Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 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 | #11718413 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11718303 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11718301 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #88254 | C4 | 1 | 1 | yes | characteristic |
| 5 | #88198 | C22 | 1 | 1 | yes | characteristic |
| 6 | #88163 | — | 2 | 1 | no | — |
| 7 | #88113 | — | 2 | 1 | no | — |
| 8 | #88112 | — | 2 | 1 | no | — |
| 9 | C13×#101 | C4 | 1 | 1 | yes | characteristic |
| 10 | #88065 | — | 2 | 1 | no | — |
| 11 | C2×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 12 | #6131 | — | 4 | 1 | no | — |
| 13 | Q8×D13 | — | 4 | 1 | no | — |
| 14 | #6127 | — | 2 | 1 | no | — |
| 15 | #6127 | — | 4 | 1 | no | — |
| 16 | C2×Dic26 | D4 | 1 | 1 | yes | characteristic |
| 17 | #6122 | — | 4 | 1 | no | — |
| 18 | C2×#1057 | — | 4 | 1 | no | — |
| 19 | C13×M16 | — | 2 | 1 | no | — |
| 20 | #6101 | — | 4 | 1 | no | — |
| 21 | C4×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 22 | Dic52 | — | 4 | 1 | no | — |
| 23 | #6095 | — | 4 | 1 | no | — |
| 24 | #1405 | — | 13 | 1 | no | maximal, Sylow |
| 25 | Q8×C13 | — | 4 | 1 | no | — |
| 26 | C2×C4×C13 | — | 2 | 1 | no | — |
| 27 | C2×C4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 28 | C22⋊D13 | — | 4 | 1 | no | — |
| 29 | C2×Dic13 | — | 2 | 1 | no | — |
| 30 | C2×Dic13 | — | 2 | 1 | no | — |
| 31 | D52 | — | 2 | 1 | no | — |
| 32 | D52 | — | 4 | 1 | no | — |
| 33 | C4×D13 | — | 4 | 1 | no | — |
| 34 | C4×D13 | — | 4 | 2 | no | — |
| 35 | Dic26 | — | 2 | 1 | no | — |
| 36 | Dic26 | — | 4 | 1 | no | — |
| 37 | Dic26 | — | 4 | 1 | no | — |
| 38 | #1057 | — | 8 | 1 | no | — |
| 39 | #1057 | — | 8 | 1 | no | — |
| 40 | C8×C13 | — | 4 | 1 | no | — |
| 41 | #456 | — | 13 | 1 | no | — |
| 42 | #356 | — | 13 | 1 | no | — |
| 43 | #333 | — | 13 | 1 | no | — |
| 44 | C22×C13 | #99 | 1 | 1 | yes | characteristic |
| 45 | C2×D13 | — | 4 | 1 | no | — |
| 46 | C4×C13 | — | 2 | 1 | no | — |
| 47 | C4×C13 | — | 4 | 1 | no | — |
| 48 | Dic13 | — | 2 | 1 | no | — |
| 49 | Dic13 | — | 2 | 1 | no | — |
| 50 | Dic13 | — | 4 | 1 | no | — |
| 51 | Dic13 | — | 4 | 1 | no | — |
| 52 | 2−1+4 | — | 13 | 1 | no | — |
| 53 | #137 | — | 26 | 1 | no | — |
| 54 | C4⋊Q8 | — | 13 | 1 | no | — |
| 55 | C4⋊C8 | — | 26 | 1 | no | — |
| 56 | #104 | — | 26 | 1 | no | — |
| 57 | #101 | — | 26 | 1 | no | — |
| 58 | #101 | #261 | 1 | 1 | yes | characteristic |
| 59 | C2×C13 | — | 2 | 1 | no | — |
| 60 | C2×C13 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 61 | D13 | — | 8 | 1 | no | — |
| 62 | #41 | — | 26 | 1 | no | — |
| 63 | #41 | — | 52 | 1 | no | — |
| 64 | #41 | — | 52 | 1 | no | — |
| 65 | C2×Q8 | — | 13 | 1 | no | — |
| 66 | C2×Q8 | — | 52 | 1 | no | — |
| 67 | C2×Q8 | C2×#261 | 1 | 1 | yes | characteristic |
| 68 | Q16 | — | 52 | 1 | no | — |
| 69 | SD16 | — | 52 | 1 | no | — |
| 70 | M16 | — | 2 | 1 | no | — |
| 71 | M16 | — | 52 | 1 | no | — |
| 72 | C2×C8 | — | 52 | 1 | no | — |
| 73 | C4⋊C4 | — | 52 | 1 | no | — |
| 74 | C42 | — | 13 | 1 | no | — |
| 75 | C13 | #1405 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 76 | Q8 | — | 4 | 1 | no | — |
| 77 | Q8 | — | 26 | 1 | no | — |
| 78 | Q8 | — | 52 | 1 | no | — |
| 79 | Q8 | — | 52 | 1 | no | — |
| 80 | D4 | — | 26 | 1 | no | — |
| 81 | D4 | — | 52 | 1 | no | — |
| 82 | D4 | — | 52 | 1 | no | — |
| 83 | C2×C4 | — | 2 | 1 | no | — |
| 84 | C2×C4 | — | 26 | 1 | no | — |
| 85 | C2×C4 | — | 26 | 1 | no | — |
| 86 | C2×C4 | — | 52 | 1 | no | — |
| 87 | C2×C4 | — | 52 | 2 | no | — |
| 88 | C2×C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 89 | C8 | — | 4 | 1 | no | — |
| 90 | C8 | — | 104 | 1 | no | — |
| 91 | C8 | — | 104 | 1 | no | — |
| 92 | C22 | — | 52 | 1 | no | — |
| 93 | C22 | #88107 | 1 | 1 | yes | characteristic |
| 94 | C4 | — | 2 | 1 | no | — |
| 95 | C4 | — | 4 | 1 | no | — |
| 96 | C4 | — | 26 | 1 | no | — |
| 97 | C4 | — | 26 | 1 | no | — |
| 98 | C4 | — | 52 | 1 | no | — |
| 99 | C4 | — | 52 | 1 | no | — |
| 100 | C2 | — | 2 | 1 | no | — |
| 101 | C2 | — | 104 | 1 | no | — |
| 102 | C2 | #11718236 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11718303 | C2 | semidirect |
| 3. #11718301 | C2 | semidirect |
| 75. C13 | #1405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718413 | 2 |
| #11718303 | 2 |
| #11718301 | 2 |
| #1405 | 13 |