Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1760 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1760 conjugacy classes of subgroups — too many to draw. Only its 131 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 | A4×#239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596582 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5919 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10596432 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D12×S4 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | D3×C4⋊S4 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10596426 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #87489 | — | 3 | 1 | no | maximal |
| 9 | #86713 | — | 3 | 1 | no | maximal |
| 10 | C2×D3×S4 | C22 | 1 | 6 | yes | complemented |
| 11 | C3×Q8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #64320 | — | 4 | 1 | no | maximal |
| 13 | A4×D12 | C22 | 1 | 3 | yes | complemented |
| 14 | C4×D3×A4 | C22 | 1 | 3 | yes | complemented |
| 15 | C4⋊(C3⋊S4) | C22 | 1 | 3 | yes | complemented |
| 16 | C4×C3⋊S4 | C22 | 1 | 3 | yes | complemented |
| 17 | C3×C4⋊S4 | C22 | 1 | 3 | yes | complemented |
| 18 | C3×C4×S4 | C22 | 1 | 3 | yes | complemented |
| 19 | #64210 | C22 | 1 | 3 | yes | complemented |
| 20 | #64209 | C22 | 1 | 3 | yes | complemented |
| 21 | #64207 | C22 | 1 | 3 | yes | complemented |
| 22 | #64204 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×#1009 | — | 3 | 1 | no | — |
| 24 | C22×#239 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | A4×#41 | — | 3 | 1 | no | — |
| 26 | #5919 | — | 3 | 1 | no | — |
| 27 | #5919 | — | 6 | 1 | no | — |
| 28 | #5919 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | D4×S4 | — | 3 | 3 | no | — |
| 30 | D4×S4 | — | 3 | 3 | no | — |
| 31 | #5912 | — | 3 | 3 | no | — |
| 32 | C2×C4⋊S4 | — | 3 | 3 | no | — |
| 33 | C3×#548 | — | 3 | 1 | no | — |
| 34 | #5834 | — | 3 | 1 | no | — |
| 35 | #5817 | — | 3 | 1 | no | — |
| 36 | #5676 | — | 3 | 3 | no | — |
| 37 | #5674 | — | 3 | 3 | no | — |
| 38 | #5630 | — | 3 | 3 | no | — |
| 39 | #5629 | — | 3 | 3 | no | — |
| 40 | #5609 | — | 3 | 3 | no | — |
| 41 | D3×#121 | — | 3 | 3 | no | — |
| 42 | #5577 | — | 3 | 1 | no | — |
| 43 | #5574 | — | 3 | 1 | no | — |
| 44 | D4×D12 | — | 3 | 3 | no | — |
| 45 | #5547 | — | 3 | 3 | no | — |
| 46 | C2×D3×A4 | C23 | 1 | 3 | yes | — |
| 47 | C2×C3⋊S4 | C23 | 1 | 3 | yes | — |
| 48 | C2×C3×S4 | C23 | 1 | 3 | yes | — |
| 49 | D3×S4 | — | 4 | 6 | no | — |
| 50 | #3832 | — | 4 | 1 | no | — |
| 51 | C3×#239 | — | 4 | 1 | no | — |
| 52 | C3×#239 | — | 4 | 1 | no | — |
| 53 | C3×C4×A4 | C23 | 1 | 3 | yes | — |
| 54 | #3802 | — | 4 | 3 | no | — |
| 55 | D3×D12 | — | 4 | 3 | no | — |
| 56 | D3×D12 | — | 4 | 3 | no | — |
| 57 | #3798 | — | 4 | 3 | no | — |
| 58 | Dic3×A4 | C23 | 1 | 1 | yes | characteristic |
| 59 | C3⋊SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 60 | C3×SL(2,ℤ/4) | C23 | 1 | 1 | yes | characteristic |
| 61 | #3488 | — | 9 | 1 | no | Sylow |
| 62 | C22×S4 | — | 3 | 6 | no | — |
| 63 | C2×C3×#41 | — | 3 | 1 | no | — |
| 64 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 65 | #1009 | — | 6 | 1 | no | — |
| 66 | #1009 | — | 6 | 3 | no | — |
| 67 | #1009 | — | 6 | 3 | no | — |
| 68 | #1009 | — | 6 | 1 | no | — |
| 69 | #1009 | — | 12 | 1 | no | — |
| 70 | C2×#239 | — | 3 | 1 | no | — |
| 71 | C2×#239 | — | 3 | 3 | no | — |
| 72 | C2×#239 | — | 3 | 3 | no | — |
| 73 | C2×#239 | — | 3 | 1 | no | — |
| 74 | C2×#239 | — | 3 | 1 | no | — |
| 75 | C2×D3×D4 | — | 3 | 3 | no | — |
| 76 | C2×D3×D4 | — | 3 | 3 | no | — |
| 77 | C2×D3×D4 | — | 3 | 6 | no | — |
| 78 | C2×#235 | — | 3 | 3 | no | — |
| 79 | C22×D12 | — | 3 | 3 | no | — |
| 80 | C22×D12 | C2×D3 | 1 | 3 | yes | complemented |
| 81 | C22×C4×D3 | C2×D3 | 1 | 3 | yes | complemented |
| 82 | Q8×A4 | — | 2 | 1 | no | — |
| 83 | Q8×A4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 84 | D4×A4 | — | 3 | 3 | no | — |
| 85 | C2×C4×A4 | — | 3 | 3 | no | — |
| 86 | GL(2,ℤ/4) | — | 3 | 3 | no | — |
| 87 | GL(2,ℤ/4) | — | 3 | 3 | no | — |
| 88 | C4⋊S4 | — | 3 | 3 | no | — |
| 89 | C4⋊S4 | — | 3 | 3 | no | — |
| 90 | C4⋊S4 | — | 6 | 3 | no | — |
| 91 | C4⋊S4 | C2×D3 | 1 | 3 | yes | complemented |
| 92 | C4×S4 | — | 3 | 3 | no | — |
| 93 | C4×S4 | — | 6 | 3 | no | — |
| 94 | C4×S4 | C2×D3 | 1 | 3 | yes | complemented |
| 95 | A4⋊Q8 | — | 3 | 1 | no | — |
| 96 | C3×#124 | — | 3 | 3 | no | — |
| 97 | C3×C22⋊Q8 | — | 3 | 3 | no | — |
| 98 | C3×#121 | — | 3 | 3 | no | — |
| 99 | C3×C4×Q8 | — | 3 | 1 | no | — |
| 100 | C3×C4×D4 | — | 3 | 3 | no | — |
| 101 | #947 | — | 3 | 3 | no | — |
| 102 | #946 | — | 3 | 3 | no | — |
| 103 | Q8×Dic3 | — | 3 | 1 | no | — |
| 104 | #940 | — | 3 | 3 | no | — |
| 105 | #939 | — | 3 | 3 | no | — |
| 106 | #938 | — | 3 | 3 | no | — |
| 107 | #937 | — | 3 | 3 | no | — |
| 108 | #930 | — | 3 | 3 | no | — |
| 109 | #930 | — | 3 | 3 | no | — |
| 110 | C4×#67 | — | 3 | 3 | no | — |
| 111 | C4×#67 | — | 3 | 3 | no | — |
| 112 | #896 | — | 3 | 3 | no | — |
| 113 | #895 | — | 3 | 6 | no | — |
| 114 | #895 | — | 3 | 3 | no | — |
| 115 | #895 | — | 3 | 3 | no | — |
| 116 | #894 | — | 3 | 3 | no | — |
| 117 | #893 | — | 3 | 3 | no | — |
| 118 | D3×C4⋊C4 | — | 3 | 3 | no | — |
| 119 | #884 | — | 3 | 3 | no | — |
| 120 | #884 | — | 3 | 6 | no | — |
| 121 | #884 | — | 3 | 6 | no | — |
| 122 | #883 | — | 3 | 3 | no | — |
| 123 | #882 | — | 3 | 6 | no | — |
| 124 | #882 | — | 3 | 6 | no | — |
| 125 | #882 | — | 3 | 3 | no | — |
| 126 | D3×C22⋊C4 | — | 3 | 6 | no | — |
| 127 | #878 | — | 3 | 1 | no | — |
| 128 | #874 | — | 3 | 3 | no | — |
| 129 | C4×D12 | — | 3 | 3 | no | — |
| 130 | C4×D12 | — | 3 | 3 | no | — |
| 131 | #872 | — | 3 | 3 | no | — |
| 132 | C2×C3×A4 | C24 | 1 | 1 | yes | characteristic |
| 133 | C2×D32 | — | 4 | 6 | no | — |
| 134 | D3×A4 | — | 2 | 3 | no | — |
| 135 | C3⋊S4 | — | 2 | 3 | no | — |
| 136 | C3×S4 | — | 2 | 3 | no | — |
| 137 | C32×Q8 | — | 4 | 1 | no | — |
| 138 | C4⋊(C3⋊D3) | — | 4 | 3 | no | — |
| 139 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 140 | C3×D12 | — | 4 | 3 | no | — |
| 141 | C3×D12 | — | 4 | 3 | no | — |
| 142 | C3×C4×D3 | — | 4 | 3 | no | — |
| 143 | C3×C4×D3 | — | 4 | 3 | no | — |
| 144 | #627 | — | 4 | 1 | no | — |
| 145 | #626 | — | 4 | 3 | no | — |
| 146 | #626 | — | 4 | 3 | no | — |
| 147 | #625 | — | 4 | 3 | no | — |
| 148 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 149 | C22×#41 | — | 3 | 1 | no | — |
| 150 | #550 | — | 9 | 1 | no | — |
| 151 | #550 | — | 9 | 1 | no | — |
| 152 | #548 | — | 3 | 1 | no | — |
| 153 | #548 | — | 9 | 1 | no | — |
| 154 | #546 | — | 9 | 3 | no | — |
| 155 | #546 | — | 9 | 3 | no | — |
| 156 | D42 | — | 9 | 3 | no | — |
| 157 | D42 | — | 9 | 3 | no | — |
| 158 | #537 | — | 9 | 3 | no | — |
| 159 | #535 | — | 9 | 3 | no | — |
| 160 | #525 | — | 9 | 3 | no | — |
| 161 | C2×#121 | — | 9 | 3 | no | — |
| 162 | #520 | — | 9 | 1 | no | — |
| 163 | C23×D3 | — | 3 | 6 | no | — |
| 164 | C23×D3 | C22×D3 | 1 | 3 | yes | — |
| 165 | C22×A4 | — | 3 | 3 | no | — |
| 166 | C2×S4 | — | 3 | 3 | no | — |
| 167 | C2×S4 | — | 6 | 3 | no | — |
| 168 | C2×S4 | — | 12 | 6 | no | — |
| 169 | C2×S4 | C22×D3 | 1 | 3 | yes | — |
| 170 | C3×#41 | — | 6 | 3 | no | — |
| 171 | C3×#41 | — | 6 | 1 | no | — |
| 172 | C3×#41 | — | 12 | 1 | no | — |
| 173 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 174 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 175 | C2×C3×D4 | — | 3 | 3 | no | — |
| 176 | C2×C3×D4 | — | 3 | 3 | no | — |
| 177 | C22×C3×C4 | — | 3 | 3 | no | — |
| 178 | C22×C3×C4 | C22×D3 | 1 | 3 | yes | — |
| 179 | C2×#67 | — | 3 | 3 | no | — |
| 180 | C2×#67 | — | 3 | 3 | no | — |
| 181 | C2×#67 | — | 3 | 3 | no | — |
| 182 | C2×#67 | — | 3 | 3 | no | — |
| 183 | C2×#67 | — | 3 | 6 | no | — |
| 184 | C22×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 185 | #239 | — | 3 | 1 | no | — |
| 186 | #239 | — | 3 | 3 | no | — |
| 187 | #239 | — | 3 | 3 | no | — |
| 188 | #239 | — | 4 | 1 | no | — |
| 189 | #239 | — | 6 | 1 | no | — |
| 190 | #239 | — | 6 | 3 | no | — |
| 191 | #239 | — | 6 | 3 | no | — |
| 192 | #239 | — | 6 | 3 | no | — |
| 193 | #239 | — | 6 | 1 | no | — |
| 194 | #239 | — | 12 | 1 | no | — |
| 195 | #239 | — | 24 | 1 | no | — |
| 196 | #239 | S4 | 1 | 1 | yes | characteristic, complemented |
| 197 | D3×D4 | — | 6 | 3 | no | — |
| 198 | D3×D4 | — | 6 | 3 | no | — |
| 199 | D3×D4 | — | 6 | 3 | no | — |
| 200 | D3×D4 | — | 6 | 6 | no | — |
| 201 | D3×D4 | — | 6 | 3 | no | — |
| 202 | D3×D4 | — | 6 | 3 | no | — |
| 203 | D3×D4 | — | 6 | 3 | no | — |
| 204 | D3×D4 | — | 12 | 3 | no | — |
| 205 | D3×D4 | — | 12 | 3 | no | — |
| 206 | D3×D4 | — | 12 | 6 | no | — |
| 207 | D3×D4 | — | 12 | 6 | no | — |
| 208 | #235 | — | 6 | 3 | no | — |
| 209 | #235 | — | 6 | 3 | no | — |
| 210 | #235 | — | 6 | 3 | no | — |
| 211 | #235 | — | 6 | 3 | no | — |
| 212 | #235 | — | 12 | 3 | no | — |
| 213 | C2×D12 | — | 3 | 3 | no | — |
| 214 | C2×D12 | — | 3 | 3 | no | — |
| 215 | C2×D12 | — | 3 | 6 | no | — |
| 216 | C2×D12 | — | 3 | 3 | no | — |
| 217 | C2×D12 | — | 3 | 3 | no | — |
| 218 | C2×D12 | — | 3 | 3 | no | — |
| 219 | C2×D12 | — | 3 | 6 | no | — |
| 220 | C2×D12 | — | 6 | 6 | no | — |
| 221 | C2×D12 | — | 6 | 3 | no | — |
| 222 | C2×D12 | — | 6 | 3 | no | — |
| 223 | C2×D12 | — | 12 | 3 | no | — |
| 224 | C2×C4×D3 | — | 3 | 3 | no | — |
| 225 | C2×C4×D3 | — | 3 | 3 | no | — |
| 226 | C2×C4×D3 | — | 3 | 3 | no | — |
| 227 | C2×C4×D3 | — | 3 | 3 | no | — |
| 228 | C2×C4×D3 | — | 3 | 3 | no | — |
| 229 | C2×C4×D3 | — | 3 | 6 | no | — |
| 230 | C2×Dic6 | — | 3 | 1 | no | — |
| 231 | C4×A4 | — | 2 | 3 | no | — |
| 232 | C4×A4 | — | 3 | 1 | no | — |
| 233 | C4×A4 | C22×D3 | 1 | 3 | yes | — |
| 234 | SL(2,ℤ/4) | — | 3 | 1 | no | — |
| 235 | SL(2,ℤ/4) | — | 6 | 1 | no | — |
| 236 | SL(2,ℤ/4) | C22×D3 | 1 | 1 | yes | characteristic |
| 237 | C3×C4⋊C4 | — | 3 | 3 | no | — |
| 238 | C3×C4⋊C4 | — | 3 | 3 | no | — |
| 239 | C3×C22⋊C4 | — | 3 | 6 | no | — |
| 240 | C3×C22⋊C4 | — | 3 | 3 | no | — |
| 241 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 242 | C3×C42 | — | 3 | 3 | no | — |
| 243 | #217 | — | 3 | 3 | no | — |
| 244 | #217 | — | 3 | 1 | no | — |
| 245 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 246 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 247 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 248 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 249 | (C2×D3)⋊C4 | — | 3 | 6 | no | — |
| 250 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 251 | (C2×D3)⋊C4 | — | 3 | 3 | no | — |
| 252 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 253 | C4⋊Dic3 | — | 3 | 3 | no | — |
| 254 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 255 | Dic3⋊C4 | — | 3 | 3 | no | — |
| 256 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 257 | Dic3⋊C4 | — | 3 | 3 | no | — |
| 258 | C4×Dic3 | — | 3 | 3 | no | — |
| 259 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 260 | C2×C3×D3 | — | 4 | 3 | no | — |
| 261 | C2×C3×D3 | — | 4 | 3 | no | — |
| 262 | C3×A4 | H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 263 | D32 | — | 16 | 6 | no | — |
| 264 | C32×C4 | — | 4 | 3 | no | — |
| 265 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 266 | C3×Dic3 | — | 4 | 1 | no | — |
| 267 | C3×Dic3 | — | 4 | 1 | no | — |
| 268 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 269 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 270 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 271 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 272 | C2×#41 | — | 3 | 1 | no | — |
| 273 | C2×#41 | — | 9 | 3 | no | — |
| 274 | C2×#41 | — | 9 | 1 | no | — |
| 275 | C2×#41 | — | 9 | 3 | no | — |
| 276 | C2×#41 | — | 9 | 3 | no | — |
| 277 | C2×#41 | — | 9 | 1 | no | — |
| 278 | C2×#41 | — | 9 | 1 | no | — |
| 279 | C22×Q8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 280 | C22×D4 | — | 3 | 3 | no | — |
| 281 | C22×D4 | — | 9 | 3 | no | — |
| 282 | C22×D4 | — | 9 | 3 | no | — |
| 283 | C22×D4 | — | 9 | 3 | no | — |
| 284 | C22×D4 | — | 9 | 6 | no | — |
| 285 | C23×C4 | — | 3 | 3 | no | — |
| 286 | #127 | — | 9 | 3 | no | — |
| 287 | #127 | — | 9 | 3 | no | — |
| 288 | #124 | — | 3 | 3 | no | — |
| 289 | #124 | — | 9 | 3 | no | — |
| 290 | #123 | — | 9 | 3 | no | — |
| 291 | #123 | — | 9 | 3 | no | — |
| 292 | C22⋊Q8 | — | 3 | 3 | no | — |
| 293 | C22⋊Q8 | — | 9 | 1 | no | — |
| 294 | C22⋊Q8 | — | 9 | 3 | no | — |
| 295 | C22⋊Q8 | — | 9 | 3 | no | — |
| 296 | #121 | — | 3 | 3 | no | — |
| 297 | #121 | — | 9 | 6 | no | — |
| 298 | #121 | — | 9 | 3 | no | — |
| 299 | #121 | — | 9 | 6 | no | — |
| 300 | #121 | — | 9 | 3 | no | — |
| 301 | #121 | — | 9 | 6 | no | — |
| 302 | #121 | — | 9 | 3 | no | — |
| 303 | #121 | — | 9 | 3 | no | — |
| 304 | #121 | — | 9 | 3 | no | — |
| 305 | #121 | — | 9 | 3 | no | — |
| 306 | #121 | — | 9 | 3 | no | — |
| 307 | #120 | — | 9 | 3 | no | — |
| 308 | #120 | — | 9 | 6 | no | — |
| 309 | #120 | — | 9 | 6 | no | — |
| 310 | #120 | — | 9 | 3 | no | — |
| 311 | C4×Q8 | — | 3 | 1 | no | — |
| 312 | C4×Q8 | — | 9 | 1 | no | — |
| 313 | C4×D4 | — | 3 | 3 | no | — |
| 314 | C4×D4 | — | 9 | 3 | no | — |
| 315 | C4×D4 | — | 9 | 3 | no | — |
| 316 | C4×D4 | — | 9 | 3 | no | — |
| 317 | C4×D4 | — | 9 | 3 | no | — |
| 318 | C4×D4 | — | 9 | 3 | no | — |
| 319 | #117 | — | 9 | 3 | no | — |
| 320 | C2×C4⋊C4 | — | 9 | 3 | no | — |
| 321 | C2×C22⋊C4 | — | 9 | 6 | no | — |
| 322 | C23×C3 | — | 3 | 3 | no | — |
| 323 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 324 | C22×D3 | — | 2 | 3 | no | — |
| 325 | C22×D3 | — | 3 | 3 | no | — |
| 326 | C22×D3 | — | 3 | 3 | no | — |
| 327 | C22×D3 | — | 3 | 3 | no | — |
| 328 | C22×D3 | — | 6 | 6 | no | — |
| 329 | C22×D3 | — | 6 | 3 | no | — |
| 330 | C22×D3 | — | 6 | 6 | no | — |
| 331 | C22×D3 | — | 12 | 6 | no | — |
| 332 | C22×D3 | — | 12 | 6 | no | — |
| 333 | C22×D3 | — | 12 | 6 | no | — |
| 334 | C2×A4 | — | 2 | 1 | no | — |
| 335 | C2×A4 | — | 6 | 3 | no | — |
| 336 | C2×A4 | C23×D3 | 1 | 1 | yes | characteristic |
| 337 | S4 | — | 2 | 3 | no | — |
| 338 | S4 | — | 6 | 3 | no | — |
| 339 | S4 | — | 12 | 3 | no | — |
| 340 | C3×Q8 | — | 3 | 3 | no | — |
| 341 | C3×Q8 | — | 4 | 1 | no | — |
| 342 | C3×Q8 | — | 6 | 1 | no | — |
| 343 | C3×Q8 | — | 8 | 1 | no | — |
| 344 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 345 | C3×D4 | — | 6 | 3 | no | — |
| 346 | C3×D4 | — | 6 | 3 | no | — |
| 347 | C3×D4 | — | 6 | 3 | no | — |
| 348 | C3×D4 | — | 6 | 3 | no | — |
| 349 | C3×D4 | — | 12 | 3 | no | — |
| 350 | C2×C3×C4 | — | 3 | 3 | no | — |
| 351 | C2×C3×C4 | — | 3 | 3 | no | — |
| 352 | C2×C3×C4 | — | 3 | 1 | no | — |
| 353 | C2×C3×C4 | — | 3 | 3 | no | — |
| 354 | C2×C3×C4 | — | 3 | 1 | no | — |
| 355 | C2×C3×C4 | — | 6 | 3 | no | — |
| 356 | C2×C3×C4 | — | 6 | 3 | no | — |
| 357 | C2×C3×C4 | — | 12 | 3 | no | — |
| 358 | #67 | — | 6 | 3 | no | — |
| 359 | #67 | — | 6 | 3 | no | — |
| 360 | #67 | — | 6 | 3 | no | — |
| 361 | #67 | — | 6 | 3 | no | — |
| 362 | #67 | — | 6 | 3 | no | — |
| 363 | #67 | — | 6 | 3 | no | — |
| 364 | #67 | — | 12 | 3 | no | — |
| 365 | #67 | — | 12 | 3 | no | — |
| 366 | #67 | — | 12 | 6 | no | — |
| 367 | #67 | — | 12 | 3 | no | — |
| 368 | C2×Dic3 | — | 3 | 1 | no | — |
| 369 | C2×Dic3 | — | 3 | 1 | no | — |
| 370 | C2×Dic3 | — | 3 | 1 | no | — |
| 371 | C2×Dic3 | — | 3 | 3 | no | — |
| 372 | C2×Dic3 | — | 3 | 1 | no | — |
| 373 | D12 | — | 3 | 6 | no | — |
| 374 | D12 | — | 3 | 3 | no | — |
| 375 | D12 | — | 4 | 3 | no | — |
| 376 | D12 | — | 6 | 3 | no | — |
| 377 | D12 | — | 6 | 3 | no | — |
| 378 | D12 | — | 6 | 3 | no | — |
| 379 | D12 | — | 6 | 3 | no | — |
| 380 | D12 | — | 6 | 3 | no | — |
| 381 | D12 | — | 12 | 3 | no | — |
| 382 | D12 | — | 12 | 3 | no | — |
| 383 | D12 | — | 12 | 3 | no | — |
| 384 | D12 | — | 12 | 6 | no | — |
| 385 | D12 | — | 24 | 3 | no | — |
| 386 | D12 | C2×S4 | 1 | 3 | yes | complemented |
| 387 | C4×D3 | — | 3 | 3 | no | — |
| 388 | C4×D3 | — | 3 | 3 | no | — |
| 389 | C4×D3 | — | 3 | 3 | no | — |
| 390 | C4×D3 | — | 4 | 3 | no | — |
| 391 | C4×D3 | — | 6 | 3 | no | — |
| 392 | C4×D3 | — | 6 | 3 | no | — |
| 393 | C4×D3 | — | 6 | 3 | no | — |
| 394 | C4×D3 | — | 12 | 3 | no | — |
| 395 | C4×D3 | — | 12 | 6 | no | — |
| 396 | C4×D3 | — | 24 | 3 | no | — |
| 397 | C4×D3 | C2×S4 | 1 | 3 | yes | complemented |
| 398 | Dic6 | — | 6 | 1 | no | — |
| 399 | Dic6 | — | 6 | 1 | no | — |
| 400 | Dic6 | — | 12 | 1 | no | — |
| 401 | C2×C32 | — | 4 | 1 | no | — |
| 402 | C3⋊D3 | — | 8 | 3 | no | — |
| 403 | C3×D3 | — | 8 | 3 | no | — |
| 404 | C3×D3 | — | 8 | 3 | no | — |
| 405 | C24 | — | 3 | 3 | no | — |
| 406 | C24 | — | 9 | 6 | no | — |
| 407 | #41 | — | 3 | 1 | no | — |
| 408 | #41 | — | 6 | 3 | no | — |
| 409 | #41 | — | 6 | 1 | no | — |
| 410 | #41 | — | 9 | 3 | no | — |
| 411 | #41 | — | 9 | 3 | no | — |
| 412 | #41 | — | 9 | 1 | no | — |
| 413 | #41 | — | 18 | 3 | no | — |
| 414 | #41 | — | 18 | 3 | no | — |
| 415 | #41 | — | 18 | 3 | no | — |
| 416 | #41 | — | 18 | 3 | no | — |
| 417 | #41 | — | 18 | 1 | no | — |
| 418 | #41 | — | 18 | 3 | no | — |
| 419 | #41 | — | 18 | 3 | no | — |
| 420 | #41 | — | 18 | 3 | no | — |
| 421 | #41 | — | 18 | 1 | no | — |
| 422 | C2×Q8 | — | 3 | 1 | no | — |
| 423 | C2×Q8 | — | 3 | 3 | no | — |
| 424 | C2×Q8 | — | 9 | 1 | no | — |
| 425 | C2×D4 | — | 3 | 3 | no | — |
| 426 | C2×D4 | — | 3 | 3 | no | — |
| 427 | C2×D4 | — | 9 | 3 | no | — |
| 428 | C2×D4 | — | 9 | 6 | no | — |
| 429 | C2×D4 | — | 9 | 3 | no | — |
| 430 | C2×D4 | — | 9 | 3 | no | — |
| 431 | C2×D4 | — | 9 | 3 | no | — |
| 432 | C2×D4 | — | 9 | 3 | no | — |
| 433 | C2×D4 | — | 9 | 6 | no | — |
| 434 | C2×D4 | — | 9 | 3 | no | — |
| 435 | C2×D4 | — | 9 | 3 | no | — |
| 436 | C2×D4 | — | 9 | 3 | no | — |
| 437 | C2×D4 | — | 9 | 3 | no | — |
| 438 | C2×D4 | — | 9 | 6 | no | — |
| 439 | C2×D4 | — | 18 | 3 | no | — |
| 440 | C2×D4 | — | 18 | 3 | no | — |
| 441 | C2×D4 | — | 18 | 6 | no | — |
| 442 | C2×D4 | — | 18 | 3 | no | — |
| 443 | C2×D4 | — | 18 | 3 | no | — |
| 444 | C2×D4 | — | 18 | 3 | no | — |
| 445 | C2×D4 | — | 18 | 3 | no | — |
| 446 | C2×D4 | — | 18 | 3 | no | — |
| 447 | C2×D4 | — | 18 | 6 | no | — |
| 448 | C2×D4 | — | 18 | 3 | no | — |
| 449 | C2×D4 | — | 36 | 6 | no | — |
| 450 | C2×D4 | — | 36 | 6 | no | — |
| 451 | C22×C4 | — | 3 | 3 | no | — |
| 452 | C22×C4 | — | 3 | 1 | no | — |
| 453 | C22×C4 | — | 9 | 3 | no | — |
| 454 | C22×C4 | — | 9 | 3 | no | — |
| 455 | C22×C4 | — | 9 | 3 | no | — |
| 456 | C22×C4 | — | 9 | 3 | no | — |
| 457 | C22×C4 | — | 9 | 3 | no | — |
| 458 | C22×C4 | — | 9 | 6 | no | — |
| 459 | C22×C4 | C2×D32 | 1 | 3 | yes | — |
| 460 | C4⋊C4 | — | 3 | 3 | no | — |
| 461 | C4⋊C4 | — | 3 | 3 | no | — |
| 462 | C4⋊C4 | — | 9 | 3 | no | — |
| 463 | C4⋊C4 | — | 9 | 3 | no | — |
| 464 | C4⋊C4 | — | 9 | 1 | no | — |
| 465 | C4⋊C4 | — | 9 | 1 | no | — |
| 466 | C4⋊C4 | — | 9 | 1 | no | — |
| 467 | C4⋊C4 | — | 9 | 3 | no | — |
| 468 | C22⋊C4 | — | 3 | 6 | no | — |
| 469 | C22⋊C4 | — | 3 | 3 | no | — |
| 470 | C22⋊C4 | — | 3 | 1 | no | — |
| 471 | C22⋊C4 | — | 9 | 3 | no | — |
| 472 | C22⋊C4 | — | 9 | 6 | no | — |
| 473 | C22⋊C4 | — | 9 | 3 | no | — |
| 474 | C22⋊C4 | — | 9 | 3 | no | — |
| 475 | C22⋊C4 | — | 9 | 3 | no | — |
| 476 | C22⋊C4 | — | 9 | 3 | no | — |
| 477 | C22⋊C4 | — | 9 | 3 | no | — |
| 478 | C22⋊C4 | — | 9 | 3 | no | — |
| 479 | C22⋊C4 | — | 9 | 1 | no | — |
| 480 | C42 | — | 3 | 3 | no | — |
| 481 | C42 | — | 9 | 3 | no | — |
| 482 | C22×C3 | — | 3 | 1 | no | — |
| 483 | C22×C3 | — | 3 | 1 | no | — |
| 484 | C22×C3 | — | 6 | 3 | no | — |
| 485 | C22×C3 | — | 6 | 3 | no | — |
| 486 | C22×C3 | — | 6 | 3 | no | — |
| 487 | C22×C3 | — | 12 | 3 | no | — |
| 488 | C22×C3 | #1009 | 1 | 1 | yes | characteristic, complemented |
| 489 | C2×D3 | — | 3 | 3 | no | — |
| 490 | C2×D3 | — | 4 | 3 | no | — |
| 491 | C2×D3 | — | 6 | 3 | no | — |
| 492 | C2×D3 | — | 6 | 3 | no | — |
| 493 | C2×D3 | — | 6 | 3 | no | — |
| 494 | C2×D3 | — | 6 | 3 | no | — |
| 495 | C2×D3 | — | 6 | 3 | no | — |
| 496 | C2×D3 | — | 6 | 3 | no | — |
| 497 | C2×D3 | — | 6 | 3 | no | — |
| 498 | C2×D3 | — | 12 | 3 | no | — |
| 499 | C2×D3 | — | 24 | 3 | no | — |
| 500 | C2×D3 | — | 24 | 6 | no | — |
| 501 | C2×D3 | — | 24 | 6 | no | — |
| 502 | C2×D3 | — | 48 | 6 | no | — |
| 503 | C2×D3 | C22×S4 | 1 | 3 | yes | — |
| 504 | A4 | — | 2 | 1 | no | — |
| 505 | A4 | #1009 | 1 | 1 | yes | characteristic, complemented |
| 506 | C3×C4 | — | 3 | 3 | no | — |
| 507 | C3×C4 | — | 4 | 3 | no | — |
| 508 | C3×C4 | — | 6 | 3 | no | — |
| 509 | C3×C4 | — | 6 | 1 | no | — |
| 510 | C3×C4 | — | 6 | 1 | no | — |
| 511 | C3×C4 | — | 8 | 3 | no | — |
| 512 | C3×C4 | — | 12 | 1 | no | — |
| 513 | C3×C4 | C22×S4 | 1 | 3 | yes | — |
| 514 | Dic3 | — | 3 | 1 | no | — |
| 515 | Dic3 | — | 4 | 1 | no | — |
| 516 | Dic3 | — | 6 | 3 | no | — |
| 517 | Dic3 | — | 6 | 1 | no | — |
| 518 | Dic3 | — | 6 | 1 | no | — |
| 519 | Dic3 | — | 12 | 1 | no | — |
| 520 | Dic3 | — | 24 | 1 | no | — |
| 521 | Dic3 | C22×S4 | 1 | 1 | yes | characteristic |
| 522 | C32 | — | 4 | 1 | no | Sylow |
| 523 | C23 | — | 3 | 3 | no | — |
| 524 | C23 | — | 6 | 3 | no | — |
| 525 | C23 | — | 9 | 3 | no | — |
| 526 | C23 | — | 9 | 3 | no | — |
| 527 | C23 | — | 9 | 3 | no | — |
| 528 | C23 | — | 18 | 6 | no | — |
| 529 | C23 | — | 18 | 3 | no | — |
| 530 | C23 | — | 18 | 6 | no | — |
| 531 | C23 | — | 36 | 6 | no | — |
| 532 | C23 | — | 36 | 6 | no | — |
| 533 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 534 | Q8 | — | 3 | 3 | no | — |
| 535 | Q8 | — | 6 | 1 | no | — |
| 536 | Q8 | — | 18 | 1 | no | — |
| 537 | Q8 | — | 18 | 1 | no | — |
| 538 | Q8 | D3×S4 | 1 | 1 | yes | characteristic, complemented |
| 539 | D4 | — | 3 | 3 | no | — |
| 540 | D4 | — | 6 | 3 | no | — |
| 541 | D4 | — | 6 | 3 | no | — |
| 542 | D4 | — | 6 | 3 | no | — |
| 543 | D4 | — | 6 | 3 | no | — |
| 544 | D4 | — | 9 | 6 | no | — |
| 545 | D4 | — | 9 | 3 | no | — |
| 546 | D4 | — | 18 | 3 | no | — |
| 547 | D4 | — | 18 | 3 | no | — |
| 548 | D4 | — | 18 | 3 | no | — |
| 549 | D4 | — | 18 | 3 | no | — |
| 550 | D4 | — | 18 | 3 | no | — |
| 551 | D4 | — | 18 | 3 | no | — |
| 552 | D4 | — | 18 | 3 | no | — |
| 553 | D4 | — | 18 | 3 | no | — |
| 554 | D4 | — | 18 | 3 | no | — |
| 555 | D4 | — | 18 | 3 | no | — |
| 556 | D4 | — | 18 | 3 | no | — |
| 557 | D4 | — | 36 | 6 | no | — |
| 558 | D4 | — | 36 | 3 | no | — |
| 559 | D4 | — | 36 | 6 | no | — |
| 560 | D4 | — | 36 | 3 | no | — |
| 561 | C2×C4 | — | 3 | 3 | no | — |
| 562 | C2×C4 | — | 3 | 3 | no | — |
| 563 | C2×C4 | — | 3 | 3 | no | — |
| 564 | C2×C4 | — | 3 | 1 | no | — |
| 565 | C2×C4 | — | 3 | 3 | no | — |
| 566 | C2×C4 | — | 3 | 1 | no | — |
| 567 | C2×C4 | — | 6 | 3 | no | — |
| 568 | C2×C4 | — | 6 | 3 | no | — |
| 569 | C2×C4 | — | 9 | 3 | no | — |
| 570 | C2×C4 | — | 9 | 1 | no | — |
| 571 | C2×C4 | — | 9 | 3 | no | — |
| 572 | C2×C4 | — | 9 | 3 | no | — |
| 573 | C2×C4 | — | 9 | 1 | no | — |
| 574 | C2×C4 | — | 9 | 1 | no | — |
| 575 | C2×C4 | — | 9 | 3 | no | — |
| 576 | C2×C4 | — | 9 | 1 | no | — |
| 577 | C2×C4 | — | 18 | 3 | no | — |
| 578 | C2×C4 | — | 18 | 3 | no | — |
| 579 | C2×C4 | — | 18 | 3 | no | — |
| 580 | C2×C4 | — | 36 | 6 | no | — |
| 581 | C2×C3 | — | 3 | 1 | no | — |
| 582 | C2×C3 | — | 3 | 1 | no | — |
| 583 | C2×C3 | — | 4 | 1 | no | — |
| 584 | C2×C3 | — | 8 | 1 | no | — |
| 585 | C2×C3 | — | 12 | 3 | no | — |
| 586 | C2×C3 | — | 24 | 3 | no | — |
| 587 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 588 | D3 | — | 2 | 3 | no | — |
| 589 | D3 | — | 6 | 3 | no | — |
| 590 | D3 | — | 8 | 3 | no | — |
| 591 | D3 | — | 12 | 3 | no | — |
| 592 | D3 | — | 24 | 3 | no | — |
| 593 | D3 | — | 48 | 3 | no | — |
| 594 | C22 | — | 3 | 1 | no | — |
| 595 | C22 | — | 3 | 1 | no | — |
| 596 | C22 | — | 3 | 3 | no | — |
| 597 | C22 | — | 6 | 3 | no | — |
| 598 | C22 | — | 6 | 3 | no | — |
| 599 | C22 | — | 6 | 3 | no | — |
| 600 | C22 | — | 9 | 3 | no | — |
| 601 | C22 | — | 18 | 3 | no | — |
| 602 | C22 | — | 18 | 3 | no | — |
| 603 | C22 | — | 18 | 3 | no | — |
| 604 | C22 | — | 18 | 3 | no | — |
| 605 | C22 | — | 18 | 3 | no | — |
| 606 | C22 | — | 18 | 3 | no | — |
| 607 | C22 | — | 18 | 3 | no | — |
| 608 | C22 | — | 72 | 6 | no | — |
| 609 | C22 | — | 72 | 6 | no | — |
| 610 | C22 | #64320 | 1 | 1 | yes | characteristic, complemented |
| 611 | C4 | — | 3 | 1 | no | — |
| 612 | C4 | — | 3 | 3 | no | — |
| 613 | C4 | — | 6 | 3 | no | — |
| 614 | C4 | — | 6 | 1 | no | — |
| 615 | C4 | — | 6 | 1 | no | — |
| 616 | C4 | — | 9 | 1 | no | — |
| 617 | C4 | — | 18 | 3 | no | — |
| 618 | C4 | — | 18 | 1 | no | — |
| 619 | C4 | — | 18 | 1 | no | — |
| 620 | C4 | C2×D3×S4 | 1 | 3 | yes | — |
| 621 | C3 | — | 4 | 1 | no | — |
| 622 | C3 | — | 8 | 1 | no | — |
| 623 | C3 | #87489 | 1 | 1 | yes | characteristic, complemented |
| 624 | C2 | — | 3 | 1 | no | — |
| 625 | C2 | — | 3 | 1 | no | — |
| 626 | C2 | — | 6 | 3 | no | — |
| 627 | C2 | — | 12 | 3 | no | — |
| 628 | C2 | — | 18 | 3 | no | — |
| 629 | C2 | — | 36 | 3 | no | — |
| 630 | C2 | C22×D3×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×S4 |
| commutator, cosocle | C2×C3×A4 | C24 |
| Fitting | C22×C3×Q8 | C2×D3 |
| socle | C23×C3 | C23×D3 |
| hypercenter | Q8 | D3×S4 |
| hypocenter | C3×A4 | H(5,𝔽2) |
| LCS | G ▷ C2×C3×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#239 | C2 | semidirect |
| 2. #10596582 | C2 | semidirect |
| 3. C3×#5919 | C2 | semidirect |
| 4. #10596432 | C2 | semidirect |
| 5. D12×S4 | C2 | semidirect |
| 6. D3×C4⋊S4 | C2 | semidirect |
| 7. #10596426 | C2 | semidirect |
| 10. C2×D3×S4 | C22 | semidirect |
| 11. C3×Q8×A4 | C22 | semidirect |
| 13. A4×D12 | C22 | semidirect |
| 14. C4×D3×A4 | C22 | semidirect |
| 15. C4⋊(C3⋊S4) | C22 | semidirect |
| 16. C4×C3⋊S4 | C22 | semidirect |
| 17. C3×C4⋊S4 | C22 | semidirect |
| 18. C3×C4×S4 | C22 | semidirect |
| 19. #64210 | C22 | semidirect |
| 20. #64209 | C22 | semidirect |
| 21. #64207 | C22 | semidirect |
| 22. #64204 | C22 | semidirect |
| 24. C22×#239 | D3 | semidirect |
| 28. #5919 | D3 | semidirect |
| 64. C22×C3×Q8 | C2×D3 | semidirect |
| 80. C22×D12 | C2×D3 | semidirect |
| 81. C22×C4×D3 | C2×D3 | semidirect |
| 83. Q8×A4 | C2×D3 | semidirect |
| 91. C4⋊S4 | C2×D3 | semidirect |
| 94. C4×S4 | C2×D3 | semidirect |
| 196. #239 | S4 | semidirect |
| 262. C3×A4 | H(5,𝔽2) | semidirect |
| 279. C22×Q8 | D32 | semidirect |
| 344. C3×Q8 | C2×S4 | semidirect |
| 386. D12 | C2×S4 | semidirect |
| 397. C4×D3 | C2×S4 | semidirect |
| 488. C22×C3 | #1009 | semidirect |
| 505. A4 | #1009 | semidirect |
| 538. Q8 | D3×S4 | semidirect |
| 610. C22 | #64320 | semidirect |
| 623. C3 | #87489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#239 | 2 |
| #10596582 | 2 |
| C3×#5919 | 2 |
| #10596432 | 2 |
| D12×S4 | 2 |
| D3×C4⋊S4 | 2 |
| #10596426 | 2 |
| #87489 | 3 |
| #86713 | 3 |
| #64320 | 4 |