Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
766 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 55 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×C9⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D9×S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×#611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C9×GL(2,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11722243 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722242 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | (C9⋊S4)⋊C4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10596473 | — | 3 | 1 | no | maximal |
| 9 | #10589692 | — | 3 | 1 | no | maximal |
| 10 | C22×C9×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×A4×D9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×C9⋊S4 | — | 2 | 2 | no | — |
| 13 | C2×C9⋊S4 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C9⋊S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×C9×S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | D9×S4 | — | 2 | 2 | no | — |
| 17 | #88668 | — | 4 | 1 | no | maximal |
| 18 | A4×Dic9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C9×SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C22×C3⋊S4 | — | 3 | 1 | no | — |
| 21 | C2×D3×S4 | — | 3 | 1 | no | — |
| 22 | A4×#67 | — | 3 | 1 | no | — |
| 23 | C3×GL(2,ℤ/4) | D3 | 1 | 1 | yes | characteristic |
| 24 | #64210 | — | 3 | 1 | no | — |
| 25 | #64207 | — | 3 | 1 | no | — |
| 26 | (C3⋊S4)⋊C4 | — | 3 | 1 | no | — |
| 27 | C22×(C22⋊C9)⋊C2 | — | 6 | 1 | no | — |
| 28 | C22×#611 | — | 3 | 1 | no | — |
| 29 | C22×#611 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×D4×D9 | — | 3 | 1 | no | — |
| 31 | C2×D4×D9 | — | 3 | 1 | no | — |
| 32 | C9×#120 | — | 3 | 1 | no | — |
| 33 | #63502 | — | 3 | 1 | no | — |
| 34 | #63501 | — | 3 | 1 | no | — |
| 35 | #63501 | — | 3 | 1 | no | — |
| 36 | #63499 | — | 3 | 1 | no | — |
| 37 | #63446 | — | 3 | 1 | no | — |
| 38 | #63446 | — | 3 | 1 | no | — |
| 39 | #63444 | — | 3 | 1 | no | — |
| 40 | #63444 | — | 3 | 1 | no | — |
| 41 | #611⋊C4 | — | 3 | 1 | no | — |
| 42 | #611⋊C4 | — | 3 | 1 | no | — |
| 43 | C22×C3⋊D9 | — | 4 | 1 | no | — |
| 44 | C2×C9×A4 | — | 2 | 1 | no | — |
| 45 | C2×C9×A4 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×D3×D9 | — | 4 | 1 | no | — |
| 47 | A4×D9 | — | 2 | 1 | no | — |
| 48 | C9⋊S4 | — | 2 | 1 | no | — |
| 49 | C9⋊S4 | D4 | 1 | 2 | yes | complemented |
| 50 | C9×S4 | — | 2 | 1 | no | — |
| 51 | C9×#67 | — | 4 | 1 | no | — |
| 52 | C3×#611 | — | 4 | 1 | no | — |
| 53 | #6195 | — | 4 | 1 | no | — |
| 54 | #6192 | — | 4 | 1 | no | — |
| 55 | (C3⋊D9)⋊C4 | — | 4 | 1 | no | — |
| 56 | D4×S4 | — | 9 | 1 | no | — |
| 57 | #5590 | — | 9 | 1 | no | — |
| 58 | C22×C3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 59 | C2×D3×A4 | — | 3 | 1 | no | — |
| 60 | C2×C3⋊S4 | — | 3 | 1 | no | — |
| 61 | C2×C3⋊S4 | — | 3 | 1 | no | — |
| 62 | C2×C3⋊S4 | — | 6 | 2 | no | — |
| 63 | C2×C3×S4 | C2×D3 | 1 | 1 | yes | characteristic |
| 64 | D3×S4 | — | 6 | 2 | no | — |
| 65 | #3811 | — | 12 | 1 | no | — |
| 66 | Dic3×A4 | — | 3 | 1 | no | — |
| 67 | C3×SL(2,ℤ/4) | C2×D3 | 1 | 1 | yes | characteristic |
| 68 | C24×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 69 | C23×D9 | — | 3 | 1 | no | — |
| 70 | C23×D9 | — | 3 | 1 | no | — |
| 71 | C23×D9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 72 | C22×C22⋊C9 | — | 2 | 1 | no | — |
| 73 | C2×(C22⋊C9)⋊C2 | — | 6 | 1 | no | — |
| 74 | C2×(C22⋊C9)⋊C2 | — | 6 | 1 | no | — |
| 75 | C2×(C22⋊C9)⋊C2 | — | 6 | 4 | no | — |
| 76 | C2×D4×C9 | — | 3 | 1 | no | — |
| 77 | C2×D4×C9 | — | 3 | 1 | no | — |
| 78 | C2×D4×C9 | — | 3 | 1 | no | — |
| 79 | C2×#611 | — | 3 | 1 | no | — |
| 80 | C2×#611 | — | 3 | 1 | no | — |
| 81 | C2×#611 | — | 3 | 1 | no | — |
| 82 | C2×#611 | — | 3 | 1 | no | — |
| 83 | C2×#611 | — | 3 | 1 | no | — |
| 84 | C2×#611 | — | 3 | 1 | no | — |
| 85 | C2×#611 | — | 3 | 1 | no | — |
| 86 | C2×#611 | — | 3 | 1 | no | — |
| 87 | C2×#611 | — | 3 | 1 | no | — |
| 88 | C2×#611 | — | 3 | 1 | no | — |
| 89 | C2×#611 | — | 6 | 2 | no | — |
| 90 | C2×#611 | — | 6 | 2 | no | — |
| 91 | C22×Dic9 | — | 3 | 1 | no | — |
| 92 | C22×Dic9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 93 | D4×D9 | — | 6 | 2 | no | — |
| 94 | D4×D9 | — | 6 | 2 | no | — |
| 95 | D4×D9 | — | 6 | 1 | no | — |
| 96 | D4×D9 | — | 6 | 1 | no | — |
| 97 | D4×D9 | — | 6 | 1 | no | — |
| 98 | D4×D9 | — | 6 | 1 | no | — |
| 99 | C2×D36 | — | 3 | 1 | no | — |
| 100 | C2×D36 | — | 3 | 1 | no | — |
| 101 | C2×D36 | — | 3 | 1 | no | — |
| 102 | C2×C4×D9 | — | 3 | 1 | no | — |
| 103 | C2×C4×D9 | — | 3 | 1 | no | — |
| 104 | C9×C22⋊C4 | — | 3 | 1 | no | — |
| 105 | C9×C22⋊C4 | — | 3 | 1 | no | — |
| 106 | C9×C22⋊C4 | — | 3 | 1 | no | — |
| 107 | #3676 | — | 3 | 1 | no | — |
| 108 | (C2×D9)⋊C4 | — | 3 | 1 | no | — |
| 109 | (C2×D9)⋊C4 | — | 3 | 1 | no | — |
| 110 | (C2×D9)⋊C4 | — | 3 | 1 | no | — |
| 111 | (C2×D9)⋊C4 | — | 3 | 1 | no | — |
| 112 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 113 | Dic9⋊C4 | — | 3 | 1 | no | — |
| 114 | C4×Dic9 | — | 3 | 1 | no | — |
| 115 | C22×C3×C9 | — | 4 | 1 | no | — |
| 116 | C2×C3⋊D9 | — | 4 | 1 | no | — |
| 117 | C2×C3⋊D9 | — | 4 | 1 | no | — |
| 118 | C2×C3⋊D9 | — | 8 | 2 | no | — |
| 119 | C2×D3×C9 | — | 4 | 1 | no | — |
| 120 | C2×C3×D9 | — | 4 | 1 | no | — |
| 121 | C9×A4 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 122 | D3×D9 | — | 8 | 2 | no | — |
| 123 | C9×Dic3 | — | 4 | 1 | no | — |
| 124 | C3×Dic9 | — | 4 | 1 | no | — |
| 125 | C22×S4 | — | 9 | 1 | no | — |
| 126 | C22×S4 | — | 9 | 1 | no | — |
| 127 | C22×S4 | — | 18 | 1 | no | — |
| 128 | C22×#67 | — | 3 | 1 | no | — |
| 129 | C22×#67 | — | 9 | 1 | no | — |
| 130 | C2×D3×D4 | — | 9 | 1 | no | — |
| 131 | C2×D3×D4 | — | 9 | 1 | no | — |
| 132 | D4×A4 | — | 9 | 1 | no | — |
| 133 | GL(2,ℤ/4) | — | 9 | 1 | no | — |
| 134 | GL(2,ℤ/4) | D9 | 1 | 1 | yes | characteristic, complemented |
| 135 | C4⋊S4 | — | 9 | 1 | no | — |
| 136 | C4×S4 | — | 9 | 1 | no | — |
| 137 | C3×#120 | — | 3 | 1 | no | — |
| 138 | #940 | — | 9 | 1 | no | — |
| 139 | #939 | — | 9 | 1 | no | — |
| 140 | #939 | — | 9 | 1 | no | — |
| 141 | #937 | — | 9 | 1 | no | — |
| 142 | #884 | — | 9 | 1 | no | — |
| 143 | #884 | — | 9 | 1 | no | — |
| 144 | #882 | — | 9 | 1 | no | — |
| 145 | #882 | — | 9 | 1 | no | — |
| 146 | #67⋊C4 | — | 9 | 1 | no | — |
| 147 | #67⋊C4 | — | 9 | 1 | no | — |
| 148 | C22×C3⋊D3 | — | 12 | 1 | no | — |
| 149 | C2×C3×A4 | — | 2 | 1 | no | — |
| 150 | C2×C3×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 151 | C2×D32 | — | 12 | 1 | no | — |
| 152 | D3×A4 | — | 6 | 1 | no | — |
| 153 | C3⋊S4 | — | 3 | 2 | no | — |
| 154 | C3⋊S4 | — | 6 | 1 | no | — |
| 155 | C3×S4 | — | 2 | 1 | no | — |
| 156 | C3×#67 | — | 4 | 1 | no | — |
| 157 | C3×#67 | — | 12 | 1 | no | — |
| 158 | #626 | — | 12 | 1 | no | — |
| 159 | #626 | — | 12 | 1 | no | — |
| 160 | #624 | — | 12 | 1 | no | — |
| 161 | C23×C9 | — | 2 | 1 | no | — |
| 162 | C23×C9 | — | 3 | 1 | no | — |
| 163 | C23×C9 | — | 3 | 1 | no | — |
| 164 | C23×C9 | — | 3 | 1 | no | — |
| 165 | C23×C9 | — | 6 | 1 | no | — |
| 166 | C23×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 167 | C22×D9 | — | 2 | 1 | no | — |
| 168 | C22×D9 | — | 3 | 1 | no | — |
| 169 | C22×D9 | — | 3 | 1 | no | — |
| 170 | C22×D9 | — | 3 | 1 | no | — |
| 171 | C22×D9 | — | 3 | 1 | no | — |
| 172 | C22×D9 | — | 6 | 2 | no | — |
| 173 | C22×D9 | — | 6 | 1 | no | — |
| 174 | C22×D9 | — | 6 | 2 | no | — |
| 175 | C22×D9 | — | 6 | 1 | no | — |
| 176 | C22×D9 | — | 6 | 1 | no | — |
| 177 | C22×D9 | — | 6 | 1 | no | — |
| 178 | C22×D9 | — | 6 | 1 | no | — |
| 179 | C22×D9 | — | 12 | 1 | no | — |
| 180 | C22×D9 | — | 12 | 1 | no | — |
| 181 | C22×D9 | — | 24 | 1 | no | — |
| 182 | C2×C22⋊C9 | — | 2 | 2 | no | — |
| 183 | C2×C22⋊C9 | — | 2 | 1 | no | — |
| 184 | (C22⋊C9)⋊C2 | — | 6 | 2 | no | — |
| 185 | (C22⋊C9)⋊C2 | — | 6 | 2 | no | — |
| 186 | D4×C9 | — | 6 | 1 | no | — |
| 187 | D4×C9 | — | 6 | 1 | no | — |
| 188 | D4×C9 | — | 6 | 1 | no | — |
| 189 | D4×C9 | — | 6 | 1 | no | — |
| 190 | D4×C9 | — | 12 | 1 | no | — |
| 191 | C2×C4×C9 | — | 3 | 1 | no | — |
| 192 | C2×C4×C9 | — | 3 | 1 | no | — |
| 193 | C2×C4×C9 | — | 3 | 1 | no | — |
| 194 | #611 | — | 3 | 2 | no | — |
| 195 | #611 | — | 3 | 2 | no | — |
| 196 | #611 | — | 3 | 1 | no | — |
| 197 | #611 | — | 3 | 1 | no | — |
| 198 | #611 | — | 3 | 1 | no | — |
| 199 | #611 | — | 6 | 1 | no | — |
| 200 | #611 | — | 6 | 2 | no | — |
| 201 | #611 | — | 6 | 1 | no | — |
| 202 | #611 | — | 6 | 2 | no | — |
| 203 | #611 | — | 6 | 2 | no | — |
| 204 | #611 | — | 6 | 1 | no | — |
| 205 | #611 | — | 6 | 1 | no | — |
| 206 | #611 | — | 6 | 1 | no | — |
| 207 | #611 | S4 | 1 | 1 | yes | characteristic, complemented |
| 208 | C2×Dic9 | — | 3 | 1 | no | — |
| 209 | C2×Dic9 | — | 3 | 1 | no | — |
| 210 | C2×Dic9 | — | 3 | 1 | no | — |
| 211 | C2×Dic9 | — | 3 | 1 | no | — |
| 212 | C2×Dic9 | — | 6 | 2 | no | — |
| 213 | D36 | — | 6 | 2 | no | — |
| 214 | D36 | — | 6 | 1 | no | — |
| 215 | D36 | — | 6 | 1 | no | — |
| 216 | D36 | — | 12 | 1 | no | — |
| 217 | C4×D9 | — | 6 | 2 | no | — |
| 218 | C4×D9 | — | 6 | 1 | no | — |
| 219 | C4×D9 | — | 6 | 1 | no | — |
| 220 | D42 | — | 27 | 1 | no | Sylow |
| 221 | C2×C3×C9 | — | 4 | 1 | no | — |
| 222 | C2×C3×C9 | — | 8 | 1 | no | — |
| 223 | C3⋊D9 | — | 4 | 2 | no | — |
| 224 | C3⋊D9 | — | 8 | 1 | no | — |
| 225 | D3×C9 | — | 8 | 1 | no | — |
| 226 | C3×D9 | — | 8 | 1 | no | — |
| 227 | C24×C3 | D32 | 1 | 1 | yes | characteristic |
| 228 | C23×D3 | — | 3 | 1 | no | — |
| 229 | C23×D3 | — | 9 | 1 | no | — |
| 230 | C23×D3 | — | 9 | 1 | no | — |
| 231 | C22×A4 | — | 2 | 1 | no | — |
| 232 | C22×A4 | — | 9 | 1 | no | — |
| 233 | C22×A4 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 234 | C2×S4 | — | 9 | 1 | no | — |
| 235 | C2×S4 | — | 9 | 1 | no | — |
| 236 | C2×S4 | — | 18 | 1 | no | — |
| 237 | C2×S4 | — | 18 | 1 | no | — |
| 238 | C2×S4 | — | 18 | 2 | no | — |
| 239 | C2×S4 | — | 18 | 2 | no | — |
| 240 | C2×S4 | — | 18 | 4 | no | — |
| 241 | C2×S4 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 242 | C2×C3×D4 | — | 3 | 1 | no | — |
| 243 | C2×C3×D4 | — | 3 | 1 | no | — |
| 244 | C2×C3×D4 | — | 3 | 1 | no | — |
| 245 | C2×#67 | — | 9 | 1 | no | — |
| 246 | C2×#67 | — | 9 | 1 | no | — |
| 247 | C2×#67 | — | 9 | 1 | no | — |
| 248 | C2×#67 | — | 9 | 1 | no | — |
| 249 | C2×#67 | — | 9 | 1 | no | — |
| 250 | C2×#67 | — | 9 | 1 | no | — |
| 251 | C2×#67 | — | 9 | 1 | no | — |
| 252 | C2×#67 | — | 9 | 1 | no | — |
| 253 | C2×#67 | — | 9 | 1 | no | — |
| 254 | C2×#67 | — | 9 | 1 | no | — |
| 255 | C2×#67 | — | 18 | 2 | no | — |
| 256 | C2×#67 | — | 18 | 2 | no | — |
| 257 | C22×Dic3 | — | 3 | 1 | no | — |
| 258 | C22×Dic3 | — | 9 | 1 | no | — |
| 259 | D3×D4 | — | 18 | 1 | no | — |
| 260 | D3×D4 | — | 18 | 2 | no | — |
| 261 | D3×D4 | — | 18 | 1 | no | — |
| 262 | D3×D4 | — | 18 | 1 | no | — |
| 263 | D3×D4 | — | 18 | 2 | no | — |
| 264 | D3×D4 | — | 18 | 1 | no | — |
| 265 | D3×D4 | — | 36 | 1 | no | — |
| 266 | C2×D12 | — | 9 | 1 | no | — |
| 267 | C2×D12 | — | 9 | 1 | no | — |
| 268 | C2×D12 | — | 9 | 1 | no | — |
| 269 | C2×C4×D3 | — | 9 | 1 | no | — |
| 270 | C2×C4×D3 | — | 9 | 1 | no | — |
| 271 | C4×A4 | — | 9 | 1 | no | — |
| 272 | SL(2,ℤ/4) | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 273 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 274 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 275 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 276 | #217 | — | 9 | 1 | no | — |
| 277 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 278 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 279 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 280 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 281 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 282 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 283 | C4×Dic3 | — | 9 | 1 | no | — |
| 284 | C22×C32 | — | 4 | 1 | no | — |
| 285 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 286 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 287 | C2×C3⋊D3 | — | 24 | 2 | no | — |
| 288 | C2×C3×D3 | — | 4 | 1 | no | — |
| 289 | C2×C3×D3 | — | 12 | 1 | no | — |
| 290 | C3×A4 | D3×D4 | 1 | 1 | yes | characteristic |
| 291 | D32 | — | 24 | 2 | no | — |
| 292 | C3×Dic3 | — | 4 | 1 | no | — |
| 293 | C3×Dic3 | — | 12 | 1 | no | — |
| 294 | C22×C9 | — | 3 | 1 | no | — |
| 295 | C22×C9 | — | 3 | 1 | no | — |
| 296 | C22×C9 | — | 3 | 1 | no | — |
| 297 | C22×C9 | — | 6 | 1 | no | — |
| 298 | C22×C9 | — | 6 | 1 | no | — |
| 299 | C22×C9 | — | 6 | 1 | no | — |
| 300 | C22×C9 | — | 6 | 1 | no | — |
| 301 | C22×C9 | — | 6 | 1 | no | — |
| 302 | C22×C9 | — | 6 | 1 | no | — |
| 303 | C22×C9 | — | 6 | 1 | no | — |
| 304 | C22×C9 | — | 8 | 1 | no | — |
| 305 | C22×C9 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 306 | C22×C9 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 307 | C2×D9 | — | 3 | 2 | no | — |
| 308 | C2×D9 | — | 3 | 1 | no | — |
| 309 | C2×D9 | — | 6 | 1 | no | — |
| 310 | C2×D9 | — | 6 | 1 | no | — |
| 311 | C2×D9 | — | 6 | 1 | no | — |
| 312 | C2×D9 | — | 6 | 1 | no | — |
| 313 | C2×D9 | — | 6 | 1 | no | — |
| 314 | C2×D9 | — | 6 | 1 | no | — |
| 315 | C2×D9 | — | 6 | 1 | no | — |
| 316 | C2×D9 | — | 6 | 1 | no | — |
| 317 | C2×D9 | — | 6 | 1 | no | — |
| 318 | C2×D9 | — | 12 | 2 | no | — |
| 319 | C2×D9 | — | 12 | 2 | no | — |
| 320 | C2×D9 | — | 12 | 2 | no | — |
| 321 | C2×D9 | — | 12 | 2 | no | — |
| 322 | C2×D9 | — | 24 | 1 | no | — |
| 323 | C2×D9 | — | 24 | 1 | no | — |
| 324 | C2×D9 | — | 24 | 4 | no | — |
| 325 | C2×D9 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 326 | C22⋊C9 | — | 2 | 1 | no | — |
| 327 | C4×C9 | — | 6 | 1 | no | — |
| 328 | C4×C9 | — | 6 | 1 | no | — |
| 329 | C4×C9 | — | 6 | 1 | no | — |
| 330 | Dic9 | — | 3 | 2 | no | — |
| 331 | Dic9 | — | 3 | 1 | no | — |
| 332 | Dic9 | — | 6 | 1 | no | — |
| 333 | Dic9 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 334 | C22×D4 | — | 9 | 1 | no | — |
| 335 | C22×D4 | — | 27 | 1 | no | — |
| 336 | C22×D4 | — | 27 | 1 | no | — |
| 337 | C22×D4 | — | 27 | 1 | no | — |
| 338 | #127 | — | 27 | 1 | no | — |
| 339 | #121 | — | 27 | 1 | no | — |
| 340 | #121 | — | 27 | 1 | no | — |
| 341 | #121 | — | 27 | 1 | no | — |
| 342 | #121 | — | 27 | 1 | no | — |
| 343 | #120 | — | 3 | 1 | no | — |
| 344 | #120 | — | 27 | 1 | no | — |
| 345 | #120 | — | 27 | 1 | no | — |
| 346 | #120 | — | 27 | 1 | no | — |
| 347 | C4×D4 | — | 27 | 1 | no | — |
| 348 | C4×D4 | — | 27 | 1 | no | — |
| 349 | C3×C9 | — | 4 | 1 | no | Sylow |
| 350 | C23×C3 | — | 2 | 1 | no | — |
| 351 | C23×C3 | — | 3 | 1 | no | — |
| 352 | C23×C3 | — | 3 | 1 | no | — |
| 353 | C23×C3 | — | 3 | 1 | no | — |
| 354 | C23×C3 | — | 6 | 1 | no | — |
| 355 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 356 | C22×D3 | — | 6 | 1 | no | — |
| 357 | C22×D3 | — | 9 | 1 | no | — |
| 358 | C22×D3 | — | 9 | 1 | no | — |
| 359 | C22×D3 | — | 9 | 1 | no | — |
| 360 | C22×D3 | — | 9 | 1 | no | — |
| 361 | C22×D3 | — | 18 | 1 | no | — |
| 362 | C22×D3 | — | 18 | 2 | no | — |
| 363 | C22×D3 | — | 18 | 1 | no | — |
| 364 | C22×D3 | — | 18 | 2 | no | — |
| 365 | C22×D3 | — | 18 | 1 | no | — |
| 366 | C22×D3 | — | 18 | 1 | no | — |
| 367 | C22×D3 | — | 18 | 1 | no | — |
| 368 | C22×D3 | — | 36 | 1 | no | — |
| 369 | C22×D3 | — | 36 | 1 | no | — |
| 370 | C22×D3 | — | 36 | 1 | no | — |
| 371 | C22×D3 | — | 36 | 1 | no | — |
| 372 | C22×D3 | — | 72 | 1 | no | — |
| 373 | C2×A4 | — | 2 | 2 | no | — |
| 374 | C2×A4 | — | 2 | 1 | no | — |
| 375 | C2×A4 | — | 2 | 1 | no | — |
| 376 | C2×A4 | — | 18 | 1 | no | — |
| 377 | C2×A4 | C22×D9 | 1 | 1 | yes | characteristic |
| 378 | S4 | — | 2 | 1 | no | — |
| 379 | S4 | — | 9 | 2 | no | — |
| 380 | S4 | — | 18 | 2 | no | — |
| 381 | S4 | — | 18 | 2 | no | — |
| 382 | S4 | — | 18 | 1 | no | — |
| 383 | C3×D4 | — | 6 | 1 | no | — |
| 384 | C3×D4 | — | 6 | 1 | no | — |
| 385 | C3×D4 | — | 6 | 1 | no | — |
| 386 | C3×D4 | — | 6 | 1 | no | — |
| 387 | C3×D4 | — | 12 | 1 | no | — |
| 388 | C3×D4 | — | 36 | 1 | no | — |
| 389 | C2×C3×C4 | — | 3 | 1 | no | — |
| 390 | C2×C3×C4 | — | 3 | 1 | no | — |
| 391 | C2×C3×C4 | — | 3 | 1 | no | — |
| 392 | #67 | — | 3 | 1 | no | — |
| 393 | #67 | — | 4 | 1 | no | — |
| 394 | #67 | — | 9 | 1 | no | — |
| 395 | #67 | — | 9 | 1 | no | — |
| 396 | #67 | — | 9 | 2 | no | — |
| 397 | #67 | — | 9 | 1 | no | — |
| 398 | #67 | — | 9 | 2 | no | — |
| 399 | #67 | — | 18 | 1 | no | — |
| 400 | #67 | — | 18 | 1 | no | — |
| 401 | #67 | — | 18 | 2 | no | — |
| 402 | #67 | — | 18 | 1 | no | — |
| 403 | #67 | — | 18 | 2 | no | — |
| 404 | #67 | — | 18 | 2 | no | — |
| 405 | #67 | — | 18 | 1 | no | — |
| 406 | #67 | — | 18 | 1 | no | — |
| 407 | #67 | — | 36 | 1 | no | — |
| 408 | C2×Dic3 | — | 9 | 1 | no | — |
| 409 | C2×Dic3 | — | 9 | 1 | no | — |
| 410 | C2×Dic3 | — | 9 | 1 | no | — |
| 411 | C2×Dic3 | — | 9 | 1 | no | — |
| 412 | C2×Dic3 | — | 18 | 2 | no | — |
| 413 | D12 | — | 18 | 1 | no | — |
| 414 | D12 | — | 18 | 2 | no | — |
| 415 | D12 | — | 18 | 1 | no | — |
| 416 | D12 | — | 36 | 1 | no | — |
| 417 | D12 | — | 36 | 1 | no | — |
| 418 | C4×D3 | — | 18 | 1 | no | — |
| 419 | C4×D3 | — | 18 | 2 | no | — |
| 420 | C4×D3 | — | 18 | 1 | no | — |
| 421 | C4×D3 | — | 36 | 1 | no | — |
| 422 | C2×C32 | — | 4 | 1 | no | — |
| 423 | C2×C32 | — | 8 | 1 | no | — |
| 424 | C3⋊D3 | — | 12 | 2 | no | — |
| 425 | C3⋊D3 | — | 24 | 1 | no | — |
| 426 | C3×D3 | — | 8 | 1 | no | — |
| 427 | C3×D3 | — | 24 | 1 | no | — |
| 428 | C2×C9 | — | 2 | 1 | no | — |
| 429 | C2×C9 | — | 3 | 1 | no | — |
| 430 | C2×C9 | — | 3 | 1 | no | — |
| 431 | C2×C9 | — | 6 | 1 | no | — |
| 432 | C2×C9 | — | 8 | 2 | no | — |
| 433 | C2×C9 | — | 8 | 1 | no | — |
| 434 | C2×C9 | — | 12 | 1 | no | — |
| 435 | C2×C9 | C22×S4 | 1 | 1 | yes | characteristic |
| 436 | D9 | — | 2 | 1 | no | — |
| 437 | D9 | — | 6 | 2 | no | — |
| 438 | D9 | — | 6 | 1 | no | — |
| 439 | D9 | — | 12 | 1 | no | — |
| 440 | D9 | — | 24 | 2 | no | — |
| 441 | D9 | — | 24 | 2 | no | — |
| 442 | C24 | — | 9 | 1 | no | — |
| 443 | C24 | — | 27 | 1 | no | — |
| 444 | C24 | — | 27 | 1 | no | — |
| 445 | C24 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 446 | C2×D4 | — | 3 | 1 | no | — |
| 447 | C2×D4 | — | 3 | 1 | no | — |
| 448 | C2×D4 | — | 3 | 1 | no | — |
| 449 | C2×D4 | — | 27 | 1 | no | — |
| 450 | C2×D4 | — | 27 | 1 | no | — |
| 451 | C2×D4 | — | 27 | 1 | no | — |
| 452 | C2×D4 | — | 27 | 1 | no | — |
| 453 | C2×D4 | — | 27 | 1 | no | — |
| 454 | C2×D4 | — | 27 | 1 | no | — |
| 455 | C2×D4 | — | 27 | 1 | no | — |
| 456 | C2×D4 | — | 27 | 1 | no | — |
| 457 | C2×D4 | — | 27 | 1 | no | — |
| 458 | C2×D4 | — | 27 | 1 | no | — |
| 459 | C2×D4 | — | 27 | 1 | no | — |
| 460 | C2×D4 | — | 27 | 1 | no | — |
| 461 | C2×D4 | — | 27 | 1 | no | — |
| 462 | C2×D4 | — | 54 | 1 | no | — |
| 463 | C2×D4 | — | 54 | 2 | no | — |
| 464 | C2×D4 | — | 54 | 1 | no | — |
| 465 | C2×D4 | — | 54 | 1 | no | — |
| 466 | C2×D4 | — | 54 | 2 | no | — |
| 467 | C2×D4 | — | 54 | 1 | no | — |
| 468 | C2×D4 | — | 54 | 2 | no | — |
| 469 | C2×D4 | — | 54 | 2 | no | — |
| 470 | C22×C4 | — | 9 | 1 | no | — |
| 471 | C22×C4 | — | 27 | 1 | no | — |
| 472 | C22×C4 | — | 27 | 1 | no | — |
| 473 | C22×C4 | — | 27 | 1 | no | — |
| 474 | C4⋊C4 | — | 27 | 1 | no | — |
| 475 | C4⋊C4 | — | 27 | 1 | no | — |
| 476 | C22⋊C4 | — | 3 | 1 | no | — |
| 477 | C22⋊C4 | — | 3 | 1 | no | — |
| 478 | C22⋊C4 | — | 3 | 1 | no | — |
| 479 | C22⋊C4 | — | 27 | 1 | no | — |
| 480 | C22⋊C4 | — | 27 | 1 | no | — |
| 481 | C22⋊C4 | — | 27 | 1 | no | — |
| 482 | C22⋊C4 | — | 27 | 1 | no | — |
| 483 | C22⋊C4 | — | 27 | 1 | no | — |
| 484 | C42 | — | 27 | 1 | no | — |
| 485 | C22×C3 | — | 3 | 1 | no | — |
| 486 | C22×C3 | — | 3 | 1 | no | — |
| 487 | C22×C3 | — | 3 | 1 | no | — |
| 488 | C22×C3 | — | 4 | 1 | no | — |
| 489 | C22×C3 | — | 6 | 1 | no | — |
| 490 | C22×C3 | — | 6 | 1 | no | — |
| 491 | C22×C3 | — | 6 | 1 | no | — |
| 492 | C22×C3 | — | 6 | 1 | no | — |
| 493 | C22×C3 | — | 6 | 1 | no | — |
| 494 | C22×C3 | — | 6 | 1 | no | — |
| 495 | C22×C3 | — | 6 | 1 | no | — |
| 496 | C22×C3 | — | 8 | 1 | no | — |
| 497 | C22×C3 | — | 36 | 1 | no | — |
| 498 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 499 | C22×C3 | D3×S4 | 1 | 1 | yes | characteristic |
| 500 | C2×D3 | — | 3 | 1 | no | — |
| 501 | C2×D3 | — | 4 | 1 | no | — |
| 502 | C2×D3 | — | 9 | 2 | no | — |
| 503 | C2×D3 | — | 9 | 1 | no | — |
| 504 | C2×D3 | — | 18 | 1 | no | — |
| 505 | C2×D3 | — | 18 | 1 | no | — |
| 506 | C2×D3 | — | 18 | 1 | no | — |
| 507 | C2×D3 | — | 18 | 1 | no | — |
| 508 | C2×D3 | — | 18 | 1 | no | — |
| 509 | C2×D3 | — | 18 | 1 | no | — |
| 510 | C2×D3 | — | 18 | 1 | no | — |
| 511 | C2×D3 | — | 18 | 1 | no | — |
| 512 | C2×D3 | — | 18 | 1 | no | — |
| 513 | C2×D3 | — | 36 | 1 | no | — |
| 514 | C2×D3 | — | 36 | 1 | no | — |
| 515 | C2×D3 | — | 36 | 2 | no | — |
| 516 | C2×D3 | — | 36 | 2 | no | — |
| 517 | C2×D3 | — | 36 | 2 | no | — |
| 518 | C2×D3 | — | 36 | 2 | no | — |
| 519 | C2×D3 | — | 72 | 1 | no | — |
| 520 | C2×D3 | — | 72 | 1 | no | — |
| 521 | C2×D3 | — | 72 | 2 | no | — |
| 522 | C2×D3 | — | 72 | 2 | no | — |
| 523 | C2×D3 | — | 72 | 4 | no | — |
| 524 | A4 | — | 2 | 1 | no | — |
| 525 | A4 | D4×D9 | 1 | 1 | yes | characteristic, complemented |
| 526 | C3×C4 | — | 6 | 1 | no | — |
| 527 | C3×C4 | — | 6 | 1 | no | — |
| 528 | C3×C4 | — | 6 | 1 | no | — |
| 529 | C3×C4 | — | 36 | 1 | no | — |
| 530 | Dic3 | — | 3 | 1 | no | — |
| 531 | Dic3 | — | 4 | 1 | no | — |
| 532 | Dic3 | — | 9 | 2 | no | — |
| 533 | Dic3 | — | 9 | 1 | no | — |
| 534 | Dic3 | — | 18 | 1 | no | — |
| 535 | C32 | — | 4 | 1 | no | — |
| 536 | C9 | — | 8 | 1 | no | — |
| 537 | C9 | D4×S4 | 1 | 1 | yes | characteristic, complemented |
| 538 | C23 | — | 2 | 1 | no | — |
| 539 | C23 | — | 3 | 1 | no | — |
| 540 | C23 | — | 3 | 1 | no | — |
| 541 | C23 | — | 3 | 1 | no | — |
| 542 | C23 | — | 6 | 1 | no | — |
| 543 | C23 | — | 18 | 1 | no | — |
| 544 | C23 | — | 27 | 1 | no | — |
| 545 | C23 | — | 27 | 1 | no | — |
| 546 | C23 | — | 27 | 1 | no | — |
| 547 | C23 | — | 27 | 1 | no | — |
| 548 | C23 | — | 54 | 1 | no | — |
| 549 | C23 | — | 54 | 1 | no | — |
| 550 | C23 | — | 54 | 1 | no | — |
| 551 | C23 | — | 54 | 2 | no | — |
| 552 | C23 | — | 54 | 2 | no | — |
| 553 | C23 | — | 54 | 1 | no | — |
| 554 | C23 | — | 54 | 1 | no | — |
| 555 | C23 | — | 108 | 1 | no | — |
| 556 | C23 | — | 108 | 1 | no | — |
| 557 | C23 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 558 | D4 | — | 6 | 1 | no | — |
| 559 | D4 | — | 6 | 1 | no | — |
| 560 | D4 | — | 6 | 1 | no | — |
| 561 | D4 | — | 6 | 1 | no | — |
| 562 | D4 | — | 9 | 1 | no | — |
| 563 | D4 | — | 12 | 1 | no | — |
| 564 | D4 | — | 27 | 1 | no | — |
| 565 | D4 | — | 27 | 1 | no | — |
| 566 | D4 | — | 27 | 2 | no | — |
| 567 | D4 | — | 27 | 1 | no | — |
| 568 | D4 | — | 27 | 2 | no | — |
| 569 | D4 | — | 54 | 1 | no | — |
| 570 | D4 | — | 54 | 2 | no | — |
| 571 | D4 | — | 54 | 1 | no | — |
| 572 | D4 | — | 54 | 1 | no | — |
| 573 | D4 | — | 54 | 1 | no | — |
| 574 | D4 | — | 54 | 2 | no | — |
| 575 | D4 | — | 54 | 2 | no | — |
| 576 | D4 | — | 54 | 1 | no | — |
| 577 | D4 | — | 54 | 1 | no | — |
| 578 | D4 | — | 54 | 2 | no | — |
| 579 | D4 | — | 54 | 1 | no | — |
| 580 | D4 | — | 108 | 1 | no | — |
| 581 | C2×C4 | — | 3 | 1 | no | — |
| 582 | C2×C4 | — | 3 | 1 | no | — |
| 583 | C2×C4 | — | 3 | 1 | no | — |
| 584 | C2×C4 | — | 27 | 1 | no | — |
| 585 | C2×C4 | — | 27 | 1 | no | — |
| 586 | C2×C4 | — | 27 | 1 | no | — |
| 587 | C2×C4 | — | 27 | 1 | no | — |
| 588 | C2×C4 | — | 54 | 1 | no | — |
| 589 | C2×C4 | — | 54 | 2 | no | — |
| 590 | C2×C4 | — | 54 | 1 | no | — |
| 591 | C2×C4 | — | 54 | 2 | no | — |
| 592 | C2×C3 | — | 2 | 1 | no | — |
| 593 | C2×C3 | — | 3 | 1 | no | — |
| 594 | C2×C3 | — | 3 | 1 | no | — |
| 595 | C2×C3 | — | 4 | 1 | no | — |
| 596 | C2×C3 | — | 6 | 1 | no | — |
| 597 | C2×C3 | — | 8 | 1 | no | — |
| 598 | C2×C3 | — | 8 | 2 | no | — |
| 599 | C2×C3 | — | 8 | 1 | no | — |
| 600 | C2×C3 | — | 12 | 1 | no | — |
| 601 | C2×C3 | — | 72 | 1 | no | — |
| 602 | C2×C3 | C2×D3×S4 | 1 | 1 | yes | characteristic |
| 603 | D3 | — | 6 | 1 | no | — |
| 604 | D3 | — | 8 | 1 | no | — |
| 605 | D3 | — | 18 | 1 | no | — |
| 606 | D3 | — | 18 | 2 | no | — |
| 607 | D3 | — | 36 | 2 | no | — |
| 608 | D3 | — | 36 | 1 | no | — |
| 609 | D3 | — | 72 | 2 | no | — |
| 610 | D3 | — | 72 | 1 | no | — |
| 611 | D3 | — | 72 | 2 | no | — |
| 612 | C22 | — | 3 | 1 | no | — |
| 613 | C22 | — | 3 | 1 | no | — |
| 614 | C22 | — | 3 | 1 | no | — |
| 615 | C22 | — | 6 | 1 | no | — |
| 616 | C22 | — | 6 | 1 | no | — |
| 617 | C22 | — | 6 | 1 | no | — |
| 618 | C22 | — | 6 | 1 | no | — |
| 619 | C22 | — | 6 | 1 | no | — |
| 620 | C22 | — | 6 | 1 | no | — |
| 621 | C22 | — | 6 | 1 | no | — |
| 622 | C22 | — | 9 | 1 | no | — |
| 623 | C22 | — | 27 | 2 | no | — |
| 624 | C22 | — | 27 | 1 | no | — |
| 625 | C22 | — | 54 | 1 | no | — |
| 626 | C22 | — | 54 | 1 | no | — |
| 627 | C22 | — | 54 | 1 | no | — |
| 628 | C22 | — | 54 | 1 | no | — |
| 629 | C22 | — | 54 | 1 | no | — |
| 630 | C22 | — | 54 | 1 | no | — |
| 631 | C22 | — | 54 | 1 | no | — |
| 632 | C22 | — | 54 | 1 | no | — |
| 633 | C22 | — | 54 | 1 | no | — |
| 634 | C22 | — | 108 | 2 | no | — |
| 635 | C22 | — | 108 | 2 | no | — |
| 636 | C22 | — | 108 | 2 | no | — |
| 637 | C22 | — | 108 | 2 | no | — |
| 638 | C22 | #88668 | 1 | 1 | yes | characteristic, complemented |
| 639 | C22 | D9×S4 | 1 | 1 | yes | characteristic, complemented |
| 640 | C4 | — | 6 | 1 | no | — |
| 641 | C4 | — | 6 | 1 | no | — |
| 642 | C4 | — | 6 | 1 | no | — |
| 643 | C4 | — | 9 | 1 | no | — |
| 644 | C4 | — | 27 | 2 | no | — |
| 645 | C4 | — | 27 | 1 | no | — |
| 646 | C4 | — | 54 | 1 | no | — |
| 647 | C3 | — | 4 | 1 | no | — |
| 648 | C3 | — | 8 | 1 | no | — |
| 649 | C3 | #10596473 | 1 | 1 | yes | characteristic |
| 650 | C2 | — | 2 | 1 | no | — |
| 651 | C2 | — | 3 | 1 | no | — |
| 652 | C2 | — | 3 | 1 | no | — |
| 653 | C2 | — | 6 | 1 | no | — |
| 654 | C2 | — | 12 | 1 | no | — |
| 655 | C2 | — | 18 | 1 | no | — |
| 656 | C2 | — | 54 | 1 | no | — |
| 657 | C2 | — | 54 | 2 | no | — |
| 658 | C2 | — | 108 | 1 | no | — |
| 659 | C2 | C2×D9×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D9×S4 |
| commutator, cosocle | C2×C9×A4 | C23 |
| Frattini | C2×C3 | C2×D3×S4 |
| Fitting | C24×C9 | C2×D3 |
| socle | C23×C3 | C2×D32 |
| hypercenter | C22 | D9×S4 |
| hypocenter | C9×A4 | C2×D4 |
| LCS | G ▷ C2×C9×A4 ▷ C9×A4 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C9⋊S4 | C2 | semidirect |
| 2. C2×D9×S4 | C2 | semidirect |
| 3. A4×#611 | C2 | semidirect |
| 4. C9×GL(2,ℤ/4) | C2 | semidirect |
| 5. #11722243 | C2 | semidirect |
| 6. #11722242 | C2 | semidirect |
| 7. (C9⋊S4)⋊C4 | C2 | semidirect |
| 10. C22×C9×A4 | C22 | semidirect |
| 11. C2×A4×D9 | C22 | semidirect |
| 14. C2×C9⋊S4 | C22 | semidirect |
| 15. C2×C9×S4 | C22 | semidirect |
| 18. A4×Dic9 | C22 | semidirect |
| 19. C9×SL(2,ℤ/4) | C22 | semidirect |
| 29. C22×#611 | D3 | semidirect |
| 49. C9⋊S4 | D4 | semidirect |
| 68. C24×C9 | C2×D3 | semidirect |
| 71. C23×D9 | C2×D3 | semidirect |
| 92. C22×Dic9 | C2×D3 | semidirect |
| 121. C9×A4 | C2×D4 | semidirect |
| 134. GL(2,ℤ/4) | D9 | semidirect |
| 207. #611 | S4 | semidirect |
| 233. C22×A4 | C2×D9 | semidirect |
| 241. C2×S4 | C2×D9 | semidirect |
| 272. SL(2,ℤ/4) | C2×D9 | semidirect |
| 305. C22×C9 | D3×D4 | semidirect |
| 306. C22×C9 | C2×S4 | semidirect |
| 325. C2×D9 | C2×S4 | semidirect |
| 333. Dic9 | C2×S4 | semidirect |
| 445. C24 | D3×D9 | semidirect |
| 525. A4 | D4×D9 | semidirect |
| 537. C9 | D4×S4 | semidirect |
| 638. C22 | #88668 | semidirect |
| 639. C22 | D9×S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9⋊S4 | 2 |
| C2×D9×S4 | 2 |
| A4×#611 | 2 |
| C9×GL(2,ℤ/4) | 2 |
| #11722243 | 2 |
| #11722242 | 2 |
| (C9⋊S4)⋊C4 | 2 |
| #10596473 | 3 |
| #10589692 | 3 |
| #88668 | 4 |