Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
188 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 25 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 | #10590856 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10590184 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10589110 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #64286 | — | 2 | 1 | no | — |
| 5 | C2×#3743 | C22 | 1 | 1 | yes | characteristic |
| 6 | #63871 | — | 2 | 1 | no | — |
| 7 | C2×#3718 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C3×#816 | — | 2 | 1 | no | — |
| 9 | C3×#812 | — | 2 | 1 | no | — |
| 10 | #63574 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | #4816 | — | 6 | 1 | no | — |
| 12 | #4514 | — | 6 | 1 | no | — |
| 13 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×Dic6 | — | 2 | 1 | no | — |
| 15 | C22⋊#157 | — | 4 | 1 | no | — |
| 16 | C4⋊#157 | — | 4 | 1 | no | — |
| 17 | C4×#157 | — | 2 | 2 | no | — |
| 18 | C2×C32×C8 | D4 | 1 | 1 | yes | characteristic |
| 19 | C2×C3⋊(C3⋊C8) | C2×C4 | 1 | 1 | yes | characteristic |
| 20 | #3743 | — | 4 | 1 | no | — |
| 21 | C3×C4⋊Dic3 | — | 2 | 1 | no | — |
| 22 | Dic3⋊Dic3 | — | 4 | 1 | no | — |
| 23 | #3722 | — | 4 | 1 | no | — |
| 24 | #3718 | — | 4 | 1 | no | — |
| 25 | C3×C3⋊C16 | — | 4 | 1 | no | — |
| 26 | #1340 | — | 9 | 1 | no | maximal, Sylow |
| 27 | #946 | — | 6 | 1 | no | — |
| 28 | C2×#216 | — | 6 | 1 | no | — |
| 29 | C2×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 30 | C2×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 31 | #897 | — | 6 | 1 | no | — |
| 32 | C3×M32 | — | 6 | 1 | no | — |
| 33 | C3×#103 | — | 6 | 1 | no | — |
| 34 | #816 | — | 2 | 1 | no | — |
| 35 | #812 | — | 2 | 1 | no | — |
| 36 | #808 | — | 6 | 1 | no | — |
| 37 | C22×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 38 | C2×#157 | — | 4 | 2 | no | — |
| 39 | C2×C32×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 40 | C2×C3⋊Dic3 | SD16 | 1 | 1 | yes | characteristic |
| 41 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 42 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 43 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 44 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 45 | C3×Dic6 | — | 4 | 1 | no | — |
| 46 | C3×Dic6 | — | 4 | 1 | no | — |
| 47 | C32×C8 | — | 2 | 1 | no | — |
| 48 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 49 | #470 | — | 9 | 1 | no | — |
| 50 | #349 | — | 9 | 1 | no | — |
| 51 | H(3,ℤ/4) | — | 9 | 1 | no | — |
| 52 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 53 | C2×C4×D3 | — | 6 | 1 | no | — |
| 54 | C2×C4×D3 | — | 6 | 1 | no | — |
| 55 | C2×Dic6 | — | 2 | 1 | no | — |
| 56 | C2×C3×C8 | — | 2 | 1 | no | — |
| 57 | C2×C3×C8 | — | 2 | 1 | no | — |
| 58 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 59 | #216 | — | 12 | 2 | no | — |
| 60 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 61 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 62 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 63 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 64 | Dic3⋊C4 | — | 12 | 1 | no | — |
| 65 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 66 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 67 | ΓL(1,𝔽25) | — | 12 | 2 | no | — |
| 68 | ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 69 | ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 70 | C3×C16 | — | 12 | 1 | no | — |
| 71 | C3⋊C16 | — | 4 | 1 | no | — |
| 72 | C22×C32 | #102 | 1 | 1 | yes | characteristic |
| 73 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 74 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 75 | #157 | — | 8 | 2 | no | — |
| 76 | C32×C4 | #99 | 1 | 1 | yes | characteristic |
| 77 | C32×C4 | #104 | 1 | 1 | yes | characteristic |
| 78 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 79 | C3×Dic3 | — | 8 | 1 | no | — |
| 80 | C3×Dic3 | — | 8 | 1 | no | — |
| 81 | C2×Q16 | — | 9 | 1 | no | — |
| 82 | C2×M16 | — | 9 | 1 | no | — |
| 83 | C22⋊Q8 | — | 18 | 1 | no | — |
| 84 | #117 | — | 18 | 1 | no | — |
| 85 | M32 | — | 6 | 1 | no | — |
| 86 | #106 | — | 9 | 1 | no | — |
| 87 | #103 | — | 6 | 1 | no | — |
| 88 | C22×D3 | — | 6 | 1 | no | — |
| 89 | C22×D3 | — | 6 | 1 | no | — |
| 90 | C3×Q8 | — | 12 | 1 | no | — |
| 91 | C3×Q8 | — | 12 | 1 | no | — |
| 92 | C2×C3×C4 | — | 2 | 1 | no | — |
| 93 | C2×C3×C4 | — | 2 | 1 | no | — |
| 94 | C2×C3×C4 | — | 12 | 1 | no | — |
| 95 | C2×C3×C4 | — | 12 | 1 | no | — |
| 96 | C2×Dic3 | — | 4 | 1 | no | — |
| 97 | C2×Dic3 | — | 4 | 1 | no | — |
| 98 | C2×Dic3 | — | 6 | 1 | no | — |
| 99 | C2×Dic3 | — | 6 | 1 | no | — |
| 100 | C4×D3 | — | 12 | 1 | no | — |
| 101 | C4×D3 | — | 12 | 1 | no | — |
| 102 | C4×D3 | — | 12 | 1 | no | — |
| 103 | C4×D3 | — | 12 | 1 | no | — |
| 104 | Dic6 | — | 4 | 1 | no | — |
| 105 | Dic6 | — | 4 | 1 | no | — |
| 106 | C3×C8 | — | 2 | 1 | no | — |
| 107 | C3×C8 | — | 2 | 1 | no | — |
| 108 | C3×C8 | — | 4 | 1 | no | — |
| 109 | C3⋊C8 | — | 6 | 2 | no | — |
| 110 | C3⋊C8 | — | 12 | 1 | no | — |
| 111 | C2×C32 | — | 2 | 1 | no | — |
| 112 | C2×C32 | #327 | 1 | 1 | yes | characteristic |
| 113 | C3⋊D3 | — | 4 | 1 | no | — |
| 114 | C2×Q8 | — | 6 | 1 | no | — |
| 115 | C22×C4 | — | 9 | 1 | no | — |
| 116 | Q16 | — | 36 | 1 | no | — |
| 117 | M16 | — | 36 | 1 | no | — |
| 118 | C2×C8 | — | 9 | 1 | no | — |
| 119 | C2×C8 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 120 | C4⋊C4 | — | 6 | 1 | no | — |
| 121 | C4⋊C4 | — | 36 | 1 | no | — |
| 122 | C4⋊C4 | — | 36 | 1 | no | — |
| 123 | C22⋊C4 | — | 36 | 1 | no | — |
| 124 | C22⋊C4 | — | 36 | 1 | no | — |
| 125 | C42 | — | 18 | 2 | no | — |
| 126 | C16 | — | 12 | 1 | no | — |
| 127 | C22×C3 | — | 2 | 1 | no | — |
| 128 | C22×C3 | — | 2 | 1 | no | — |
| 129 | C2×D3 | — | 12 | 1 | no | — |
| 130 | C2×D3 | — | 12 | 1 | no | — |
| 131 | C2×D3 | — | 12 | 1 | no | — |
| 132 | C2×D3 | — | 12 | 1 | no | — |
| 133 | C2×D3 | — | 24 | 1 | no | — |
| 134 | C3×C4 | — | 2 | 1 | no | — |
| 135 | C3×C4 | — | 2 | 1 | no | — |
| 136 | C3×C4 | — | 2 | 1 | no | — |
| 137 | C3×C4 | — | 2 | 1 | no | — |
| 138 | C3×C4 | — | 24 | 1 | no | — |
| 139 | C3×C4 | — | 24 | 1 | no | — |
| 140 | Dic3 | — | 8 | 1 | no | — |
| 141 | Dic3 | — | 8 | 1 | no | — |
| 142 | Dic3 | — | 12 | 1 | no | — |
| 143 | Dic3 | — | 12 | 1 | no | — |
| 144 | C32 | #1340 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 145 | C23 | — | 9 | 1 | no | — |
| 146 | Q8 | — | 12 | 1 | no | — |
| 147 | Q8 | — | 12 | 1 | no | — |
| 148 | C2×C4 | — | 9 | 1 | no | — |
| 149 | C2×C4 | — | 12 | 1 | no | — |
| 150 | C2×C4 | — | 12 | 1 | no | — |
| 151 | C2×C4 | — | 18 | 1 | no | — |
| 152 | C2×C4 | — | 18 | 1 | no | — |
| 153 | C2×C4 | — | 36 | 2 | no | — |
| 154 | C2×C4 | D32⋊C4 | 1 | 1 | yes | characteristic |
| 155 | C8 | — | 2 | 1 | no | — |
| 156 | C8 | — | 18 | 1 | no | — |
| 157 | C2×C3 | — | 2 | 1 | no | — |
| 158 | C2×C3 | — | 2 | 1 | no | — |
| 159 | C2×C3 | — | 2 | 1 | no | — |
| 160 | C2×C3 | — | 2 | 1 | no | — |
| 161 | C2×C3 | — | 4 | 1 | no | — |
| 162 | D3 | — | 24 | 1 | no | — |
| 163 | D3 | — | 24 | 1 | no | — |
| 164 | C22 | — | 18 | 1 | no | — |
| 165 | C22 | — | 36 | 1 | no | — |
| 166 | C22 | #63729 | 1 | 1 | yes | characteristic |
| 167 | C4 | — | 18 | 1 | no | — |
| 168 | C4 | — | 24 | 1 | no | — |
| 169 | C4 | — | 24 | 1 | no | — |
| 170 | C4 | — | 72 | 2 | no | — |
| 171 | C4 | #63731 | 1 | 1 | yes | characteristic |
| 172 | C4 | #63738 | 1 | 1 | yes | characteristic |
| 173 | C3 | — | 2 | 1 | no | — |
| 174 | C3 | — | 2 | 1 | no | — |
| 175 | C2 | — | 2 | 1 | no | — |
| 176 | C2 | — | 36 | 1 | no | — |
| 177 | C2 | #10590033 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×#3718 | C4 | semidirect |
| 10. #63574 | C4 | semidirect |
| 144. C32 | #1340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590856 | 2 |
| #10590184 | 2 |
| #10589110 | 2 |
| #1340 | 9 |