Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2234 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 2234 conjugacy classes of subgroups — too many to draw. Only its 750 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 | #10596760 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10596648 | C2 | 1 | 10 | yes | maximal, complemented |
| 3 | #10596647 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #10596644 | C2 | 1 | 5 | yes | maximal, complemented |
| 5 | C2×#64289 | C2 | 1 | 5 | yes | maximal, complemented |
| 6 | C32×2−1+4 | C4 | 1 | 1 | yes | characteristic |
| 7 | #64366 | C4 | 1 | 10 | yes | — |
| 8 | #41×C3⋊D3 | C22 | 1 | 10 | yes | — |
| 9 | #64364 | C4 | 1 | 5 | yes | — |
| 10 | C2×#3832 | C22 | 1 | 5 | yes | — |
| 11 | #64289 | C22 | 1 | 10 | yes | complemented |
| 12 | #64289 | C22 | 1 | 20 | yes | complemented |
| 13 | #64289 | C22 | 1 | 10 | yes | complemented |
| 14 | #64287 | C22 | 1 | 10 | yes | complemented |
| 15 | #64287 | C22 | 1 | 30 | yes | complemented |
| 16 | #64283 | C22 | 1 | 30 | yes | complemented |
| 17 | C2×#3788 | C22 | 1 | 15 | yes | complemented |
| 18 | C2×#3787 | C22 | 1 | 15 | yes | complemented |
| 19 | #5968 | — | 6 | 2 | no | — |
| 20 | C32×#41 | C2×C4 | 1 | 10 | yes | — |
| 21 | C2×C32×Q8 | C2×C4 | 1 | 5 | yes | — |
| 22 | #3832 | C2×C4 | 1 | 20 | yes | — |
| 23 | #3832 | C23 | 1 | 10 | yes | — |
| 24 | Q8×C3⋊D3 | C2×C4 | 1 | 10 | yes | — |
| 25 | #3830 | C23 | 1 | 10 | yes | — |
| 26 | D4×C3⋊D3 | C2×C4 | 1 | 30 | yes | — |
| 27 | #3828 | C2×C4 | 1 | 30 | yes | — |
| 28 | C2×C4⋊(C3⋊D3) | C2×C4 | 1 | 15 | yes | — |
| 29 | C2×C4×C3⋊D3 | C23 | 1 | 15 | yes | — |
| 30 | #3792 | C23 | 1 | 20 | yes | — |
| 31 | C2×#622 | C23 | 1 | 5 | yes | — |
| 32 | C2×#622 | C23 | 1 | 15 | yes | — |
| 33 | #3788 | C23 | 1 | 30 | yes | — |
| 34 | #3788 | C23 | 1 | 10 | yes | — |
| 35 | #3787 | C23 | 1 | 10 | yes | — |
| 36 | #3787 | C23 | 1 | 30 | yes | — |
| 37 | #3573 | — | 9 | 1 | no | maximal, Sylow |
| 38 | C3×2−1+4 | — | 2 | 2 | no | — |
| 39 | #1009 | — | 6 | 20 | no | — |
| 40 | D3×#41 | — | 6 | 20 | no | — |
| 41 | #1007 | — | 6 | 10 | no | — |
| 42 | C2×#239 | — | 6 | 10 | no | — |
| 43 | C22×C3⋊D3 | C22×C4 | 1 | 15 | yes | — |
| 44 | C32×Q8 | C22×C4 | 1 | 10 | yes | — |
| 45 | C32×D4 | C22×C4 | 1 | 10 | yes | — |
| 46 | C2×C32×C4 | C22×C4 | 1 | 15 | yes | — |
| 47 | #638 | C22×C4 | 1 | 20 | yes | — |
| 48 | C2×C3⋊Dic3 | C24 | 1 | 5 | yes | — |
| 49 | C4⋊(C3⋊D3) | C22×C4 | 1 | 30 | yes | — |
| 50 | C4×C3⋊D3 | C22×C4 | 1 | 30 | yes | — |
| 51 | C4×C3⋊D3 | C24 | 1 | 10 | yes | — |
| 52 | #634 | C22×C4 | 1 | 10 | yes | — |
| 53 | #622 | C24 | 1 | 1 | yes | characteristic |
| 54 | #622 | C24 | 1 | 5 | yes | — |
| 55 | #622 | C24 | 1 | 10 | yes | — |
| 56 | #585 | — | 9 | 1 | no | — |
| 57 | #568 | — | 9 | 5 | no | — |
| 58 | #568 | — | 9 | 10 | no | — |
| 59 | C2×#131 | — | 9 | 5 | no | — |
| 60 | C2×#131 | — | 9 | 10 | no | — |
| 61 | C3×#41 | — | 2 | 20 | no | — |
| 62 | C2×C3×Q8 | — | 2 | 10 | no | — |
| 63 | #239 | — | 6 | 20 | no | — |
| 64 | #239 | — | 6 | 40 | no | — |
| 65 | D3×Q8 | — | 6 | 20 | no | — |
| 66 | #237 | — | 6 | 20 | no | — |
| 67 | D3×D4 | — | 6 | 60 | no | — |
| 68 | #235 | — | 6 | 60 | no | — |
| 69 | C2×D12 | — | 6 | 30 | no | — |
| 70 | C2×C4×D3 | — | 6 | 30 | no | — |
| 71 | C22×C32 | C23×C4 | 1 | 5 | yes | — |
| 72 | C2×C3⋊D3 | — | 4 | 15 | no | — |
| 73 | C2×C3⋊D3 | C23×C4 | 1 | 10 | yes | — |
| 74 | C32×C4 | C23×C4 | 1 | 10 | yes | — |
| 75 | C3⋊Dic3 | C23×C4 | 1 | 5 | yes | — |
| 76 | C3⋊Dic3 | C25 | 1 | 1 | yes | characteristic |
| 77 | 2−1+4 | — | 9 | 5 | no | — |
| 78 | 2−1+4 | #157 | 1 | 1 | yes | characteristic |
| 79 | H(5,𝔽2) | — | 9 | 10 | no | — |
| 80 | C2×#41 | — | 9 | 10 | no | — |
| 81 | C2×#41 | — | 9 | 5 | no | — |
| 82 | #131 | — | 9 | 10 | no | — |
| 83 | #131 | — | 9 | 30 | no | — |
| 84 | #131 | — | 9 | 10 | no | — |
| 85 | #131 | — | 9 | 20 | no | — |
| 86 | #131 | — | 9 | 10 | no | — |
| 87 | C2×M16 | — | 9 | 15 | no | — |
| 88 | C2×M16 | — | 9 | 30 | no | — |
| 89 | C22×C8 | — | 9 | 15 | no | — |
| 90 | C22×D3 | — | 6 | 30 | no | — |
| 91 | C3×Q8 | — | 2 | 20 | no | — |
| 92 | C3×D4 | — | 2 | 20 | no | — |
| 93 | C2×C3×C4 | — | 2 | 30 | no | — |
| 94 | #67 | — | 6 | 40 | no | — |
| 95 | C2×Dic3 | — | 6 | 10 | no | — |
| 96 | D12 | — | 6 | 60 | no | — |
| 97 | C4×D3 | — | 6 | 60 | no | — |
| 98 | C4×D3 | — | 6 | 20 | no | — |
| 99 | Dic6 | — | 6 | 20 | no | — |
| 100 | C2×C32 | — | 2 | 5 | no | — |
| 101 | C2×C32 | C24×C4 | 1 | 1 | yes | characteristic |
| 102 | C3⋊D3 | — | 2 | 10 | no | — |
| 103 | #41 | — | 9 | 10 | no | — |
| 104 | #41 | — | 9 | 20 | no | — |
| 105 | #41 | — | 9 | 10 | no | — |
| 106 | #41 | — | 9 | 30 | no | — |
| 107 | #41 | C2×#157 | 1 | 10 | yes | — |
| 108 | C2×Q8 | — | 9 | 10 | no | — |
| 109 | C2×Q8 | C2×#157 | 1 | 5 | yes | — |
| 110 | C2×D4 | — | 9 | 30 | no | — |
| 111 | C2×D4 | — | 9 | 15 | no | — |
| 112 | C22×C4 | — | 9 | 15 | no | — |
| 113 | M16 | — | 9 | 30 | no | — |
| 114 | M16 | — | 9 | 10 | no | — |
| 115 | M16 | — | 9 | 20 | no | — |
| 116 | C2×C8 | — | 9 | 10 | no | — |
| 117 | C2×C8 | — | 9 | 5 | no | — |
| 118 | C2×C8 | — | 9 | 30 | no | — |
| 119 | C2×C8 | — | 9 | 15 | no | — |
| 120 | C22×C3 | — | 2 | 10 | no | — |
| 121 | C2×D3 | — | 6 | 20 | no | — |
| 122 | C2×D3 | — | 24 | 30 | no | — |
| 123 | C3×C4 | — | 2 | 20 | no | — |
| 124 | Dic3 | — | 6 | 10 | no | — |
| 125 | Dic3 | — | 6 | 2 | no | — |
| 126 | C32 | #3573 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 127 | C23 | — | 9 | 15 | no | — |
| 128 | Q8 | — | 9 | 10 | no | — |
| 129 | Q8 | C22×#157 | 1 | 10 | yes | — |
| 130 | D4 | — | 9 | 20 | no | — |
| 131 | D4 | — | 9 | 30 | no | — |
| 132 | D4 | C22×#157 | 1 | 10 | yes | — |
| 133 | C2×C4 | — | 9 | 5 | no | — |
| 134 | C2×C4 | — | 9 | 10 | no | — |
| 135 | C2×C4 | — | 9 | 30 | no | — |
| 136 | C2×C4 | C22×#157 | 1 | 15 | yes | — |
| 137 | C8 | — | 9 | 1 | no | — |
| 138 | C8 | — | 9 | 10 | no | — |
| 139 | C8 | — | 9 | 5 | no | — |
| 140 | C2×C3 | — | 2 | 2 | no | — |
| 141 | C2×C3 | — | 4 | 10 | no | — |
| 142 | D3 | — | 12 | 20 | no | — |
| 143 | C22 | — | 9 | 10 | no | — |
| 144 | C22 | — | 36 | 15 | no | — |
| 145 | C22 | C23×#157 | 1 | 5 | yes | — |
| 146 | C4 | — | 9 | 1 | no | — |
| 147 | C4 | — | 9 | 5 | no | — |
| 148 | C4 | C23×#157 | 1 | 10 | yes | — |
| 149 | C3 | — | 2 | 2 | no | — |
| 150 | C2 | — | 2 | 5 | no | — |
| 151 | C2 | — | 18 | 10 | no | — |
| 152 | C2 | C24×#157 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10596648 | C2 | semidirect |
| 3. #10596647 | C2 | semidirect |
| 4. #10596644 | C2 | semidirect |
| 5. C2×#64289 | C2 | semidirect |
| 11. #64289 | C22 | semidirect |
| 12. #64289 | C22 | semidirect |
| 13. #64289 | C22 | semidirect |
| 14. #64287 | C22 | semidirect |
| 15. #64287 | C22 | semidirect |
| 16. #64283 | C22 | semidirect |
| 17. C2×#3788 | C22 | semidirect |
| 18. C2×#3787 | C22 | semidirect |
| 126. C32 | #3573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596760 | 2 |
| #10596648 | 2 |
| #10596647 | 2 |
| #10596644 | 2 |
| C2×#64289 | 2 |
| #3573 | 9 |