Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
236 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 236 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 |
| 2 | #14543601 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14529941 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#10587539 | — | 2 | 1 | no | — |
| 5 | #11763675 | — | 2 | 1 | no | — |
| 6 | #11763440 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | #11762815 | — | 2 | 1 | no | — |
| 8 | #11762710 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11762570 | — | 2 | 1 | no | — |
| 10 | C17×#343 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C22×D68 | D4 | 1 | 1 | yes | characteristic |
| 12 | C2×C22⋊#595 | — | 4 | 1 | no | — |
| 13 | C22×#3624 | — | 4 | 1 | no | — |
| 14 | C2×M16×C17 | — | 2 | 1 | no | — |
| 15 | C2×C4⋊C4×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | C2×#63227 | — | 4 | 1 | no | — |
| 17 | #10587612 | — | 2 | 1 | no | — |
| 18 | #10587610 | — | 4 | 1 | no | — |
| 19 | C2×C4×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 20 | #10587576 | — | 4 | 1 | no | — |
| 21 | #10587574 | — | 4 | 1 | no | — |
| 22 | #10587539 | — | 2 | 2 | no | — |
| 23 | #10587539 | — | 4 | 1 | no | — |
| 24 | #10587492 | — | 4 | 1 | no | — |
| 25 | #10587492 | — | 4 | 1 | no | — |
| 26 | C23×D17 | — | 2 | 1 | no | — |
| 27 | C22×#595 | — | 8 | 1 | no | — |
| 28 | C22×C4×C17 | — | 2 | 1 | no | — |
| 29 | C22×C4×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 30 | C22×Dic17 | — | 2 | 1 | no | — |
| 31 | C2×D68 | — | 2 | 1 | no | — |
| 32 | C2×D68 | — | 4 | 1 | no | — |
| 33 | C2×D68 | — | 4 | 1 | no | — |
| 34 | C2×D68 | SD16 | 1 | 1 | yes | characteristic |
| 35 | C2×D68 | Q16 | 1 | 1 | yes | characteristic |
| 36 | C2×Dic34 | — | 4 | 1 | no | — |
| 37 | C22⋊#595 | — | 4 | 2 | no | — |
| 38 | C22⋊#595 | — | 8 | 1 | no | — |
| 39 | C2×#3624 | — | 4 | 2 | no | — |
| 40 | C2×#3624 | — | 8 | 1 | no | — |
| 41 | C2×#3624 | — | 8 | 1 | no | — |
| 42 | M16×C17 | — | 4 | 1 | no | — |
| 43 | M16×C17 | — | 4 | 1 | no | — |
| 44 | C2×C8×C17 | — | 4 | 1 | no | — |
| 45 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 46 | C22⋊Dic17 | — | 4 | 1 | no | — |
| 47 | #63227 | — | 8 | 1 | no | — |
| 48 | #63227 | — | 8 | 1 | no | — |
| 49 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 50 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 51 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 52 | #63225 | — | 4 | 2 | no | — |
| 53 | C4×Dic17 | — | 4 | 1 | no | — |
| 54 | C4×Dic17 | — | 4 | 1 | no | — |
| 55 | #7430 | — | 17 | 1 | no | maximal, Sylow |
| 56 | C23×C17 | #99 | 1 | 1 | yes | characteristic |
| 57 | C22×D17 | — | 2 | 1 | no | — |
| 58 | C22×D17 | — | 2 | 1 | no | — |
| 59 | C22×D17 | — | 4 | 1 | no | — |
| 60 | C22×D17 | — | 4 | 1 | no | — |
| 61 | C22×D17 | — | 8 | 1 | no | — |
| 62 | C22×D17 | — | 8 | 1 | no | — |
| 63 | C2×#595 | — | 8 | 2 | no | — |
| 64 | C2×#595 | — | 16 | 1 | no | — |
| 65 | C2×#595 | — | 16 | 1 | no | — |
| 66 | C2×C4×C17 | — | 2 | 1 | no | — |
| 67 | C2×C4×C17 | — | 2 | 1 | no | — |
| 68 | C2×C4×C17 | — | 4 | 1 | no | — |
| 69 | C2×C4×C17 | — | 8 | 1 | no | — |
| 70 | C2×C4×C17 | #103 | 1 | 1 | yes | characteristic |
| 71 | C2×C4×C17 | #104 | 1 | 1 | yes | characteristic |
| 72 | C2×Dic17 | — | 2 | 1 | no | — |
| 73 | C2×Dic17 | — | 2 | 1 | no | — |
| 74 | C2×Dic17 | — | 4 | 1 | no | — |
| 75 | C2×Dic17 | — | 4 | 1 | no | — |
| 76 | C2×Dic17 | — | 4 | 1 | no | — |
| 77 | C2×Dic17 | — | 4 | 1 | no | — |
| 78 | D68 | — | 4 | 1 | no | — |
| 79 | D68 | — | 4 | 1 | no | — |
| 80 | D68 | — | 8 | 1 | no | — |
| 81 | Dic34 | — | 16 | 1 | no | — |
| 82 | #3624 | — | 8 | 2 | no | — |
| 83 | C8×C17 | — | 8 | 1 | no | — |
| 84 | #2027 | — | 17 | 1 | no | — |
| 85 | #1393 | — | 17 | 1 | no | — |
| 86 | #1270 | — | 17 | 1 | no | — |
| 87 | C22×C17 | — | 2 | 1 | no | — |
| 88 | C22×C17 | — | 2 | 1 | no | — |
| 89 | C22×C17 | #328 | 1 | 1 | yes | characteristic |
| 90 | C22×C17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 91 | C22×C17 | #354 | 1 | 1 | yes | characteristic |
| 92 | C2×D17 | — | 4 | 1 | no | — |
| 93 | C2×D17 | — | 4 | 1 | no | — |
| 94 | C2×D17 | — | 8 | 1 | no | — |
| 95 | C2×D17 | — | 8 | 1 | no | — |
| 96 | C2×D17 | — | 8 | 1 | no | — |
| 97 | C2×D17 | — | 8 | 1 | no | — |
| 98 | C2×D17 | — | 16 | 1 | no | — |
| 99 | #595 | — | 16 | 2 | no | — |
| 100 | C4×C17 | — | 2 | 1 | no | — |
| 101 | C4×C17 | — | 2 | 1 | no | — |
| 102 | C4×C17 | — | 8 | 1 | no | — |
| 103 | Dic17 | — | 4 | 1 | no | — |
| 104 | Dic17 | — | 4 | 1 | no | — |
| 105 | Dic17 | — | 8 | 1 | no | — |
| 106 | Dic17 | — | 8 | 1 | no | — |
| 107 | #544 | — | 17 | 1 | no | — |
| 108 | #418 | — | 34 | 1 | no | — |
| 109 | C2×#99 | — | 34 | 1 | no | — |
| 110 | #390 | — | 17 | 1 | no | — |
| 111 | #343 | #595 | 1 | 1 | yes | characteristic, complemented |
| 112 | #339 | — | 34 | 1 | no | — |
| 113 | #336 | — | 34 | 1 | no | — |
| 114 | C2×C17 | — | 2 | 1 | no | — |
| 115 | C2×C17 | — | 2 | 1 | no | — |
| 116 | C2×C17 | #1351 | 1 | 1 | yes | characteristic |
| 117 | C2×C17 | #1402 | 1 | 1 | yes | characteristic |
| 118 | C2×C17 | #1404 | 1 | 1 | yes | characteristic |
| 119 | D17 | — | 8 | 1 | no | — |
| 120 | D17 | — | 8 | 1 | no | — |
| 121 | C22×D4 | — | 17 | 1 | no | — |
| 122 | C2×M16 | — | 2 | 1 | no | — |
| 123 | C22×C8 | — | 68 | 1 | no | — |
| 124 | C4⋊Q8 | — | 68 | 1 | no | — |
| 125 | #125 | — | 68 | 1 | no | — |
| 126 | C22⋊Q8 | — | 68 | 1 | no | — |
| 127 | #117 | — | 34 | 1 | no | — |
| 128 | C2×C4⋊C4 | C2×#595 | 1 | 1 | yes | characteristic |
| 129 | C2×C22⋊C4 | — | 68 | 1 | no | — |
| 130 | C2×C22⋊C4 | — | 68 | 1 | no | — |
| 131 | C2×C42 | — | 17 | 1 | no | — |
| 132 | #102 | — | 68 | 1 | no | — |
| 133 | #102 | — | 68 | 1 | no | — |
| 134 | #99 | — | 34 | 2 | no | — |
| 135 | #99 | — | 68 | 1 | no | — |
| 136 | C17 | #7430 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 137 | C24 | — | 34 | 1 | no | — |
| 138 | C2×Q8 | — | 68 | 1 | no | — |
| 139 | C2×D4 | — | 17 | 1 | no | — |
| 140 | C2×D4 | — | 17 | 1 | no | — |
| 141 | C2×D4 | — | 34 | 1 | no | — |
| 142 | C2×D4 | — | 68 | 1 | no | — |
| 143 | C2×D4 | — | 68 | 1 | no | — |
| 144 | C22×C4 | — | 2 | 1 | no | — |
| 145 | C22×C4 | — | 34 | 1 | no | — |
| 146 | C22×C4 | — | 136 | 1 | no | — |
| 147 | C22×C4 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 148 | M16 | — | 4 | 1 | no | — |
| 149 | M16 | — | 4 | 1 | no | — |
| 150 | C2×C8 | — | 4 | 1 | no | — |
| 151 | C2×C8 | — | 68 | 2 | no | — |
| 152 | C2×C8 | — | 136 | 1 | no | — |
| 153 | C2×C8 | — | 136 | 1 | no | — |
| 154 | C4⋊C4 | — | 4 | 1 | no | — |
| 155 | C4⋊C4 | — | 34 | 1 | no | — |
| 156 | C4⋊C4 | — | 34 | 1 | no | — |
| 157 | C4⋊C4 | — | 68 | 1 | no | — |
| 158 | C4⋊C4 | — | 68 | 2 | no | — |
| 159 | C22⋊C4 | — | 68 | 1 | no | — |
| 160 | C22⋊C4 | — | 68 | 2 | no | — |
| 161 | C22⋊C4 | — | 136 | 1 | no | — |
| 162 | C22⋊C4 | — | 136 | 1 | no | — |
| 163 | C22⋊C4 | — | 136 | 1 | no | — |
| 164 | C42 | — | 68 | 1 | no | — |
| 165 | C42 | — | 68 | 1 | no | — |
| 166 | C23 | — | 34 | 1 | no | — |
| 167 | C23 | — | 34 | 1 | no | — |
| 168 | C23 | — | 68 | 1 | no | — |
| 169 | C23 | — | 68 | 1 | no | — |
| 170 | C23 | — | 136 | 1 | no | — |
| 171 | C23 | — | 136 | 1 | no | — |
| 172 | C23 | #10587539 | 1 | 1 | yes | characteristic |
| 173 | Q8 | — | 272 | 1 | no | — |
| 174 | D4 | — | 68 | 1 | no | — |
| 175 | D4 | — | 68 | 1 | no | — |
| 176 | D4 | — | 136 | 1 | no | — |
| 177 | C2×C4 | — | 2 | 1 | no | — |
| 178 | C2×C4 | — | 2 | 1 | no | — |
| 179 | C2×C4 | — | 4 | 1 | no | — |
| 180 | C2×C4 | — | 8 | 1 | no | — |
| 181 | C2×C4 | — | 272 | 1 | no | — |
| 182 | C2×C4 | — | 272 | 1 | no | — |
| 183 | C2×C4 | — | 34 | 1 | no | — |
| 184 | C2×C4 | — | 34 | 1 | no | — |
| 185 | C2×C4 | — | 68 | 1 | no | — |
| 186 | C2×C4 | — | 68 | 1 | no | — |
| 187 | C2×C4 | — | 68 | 1 | no | — |
| 188 | C2×C4 | — | 68 | 1 | no | — |
| 189 | C2×C4 | — | 136 | 2 | no | — |
| 190 | C2×C4 | #10587548 | 1 | 1 | yes | characteristic |
| 191 | C2×C4 | #10587549 | 1 | 1 | yes | characteristic |
| 192 | C8 | — | 8 | 1 | no | — |
| 193 | C8 | — | 136 | 2 | no | — |
| 194 | C22 | — | 2 | 1 | no | — |
| 195 | C22 | — | 2 | 1 | no | — |
| 196 | C22 | — | 272 | 1 | no | — |
| 197 | C22 | — | 68 | 1 | no | — |
| 198 | C22 | — | 68 | 1 | no | — |
| 199 | C22 | — | 136 | 1 | no | — |
| 200 | C22 | — | 136 | 1 | no | — |
| 201 | C22 | — | 136 | 1 | no | — |
| 202 | C22 | — | 136 | 1 | no | — |
| 203 | C22 | #11763662 | 1 | 1 | yes | characteristic |
| 204 | C22 | #11763710 | 1 | 1 | yes | characteristic |
| 205 | C22 | #11763716 | 1 | 1 | yes | characteristic |
| 206 | C4 | — | 2 | 1 | no | — |
| 207 | C4 | — | 2 | 1 | no | — |
| 208 | C4 | — | 8 | 1 | no | — |
| 209 | C4 | — | 272 | 2 | no | — |
| 210 | C4 | — | 68 | 1 | no | — |
| 211 | C4 | — | 68 | 1 | no | — |
| 212 | C4 | — | 136 | 1 | no | — |
| 213 | C4 | — | 136 | 1 | no | — |
| 214 | C2 | — | 2 | 1 | no | — |
| 215 | C2 | — | 2 | 1 | no | — |
| 216 | C2 | — | 136 | 1 | no | — |
| 217 | C2 | — | 136 | 1 | no | — |
| 218 | C2 | #14543778 | 1 | 1 | yes | characteristic |
| 219 | C2 | #14543904 | 1 | 1 | yes | characteristic |
| 220 | C2 | #14543908 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #11763440 | C4 | semidirect |
| 10. C17×#343 | C4 | semidirect |
| 111. #343 | #595 | semidirect |
| 136. C17 | #7430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543879 | 2 |
| #14543601 | 2 |
| #14529941 | 2 |
| #7430 | 17 |