Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
822 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 128 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 | #10593139 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C9×#410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10588912 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10588685 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10588683 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #70054 | — | 3 | 1 | no | maximal |
| 7 | C2×C9×#41 | C22 | 1 | 1 | yes | characteristic |
| 8 | #63716 | — | 2 | 2 | no | — |
| 9 | #63715 | — | 2 | 2 | no | — |
| 10 | #41×D9 | — | 2 | 4 | no | — |
| 11 | #63713 | C4 | 1 | 2 | yes | complemented |
| 12 | #63710 | — | 2 | 2 | no | — |
| 13 | #63710 | C4 | 1 | 2 | yes | complemented |
| 14 | C2×#3697 | — | 2 | 2 | no | — |
| 15 | C2×#3697 | C22 | 1 | 2 | yes | — |
| 16 | C9×#117 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×#3667 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C22×C9⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C9×#99 | — | 2 | 2 | no | — |
| 20 | #63389 | — | 2 | 2 | no | — |
| 21 | #63369 | — | 2 | 2 | no | — |
| 22 | #63368 | — | 2 | 2 | no | — |
| 23 | #63364 | — | 2 | 4 | no | — |
| 24 | #5964 | — | 3 | 1 | no | — |
| 25 | C3×#410 | D3 | 1 | 1 | yes | characteristic |
| 26 | #5234 | — | 3 | 1 | no | — |
| 27 | #5005 | — | 3 | 2 | no | — |
| 28 | #5002 | — | 3 | 2 | no | — |
| 29 | C9×#41 | — | 2 | 2 | no | — |
| 30 | C9×#41 | — | 2 | 2 | no | — |
| 31 | C2×Q8×C9 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×D4×C9 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C2×D4×C9 | D4 | 1 | 2 | yes | — |
| 34 | C22×C4×C9 | D4 | 1 | 2 | yes | — |
| 35 | C22×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 36 | C2×#611 | — | 2 | 4 | no | — |
| 37 | C2×#611 | — | 2 | 2 | no | — |
| 38 | #3701 | — | 2 | 4 | no | — |
| 39 | Q8×D9 | — | 2 | 4 | no | — |
| 40 | #3699 | — | 2 | 8 | no | — |
| 41 | #3699 | — | 2 | 4 | no | — |
| 42 | D4×D9 | — | 2 | 8 | no | — |
| 43 | D4×D9 | — | 2 | 4 | no | — |
| 44 | #3697 | — | 2 | 4 | no | — |
| 45 | #3697 | — | 2 | 4 | no | — |
| 46 | #3697 | — | 2 | 4 | no | — |
| 47 | #3697 | — | 2 | 2 | no | — |
| 48 | #3697 | — | 2 | 2 | no | — |
| 49 | #3697 | C2×C4 | 1 | 4 | yes | — |
| 50 | #3697 | D4 | 1 | 4 | yes | — |
| 51 | C2×D36 | — | 2 | 2 | no | — |
| 52 | C2×D36 | D4 | 1 | 2 | yes | — |
| 53 | C2×C4×D9 | — | 2 | 4 | no | — |
| 54 | C2×C4×D9 | — | 2 | 2 | no | — |
| 55 | C2×Dic18 | — | 2 | 2 | no | — |
| 56 | C2×Dic18 | D4 | 1 | 2 | yes | — |
| 57 | C9×C4⋊C4 | — | 2 | 2 | no | — |
| 58 | C9×C22⋊C4 | — | 2 | 2 | no | — |
| 59 | C42×C9 | — | 2 | 2 | no | — |
| 60 | #3667 | — | 2 | 2 | no | — |
| 61 | C2×C9⋊C8 | — | 2 | 2 | no | — |
| 62 | C2×C9⋊C8 | — | 2 | 1 | no | — |
| 63 | C2×C9⋊C8 | — | 2 | 1 | no | — |
| 64 | #1794 | — | 9 | 1 | no | Sylow |
| 65 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 66 | #1010 | — | 6 | 2 | no | — |
| 67 | #1009 | — | 6 | 2 | no | — |
| 68 | D3×#41 | — | 6 | 4 | no | — |
| 69 | #1007 | — | 3 | 2 | no | — |
| 70 | #1004 | — | 3 | 2 | no | — |
| 71 | #1004 | — | 6 | 2 | no | — |
| 72 | C2×#235 | — | 3 | 2 | no | — |
| 73 | C2×#235 | — | 6 | 2 | no | — |
| 74 | C3×#117 | C2×D3 | 1 | 2 | yes | — |
| 75 | C2×#208 | — | 3 | 1 | no | — |
| 76 | C22×C3⋊C8 | — | 3 | 1 | no | — |
| 77 | C3×#99 | — | 2 | 2 | no | — |
| 78 | #830 | — | 6 | 2 | no | — |
| 79 | #810 | — | 6 | 2 | no | — |
| 80 | #809 | — | 6 | 2 | no | — |
| 81 | #805 | — | 6 | 4 | no | — |
| 82 | C23×C9 | C22⋊C4 | 1 | 2 | yes | — |
| 83 | C23×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C22×D9 | — | 2 | 4 | no | — |
| 85 | C22×D9 | — | 2 | 2 | no | — |
| 86 | Q8×C9 | — | 2 | 2 | no | — |
| 87 | D4×C9 | — | 2 | 4 | no | — |
| 88 | D4×C9 | — | 2 | 2 | no | — |
| 89 | C2×C4×C9 | — | 2 | 2 | no | — |
| 90 | C2×C4×C9 | — | 2 | 2 | no | — |
| 91 | C2×C4×C9 | — | 4 | 2 | no | — |
| 92 | C2×C4×C9 | C22⋊C4 | 1 | 2 | yes | — |
| 93 | C2×C4×C9 | C22×C4 | 1 | 1 | yes | characteristic |
| 94 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C9 | C2×D4 | 1 | 2 | yes | — |
| 96 | C2×C4×C9 | C2×D4 | 1 | 2 | yes | — |
| 97 | #611 | — | 2 | 8 | no | — |
| 98 | #611 | — | 2 | 4 | no | — |
| 99 | #611 | — | 2 | 4 | no | — |
| 100 | C2×Dic9 | — | 2 | 4 | no | — |
| 101 | C2×Dic9 | — | 2 | 2 | no | — |
| 102 | D36 | — | 2 | 4 | no | — |
| 103 | D36 | — | 2 | 2 | no | — |
| 104 | D36 | C22⋊C4 | 1 | 4 | yes | — |
| 105 | C4×D9 | — | 2 | 8 | no | — |
| 106 | C4×D9 | — | 2 | 4 | no | — |
| 107 | C4×D9 | — | 2 | 4 | no | — |
| 108 | Dic18 | — | 2 | 4 | no | — |
| 109 | Dic18 | — | 2 | 2 | no | — |
| 110 | Dic18 | C22⋊C4 | 1 | 4 | yes | — |
| 111 | C9⋊C8 | — | 4 | 1 | no | — |
| 112 | C9⋊C8 | — | 4 | 1 | no | — |
| 113 | #585 | — | 9 | 1 | no | — |
| 114 | #421 | — | 9 | 2 | no | — |
| 115 | #416 | — | 9 | 2 | no | — |
| 116 | #410 | D9 | 1 | 1 | yes | characteristic, complemented |
| 117 | #408 | — | 9 | 1 | no | — |
| 118 | C3×#41 | — | 2 | 2 | no | — |
| 119 | C3×#41 | — | 2 | 2 | no | — |
| 120 | C2×C3×Q8 | C4×D3 | 1 | 1 | yes | characteristic |
| 121 | C2×C3×D4 | C4×D3 | 1 | 1 | yes | characteristic |
| 122 | C2×C3×D4 | #67 | 1 | 2 | yes | — |
| 123 | C22×C3×C4 | D12 | 1 | 2 | yes | — |
| 124 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 125 | C2×#67 | — | 6 | 4 | no | — |
| 126 | C2×#67 | — | 6 | 2 | no | — |
| 127 | #239 | — | 6 | 4 | no | — |
| 128 | D3×Q8 | — | 6 | 4 | no | — |
| 129 | #237 | — | 6 | 4 | no | — |
| 130 | #237 | — | 6 | 8 | no | — |
| 131 | D3×D4 | — | 6 | 4 | no | — |
| 132 | D3×D4 | — | 6 | 8 | no | — |
| 133 | #235 | — | 3 | 4 | no | — |
| 134 | #235 | — | 3 | 4 | no | — |
| 135 | #235 | — | 6 | 4 | no | — |
| 136 | #235 | — | 6 | 4 | no | — |
| 137 | #235 | — | 6 | 4 | no | — |
| 138 | #235 | — | 6 | 2 | no | — |
| 139 | #235 | — | 6 | 2 | no | — |
| 140 | C2×D12 | — | 3 | 2 | no | — |
| 141 | C2×D12 | — | 6 | 2 | no | — |
| 142 | C2×C4×D3 | — | 6 | 4 | no | — |
| 143 | C2×C4×D3 | — | 6 | 2 | no | — |
| 144 | C2×Dic6 | — | 3 | 2 | no | — |
| 145 | C2×Dic6 | — | 6 | 2 | no | — |
| 146 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 147 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 148 | C3×C42 | — | 2 | 2 | no | — |
| 149 | #208 | — | 6 | 2 | no | — |
| 150 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 151 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 152 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 153 | C22×C9 | — | 2 | 2 | no | — |
| 154 | C22×C9 | — | 4 | 1 | no | — |
| 155 | C22×C9 | — | 4 | 2 | no | — |
| 156 | C22×C9 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 157 | C22×C9 | #120 | 1 | 2 | yes | — |
| 158 | C2×D9 | — | 2 | 4 | no | — |
| 159 | C2×D9 | — | 8 | 2 | no | — |
| 160 | C2×D9 | — | 8 | 4 | no | — |
| 161 | C4×C9 | — | 2 | 2 | no | — |
| 162 | C4×C9 | — | 8 | 2 | no | — |
| 163 | C4×C9 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 164 | C4×C9 | #120 | 1 | 1 | yes | characteristic |
| 165 | C4×C9 | #120 | 1 | 1 | yes | characteristic |
| 166 | Dic9 | — | 2 | 4 | no | — |
| 167 | 2−1+4 | — | 9 | 2 | no | — |
| 168 | 2−1+4 | — | 18 | 2 | no | — |
| 169 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 170 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 171 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 172 | C2×#41 | — | 9 | 2 | no | — |
| 173 | C2×#41 | — | 18 | 4 | no | — |
| 174 | C2×#41 | — | 18 | 2 | no | — |
| 175 | C2×#41 | C2×D9 | 1 | 1 | yes | characteristic |
| 176 | C2×M16 | — | 9 | 1 | no | — |
| 177 | C22×C8 | — | 9 | 1 | no | — |
| 178 | #117 | C2×D9 | 1 | 2 | yes | complemented |
| 179 | #104 | — | 18 | 4 | no | — |
| 180 | #103 | — | 18 | 2 | no | — |
| 181 | #102 | — | 18 | 2 | no | — |
| 182 | #99 | — | 2 | 2 | no | — |
| 183 | C22⋊C8 | — | 18 | 2 | no | — |
| 184 | C23×C3 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 185 | C23×C3 | C2×#67 | 1 | 1 | yes | characteristic |
| 186 | C22×D3 | — | 6 | 4 | no | — |
| 187 | C22×D3 | — | 6 | 2 | no | — |
| 188 | C3×Q8 | — | 2 | 2 | no | — |
| 189 | C3×D4 | — | 2 | 4 | no | — |
| 190 | C3×D4 | — | 2 | 2 | no | — |
| 191 | C2×C3×C4 | — | 2 | 2 | no | — |
| 192 | C2×C3×C4 | — | 2 | 2 | no | — |
| 193 | C2×C3×C4 | — | 4 | 2 | no | — |
| 194 | C2×C3×C4 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 195 | C2×C3×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 196 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 197 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 198 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 199 | #67 | — | 6 | 8 | no | — |
| 200 | #67 | — | 6 | 4 | no | — |
| 201 | #67 | — | 6 | 4 | no | — |
| 202 | C2×Dic3 | — | 6 | 4 | no | — |
| 203 | C2×Dic3 | — | 6 | 2 | no | — |
| 204 | D12 | — | 3 | 4 | no | — |
| 205 | D12 | — | 6 | 4 | no | — |
| 206 | D12 | — | 6 | 2 | no | — |
| 207 | C4×D3 | — | 6 | 8 | no | — |
| 208 | C4×D3 | — | 6 | 4 | no | — |
| 209 | C4×D3 | — | 6 | 4 | no | — |
| 210 | Dic6 | — | 3 | 4 | no | — |
| 211 | Dic6 | — | 6 | 4 | no | — |
| 212 | Dic6 | — | 6 | 2 | no | — |
| 213 | C3⋊C8 | — | 12 | 1 | no | — |
| 214 | C3⋊C8 | — | 12 | 1 | no | — |
| 215 | C2×C9 | — | 2 | 2 | no | — |
| 216 | C2×C9 | — | 2 | 1 | no | — |
| 217 | C2×C9 | — | 4 | 2 | no | — |
| 218 | C2×C9 | #379 | 1 | 1 | yes | characteristic |
| 219 | D9 | — | 4 | 4 | no | — |
| 220 | #41 | — | 2 | 2 | no | — |
| 221 | #41 | — | 2 | 2 | no | — |
| 222 | #41 | — | 9 | 4 | no | — |
| 223 | #41 | — | 9 | 4 | no | — |
| 224 | #41 | — | 18 | 4 | no | — |
| 225 | #41 | — | 18 | 4 | no | — |
| 226 | #41 | — | 18 | 4 | no | — |
| 227 | #41 | — | 18 | 8 | no | — |
| 228 | #41 | — | 18 | 4 | no | — |
| 229 | #41 | — | 18 | 4 | no | — |
| 230 | #41 | — | 18 | 2 | no | — |
| 231 | #41 | — | 18 | 2 | no | — |
| 232 | C2×Q8 | — | 9 | 2 | no | — |
| 233 | C2×Q8 | — | 18 | 2 | no | — |
| 234 | C2×Q8 | — | 18 | 4 | no | — |
| 235 | C2×Q8 | C4×D9 | 1 | 1 | yes | characteristic |
| 236 | C2×D4 | — | 9 | 2 | no | — |
| 237 | C2×D4 | — | 18 | 2 | no | — |
| 238 | C2×D4 | — | 18 | 4 | no | — |
| 239 | C2×D4 | — | 18 | 8 | no | — |
| 240 | C2×D4 | — | 18 | 4 | no | — |
| 241 | C2×D4 | — | 18 | 2 | no | — |
| 242 | C2×D4 | C4×D9 | 1 | 1 | yes | characteristic |
| 243 | C2×D4 | #611 | 1 | 2 | yes | — |
| 244 | C22×C4 | — | 18 | 4 | no | — |
| 245 | C22×C4 | — | 18 | 2 | no | — |
| 246 | C22×C4 | D36 | 1 | 2 | yes | — |
| 247 | C22×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 248 | M16 | — | 18 | 2 | no | — |
| 249 | C2×C8 | — | 18 | 1 | no | — |
| 250 | C2×C8 | — | 18 | 1 | no | — |
| 251 | C2×C8 | — | 18 | 2 | no | — |
| 252 | C4⋊C4 | — | 2 | 2 | no | — |
| 253 | C22⋊C4 | — | 2 | 2 | no | — |
| 254 | C42 | — | 2 | 2 | no | — |
| 255 | C22×C3 | — | 2 | 2 | no | — |
| 256 | C22×C3 | — | 4 | 1 | no | — |
| 257 | C22×C3 | — | 4 | 2 | no | — |
| 258 | C22×C3 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 259 | C22×C3 | #937 | 1 | 2 | yes | — |
| 260 | C2×D3 | — | 6 | 4 | no | — |
| 261 | C2×D3 | — | 24 | 2 | no | — |
| 262 | C2×D3 | — | 24 | 4 | no | — |
| 263 | C3×C4 | — | 2 | 2 | no | — |
| 264 | C3×C4 | — | 8 | 2 | no | — |
| 265 | C3×C4 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 266 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 267 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 268 | Dic3 | — | 6 | 4 | no | — |
| 269 | C9 | #1794 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 270 | C23 | — | 18 | 4 | no | — |
| 271 | C23 | — | 18 | 2 | no | — |
| 272 | C23 | (C2×D9)⋊C4 | 1 | 2 | yes | — |
| 273 | C23 | C2×#611 | 1 | 1 | yes | characteristic |
| 274 | Q8 | — | 2 | 2 | no | — |
| 275 | Q8 | — | 9 | 4 | no | — |
| 276 | Q8 | — | 18 | 4 | no | — |
| 277 | Q8 | — | 18 | 2 | no | — |
| 278 | D4 | — | 2 | 4 | no | — |
| 279 | D4 | — | 2 | 2 | no | — |
| 280 | D4 | — | 9 | 4 | no | — |
| 281 | D4 | — | 18 | 4 | no | — |
| 282 | D4 | — | 18 | 8 | no | — |
| 283 | D4 | — | 18 | 4 | no | — |
| 284 | D4 | — | 18 | 4 | no | — |
| 285 | D4 | — | 18 | 2 | no | — |
| 286 | C2×C4 | — | 2 | 2 | no | — |
| 287 | C2×C4 | — | 2 | 2 | no | — |
| 288 | C2×C4 | — | 4 | 2 | no | — |
| 289 | C2×C4 | — | 18 | 8 | no | — |
| 290 | C2×C4 | — | 18 | 4 | no | — |
| 291 | C2×C4 | — | 18 | 2 | no | — |
| 292 | C2×C4 | — | 18 | 4 | no | — |
| 293 | C2×C4 | — | 18 | 4 | no | — |
| 294 | C2×C4 | (C2×D9)⋊C4 | 1 | 2 | yes | — |
| 295 | C2×C4 | C2×C4×D9 | 1 | 1 | yes | characteristic |
| 296 | C2×C4 | C2×D36 | 1 | 1 | yes | characteristic |
| 297 | C2×C4 | D4×D9 | 1 | 2 | yes | — |
| 298 | C2×C4 | D4×D9 | 1 | 2 | yes | — |
| 299 | C8 | — | 36 | 1 | no | — |
| 300 | C8 | — | 36 | 1 | no | — |
| 301 | C2×C3 | — | 2 | 2 | no | — |
| 302 | C2×C3 | — | 2 | 1 | no | — |
| 303 | C2×C3 | — | 4 | 2 | no | — |
| 304 | C2×C3 | #4955 | 1 | 1 | yes | characteristic |
| 305 | D3 | — | 12 | 4 | no | — |
| 306 | C22 | — | 2 | 2 | no | — |
| 307 | C22 | — | 4 | 1 | no | — |
| 308 | C22 | — | 4 | 2 | no | — |
| 309 | C22 | — | 18 | 4 | no | — |
| 310 | C22 | — | 72 | 2 | no | — |
| 311 | C22 | — | 72 | 4 | no | — |
| 312 | C22 | C2×(C2×D9)⋊C4 | 1 | 1 | yes | characteristic |
| 313 | C22 | #63499 | 1 | 2 | yes | — |
| 314 | C4 | — | 2 | 2 | no | — |
| 315 | C4 | — | 8 | 2 | no | — |
| 316 | C4 | — | 18 | 4 | no | — |
| 317 | C4 | C22⋊C4×D9 | 1 | 2 | yes | — |
| 318 | C4 | #63444 | 1 | 1 | yes | characteristic |
| 319 | C4 | #63444 | 1 | 1 | yes | characteristic |
| 320 | C3 | #70054 | 1 | 1 | yes | characteristic |
| 321 | C2 | — | 2 | 2 | no | — |
| 322 | C2 | — | 2 | 1 | no | — |
| 323 | C2 | — | 4 | 2 | no | — |
| 324 | C2 | — | 36 | 4 | no | — |
| 325 | C2 | #10588635 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#410 | C2 | semidirect |
| 3. #10588912 | C2 | semidirect |
| 4. #10588685 | C2 | semidirect |
| 5. #10588683 | C2 | semidirect |
| 11. #63713 | C4 | semidirect |
| 13. #63710 | C4 | semidirect |
| 16. C9×#117 | C22 | semidirect |
| 17. C2×#3667 | C22 | semidirect |
| 18. C22×C9⋊C8 | C22 | semidirect |
| 116. #410 | D9 | semidirect |
| 178. #117 | C2×D9 | semidirect |
| 269. C9 | #1794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593139 | 2 |
| C9×#410 | 2 |
| #10588912 | 2 |
| #10588685 | 2 |
| #10588683 | 2 |
| #70054 | 3 |