Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
660 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 115 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 | #10595412 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10595351 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×#622 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10593442 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #10593439 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10593437 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C4×#3775 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×C3×#239 | — | 2 | 1 | no | — |
| 9 | C2×#3775 | C22 | 1 | 3 | yes | — |
| 10 | C2×#3775 | C22 | 1 | 6 | yes | — |
| 11 | Q8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×Q8×Dic3 | — | 2 | 1 | no | — |
| 13 | #63919 | C22 | 1 | 3 | yes | — |
| 14 | C4×#627 | C22 | 1 | 3 | yes | — |
| 15 | #63914 | C22 | 1 | 3 | yes | — |
| 16 | #63908 | — | 2 | 3 | no | — |
| 17 | C4×#625 | C22 | 1 | 3 | yes | — |
| 18 | #63869 | — | 2 | 3 | no | — |
| 19 | C4⋊#622 | C22 | 1 | 3 | yes | — |
| 20 | C4×#622 | C22 | 1 | 3 | yes | — |
| 21 | #63742 | C22 | 1 | 1 | yes | characteristic |
| 22 | #63740 | C22 | 1 | 3 | yes | — |
| 23 | #63739 | C22 | 1 | 3 | yes | — |
| 24 | #5834 | — | 6 | 1 | no | — |
| 25 | #5569 | — | 6 | 1 | no | — |
| 26 | C2×C32×Q8 | D4 | 1 | 1 | yes | characteristic |
| 27 | C3×#239 | — | 4 | 4 | no | — |
| 28 | C2×C3×D12 | — | 2 | 3 | no | — |
| 29 | C2×C3×C4×D3 | — | 2 | 3 | no | — |
| 30 | C2×#627 | C23 | 1 | 3 | yes | — |
| 31 | C2×#625 | — | 2 | 3 | no | — |
| 32 | C2×#625 | C23 | 1 | 3 | yes | — |
| 33 | C2×#622 | C23 | 1 | 3 | yes | — |
| 34 | C2×#622 | C23 | 1 | 1 | yes | characteristic |
| 35 | #3775 | — | 2 | 6 | no | — |
| 36 | #3775 | — | 4 | 6 | no | — |
| 37 | C4⋊(C3⋊Dic3) | D4 | 1 | 3 | yes | — |
| 38 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 39 | C3×C4⋊Dic3 | — | 2 | 3 | no | — |
| 40 | C3×C4×Dic3 | — | 2 | 3 | no | — |
| 41 | #3724 | — | 2 | 3 | no | — |
| 42 | #3724 | C23 | 1 | 1 | yes | characteristic |
| 43 | #3724 | C23 | 1 | 1 | yes | characteristic |
| 44 | Dic3⋊Dic3 | — | 2 | 3 | no | — |
| 45 | (C2×D3)⋊Dic3 | — | 2 | 3 | no | — |
| 46 | #3392 | — | 9 | 1 | no | maximal, Sylow |
| 47 | C2×C3×#41 | — | 6 | 1 | no | — |
| 48 | C2×#239 | — | 2 | 1 | no | — |
| 49 | C3×C4×Q8 | — | 6 | 1 | no | — |
| 50 | Q8×Dic3 | — | 2 | 1 | no | — |
| 51 | Q8×Dic3 | — | 6 | 1 | no | — |
| 52 | Q8×Dic3 | — | 6 | 1 | no | — |
| 53 | #940 | — | 6 | 3 | no | — |
| 54 | #938 | — | 6 | 3 | no | — |
| 55 | #930 | — | 6 | 3 | no | — |
| 56 | C4×#67 | — | 6 | 3 | no | — |
| 57 | #890 | — | 6 | 3 | no | — |
| 58 | #888 | — | 6 | 3 | no | — |
| 59 | #870 | — | 6 | 3 | no | — |
| 60 | C4×Dic6 | — | 6 | 3 | no | — |
| 61 | C22×C3×D3 | — | 2 | 3 | no | — |
| 62 | C32×Q8 | SD16 | 1 | 4 | yes | complemented |
| 63 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 64 | C2×C3⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 65 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 66 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 67 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 68 | C2×C3×Dic3 | — | 2 | 3 | no | — |
| 69 | C3×D12 | — | 4 | 6 | no | — |
| 70 | C3×C4×D3 | — | 4 | 6 | no | — |
| 71 | #627 | — | 2 | 3 | no | — |
| 72 | #627 | — | 2 | 3 | no | — |
| 73 | #625 | — | 2 | 3 | no | — |
| 74 | #625 | — | 2 | 3 | no | — |
| 75 | #625 | — | 8 | 3 | no | — |
| 76 | #622 | — | 2 | 3 | no | — |
| 77 | #622 | #41 | 1 | 2 | yes | complemented |
| 78 | #557 | — | 9 | 1 | no | — |
| 79 | #550 | — | 9 | 1 | no | — |
| 80 | #492 | — | 9 | 3 | no | — |
| 81 | #461 | — | 9 | 3 | no | — |
| 82 | #460 | — | 9 | 3 | no | — |
| 83 | C8×Q8 | — | 9 | 1 | no | — |
| 84 | C4×SD16 | — | 9 | 3 | no | — |
| 85 | C3×#41 | — | 12 | 4 | no | — |
| 86 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 87 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 88 | C2×C3×D4 | — | 6 | 3 | no | — |
| 89 | C22×C3×C4 | — | 6 | 3 | no | — |
| 90 | C2×#67 | — | 6 | 3 | no | — |
| 91 | C2×#67 | — | 6 | 6 | no | — |
| 92 | #239 | — | 4 | 4 | no | — |
| 93 | C2×D12 | — | 2 | 3 | no | — |
| 94 | C2×C4×D3 | — | 2 | 3 | no | — |
| 95 | C2×Dic6 | — | 6 | 3 | no | — |
| 96 | C3×C4⋊C4 | — | 6 | 3 | no | — |
| 97 | C3×C42 | — | 6 | 3 | no | — |
| 98 | #217 | — | 6 | 3 | no | — |
| 99 | (C2×D3)⋊C4 | — | 6 | 3 | no | — |
| 100 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 101 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 102 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 103 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 104 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 105 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 106 | Dic3⋊C4 | — | 6 | 3 | no | — |
| 107 | Dic3⋊C4 | — | 6 | 6 | no | — |
| 108 | C4×Dic3 | — | 2 | 3 | no | — |
| 109 | C4×Dic3 | — | 6 | 3 | no | — |
| 110 | C4×Dic3 | — | 6 | 3 | no | — |
| 111 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C3×D3 | — | 4 | 3 | no | — |
| 113 | C2×C3×D3 | — | 4 | 3 | no | — |
| 114 | C2×C3×D3 | — | 4 | 3 | no | — |
| 115 | C32×C4 | C2×SD16 | 1 | 6 | yes | — |
| 116 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 117 | C3⋊Dic3 | C2×#41 | 1 | 1 | yes | characteristic |
| 118 | C3⋊Dic3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 119 | C3×Dic3 | — | 4 | 3 | no | — |
| 120 | C3×Dic3 | — | 4 | 1 | no | — |
| 121 | C3×Dic3 | — | 4 | 1 | no | — |
| 122 | C2×#41 | — | 6 | 1 | no | — |
| 123 | C2×SD16 | — | 9 | 3 | no | — |
| 124 | C2×SD16 | — | 9 | 6 | no | — |
| 125 | C4⋊Q8 | — | 9 | 3 | no | — |
| 126 | #127 | — | 9 | 3 | no | — |
| 127 | #125 | — | 18 | 3 | no | — |
| 128 | #121 | — | 18 | 3 | no | — |
| 129 | C4×Q8 | — | 6 | 1 | no | — |
| 130 | C4×Q8 | — | 9 | 3 | no | — |
| 131 | C4×Q8 | — | 9 | 1 | no | — |
| 132 | C4×D4 | — | 9 | 3 | no | — |
| 133 | #106 | — | 9 | 1 | no | — |
| 134 | C4⋊C8 | — | 9 | 3 | no | — |
| 135 | #103 | — | 9 | 3 | no | — |
| 136 | #102 | — | 9 | 3 | no | — |
| 137 | C4×C8 | — | 9 | 3 | no | — |
| 138 | C23×C3 | — | 6 | 3 | no | — |
| 139 | C22×D3 | — | 2 | 3 | no | — |
| 140 | C3×Q8 | — | 2 | 4 | no | — |
| 141 | C3×Q8 | — | 2 | 4 | no | — |
| 142 | C3×D4 | — | 12 | 6 | no | — |
| 143 | C2×C3×C4 | — | 2 | 3 | no | — |
| 144 | C2×C3×C4 | — | 2 | 3 | no | — |
| 145 | C2×C3×C4 | — | 6 | 1 | no | — |
| 146 | C2×C3×C4 | — | 6 | 3 | no | — |
| 147 | C2×C3×C4 | — | 6 | 1 | no | — |
| 148 | C2×C3×C4 | — | 12 | 6 | no | — |
| 149 | #67 | — | 12 | 3 | no | — |
| 150 | #67 | — | 12 | 3 | no | — |
| 151 | #67 | — | 24 | 6 | no | — |
| 152 | C2×Dic3 | — | 2 | 1 | no | — |
| 153 | C2×Dic3 | — | 2 | 3 | no | — |
| 154 | C2×Dic3 | — | 2 | 1 | no | — |
| 155 | C2×Dic3 | — | 6 | 1 | no | — |
| 156 | C2×Dic3 | — | 6 | 1 | no | — |
| 157 | C2×Dic3 | — | 6 | 3 | no | — |
| 158 | C2×Dic3 | — | 6 | 3 | no | — |
| 159 | D12 | — | 4 | 6 | no | — |
| 160 | C4×D3 | — | 4 | 6 | no | — |
| 161 | Dic6 | — | 12 | 3 | no | — |
| 162 | Dic6 | — | 12 | 3 | no | — |
| 163 | C2×C32 | #550 | 1 | 1 | yes | characteristic |
| 164 | C2×C32 | C22×SD16 | 1 | 1 | yes | characteristic |
| 165 | C2×C32 | #577 | 1 | 1 | yes | characteristic |
| 166 | C3×D3 | — | 8 | 3 | no | — |
| 167 | #41 | — | 12 | 4 | no | — |
| 168 | C2×Q8 | — | 9 | 3 | no | — |
| 169 | C2×Q8 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 170 | C2×D4 | — | 6 | 3 | no | — |
| 171 | C2×D4 | — | 9 | 3 | no | — |
| 172 | C2×D4 | — | 18 | 3 | no | — |
| 173 | C22×C4 | — | 6 | 3 | no | — |
| 174 | SD16 | — | 18 | 6 | no | — |
| 175 | SD16 | — | 36 | 6 | no | — |
| 176 | C2×C8 | — | 9 | 1 | no | — |
| 177 | C2×C8 | — | 9 | 3 | no | — |
| 178 | C4⋊C4 | — | 6 | 3 | no | — |
| 179 | C4⋊C4 | — | 9 | 1 | no | — |
| 180 | C4⋊C4 | — | 9 | 1 | no | — |
| 181 | C4⋊C4 | — | 9 | 3 | no | — |
| 182 | C4⋊C4 | — | 18 | 3 | no | — |
| 183 | C4⋊C4 | — | 18 | 3 | no | — |
| 184 | C22⋊C4 | — | 18 | 3 | no | — |
| 185 | C42 | — | 6 | 3 | no | — |
| 186 | C42 | — | 9 | 3 | no | — |
| 187 | C22×C3 | — | 2 | 1 | no | — |
| 188 | C22×C3 | — | 2 | 1 | no | — |
| 189 | C22×C3 | — | 12 | 3 | no | — |
| 190 | C22×C3 | — | 12 | 3 | no | — |
| 191 | C22×C3 | — | 12 | 3 | no | — |
| 192 | C2×D3 | — | 4 | 3 | no | — |
| 193 | C2×D3 | — | 4 | 3 | no | — |
| 194 | C2×D3 | — | 4 | 3 | no | — |
| 195 | C3×C4 | — | 2 | 6 | no | — |
| 196 | C3×C4 | — | 2 | 6 | no | — |
| 197 | C3×C4 | — | 12 | 3 | no | — |
| 198 | C3×C4 | — | 12 | 1 | no | — |
| 199 | C3×C4 | — | 12 | 1 | no | — |
| 200 | Dic3 | — | 4 | 3 | no | — |
| 201 | Dic3 | — | 4 | 1 | no | — |
| 202 | Dic3 | — | 4 | 1 | no | — |
| 203 | Dic3 | — | 6 | 1 | no | — |
| 204 | Dic3 | — | 6 | 1 | no | — |
| 205 | Dic3 | — | 6 | 1 | no | — |
| 206 | Dic3 | — | 6 | 1 | no | — |
| 207 | Dic3 | — | 12 | 3 | no | — |
| 208 | Dic3 | — | 12 | 3 | no | — |
| 209 | C32 | #3392 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 210 | C23 | — | 6 | 3 | no | — |
| 211 | Q8 | — | 18 | 3 | no | — |
| 212 | Q8 | — | 18 | 3 | no | — |
| 213 | Q8 | #3775 | 1 | 4 | yes | complemented |
| 214 | D4 | — | 12 | 6 | no | — |
| 215 | D4 | — | 18 | 3 | no | — |
| 216 | D4 | — | 18 | 3 | no | — |
| 217 | D4 | — | 72 | 3 | no | — |
| 218 | C2×C4 | — | 6 | 1 | no | — |
| 219 | C2×C4 | — | 6 | 3 | no | — |
| 220 | C2×C4 | — | 6 | 1 | no | — |
| 221 | C2×C4 | — | 9 | 1 | no | — |
| 222 | C2×C4 | — | 9 | 3 | no | — |
| 223 | C2×C4 | — | 12 | 6 | no | — |
| 224 | C2×C4 | C2×GO+(4,𝔽2) | 1 | 3 | yes | — |
| 225 | C8 | — | 9 | 2 | no | — |
| 226 | C8 | — | 18 | 3 | no | — |
| 227 | C2×C3 | — | 2 | 1 | no | — |
| 228 | C2×C3 | — | 2 | 1 | no | — |
| 229 | C2×C3 | — | 2 | 1 | no | — |
| 230 | C2×C3 | — | 2 | 1 | no | — |
| 231 | C2×C3 | — | 2 | 1 | no | — |
| 232 | C2×C3 | — | 2 | 1 | no | — |
| 233 | C2×C3 | — | 24 | 3 | no | — |
| 234 | D3 | — | 8 | 3 | no | — |
| 235 | C22 | — | 12 | 3 | no | — |
| 236 | C22 | — | 12 | 3 | no | — |
| 237 | C22 | — | 12 | 3 | no | — |
| 238 | C22 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 239 | C4 | — | 9 | 1 | no | — |
| 240 | C4 | — | 9 | 1 | no | — |
| 241 | C4 | — | 12 | 1 | no | — |
| 242 | C4 | — | 12 | 3 | no | — |
| 243 | C4 | — | 12 | 1 | no | — |
| 244 | C4 | — | 18 | 3 | no | — |
| 245 | C4 | C2×#3775 | 1 | 6 | yes | — |
| 246 | C3 | — | 2 | 1 | no | — |
| 247 | C3 | — | 2 | 1 | no | — |
| 248 | C2 | — | 24 | 3 | no | — |
| 249 | C2 | #10596521 | 1 | 1 | yes | characteristic |
| 250 | C2 | #10596525 | 1 | 1 | yes | characteristic |
| 251 | C2 | C22×#3775 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10595351 | C2 | semidirect |
| 3. Q8×#622 | C2 | semidirect |
| 4. #10593442 | C2 | semidirect |
| 5. #10593439 | C2 | semidirect |
| 6. #10593437 | C2 | semidirect |
| 7. C4×#3775 | C2 | semidirect |
| 62. C32×Q8 | SD16 | semidirect |
| 77. #622 | #41 | semidirect |
| 209. C32 | #3392 | semidirect |
| 213. Q8 | #3775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595412 | 2 |
| #10595351 | 2 |
| Q8×#622 | 2 |
| #10593442 | 2 |
| #10593439 | 2 |
| #10593437 | 2 |
| C4×#3775 | 2 |
| #3392 | 9 |