Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
164 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 164 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 | #14543920 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14543918 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14528451 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11763720 | — | 2 | 1 | no | — |
| 5 | #11763714 | — | 2 | 1 | no | — |
| 6 | #11763185 | — | 2 | 1 | no | — |
| 7 | #11763182 | C22 | 1 | 1 | yes | characteristic |
| 8 | #11763155 | — | 2 | 1 | no | — |
| 9 | #11762530 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C17×#493 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×D8×C17 | — | 4 | 1 | no | — |
| 12 | C17×#127 | — | 2 | 1 | no | — |
| 13 | C2×#63228 | — | 4 | 2 | no | — |
| 14 | C2×#63219 | — | 4 | 1 | no | — |
| 15 | #10587560 | D4 | 1 | 1 | yes | characteristic |
| 16 | #10587555 | D4 | 1 | 1 | yes | characteristic |
| 17 | #10587545 | — | 4 | 1 | no | — |
| 18 | #10587539 | — | 4 | 1 | no | — |
| 19 | C4×C8×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 20 | #10587503 | — | 4 | 2 | no | — |
| 21 | C4×#3622 | — | 2 | 1 | no | — |
| 22 | C2×D4×C17 | — | 4 | 1 | no | — |
| 23 | C2×D4×C17 | — | 4 | 1 | no | — |
| 24 | C2×D4×C17 | — | 4 | 1 | no | — |
| 25 | C2×D68 | — | 2 | 1 | no | — |
| 26 | C2×D68 | — | 4 | 1 | no | — |
| 27 | C2×Dic34 | — | 2 | 1 | no | — |
| 28 | C22⋊#595 | — | 8 | 1 | no | — |
| 29 | #63247 | — | 8 | 1 | no | — |
| 30 | D8×C17 | — | 8 | 2 | no | — |
| 31 | C2×C8×C17 | — | 2 | 1 | no | — |
| 32 | C42×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 33 | #63228 | — | 8 | 4 | no | — |
| 34 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 35 | C2×#3622 | — | 2 | 2 | no | — |
| 36 | #63219 | — | 8 | 2 | no | — |
| 37 | #7527 | — | 17 | 1 | no | maximal, Sylow |
| 38 | C23×C17 | — | 8 | 1 | no | — |
| 39 | C22×D17 | — | 4 | 1 | no | — |
| 40 | C2×#595 | — | 16 | 1 | no | — |
| 41 | D4×C17 | — | 8 | 2 | no | — |
| 42 | D4×C17 | — | 8 | 2 | no | — |
| 43 | D4×C17 | — | 8 | 2 | no | — |
| 44 | C2×C4×C17 | — | 2 | 1 | no | — |
| 45 | C2×C4×C17 | #99 | 1 | 1 | yes | characteristic |
| 46 | C2×Dic17 | — | 4 | 1 | no | — |
| 47 | D68 | — | 8 | 1 | no | — |
| 48 | D68 | — | 8 | 2 | no | — |
| 49 | Dic34 | — | 8 | 1 | no | — |
| 50 | #3624 | — | 16 | 1 | no | — |
| 51 | C8×C17 | — | 2 | 2 | no | — |
| 52 | #3622 | — | 4 | 2 | no | — |
| 53 | #1721 | — | 17 | 1 | no | — |
| 54 | #1410 | — | 17 | 1 | no | — |
| 55 | #1409 | — | 17 | 1 | no | — |
| 56 | C22×C17 | — | 16 | 1 | no | — |
| 57 | C22×C17 | — | 16 | 1 | no | — |
| 58 | C22×C17 | — | 16 | 1 | no | — |
| 59 | C22×C17 | #353 | 1 | 1 | yes | characteristic |
| 60 | C2×D17 | — | 8 | 1 | no | — |
| 61 | C2×D17 | — | 16 | 1 | no | — |
| 62 | #595 | — | 32 | 1 | no | — |
| 63 | C4×C17 | — | 2 | 2 | no | — |
| 64 | C4×C17 | — | 2 | 1 | no | — |
| 65 | Dic17 | — | 8 | 1 | no | — |
| 66 | #493 | — | 34 | 1 | no | — |
| 67 | #493 | #595 | 1 | 1 | yes | characteristic, complemented |
| 68 | #492 | — | 17 | 1 | no | — |
| 69 | #486 | — | 34 | 1 | no | — |
| 70 | #356 | — | 34 | 1 | no | — |
| 71 | #353 | — | 34 | 1 | no | — |
| 72 | #322 | — | 17 | 1 | no | — |
| 73 | C2×C17 | — | 2 | 1 | no | — |
| 74 | C2×C17 | — | 32 | 1 | no | — |
| 75 | C2×C17 | #1408 | 1 | 1 | yes | characteristic |
| 76 | D17 | — | 16 | 1 | no | — |
| 77 | C2×SD16 | — | 68 | 1 | no | — |
| 78 | C2×D8 | — | 4 | 1 | no | — |
| 79 | C2×D8 | — | 68 | 2 | no | — |
| 80 | C4⋊Q8 | — | 17 | 1 | no | — |
| 81 | #127 | — | 2 | 1 | no | — |
| 82 | #127 | — | 17 | 1 | no | — |
| 83 | #102 | — | 68 | 2 | no | — |
| 84 | #101 | — | 68 | 1 | no | — |
| 85 | #99 | — | 68 | 1 | no | — |
| 86 | C4×C8 | — | 34 | 1 | no | — |
| 87 | C4×C8 | C2×#595 | 1 | 1 | yes | characteristic |
| 88 | C17 | #7527 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 89 | C2×Q8 | — | 34 | 1 | no | — |
| 90 | C2×D4 | — | 4 | 1 | no | — |
| 91 | C2×D4 | — | 4 | 1 | no | — |
| 92 | C2×D4 | — | 4 | 1 | no | — |
| 93 | C2×D4 | — | 34 | 1 | no | — |
| 94 | C2×D4 | — | 68 | 1 | no | — |
| 95 | SD16 | — | 136 | 2 | no | — |
| 96 | D8 | — | 8 | 2 | no | — |
| 97 | D8 | — | 136 | 4 | no | — |
| 98 | M16 | — | 136 | 1 | no | — |
| 99 | C2×C8 | — | 2 | 1 | no | — |
| 100 | C2×C8 | — | 34 | 2 | no | — |
| 101 | C4⋊C4 | — | 68 | 1 | no | — |
| 102 | C22⋊C4 | — | 136 | 1 | no | — |
| 103 | C42 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 104 | C23 | — | 8 | 1 | no | — |
| 105 | C23 | — | 68 | 1 | no | — |
| 106 | Q8 | — | 136 | 1 | no | — |
| 107 | D4 | — | 8 | 2 | no | — |
| 108 | D4 | — | 8 | 2 | no | — |
| 109 | D4 | — | 8 | 2 | no | — |
| 110 | D4 | — | 136 | 2 | no | — |
| 111 | D4 | — | 136 | 1 | no | — |
| 112 | C2×C4 | — | 2 | 1 | no | — |
| 113 | C2×C4 | — | 272 | 1 | no | — |
| 114 | C2×C4 | — | 68 | 1 | no | — |
| 115 | C2×C4 | #10587551 | 1 | 1 | yes | characteristic |
| 116 | C8 | — | 2 | 2 | no | — |
| 117 | C8 | — | 272 | 1 | no | — |
| 118 | C8 | — | 68 | 2 | no | — |
| 119 | C22 | — | 16 | 1 | no | — |
| 120 | C22 | — | 16 | 1 | no | — |
| 121 | C22 | — | 16 | 1 | no | — |
| 122 | C22 | — | 272 | 1 | no | — |
| 123 | C22 | — | 136 | 1 | no | — |
| 124 | C22 | #11763713 | 1 | 1 | yes | characteristic |
| 125 | C4 | — | 2 | 2 | no | — |
| 126 | C4 | — | 2 | 1 | no | — |
| 127 | C4 | — | 544 | 1 | no | — |
| 128 | C4 | — | 136 | 1 | no | — |
| 129 | C2 | — | 2 | 1 | no | — |
| 130 | C2 | — | 272 | 1 | no | — |
| 131 | C2 | — | 32 | 1 | no | — |
| 132 | C2 | #14543915 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14543920 | C2 | semidirect |
| 2. #14543918 | C2 | semidirect |
| 9. #11762530 | C4 | semidirect |
| 10. C17×#493 | C4 | semidirect |
| 67. #493 | #595 | semidirect |
| 88. C17 | #7527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543920 | 2 |
| #14543918 | 2 |
| #14528451 | 2 |
| #7527 | 17 |