Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
826 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 97 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 | C3×2−1+4⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722391 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11722390 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722385 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×C3⋊#3689 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10596308 | — | 3 | 1 | no | maximal |
| 7 | #10593101 | — | 3 | 3 | no | maximal |
| 8 | D4×C3⋊D9 | — | 4 | 1 | no | maximal |
| 9 | C3×#41⋊C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×C3×Q8⋊C9 | C22 | 1 | 2 | yes | complemented |
| 11 | C3⋊#3689 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3⋊#3689 | C22 | 1 | 2 | yes | complemented |
| 13 | C3⋊#3688 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C32×2−1+4 | D3 | 1 | 1 | yes | characteristic |
| 15 | #64366 | — | 3 | 1 | no | — |
| 16 | #64159 | — | 3 | 2 | no | — |
| 17 | #64159 | — | 3 | 1 | no | — |
| 18 | #64158 | — | 3 | 2 | no | — |
| 19 | #64158 | — | 3 | 1 | no | — |
| 20 | #64157 | — | 3 | 1 | no | — |
| 21 | #64151 | — | 3 | 1 | no | — |
| 22 | #64151 | — | 3 | 2 | no | — |
| 23 | C2×#3755 | — | 3 | 1 | no | — |
| 24 | C2×#3755 | — | 3 | 2 | no | — |
| 25 | 2−1+4⋊C9 | D3 | 1 | 3 | yes | complemented |
| 26 | #63692 | — | 3 | 3 | no | — |
| 27 | #63691 | — | 3 | 3 | no | — |
| 28 | #63689 | — | 3 | 6 | no | — |
| 29 | C2×#3689 | — | 3 | 6 | no | — |
| 30 | C22×C3⋊D9 | — | 4 | 2 | no | — |
| 31 | C3×D4×C9 | — | 4 | 1 | no | — |
| 32 | #6233 | — | 4 | 2 | no | — |
| 33 | C4⋊(C3⋊D9) | — | 4 | 1 | no | — |
| 34 | C4×C3⋊D9 | — | 4 | 1 | no | — |
| 35 | C3×Q8⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 36 | #5837 | — | 9 | 3 | no | — |
| 37 | #5837 | — | 9 | 1 | no | — |
| 38 | C32×#41 | — | 3 | 1 | no | — |
| 39 | C32×#41 | — | 3 | 2 | no | — |
| 40 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 41 | C2×C32×Q8 | — | 3 | 1 | no | — |
| 42 | C2×C32×Q8 | C2×D3 | 1 | 2 | yes | — |
| 43 | #3832 | — | 6 | 1 | no | — |
| 44 | D4×C3⋊D3 | — | 6 | 2 | no | — |
| 45 | D4×C3⋊D3 | — | 6 | 1 | no | — |
| 46 | #3828 | — | 3 | 2 | no | — |
| 47 | #3828 | — | 3 | 1 | no | — |
| 48 | C2×C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 49 | C2×C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 50 | #3756 | — | 3 | 2 | no | — |
| 51 | #3756 | — | 3 | 1 | no | — |
| 52 | #3755 | — | 3 | 2 | no | — |
| 53 | #3755 | — | 3 | 2 | no | — |
| 54 | #3755 | — | 3 | 2 | no | — |
| 55 | #3755 | — | 3 | 1 | no | — |
| 56 | #3755 | — | 3 | 2 | no | — |
| 57 | #3754 | — | 3 | 1 | no | — |
| 58 | #3753 | — | 3 | 1 | no | — |
| 59 | #3753 | — | 3 | 2 | no | — |
| 60 | #3748 | — | 3 | 2 | no | — |
| 61 | #3748 | — | 3 | 1 | no | — |
| 62 | C2×C3⋊(C3⋊C8) | — | 3 | 2 | no | — |
| 63 | C2×C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 64 | D4×D9 | — | 12 | 3 | no | — |
| 65 | #41⋊C9 | C2×D3 | 1 | 3 | yes | complemented |
| 66 | C2×Q8⋊C9 | C2×D3 | 1 | 6 | yes | complemented |
| 67 | #3689 | — | 3 | 3 | no | — |
| 68 | #3689 | — | 3 | 6 | no | — |
| 69 | #3688 | — | 3 | 3 | no | — |
| 70 | C22×C3×C9 | — | 4 | 2 | no | — |
| 71 | C2×C3⋊D9 | — | 4 | 1 | no | — |
| 72 | C2×C3⋊D9 | — | 4 | 2 | no | — |
| 73 | C2×C3⋊D9 | — | 8 | 4 | no | — |
| 74 | C3×C4×C9 | — | 4 | 1 | no | — |
| 75 | C3⋊Dic9 | — | 4 | 1 | no | — |
| 76 | C3×2−1+4 | D9 | 1 | 3 | yes | complemented |
| 77 | C3×2−1+4 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 78 | #1009 | — | 9 | 3 | no | — |
| 79 | #1009 | — | 9 | 1 | no | — |
| 80 | #950 | — | 9 | 6 | no | — |
| 81 | #950 | — | 9 | 2 | no | — |
| 82 | #950 | — | 9 | 3 | no | — |
| 83 | #950 | — | 9 | 1 | no | — |
| 84 | #949 | — | 9 | 6 | no | — |
| 85 | #949 | — | 9 | 2 | no | — |
| 86 | #949 | — | 9 | 3 | no | — |
| 87 | #949 | — | 9 | 1 | no | — |
| 88 | #948 | — | 9 | 3 | no | — |
| 89 | #948 | — | 9 | 1 | no | — |
| 90 | #942 | — | 9 | 3 | no | — |
| 91 | #942 | — | 9 | 1 | no | — |
| 92 | #942 | — | 9 | 6 | no | — |
| 93 | #942 | — | 9 | 2 | no | — |
| 94 | C2×#215 | — | 9 | 3 | no | — |
| 95 | C2×#215 | — | 9 | 1 | no | — |
| 96 | C2×#215 | — | 9 | 6 | no | — |
| 97 | C2×#215 | — | 9 | 2 | no | — |
| 98 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 99 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 100 | C32×Q8 | — | 3 | 2 | no | — |
| 101 | C32×Q8 | — | 3 | 1 | no | — |
| 102 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 103 | C32×D4 | — | 3 | 1 | no | — |
| 104 | C32×D4 | — | 3 | 2 | no | — |
| 105 | C32×D4 | S4 | 1 | 1 | yes | characteristic |
| 106 | C2×C32×C4 | — | 3 | 2 | no | — |
| 107 | C2×C32×C4 | — | 3 | 1 | no | — |
| 108 | C2×C32×C4 | — | 6 | 1 | no | — |
| 109 | #638 | — | 6 | 1 | no | — |
| 110 | #638 | — | 6 | 2 | no | — |
| 111 | C4⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 112 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 113 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 114 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 115 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 116 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 117 | #634 | — | 3 | 1 | no | — |
| 118 | C22×D9 | — | 12 | 6 | no | — |
| 119 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 120 | C3⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 121 | C3⋊(C3⋊C8) | — | 3 | 2 | no | — |
| 122 | D4×C9 | — | 4 | 3 | no | — |
| 123 | #611 | — | 12 | 6 | no | — |
| 124 | D36 | — | 12 | 3 | no | — |
| 125 | C4×D9 | — | 12 | 3 | no | — |
| 126 | Q8⋊C9 | C22×D3 | 1 | 3 | yes | — |
| 127 | #577 | — | 27 | 1 | no | Sylow |
| 128 | C2×C3×C9 | — | 4 | 1 | no | — |
| 129 | C2×C3×C9 | — | 8 | 2 | no | — |
| 130 | C3⋊D9 | — | 4 | 2 | no | — |
| 131 | C3⋊D9 | — | 8 | 2 | no | — |
| 132 | C3×#41 | — | 3 | 3 | no | — |
| 133 | C3×#41 | — | 3 | 1 | no | — |
| 134 | C3×#41 | — | 3 | 6 | no | — |
| 135 | C3×#41 | — | 3 | 2 | no | — |
| 136 | C3×#41 | C2×D9 | 1 | 3 | yes | complemented |
| 137 | C3×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 138 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 139 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 140 | C2×C3×Q8 | C2×D9 | 1 | 6 | yes | complemented |
| 141 | C2×C3×Q8 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 142 | #239 | — | 18 | 1 | no | — |
| 143 | #239 | — | 18 | 3 | no | — |
| 144 | D3×D4 | — | 18 | 2 | no | — |
| 145 | D3×D4 | — | 18 | 6 | no | — |
| 146 | D3×D4 | — | 18 | 3 | no | — |
| 147 | D3×D4 | — | 18 | 1 | no | — |
| 148 | #235 | — | 9 | 2 | no | — |
| 149 | #235 | — | 9 | 6 | no | — |
| 150 | #235 | — | 9 | 1 | no | — |
| 151 | #235 | — | 9 | 3 | no | — |
| 152 | C2×D12 | — | 9 | 2 | no | — |
| 153 | C2×D12 | — | 9 | 6 | no | — |
| 154 | C2×D12 | — | 9 | 1 | no | — |
| 155 | C2×D12 | — | 9 | 3 | no | — |
| 156 | #216 | — | 9 | 6 | no | — |
| 157 | #216 | — | 9 | 2 | no | — |
| 158 | #216 | — | 9 | 3 | no | — |
| 159 | #216 | — | 9 | 1 | no | — |
| 160 | #215 | — | 9 | 6 | no | — |
| 161 | #215 | — | 9 | 2 | no | — |
| 162 | #215 | — | 9 | 6 | no | — |
| 163 | #215 | — | 9 | 6 | no | — |
| 164 | #215 | — | 9 | 2 | no | — |
| 165 | #215 | — | 9 | 2 | no | — |
| 166 | #215 | — | 9 | 3 | no | — |
| 167 | #215 | — | 9 | 6 | no | — |
| 168 | #215 | — | 9 | 1 | no | — |
| 169 | #215 | — | 9 | 2 | no | — |
| 170 | #214 | — | 9 | 3 | no | — |
| 171 | #214 | — | 9 | 1 | no | — |
| 172 | #213 | — | 9 | 3 | no | — |
| 173 | #213 | — | 9 | 6 | no | — |
| 174 | #213 | — | 9 | 1 | no | — |
| 175 | #213 | — | 9 | 2 | no | — |
| 176 | #208 | — | 9 | 2 | no | — |
| 177 | #208 | — | 9 | 6 | no | — |
| 178 | #208 | — | 9 | 1 | no | — |
| 179 | #208 | — | 9 | 3 | no | — |
| 180 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 181 | C2×C3⋊C8 | — | 9 | 6 | no | — |
| 182 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 183 | C2×C3⋊C8 | — | 9 | 3 | no | — |
| 184 | C22×C32 | — | 3 | 1 | no | — |
| 185 | C22×C32 | C2×S4 | 1 | 2 | yes | — |
| 186 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 187 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 188 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 189 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 190 | C32×C4 | — | 3 | 1 | no | — |
| 191 | C32×C4 | — | 3 | 2 | no | — |
| 192 | C32×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 193 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 194 | C22×C9 | — | 4 | 6 | no | — |
| 195 | C2×D9 | — | 12 | 3 | no | — |
| 196 | C2×D9 | — | 12 | 6 | no | — |
| 197 | C2×D9 | — | 24 | 12 | no | — |
| 198 | C4×C9 | — | 4 | 3 | no | — |
| 199 | Dic9 | — | 12 | 3 | no | — |
| 200 | 2−1+4 | C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 201 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 202 | #137 | — | 27 | 1 | no | — |
| 203 | #137 | — | 27 | 2 | no | — |
| 204 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 205 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 206 | #135 | — | 27 | 2 | no | — |
| 207 | #135 | — | 27 | 1 | no | — |
| 208 | C2×SD16 | — | 27 | 1 | no | — |
| 209 | C2×SD16 | — | 27 | 2 | no | — |
| 210 | #131 | — | 27 | 1 | no | — |
| 211 | C3×C9 | — | 4 | 1 | no | Sylow |
| 212 | C22×D3 | — | 18 | 1 | no | — |
| 213 | C22×D3 | — | 18 | 3 | no | — |
| 214 | C22×D3 | — | 18 | 2 | no | — |
| 215 | C22×D3 | — | 18 | 6 | no | — |
| 216 | C3×Q8 | — | 3 | 6 | no | — |
| 217 | C3×Q8 | — | 3 | 2 | no | — |
| 218 | C3×Q8 | — | 3 | 1 | no | — |
| 219 | C3×Q8 | — | 3 | 3 | no | — |
| 220 | C3×Q8 | C22×D9 | 1 | 3 | yes | — |
| 221 | C3×Q8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 222 | C3×D4 | — | 3 | 3 | no | — |
| 223 | C3×D4 | — | 3 | 1 | no | — |
| 224 | C3×D4 | — | 3 | 2 | no | — |
| 225 | C3×D4 | — | 3 | 6 | no | — |
| 226 | C3×D4 | (C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 227 | C3×D4 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 228 | C2×C3×C4 | — | 3 | 2 | no | — |
| 229 | C2×C3×C4 | — | 3 | 6 | no | — |
| 230 | C2×C3×C4 | — | 3 | 1 | no | — |
| 231 | C2×C3×C4 | — | 3 | 3 | no | — |
| 232 | C2×C3×C4 | — | 6 | 1 | no | — |
| 233 | C2×C3×C4 | — | 6 | 3 | no | — |
| 234 | #67 | — | 18 | 1 | no | — |
| 235 | #67 | — | 18 | 3 | no | — |
| 236 | #67 | — | 18 | 2 | no | — |
| 237 | #67 | — | 18 | 6 | no | — |
| 238 | D12 | — | 9 | 2 | no | — |
| 239 | D12 | — | 9 | 1 | no | — |
| 240 | D12 | — | 9 | 6 | no | — |
| 241 | D12 | — | 9 | 3 | no | — |
| 242 | D12 | — | 18 | 2 | no | — |
| 243 | D12 | — | 18 | 6 | no | — |
| 244 | D12 | — | 18 | 1 | no | — |
| 245 | D12 | — | 18 | 3 | no | — |
| 246 | C4×D3 | — | 18 | 2 | no | — |
| 247 | C4×D3 | — | 18 | 6 | no | — |
| 248 | C4×D3 | — | 18 | 1 | no | — |
| 249 | C4×D3 | — | 18 | 3 | no | — |
| 250 | Dic6 | — | 9 | 1 | no | — |
| 251 | Dic6 | — | 9 | 3 | no | — |
| 252 | C3⋊C8 | — | 9 | 1 | no | — |
| 253 | C3⋊C8 | — | 9 | 3 | no | — |
| 254 | C3⋊C8 | — | 9 | 1 | no | — |
| 255 | C3⋊C8 | — | 9 | 2 | no | — |
| 256 | C3⋊C8 | — | 9 | 3 | no | — |
| 257 | C3⋊C8 | — | 9 | 6 | no | — |
| 258 | C2×C32 | — | 2 | 2 | no | — |
| 259 | C2×C32 | — | 6 | 1 | no | — |
| 260 | C2×C32 | C22×S4 | 1 | 1 | yes | characteristic |
| 261 | C3⋊D3 | — | 12 | 1 | no | — |
| 262 | C3⋊D3 | — | 12 | 2 | no | — |
| 263 | C2×C9 | — | 4 | 3 | no | — |
| 264 | C2×C9 | — | 8 | 6 | no | — |
| 265 | D9 | — | 12 | 6 | no | — |
| 266 | D9 | — | 24 | 6 | no | — |
| 267 | #41 | — | 3 | 1 | no | — |
| 268 | #41 | — | 3 | 2 | no | — |
| 269 | #41 | — | 27 | 2 | no | — |
| 270 | #41 | — | 27 | 1 | no | — |
| 271 | #41 | — | 54 | 1 | no | — |
| 272 | #41 | C2×C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 273 | C2×Q8 | — | 3 | 1 | no | — |
| 274 | C2×Q8 | C2×C3⋊D9 | 1 | 2 | yes | complemented |
| 275 | C2×D4 | — | 27 | 2 | no | — |
| 276 | C2×D4 | — | 27 | 1 | no | — |
| 277 | C2×D4 | — | 54 | 2 | no | — |
| 278 | C2×D4 | — | 54 | 1 | no | — |
| 279 | Q16 | — | 27 | 2 | no | — |
| 280 | Q16 | — | 27 | 1 | no | — |
| 281 | SD16 | — | 27 | 1 | no | — |
| 282 | SD16 | — | 27 | 2 | no | — |
| 283 | SD16 | — | 27 | 2 | no | — |
| 284 | SD16 | — | 27 | 2 | no | — |
| 285 | SD16 | — | 27 | 1 | no | — |
| 286 | SD16 | — | 27 | 2 | no | — |
| 287 | D8 | — | 27 | 2 | no | — |
| 288 | D8 | — | 27 | 1 | no | — |
| 289 | M16 | — | 27 | 2 | no | — |
| 290 | M16 | — | 27 | 1 | no | — |
| 291 | C2×C8 | — | 27 | 2 | no | — |
| 292 | C2×C8 | — | 27 | 1 | no | — |
| 293 | C22×C3 | — | 3 | 1 | no | — |
| 294 | C22×C3 | — | 3 | 3 | no | — |
| 295 | C22×C3 | C2×(C22⋊C9)⋊C2 | 1 | 6 | yes | — |
| 296 | C22×C3 | C2×C3⋊S4 | 1 | 2 | yes | — |
| 297 | C2×D3 | — | 18 | 1 | no | — |
| 298 | C2×D3 | — | 18 | 2 | no | — |
| 299 | C2×D3 | — | 18 | 6 | no | — |
| 300 | C2×D3 | — | 18 | 3 | no | — |
| 301 | C2×D3 | — | 72 | 2 | no | — |
| 302 | C2×D3 | — | 72 | 6 | no | — |
| 303 | C2×D3 | — | 72 | 3 | no | — |
| 304 | C2×D3 | — | 72 | 1 | no | — |
| 305 | C3×C4 | — | 3 | 1 | no | — |
| 306 | C3×C4 | — | 3 | 2 | no | — |
| 307 | C3×C4 | — | 3 | 3 | no | — |
| 308 | C3×C4 | — | 3 | 6 | no | — |
| 309 | C3×C4 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 310 | C3×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 311 | Dic3 | — | 18 | 1 | no | — |
| 312 | Dic3 | — | 18 | 3 | no | — |
| 313 | C32 | #5926 | 1 | 1 | yes | characteristic |
| 314 | C9 | — | 4 | 3 | no | — |
| 315 | C23 | — | 54 | 1 | no | — |
| 316 | C23 | — | 54 | 2 | no | — |
| 317 | Q8 | — | 3 | 2 | no | — |
| 318 | Q8 | — | 3 | 1 | no | — |
| 319 | Q8 | — | 27 | 1 | no | — |
| 320 | Q8 | C22×C3⋊D9 | 1 | 1 | yes | characteristic |
| 321 | D4 | — | 3 | 1 | no | — |
| 322 | D4 | — | 3 | 2 | no | — |
| 323 | D4 | — | 27 | 2 | no | — |
| 324 | D4 | — | 27 | 1 | no | — |
| 325 | D4 | — | 54 | 2 | no | — |
| 326 | D4 | — | 54 | 1 | no | — |
| 327 | D4 | — | 54 | 2 | no | — |
| 328 | D4 | — | 54 | 1 | no | — |
| 329 | D4 | C3⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic |
| 330 | C2×C4 | — | 3 | 2 | no | — |
| 331 | C2×C4 | — | 3 | 1 | no | — |
| 332 | C2×C4 | — | 6 | 1 | no | — |
| 333 | C2×C4 | — | 54 | 2 | no | — |
| 334 | C2×C4 | — | 54 | 1 | no | — |
| 335 | C8 | — | 27 | 1 | no | — |
| 336 | C8 | — | 27 | 1 | no | — |
| 337 | C8 | — | 27 | 2 | no | — |
| 338 | C2×C3 | — | 2 | 6 | no | — |
| 339 | C2×C3 | — | 2 | 2 | no | — |
| 340 | C2×C3 | — | 6 | 3 | no | — |
| 341 | C2×C3 | — | 6 | 1 | no | — |
| 342 | C2×C3 | C22×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 343 | C2×C3 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 344 | D3 | — | 36 | 3 | no | — |
| 345 | D3 | — | 36 | 6 | no | — |
| 346 | D3 | — | 36 | 1 | no | — |
| 347 | D3 | — | 36 | 2 | no | — |
| 348 | C22 | — | 3 | 1 | no | — |
| 349 | C22 | — | 54 | 2 | no | — |
| 350 | C22 | — | 54 | 1 | no | — |
| 351 | C22 | — | 216 | 2 | no | — |
| 352 | C22 | — | 216 | 1 | no | — |
| 353 | C22 | C2×C3⋊((C22⋊C9)⋊C2) | 1 | 2 | yes | — |
| 354 | C4 | — | 3 | 1 | no | — |
| 355 | C4 | — | 3 | 2 | no | — |
| 356 | C4 | — | 54 | 1 | no | — |
| 357 | C4 | C2×C3⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic |
| 358 | C3 | #10593101 | 1 | 3 | yes | complemented |
| 359 | C3 | #10596589 | 1 | 1 | yes | characteristic |
| 360 | C2 | — | 2 | 2 | no | — |
| 361 | C2 | — | 6 | 1 | no | — |
| 362 | C2 | — | 108 | 1 | no | — |
| 363 | C2 | — | 108 | 2 | no | — |
| 364 | C2 | C22×C3⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C3⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C3×Q8⋊C9 | C23 |
| Frattini | C2×C3 | C22×C3⋊S4 |
| Fitting | C32×2−1+4 | D3 |
| socle | C2×C32 | C22×S4 |
| hypercenter | D4 | C3⋊((C22⋊C9)⋊C2) |
| LCS | G ▷ C3×Q8⋊C9 | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×2−1+4⋊C9 | C2 | semidirect |
| 2. #11722391 | C2 | semidirect |
| 3. #11722390 | C2 | semidirect |
| 4. #11722385 | C2 | semidirect |
| 5. C2×C3⋊#3689 | C2 | semidirect |
| 9. C3×#41⋊C9 | C22 | semidirect |
| 10. C2×C3×Q8⋊C9 | C22 | semidirect |
| 11. C3⋊#3689 | C22 | semidirect |
| 12. C3⋊#3689 | C22 | semidirect |
| 13. C3⋊#3688 | C22 | semidirect |
| 25. 2−1+4⋊C9 | D3 | semidirect |
| 65. #41⋊C9 | C2×D3 | semidirect |
| 66. C2×Q8⋊C9 | C2×D3 | semidirect |
| 76. C3×2−1+4 | D9 | semidirect |
| 136. C3×#41 | C2×D9 | semidirect |
| 140. C2×C3×Q8 | C2×D9 | semidirect |
| 200. 2−1+4 | C3⋊D9 | semidirect |
| 272. #41 | C2×C3⋊D9 | semidirect |
| 274. C2×Q8 | C2×C3⋊D9 | semidirect |
| 358. C3 | #10593101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×2−1+4⋊C9 | 2 |
| #11722391 | 2 |
| #11722390 | 2 |
| #11722385 | 2 |
| C2×C3⋊#3689 | 2 |
| #10596308 | 3 |
| #10593101 | 3 |
| D4×C3⋊D9 | 4 |