Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
458 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #14545057 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #14543916 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #14539236 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11763788 | — | 2 | 2 | no | — |
| 5 | #11763716 | — | 2 | 2 | no | — |
| 6 | #11763714 | C22 | 1 | 4 | yes | complemented |
| 7 | C2×#10587594 | — | 2 | 2 | no | — |
| 8 | #11763359 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#10587560 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #11763198 | — | 2 | 2 | no | — |
| 11 | #11763186 | C22 | 1 | 2 | yes | — |
| 12 | #11763182 | C4 | 1 | 2 | yes | complemented |
| 13 | C4×M16×C17 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×#63252 | D4 | 1 | 2 | yes | — |
| 15 | C22×D68 | — | 2 | 1 | no | — |
| 16 | C22×D68 | — | 4 | 1 | no | — |
| 17 | #10587677 | — | 4 | 2 | no | — |
| 18 | C2×M16×C17 | — | 2 | 1 | no | — |
| 19 | C2×C42×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 20 | #10587616 | — | 4 | 1 | no | — |
| 21 | #10587594 | — | 4 | 4 | no | — |
| 22 | #10587594 | — | 4 | 4 | no | — |
| 23 | C2×D136 | — | 2 | 4 | no | — |
| 24 | C2×#63219 | — | 2 | 4 | no | — |
| 25 | #10587561 | D4 | 1 | 2 | yes | — |
| 26 | #10587560 | — | 2 | 1 | no | — |
| 27 | #10587560 | — | 4 | 1 | no | — |
| 28 | #10587560 | C2×C4 | 1 | 2 | yes | — |
| 29 | #10587560 | C23 | 1 | 1 | yes | characteristic |
| 30 | C4×D68 | — | 4 | 1 | no | — |
| 31 | #10587555 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | #10587551 | — | 4 | 2 | no | — |
| 33 | #10587539 | — | 2 | 4 | no | — |
| 34 | C17×#97 | — | 2 | 1 | no | — |
| 35 | C4×C8×C17 | C2×C4 | 1 | 2 | yes | — |
| 36 | C23×D17 | — | 4 | 1 | no | — |
| 37 | C22×C4×C17 | — | 2 | 1 | no | — |
| 38 | C22×C4×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 39 | C2×C22⋊D17 | — | 2 | 2 | no | — |
| 40 | #63252 | — | 4 | 2 | no | — |
| 41 | #63252 | — | 4 | 2 | no | — |
| 42 | C2×D68 | — | 2 | 2 | no | — |
| 43 | C2×D68 | — | 4 | 2 | no | — |
| 44 | C2×D68 | — | 4 | 2 | no | — |
| 45 | C2×D68 | — | 4 | 1 | no | — |
| 46 | C2×D68 | — | 4 | 2 | no | — |
| 47 | C2×D68 | — | 4 | 2 | no | — |
| 48 | C2×D68 | — | 4 | 1 | no | — |
| 49 | C2×D68 | — | 8 | 4 | no | — |
| 50 | C2×D68 | C2×D4 | 1 | 2 | yes | — |
| 51 | C2×C4×D17 | — | 2 | 2 | no | — |
| 52 | C2×Dic34 | C22⋊C4 | 1 | 2 | yes | — |
| 53 | C22⋊#595 | — | 4 | 4 | no | — |
| 54 | C4⋊#595 | — | 8 | 2 | no | — |
| 55 | C4×#595 | — | 8 | 2 | no | — |
| 56 | M16×C17 | — | 2 | 4 | no | — |
| 57 | C2×C8×C17 | — | 2 | 2 | no | — |
| 58 | C42×C17 | — | 2 | 1 | no | — |
| 59 | C42×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 60 | C42×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 61 | #63227 | — | 4 | 2 | no | — |
| 62 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 63 | D136 | — | 4 | 8 | no | — |
| 64 | #63219 | — | 4 | 8 | no | — |
| 65 | #13585 | — | 17 | 1 | no | maximal, Sylow |
| 66 | C23×C17 | #99 | 1 | 1 | yes | characteristic |
| 67 | C22×D17 | — | 2 | 2 | no | — |
| 68 | C22×D17 | — | 4 | 2 | no | — |
| 69 | C22×D17 | — | 8 | 1 | no | — |
| 70 | C22×D17 | — | 8 | 1 | no | — |
| 71 | C22×D17 | — | 8 | 4 | no | — |
| 72 | C2×#595 | — | 8 | 4 | no | — |
| 73 | C2×C4×C17 | — | 2 | 1 | no | — |
| 74 | C2×C4×C17 | — | 2 | 2 | no | — |
| 75 | C2×C4×C17 | — | 2 | 1 | no | — |
| 76 | C2×C4×C17 | — | 4 | 2 | no | — |
| 77 | C2×C4×C17 | #99 | 1 | 1 | yes | characteristic |
| 78 | C2×C4×C17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 79 | C22⋊D17 | — | 8 | 2 | no | — |
| 80 | C2×Dic17 | — | 2 | 2 | no | — |
| 81 | D68 | — | 4 | 2 | no | — |
| 82 | D68 | — | 4 | 4 | no | — |
| 83 | D68 | — | 8 | 2 | no | — |
| 84 | D68 | — | 8 | 4 | no | — |
| 85 | D68 | — | 8 | 4 | no | — |
| 86 | D68 | — | 8 | 2 | no | — |
| 87 | C4×D17 | — | 4 | 2 | no | — |
| 88 | C4×D17 | — | 4 | 2 | no | — |
| 89 | Dic34 | — | 4 | 2 | no | — |
| 90 | C8×C17 | — | 2 | 4 | no | — |
| 91 | #3151 | — | 17 | 1 | no | — |
| 92 | #2126 | — | 17 | 2 | no | — |
| 93 | #1408 | — | 17 | 4 | no | — |
| 94 | C22×C17 | — | 2 | 1 | no | — |
| 95 | C22×C17 | — | 4 | 1 | no | — |
| 96 | C22×C17 | C2×#99 | 1 | 1 | yes | characteristic |
| 97 | C2×D17 | — | 4 | 2 | no | — |
| 98 | C2×D17 | — | 8 | 2 | no | — |
| 99 | C2×D17 | — | 8 | 4 | no | — |
| 100 | C2×D17 | — | 8 | 2 | no | — |
| 101 | C2×D17 | — | 16 | 2 | no | — |
| 102 | C2×D17 | — | 16 | 2 | no | — |
| 103 | #595 | — | 16 | 4 | no | — |
| 104 | C4×C17 | — | 2 | 2 | no | — |
| 105 | C4×C17 | — | 2 | 1 | no | — |
| 106 | C4×C17 | — | 4 | 1 | no | — |
| 107 | C4×C17 | #353 | 1 | 2 | yes | — |
| 108 | Dic17 | — | 4 | 2 | no | — |
| 109 | C2×AGL(1,ℤ/8) | — | 34 | 2 | no | — |
| 110 | #532 | — | 17 | 1 | no | — |
| 111 | C2×#127 | — | 17 | 1 | no | — |
| 112 | #496 | — | 34 | 2 | no | — |
| 113 | #493 | — | 17 | 2 | no | — |
| 114 | #492 | — | 17 | 2 | no | — |
| 115 | #410 | — | 34 | 2 | no | — |
| 116 | C4×M16 | #595 | 1 | 1 | yes | characteristic, complemented |
| 117 | #354 | — | 34 | 2 | no | — |
| 118 | #353 | — | 17 | 4 | no | — |
| 119 | C2×C17 | — | 2 | 1 | no | — |
| 120 | C2×C17 | — | 4 | 1 | no | — |
| 121 | C2×C17 | C2×#353 | 1 | 1 | yes | characteristic |
| 122 | D17 | — | 8 | 2 | no | — |
| 123 | D17 | — | 16 | 2 | no | — |
| 124 | C2×#41 | — | 17 | 2 | no | — |
| 125 | C22×D4 | — | 34 | 1 | no | — |
| 126 | C22×D4 | — | 68 | 1 | no | — |
| 127 | AGL(1,ℤ/8) | — | 68 | 4 | no | — |
| 128 | AGL(1,ℤ/8) | — | 68 | 4 | no | — |
| 129 | C2×SD16 | — | 34 | 4 | no | — |
| 130 | C2×D8 | — | 34 | 4 | no | — |
| 131 | C2×M16 | — | 2 | 1 | no | — |
| 132 | C4⋊Q8 | — | 17 | 1 | no | — |
| 133 | #127 | — | 17 | 1 | no | — |
| 134 | #127 | — | 17 | 2 | no | — |
| 135 | #127 | — | 34 | 1 | no | — |
| 136 | #127 | — | 68 | 1 | no | — |
| 137 | #124 | — | 17 | 2 | no | — |
| 138 | #121 | — | 68 | 1 | no | — |
| 139 | C4×D4 | — | 68 | 1 | no | — |
| 140 | #117 | — | 68 | 2 | no | — |
| 141 | C2×C42 | C2×#595 | 1 | 1 | yes | characteristic |
| 142 | #99 | — | 34 | 4 | no | — |
| 143 | #99 | — | 68 | 2 | no | — |
| 144 | #97 | — | 2 | 1 | no | — |
| 145 | C4×C8 | C2×#595 | 1 | 2 | yes | — |
| 146 | C17 | #13585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 147 | C24 | — | 68 | 1 | no | — |
| 148 | #41 | — | 68 | 2 | no | — |
| 149 | #41 | — | 68 | 2 | no | — |
| 150 | C2×Q8 | — | 17 | 2 | no | — |
| 151 | C2×D4 | — | 17 | 2 | no | — |
| 152 | C2×D4 | — | 34 | 2 | no | — |
| 153 | C2×D4 | — | 34 | 2 | no | — |
| 154 | C2×D4 | — | 68 | 2 | no | — |
| 155 | C2×D4 | — | 68 | 2 | no | — |
| 156 | C2×D4 | — | 68 | 1 | no | — |
| 157 | C2×D4 | — | 68 | 2 | no | — |
| 158 | C2×D4 | — | 68 | 2 | no | — |
| 159 | C2×D4 | — | 68 | 1 | no | — |
| 160 | C2×D4 | — | 136 | 4 | no | — |
| 161 | C22×C4 | — | 2 | 1 | no | — |
| 162 | C22×C4 | — | 34 | 2 | no | — |
| 163 | C22×C4 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 164 | SD16 | — | 68 | 8 | no | — |
| 165 | D8 | — | 68 | 8 | no | — |
| 166 | M16 | — | 2 | 4 | no | — |
| 167 | C2×C8 | — | 2 | 2 | no | — |
| 168 | C4⋊C4 | — | 68 | 1 | no | — |
| 169 | C4⋊C4 | — | 136 | 2 | no | — |
| 170 | C22⋊C4 | — | 68 | 2 | no | — |
| 171 | C22⋊C4 | — | 68 | 4 | no | — |
| 172 | C42 | — | 2 | 1 | no | — |
| 173 | C42 | — | 136 | 2 | no | — |
| 174 | C42 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 175 | C42 | C22×#595 | 1 | 1 | yes | characteristic |
| 176 | C23 | — | 34 | 2 | no | — |
| 177 | C23 | — | 68 | 2 | no | — |
| 178 | C23 | — | 136 | 1 | no | — |
| 179 | C23 | — | 136 | 1 | no | — |
| 180 | C23 | — | 136 | 4 | no | — |
| 181 | C23 | #10587539 | 1 | 1 | yes | characteristic |
| 182 | Q8 | — | 68 | 2 | no | — |
| 183 | D4 | — | 68 | 2 | no | — |
| 184 | D4 | — | 68 | 4 | no | — |
| 185 | D4 | — | 136 | 4 | no | — |
| 186 | D4 | — | 136 | 2 | no | — |
| 187 | D4 | — | 136 | 4 | no | — |
| 188 | D4 | — | 136 | 2 | no | — |
| 189 | D4 | — | 136 | 2 | no | — |
| 190 | C2×C4 | — | 2 | 1 | no | — |
| 191 | C2×C4 | — | 2 | 2 | no | — |
| 192 | C2×C4 | — | 2 | 1 | no | — |
| 193 | C2×C4 | — | 4 | 2 | no | — |
| 194 | C2×C4 | — | 34 | 2 | no | — |
| 195 | C2×C4 | — | 68 | 2 | no | — |
| 196 | C2×C4 | — | 68 | 2 | no | — |
| 197 | C2×C4 | — | 136 | 4 | no | — |
| 198 | C2×C4 | #10587539 | 1 | 1 | yes | characteristic |
| 199 | C2×C4 | C2×C22⋊#595 | 1 | 1 | yes | characteristic |
| 200 | C8 | — | 2 | 4 | no | — |
| 201 | C22 | — | 2 | 1 | no | — |
| 202 | C22 | — | 4 | 1 | no | — |
| 203 | C22 | — | 272 | 2 | no | — |
| 204 | C22 | — | 272 | 2 | no | — |
| 205 | C22 | — | 68 | 2 | no | — |
| 206 | C22 | — | 136 | 4 | no | — |
| 207 | C22 | — | 136 | 2 | no | — |
| 208 | C22 | — | 136 | 2 | no | — |
| 209 | C22 | C2×#10587539 | 1 | 1 | yes | characteristic |
| 210 | C4 | — | 2 | 2 | no | — |
| 211 | C4 | — | 2 | 1 | no | — |
| 212 | C4 | — | 4 | 1 | no | — |
| 213 | C4 | — | 272 | 4 | no | — |
| 214 | C4 | — | 68 | 2 | no | — |
| 215 | C4 | #11763714 | 1 | 2 | yes | — |
| 216 | C2 | — | 2 | 1 | no | — |
| 217 | C2 | — | 4 | 1 | no | — |
| 218 | C2 | — | 272 | 2 | no | — |
| 219 | C2 | — | 136 | 2 | no | — |
| 220 | C2 | C2×#11763714 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545057 | C2 | semidirect |
| 2. #14543916 | C2 | semidirect |
| 6. #11763714 | C22 | semidirect |
| 9. C2×#10587560 | C4 | semidirect |
| 12. #11763182 | C4 | semidirect |
| 13. C4×M16×C17 | C4 | semidirect |
| 116. C4×M16 | #595 | semidirect |
| 146. C17 | #13585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545057 | 2 |
| #14543916 | 2 |
| #14539236 | 2 |
| #13585 | 17 |