Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
806 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 120 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 | C2×#63781 | C2 | 1 | 3 | yes | maximal |
| 2 | C2×#63781 | C2 | 1 | 3 | yes | maximal |
| 3 | C3⋊D3×#95 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C23×#157 | C22 | 1 | 3 | yes | — |
| 5 | C23×#157 | C22 | 1 | 1 | yes | characteristic |
| 6 | C22×C4×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 7 | #63781 | — | 2 | 6 | no | — |
| 8 | #63781 | — | 2 | 6 | no | — |
| 9 | C32×#95 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #63658 | C4 | 1 | 3 | yes | complemented |
| 11 | D3×#95 | — | 6 | 2 | no | — |
| 12 | C23×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 13 | C22×#157 | — | 2 | 3 | no | — |
| 14 | C22×#157 | — | 2 | 3 | no | — |
| 15 | C22×#157 | — | 2 | 3 | no | — |
| 16 | C22×#157 | — | 2 | 3 | no | — |
| 17 | C22×#157 | — | 2 | 3 | no | — |
| 18 | C22×#157 | — | 2 | 3 | no | — |
| 19 | C22×#157 | — | 2 | 3 | no | — |
| 20 | C22×#157 | — | 2 | 3 | no | — |
| 21 | C22×#157 | D4 | 1 | 6 | yes | — |
| 22 | C22×#157 | Q8 | 1 | 2 | yes | — |
| 23 | C22×C32×C4 | C2×C4 | 1 | 3 | yes | — |
| 24 | C22×C3⋊Dic3 | C2×C4 | 1 | 3 | yes | — |
| 25 | C2×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 26 | C2×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 27 | C2×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 28 | C2×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 29 | C2×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 30 | C2×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 31 | #1443 | — | 9 | 1 | no | maximal, Sylow |
| 32 | C22×C4×D3 | — | 6 | 6 | no | — |
| 33 | C3×#95 | — | 2 | 2 | no | — |
| 34 | C3⋊#95 | — | 6 | 6 | no | — |
| 35 | C23×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 36 | C22×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 37 | C22×C3⋊D3 | C2×Q8 | 1 | 1 | yes | characteristic |
| 38 | C22×C3⋊D3 | #41 | 1 | 3 | yes | — |
| 39 | C22×C3⋊D3 | #41 | 1 | 1 | yes | characteristic |
| 40 | C22×C3⋊D3 | #41 | 1 | 3 | yes | — |
| 41 | C22×C3⋊D3 | #41 | 1 | 3 | yes | — |
| 42 | C2×#157 | — | 2 | 6 | no | — |
| 43 | C2×#157 | — | 2 | 6 | no | — |
| 44 | C2×#157 | — | 2 | 6 | no | — |
| 45 | C2×#157 | — | 2 | 6 | no | — |
| 46 | C2×#157 | — | 4 | 3 | no | — |
| 47 | C2×#157 | — | 4 | 3 | no | — |
| 48 | C2×#157 | — | 4 | 3 | no | — |
| 49 | C2×#157 | — | 4 | 1 | no | — |
| 50 | C2×#157 | — | 4 | 3 | no | — |
| 51 | C2×#157 | — | 4 | 3 | no | — |
| 52 | C2×C32×C4 | — | 2 | 3 | no | — |
| 53 | C2×C32×C4 | — | 2 | 3 | no | — |
| 54 | C2×C32×C4 | — | 2 | 3 | no | — |
| 55 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 56 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 57 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 58 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 59 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 60 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 61 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 62 | C2×#95 | — | 9 | 1 | no | — |
| 63 | C2×#95 | — | 9 | 3 | no | — |
| 64 | C2×#95 | — | 9 | 3 | no | — |
| 65 | C23×D3 | — | 6 | 2 | no | — |
| 66 | C22×C3×C4 | — | 2 | 6 | no | — |
| 67 | C22×Dic3 | — | 6 | 6 | no | — |
| 68 | C2×C4×D3 | — | 6 | 12 | no | — |
| 69 | C2×C4×D3 | — | 6 | 12 | no | — |
| 70 | C2×C4×D3 | — | 12 | 6 | no | — |
| 71 | C2×C4×D3 | — | 12 | 6 | no | — |
| 72 | C2×C4×D3 | — | 12 | 6 | no | — |
| 73 | C2×C4×D3 | — | 12 | 6 | no | — |
| 74 | C22×C32 | #117 | 1 | 3 | yes | — |
| 75 | C22×C32 | C4×D4 | 1 | 3 | yes | — |
| 76 | C22×C32 | C4×Q8 | 1 | 1 | yes | characteristic |
| 77 | C2×C3⋊D3 | #121 | 1 | 3 | yes | — |
| 78 | C2×C3⋊D3 | C22⋊Q8 | 1 | 3 | yes | — |
| 79 | C2×C3⋊D3 | #123 | 1 | 3 | yes | — |
| 80 | C2×C3⋊D3 | #123 | 1 | 3 | yes | — |
| 81 | C2×C3⋊D3 | #124 | 1 | 3 | yes | — |
| 82 | C2×C3⋊D3 | #125 | 1 | 3 | yes | — |
| 83 | C2×C3⋊D3 | #126 | 1 | 1 | yes | characteristic |
| 84 | C2×C3⋊D3 | #126 | 1 | 3 | yes | — |
| 85 | C2×C3⋊D3 | #126 | 1 | 3 | yes | — |
| 86 | C2×C3⋊D3 | #126 | 1 | 3 | yes | — |
| 87 | #157 | — | 4 | 2 | no | — |
| 88 | #157 | — | 4 | 6 | no | — |
| 89 | C32×C4 | — | 4 | 3 | no | — |
| 90 | C3⋊Dic3 | — | 4 | 3 | no | — |
| 91 | C23×C4 | — | 9 | 3 | no | — |
| 92 | C23×C4 | — | 9 | 1 | no | — |
| 93 | C23×C4 | — | 9 | 3 | no | — |
| 94 | #95 | — | 9 | 3 | no | — |
| 95 | #95 | — | 18 | 6 | no | — |
| 96 | #95 | — | 18 | 6 | no | — |
| 97 | #95 | #157 | 1 | 1 | yes | characteristic, complemented |
| 98 | C23×C3 | — | 2 | 2 | no | — |
| 99 | C22×D3 | — | 6 | 6 | no | — |
| 100 | C22×D3 | — | 6 | 2 | no | — |
| 101 | C22×D3 | — | 6 | 6 | no | — |
| 102 | C22×D3 | — | 6 | 6 | no | — |
| 103 | C22×D3 | — | 6 | 6 | no | — |
| 104 | C22×D3 | — | 6 | 2 | no | — |
| 105 | C2×C3×C4 | — | 2 | 12 | no | — |
| 106 | C2×C3×C4 | — | 4 | 6 | no | — |
| 107 | C2×C3×C4 | — | 4 | 6 | no | — |
| 108 | C2×Dic3 | — | 6 | 12 | no | — |
| 109 | C2×Dic3 | — | 12 | 6 | no | — |
| 110 | C2×Dic3 | — | 12 | 6 | no | — |
| 111 | C4×D3 | — | 12 | 12 | no | — |
| 112 | C4×D3 | — | 12 | 12 | no | — |
| 113 | C4×D3 | — | 12 | 12 | no | — |
| 114 | C4×D3 | — | 12 | 12 | no | — |
| 115 | C2×C32 | #383 | 1 | 1 | yes | characteristic |
| 116 | C2×C32 | #387 | 1 | 3 | yes | — |
| 117 | C2×C32 | #388 | 1 | 3 | yes | — |
| 118 | C3⋊D3 | #396 | 1 | 1 | yes | characteristic |
| 119 | C3⋊D3 | #397 | 1 | 3 | yes | — |
| 120 | C3⋊D3 | #400 | 1 | 3 | yes | — |
| 121 | C3⋊D3 | #401 | 1 | 1 | yes | characteristic |
| 122 | C24 | — | 9 | 1 | no | — |
| 123 | C22×C4 | — | 9 | 6 | no | — |
| 124 | C22×C4 | — | 9 | 2 | no | — |
| 125 | C22×C4 | — | 9 | 3 | no | — |
| 126 | C22×C4 | — | 18 | 3 | no | — |
| 127 | C22×C4 | — | 18 | 3 | no | — |
| 128 | C22×C4 | — | 18 | 3 | no | — |
| 129 | C22×C4 | — | 18 | 3 | no | — |
| 130 | C22×C4 | — | 18 | 3 | no | — |
| 131 | C22×C4 | — | 18 | 3 | no | — |
| 132 | C22×C4 | — | 18 | 3 | no | — |
| 133 | C22×C4 | — | 18 | 3 | no | — |
| 134 | C22×C4 | — | 18 | 3 | no | — |
| 135 | C22×C4 | — | 18 | 3 | no | — |
| 136 | C22×C4 | — | 18 | 3 | no | — |
| 137 | C22×C4 | — | 18 | 3 | no | — |
| 138 | C22×C4 | — | 18 | 3 | no | — |
| 139 | C22×C4 | — | 18 | 3 | no | — |
| 140 | C22×C4 | C2×#157 | 1 | 3 | yes | — |
| 141 | C22×C3 | — | 2 | 6 | no | — |
| 142 | C22×C3 | — | 2 | 6 | no | — |
| 143 | C22×C3 | — | 2 | 2 | no | — |
| 144 | C2×D3 | — | 6 | 6 | no | — |
| 145 | C2×D3 | — | 6 | 6 | no | — |
| 146 | C2×D3 | — | 6 | 6 | no | — |
| 147 | C2×D3 | — | 6 | 6 | no | — |
| 148 | C2×D3 | — | 6 | 6 | no | — |
| 149 | C2×D3 | — | 6 | 6 | no | — |
| 150 | C2×D3 | — | 6 | 6 | no | — |
| 151 | C2×D3 | — | 6 | 2 | no | — |
| 152 | C2×D3 | — | 6 | 6 | no | — |
| 153 | C2×D3 | — | 6 | 6 | no | — |
| 154 | C3×C4 | — | 4 | 12 | no | — |
| 155 | Dic3 | — | 12 | 12 | no | — |
| 156 | C32 | #1443 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 157 | C23 | — | 9 | 3 | no | — |
| 158 | C23 | — | 9 | 3 | no | — |
| 159 | C23 | — | 9 | 3 | no | — |
| 160 | C23 | — | 9 | 3 | no | — |
| 161 | C23 | — | 9 | 1 | no | — |
| 162 | C23 | — | 9 | 1 | no | — |
| 163 | C23 | C22×#157 | 1 | 1 | yes | characteristic |
| 164 | C2×C4 | — | 2 | 3 | no | — |
| 165 | C2×C4 | — | 2 | 3 | no | — |
| 166 | C2×C4 | — | 2 | 3 | no | — |
| 167 | C2×C4 | — | 18 | 6 | no | — |
| 168 | C2×C4 | — | 18 | 6 | no | — |
| 169 | C2×C4 | — | 18 | 6 | no | — |
| 170 | C2×C4 | — | 18 | 6 | no | — |
| 171 | C2×C4 | — | 18 | 3 | no | — |
| 172 | C2×C4 | — | 18 | 3 | no | — |
| 173 | C2×C4 | — | 18 | 3 | no | — |
| 174 | C2×C4 | — | 36 | 3 | no | — |
| 175 | C2×C4 | — | 36 | 3 | no | — |
| 176 | C2×C4 | — | 36 | 3 | no | — |
| 177 | C2×C4 | — | 36 | 3 | no | — |
| 178 | C2×C4 | — | 36 | 1 | no | — |
| 179 | C2×C4 | — | 36 | 3 | no | — |
| 180 | C2×C4 | — | 36 | 3 | no | — |
| 181 | C2×C4 | — | 36 | 3 | no | — |
| 182 | C2×C4 | — | 36 | 3 | no | — |
| 183 | C2×C4 | — | 36 | 3 | no | — |
| 184 | C2×C3 | — | 2 | 2 | no | — |
| 185 | C2×C3 | — | 2 | 6 | no | — |
| 186 | C2×C3 | — | 2 | 6 | no | — |
| 187 | D3 | — | 6 | 2 | no | — |
| 188 | D3 | — | 6 | 6 | no | — |
| 189 | D3 | — | 6 | 6 | no | — |
| 190 | D3 | — | 6 | 2 | no | — |
| 191 | C22 | — | 9 | 1 | no | — |
| 192 | C22 | — | 9 | 3 | no | — |
| 193 | C22 | — | 9 | 3 | no | — |
| 194 | C22 | — | 9 | 3 | no | — |
| 195 | C22 | — | 9 | 3 | no | — |
| 196 | C22 | — | 9 | 3 | no | — |
| 197 | C22 | — | 9 | 3 | no | — |
| 198 | C22 | — | 9 | 3 | no | — |
| 199 | C22 | — | 9 | 3 | no | — |
| 200 | C22 | — | 9 | 3 | no | — |
| 201 | C22 | #64286 | 1 | 3 | yes | — |
| 202 | C22 | D4×#157 | 1 | 3 | yes | — |
| 203 | C22 | Q8×#157 | 1 | 1 | yes | characteristic |
| 204 | C4 | — | 4 | 3 | no | — |
| 205 | C4 | — | 36 | 2 | no | — |
| 206 | C4 | — | 36 | 6 | no | — |
| 207 | C4 | — | 36 | 3 | no | — |
| 208 | C3 | — | 2 | 2 | no | — |
| 209 | C2 | — | 9 | 1 | no | — |
| 210 | C2 | — | 9 | 3 | no | — |
| 211 | C2 | — | 9 | 3 | no | — |
| 212 | C2 | — | 9 | 1 | no | — |
| 213 | C2 | #10593737 | 1 | 1 | yes | characteristic |
| 214 | C2 | #10593747 | 1 | 3 | yes | — |
| 215 | C2 | #10593758 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#157 |
| commutator, socle | C23×C32 | C22×C4 |
| Fitting | C32×#95 | C4 |
| prime radical, cosocle | C23×C3⋊D3 | C23 |
| hypercenter | #95 | #157 |
| hypocenter | C32 | #1443 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C32×#95 | C4 | semidirect |
| 10. #63658 | C4 | semidirect |
| 97. #95 | #157 | semidirect |
| 156. C32 | #1443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63781 | 2 |
| C3⋊D3×#95 | 2 |
| #1443 | 9 |