Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
141 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 12 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 | #10596399 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #5932⋊C3 | C2 | 1 | 2 | yes | maximal |
| 3 | #73029 | — | 3 | 2 | no | maximal |
| 4 | Ω+(4,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 5 | #5933 | — | 3 | 2 | no | — |
| 6 | #5932 | D3 | 1 | 2 | yes | — |
| 7 | #5428 | — | 6 | 1 | no | — |
| 8 | #458⋊C3 | — | 3 | 2 | no | — |
| 9 | C3⋊#226 | — | 8 | 1 | no | — |
| 10 | #2201 | — | 9 | 1 | no | Sylow |
| 11 | #997 | C2×D3 | 1 | 2 | yes | — |
| 12 | #994 | — | 2 | 1 | no | — |
| 13 | #984 | — | 6 | 1 | no | — |
| 14 | A4⋊Q8 | — | 12 | 2 | no | — |
| 15 | GU(2,𝔽3) | — | 6 | 1 | no | — |
| 16 | C3×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 17 | #627 | — | 16 | 1 | no | maximal |
| 18 | #563 | — | 9 | 1 | no | — |
| 19 | #458 | — | 3 | 2 | no | — |
| 20 | #455 | — | 9 | 1 | no | — |
| 21 | #354 | — | 9 | 1 | no | — |
| 22 | #352 | — | 9 | 2 | no | — |
| 23 | #41⋊C3 | — | 6 | 1 | no | — |
| 24 | C4×A4 | — | 12 | 2 | no | — |
| 25 | SL(2,ℤ/4) | — | 12 | 2 | no | — |
| 26 | SL(2,ℤ/4) | — | 12 | 2 | no | — |
| 27 | #226 | — | 12 | 1 | no | — |
| 28 | #226 | — | 24 | 2 | no | — |
| 29 | #216 | — | 24 | 1 | no | — |
| 30 | C3⋊Dic3 | — | 16 | 1 | no | — |
| 31 | C3×Dic3 | — | 16 | 2 | no | — |
| 32 | H(5,𝔽2) | D32 | 1 | 1 | yes | characteristic |
| 33 | #137 | — | 18 | 1 | no | — |
| 34 | C4⋊Q8 | — | 18 | 1 | no | — |
| 35 | #126 | — | 18 | 2 | no | — |
| 36 | #125 | — | 18 | 1 | no | — |
| 37 | #124 | — | 9 | 1 | no | — |
| 38 | #123 | — | 9 | 2 | no | — |
| 39 | C22⋊Q8 | — | 18 | 2 | no | — |
| 40 | #104 | — | 18 | 1 | no | — |
| 41 | #100 | — | 9 | 1 | no | — |
| 42 | #99 | — | 9 | 2 | no | — |
| 43 | C2×A4 | — | 12 | 2 | no | — |
| 44 | C3×Q8 | — | 8 | 1 | no | — |
| 45 | Dic6 | — | 24 | 1 | no | — |
| 46 | Dic6 | — | 48 | 2 | no | — |
| 47 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 48 | SL(2,𝔽3) | — | 8 | 2 | no | — |
| 49 | C3⋊C8 | — | 24 | 1 | no | — |
| 50 | C2×C32 | — | 16 | 1 | no | — |
| 51 | #41 | — | 6 | 1 | no | — |
| 52 | C2×Q8 | — | 9 | 1 | no | — |
| 53 | C2×Q8 | — | 18 | 1 | no | — |
| 54 | C2×D4 | — | 9 | 1 | no | — |
| 55 | C22×C4 | — | 3 | 2 | no | — |
| 56 | Q16 | — | 36 | 1 | no | — |
| 57 | SD16 | — | 36 | 1 | no | — |
| 58 | M16 | — | 18 | 1 | no | — |
| 59 | C4⋊C4 | — | 18 | 2 | no | — |
| 60 | C4⋊C4 | — | 18 | 1 | no | — |
| 61 | C4⋊C4 | — | 18 | 2 | no | — |
| 62 | C4⋊C4 | — | 18 | 2 | no | — |
| 63 | C4⋊C4 | — | 18 | 1 | no | — |
| 64 | C22⋊C4 | — | 9 | 2 | no | — |
| 65 | C22⋊C4 | — | 18 | 2 | no | — |
| 66 | C22⋊C4 | — | 18 | 2 | no | — |
| 67 | C42 | — | 9 | 1 | no | — |
| 68 | C42 | — | 18 | 1 | no | — |
| 69 | A4 | — | 12 | 2 | no | — |
| 70 | C3×C4 | — | 24 | 1 | no | — |
| 71 | C3×C4 | — | 48 | 2 | no | — |
| 72 | Dic3 | — | 16 | 2 | no | — |
| 73 | Dic3 | — | 48 | 1 | no | — |
| 74 | Dic3 | — | 48 | 2 | no | — |
| 75 | C32 | — | 16 | 1 | no | Sylow |
| 76 | C23 | — | 3 | 2 | no | — |
| 77 | Q8 | — | 2 | 1 | no | — |
| 78 | Q8 | — | 36 | 1 | no | — |
| 79 | Q8 | — | 72 | 1 | no | — |
| 80 | D4 | — | 18 | 1 | no | — |
| 81 | C2×C4 | — | 9 | 1 | no | — |
| 82 | C2×C4 | — | 18 | 2 | no | — |
| 83 | C2×C4 | — | 18 | 1 | no | — |
| 84 | C2×C4 | — | 18 | 2 | no | — |
| 85 | C2×C4 | — | 18 | 1 | no | — |
| 86 | C8 | — | 36 | 1 | no | — |
| 87 | C2×C3 | — | 8 | 1 | no | — |
| 88 | C2×C3 | — | 16 | 2 | no | — |
| 89 | C22 | — | 9 | 1 | no | — |
| 90 | C22 | — | 12 | 2 | no | — |
| 91 | C4 | — | 6 | 1 | no | — |
| 92 | C4 | — | 12 | 2 | no | — |
| 93 | C4 | — | 36 | 1 | no | — |
| 94 | C4 | — | 36 | 2 | no | — |
| 95 | C4 | — | 36 | 1 | no | — |
| 96 | C3 | — | 8 | 1 | no | — |
| 97 | C3 | — | 16 | 2 | no | — |
| 98 | C2 | — | 18 | 1 | no | — |
| 99 | C2 | (#1020⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2 | (#1020⋊C3)⋊C2 |
| commutator, prime radical, cosocle, hypocenter | Ω+(4,𝔽3) | C22 |
| Fitting | H(5,𝔽2) | D32 |
| LCS | G ▷ Ω+(4,𝔽3) | |
| UCS | C1 ◁ C2 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596399 | 2 |
| #5932⋊C3 | 2 |
| #73029 | 3 |
| #627 | 16 |