Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
744 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C32×H(3,𝔽4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10592761 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10589408 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #71951 | — | 3 | 4 | no | maximal |
| 5 | #64364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 6 | C32×#124 | — | 2 | 3 | no | — |
| 7 | C32×#124 | C22 | 1 | 3 | yes | — |
| 8 | C32×#120 | — | 2 | 3 | no | — |
| 9 | #64141 | — | 2 | 3 | no | — |
| 10 | #63663 | C22 | 1 | 3 | yes | complemented |
| 11 | #63632 | — | 2 | 3 | no | — |
| 12 | C3×H(3,𝔽4) | D3 | 1 | 4 | yes | complemented |
| 13 | #5062 | — | 3 | 12 | no | — |
| 14 | #4542 | — | 3 | 12 | no | — |
| 15 | C24×C32 | — | 2 | 1 | no | — |
| 16 | C2×C32×Q8 | — | 2 | 1 | no | — |
| 17 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 18 | C2×C32×D4 | — | 2 | 3 | no | — |
| 19 | C2×C32×D4 | D4 | 1 | 3 | yes | — |
| 20 | #3832 | — | 4 | 1 | no | — |
| 21 | Q8×C3⋊D3 | — | 4 | 1 | no | — |
| 22 | #3828 | — | 2 | 3 | no | — |
| 23 | C32×C22⋊C4 | — | 2 | 3 | no | — |
| 24 | C32×C22⋊C4 | — | 2 | 6 | no | — |
| 25 | C32×C42 | D4 | 1 | 3 | yes | — |
| 26 | #3754 | — | 4 | 3 | no | — |
| 27 | #3753 | — | 4 | 3 | no | — |
| 28 | #3748 | — | 2 | 3 | no | — |
| 29 | #2202 | — | 9 | 1 | no | Sylow |
| 30 | #1007 | — | 3 | 4 | no | — |
| 31 | C3×#124 | — | 2 | 12 | no | — |
| 32 | C3×#124 | C2×D3 | 1 | 12 | yes | — |
| 33 | C3×#120 | — | 2 | 12 | no | — |
| 34 | #932 | — | 6 | 12 | no | — |
| 35 | #836 | — | 3 | 12 | no | — |
| 36 | #805 | — | 6 | 12 | no | — |
| 37 | C23×C32 | — | 2 | 3 | no | — |
| 38 | C23×C32 | — | 8 | 2 | no | — |
| 39 | C23×C32 | — | 8 | 1 | no | — |
| 40 | C32×Q8 | — | 4 | 1 | no | — |
| 41 | C32×Q8 | — | 8 | 1 | no | — |
| 42 | C32×D4 | — | 4 | 3 | no | — |
| 43 | C32×D4 | — | 8 | 3 | no | — |
| 44 | C2×C32×C4 | — | 2 | 3 | no | — |
| 45 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 46 | #638 | — | 4 | 1 | no | — |
| 47 | C4⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 48 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 49 | #634 | — | 2 | 3 | no | — |
| 50 | C3⋊(C3⋊C8) | — | 4 | 3 | no | — |
| 51 | H(3,𝔽4) | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #454 | — | 9 | 3 | no | — |
| 53 | #355 | — | 9 | 3 | no | — |
| 54 | C24×C3 | — | 2 | 4 | no | — |
| 55 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 56 | C2×C3×Q8 | C22×D3 | 1 | 4 | yes | — |
| 57 | C2×C3×D4 | — | 2 | 12 | no | — |
| 58 | C2×C3×D4 | #67 | 1 | 12 | yes | — |
| 59 | #239 | — | 12 | 4 | no | — |
| 60 | D3×Q8 | — | 12 | 4 | no | — |
| 61 | #235 | — | 6 | 12 | no | — |
| 62 | C3×C22⋊C4 | — | 2 | 12 | no | — |
| 63 | C3×C22⋊C4 | — | 2 | 24 | no | — |
| 64 | C3×C42 | #67 | 1 | 12 | yes | — |
| 65 | #214 | — | 12 | 12 | no | — |
| 66 | #213 | — | 12 | 12 | no | — |
| 67 | #208 | — | 6 | 12 | no | — |
| 68 | C22×C32 | — | 4 | 6 | no | — |
| 69 | C22×C32 | — | 4 | 3 | no | — |
| 70 | C22×C32 | — | 8 | 4 | no | — |
| 71 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 72 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 73 | C32×C4 | — | 2 | 3 | no | — |
| 74 | C32×C4 | — | 4 | 3 | no | — |
| 75 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 76 | 2−1+4 | — | 9 | 1 | no | — |
| 77 | AGL(1,ℤ/8) | — | 18 | 3 | no | — |
| 78 | #124 | — | 2 | 3 | no | — |
| 79 | #124 | C2×C3⋊D3 | 1 | 3 | yes | — |
| 80 | #120 | — | 2 | 3 | no | — |
| 81 | #104 | — | 18 | 3 | no | — |
| 82 | #101 | — | 9 | 3 | no | — |
| 83 | C23×C3 | — | 2 | 12 | no | — |
| 84 | C23×C3 | — | 8 | 8 | no | — |
| 85 | C23×C3 | — | 8 | 4 | no | — |
| 86 | C3×Q8 | — | 4 | 4 | no | — |
| 87 | C3×Q8 | — | 8 | 4 | no | — |
| 88 | C3×D4 | — | 4 | 12 | no | — |
| 89 | C3×D4 | — | 8 | 12 | no | — |
| 90 | C2×C3×C4 | — | 2 | 12 | no | — |
| 91 | C2×C3×C4 | C2×#67 | 1 | 12 | yes | — |
| 92 | #67 | — | 12 | 4 | no | — |
| 93 | D12 | — | 6 | 12 | no | — |
| 94 | C4×D3 | — | 12 | 12 | no | — |
| 95 | Dic6 | — | 6 | 12 | no | — |
| 96 | C3⋊C8 | — | 12 | 12 | no | — |
| 97 | C2×C32 | — | 2 | 1 | no | — |
| 98 | C2×C32 | — | 8 | 3 | no | — |
| 99 | C2×C32 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 100 | C3⋊D3 | — | 8 | 1 | no | — |
| 101 | C24 | — | 2 | 1 | no | — |
| 102 | #41 | — | 18 | 3 | no | — |
| 103 | #41 | — | 36 | 1 | no | — |
| 104 | C2×Q8 | — | 2 | 1 | no | — |
| 105 | C2×Q8 | — | 36 | 1 | no | — |
| 106 | C2×Q8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 107 | C2×D4 | — | 2 | 3 | no | — |
| 108 | C2×D4 | #638 | 1 | 3 | yes | — |
| 109 | SD16 | — | 36 | 3 | no | — |
| 110 | D8 | — | 36 | 3 | no | — |
| 111 | M16 | — | 18 | 3 | no | — |
| 112 | C22⋊C4 | — | 2 | 3 | no | — |
| 113 | C22⋊C4 | — | 2 | 6 | no | — |
| 114 | C42 | #638 | 1 | 3 | yes | — |
| 115 | C22×C3 | — | 4 | 24 | no | — |
| 116 | C22×C3 | — | 4 | 12 | no | — |
| 117 | C22×C3 | — | 8 | 16 | no | — |
| 118 | C22×C3 | #953 | 1 | 4 | yes | — |
| 119 | C2×D3 | — | 12 | 4 | no | — |
| 120 | C3×C4 | — | 2 | 12 | no | — |
| 121 | C3×C4 | — | 4 | 12 | no | — |
| 122 | Dic3 | — | 12 | 4 | no | — |
| 123 | C32 | #2202 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 124 | C23 | — | 2 | 3 | no | — |
| 125 | C23 | — | 8 | 2 | no | — |
| 126 | C23 | — | 8 | 1 | no | — |
| 127 | Q8 | — | 4 | 1 | no | — |
| 128 | Q8 | — | 8 | 1 | no | — |
| 129 | Q8 | — | 18 | 3 | no | — |
| 130 | D4 | — | 4 | 3 | no | — |
| 131 | D4 | — | 8 | 3 | no | — |
| 132 | D4 | — | 18 | 3 | no | — |
| 133 | D4 | — | 36 | 1 | no | — |
| 134 | C2×C4 | — | 2 | 3 | no | — |
| 135 | C2×C4 | — | 36 | 3 | no | — |
| 136 | C2×C4 | C2×#638 | 1 | 3 | yes | — |
| 137 | C8 | — | 36 | 3 | no | — |
| 138 | C2×C3 | — | 2 | 4 | no | — |
| 139 | C2×C3 | — | 8 | 12 | no | — |
| 140 | C2×C3 | #5244 | 1 | 4 | yes | — |
| 141 | D3 | — | 24 | 4 | no | — |
| 142 | C22 | — | 4 | 6 | no | — |
| 143 | C22 | — | 4 | 3 | no | — |
| 144 | C22 | — | 8 | 4 | no | — |
| 145 | C22 | — | 36 | 1 | no | — |
| 146 | C22 | #64162 | 1 | 1 | yes | characteristic |
| 147 | C4 | — | 2 | 3 | no | — |
| 148 | C4 | — | 4 | 3 | no | — |
| 149 | C4 | — | 36 | 1 | no | — |
| 150 | C3 | #71951 | 1 | 4 | yes | complemented |
| 151 | C2 | — | 2 | 1 | no | — |
| 152 | C2 | — | 8 | 3 | no | — |
| 153 | C2 | — | 72 | 1 | no | — |
| 154 | C2 | #10592943 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×H(3,𝔽4) | C2 | semidirect |
| 2. #10592761 | C2 | semidirect |
| 3. #10589408 | C2 | semidirect |
| 5. #64364 | C22 | semidirect |
| 10. #63663 | C22 | semidirect |
| 12. C3×H(3,𝔽4) | D3 | semidirect |
| 51. H(3,𝔽4) | C3⋊D3 | semidirect |
| 123. C32 | #2202 | semidirect |
| 150. C3 | #71951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(3,𝔽4) | 2 |
| #10592761 | 2 |
| #10589408 | 2 |
| #71951 | 3 |