Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
550 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #10593120 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10589525 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C2×#63422 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #84120 | — | 3 | 1 | no | maximal |
| 5 | 2−1+4⋊C9 | C4 | 1 | 3 | yes | complemented |
| 6 | #63700 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×#41⋊C9 | C22 | 1 | 3 | yes | — |
| 8 | #63510 | — | 4 | 1 | no | maximal |
| 9 | #63422 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #63422 | C22 | 1 | 3 | yes | complemented |
| 11 | C3×#585 | D3 | 1 | 1 | yes | characteristic |
| 12 | Dic3×#41 | — | 3 | 1 | no | — |
| 13 | #5819 | — | 3 | 1 | no | — |
| 14 | #5236 | — | 3 | 3 | no | — |
| 15 | #5236 | — | 3 | 3 | no | — |
| 16 | C2×#837 | — | 3 | 3 | no | — |
| 17 | C2×#837 | — | 3 | 3 | no | — |
| 18 | C9×#41 | — | 4 | 1 | no | — |
| 19 | #41⋊C9 | C2×C4 | 1 | 3 | yes | complemented |
| 20 | #41⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 21 | C2×Q8⋊C9 | C2×C4 | 1 | 3 | yes | complemented |
| 22 | #3667 | — | 4 | 3 | no | — |
| 23 | C2×C9⋊C8 | — | 4 | 3 | no | — |
| 24 | #2901 | — | 9 | 1 | no | Sylow |
| 25 | C3×2−1+4 | — | 3 | 1 | no | — |
| 26 | C3×2−1+4 | Dic3 | 1 | 3 | yes | — |
| 27 | C3×H(5,𝔽2) | — | 3 | 3 | no | — |
| 28 | C3×H(5,𝔽2) | Dic3 | 1 | 1 | yes | characteristic |
| 29 | C2×C3×#41 | — | 3 | 1 | no | — |
| 30 | C2×C3×#41 | — | 3 | 3 | no | — |
| 31 | C2×C3×#41 | C2×D3 | 1 | 3 | yes | — |
| 32 | #948 | — | 6 | 3 | no | — |
| 33 | #948 | — | 6 | 1 | no | — |
| 34 | Q8×Dic3 | — | 6 | 1 | no | — |
| 35 | D4×Dic3 | — | 6 | 3 | no | — |
| 36 | #926 | — | 3 | 3 | no | — |
| 37 | C2×C4×Dic3 | — | 3 | 3 | no | — |
| 38 | C2×#208 | — | 3 | 3 | no | — |
| 39 | C2×#208 | — | 3 | 3 | no | — |
| 40 | #837 | — | 3 | 3 | no | — |
| 41 | #837 | — | 3 | 6 | no | — |
| 42 | #837 | — | 3 | 3 | no | — |
| 43 | #837 | — | 3 | 1 | no | — |
| 44 | #837 | — | 3 | 3 | no | — |
| 45 | Q8×C9 | — | 4 | 1 | no | — |
| 46 | D4×C9 | — | 4 | 3 | no | — |
| 47 | C2×C4×C9 | — | 4 | 3 | no | — |
| 48 | Q8⋊C9 | C22×C4 | 1 | 1 | yes | characteristic |
| 49 | C9⋊C8 | — | 4 | 1 | no | — |
| 50 | C9⋊C8 | — | 4 | 3 | no | — |
| 51 | #585 | D9 | 1 | 1 | yes | characteristic |
| 52 | #568 | — | 9 | 1 | no | — |
| 53 | C4×#41 | — | 9 | 1 | no | — |
| 54 | #421 | — | 9 | 3 | no | — |
| 55 | #421 | — | 9 | 3 | no | — |
| 56 | C2×#104 | — | 9 | 3 | no | — |
| 57 | C2×#104 | — | 9 | 3 | no | — |
| 58 | C3×#41 | — | 3 | 1 | no | — |
| 59 | C3×#41 | — | 3 | 3 | no | — |
| 60 | C3×#41 | — | 3 | 3 | no | — |
| 61 | C3×#41 | — | 3 | 3 | no | — |
| 62 | C3×#41 | — | 3 | 3 | no | — |
| 63 | C3×#41 | — | 3 | 6 | no | — |
| 64 | C3×#41 | — | 6 | 3 | no | — |
| 65 | C3×#41 | C2×Dic3 | 1 | 3 | yes | — |
| 66 | C3×#41 | S4 | 1 | 1 | yes | characteristic |
| 67 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 68 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 69 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 70 | C2×C3×Q8 | C2×Dic3 | 1 | 3 | yes | — |
| 71 | C2×C3×D4 | — | 3 | 3 | no | — |
| 72 | C2×C3×D4 | — | 3 | 3 | no | — |
| 73 | C2×C3×D4 | — | 3 | 3 | no | — |
| 74 | C2×C3×D4 | — | 6 | 3 | no | — |
| 75 | C22×C3×C4 | — | 3 | 3 | no | — |
| 76 | C22×C3×C4 | — | 6 | 1 | no | — |
| 77 | C22×Dic3 | — | 6 | 3 | no | — |
| 78 | #217 | — | 6 | 3 | no | — |
| 79 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 80 | C4×Dic3 | — | 3 | 1 | no | — |
| 81 | C4×Dic3 | — | 3 | 3 | no | — |
| 82 | C4×Dic3 | — | 6 | 3 | no | — |
| 83 | #208 | — | 3 | 3 | no | — |
| 84 | #208 | — | 3 | 1 | no | — |
| 85 | #208 | — | 6 | 3 | no | — |
| 86 | #208 | — | 6 | 3 | no | — |
| 87 | C2×C3⋊C8 | — | 6 | 3 | no | — |
| 88 | C2×C3⋊C8 | — | 6 | 3 | no | — |
| 89 | C22×C9 | — | 4 | 3 | no | — |
| 90 | C4×C9 | — | 4 | 3 | no | — |
| 91 | C4×C9 | — | 4 | 1 | no | — |
| 92 | 2−1+4 | — | 3 | 1 | no | — |
| 93 | 2−1+4 | Dic9 | 1 | 3 | yes | — |
| 94 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 95 | H(5,𝔽2) | Dic9 | 1 | 1 | yes | characteristic |
| 96 | C2×#41 | — | 3 | 1 | no | — |
| 97 | C2×#41 | — | 3 | 3 | no | — |
| 98 | C2×#41 | C2×D9 | 1 | 3 | yes | — |
| 99 | #131 | — | 18 | 3 | no | — |
| 100 | #131 | — | 18 | 1 | no | — |
| 101 | C2×M16 | — | 9 | 3 | no | — |
| 102 | C2×M16 | — | 9 | 3 | no | — |
| 103 | C4×Q8 | — | 18 | 1 | no | — |
| 104 | C4×D4 | — | 18 | 3 | no | — |
| 105 | #117 | — | 9 | 3 | no | — |
| 106 | C2×C42 | — | 9 | 3 | no | — |
| 107 | #104 | — | 9 | 3 | no | — |
| 108 | #104 | — | 9 | 6 | no | — |
| 109 | #104 | — | 9 | 3 | no | — |
| 110 | #104 | — | 9 | 1 | no | — |
| 111 | #104 | — | 9 | 3 | no | — |
| 112 | C23×C3 | — | 3 | 3 | no | — |
| 113 | C23×C3 | — | 6 | 1 | no | — |
| 114 | C3×Q8 | — | 3 | 3 | no | — |
| 115 | C3×Q8 | — | 3 | 3 | no | — |
| 116 | C3×Q8 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 117 | C3×Q8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 118 | C3×D4 | — | 3 | 3 | no | — |
| 119 | C3×D4 | — | 3 | 1 | no | — |
| 120 | C3×D4 | — | 3 | 6 | no | — |
| 121 | C3×D4 | — | 3 | 3 | no | — |
| 122 | C3×D4 | — | 6 | 3 | no | — |
| 123 | C3×D4 | SL(2,ℤ/4) | 1 | 3 | yes | — |
| 124 | C2×C3×C4 | — | 3 | 3 | no | — |
| 125 | C2×C3×C4 | — | 3 | 3 | no | — |
| 126 | C2×C3×C4 | — | 3 | 3 | no | — |
| 127 | C2×C3×C4 | — | 3 | 3 | no | — |
| 128 | C2×C3×C4 | — | 3 | 1 | no | — |
| 129 | C2×C3×C4 | — | 6 | 3 | no | — |
| 130 | C2×C3×C4 | C2×S4 | 1 | 3 | yes | — |
| 131 | C2×Dic3 | — | 6 | 1 | no | — |
| 132 | C2×Dic3 | — | 6 | 3 | no | — |
| 133 | C2×Dic3 | — | 12 | 6 | no | — |
| 134 | C3⋊C8 | — | 6 | 1 | no | — |
| 135 | C3⋊C8 | — | 6 | 3 | no | — |
| 136 | C2×C9 | — | 4 | 1 | no | — |
| 137 | C2×C9 | — | 8 | 3 | no | — |
| 138 | #41 | — | 3 | 1 | no | — |
| 139 | #41 | — | 3 | 3 | no | — |
| 140 | #41 | — | 3 | 3 | no | — |
| 141 | #41 | — | 3 | 3 | no | — |
| 142 | #41 | — | 3 | 3 | no | — |
| 143 | #41 | — | 3 | 6 | no | — |
| 144 | #41 | — | 6 | 3 | no | — |
| 145 | #41 | C2×Dic9 | 1 | 3 | yes | — |
| 146 | #41 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 147 | #41 | C22×D9 | 1 | 1 | yes | characteristic |
| 148 | C2×Q8 | — | 3 | 1 | no | — |
| 149 | C2×Q8 | — | 3 | 3 | no | — |
| 150 | C2×Q8 | C2×Dic9 | 1 | 3 | yes | — |
| 151 | C2×D4 | — | 3 | 3 | no | — |
| 152 | C2×D4 | — | 3 | 3 | no | — |
| 153 | C2×D4 | — | 3 | 3 | no | — |
| 154 | C2×D4 | — | 6 | 3 | no | — |
| 155 | C22×C4 | — | 3 | 3 | no | — |
| 156 | C22×C4 | — | 6 | 1 | no | — |
| 157 | C22×C4 | — | 18 | 3 | no | — |
| 158 | M16 | — | 9 | 3 | no | — |
| 159 | M16 | — | 9 | 1 | no | — |
| 160 | M16 | — | 18 | 3 | no | — |
| 161 | M16 | — | 18 | 3 | no | — |
| 162 | C2×C8 | — | 18 | 3 | no | — |
| 163 | C2×C8 | — | 18 | 3 | no | — |
| 164 | C4⋊C4 | — | 18 | 3 | no | — |
| 165 | C22⋊C4 | — | 18 | 3 | no | — |
| 166 | C42 | — | 9 | 1 | no | — |
| 167 | C42 | — | 9 | 3 | no | — |
| 168 | C42 | — | 18 | 3 | no | — |
| 169 | C22×C3 | — | 3 | 1 | no | — |
| 170 | C22×C3 | — | 3 | 3 | no | — |
| 171 | C22×C3 | — | 12 | 3 | no | — |
| 172 | C22×C3 | — | 24 | 1 | no | — |
| 173 | C22×C3 | C2×SL(2,ℤ/4) | 1 | 3 | yes | — |
| 174 | C3×C4 | — | 3 | 1 | no | — |
| 175 | C3×C4 | — | 3 | 3 | no | — |
| 176 | C3×C4 | C2×SL(2,ℤ/4) | 1 | 3 | yes | — |
| 177 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 178 | Dic3 | — | 6 | 2 | no | — |
| 179 | Dic3 | — | 12 | 3 | no | — |
| 180 | C9 | — | 4 | 1 | no | Sylow |
| 181 | C23 | — | 3 | 3 | no | — |
| 182 | C23 | — | 6 | 1 | no | — |
| 183 | Q8 | — | 3 | 3 | no | — |
| 184 | Q8 | — | 3 | 3 | no | — |
| 185 | Q8 | (C22⋊C9)⋊C4 | 1 | 1 | yes | characteristic |
| 186 | Q8 | C22×Dic9 | 1 | 1 | yes | characteristic |
| 187 | D4 | — | 3 | 3 | no | — |
| 188 | D4 | — | 3 | 1 | no | — |
| 189 | D4 | — | 3 | 6 | no | — |
| 190 | D4 | — | 3 | 3 | no | — |
| 191 | D4 | — | 6 | 3 | no | — |
| 192 | D4 | (C22⋊C9)⋊C4 | 1 | 3 | yes | — |
| 193 | C2×C4 | — | 3 | 3 | no | — |
| 194 | C2×C4 | — | 3 | 1 | no | — |
| 195 | C2×C4 | — | 3 | 3 | no | — |
| 196 | C2×C4 | — | 3 | 3 | no | — |
| 197 | C2×C4 | — | 3 | 3 | no | — |
| 198 | C2×C4 | — | 6 | 3 | no | — |
| 199 | C2×C4 | — | 18 | 1 | no | — |
| 200 | C2×C4 | — | 18 | 3 | no | — |
| 201 | C2×C4 | — | 36 | 6 | no | — |
| 202 | C2×C4 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 203 | C8 | — | 18 | 3 | no | — |
| 204 | C8 | — | 18 | 1 | no | — |
| 205 | C2×C3 | — | 2 | 3 | no | — |
| 206 | C2×C3 | — | 6 | 1 | no | — |
| 207 | C2×C3 | — | 6 | 3 | no | — |
| 208 | C2×C3 | C22×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 209 | C22 | — | 3 | 1 | no | — |
| 210 | C22 | — | 3 | 3 | no | — |
| 211 | C22 | — | 12 | 3 | no | — |
| 212 | C22 | — | 24 | 1 | no | — |
| 213 | C22 | C2×(C22⋊C9)⋊C4 | 1 | 3 | yes | — |
| 214 | C4 | — | 3 | 1 | no | — |
| 215 | C4 | — | 3 | 3 | no | — |
| 216 | C4 | — | 18 | 2 | no | — |
| 217 | C4 | — | 36 | 3 | no | — |
| 218 | C4 | C2×(C22⋊C9)⋊C4 | 1 | 3 | yes | — |
| 219 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 220 | C3 | #85541 | 1 | 1 | yes | characteristic |
| 221 | C2 | — | 2 | 3 | no | — |
| 222 | C2 | — | 6 | 1 | no | — |
| 223 | C2 | — | 6 | 3 | no | — |
| 224 | C2 | C22×(C22⋊C9)⋊C4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10589525 | C2 | semidirect |
| 3. C2×#63422 | C2 | semidirect |
| 5. 2−1+4⋊C9 | C4 | semidirect |
| 6. #63700 | C4 | semidirect |
| 9. #63422 | C22 | semidirect |
| 10. #63422 | C22 | semidirect |
| 19. #41⋊C9 | C2×C4 | semidirect |
| 21. C2×Q8⋊C9 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593120 | 2 |
| #10589525 | 2 |
| C2×#63422 | 2 |
| #84120 | 3 |
| #63510 | 4 |