Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
673 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 673 conjugacy classes of subgroups — too many to draw. Only its 89 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 | C2×C4×C9×A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722376 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C4⋊(C9⋊S4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C4×C9⋊S4 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11722366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10596575 | — | 3 | 1 | no | maximal |
| 7 | #10593087 | — | 3 | 2 | no | maximal |
| 8 | #10589893 | — | 3 | 1 | no | maximal |
| 9 | C22×C9×A4 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C9⋊S4 | C22 | 1 | 2 | yes | — |
| 11 | #88736 | — | 4 | 1 | no | maximal |
| 12 | C4×C9×A4 | C22 | 1 | 1 | yes | characteristic |
| 13 | C4×C9×A4 | C22 | 1 | 1 | yes | characteristic |
| 14 | C9⋊SL(2,ℤ/4) | C22 | 1 | 2 | yes | — |
| 15 | C2×C3×C4×A4 | D3 | 1 | 1 | yes | characteristic |
| 16 | #64269 | — | 3 | 2 | no | — |
| 17 | C4⋊(C3⋊S4) | — | 3 | 1 | no | — |
| 18 | C4×C3⋊S4 | — | 3 | 2 | no | — |
| 19 | #64259 | — | 3 | 1 | no | — |
| 20 | C23×C4×C9 | D3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#3697 | — | 3 | 1 | no | — |
| 22 | C2×C4×C22⋊C9 | D3 | 1 | 2 | yes | complemented |
| 23 | #63694 | — | 3 | 4 | no | — |
| 24 | C4⋊((C22⋊C9)⋊C2) | — | 3 | 2 | no | — |
| 25 | C4×(C22⋊C9)⋊C2 | — | 3 | 4 | no | — |
| 26 | (C22⋊C9)⋊Q8 | — | 3 | 2 | no | — |
| 27 | #63515 | — | 3 | 2 | no | — |
| 28 | #63492 | — | 3 | 1 | no | — |
| 29 | #63492 | — | 3 | 1 | no | — |
| 30 | #63491 | — | 3 | 2 | no | — |
| 31 | C4×#611 | — | 3 | 2 | no | — |
| 32 | C4×#611 | — | 3 | 2 | no | — |
| 33 | #63488 | — | 3 | 1 | no | — |
| 34 | #63486 | — | 3 | 1 | no | — |
| 35 | #63486 | — | 3 | 1 | no | — |
| 36 | C2×C9×A4 | — | 2 | 1 | no | — |
| 37 | C2×C9×A4 | C23 | 1 | 1 | yes | characteristic |
| 38 | C9⋊S4 | — | 2 | 2 | no | — |
| 39 | C2×C3×C4×C9 | — | 4 | 1 | no | — |
| 40 | #6233 | — | 4 | 2 | no | — |
| 41 | C4⋊(C3⋊D9) | — | 4 | 1 | no | — |
| 42 | C4×C3⋊D9 | — | 4 | 2 | no | — |
| 43 | #6226 | — | 4 | 1 | no | — |
| 44 | #5912 | — | 9 | 3 | no | — |
| 45 | #5791 | — | 9 | 1 | no | — |
| 46 | C22×C3×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 47 | C2×C3⋊S4 | — | 3 | 2 | no | — |
| 48 | #3828 | — | 12 | 1 | no | — |
| 49 | C3×C4×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 50 | C3×C4×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 51 | C3⋊SL(2,ℤ/4) | — | 3 | 2 | no | — |
| 52 | C24×C9 | C2×D3 | 1 | 1 | yes | characteristic |
| 53 | C22×C22⋊C9 | C2×D3 | 1 | 2 | yes | — |
| 54 | C2×(C22⋊C9)⋊C2 | — | 3 | 4 | no | — |
| 55 | C22×C4×C9 | — | 3 | 1 | no | — |
| 56 | C22×C4×C9 | — | 3 | 1 | no | — |
| 57 | C22×C4×C9 | — | 3 | 1 | no | — |
| 58 | C22×C4×C9 | — | 3 | 1 | no | — |
| 59 | C22×C4×C9 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | C22×C4×C9 | C2×D3 | 1 | 1 | yes | characteristic |
| 61 | C2×#611 | — | 3 | 2 | no | — |
| 62 | C2×#611 | — | 3 | 2 | no | — |
| 63 | C2×#611 | — | 3 | 2 | no | — |
| 64 | #3697 | — | 6 | 1 | no | — |
| 65 | #3697 | — | 6 | 1 | no | — |
| 66 | #3697 | — | 6 | 1 | no | — |
| 67 | #3697 | — | 6 | 1 | no | — |
| 68 | #3697 | — | 12 | 2 | no | — |
| 69 | C2×D36 | — | 3 | 1 | no | — |
| 70 | C2×C4×D9 | — | 3 | 2 | no | — |
| 71 | C2×Dic18 | — | 3 | 1 | no | — |
| 72 | C4×C22⋊C9 | C2×D3 | 1 | 2 | yes | — |
| 73 | C4×C22⋊C9 | C2×D3 | 1 | 2 | yes | — |
| 74 | (C22⋊C9)⋊C4 | — | 3 | 4 | no | — |
| 75 | #3676 | — | 3 | 2 | no | — |
| 76 | #3676 | — | 3 | 2 | no | — |
| 77 | #3676 | — | 3 | 2 | no | — |
| 78 | (C2×D9)⋊C4 | — | 3 | 2 | no | — |
| 79 | (C2×D9)⋊C4 | — | 3 | 2 | no | — |
| 80 | C4⋊Dic9 | — | 3 | 1 | no | — |
| 81 | C4⋊Dic9 | — | 3 | 1 | no | — |
| 82 | Dic9⋊C4 | — | 3 | 2 | no | — |
| 83 | Dic9⋊C4 | — | 3 | 2 | no | — |
| 84 | C4×Dic9 | — | 3 | 2 | no | — |
| 85 | C22×C3×C9 | — | 4 | 1 | no | — |
| 86 | C2×C3⋊D9 | — | 4 | 2 | no | — |
| 87 | C9×A4 | #41 | 1 | 1 | yes | characteristic, complemented |
| 88 | C3×C4×C9 | — | 4 | 1 | no | — |
| 89 | C3×C4×C9 | — | 4 | 1 | no | — |
| 90 | C3⋊Dic9 | — | 4 | 2 | no | — |
| 91 | C23×C3×C4 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 92 | C2×#235 | — | 9 | 1 | no | — |
| 93 | C2×C4×A4 | D9 | 1 | 3 | yes | complemented |
| 94 | GL(2,ℤ/4) | — | 9 | 6 | no | — |
| 95 | C4⋊S4 | — | 9 | 3 | no | — |
| 96 | C4×S4 | — | 9 | 6 | no | — |
| 97 | A4⋊Q8 | — | 9 | 3 | no | — |
| 98 | #953 | — | 9 | 2 | no | — |
| 99 | #930 | — | 9 | 1 | no | — |
| 100 | #930 | — | 9 | 1 | no | — |
| 101 | #929 | — | 9 | 2 | no | — |
| 102 | C4×#67 | — | 9 | 2 | no | — |
| 103 | C4×#67 | — | 9 | 2 | no | — |
| 104 | #926 | — | 9 | 1 | no | — |
| 105 | #924 | — | 9 | 1 | no | — |
| 106 | #924 | — | 9 | 1 | no | — |
| 107 | C2×C3×A4 | — | 2 | 1 | no | — |
| 108 | C2×C3×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 109 | C3⋊S4 | — | 6 | 2 | no | — |
| 110 | C2×C32×C4 | — | 4 | 1 | no | — |
| 111 | #638 | — | 12 | 2 | no | — |
| 112 | C4⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 113 | C4×C3⋊D3 | — | 12 | 2 | no | — |
| 114 | #634 | — | 12 | 1 | no | — |
| 115 | C23×C9 | — | 2 | 1 | no | — |
| 116 | C23×C9 | — | 3 | 1 | no | — |
| 117 | C23×C9 | — | 3 | 1 | no | — |
| 118 | C23×C9 | — | 6 | 1 | no | — |
| 119 | C23×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 120 | C22×D9 | — | 3 | 2 | no | — |
| 121 | C2×C22⋊C9 | — | 2 | 2 | no | — |
| 122 | C2×C22⋊C9 | C22×D3 | 1 | 2 | yes | — |
| 123 | (C22⋊C9)⋊C2 | — | 6 | 4 | no | — |
| 124 | C2×C4×C9 | — | 3 | 1 | no | — |
| 125 | C2×C4×C9 | — | 3 | 1 | no | — |
| 126 | C2×C4×C9 | — | 3 | 1 | no | — |
| 127 | C2×C4×C9 | — | 3 | 1 | no | — |
| 128 | C2×C4×C9 | — | 3 | 1 | no | — |
| 129 | C2×C4×C9 | — | 3 | 1 | no | — |
| 130 | C2×C4×C9 | — | 3 | 1 | no | — |
| 131 | C2×C4×C9 | — | 4 | 2 | no | — |
| 132 | C2×C4×C9 | — | 6 | 1 | no | — |
| 133 | C2×C4×C9 | S4 | 1 | 1 | yes | characteristic, complemented |
| 134 | #611 | — | 6 | 2 | no | — |
| 135 | #611 | — | 6 | 2 | no | — |
| 136 | #611 | — | 6 | 4 | no | — |
| 137 | #611 | — | 6 | 2 | no | — |
| 138 | #611 | — | 6 | 2 | no | — |
| 139 | #611 | — | 12 | 4 | no | — |
| 140 | C2×Dic9 | — | 3 | 2 | no | — |
| 141 | C2×Dic9 | — | 3 | 2 | no | — |
| 142 | C2×Dic9 | — | 3 | 2 | no | — |
| 143 | D36 | — | 6 | 1 | no | — |
| 144 | D36 | — | 6 | 1 | no | — |
| 145 | D36 | — | 12 | 2 | no | — |
| 146 | C4×D9 | — | 6 | 2 | no | — |
| 147 | C4×D9 | — | 6 | 2 | no | — |
| 148 | C4×D9 | — | 12 | 4 | no | — |
| 149 | Dic18 | — | 6 | 1 | no | — |
| 150 | Dic18 | — | 6 | 1 | no | — |
| 151 | Dic18 | — | 12 | 2 | no | — |
| 152 | #525 | — | 27 | 1 | no | Sylow |
| 153 | C2×C3×C9 | — | 4 | 1 | no | — |
| 154 | C2×C3×C9 | — | 8 | 1 | no | — |
| 155 | C3⋊D9 | — | 8 | 2 | no | — |
| 156 | C24×C3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 157 | C22×A4 | C2×D9 | 1 | 3 | yes | — |
| 158 | C2×S4 | — | 9 | 6 | no | — |
| 159 | C22×C3×C4 | — | 3 | 1 | no | — |
| 160 | C22×C3×C4 | — | 3 | 1 | no | — |
| 161 | C22×C3×C4 | — | 3 | 1 | no | — |
| 162 | C22×C3×C4 | — | 3 | 1 | no | — |
| 163 | C22×C3×C4 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 164 | C22×C3×C4 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 165 | C2×#67 | — | 9 | 2 | no | — |
| 166 | C2×#67 | — | 9 | 2 | no | — |
| 167 | C2×#67 | — | 9 | 2 | no | — |
| 168 | #235 | — | 18 | 1 | no | — |
| 169 | #235 | — | 18 | 1 | no | — |
| 170 | #235 | — | 18 | 1 | no | — |
| 171 | #235 | — | 18 | 1 | no | — |
| 172 | #235 | — | 36 | 3 | no | — |
| 173 | C2×D12 | — | 9 | 1 | no | — |
| 174 | C2×C4×D3 | — | 9 | 2 | no | — |
| 175 | C2×Dic6 | — | 9 | 1 | no | — |
| 176 | C4×A4 | C2×D9 | 1 | 3 | yes | — |
| 177 | C4×A4 | C2×D9 | 1 | 3 | yes | — |
| 178 | SL(2,ℤ/4) | — | 9 | 6 | no | — |
| 179 | #217 | — | 9 | 2 | no | — |
| 180 | #217 | — | 9 | 2 | no | — |
| 181 | #217 | — | 9 | 2 | no | — |
| 182 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 183 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 184 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 185 | C4⋊Dic3 | — | 9 | 1 | no | — |
| 186 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 187 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 188 | C4×Dic3 | — | 9 | 2 | no | — |
| 189 | C22×C32 | — | 4 | 1 | no | — |
| 190 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 191 | C3×A4 | #235 | 1 | 1 | yes | characteristic |
| 192 | C32×C4 | — | 4 | 1 | no | — |
| 193 | C32×C4 | — | 4 | 1 | no | — |
| 194 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 195 | C22×C9 | — | 3 | 1 | no | — |
| 196 | C22×C9 | — | 3 | 1 | no | — |
| 197 | C22×C9 | — | 3 | 2 | no | — |
| 198 | C22×C9 | — | 3 | 1 | no | — |
| 199 | C22×C9 | — | 4 | 2 | no | — |
| 200 | C22×C9 | — | 6 | 1 | no | — |
| 201 | C22×C9 | — | 6 | 1 | no | — |
| 202 | C22×C9 | — | 6 | 1 | no | — |
| 203 | C22×C9 | #235 | 1 | 1 | yes | characteristic, complemented |
| 204 | C22×C9 | C2×S4 | 1 | 1 | yes | characteristic |
| 205 | C2×D9 | — | 6 | 2 | no | — |
| 206 | C2×D9 | — | 6 | 2 | no | — |
| 207 | C2×D9 | — | 6 | 2 | no | — |
| 208 | C2×D9 | — | 12 | 4 | no | — |
| 209 | C22⋊C9 | #235 | 1 | 2 | yes | complemented |
| 210 | C4×C9 | — | 3 | 1 | no | — |
| 211 | C4×C9 | — | 3 | 1 | no | — |
| 212 | C4×C9 | — | 4 | 2 | no | — |
| 213 | C4×C9 | — | 4 | 2 | no | — |
| 214 | C4×C9 | C2×S4 | 1 | 1 | yes | characteristic |
| 215 | C4×C9 | C2×S4 | 1 | 1 | yes | characteristic |
| 216 | Dic9 | — | 6 | 2 | no | — |
| 217 | Dic9 | — | 6 | 2 | no | — |
| 218 | Dic9 | — | 6 | 2 | no | — |
| 219 | Dic9 | — | 12 | 4 | no | — |
| 220 | C2×#41 | — | 27 | 1 | no | — |
| 221 | C23×C4 | C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 222 | #123 | — | 27 | 2 | no | — |
| 223 | C22⋊Q8 | — | 27 | 1 | no | — |
| 224 | C22⋊Q8 | — | 27 | 1 | no | — |
| 225 | #121 | — | 27 | 1 | no | — |
| 226 | #121 | — | 27 | 1 | no | — |
| 227 | #120 | — | 27 | 2 | no | — |
| 228 | C4×D4 | — | 27 | 2 | no | — |
| 229 | C4×D4 | — | 27 | 2 | no | — |
| 230 | #117 | — | 27 | 1 | no | — |
| 231 | C3×C9 | — | 4 | 1 | no | Sylow |
| 232 | C23×C3 | — | 2 | 1 | no | — |
| 233 | C23×C3 | — | 3 | 1 | no | — |
| 234 | C23×C3 | — | 3 | 1 | no | — |
| 235 | C23×C3 | — | 6 | 1 | no | — |
| 236 | C23×C3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 237 | C22×D3 | — | 9 | 2 | no | — |
| 238 | C2×A4 | — | 2 | 3 | no | — |
| 239 | C2×A4 | C22×D9 | 1 | 3 | yes | — |
| 240 | S4 | — | 18 | 6 | no | — |
| 241 | C2×C3×C4 | — | 3 | 1 | no | — |
| 242 | C2×C3×C4 | — | 3 | 1 | no | — |
| 243 | C2×C3×C4 | — | 3 | 1 | no | — |
| 244 | C2×C3×C4 | — | 3 | 1 | no | — |
| 245 | C2×C3×C4 | — | 3 | 1 | no | — |
| 246 | C2×C3×C4 | — | 3 | 1 | no | — |
| 247 | C2×C3×C4 | — | 3 | 1 | no | — |
| 248 | C2×C3×C4 | — | 4 | 3 | no | — |
| 249 | C2×C3×C4 | — | 6 | 1 | no | — |
| 250 | C2×C3×C4 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 251 | #67 | — | 18 | 2 | no | — |
| 252 | #67 | — | 18 | 2 | no | — |
| 253 | #67 | — | 18 | 4 | no | — |
| 254 | #67 | — | 18 | 2 | no | — |
| 255 | #67 | — | 18 | 2 | no | — |
| 256 | #67 | — | 36 | 6 | no | — |
| 257 | C2×Dic3 | — | 9 | 2 | no | — |
| 258 | C2×Dic3 | — | 9 | 2 | no | — |
| 259 | C2×Dic3 | — | 9 | 2 | no | — |
| 260 | D12 | — | 18 | 1 | no | — |
| 261 | D12 | — | 18 | 1 | no | — |
| 262 | D12 | — | 36 | 3 | no | — |
| 263 | C4×D3 | — | 18 | 2 | no | — |
| 264 | C4×D3 | — | 18 | 2 | no | — |
| 265 | C4×D3 | — | 36 | 6 | no | — |
| 266 | Dic6 | — | 18 | 1 | no | — |
| 267 | Dic6 | — | 18 | 1 | no | — |
| 268 | Dic6 | — | 36 | 3 | no | — |
| 269 | C2×C32 | — | 4 | 1 | no | — |
| 270 | C2×C32 | — | 8 | 1 | no | — |
| 271 | C3⋊D3 | — | 24 | 2 | no | — |
| 272 | C2×C9 | — | 2 | 1 | no | — |
| 273 | C2×C9 | — | 3 | 1 | no | — |
| 274 | C2×C9 | — | 3 | 1 | no | — |
| 275 | C2×C9 | — | 4 | 2 | no | — |
| 276 | C2×C9 | — | 6 | 1 | no | — |
| 277 | C2×C9 | — | 8 | 2 | no | — |
| 278 | C2×C9 | C22×S4 | 1 | 1 | yes | characteristic |
| 279 | D9 | — | 12 | 2 | no | — |
| 280 | D9 | — | 24 | 4 | no | — |
| 281 | C24 | C2×C3⋊D9 | 1 | 1 | yes | characteristic |
| 282 | #41 | — | 54 | 1 | no | — |
| 283 | #41 | — | 54 | 1 | no | — |
| 284 | #41 | — | 54 | 1 | no | — |
| 285 | #41 | — | 54 | 1 | no | — |
| 286 | C2×Q8 | — | 27 | 1 | no | — |
| 287 | C2×D4 | — | 27 | 1 | no | — |
| 288 | C2×D4 | — | 27 | 2 | no | — |
| 289 | C2×D4 | — | 27 | 2 | no | — |
| 290 | C2×D4 | — | 27 | 2 | no | — |
| 291 | C22×C4 | — | 3 | 1 | no | — |
| 292 | C22×C4 | — | 3 | 1 | no | — |
| 293 | C22×C4 | — | 3 | 1 | no | — |
| 294 | C22×C4 | — | 3 | 1 | no | — |
| 295 | C22×C4 | — | 27 | 2 | no | — |
| 296 | C22×C4 | C2×C3⋊D9 | 1 | 1 | yes | characteristic |
| 297 | C22×C4 | C2×C3⋊D9 | 1 | 1 | yes | characteristic |
| 298 | C4⋊C4 | — | 27 | 1 | no | — |
| 299 | C4⋊C4 | — | 27 | 1 | no | — |
| 300 | C4⋊C4 | — | 27 | 2 | no | — |
| 301 | C4⋊C4 | — | 27 | 2 | no | — |
| 302 | C22⋊C4 | — | 27 | 2 | no | — |
| 303 | C22⋊C4 | — | 27 | 2 | no | — |
| 304 | C22⋊C4 | — | 27 | 2 | no | — |
| 305 | C22⋊C4 | — | 27 | 2 | no | — |
| 306 | C22⋊C4 | — | 27 | 2 | no | — |
| 307 | C42 | — | 27 | 2 | no | — |
| 308 | C22×C3 | — | 3 | 1 | no | — |
| 309 | C22×C3 | — | 3 | 1 | no | — |
| 310 | C22×C3 | — | 3 | 2 | no | — |
| 311 | C22×C3 | — | 3 | 1 | no | — |
| 312 | C22×C3 | — | 4 | 3 | no | — |
| 313 | C22×C3 | — | 6 | 1 | no | — |
| 314 | C22×C3 | — | 6 | 1 | no | — |
| 315 | C22×C3 | — | 6 | 1 | no | — |
| 316 | C22×C3 | #3828 | 1 | 1 | yes | characteristic |
| 317 | C22×C3 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 318 | C2×D3 | — | 18 | 2 | no | — |
| 319 | C2×D3 | — | 18 | 2 | no | — |
| 320 | C2×D3 | — | 18 | 2 | no | — |
| 321 | C2×D3 | — | 36 | 6 | no | — |
| 322 | A4 | #3697 | 1 | 3 | yes | complemented |
| 323 | C3×C4 | — | 3 | 1 | no | — |
| 324 | C3×C4 | — | 3 | 1 | no | — |
| 325 | C3×C4 | — | 4 | 3 | no | — |
| 326 | C3×C4 | — | 4 | 3 | no | — |
| 327 | C3×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 328 | C3×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 329 | Dic3 | — | 18 | 2 | no | — |
| 330 | Dic3 | — | 18 | 2 | no | — |
| 331 | Dic3 | — | 18 | 2 | no | — |
| 332 | Dic3 | — | 36 | 6 | no | — |
| 333 | C32 | — | 4 | 1 | no | — |
| 334 | C9 | — | 4 | 2 | no | — |
| 335 | C9 | #5912 | 1 | 1 | yes | characteristic, complemented |
| 336 | C23 | — | 2 | 1 | no | — |
| 337 | C23 | — | 3 | 1 | no | — |
| 338 | C23 | — | 3 | 1 | no | — |
| 339 | C23 | — | 6 | 1 | no | — |
| 340 | C23 | — | 27 | 2 | no | — |
| 341 | C23 | C22×C3⋊D9 | 1 | 1 | yes | characteristic |
| 342 | Q8 | — | 54 | 1 | no | — |
| 343 | Q8 | — | 54 | 1 | no | — |
| 344 | D4 | — | 54 | 1 | no | — |
| 345 | D4 | — | 54 | 2 | no | — |
| 346 | D4 | — | 54 | 2 | no | — |
| 347 | D4 | — | 54 | 4 | no | — |
| 348 | D4 | — | 54 | 2 | no | — |
| 349 | D4 | — | 54 | 2 | no | — |
| 350 | D4 | — | 54 | 1 | no | — |
| 351 | C2×C4 | — | 3 | 1 | no | — |
| 352 | C2×C4 | — | 3 | 1 | no | — |
| 353 | C2×C4 | — | 3 | 1 | no | — |
| 354 | C2×C4 | — | 3 | 1 | no | — |
| 355 | C2×C4 | — | 3 | 1 | no | — |
| 356 | C2×C4 | — | 3 | 1 | no | — |
| 357 | C2×C4 | — | 3 | 1 | no | — |
| 358 | C2×C4 | — | 6 | 1 | no | — |
| 359 | C2×C4 | — | 27 | 2 | no | — |
| 360 | C2×C4 | — | 27 | 2 | no | — |
| 361 | C2×C4 | — | 27 | 2 | no | — |
| 362 | C2×C4 | — | 54 | 2 | no | — |
| 363 | C2×C4 | — | 54 | 2 | no | — |
| 364 | C2×C4 | C9⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 365 | C2×C3 | — | 2 | 1 | no | — |
| 366 | C2×C3 | — | 3 | 1 | no | — |
| 367 | C2×C3 | — | 3 | 1 | no | — |
| 368 | C2×C3 | — | 4 | 3 | no | — |
| 369 | C2×C3 | — | 6 | 1 | no | — |
| 370 | C2×C3 | — | 8 | 3 | no | — |
| 371 | C2×C3 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 372 | D3 | — | 36 | 2 | no | — |
| 373 | D3 | — | 72 | 6 | no | — |
| 374 | C22 | — | 3 | 1 | no | — |
| 375 | C22 | — | 3 | 1 | no | — |
| 376 | C22 | — | 3 | 2 | no | — |
| 377 | C22 | — | 3 | 1 | no | — |
| 378 | C22 | — | 6 | 1 | no | — |
| 379 | C22 | — | 6 | 1 | no | — |
| 380 | C22 | — | 6 | 1 | no | — |
| 381 | C22 | — | 54 | 2 | no | — |
| 382 | C22 | — | 54 | 2 | no | — |
| 383 | C22 | — | 54 | 2 | no | — |
| 384 | C22 | #88736 | 1 | 1 | yes | characteristic, complemented |
| 385 | C22 | C2×C9⋊S4 | 1 | 1 | yes | characteristic |
| 386 | C4 | — | 3 | 1 | no | — |
| 387 | C4 | — | 3 | 1 | no | — |
| 388 | C4 | — | 54 | 2 | no | — |
| 389 | C4 | — | 54 | 2 | no | — |
| 390 | C4 | — | 54 | 2 | no | — |
| 391 | C4 | C2×C9⋊S4 | 1 | 1 | yes | characteristic |
| 392 | C4 | C2×C9⋊S4 | 1 | 1 | yes | characteristic |
| 393 | C3 | — | 4 | 3 | no | — |
| 394 | C3 | #10596575 | 1 | 1 | yes | characteristic |
| 395 | C2 | — | 2 | 1 | no | — |
| 396 | C2 | — | 3 | 1 | no | — |
| 397 | C2 | — | 3 | 1 | no | — |
| 398 | C2 | — | 6 | 1 | no | — |
| 399 | C2 | — | 108 | 2 | no | — |
| 400 | C2 | C22×C9⋊S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C9⋊S4 |
| commutator, cosocle | C2×C9×A4 | C23 |
| Frattini | C2×C3 | C22×C3⋊S4 |
| Fitting | C23×C4×C9 | D3 |
| socle | C23×C3 | C22×C3⋊D3 |
| hypercenter | C2×C4 | C9⋊S4 |
| hypocenter | C9×A4 | #41 |
| LCS | G ▷ C2×C9×A4 ▷ C9×A4 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C9×A4 | C2 | semidirect |
| 2. #11722376 | C2 | semidirect |
| 3. C4⋊(C9⋊S4) | C2 | semidirect |
| 4. C4×C9⋊S4 | C2 | semidirect |
| 5. #11722366 | C2 | semidirect |
| 20. C23×C4×C9 | D3 | semidirect |
| 22. C2×C4×C22⋊C9 | D3 | semidirect |
| 87. C9×A4 | #41 | semidirect |
| 93. C2×C4×A4 | D9 | semidirect |
| 133. C2×C4×C9 | S4 | semidirect |
| 203. C22×C9 | #235 | semidirect |
| 209. C22⋊C9 | #235 | semidirect |
| 221. C23×C4 | C3⋊D9 | semidirect |
| 322. A4 | #3697 | semidirect |
| 335. C9 | #5912 | semidirect |
| 364. C2×C4 | C9⋊S4 | semidirect |
| 384. C22 | #88736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9×A4 | 2 |
| #11722376 | 2 |
| C4⋊(C9⋊S4) | 2 |
| C4×C9⋊S4 | 2 |
| #11722366 | 2 |
| #10596575 | 3 |
| #10593087 | 3 |
| #10589893 | 3 |
| #88736 | 4 |