Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
955 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 955 conjugacy classes of subgroups — too many to draw. Only its 79 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 | C22×C3⋊((C22⋊C9)⋊C2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×C3×(C22⋊C9)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×Dic3×C22⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722264 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 5 | C2×#63978 | — | 3 | 1 | no | maximal |
| 6 | C2×C4⋊((C22⋊C9)⋊C2) | — | 3 | 1 | no | maximal |
| 7 | C22×C3×C22⋊C9 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×C3⋊((C22⋊C9)⋊C2) | — | 2 | 2 | no | — |
| 9 | C2×C3⋊((C22⋊C9)⋊C2) | C22 | 1 | 2 | yes | complemented |
| 10 | C2×C3×(C22⋊C9)⋊C2 | — | 2 | 2 | no | — |
| 11 | C2×C3×(C22⋊C9)⋊C2 | C22 | 1 | 2 | yes | complemented |
| 12 | C2×#6192 | — | 4 | 1 | no | maximal |
| 13 | Dic3×C22⋊C9 | C22 | 1 | 2 | yes | complemented |
| 14 | C22×#638 | — | 3 | 1 | no | — |
| 15 | C22×C3×#67 | — | 3 | 1 | no | — |
| 16 | C23×C3×Dic3 | D3 | 1 | 1 | yes | characteristic |
| 17 | C22×#626 | — | 3 | 1 | no | — |
| 18 | C22×(C22⋊C9)⋊C2 | — | 3 | 1 | no | — |
| 19 | C22×(C22⋊C9)⋊C2 | — | 6 | 1 | no | — |
| 20 | C22×(C22⋊C9)⋊C2 | D3 | 1 | 1 | yes | characteristic, complemented |
| 21 | #63978 | — | 3 | 4 | no | — |
| 22 | #63978 | — | 3 | 4 | no | — |
| 23 | C2×Dic3⋊Dic3 | — | 3 | 1 | no | — |
| 24 | C2×#3722 | — | 3 | 1 | no | — |
| 25 | C2×(C2×D3)⋊Dic3 | — | 3 | 1 | no | — |
| 26 | C2×C4×C22⋊C9 | — | 3 | 1 | no | — |
| 27 | C4⋊((C22⋊C9)⋊C2) | — | 3 | 4 | no | — |
| 28 | C22×C3⋊D9 | — | 4 | 1 | no | — |
| 29 | C22×C3×D9 | — | 4 | 1 | no | — |
| 30 | C2×C3×C22⋊C9 | D4 | 1 | 2 | yes | complemented |
| 31 | C2×C3×C22⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 32 | C3⋊((C22⋊C9)⋊C2) | — | 2 | 2 | no | — |
| 33 | C3×(C22⋊C9)⋊C2 | — | 2 | 2 | no | — |
| 34 | C2×C9×Dic3 | — | 4 | 1 | no | — |
| 35 | #6192 | — | 4 | 4 | no | — |
| 36 | C2×#939 | — | 9 | 1 | no | — |
| 37 | C2×#930 | — | 9 | 1 | no | — |
| 38 | C24×C32 | C2×D3 | 1 | 1 | yes | characteristic |
| 39 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 40 | C23×C3×D3 | — | 3 | 1 | no | — |
| 41 | C2×#638 | — | 3 | 2 | no | — |
| 42 | C2×#638 | — | 3 | 2 | no | — |
| 43 | C2×#638 | — | 6 | 2 | no | — |
| 44 | C2×#638 | — | 6 | 2 | no | — |
| 45 | C22×C3⋊Dic3 | — | 3 | 1 | no | — |
| 46 | C2×C3×#67 | — | 3 | 2 | no | — |
| 47 | C2×C3×#67 | — | 3 | 2 | no | — |
| 48 | C2×C3×#67 | — | 6 | 2 | no | — |
| 49 | C2×C3×#67 | — | 6 | 2 | no | — |
| 50 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 51 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 52 | C22×C3×Dic3 | — | 3 | 2 | no | — |
| 53 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 54 | C22×C3×Dic3 | C2×D3 | 1 | 2 | yes | — |
| 55 | C2×#626 | — | 3 | 4 | no | — |
| 56 | C2×#626 | — | 6 | 1 | no | — |
| 57 | C2×#626 | — | 6 | 2 | no | — |
| 58 | C2×#626 | — | 6 | 1 | no | — |
| 59 | C22×C22⋊C9 | — | 2 | 1 | no | — |
| 60 | C22×C22⋊C9 | C2×D3 | 1 | 1 | yes | characteristic |
| 61 | C2×(C22⋊C9)⋊C2 | — | 2 | 2 | no | — |
| 62 | C2×(C22⋊C9)⋊C2 | — | 3 | 2 | no | — |
| 63 | C2×(C22⋊C9)⋊C2 | — | 6 | 2 | no | — |
| 64 | C2×(C22⋊C9)⋊C2 | — | 6 | 4 | no | — |
| 65 | C2×(C22⋊C9)⋊C2 | — | 6 | 2 | no | — |
| 66 | C2×(C22⋊C9)⋊C2 | C2×D3 | 1 | 2 | yes | complemented |
| 67 | Dic3⋊Dic3 | — | 3 | 4 | no | — |
| 68 | #3722 | — | 3 | 4 | no | — |
| 69 | (C2×D3)⋊Dic3 | — | 3 | 4 | no | — |
| 70 | C2×D36 | — | 12 | 1 | no | — |
| 71 | C4×C22⋊C9 | — | 3 | 2 | no | — |
| 72 | C22×C3×C9 | — | 4 | 1 | no | — |
| 73 | C2×C3⋊D9 | — | 4 | 2 | no | — |
| 74 | C2×C3⋊D9 | — | 8 | 2 | no | — |
| 75 | C2×C3×D9 | — | 4 | 2 | no | — |
| 76 | C2×C3×D9 | — | 8 | 2 | no | — |
| 77 | C3×C22⋊C9 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 78 | C9×Dic3 | — | 4 | 2 | no | — |
| 79 | C22×C3×D4 | — | 9 | 1 | no | — |
| 80 | C23×C3×C4 | — | 3 | 1 | no | — |
| 81 | C22×#67 | — | 3 | 1 | no | — |
| 82 | C22×#67 | — | 9 | 1 | no | — |
| 83 | C22×#67 | — | 9 | 1 | no | — |
| 84 | C22×#67 | — | 9 | 1 | no | — |
| 85 | C22×#67 | — | 18 | 1 | no | — |
| 86 | C23×Dic3 | D9 | 1 | 1 | yes | characteristic, complemented |
| 87 | C22×D12 | — | 9 | 1 | no | — |
| 88 | C2×#217 | — | 9 | 1 | no | — |
| 89 | #939 | — | 9 | 4 | no | — |
| 90 | #939 | — | 9 | 4 | no | — |
| 91 | #930 | — | 9 | 4 | no | — |
| 92 | #930 | — | 9 | 4 | no | — |
| 93 | C2×(C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 94 | C2×(C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 95 | C2×(C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 96 | C2×C4⋊Dic3 | — | 9 | 1 | no | — |
| 97 | C2×Dic3⋊C4 | — | 9 | 1 | no | — |
| 98 | C23×C32 | — | 3 | 1 | no | — |
| 99 | C23×C32 | — | 3 | 1 | no | — |
| 100 | C23×C32 | — | 3 | 2 | no | — |
| 101 | C23×C32 | D12 | 1 | 2 | yes | — |
| 102 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 103 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 104 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 105 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 106 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 107 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 108 | C22×C3×D3 | — | 3 | 2 | no | — |
| 109 | C22×C3×D3 | — | 6 | 2 | no | — |
| 110 | C22×C3×D3 | — | 6 | 1 | no | — |
| 111 | C22×C3×D3 | — | 6 | 2 | no | — |
| 112 | C22×C3×D3 | — | 6 | 1 | no | — |
| 113 | #638 | — | 6 | 4 | no | — |
| 114 | #638 | — | 6 | 2 | no | — |
| 115 | #638 | — | 6 | 2 | no | — |
| 116 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 117 | C2×C3⋊Dic3 | — | 6 | 2 | no | — |
| 118 | C3×#67 | — | 6 | 4 | no | — |
| 119 | C3×#67 | — | 6 | 2 | no | — |
| 120 | C3×#67 | — | 6 | 2 | no | — |
| 121 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 122 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 123 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 124 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 125 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 126 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 127 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 128 | C2×C3×Dic3 | S4 | 1 | 1 | yes | characteristic |
| 129 | #626 | — | 6 | 4 | no | — |
| 130 | #626 | — | 6 | 4 | no | — |
| 131 | C22×D9 | — | 4 | 1 | no | — |
| 132 | C22×D9 | — | 12 | 1 | no | — |
| 133 | C22×D9 | — | 24 | 1 | no | — |
| 134 | C2×C22⋊C9 | — | 2 | 2 | no | — |
| 135 | C2×C22⋊C9 | — | 2 | 1 | no | — |
| 136 | C2×C22⋊C9 | #67 | 1 | 2 | yes | complemented |
| 137 | C2×C22⋊C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 138 | (C22⋊C9)⋊C2 | — | 2 | 2 | no | — |
| 139 | (C22⋊C9)⋊C2 | — | 6 | 4 | no | — |
| 140 | (C22⋊C9)⋊C2 | — | 6 | 2 | no | — |
| 141 | C2×C4×C9 | — | 12 | 1 | no | — |
| 142 | D36 | — | 12 | 4 | no | — |
| 143 | C2×#121 | — | 27 | 1 | no | Sylow |
| 144 | C2×C3×C9 | — | 4 | 2 | no | — |
| 145 | C2×C3×C9 | — | 4 | 1 | no | — |
| 146 | C3⋊D9 | — | 8 | 2 | no | — |
| 147 | C3×D9 | — | 8 | 2 | no | — |
| 148 | C24×C3 | — | 2 | 1 | no | — |
| 149 | C24×C3 | — | 9 | 1 | no | — |
| 150 | C24×C3 | C2×D9 | 1 | 1 | yes | characteristic |
| 151 | C24×C3 | D32 | 1 | 1 | yes | characteristic |
| 152 | C23×D3 | — | 3 | 1 | no | — |
| 153 | C23×D3 | — | 9 | 1 | no | — |
| 154 | C23×D3 | — | 9 | 1 | no | — |
| 155 | C23×D3 | — | 18 | 1 | no | — |
| 156 | C2×C3×D4 | — | 9 | 2 | no | — |
| 157 | C2×C3×D4 | — | 9 | 2 | no | — |
| 158 | C2×C3×D4 | — | 18 | 2 | no | — |
| 159 | C2×C3×D4 | — | 18 | 2 | no | — |
| 160 | C22×C3×C4 | — | 3 | 2 | no | — |
| 161 | C22×C3×C4 | — | 9 | 1 | no | — |
| 162 | C22×C3×C4 | — | 9 | 1 | no | — |
| 163 | C22×C3×C4 | — | 9 | 2 | no | — |
| 164 | C22×C3×C4 | — | 9 | 1 | no | — |
| 165 | C2×#67 | — | 3 | 2 | no | — |
| 166 | C2×#67 | — | 3 | 2 | no | — |
| 167 | C2×#67 | — | 6 | 2 | no | — |
| 168 | C2×#67 | — | 6 | 2 | no | — |
| 169 | C2×#67 | — | 9 | 4 | no | — |
| 170 | C2×#67 | — | 9 | 2 | no | — |
| 171 | C2×#67 | — | 9 | 2 | no | — |
| 172 | C2×#67 | — | 9 | 2 | no | — |
| 173 | C2×#67 | — | 9 | 2 | no | — |
| 174 | C2×#67 | — | 18 | 2 | no | — |
| 175 | C2×#67 | — | 18 | 2 | no | — |
| 176 | C2×#67 | — | 18 | 1 | no | — |
| 177 | C2×#67 | — | 18 | 2 | no | — |
| 178 | C2×#67 | — | 18 | 4 | no | — |
| 179 | C2×#67 | — | 18 | 2 | no | — |
| 180 | C2×#67 | — | 18 | 2 | no | — |
| 181 | C2×#67 | — | 18 | 4 | no | — |
| 182 | C2×#67 | — | 18 | 2 | no | — |
| 183 | C2×#67 | — | 18 | 2 | no | — |
| 184 | C2×#67 | — | 18 | 1 | no | — |
| 185 | C22×Dic3 | — | 3 | 1 | no | — |
| 186 | C22×Dic3 | — | 3 | 1 | no | — |
| 187 | C22×Dic3 | — | 3 | 2 | no | — |
| 188 | C22×Dic3 | — | 3 | 1 | no | — |
| 189 | C22×Dic3 | — | 9 | 1 | no | — |
| 190 | C22×Dic3 | — | 9 | 1 | no | — |
| 191 | C22×Dic3 | — | 18 | 1 | no | — |
| 192 | C22×Dic3 | C2×D9 | 1 | 2 | yes | complemented |
| 193 | C2×D12 | — | 9 | 4 | no | — |
| 194 | C2×D12 | — | 18 | 1 | no | — |
| 195 | C2×D12 | — | 18 | 2 | no | — |
| 196 | C2×D12 | — | 18 | 1 | no | — |
| 197 | #217 | — | 9 | 4 | no | — |
| 198 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 199 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 200 | (C2×D3)⋊C4 | — | 9 | 4 | no | — |
| 201 | C4⋊Dic3 | — | 9 | 4 | no | — |
| 202 | Dic3⋊C4 | — | 9 | 4 | no | — |
| 203 | C22×C32 | — | 3 | 2 | no | — |
| 204 | C22×C32 | — | 3 | 1 | no | — |
| 205 | C22×C32 | — | 3 | 2 | no | — |
| 206 | C22×C32 | — | 3 | 2 | no | — |
| 207 | C22×C32 | — | 3 | 1 | no | — |
| 208 | C22×C32 | — | 3 | 1 | no | — |
| 209 | C22×C32 | — | 6 | 1 | no | — |
| 210 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 211 | C22×C32 | C2×S4 | 1 | 1 | yes | characteristic |
| 212 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 213 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 214 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 215 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 216 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 217 | C2×C3×D3 | — | 6 | 2 | no | — |
| 218 | C2×C3×D3 | — | 6 | 2 | no | — |
| 219 | C2×C3×D3 | — | 6 | 2 | no | — |
| 220 | C2×C3×D3 | — | 12 | 2 | no | — |
| 221 | C2×C3×D3 | — | 12 | 2 | no | — |
| 222 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 223 | C3×Dic3 | — | 3 | 2 | no | — |
| 224 | C3×Dic3 | — | 6 | 2 | no | — |
| 225 | C3×Dic3 | C2×S4 | 1 | 2 | yes | — |
| 226 | C22×C9 | — | 4 | 1 | no | — |
| 227 | C22×C9 | — | 8 | 1 | no | — |
| 228 | C2×D9 | — | 4 | 2 | no | — |
| 229 | C2×D9 | — | 8 | 2 | no | — |
| 230 | C2×D9 | — | 12 | 2 | no | — |
| 231 | C2×D9 | — | 24 | 2 | no | — |
| 232 | C2×D9 | — | 24 | 2 | no | — |
| 233 | C2×D9 | — | 24 | 4 | no | — |
| 234 | C22⋊C9 | — | 2 | 1 | no | — |
| 235 | C22⋊C9 | C2×#67 | 1 | 1 | yes | characteristic, complemented |
| 236 | C4×C9 | — | 12 | 2 | no | — |
| 237 | C22×D4 | — | 9 | 1 | no | — |
| 238 | C22×D4 | — | 27 | 1 | no | — |
| 239 | C22×D4 | — | 27 | 1 | no | — |
| 240 | C23×C4 | — | 3 | 1 | no | — |
| 241 | #121 | — | 27 | 4 | no | — |
| 242 | #121 | — | 27 | 4 | no | — |
| 243 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 244 | C2×C22⋊C4 | — | 27 | 1 | no | — |
| 245 | C2×C22⋊C4 | — | 27 | 1 | no | — |
| 246 | C3×C9 | — | 4 | 1 | no | Sylow |
| 247 | C23×C3 | — | 2 | 2 | no | — |
| 248 | C23×C3 | — | 2 | 1 | no | — |
| 249 | C23×C3 | — | 3 | 1 | no | — |
| 250 | C23×C3 | — | 3 | 1 | no | — |
| 251 | C23×C3 | — | 3 | 1 | no | — |
| 252 | C23×C3 | — | 3 | 1 | no | — |
| 253 | C23×C3 | — | 3 | 2 | no | — |
| 254 | C23×C3 | — | 3 | 2 | no | — |
| 255 | C23×C3 | — | 6 | 1 | no | — |
| 256 | C23×C3 | — | 6 | 1 | no | — |
| 257 | C23×C3 | — | 6 | 2 | no | — |
| 258 | C23×C3 | — | 9 | 2 | no | — |
| 259 | C23×C3 | — | 18 | 1 | no | — |
| 260 | C23×C3 | — | 18 | 2 | no | — |
| 261 | C23×C3 | — | 18 | 2 | no | — |
| 262 | C23×C3 | — | 18 | 1 | no | — |
| 263 | C23×C3 | D36 | 1 | 2 | yes | complemented |
| 264 | C23×C3 | C22×D9 | 1 | 1 | yes | characteristic |
| 265 | C23×C3 | #626 | 1 | 2 | yes | — |
| 266 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 267 | C22×D3 | — | 3 | 2 | no | — |
| 268 | C22×D3 | — | 6 | 1 | no | — |
| 269 | C22×D3 | — | 6 | 2 | no | — |
| 270 | C22×D3 | — | 6 | 2 | no | — |
| 271 | C22×D3 | — | 6 | 1 | no | — |
| 272 | C22×D3 | — | 9 | 2 | no | — |
| 273 | C22×D3 | — | 9 | 2 | no | — |
| 274 | C22×D3 | — | 18 | 2 | no | — |
| 275 | C22×D3 | — | 18 | 1 | no | — |
| 276 | C22×D3 | — | 18 | 2 | no | — |
| 277 | C22×D3 | — | 18 | 2 | no | — |
| 278 | C22×D3 | — | 18 | 1 | no | — |
| 279 | C22×D3 | — | 18 | 2 | no | — |
| 280 | C22×D3 | — | 18 | 2 | no | — |
| 281 | C22×D3 | — | 18 | 4 | no | — |
| 282 | C22×D3 | — | 18 | 1 | no | — |
| 283 | C22×D3 | — | 18 | 1 | no | — |
| 284 | C22×D3 | — | 36 | 1 | no | — |
| 285 | C22×D3 | — | 36 | 1 | no | — |
| 286 | C22×D3 | — | 36 | 2 | no | — |
| 287 | C3×D4 | — | 18 | 4 | no | — |
| 288 | C3×D4 | — | 18 | 2 | no | — |
| 289 | C3×D4 | — | 18 | 2 | no | — |
| 290 | C2×C3×C4 | — | 3 | 1 | no | — |
| 291 | C2×C3×C4 | — | 9 | 2 | no | — |
| 292 | C2×C3×C4 | — | 9 | 2 | no | — |
| 293 | C2×C3×C4 | — | 9 | 1 | no | — |
| 294 | C2×C3×C4 | — | 9 | 2 | no | — |
| 295 | C2×C3×C4 | — | 9 | 2 | no | — |
| 296 | C2×C3×C4 | — | 18 | 1 | no | — |
| 297 | C2×C3×C4 | — | 18 | 2 | no | — |
| 298 | #67 | — | 6 | 4 | no | — |
| 299 | #67 | — | 6 | 2 | no | — |
| 300 | #67 | — | 6 | 2 | no | — |
| 301 | #67 | — | 18 | 4 | no | — |
| 302 | #67 | — | 18 | 4 | no | — |
| 303 | #67 | — | 18 | 4 | no | — |
| 304 | #67 | — | 18 | 2 | no | — |
| 305 | #67 | — | 18 | 4 | no | — |
| 306 | #67 | — | 18 | 2 | no | — |
| 307 | #67 | — | 18 | 4 | no | — |
| 308 | #67 | — | 18 | 8 | no | — |
| 309 | #67 | — | 18 | 2 | no | — |
| 310 | #67 | — | 18 | 2 | no | — |
| 311 | #67 | — | 18 | 4 | no | — |
| 312 | C2×Dic3 | — | 3 | 1 | no | — |
| 313 | C2×Dic3 | — | 3 | 2 | no | — |
| 314 | C2×Dic3 | — | 3 | 2 | no | — |
| 315 | C2×Dic3 | — | 3 | 2 | no | — |
| 316 | C2×Dic3 | — | 3 | 2 | no | — |
| 317 | C2×Dic3 | — | 6 | 1 | no | — |
| 318 | C2×Dic3 | — | 6 | 2 | no | — |
| 319 | C2×Dic3 | — | 9 | 2 | no | — |
| 320 | C2×Dic3 | — | 9 | 2 | no | — |
| 321 | C2×Dic3 | — | 18 | 2 | no | — |
| 322 | C2×Dic3 | — | 18 | 2 | no | — |
| 323 | C2×Dic3 | — | 18 | 2 | no | — |
| 324 | C2×Dic3 | — | 18 | 4 | no | — |
| 325 | C2×Dic3 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 326 | D12 | — | 18 | 4 | no | — |
| 327 | D12 | — | 18 | 4 | no | — |
| 328 | C2×C32 | — | 3 | 1 | no | — |
| 329 | C2×C32 | — | 3 | 1 | no | — |
| 330 | C2×C32 | — | 3 | 2 | no | — |
| 331 | C2×C32 | C4⋊S4 | 1 | 2 | yes | — |
| 332 | C2×C32 | C22×S4 | 1 | 1 | yes | characteristic |
| 333 | C3⋊D3 | — | 12 | 2 | no | — |
| 334 | C3×D3 | — | 12 | 2 | no | — |
| 335 | C2×C9 | — | 4 | 1 | no | — |
| 336 | C2×C9 | — | 4 | 2 | no | — |
| 337 | C2×C9 | — | 8 | 1 | no | — |
| 338 | C2×C9 | — | 8 | 2 | no | — |
| 339 | D9 | — | 8 | 2 | no | — |
| 340 | D9 | — | 24 | 2 | no | — |
| 341 | D9 | — | 24 | 4 | no | — |
| 342 | C24 | — | 9 | 1 | no | — |
| 343 | C24 | — | 27 | 1 | no | — |
| 344 | C24 | D3×D9 | 1 | 1 | yes | characteristic |
| 345 | C2×D4 | — | 9 | 2 | no | — |
| 346 | C2×D4 | — | 9 | 2 | no | — |
| 347 | C2×D4 | — | 18 | 2 | no | — |
| 348 | C2×D4 | — | 18 | 2 | no | — |
| 349 | C2×D4 | — | 27 | 4 | no | — |
| 350 | C2×D4 | — | 27 | 2 | no | — |
| 351 | C2×D4 | — | 27 | 2 | no | — |
| 352 | C2×D4 | — | 54 | 1 | no | — |
| 353 | C2×D4 | — | 54 | 2 | no | — |
| 354 | C2×D4 | — | 54 | 1 | no | — |
| 355 | C2×D4 | — | 54 | 2 | no | — |
| 356 | C2×D4 | — | 54 | 2 | no | — |
| 357 | C22×C4 | — | 3 | 2 | no | — |
| 358 | C22×C4 | — | 9 | 1 | no | — |
| 359 | C22×C4 | — | 9 | 1 | no | — |
| 360 | C22×C4 | — | 9 | 2 | no | — |
| 361 | C22×C4 | — | 9 | 1 | no | — |
| 362 | C22×C4 | — | 27 | 1 | no | — |
| 363 | C4⋊C4 | — | 27 | 4 | no | — |
| 364 | C22⋊C4 | — | 27 | 4 | no | — |
| 365 | C22⋊C4 | — | 27 | 4 | no | — |
| 366 | C22×C3 | — | 2 | 1 | no | — |
| 367 | C22×C3 | — | 2 | 1 | no | — |
| 368 | C22×C3 | — | 3 | 2 | no | — |
| 369 | C22×C3 | — | 3 | 1 | no | — |
| 370 | C22×C3 | — | 3 | 2 | no | — |
| 371 | C22×C3 | — | 3 | 1 | no | — |
| 372 | C22×C3 | — | 3 | 1 | no | — |
| 373 | C22×C3 | — | 3 | 1 | no | — |
| 374 | C22×C3 | — | 3 | 1 | no | — |
| 375 | C22×C3 | — | 3 | 1 | no | — |
| 376 | C22×C3 | — | 3 | 2 | no | — |
| 377 | C22×C3 | — | 3 | 2 | no | — |
| 378 | C22×C3 | — | 3 | 2 | no | — |
| 379 | C22×C3 | — | 3 | 2 | no | — |
| 380 | C22×C3 | — | 6 | 1 | no | — |
| 381 | C22×C3 | — | 6 | 2 | no | — |
| 382 | C22×C3 | — | 6 | 1 | no | — |
| 383 | C22×C3 | — | 6 | 2 | no | — |
| 384 | C22×C3 | — | 6 | 2 | no | — |
| 385 | C22×C3 | — | 6 | 1 | no | — |
| 386 | C22×C3 | — | 6 | 1 | no | — |
| 387 | C22×C3 | — | 6 | 1 | no | — |
| 388 | C22×C3 | — | 12 | 1 | no | — |
| 389 | C22×C3 | — | 18 | 2 | no | — |
| 390 | C22×C3 | — | 18 | 2 | no | — |
| 391 | C22×C3 | — | 18 | 2 | no | — |
| 392 | C22×C3 | — | 36 | 2 | no | — |
| 393 | C22×C3 | — | 36 | 2 | no | — |
| 394 | C22×C3 | C2×D36 | 1 | 1 | yes | characteristic, complemented |
| 395 | C22×C3 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 396 | C22×C3 | C2×#626 | 1 | 1 | yes | characteristic |
| 397 | C22×C3 | D3×S4 | 1 | 1 | yes | characteristic |
| 398 | C2×D3 | — | 6 | 2 | no | — |
| 399 | C2×D3 | — | 6 | 2 | no | — |
| 400 | C2×D3 | — | 6 | 2 | no | — |
| 401 | C2×D3 | — | 12 | 2 | no | — |
| 402 | C2×D3 | — | 12 | 2 | no | — |
| 403 | C2×D3 | — | 18 | 2 | no | — |
| 404 | C2×D3 | — | 18 | 2 | no | — |
| 405 | C2×D3 | — | 18 | 2 | no | — |
| 406 | C2×D3 | — | 18 | 2 | no | — |
| 407 | C2×D3 | — | 18 | 4 | no | — |
| 408 | C2×D3 | — | 18 | 2 | no | — |
| 409 | C2×D3 | — | 18 | 2 | no | — |
| 410 | C2×D3 | — | 36 | 2 | no | — |
| 411 | C2×D3 | — | 36 | 2 | no | — |
| 412 | C2×D3 | — | 36 | 4 | no | — |
| 413 | C2×D3 | — | 36 | 2 | no | — |
| 414 | C2×D3 | — | 36 | 2 | no | — |
| 415 | C2×D3 | — | 36 | 4 | no | — |
| 416 | C2×D3 | — | 36 | 2 | no | — |
| 417 | C2×D3 | — | 36 | 2 | no | — |
| 418 | C3×C4 | — | 3 | 2 | no | — |
| 419 | C3×C4 | — | 9 | 2 | no | — |
| 420 | C3×C4 | — | 18 | 2 | no | — |
| 421 | Dic3 | — | 3 | 2 | no | — |
| 422 | Dic3 | — | 6 | 2 | no | — |
| 423 | Dic3 | — | 18 | 2 | no | — |
| 424 | Dic3 | — | 18 | 2 | no | — |
| 425 | Dic3 | — | 18 | 4 | no | — |
| 426 | Dic3 | C2×(C22⋊C9)⋊C2 | 1 | 2 | yes | complemented |
| 427 | C32 | C2×C4⋊S4 | 1 | 1 | yes | characteristic |
| 428 | C9 | — | 4 | 1 | no | — |
| 429 | C9 | — | 8 | 1 | no | — |
| 430 | C23 | — | 3 | 1 | no | — |
| 431 | C23 | — | 3 | 1 | no | — |
| 432 | C23 | — | 3 | 2 | no | — |
| 433 | C23 | — | 9 | 2 | no | — |
| 434 | C23 | — | 18 | 2 | no | — |
| 435 | C23 | — | 18 | 1 | no | — |
| 436 | C23 | — | 18 | 2 | no | — |
| 437 | C23 | — | 18 | 1 | no | — |
| 438 | C23 | — | 27 | 2 | no | — |
| 439 | C23 | — | 54 | 2 | no | — |
| 440 | C23 | — | 54 | 1 | no | — |
| 441 | C23 | — | 54 | 2 | no | — |
| 442 | C23 | — | 54 | 1 | no | — |
| 443 | C23 | #6192 | 1 | 2 | yes | complemented |
| 444 | C23 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 445 | D4 | — | 18 | 4 | no | — |
| 446 | D4 | — | 18 | 2 | no | — |
| 447 | D4 | — | 18 | 2 | no | — |
| 448 | D4 | — | 54 | 4 | no | — |
| 449 | D4 | — | 54 | 4 | no | — |
| 450 | D4 | — | 54 | 4 | no | — |
| 451 | D4 | — | 54 | 2 | no | — |
| 452 | D4 | — | 54 | 2 | no | — |
| 453 | C2×C4 | — | 3 | 1 | no | — |
| 454 | C2×C4 | — | 9 | 2 | no | — |
| 455 | C2×C4 | — | 9 | 2 | no | — |
| 456 | C2×C4 | — | 9 | 1 | no | — |
| 457 | C2×C4 | — | 9 | 2 | no | — |
| 458 | C2×C4 | — | 9 | 2 | no | — |
| 459 | C2×C4 | — | 18 | 1 | no | — |
| 460 | C2×C4 | — | 18 | 2 | no | — |
| 461 | C2×C4 | — | 27 | 2 | no | — |
| 462 | C2×C4 | — | 54 | 2 | no | — |
| 463 | C2×C3 | — | 2 | 1 | no | — |
| 464 | C2×C3 | — | 2 | 2 | no | — |
| 465 | C2×C3 | — | 3 | 1 | no | — |
| 466 | C2×C3 | — | 3 | 1 | no | — |
| 467 | C2×C3 | — | 3 | 2 | no | — |
| 468 | C2×C3 | — | 3 | 1 | no | — |
| 469 | C2×C3 | — | 3 | 1 | no | — |
| 470 | C2×C3 | — | 3 | 2 | no | — |
| 471 | C2×C3 | — | 6 | 1 | no | — |
| 472 | C2×C3 | — | 6 | 1 | no | — |
| 473 | C2×C3 | — | 6 | 2 | no | — |
| 474 | C2×C3 | — | 36 | 2 | no | — |
| 475 | C2×C3 | C4⋊((C22⋊C9)⋊C2) | 1 | 2 | yes | complemented |
| 476 | C2×C3 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 477 | C2×C3 | #64207 | 1 | 2 | yes | — |
| 478 | C2×C3 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 479 | D3 | — | 12 | 2 | no | — |
| 480 | D3 | — | 36 | 4 | no | — |
| 481 | D3 | — | 36 | 2 | no | — |
| 482 | D3 | — | 36 | 2 | no | — |
| 483 | C22 | — | 3 | 2 | no | — |
| 484 | C22 | — | 3 | 1 | no | — |
| 485 | C22 | — | 3 | 1 | no | — |
| 486 | C22 | — | 3 | 1 | no | — |
| 487 | C22 | — | 3 | 2 | no | — |
| 488 | C22 | — | 3 | 2 | no | — |
| 489 | C22 | — | 6 | 1 | no | — |
| 490 | C22 | — | 18 | 2 | no | — |
| 491 | C22 | — | 18 | 2 | no | — |
| 492 | C22 | — | 18 | 2 | no | — |
| 493 | C22 | — | 36 | 2 | no | — |
| 494 | C22 | — | 36 | 2 | no | — |
| 495 | C22 | — | 54 | 2 | no | — |
| 496 | C22 | — | 54 | 2 | no | — |
| 497 | C22 | — | 54 | 2 | no | — |
| 498 | C22 | — | 108 | 2 | no | — |
| 499 | C22 | — | 108 | 2 | no | — |
| 500 | C22 | C2×#6192 | 1 | 1 | yes | characteristic, complemented |
| 501 | C22 | D3×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 502 | C4 | — | 3 | 2 | no | — |
| 503 | C4 | — | 9 | 2 | no | — |
| 504 | C4 | — | 18 | 2 | no | — |
| 505 | C4 | — | 54 | 2 | no | — |
| 506 | C3 | — | 2 | 1 | no | — |
| 507 | C3 | C2×C4⋊((C22⋊C9)⋊C2) | 1 | 1 | yes | characteristic, complemented |
| 508 | C3 | C2×#64207 | 1 | 1 | yes | characteristic |
| 509 | C2 | — | 3 | 1 | no | — |
| 510 | C2 | — | 3 | 1 | no | — |
| 511 | C2 | — | 3 | 2 | no | — |
| 512 | C2 | — | 36 | 2 | no | — |
| 513 | C2 | — | 108 | 2 | no | — |
| 514 | C2 | #11722264 | 1 | 2 | yes | direct product factor |
| 515 | C2 | C2×D3×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×(C22⋊C9)⋊C2 |
| commutator, cosocle | C2×C3×C22⋊C9 | C23 |
| Frattini | C2×C3 | C2×D3×S4 |
| Fitting, socle | C24×C32 | C2×D3 |
| hypocenter | C3×C22⋊C9 | C2×D4 |
| LCS | G ▷ C2×C3×C22⋊C9 ▷ C3×C22⋊C9 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3⋊((C22⋊C9)⋊C2) | C2 | semidirect |
| 2. C22×C3×(C22⋊C9)⋊C2 | C2 | semidirect |
| 3. C2×Dic3×C22⋊C9 | C2 | semidirect |
| 4. #11722264 | C2 | direct (N × H) |
| 9. C2×C3⋊((C22⋊C9)⋊C2) | C22 | semidirect |
| 11. C2×C3×(C22⋊C9)⋊C2 | C22 | semidirect |
| 13. Dic3×C22⋊C9 | C22 | semidirect |
| 20. C22×(C22⋊C9)⋊C2 | D3 | semidirect |
| 30. C2×C3×C22⋊C9 | D4 | semidirect |
| 66. C2×(C22⋊C9)⋊C2 | C2×D3 | semidirect |
| 77. C3×C22⋊C9 | C2×D4 | semidirect |
| 86. C23×Dic3 | D9 | semidirect |
| 136. C2×C22⋊C9 | #67 | semidirect |
| 192. C22×Dic3 | C2×D9 | semidirect |
| 235. C22⋊C9 | C2×#67 | semidirect |
| 263. C23×C3 | D36 | semidirect |
| 325. C2×Dic3 | (C22⋊C9)⋊C2 | semidirect |
| 394. C22×C3 | C2×D36 | semidirect |
| 426. Dic3 | C2×(C22⋊C9)⋊C2 | semidirect |
| 443. C23 | #6192 | semidirect |
| 475. C2×C3 | C4⋊((C22⋊C9)⋊C2) | semidirect |
| 500. C22 | C2×#6192 | semidirect |
| 507. C3 | C2×C4⋊((C22⋊C9)⋊C2) | semidirect |
| 514. C2 | #11722264 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊((C22⋊C9)⋊C2) | 2 |
| C22×C3×(C22⋊C9)⋊C2 | 2 |
| C2×Dic3×C22⋊C9 | 2 |
| #11722264 | 2 |
| C2×#63978 | 3 |
| C2×C4⋊((C22⋊C9)⋊C2) | 3 |
| C2×#6192 | 4 |