Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2052 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 2052 conjugacy classes of subgroups — too many to draw. Only its 187 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×A4×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596582 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | D4×C3⋊S4 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #10596575 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×C4⋊(C3⋊S4) | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #87489 | — | 3 | 3 | no | maximal |
| 7 | #87275 | — | 3 | 1 | no | maximal |
| 8 | C22×C3⋊S4 | C22 | 1 | 6 | yes | complemented |
| 9 | #64366 | — | 4 | 1 | no | maximal |
| 10 | C3×Q8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3×D4×A4 | C22 | 1 | 3 | yes | complemented |
| 12 | C2×C3×C4×A4 | C22 | 1 | 3 | yes | complemented |
| 13 | #64269 | C22 | 1 | 6 | yes | complemented |
| 14 | C4⋊(C3⋊S4) | C22 | 1 | 3 | yes | complemented |
| 15 | C4⋊(C3⋊S4) | C22 | 1 | 6 | yes | complemented |
| 16 | C4×C3⋊S4 | C22 | 1 | 6 | yes | complemented |
| 17 | #64259 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C22×C3×#41 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#1009 | — | 3 | 1 | no | — |
| 20 | A4×#41 | D3 | 1 | 3 | yes | complemented |
| 21 | #5919 | — | 3 | 6 | no | — |
| 22 | D4×S4 | — | 3 | 18 | no | — |
| 23 | #5912 | — | 3 | 9 | no | — |
| 24 | C2×C4⋊S4 | — | 3 | 9 | no | — |
| 25 | #5834 | — | 3 | 2 | no | — |
| 26 | #5833 | — | 3 | 3 | no | — |
| 27 | #5830 | — | 3 | 3 | no | — |
| 28 | #5829 | — | 3 | 6 | no | — |
| 29 | #5827 | — | 3 | 1 | no | — |
| 30 | #5817 | — | 3 | 2 | no | — |
| 31 | D4×#67 | — | 3 | 6 | no | — |
| 32 | #5791 | — | 3 | 3 | no | — |
| 33 | C2×#930 | — | 3 | 3 | no | — |
| 34 | C22×C3×A4 | C23 | 1 | 3 | yes | — |
| 35 | C2×C3⋊S4 | — | 4 | 6 | no | — |
| 36 | C2×C3⋊S4 | C23 | 1 | 6 | yes | — |
| 37 | C32×#41 | — | 4 | 1 | no | — |
| 38 | #3832 | — | 4 | 2 | no | — |
| 39 | D4×C3⋊D3 | — | 4 | 6 | no | — |
| 40 | #3828 | — | 4 | 3 | no | — |
| 41 | C2×C4⋊(C3⋊D3) | — | 4 | 3 | no | — |
| 42 | C3×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 43 | C3×C4×A4 | C23 | 1 | 3 | yes | — |
| 44 | C3⋊SL(2,ℤ/4) | C23 | 1 | 2 | yes | — |
| 45 | #3488 | — | 9 | 1 | no | Sylow |
| 46 | C22×S4 | — | 3 | 18 | no | — |
| 47 | C2×C3×#41 | — | 3 | 1 | no | — |
| 48 | C2×C3×#41 | — | 3 | 3 | no | — |
| 49 | C2×C3×#41 | — | 3 | 3 | no | — |
| 50 | C2×C3×#41 | — | 3 | 1 | no | — |
| 51 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | C22×C3×D4 | C2×D3 | 1 | 3 | yes | complemented |
| 53 | C23×C3×C4 | C2×D3 | 1 | 3 | yes | complemented |
| 54 | C22×#67 | — | 3 | 6 | no | — |
| 55 | #1009 | — | 6 | 1 | no | — |
| 56 | #1009 | — | 6 | 3 | no | — |
| 57 | #1009 | — | 6 | 3 | no | — |
| 58 | #1009 | — | 6 | 1 | no | — |
| 59 | #1009 | — | 12 | 3 | no | — |
| 60 | C2×#239 | — | 3 | 2 | no | — |
| 61 | C2×D3×D4 | — | 3 | 6 | no | — |
| 62 | C2×#235 | — | 3 | 3 | no | — |
| 63 | C22×D12 | — | 3 | 3 | no | — |
| 64 | Q8×A4 | C2×D3 | 1 | 3 | yes | complemented |
| 65 | D4×A4 | C2×D3 | 1 | 9 | yes | complemented |
| 66 | C2×C4×A4 | C2×D3 | 1 | 9 | yes | complemented |
| 67 | GL(2,ℤ/4) | — | 3 | 18 | no | — |
| 68 | C4⋊S4 | — | 3 | 9 | no | — |
| 69 | C4⋊S4 | — | 3 | 18 | no | — |
| 70 | C4×S4 | — | 3 | 18 | no | — |
| 71 | A4⋊Q8 | — | 3 | 3 | no | — |
| 72 | #953 | — | 3 | 6 | no | — |
| 73 | #947 | — | 3 | 6 | no | — |
| 74 | #946 | — | 3 | 6 | no | — |
| 75 | Q8×Dic3 | — | 3 | 2 | no | — |
| 76 | #940 | — | 3 | 6 | no | — |
| 77 | #939 | — | 3 | 12 | no | — |
| 78 | #938 | — | 3 | 6 | no | — |
| 79 | #937 | — | 3 | 12 | no | — |
| 80 | D4×Dic3 | — | 3 | 6 | no | — |
| 81 | #930 | — | 3 | 6 | no | — |
| 82 | #930 | — | 3 | 6 | no | — |
| 83 | #930 | — | 3 | 3 | no | — |
| 84 | #930 | — | 3 | 3 | no | — |
| 85 | #930 | — | 3 | 6 | no | — |
| 86 | #929 | — | 3 | 6 | no | — |
| 87 | C4×#67 | — | 3 | 6 | no | — |
| 88 | C4×#67 | — | 3 | 6 | no | — |
| 89 | C2×(C2×D3)⋊C4 | — | 3 | 6 | no | — |
| 90 | #926 | — | 3 | 3 | no | — |
| 91 | C2×C4⋊Dic3 | — | 3 | 3 | no | — |
| 92 | #924 | — | 3 | 3 | no | — |
| 93 | #924 | — | 3 | 1 | no | — |
| 94 | C22×C3⋊D3 | — | 4 | 6 | no | — |
| 95 | C2×C3×A4 | — | 2 | 3 | no | — |
| 96 | C2×C3×A4 | C24 | 1 | 1 | yes | characteristic |
| 97 | C3⋊S4 | — | 2 | 6 | no | — |
| 98 | C32×Q8 | — | 4 | 1 | no | — |
| 99 | C32×D4 | — | 4 | 3 | no | — |
| 100 | C2×C32×C4 | — | 4 | 3 | no | — |
| 101 | #638 | — | 4 | 6 | no | — |
| 102 | C4⋊(C3⋊D3) | — | 4 | 3 | no | — |
| 103 | C4⋊(C3⋊D3) | — | 4 | 6 | no | — |
| 104 | C4×C3⋊D3 | — | 4 | 6 | no | — |
| 105 | #634 | — | 4 | 1 | no | — |
| 106 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 107 | C22×#41 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 108 | #550 | — | 9 | 2 | no | — |
| 109 | #548 | — | 9 | 2 | no | — |
| 110 | #546 | — | 9 | 6 | no | — |
| 111 | D42 | — | 9 | 6 | no | — |
| 112 | #537 | — | 9 | 3 | no | — |
| 113 | #535 | — | 9 | 3 | no | — |
| 114 | #525 | — | 9 | 3 | no | — |
| 115 | C2×#121 | — | 9 | 3 | no | — |
| 116 | #520 | — | 9 | 1 | no | — |
| 117 | C24×C3 | C22×D3 | 1 | 3 | yes | — |
| 118 | C23×D3 | — | 3 | 6 | no | — |
| 119 | C22×A4 | C22×D3 | 1 | 9 | yes | — |
| 120 | C2×S4 | — | 3 | 18 | no | — |
| 121 | C2×S4 | — | 12 | 18 | no | — |
| 122 | C3×#41 | — | 3 | 1 | no | — |
| 123 | C3×#41 | — | 3 | 3 | no | — |
| 124 | C3×#41 | — | 3 | 3 | no | — |
| 125 | C3×#41 | — | 4 | 3 | no | — |
| 126 | C3×#41 | — | 6 | 1 | no | — |
| 127 | C3×#41 | — | 6 | 3 | no | — |
| 128 | C3×#41 | — | 6 | 3 | no | — |
| 129 | C3×#41 | S4 | 1 | 1 | yes | characteristic, complemented |
| 130 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 131 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 132 | C2×C3×D4 | — | 3 | 3 | no | — |
| 133 | C2×C3×D4 | — | 3 | 6 | no | — |
| 134 | C2×C3×D4 | — | 3 | 3 | no | — |
| 135 | C22×C3×C4 | — | 3 | 3 | no | — |
| 136 | C22×C3×C4 | — | 3 | 3 | no | — |
| 137 | C22×C3×C4 | — | 3 | 3 | no | — |
| 138 | C22×C3×C4 | — | 3 | 3 | no | — |
| 139 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | C22×C3×C4 | C22×D3 | 1 | 3 | yes | — |
| 141 | C2×#67 | — | 3 | 6 | no | — |
| 142 | C2×#67 | — | 3 | 6 | no | — |
| 143 | C2×#67 | — | 3 | 6 | no | — |
| 144 | C2×#67 | — | 3 | 12 | no | — |
| 145 | C2×#67 | — | 12 | 6 | no | — |
| 146 | C2×#67 | — | 12 | 6 | no | — |
| 147 | C22×Dic3 | — | 3 | 6 | no | — |
| 148 | #239 | — | 6 | 6 | no | — |
| 149 | #239 | — | 6 | 2 | no | — |
| 150 | #239 | — | 12 | 6 | no | — |
| 151 | D3×D4 | — | 6 | 12 | no | — |
| 152 | D3×D4 | — | 6 | 6 | no | — |
| 153 | D3×D4 | — | 6 | 6 | no | — |
| 154 | D3×D4 | — | 12 | 18 | no | — |
| 155 | #235 | — | 6 | 3 | no | — |
| 156 | #235 | — | 6 | 3 | no | — |
| 157 | #235 | — | 6 | 3 | no | — |
| 158 | #235 | — | 6 | 3 | no | — |
| 159 | #235 | — | 12 | 9 | no | — |
| 160 | C2×D12 | — | 3 | 3 | no | — |
| 161 | C2×D12 | — | 3 | 6 | no | — |
| 162 | C2×D12 | — | 6 | 3 | no | — |
| 163 | C2×D12 | — | 6 | 3 | no | — |
| 164 | C2×D12 | — | 6 | 3 | no | — |
| 165 | C2×D12 | — | 6 | 3 | no | — |
| 166 | C2×D12 | — | 12 | 9 | no | — |
| 167 | C2×C4×D3 | — | 3 | 6 | no | — |
| 168 | C2×Dic6 | — | 3 | 1 | no | — |
| 169 | C4×A4 | C22×D3 | 1 | 3 | yes | — |
| 170 | C4×A4 | C22×D3 | 1 | 9 | yes | — |
| 171 | SL(2,ℤ/4) | — | 3 | 6 | no | — |
| 172 | #217 | — | 3 | 6 | no | — |
| 173 | #217 | — | 3 | 6 | no | — |
| 174 | #217 | — | 3 | 2 | no | — |
| 175 | (C2×D3)⋊C4 | — | 3 | 6 | no | — |
| 176 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 177 | (C2×D3)⋊C4 | — | 3 | 6 | no | — |
| 178 | C4⋊Dic3 | — | 3 | 3 | no | — |
| 179 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 180 | C4⋊Dic3 | — | 3 | 6 | no | — |
| 181 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 182 | Dic3⋊C4 | — | 3 | 6 | no | — |
| 183 | C4×Dic3 | — | 3 | 6 | no | — |
| 184 | C22×C32 | — | 4 | 3 | no | — |
| 185 | C2×C3⋊D3 | — | 4 | 6 | no | — |
| 186 | C2×C3⋊D3 | — | 16 | 6 | no | — |
| 187 | C3×A4 | H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 188 | C32×C4 | — | 4 | 1 | no | — |
| 189 | C32×C4 | — | 4 | 3 | no | — |
| 190 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 191 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 192 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 193 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 194 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 195 | C2×#41 | — | 3 | 1 | no | — |
| 196 | C2×#41 | — | 3 | 3 | no | — |
| 197 | C2×#41 | — | 3 | 3 | no | — |
| 198 | C2×#41 | — | 3 | 1 | no | — |
| 199 | C2×#41 | — | 9 | 3 | no | — |
| 200 | C2×#41 | — | 9 | 2 | no | — |
| 201 | C22×Q8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 202 | C22×D4 | — | 9 | 3 | no | — |
| 203 | C22×D4 | — | 9 | 6 | no | — |
| 204 | C22×D4 | — | 9 | 6 | no | — |
| 205 | C22×D4 | C2×C3⋊D3 | 1 | 3 | yes | complemented |
| 206 | C23×C4 | C2×C3⋊D3 | 1 | 3 | yes | complemented |
| 207 | #127 | — | 9 | 6 | no | — |
| 208 | #124 | — | 9 | 6 | no | — |
| 209 | #123 | — | 9 | 6 | no | — |
| 210 | C22⋊Q8 | — | 9 | 3 | no | — |
| 211 | C22⋊Q8 | — | 9 | 6 | no | — |
| 212 | C22⋊Q8 | — | 9 | 1 | no | — |
| 213 | #121 | — | 9 | 6 | no | — |
| 214 | #121 | — | 9 | 6 | no | — |
| 215 | #121 | — | 9 | 3 | no | — |
| 216 | #121 | — | 9 | 12 | no | — |
| 217 | #121 | — | 9 | 6 | no | — |
| 218 | #121 | — | 9 | 3 | no | — |
| 219 | #121 | — | 9 | 6 | no | — |
| 220 | #120 | — | 9 | 12 | no | — |
| 221 | #120 | — | 9 | 6 | no | — |
| 222 | C4×Q8 | — | 9 | 2 | no | — |
| 223 | C4×D4 | — | 9 | 6 | no | — |
| 224 | C4×D4 | — | 9 | 6 | no | — |
| 225 | C4×D4 | — | 9 | 6 | no | — |
| 226 | #117 | — | 9 | 3 | no | — |
| 227 | C2×C4⋊C4 | — | 9 | 3 | no | — |
| 228 | C2×C22⋊C4 | — | 9 | 6 | no | — |
| 229 | C23×C3 | — | 2 | 3 | no | — |
| 230 | C23×C3 | — | 3 | 3 | no | — |
| 231 | C23×C3 | — | 3 | 3 | no | — |
| 232 | C23×C3 | — | 6 | 3 | no | — |
| 233 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 234 | C22×D3 | — | 3 | 6 | no | — |
| 235 | C22×D3 | — | 6 | 6 | no | — |
| 236 | C22×D3 | — | 6 | 6 | no | — |
| 237 | C22×D3 | — | 12 | 18 | no | — |
| 238 | C22×D3 | — | 12 | 6 | no | — |
| 239 | C22×D3 | — | 12 | 6 | no | — |
| 240 | C2×A4 | — | 2 | 9 | no | — |
| 241 | C2×A4 | C23×D3 | 1 | 3 | yes | — |
| 242 | S4 | — | 6 | 18 | no | — |
| 243 | C3×Q8 | — | 3 | 3 | no | — |
| 244 | C3×Q8 | — | 4 | 3 | no | — |
| 245 | C3×Q8 | — | 6 | 1 | no | — |
| 246 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 247 | C3×D4 | — | 3 | 6 | no | — |
| 248 | C3×D4 | — | 3 | 3 | no | — |
| 249 | C3×D4 | — | 4 | 9 | no | — |
| 250 | C3×D4 | — | 6 | 3 | no | — |
| 251 | C3×D4 | C2×S4 | 1 | 3 | yes | complemented |
| 252 | C2×C3×C4 | — | 3 | 3 | no | — |
| 253 | C2×C3×C4 | — | 3 | 3 | no | — |
| 254 | C2×C3×C4 | — | 3 | 1 | no | — |
| 255 | C2×C3×C4 | — | 3 | 3 | no | — |
| 256 | C2×C3×C4 | — | 3 | 3 | no | — |
| 257 | C2×C3×C4 | — | 3 | 1 | no | — |
| 258 | C2×C3×C4 | — | 3 | 3 | no | — |
| 259 | C2×C3×C4 | — | 4 | 9 | no | — |
| 260 | C2×C3×C4 | — | 6 | 3 | no | — |
| 261 | C2×C3×C4 | C2×S4 | 1 | 3 | yes | complemented |
| 262 | #67 | — | 6 | 6 | no | — |
| 263 | #67 | — | 6 | 6 | no | — |
| 264 | #67 | — | 6 | 6 | no | — |
| 265 | #67 | — | 6 | 6 | no | — |
| 266 | #67 | — | 12 | 18 | no | — |
| 267 | #67 | — | 12 | 6 | no | — |
| 268 | #67 | — | 12 | 12 | no | — |
| 269 | C2×Dic3 | — | 3 | 2 | no | — |
| 270 | C2×Dic3 | — | 3 | 6 | no | — |
| 271 | C2×Dic3 | — | 3 | 2 | no | — |
| 272 | C2×Dic3 | — | 12 | 6 | no | — |
| 273 | D12 | — | 6 | 3 | no | — |
| 274 | D12 | — | 6 | 6 | no | — |
| 275 | D12 | — | 6 | 3 | no | — |
| 276 | D12 | — | 6 | 6 | no | — |
| 277 | D12 | — | 12 | 9 | no | — |
| 278 | D12 | — | 12 | 18 | no | — |
| 279 | C4×D3 | — | 6 | 6 | no | — |
| 280 | C4×D3 | — | 6 | 6 | no | — |
| 281 | C4×D3 | — | 12 | 18 | no | — |
| 282 | Dic6 | — | 6 | 1 | no | — |
| 283 | Dic6 | — | 6 | 1 | no | — |
| 284 | Dic6 | — | 12 | 3 | no | — |
| 285 | C2×C32 | — | 4 | 1 | no | — |
| 286 | C2×C32 | — | 8 | 3 | no | — |
| 287 | C3⋊D3 | — | 8 | 6 | no | — |
| 288 | C24 | — | 9 | 6 | no | — |
| 289 | C24 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 290 | #41 | — | 3 | 1 | no | — |
| 291 | #41 | — | 3 | 3 | no | — |
| 292 | #41 | — | 3 | 3 | no | — |
| 293 | #41 | — | 6 | 1 | no | — |
| 294 | #41 | — | 6 | 3 | no | — |
| 295 | #41 | — | 6 | 3 | no | — |
| 296 | #41 | — | 18 | 3 | no | — |
| 297 | #41 | — | 18 | 3 | no | — |
| 298 | #41 | — | 18 | 3 | no | — |
| 299 | #41 | — | 18 | 6 | no | — |
| 300 | #41 | — | 18 | 2 | no | — |
| 301 | #41 | — | 18 | 3 | no | — |
| 302 | #41 | C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 303 | C2×Q8 | — | 3 | 1 | no | — |
| 304 | C2×Q8 | — | 3 | 3 | no | — |
| 305 | C2×Q8 | — | 9 | 1 | no | — |
| 306 | C2×D4 | — | 3 | 3 | no | — |
| 307 | C2×D4 | — | 3 | 6 | no | — |
| 308 | C2×D4 | — | 3 | 3 | no | — |
| 309 | C2×D4 | — | 9 | 3 | no | — |
| 310 | C2×D4 | — | 9 | 6 | no | — |
| 311 | C2×D4 | — | 9 | 6 | no | — |
| 312 | C2×D4 | — | 9 | 6 | no | — |
| 313 | C2×D4 | — | 9 | 6 | no | — |
| 314 | C2×D4 | — | 9 | 12 | no | — |
| 315 | C2×D4 | — | 18 | 3 | no | — |
| 316 | C2×D4 | — | 18 | 3 | no | — |
| 317 | C2×D4 | — | 18 | 3 | no | — |
| 318 | C2×D4 | — | 18 | 12 | no | — |
| 319 | C2×D4 | — | 18 | 6 | no | — |
| 320 | C2×D4 | — | 18 | 6 | no | — |
| 321 | C2×D4 | — | 18 | 3 | no | — |
| 322 | C2×D4 | — | 36 | 6 | no | — |
| 323 | C2×D4 | — | 36 | 6 | no | — |
| 324 | C22×C4 | — | 3 | 3 | no | — |
| 325 | C22×C4 | — | 3 | 3 | no | — |
| 326 | C22×C4 | — | 3 | 3 | no | — |
| 327 | C22×C4 | — | 3 | 3 | no | — |
| 328 | C22×C4 | — | 9 | 6 | no | — |
| 329 | C22×C4 | — | 9 | 6 | no | — |
| 330 | C22×C4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 331 | C22×C4 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 332 | C4⋊C4 | — | 9 | 3 | no | — |
| 333 | C4⋊C4 | — | 9 | 6 | no | — |
| 334 | C4⋊C4 | — | 9 | 1 | no | — |
| 335 | C4⋊C4 | — | 9 | 2 | no | — |
| 336 | C4⋊C4 | — | 9 | 6 | no | — |
| 337 | C22⋊C4 | — | 9 | 6 | no | — |
| 338 | C22⋊C4 | — | 9 | 12 | no | — |
| 339 | C22⋊C4 | — | 9 | 6 | no | — |
| 340 | C22⋊C4 | — | 9 | 6 | no | — |
| 341 | C22⋊C4 | — | 9 | 6 | no | — |
| 342 | C22⋊C4 | — | 9 | 2 | no | — |
| 343 | C42 | — | 9 | 6 | no | — |
| 344 | C22×C3 | — | 3 | 1 | no | — |
| 345 | C22×C3 | — | 3 | 1 | no | — |
| 346 | C22×C3 | — | 3 | 3 | no | — |
| 347 | C22×C3 | — | 4 | 9 | no | — |
| 348 | C22×C3 | — | 6 | 3 | no | — |
| 349 | C22×C3 | — | 6 | 3 | no | — |
| 350 | C22×C3 | — | 6 | 3 | no | — |
| 351 | C22×C3 | — | 6 | 3 | no | — |
| 352 | C22×C3 | #1009 | 1 | 1 | yes | characteristic, complemented |
| 353 | C22×C3 | C22×S4 | 1 | 3 | yes | — |
| 354 | C2×D3 | — | 6 | 6 | no | — |
| 355 | C2×D3 | — | 6 | 6 | no | — |
| 356 | C2×D3 | — | 6 | 6 | no | — |
| 357 | C2×D3 | — | 12 | 18 | no | — |
| 358 | C2×D3 | — | 24 | 6 | no | — |
| 359 | C2×D3 | — | 24 | 6 | no | — |
| 360 | C2×D3 | — | 48 | 18 | no | — |
| 361 | A4 | #1009 | 1 | 3 | yes | complemented |
| 362 | C3×C4 | — | 3 | 1 | no | — |
| 363 | C3×C4 | — | 3 | 3 | no | — |
| 364 | C3×C4 | — | 4 | 3 | no | — |
| 365 | C3×C4 | — | 4 | 9 | no | — |
| 366 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 367 | C3×C4 | C22×S4 | 1 | 3 | yes | — |
| 368 | Dic3 | — | 6 | 6 | no | — |
| 369 | Dic3 | — | 6 | 2 | no | — |
| 370 | Dic3 | — | 6 | 2 | no | — |
| 371 | Dic3 | — | 12 | 6 | no | — |
| 372 | C32 | — | 4 | 1 | no | Sylow |
| 373 | C23 | — | 2 | 3 | no | — |
| 374 | C23 | — | 3 | 3 | no | — |
| 375 | C23 | — | 3 | 3 | no | — |
| 376 | C23 | — | 6 | 3 | no | — |
| 377 | C23 | — | 9 | 6 | no | — |
| 378 | C23 | — | 18 | 6 | no | — |
| 379 | C23 | — | 18 | 6 | no | — |
| 380 | C23 | — | 36 | 6 | no | — |
| 381 | C23 | — | 36 | 6 | no | — |
| 382 | C23 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 383 | Q8 | — | 3 | 3 | no | — |
| 384 | Q8 | — | 6 | 1 | no | — |
| 385 | Q8 | — | 18 | 1 | no | — |
| 386 | Q8 | — | 18 | 1 | no | — |
| 387 | Q8 | C2×C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 388 | D4 | — | 3 | 6 | no | — |
| 389 | D4 | — | 3 | 3 | no | — |
| 390 | D4 | — | 6 | 3 | no | — |
| 391 | D4 | — | 18 | 3 | no | — |
| 392 | D4 | — | 18 | 6 | no | — |
| 393 | D4 | — | 18 | 6 | no | — |
| 394 | D4 | — | 18 | 6 | no | — |
| 395 | D4 | — | 18 | 6 | no | — |
| 396 | D4 | — | 18 | 6 | no | — |
| 397 | D4 | — | 18 | 3 | no | — |
| 398 | D4 | — | 18 | 6 | no | — |
| 399 | D4 | — | 36 | 12 | no | — |
| 400 | D4 | — | 36 | 6 | no | — |
| 401 | D4 | C2×C3⋊S4 | 1 | 3 | yes | complemented |
| 402 | C2×C4 | — | 3 | 3 | no | — |
| 403 | C2×C4 | — | 3 | 3 | no | — |
| 404 | C2×C4 | — | 3 | 1 | no | — |
| 405 | C2×C4 | — | 3 | 3 | no | — |
| 406 | C2×C4 | — | 3 | 3 | no | — |
| 407 | C2×C4 | — | 3 | 1 | no | — |
| 408 | C2×C4 | — | 3 | 3 | no | — |
| 409 | C2×C4 | — | 6 | 3 | no | — |
| 410 | C2×C4 | — | 9 | 2 | no | — |
| 411 | C2×C4 | — | 9 | 6 | no | — |
| 412 | C2×C4 | — | 9 | 2 | no | — |
| 413 | C2×C4 | — | 18 | 6 | no | — |
| 414 | C2×C4 | — | 18 | 6 | no | — |
| 415 | C2×C4 | — | 36 | 6 | no | — |
| 416 | C2×C4 | C2×C3⋊S4 | 1 | 3 | yes | complemented |
| 417 | C2×C3 | — | 2 | 3 | no | — |
| 418 | C2×C3 | — | 3 | 1 | no | — |
| 419 | C2×C3 | — | 3 | 1 | no | — |
| 420 | C2×C3 | — | 4 | 3 | no | — |
| 421 | C2×C3 | — | 6 | 3 | no | — |
| 422 | C2×C3 | — | 8 | 9 | no | — |
| 423 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 424 | D3 | — | 12 | 6 | no | — |
| 425 | D3 | — | 24 | 18 | no | — |
| 426 | C22 | — | 3 | 1 | no | — |
| 427 | C22 | — | 3 | 1 | no | — |
| 428 | C22 | — | 3 | 3 | no | — |
| 429 | C22 | — | 6 | 3 | no | — |
| 430 | C22 | — | 6 | 3 | no | — |
| 431 | C22 | — | 6 | 3 | no | — |
| 432 | C22 | — | 6 | 3 | no | — |
| 433 | C22 | — | 18 | 6 | no | — |
| 434 | C22 | — | 18 | 6 | no | — |
| 435 | C22 | — | 18 | 6 | no | — |
| 436 | C22 | — | 72 | 6 | no | — |
| 437 | C22 | — | 72 | 6 | no | — |
| 438 | C22 | #64366 | 1 | 1 | yes | characteristic, complemented |
| 439 | C22 | C22×C3⋊S4 | 1 | 3 | yes | — |
| 440 | C4 | — | 3 | 1 | no | — |
| 441 | C4 | — | 3 | 3 | no | — |
| 442 | C4 | — | 18 | 6 | no | — |
| 443 | C4 | — | 18 | 2 | no | — |
| 444 | C4 | — | 18 | 2 | no | — |
| 445 | C4 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 446 | C4 | C22×C3⋊S4 | 1 | 3 | yes | — |
| 447 | C3 | — | 4 | 3 | no | — |
| 448 | C3 | #87489 | 1 | 1 | yes | characteristic, complemented |
| 449 | C2 | — | 2 | 3 | no | — |
| 450 | C2 | — | 3 | 1 | no | — |
| 451 | C2 | — | 3 | 1 | no | — |
| 452 | C2 | — | 6 | 3 | no | — |
| 453 | C2 | — | 36 | 6 | no | — |
| 454 | C2 | C23×C3⋊S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×C3⋊S4 |
| commutator, cosocle | C2×C3×A4 | C24 |
| Fitting | C22×C3×#41 | D3 |
| socle | C23×C3 | C23×D3 |
| hypercenter | #41 | C3⋊S4 |
| hypocenter | C3×A4 | H(5,𝔽2) |
| LCS | G ▷ C2×C3×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×#41 | C2 | semidirect |
| 2. #10596582 | C2 | semidirect |
| 3. D4×C3⋊S4 | C2 | semidirect |
| 4. #10596575 | C2 | semidirect |
| 5. C2×C4⋊(C3⋊S4) | C2 | semidirect |
| 8. C22×C3⋊S4 | C22 | semidirect |
| 10. C3×Q8×A4 | C22 | semidirect |
| 11. C3×D4×A4 | C22 | semidirect |
| 12. C2×C3×C4×A4 | C22 | semidirect |
| 13. #64269 | C22 | semidirect |
| 14. C4⋊(C3⋊S4) | C22 | semidirect |
| 15. C4⋊(C3⋊S4) | C22 | semidirect |
| 16. C4×C3⋊S4 | C22 | semidirect |
| 17. #64259 | C22 | semidirect |
| 18. C22×C3×#41 | D3 | semidirect |
| 20. A4×#41 | D3 | semidirect |
| 51. C22×C3×Q8 | C2×D3 | semidirect |
| 52. C22×C3×D4 | C2×D3 | semidirect |
| 53. C23×C3×C4 | C2×D3 | semidirect |
| 64. Q8×A4 | C2×D3 | semidirect |
| 65. D4×A4 | C2×D3 | semidirect |
| 66. C2×C4×A4 | C2×D3 | semidirect |
| 107. C22×#41 | C3⋊D3 | semidirect |
| 129. C3×#41 | S4 | semidirect |
| 187. C3×A4 | H(5,𝔽2) | semidirect |
| 201. C22×Q8 | C2×C3⋊D3 | semidirect |
| 205. C22×D4 | C2×C3⋊D3 | semidirect |
| 206. C23×C4 | C2×C3⋊D3 | semidirect |
| 246. C3×Q8 | C2×S4 | semidirect |
| 251. C3×D4 | C2×S4 | semidirect |
| 261. C2×C3×C4 | C2×S4 | semidirect |
| 302. #41 | C3⋊S4 | semidirect |
| 352. C22×C3 | #1009 | semidirect |
| 361. A4 | #1009 | semidirect |
| 387. Q8 | C2×C3⋊S4 | semidirect |
| 401. D4 | C2×C3⋊S4 | semidirect |
| 416. C2×C4 | C2×C3⋊S4 | semidirect |
| 438. C22 | #64366 | semidirect |
| 448. C3 | #87489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×#41 | 2 |
| #10596582 | 2 |
| D4×C3⋊S4 | 2 |
| #10596575 | 2 |
| C2×C4⋊(C3⋊S4) | 2 |
| #87489 | 3 |
| #87275 | 3 |
| #64366 | 4 |