Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 133 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, complemented |
| 2 | #10593101 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #10593100 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10593098 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×#63692 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #87298 | — | 3 | 1 | no | maximal |
| 7 | #63715 | — | 4 | 1 | no | maximal |
| 8 | 2−1+4⋊C9 | C22 | 1 | 3 | yes | complemented |
| 9 | #63700 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×#41⋊C9 | C22 | 1 | 3 | yes | complemented |
| 11 | #63692 | C22 | 1 | 3 | yes | complemented |
| 12 | #63692 | C22 | 1 | 6 | yes | complemented |
| 13 | #63691 | C22 | 1 | 6 | yes | complemented |
| 14 | #63690 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #63689 | C22 | 1 | 6 | yes | complemented |
| 16 | C2×#3689 | C22 | 1 | 6 | yes | complemented |
| 17 | C3×#585 | D3 | 1 | 1 | yes | characteristic |
| 18 | C2×#1009 | — | 3 | 1 | no | — |
| 19 | #5837 | — | 3 | 2 | no | — |
| 20 | #5837 | — | 3 | 6 | no | — |
| 21 | #5835 | — | 3 | 6 | no | — |
| 22 | #5835 | — | 3 | 2 | no | — |
| 23 | #5822 | — | 3 | 3 | no | — |
| 24 | #5822 | — | 3 | 3 | no | — |
| 25 | C2×#949 | — | 3 | 3 | no | — |
| 26 | C2×#949 | — | 3 | 3 | no | — |
| 27 | #5819 | — | 3 | 1 | no | — |
| 28 | C9×#41 | — | 4 | 1 | no | — |
| 29 | #3701 | — | 4 | 2 | no | — |
| 30 | D4×D9 | — | 4 | 6 | no | — |
| 31 | #3697 | — | 4 | 3 | no | — |
| 32 | C2×D36 | — | 4 | 3 | no | — |
| 33 | #41⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 34 | #41⋊C9 | C23 | 1 | 3 | yes | complemented |
| 35 | C2×Q8⋊C9 | C23 | 1 | 3 | yes | complemented |
| 36 | #3689 | C23 | 1 | 6 | yes | complemented |
| 37 | #3688 | C23 | 1 | 2 | yes | complemented |
| 38 | #3585 | — | 9 | 1 | no | Sylow |
| 39 | C3×2−1+4 | — | 3 | 1 | no | — |
| 40 | C3×2−1+4 | C2×D3 | 1 | 3 | yes | — |
| 41 | C3×H(5,𝔽2) | — | 3 | 3 | no | — |
| 42 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 43 | C2×C3×#41 | — | 3 | 1 | no | — |
| 44 | C2×C3×#41 | — | 3 | 3 | no | — |
| 45 | C2×C3×#41 | C2×D3 | 1 | 3 | yes | — |
| 46 | #1009 | — | 3 | 2 | no | — |
| 47 | #1009 | — | 3 | 6 | no | — |
| 48 | #1009 | — | 6 | 3 | no | — |
| 49 | #1009 | — | 6 | 1 | no | — |
| 50 | C2×#239 | — | 6 | 1 | no | — |
| 51 | C2×D3×D4 | — | 6 | 3 | no | — |
| 52 | C2×#235 | — | 3 | 3 | no | — |
| 53 | C22×D12 | — | 3 | 3 | no | — |
| 54 | #951 | — | 3 | 3 | no | — |
| 55 | #951 | — | 3 | 1 | no | — |
| 56 | #950 | — | 3 | 6 | no | — |
| 57 | #950 | — | 3 | 12 | no | — |
| 58 | #950 | — | 3 | 6 | no | — |
| 59 | #949 | — | 3 | 3 | no | — |
| 60 | #949 | — | 3 | 6 | no | — |
| 61 | #949 | — | 3 | 6 | no | — |
| 62 | #949 | — | 3 | 12 | no | — |
| 63 | #949 | — | 3 | 3 | no | — |
| 64 | #949 | — | 3 | 6 | no | — |
| 65 | #948 | — | 3 | 2 | no | — |
| 66 | #948 | — | 3 | 6 | no | — |
| 67 | #942 | — | 3 | 6 | no | — |
| 68 | #942 | — | 3 | 6 | no | — |
| 69 | C2×#215 | — | 3 | 6 | no | — |
| 70 | C2×#215 | — | 3 | 6 | no | — |
| 71 | #932 | — | 3 | 6 | no | — |
| 72 | #932 | — | 3 | 6 | no | — |
| 73 | C2×#213 | — | 3 | 6 | no | — |
| 74 | C2×#213 | — | 3 | 6 | no | — |
| 75 | C2×#208 | — | 3 | 3 | no | — |
| 76 | C2×#208 | — | 3 | 3 | no | — |
| 77 | C22×D9 | — | 4 | 6 | no | — |
| 78 | Q8×C9 | — | 4 | 1 | no | — |
| 79 | D4×C9 | — | 4 | 3 | no | — |
| 80 | C2×C4×C9 | — | 4 | 3 | no | — |
| 81 | #611 | — | 4 | 6 | no | — |
| 82 | D36 | — | 4 | 3 | no | — |
| 83 | D36 | — | 4 | 6 | no | — |
| 84 | C4×D9 | — | 4 | 6 | no | — |
| 85 | Dic18 | — | 4 | 1 | no | — |
| 86 | Q8⋊C9 | C24 | 1 | 1 | yes | characteristic |
| 87 | #585 | D9 | 1 | 1 | yes | characteristic, complemented |
| 88 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 89 | #577 | — | 9 | 2 | no | — |
| 90 | #577 | — | 9 | 6 | no | — |
| 91 | #576 | — | 9 | 6 | no | — |
| 92 | #576 | — | 9 | 2 | no | — |
| 93 | #575 | — | 9 | 3 | no | — |
| 94 | #575 | — | 9 | 3 | no | — |
| 95 | C2×AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 96 | C2×AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 97 | #568 | — | 9 | 1 | no | — |
| 98 | C23×D3 | — | 6 | 3 | no | — |
| 99 | C3×#41 | — | 3 | 1 | no | — |
| 100 | C3×#41 | — | 3 | 3 | no | — |
| 101 | C3×#41 | — | 3 | 3 | no | — |
| 102 | C3×#41 | — | 3 | 3 | no | — |
| 103 | C3×#41 | — | 3 | 3 | no | — |
| 104 | C3×#41 | — | 3 | 6 | no | — |
| 105 | C3×#41 | — | 6 | 3 | no | — |
| 106 | C3×#41 | S4 | 1 | 1 | yes | characteristic |
| 107 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 108 | C3×#41 | C22×D3 | 1 | 3 | yes | — |
| 109 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 110 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 111 | C2×C3×Q8 | C22×D3 | 1 | 3 | yes | — |
| 112 | C2×C3×D4 | — | 3 | 3 | no | — |
| 113 | C2×C3×D4 | — | 3 | 3 | no | — |
| 114 | C2×C3×D4 | — | 3 | 3 | no | — |
| 115 | C2×C3×D4 | — | 6 | 3 | no | — |
| 116 | C22×C3×C4 | — | 3 | 3 | no | — |
| 117 | C22×C3×C4 | — | 6 | 1 | no | — |
| 118 | C2×#67 | — | 6 | 3 | no | — |
| 119 | #239 | — | 6 | 6 | no | — |
| 120 | #239 | — | 6 | 2 | no | — |
| 121 | D3×D4 | — | 6 | 12 | no | — |
| 122 | D3×D4 | — | 6 | 6 | no | — |
| 123 | D3×D4 | — | 6 | 6 | no | — |
| 124 | #235 | — | 3 | 6 | no | — |
| 125 | #235 | — | 3 | 6 | no | — |
| 126 | #235 | — | 6 | 3 | no | — |
| 127 | #235 | — | 6 | 3 | no | — |
| 128 | C2×D12 | — | 3 | 6 | no | — |
| 129 | C2×D12 | — | 3 | 6 | no | — |
| 130 | C2×D12 | — | 3 | 3 | no | — |
| 131 | C2×D12 | — | 6 | 3 | no | — |
| 132 | C2×D12 | — | 6 | 3 | no | — |
| 133 | C2×D12 | — | 6 | 3 | no | — |
| 134 | C2×C4×D3 | — | 6 | 3 | no | — |
| 135 | C2×Dic6 | — | 3 | 1 | no | — |
| 136 | #216 | — | 3 | 6 | no | — |
| 137 | #216 | — | 3 | 2 | no | — |
| 138 | #215 | — | 3 | 6 | no | — |
| 139 | #215 | — | 3 | 12 | no | — |
| 140 | #215 | — | 3 | 6 | no | — |
| 141 | #214 | — | 3 | 2 | no | — |
| 142 | #214 | — | 3 | 6 | no | — |
| 143 | #213 | — | 3 | 6 | no | — |
| 144 | #213 | — | 3 | 12 | no | — |
| 145 | #213 | — | 3 | 6 | no | — |
| 146 | #208 | — | 3 | 1 | no | — |
| 147 | #208 | — | 3 | 3 | no | — |
| 148 | #208 | — | 3 | 6 | no | — |
| 149 | #208 | — | 3 | 6 | no | — |
| 150 | C2×C3⋊C8 | — | 3 | 6 | no | — |
| 151 | C2×C3⋊C8 | — | 3 | 6 | no | — |
| 152 | C22×C9 | — | 4 | 3 | no | — |
| 153 | C2×D9 | — | 4 | 6 | no | — |
| 154 | C2×D9 | — | 16 | 6 | no | — |
| 155 | C4×C9 | — | 4 | 1 | no | — |
| 156 | C4×C9 | — | 4 | 3 | no | — |
| 157 | Dic9 | — | 4 | 2 | no | — |
| 158 | 2−1+4 | — | 3 | 1 | no | — |
| 159 | 2−1+4 | C2×D9 | 1 | 3 | yes | complemented |
| 160 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 161 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 162 | H(5,𝔽2) | — | 9 | 6 | no | — |
| 163 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 164 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 165 | H(5,𝔽2) | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 166 | C2×#41 | — | 3 | 1 | no | — |
| 167 | C2×#41 | — | 3 | 3 | no | — |
| 168 | C2×#41 | — | 9 | 3 | no | — |
| 169 | C2×#41 | — | 18 | 1 | no | — |
| 170 | C2×#41 | C2×D9 | 1 | 3 | yes | complemented |
| 171 | C22×D4 | — | 9 | 3 | no | — |
| 172 | C22×D4 | — | 18 | 3 | no | — |
| 173 | #137 | — | 9 | 6 | no | — |
| 174 | #137 | — | 9 | 3 | no | — |
| 175 | #137 | — | 9 | 1 | no | — |
| 176 | #137 | — | 9 | 6 | no | — |
| 177 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 178 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 179 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 180 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 181 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 182 | AGL(1,ℤ/8) | — | 9 | 12 | no | — |
| 183 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 184 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 185 | #135 | — | 9 | 6 | no | — |
| 186 | #135 | — | 9 | 12 | no | — |
| 187 | #135 | — | 9 | 6 | no | — |
| 188 | C2×SD16 | — | 9 | 6 | no | — |
| 189 | C2×SD16 | — | 9 | 6 | no | — |
| 190 | C2×D8 | — | 9 | 6 | no | — |
| 191 | C2×D8 | — | 9 | 6 | no | — |
| 192 | #131 | — | 9 | 2 | no | — |
| 193 | #131 | — | 9 | 6 | no | — |
| 194 | C2×M16 | — | 9 | 3 | no | — |
| 195 | C2×M16 | — | 9 | 3 | no | — |
| 196 | C23×C3 | — | 3 | 3 | no | — |
| 197 | C23×C3 | — | 6 | 1 | no | — |
| 198 | C22×D3 | — | 6 | 3 | no | — |
| 199 | C22×D3 | — | 6 | 6 | no | — |
| 200 | C22×D3 | — | 6 | 6 | no | — |
| 201 | C22×D3 | — | 24 | 6 | no | — |
| 202 | C3×Q8 | — | 3 | 3 | no | — |
| 203 | C3×Q8 | — | 3 | 3 | no | — |
| 204 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 205 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 206 | C3×D4 | — | 3 | 1 | no | — |
| 207 | C3×D4 | — | 3 | 3 | no | — |
| 208 | C3×D4 | — | 3 | 6 | no | — |
| 209 | C3×D4 | — | 3 | 3 | no | — |
| 210 | C3×D4 | — | 6 | 3 | no | — |
| 211 | C3×D4 | C2×S4 | 1 | 3 | yes | — |
| 212 | C2×C3×C4 | — | 3 | 3 | no | — |
| 213 | C2×C3×C4 | — | 3 | 3 | no | — |
| 214 | C2×C3×C4 | — | 3 | 1 | no | — |
| 215 | C2×C3×C4 | — | 3 | 3 | no | — |
| 216 | C2×C3×C4 | — | 3 | 3 | no | — |
| 217 | C2×C3×C4 | — | 6 | 3 | no | — |
| 218 | C2×C3×C4 | C2×S4 | 1 | 3 | yes | — |
| 219 | #67 | — | 6 | 6 | no | — |
| 220 | #67 | — | 6 | 6 | no | — |
| 221 | C2×Dic3 | — | 6 | 1 | no | — |
| 222 | D12 | — | 3 | 6 | no | — |
| 223 | D12 | — | 6 | 6 | no | — |
| 224 | D12 | — | 6 | 3 | no | — |
| 225 | D12 | — | 6 | 6 | no | — |
| 226 | C4×D3 | — | 6 | 6 | no | — |
| 227 | C4×D3 | — | 6 | 6 | no | — |
| 228 | Dic6 | — | 3 | 2 | no | — |
| 229 | Dic6 | — | 6 | 1 | no | — |
| 230 | C3⋊C8 | — | 3 | 2 | no | — |
| 231 | C3⋊C8 | — | 3 | 6 | no | — |
| 232 | C2×C9 | — | 4 | 1 | no | — |
| 233 | C2×C9 | — | 8 | 3 | no | — |
| 234 | D9 | — | 8 | 6 | no | — |
| 235 | C24 | — | 18 | 3 | no | — |
| 236 | #41 | — | 3 | 1 | no | — |
| 237 | #41 | — | 3 | 3 | no | — |
| 238 | #41 | — | 3 | 3 | no | — |
| 239 | #41 | — | 3 | 3 | no | — |
| 240 | #41 | — | 3 | 3 | no | — |
| 241 | #41 | — | 3 | 6 | no | — |
| 242 | #41 | — | 6 | 3 | no | — |
| 243 | #41 | — | 9 | 6 | no | — |
| 244 | #41 | — | 9 | 6 | no | — |
| 245 | #41 | — | 18 | 3 | no | — |
| 246 | #41 | — | 18 | 6 | no | — |
| 247 | #41 | — | 18 | 2 | no | — |
| 248 | #41 | — | 18 | 3 | no | — |
| 249 | #41 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 250 | #41 | C22×D9 | 1 | 3 | yes | — |
| 251 | #41 | C22×D9 | 1 | 1 | yes | characteristic |
| 252 | C2×Q8 | — | 3 | 1 | no | — |
| 253 | C2×Q8 | — | 3 | 3 | no | — |
| 254 | C2×Q8 | — | 9 | 1 | no | — |
| 255 | C2×Q8 | C22×D9 | 1 | 3 | yes | — |
| 256 | C2×D4 | — | 3 | 3 | no | — |
| 257 | C2×D4 | — | 3 | 3 | no | — |
| 258 | C2×D4 | — | 3 | 3 | no | — |
| 259 | C2×D4 | — | 6 | 3 | no | — |
| 260 | C2×D4 | — | 9 | 6 | no | — |
| 261 | C2×D4 | — | 9 | 6 | no | — |
| 262 | C2×D4 | — | 9 | 3 | no | — |
| 263 | C2×D4 | — | 18 | 3 | no | — |
| 264 | C2×D4 | — | 18 | 3 | no | — |
| 265 | C2×D4 | — | 18 | 12 | no | — |
| 266 | C2×D4 | — | 18 | 6 | no | — |
| 267 | C2×D4 | — | 18 | 3 | no | — |
| 268 | C2×D4 | — | 18 | 6 | no | — |
| 269 | C2×D4 | — | 18 | 3 | no | — |
| 270 | C22×C4 | — | 3 | 3 | no | — |
| 271 | C22×C4 | — | 6 | 1 | no | — |
| 272 | C22×C4 | — | 18 | 3 | no | — |
| 273 | Q16 | — | 9 | 6 | no | — |
| 274 | Q16 | — | 9 | 2 | no | — |
| 275 | SD16 | — | 9 | 2 | no | — |
| 276 | SD16 | — | 9 | 6 | no | — |
| 277 | SD16 | — | 9 | 6 | no | — |
| 278 | SD16 | — | 9 | 12 | no | — |
| 279 | SD16 | — | 9 | 6 | no | — |
| 280 | D8 | — | 9 | 12 | no | — |
| 281 | D8 | — | 9 | 6 | no | — |
| 282 | D8 | — | 9 | 6 | no | — |
| 283 | M16 | — | 9 | 1 | no | — |
| 284 | M16 | — | 9 | 3 | no | — |
| 285 | M16 | — | 9 | 6 | no | — |
| 286 | M16 | — | 9 | 6 | no | — |
| 287 | C2×C8 | — | 9 | 6 | no | — |
| 288 | C2×C8 | — | 9 | 6 | no | — |
| 289 | C22×C3 | — | 3 | 1 | no | — |
| 290 | C22×C3 | — | 3 | 3 | no | — |
| 291 | C22×C3 | — | 12 | 3 | no | — |
| 292 | C22×C3 | — | 24 | 1 | no | — |
| 293 | C22×C3 | C22×S4 | 1 | 3 | yes | — |
| 294 | C2×D3 | — | 6 | 6 | no | — |
| 295 | C2×D3 | — | 12 | 6 | no | — |
| 296 | C2×D3 | — | 24 | 6 | no | — |
| 297 | C2×D3 | — | 24 | 6 | no | — |
| 298 | C3×C4 | — | 3 | 1 | no | — |
| 299 | C3×C4 | — | 3 | 3 | no | — |
| 300 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 301 | C3×C4 | C22×S4 | 1 | 3 | yes | — |
| 302 | Dic3 | — | 6 | 2 | no | — |
| 303 | C9 | — | 4 | 1 | no | Sylow |
| 304 | C23 | — | 3 | 3 | no | — |
| 305 | C23 | — | 6 | 1 | no | — |
| 306 | C23 | — | 18 | 3 | no | — |
| 307 | C23 | — | 18 | 6 | no | — |
| 308 | C23 | — | 18 | 6 | no | — |
| 309 | C23 | — | 72 | 6 | no | — |
| 310 | Q8 | — | 3 | 3 | no | — |
| 311 | Q8 | — | 3 | 3 | no | — |
| 312 | Q8 | — | 9 | 2 | no | — |
| 313 | Q8 | — | 18 | 1 | no | — |
| 314 | Q8 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 315 | Q8 | C23×D9 | 1 | 1 | yes | characteristic |
| 316 | D4 | — | 3 | 1 | no | — |
| 317 | D4 | — | 3 | 3 | no | — |
| 318 | D4 | — | 3 | 6 | no | — |
| 319 | D4 | — | 3 | 3 | no | — |
| 320 | D4 | — | 6 | 3 | no | — |
| 321 | D4 | — | 9 | 6 | no | — |
| 322 | D4 | — | 18 | 6 | no | — |
| 323 | D4 | — | 18 | 6 | no | — |
| 324 | D4 | — | 18 | 6 | no | — |
| 325 | D4 | — | 18 | 3 | no | — |
| 326 | D4 | — | 18 | 6 | no | — |
| 327 | D4 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 328 | C2×C4 | — | 3 | 3 | no | — |
| 329 | C2×C4 | — | 3 | 3 | no | — |
| 330 | C2×C4 | — | 3 | 1 | no | — |
| 331 | C2×C4 | — | 3 | 3 | no | — |
| 332 | C2×C4 | — | 3 | 3 | no | — |
| 333 | C2×C4 | — | 6 | 3 | no | — |
| 334 | C2×C4 | — | 18 | 6 | no | — |
| 335 | C2×C4 | — | 18 | 1 | no | — |
| 336 | C2×C4 | — | 18 | 6 | no | — |
| 337 | C2×C4 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 338 | C8 | — | 9 | 2 | no | — |
| 339 | C8 | — | 9 | 6 | no | — |
| 340 | C2×C3 | — | 2 | 3 | no | — |
| 341 | C2×C3 | — | 6 | 1 | no | — |
| 342 | C2×C3 | — | 6 | 3 | no | — |
| 343 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 344 | D3 | — | 12 | 6 | no | — |
| 345 | C22 | — | 3 | 1 | no | — |
| 346 | C22 | — | 3 | 3 | no | — |
| 347 | C22 | — | 12 | 3 | no | — |
| 348 | C22 | — | 18 | 6 | no | — |
| 349 | C22 | — | 24 | 1 | no | — |
| 350 | C22 | — | 36 | 6 | no | — |
| 351 | C22 | — | 72 | 6 | no | — |
| 352 | C22 | — | 72 | 6 | no | — |
| 353 | C22 | C22×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 354 | C4 | — | 3 | 1 | no | — |
| 355 | C4 | — | 3 | 3 | no | — |
| 356 | C4 | — | 18 | 2 | no | — |
| 357 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 358 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 359 | C3 | #87498 | 1 | 1 | yes | characteristic |
| 360 | C2 | — | 2 | 3 | no | — |
| 361 | C2 | — | 6 | 1 | no | — |
| 362 | C2 | — | 6 | 3 | no | — |
| 363 | C2 | — | 36 | 6 | no | — |
| 364 | C2 | C23×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×(C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C24 |
| Frattini, socle | C2×C3 | C23×S4 |
| Fitting | C3×#585 | D3 |
| hypercenter | #41 | (C22⋊C9)⋊C2 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10593120 | C2 | semidirect |
| 2. #10593101 | C2 | semidirect |
| 3. #10593100 | C2 | semidirect |
| 4. #10593098 | C2 | semidirect |
| 5. C2×#63692 | C2 | semidirect |
| 8. 2−1+4⋊C9 | C22 | semidirect |
| 9. #63700 | C22 | semidirect |
| 10. C2×#41⋊C9 | C22 | semidirect |
| 11. #63692 | C22 | semidirect |
| 12. #63692 | C22 | semidirect |
| 13. #63691 | C22 | semidirect |
| 14. #63690 | C22 | semidirect |
| 15. #63689 | C22 | semidirect |
| 16. C2×#3689 | C22 | semidirect |
| 34. #41⋊C9 | C23 | semidirect |
| 35. C2×Q8⋊C9 | C23 | semidirect |
| 36. #3689 | C23 | semidirect |
| 37. #3688 | C23 | semidirect |
| 87. #585 | D9 | semidirect |
| 159. 2−1+4 | C2×D9 | semidirect |
| 165. H(5,𝔽2) | C2×D9 | semidirect |
| 170. C2×#41 | C2×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593120 | 2 |
| #10593101 | 2 |
| #10593100 | 2 |
| #10593098 | 2 |
| C2×#63692 | 2 |
| #87298 | 3 |
| #63715 | 4 |