Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
158 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 22 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 | #14543923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14543787 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14528079 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11763714 | — | 2 | 1 | no | — |
| 5 | #11763701 | — | 2 | 1 | no | — |
| 6 | #11763557 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | #11763198 | — | 2 | 1 | no | — |
| 8 | #11763175 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11762548 | — | 2 | 1 | no | — |
| 10 | C17×#330 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C17×#125 | C2×C4 | 1 | 1 | yes | characteristic |
| 12 | C2×D136 | — | 4 | 1 | no | — |
| 13 | C2×#63219 | — | 4 | 1 | no | — |
| 14 | #10587582 | — | 4 | 1 | no | — |
| 15 | #10587581 | — | 4 | 1 | no | — |
| 16 | #10587580 | — | 4 | 1 | no | — |
| 17 | #10587561 | — | 2 | 1 | no | — |
| 18 | #10587560 | D4 | 1 | 1 | yes | characteristic |
| 19 | #10587539 | — | 4 | 1 | no | — |
| 20 | #10587538 | — | 4 | 1 | no | — |
| 21 | C17×#97 | — | 2 | 1 | no | — |
| 22 | #10587480 | — | 4 | 1 | no | — |
| 23 | #10587474 | D4 | 1 | 1 | yes | characteristic |
| 24 | C2×D68 | — | 2 | 1 | no | — |
| 25 | C2×D68 | — | 2 | 1 | no | — |
| 26 | C2×D68 | — | 4 | 1 | no | — |
| 27 | C2×D68 | — | 4 | 1 | no | — |
| 28 | C2×C4×D17 | — | 4 | 1 | no | — |
| 29 | C2×Dic34 | — | 2 | 1 | no | — |
| 30 | C22⋊#595 | — | 8 | 1 | no | — |
| 31 | C2×C8×C17 | — | 4 | 1 | no | — |
| 32 | C4⋊C4×C17 | — | 2 | 1 | no | — |
| 33 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 34 | C42×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 35 | #63227 | — | 4 | 1 | no | — |
| 36 | #63227 | — | 4 | 1 | no | — |
| 37 | #63227 | — | 4 | 1 | no | — |
| 38 | #63225 | — | 4 | 1 | no | — |
| 39 | C2×#3622 | — | 2 | 1 | no | — |
| 40 | D136 | — | 8 | 2 | no | — |
| 41 | #63219 | — | 8 | 2 | no | — |
| 42 | #63216 | — | 4 | 2 | no | — |
| 43 | #7523 | — | 17 | 1 | no | maximal, Sylow |
| 44 | C22×D17 | — | 4 | 1 | no | — |
| 45 | C22×D17 | — | 4 | 1 | no | — |
| 46 | C2×#595 | — | 16 | 1 | no | — |
| 47 | C2×C4×C17 | — | 2 | 1 | no | — |
| 48 | C2×C4×C17 | — | 4 | 1 | no | — |
| 49 | C2×C4×C17 | #99 | 1 | 1 | yes | characteristic |
| 50 | C2×Dic17 | — | 4 | 1 | no | — |
| 51 | D68 | — | 8 | 1 | no | — |
| 52 | D68 | — | 8 | 1 | no | — |
| 53 | D68 | — | 8 | 1 | no | — |
| 54 | D68 | — | 8 | 1 | no | — |
| 55 | D68 | — | 16 | 1 | no | — |
| 56 | C4×D17 | — | 16 | 1 | no | — |
| 57 | Dic34 | — | 8 | 1 | no | — |
| 58 | C8×C17 | — | 4 | 2 | no | — |
| 59 | #3622 | — | 4 | 1 | no | — |
| 60 | #1656 | — | 17 | 1 | no | — |
| 61 | #1412 | — | 17 | 1 | no | — |
| 62 | #1355 | — | 17 | 1 | no | — |
| 63 | C22×C17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 64 | C2×D17 | — | 8 | 1 | no | — |
| 65 | C2×D17 | — | 8 | 1 | no | — |
| 66 | C2×D17 | — | 8 | 1 | no | — |
| 67 | C2×D17 | — | 8 | 1 | no | — |
| 68 | C2×D17 | — | 16 | 1 | no | — |
| 69 | #595 | — | 32 | 1 | no | — |
| 70 | C4×C17 | — | 2 | 1 | no | — |
| 71 | C4×C17 | — | 4 | 1 | no | — |
| 72 | C4×C17 | — | 8 | 1 | no | — |
| 73 | Dic17 | — | 8 | 1 | no | — |
| 74 | #562 | — | 17 | 1 | no | — |
| 75 | #496 | — | 34 | 1 | no | — |
| 76 | #490 | — | 17 | 1 | no | — |
| 77 | #353 | — | 34 | 1 | no | — |
| 78 | #347 | — | 34 | 1 | no | — |
| 79 | #330 | #595 | 1 | 1 | yes | characteristic, complemented |
| 80 | #329 | — | 34 | 1 | no | — |
| 81 | C2×C17 | — | 2 | 1 | no | — |
| 82 | C2×C17 | #1404 | 1 | 1 | yes | characteristic |
| 83 | D17 | — | 16 | 1 | no | — |
| 84 | D17 | — | 16 | 1 | no | — |
| 85 | C2×SD16 | — | 68 | 1 | no | — |
| 86 | C2×D8 | — | 68 | 1 | no | — |
| 87 | #127 | — | 17 | 1 | no | — |
| 88 | #125 | C2×#595 | 1 | 1 | yes | characteristic |
| 89 | #124 | — | 34 | 1 | no | — |
| 90 | #123 | — | 68 | 1 | no | — |
| 91 | C22⋊Q8 | — | 68 | 1 | no | — |
| 92 | #121 | — | 68 | 1 | no | — |
| 93 | M32 | — | 68 | 1 | no | — |
| 94 | #102 | — | 68 | 1 | no | — |
| 95 | #99 | — | 68 | 1 | no | — |
| 96 | #97 | — | 2 | 1 | no | — |
| 97 | #97 | — | 17 | 1 | no | — |
| 98 | C17 | #7523 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 99 | C2×Q8 | — | 34 | 1 | no | — |
| 100 | C2×D4 | — | 34 | 1 | no | — |
| 101 | C2×D4 | — | 34 | 1 | no | — |
| 102 | C2×D4 | — | 68 | 1 | no | — |
| 103 | C2×D4 | — | 68 | 1 | no | — |
| 104 | C22×C4 | — | 68 | 1 | no | — |
| 105 | SD16 | — | 136 | 2 | no | — |
| 106 | D8 | — | 136 | 2 | no | — |
| 107 | C2×C8 | — | 4 | 1 | no | — |
| 108 | C2×C8 | — | 34 | 1 | no | — |
| 109 | C4⋊C4 | — | 2 | 1 | no | — |
| 110 | C4⋊C4 | — | 4 | 1 | no | — |
| 111 | C4⋊C4 | — | 68 | 1 | no | — |
| 112 | C22⋊C4 | — | 68 | 1 | no | — |
| 113 | C22⋊C4 | — | 68 | 1 | no | — |
| 114 | C22⋊C4 | — | 68 | 1 | no | — |
| 115 | C22⋊C4 | — | 136 | 1 | no | — |
| 116 | C42 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 117 | C16 | — | 68 | 2 | no | — |
| 118 | C23 | — | 68 | 1 | no | — |
| 119 | C23 | — | 68 | 1 | no | — |
| 120 | Q8 | — | 136 | 1 | no | — |
| 121 | D4 | — | 272 | 1 | no | — |
| 122 | D4 | — | 136 | 1 | no | — |
| 123 | D4 | — | 136 | 1 | no | — |
| 124 | D4 | — | 136 | 1 | no | — |
| 125 | D4 | — | 136 | 1 | no | — |
| 126 | C2×C4 | — | 2 | 1 | no | — |
| 127 | C2×C4 | — | 4 | 1 | no | — |
| 128 | C2×C4 | — | 272 | 1 | no | — |
| 129 | C2×C4 | — | 272 | 1 | no | — |
| 130 | C2×C4 | — | 68 | 1 | no | — |
| 131 | C2×C4 | #10587539 | 1 | 1 | yes | characteristic |
| 132 | C8 | — | 4 | 2 | no | — |
| 133 | C8 | — | 68 | 1 | no | — |
| 134 | C22 | — | 272 | 1 | no | — |
| 135 | C22 | — | 136 | 1 | no | — |
| 136 | C22 | — | 136 | 1 | no | — |
| 137 | C22 | — | 136 | 1 | no | — |
| 138 | C22 | — | 136 | 1 | no | — |
| 139 | C22 | #11763710 | 1 | 1 | yes | characteristic |
| 140 | C4 | — | 2 | 1 | no | — |
| 141 | C4 | — | 4 | 1 | no | — |
| 142 | C4 | — | 8 | 1 | no | — |
| 143 | C4 | — | 544 | 1 | no | — |
| 144 | C4 | — | 136 | 1 | no | — |
| 145 | C2 | — | 2 | 1 | no | — |
| 146 | C2 | — | 272 | 1 | no | — |
| 147 | C2 | — | 272 | 1 | no | — |
| 148 | C2 | #14543908 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14543923 | C2 | semidirect |
| 2. #14543787 | C2 | semidirect |
| 6. #11763557 | C4 | semidirect |
| 10. C17×#330 | C4 | semidirect |
| 79. #330 | #595 | semidirect |
| 98. C17 | #7523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543923 | 2 |
| #14543787 | 2 |
| #14528079 | 2 |
| #7523 | 17 |