 | — | 8 | 1 | no | — |
| 111 | C22×C17 | — | 8 | 1 | no | — |
| 112 | C22×C17 | #327 | 1 | 1 | yes | characteristic |
| 113 | C22×C17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 114 | C22×C17 | #353 | 1 | 1 | yes | characteristic |
| 115 | C2×D17 | — | 4 | 1 | no | — |
| 116 | C2×D17 | — | 4 | 1 | no | — |
| 117 | C2×D17 | — | 8 | 1 | no | — |
| 118 | C2×D17 | — | 8 | 1 | no | — |
| 119 | C2×D17 | — | 8 | 1 | no | — |
| 120 | C2×D17 | — | 8 | 1 | no | — |
| 121 | C2×D17 | — | 16 | 1 | no | — |
| 122 | #595 | — | 16 | 2 | no | — |
| 123 | C4×C17 | — | 2 | 1 | no | — |
| 124 | C4×C17 | — | 2 | 1 | no | — |
| 125 | C4×C17 | — | 8 | 1 | no | — |
| 126 | C4×C17 | — | 8 | 1 | no | — |
| 127 | Dic17 | — | 4 | 1 | no | — |
| 128 | Dic17 | — | 4 | 1 | no | — |
| 129 | C2×AGL(1,ℤ/8) | — | 34 | 1 | no | — |
| 130 | #537 | #595 | 1 | 1 | yes | characteristic, complemented |
| 131 | C2×#104 | — | 34 | 1 | no | — |
| 132 | C2×#99 | — | 34 | 1 | no | — |
| 133 | #390 | — | 17 | 1 | no | — |
| 134 | #343 | — | 17 | 1 | no | — |
| 135 | #336 | — | 34 | 1 | no | — |
| 136 | C2×C17 | — | 2 | 1 | no | — |
| 137 | C2×C17 | — | 2 | 1 | no | — |
| 138 | C2×C17 | — | 16 | 1 | no | — |
| 139 | C2×C17 | #1343 | 1 | 1 | yes | characteristic |
| 140 | C2×C17 | #1402 | 1 | 1 | yes | characteristic |
| 141 | C2×C17 | #1404 | 1 | 1 | yes | characteristic |
| 142 | D17 | — | 8 | 1 | no | — |
| 143 | D17 | — | 8 | 1 | no | — |
| 144 | C2×#41 | — | 2 | 1 | no | — |
| 145 | C22×D4 | — | 17 | 1 | no | — |
| 146 | AGL(1,ℤ/8) | — | 68 | 2 | no | — |
| 147 | AGL(1,ℤ/8) | — | 68 | 1 | no | — |
| 148 | AGL(1,ℤ/8) | — | 68 | 1 | no | — |
| 149 | C2×SD16 | — | 68 | 1 | no | — |
| 150 | C2×D8 | — | 68 | 1 | no | — |
| 151 | C2×M16 | — | 34 | 1 | no | — |
| 152 | C22×C8 | — | 68 | 1 | no | — |
| 153 | C22⋊Q8 | — | 4 | 1 | no | — |
| 154 | #121 | — | 4 | 1 | no | — |
| 155 | #121 | — | 4 | 1 | no | — |
| 156 | C2×C4⋊C4 | C2×#595 | 1 | 1 | yes | characteristic |
| 157 | C2×C22⋊C4 | — | 68 | 1 | no | — |
| 158 | C2×C22⋊C4 | — | 68 | 1 | no | — |
| 159 | C2×C42 | — | 17 | 1 | no | — |
| 160 | #104 | — | 68 | 2 | no | — |
| 161 | #99 | — | 34 | 2 | no | — |
| 162 | #99 | — | 68 | 1 | no | — |
| 163 | C17 | #7408 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 164 | C24 | — | 34 | 1 | no | — |
| 165 | #41 | — | 4 | 1 | no | — |
| 166 | #41 | — | 4 | 1 | no | — |
| 167 | #41 | — | 4 | 1 | no | — |
| 168 | #41 | — | 4 | 1 | no | — |
| 169 | C2×Q8 | — | 2 | 1 | no | — |
| 170 | C2×D4 | — | 2 | 1 | no | — |
| 171 | C2×D4 | — | 4 | 1 | no | — |
| 172 | C2×D4 | — | 4 | 1 | no | — |
| 173 | C2×D4 | — | 17 | 1 | no | — |
| 174 | C2×D4 | — | 17 | 1 | no | — |
| 175 | C2×D4 | — | 34 | 1 | no | — |
| 176 | C2×D4 | — | 68 | 1 | no | — |
| 177 | C2×D4 | — | 68 | 1 | no | — |
| 178 | C22×C4 | — | 2 | 1 | no | — |
| 179 | C22×C4 | — | 4 | 1 | no | — |
| 180 | C22×C4 | — | 34 | 1 | no | — |
| 181 | C22×C4 | — | 136 | 1 | no | — |
| 182 | C22×C4 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 183 | SD16 | — | 68 | 2 | no | — |
| 184 | SD16 | — | 68 | 2 | no | — |
| 185 | D8 | — | 68 | 2 | no | — |
| 186 | D8 | — | 68 | 2 | no | — |
| 187 | M16 | — | 34 | 2 | no | — |
| 188 | M16 | — | 68 | 1 | no | — |
| 189 | C2×C8 | — | 68 | 1 | no | — |
| 190 | C2×C8 | — | 68 | 2 | no | — |
| 191 | C2×C8 | — | 136 | 1 | no | — |
| 192 | C2×C8 | — | 136 | 1 | no | — |
| 193 | C4⋊C4 | — | 4 | 1 | no | — |
| 194 | C4⋊C4 | — | 4 | 1 | no | — |
| 195 | C22⋊C4 | — | 4 | 2 | no | — |
| 196 | C22⋊C4 | — | 68 | 2 | no | — |
| 197 | C22⋊C4 | — | 136 | 1 | no | — |
| 198 | C22⋊C4 | — | 136 | 1 | no | — |
| 199 | C22⋊C4 | — | 136 | 1 | no | — |
| 200 | C42 | — | 68 | 1 | no | — |
| 201 | C23 | — | 4 | 1 | no | — |
| 202 | C23 | — | 34 | 1 | no | — |
| 203 | C23 | — | 34 | 1 | no | — |
| 204 | C23 | — | 68 | 1 | no | — |
| 205 | C23 | — | 68 | 1 | no | — |
| 206 | C23 | — | 136 | 1 | no | — |
| 207 | C23 | — | 136 | 1 | no | — |
| 208 | C23 | #10587551 | 1 | 1 | yes | characteristic |
| 209 | Q8 | — | 4 | 1 | no | — |
| 210 | Q8 | — | 4 | 1 | no | — |
| 211 | D4 | — | 4 | 1 | no | — |
| 212 | D4 | — | 4 | 1 | no | — |
| 213 | D4 | — | 8 | 1 | no | — |
| 214 | D4 | — | 8 | 1 | no | — |
| 215 | D4 | — | 16 | 1 | no | — |
| 216 | D4 | — | 68 | 1 | no | — |
| 217 | D4 | — | 68 | 1 | no | — |
| 218 | D4 | — | 136 | 1 | no | — |
| 219 | C2×C4 | — | 2 | 1 | no | — |
| 220 | C2×C4 | — | 2 | 1 | no | — |
| 221 | C2×C4 | — | 4 | 1 | no | — |
| 222 | C2×C4 | — | 4 | 1 | no | — |
| 223 | C2×C4 | — | 8 | 1 | no | — |
| 224 | C2×C4 | — | 8 | 1 | no | — |
| 225 | C2×C4 | — | 8 | 1 | no | — |
| 226 | C2×C4 | — | 272 | 1 | no | — |
| 227 | C2×C4 | — | 272 | 1 | no | — |
| 228 | C2×C4 | — | 34 | 1 | no | — |
| 229 | C2×C4 | — | 34 | 1 | no | — |
| 230 | C2×C4 | — | 68 | 1 | no | — |
| 231 | C2×C4 | — | 68 | 1 | no | — |
| 232 | C2×C4 | — | 136 | 2 | no | — |
| 233 | C2×C4 | #10587547 | 1 | 1 | yes | characteristic |
| 234 | C2×C4 | #10587548 | 1 | 1 | yes | characteristic |
| 235 | C8 | — | 68 | 2 | no | — |
| 236 | C8 | — | 136 | 2 | no | — |
| 237 | C22 | — | 2 | 1 | no | — |
| 238 | C22 | — | 2 | 1 | no | — |
| 239 | C22 | — | 8 | 1 | no | — |
| 240 | C22 | — | 8 | 1 | no | — |
| 241 | C22 | — | 8 | 1 | no | — |
| 242 | C22 | — | 272 | 1 | no | — |
| 243 | C22 | — | 68 | 1 | no | — |
| 244 | C22 | — | 68 | 1 | no | — |
| 245 | C22 | — | 136 | 1 | no | — |
| 246 | C22 | — | 136 | 1 | no | — |
| 247 | C22 | — | 136 | 1 | no | — |
| 248 | C22 | — | 136 | 1 | no | — |
| 249 | C22 | #11763660 | 1 | 1 | yes | characteristic |
| 250 | C22 | #11763709 | 1 | 1 | yes | characteristic |
| 251 | C22 | #11763713 | 1 | 1 | yes | characteristic |
| 252 | C4 | — | 2 | 1 | no | — |
| 253 | C4 | — | 2 | 1 | no | — |
| 254 | C4 | — | 8 | 1 | no | — |
| 255 | C4 | — | 8 | 1 | no | — |
| 256 | C4 | — | 272 | 2 | no | — |
| 257 | C4 | — | 68 | 1 | no | — |
| 258 | C4 | — | 68 | 1 | no | — |
| 259 | C2 | — | 2 | 1 | no | — |
| 260 | C2 | — | 2 | 1 | no | — |
| 261 | C2 | — | 16 | 1 | no | — |
| 262 | C2 | — | 136 | 1 | no | — |
| 263 | C2 | — | 136 | 1 | no | — |
| 264 | C2 | #14543762 | 1 | 1 | yes | characteristic |
| 265 | C2 | #14543903 | 1 | 1 | yes | characteristic |
| 266 | C2 | #14543907 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14543879 | C2 | semidirect |
| 2. #14543601 | C2 | semidirect |
| 9. #11762578 | C4 | semidirect |
| 10. C17×#537 | C4 | semidirect |
| 130. #537 | #595 | semidirect |
| 163. C17 | #7408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543879 | 2 |
| #14543601 | 2 |
| #14529826 | 2 |
| #7408 | 17 |