Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1585 conjugacy classes of subgroups.
The subgroup lattice has 530 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64319 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | D32×M16 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3⋊D3×#101 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#4751 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10591639 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10591637 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10591006 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10591001 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | D3×#413 | — | 3 | 2 | no | maximal |
| 10 | C2×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×#239 | C22 | 1 | 2 | yes | — |
| 12 | #64319 | — | 2 | 2 | no | — |
| 13 | #64319 | — | 2 | 4 | no | — |
| 14 | #64319 | — | 2 | 2 | no | — |
| 15 | C2×#3802 | C4 | 1 | 2 | yes | — |
| 16 | C2×#3802 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×D32 | C4 | 1 | 2 | yes | — |
| 18 | C2×C4×D32 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#3795 | C4 | 1 | 4 | yes | — |
| 20 | C2×#3795 | C22 | 1 | 2 | yes | — |
| 21 | M16×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 22 | C3×D3×M16 | C22 | 1 | 4 | yes | complemented |
| 23 | #63818 | C22 | 1 | 2 | yes | — |
| 24 | D3×#208 | C22 | 1 | 4 | yes | complemented |
| 25 | #63791 | — | 2 | 2 | no | — |
| 26 | D3×ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 27 | D32×C8 | — | 2 | 2 | no | — |
| 28 | C32×#101 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #63663 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #63651 | C22 | 1 | 2 | yes | complemented |
| 31 | C3×#836 | C22 | 1 | 2 | yes | complemented |
| 32 | C3×#823 | C22 | 1 | 4 | yes | complemented |
| 33 | #63561 | C22 | 1 | 2 | yes | complemented |
| 34 | #63558 | C22 | 1 | 4 | yes | complemented |
| 35 | C2×D3×#41 | — | 3 | 2 | no | — |
| 36 | C2×D3×M16 | — | 3 | 4 | no | — |
| 37 | C3×#413 | — | 3 | 2 | no | — |
| 38 | #5237 | — | 3 | 2 | no | — |
| 39 | #5132 | — | 3 | 4 | no | — |
| 40 | #4751 | — | 3 | 2 | no | — |
| 41 | #4751 | D3 | 1 | 2 | yes | complemented |
| 42 | D3×#101 | — | 3 | 2 | no | — |
| 43 | D3×#101 | — | 3 | 2 | no | — |
| 44 | D3×#101 | — | 6 | 1 | no | — |
| 45 | #4745 | — | 3 | 4 | no | — |
| 46 | D3×#100 | — | 3 | 4 | no | — |
| 47 | C22×D32 | C2×C4 | 1 | 2 | yes | — |
| 48 | C22×D32 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 50 | Q8×C3⋊D3 | — | 2 | 2 | no | — |
| 51 | Q8×C3⋊D3 | — | 2 | 2 | no | — |
| 52 | C2×C4×C3⋊D3 | C2×C4 | 1 | 2 | yes | — |
| 53 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×#634 | C2×C4 | 1 | 2 | yes | — |
| 55 | C2×#634 | C23 | 1 | 1 | yes | characteristic |
| 56 | C3×#239 | — | 2 | 4 | no | — |
| 57 | C3×#239 | — | 2 | 4 | no | — |
| 58 | C2×C3×D12 | C2×C4 | 1 | 4 | yes | — |
| 59 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 60 | C2×C3×C4×D3 | C2×C4 | 1 | 4 | yes | — |
| 61 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 62 | C2×#625 | C2×C4 | 1 | 2 | yes | — |
| 63 | C2×#625 | C2×C4 | 1 | 4 | yes | — |
| 64 | C2×#624 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C2×D3×Dic3 | C2×C4 | 1 | 4 | yes | — |
| 66 | C2×D3×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 67 | #3802 | — | 2 | 4 | no | — |
| 68 | #3802 | — | 2 | 4 | no | — |
| 69 | #3802 | — | 2 | 2 | no | — |
| 70 | #3802 | — | 2 | 2 | no | — |
| 71 | C4×D32 | — | 2 | 4 | no | — |
| 72 | C4×D32 | — | 2 | 2 | no | — |
| 73 | C4×D32 | — | 2 | 2 | no | — |
| 74 | C4×D32 | D4 | 1 | 2 | yes | — |
| 75 | C4×D32 | D4 | 1 | 4 | yes | — |
| 76 | C4×D32 | D4 | 1 | 2 | yes | — |
| 77 | #3795 | — | 2 | 4 | no | — |
| 78 | #3795 | — | 2 | 4 | no | — |
| 79 | #3795 | — | 2 | 8 | no | — |
| 80 | #3795 | — | 2 | 8 | no | — |
| 81 | C32×M16 | C23 | 1 | 2 | yes | — |
| 82 | #3748 | C23 | 1 | 2 | yes | — |
| 83 | #3743 | — | 2 | 2 | no | — |
| 84 | C8×C3⋊D3 | — | 2 | 2 | no | — |
| 85 | C3×#208 | C23 | 1 | 4 | yes | — |
| 86 | C3×ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 87 | C3×D3×C8 | — | 2 | 4 | no | — |
| 88 | #3712 | — | 2 | 2 | no | — |
| 89 | #3711 | — | 2 | 4 | no | — |
| 90 | #3710 | — | 2 | 2 | no | — |
| 91 | D3×C3⋊C8 | — | 2 | 4 | no | — |
| 92 | C2×#413 | — | 9 | 1 | no | Sylow |
| 93 | C2×C3×#41 | — | 3 | 2 | no | — |
| 94 | D3×#41 | — | 6 | 4 | no | — |
| 95 | D3×#41 | — | 6 | 4 | no | — |
| 96 | D3×#41 | — | 6 | 4 | no | — |
| 97 | D3×#41 | — | 6 | 4 | no | — |
| 98 | C2×#239 | C2×D3 | 1 | 2 | yes | — |
| 99 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 100 | C2×D3×Q8 | — | 6 | 1 | no | — |
| 101 | C2×#237 | — | 3 | 4 | no | — |
| 102 | C2×#237 | — | 3 | 2 | no | — |
| 103 | C2×D3×D4 | — | 3 | 4 | no | — |
| 104 | C2×D3×D4 | — | 3 | 2 | no | — |
| 105 | C2×#235 | — | 3 | 4 | no | — |
| 106 | C2×#235 | — | 3 | 2 | no | — |
| 107 | C22×C4×D3 | — | 3 | 2 | no | — |
| 108 | C22×C4×D3 | — | 3 | 4 | no | — |
| 109 | C2×C3×M16 | — | 3 | 4 | no | — |
| 110 | C2×#208 | — | 3 | 4 | no | — |
| 111 | D3×M16 | — | 3 | 4 | no | — |
| 112 | D3×M16 | — | 3 | 4 | no | — |
| 113 | D3×M16 | — | 3 | 4 | no | — |
| 114 | D3×M16 | — | 6 | 2 | no | — |
| 115 | D3×M16 | — | 6 | 4 | no | — |
| 116 | D3×M16 | — | 6 | 4 | no | — |
| 117 | D3×M16 | C2×D3 | 1 | 4 | yes | complemented |
| 118 | C2×ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 119 | C2×D3×C8 | — | 6 | 4 | no | — |
| 120 | C3×#101 | — | 2 | 1 | no | — |
| 121 | C3×#101 | — | 3 | 2 | no | — |
| 122 | C3×#101 | C2×D3 | 1 | 2 | yes | complemented |
| 123 | C3×#100 | — | 3 | 4 | no | — |
| 124 | #836 | — | 3 | 2 | no | — |
| 125 | #836 | — | 6 | 1 | no | — |
| 126 | #836 | C2×D3 | 1 | 2 | yes | complemented |
| 127 | #833 | — | 3 | 4 | no | — |
| 128 | #824 | — | 3 | 4 | no | — |
| 129 | #824 | — | 3 | 4 | no | — |
| 130 | #824 | — | 6 | 2 | no | — |
| 131 | #823 | — | 3 | 4 | no | — |
| 132 | #823 | C2×D3 | 1 | 4 | yes | complemented |
| 133 | C22×C3⋊D3 | C22×C4 | 1 | 1 | yes | characteristic |
| 134 | C22×C3×D3 | C22×C4 | 1 | 4 | yes | — |
| 135 | C22×C3×D3 | C22×C4 | 1 | 2 | yes | — |
| 136 | C2×D32 | — | 2 | 2 | no | — |
| 137 | C2×D32 | — | 2 | 2 | no | — |
| 138 | C2×D32 | — | 4 | 2 | no | — |
| 139 | C2×D32 | — | 4 | 4 | no | — |
| 140 | C2×D32 | C22⋊C4 | 1 | 2 | yes | — |
| 141 | C2×D32 | C22⋊C4 | 1 | 2 | yes | — |
| 142 | C32×Q8 | — | 2 | 2 | no | — |
| 143 | C2×C32×C4 | C22×C4 | 1 | 2 | yes | — |
| 144 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 145 | C2×C3⋊Dic3 | C22×C4 | 1 | 2 | yes | — |
| 146 | C2×C3⋊Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 147 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 148 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 149 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 150 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 151 | #634 | — | 2 | 2 | no | — |
| 152 | #634 | — | 2 | 4 | no | — |
| 153 | C2×C3×Dic3 | C22×C4 | 1 | 2 | yes | — |
| 154 | C3×D12 | — | 2 | 8 | no | — |
| 155 | C3×D12 | — | 2 | 4 | no | — |
| 156 | C3×C4×D3 | — | 2 | 4 | no | — |
| 157 | C3×C4×D3 | — | 2 | 4 | no | — |
| 158 | C3×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 159 | C3×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 160 | #625 | — | 2 | 8 | no | — |
| 161 | #625 | — | 2 | 4 | no | — |
| 162 | #624 | C22⋊C4 | 1 | 2 | yes | — |
| 163 | #624 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 164 | #624 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | D3×Dic3 | — | 2 | 4 | no | — |
| 166 | D3×Dic3 | — | 2 | 4 | no | — |
| 167 | D3×Dic3 | C22⋊C4 | 1 | 4 | yes | — |
| 168 | D3×Dic3 | C22⋊C4 | 1 | 4 | yes | — |
| 169 | C32×C8 | — | 2 | 2 | no | — |
| 170 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 171 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 172 | C22×#41 | — | 9 | 1 | no | — |
| 173 | C22×M16 | — | 9 | 2 | no | — |
| 174 | #413 | — | 3 | 2 | no | — |
| 175 | #413 | — | 9 | 4 | no | — |
| 176 | #413 | — | 9 | 2 | no | — |
| 177 | C2×#101 | — | 9 | 1 | no | — |
| 178 | C2×#101 | — | 9 | 1 | no | — |
| 179 | C2×#100 | — | 9 | 2 | no | — |
| 180 | C23×D3 | — | 3 | 2 | no | — |
| 181 | C23×D3 | — | 3 | 4 | no | — |
| 182 | C3×#41 | — | 6 | 4 | no | — |
| 183 | C3×#41 | — | 6 | 4 | no | — |
| 184 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 185 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 186 | C2×C3×D4 | — | 3 | 4 | no | — |
| 187 | C2×C3×D4 | — | 3 | 2 | no | — |
| 188 | C22×C3×C4 | — | 3 | 2 | no | — |
| 189 | C22×C3×C4 | — | 3 | 4 | no | — |
| 190 | C2×#67 | — | 3 | 4 | no | — |
| 191 | C2×#67 | — | 3 | 4 | no | — |
| 192 | C2×#67 | — | 3 | 4 | no | — |
| 193 | C22×Dic3 | — | 3 | 2 | no | — |
| 194 | C22×Dic3 | — | 3 | 4 | no | — |
| 195 | #239 | — | 2 | 4 | no | — |
| 196 | #239 | — | 2 | 4 | no | — |
| 197 | D3×Q8 | — | 6 | 4 | no | — |
| 198 | D3×Q8 | — | 6 | 4 | no | — |
| 199 | D3×Q8 | — | 12 | 2 | no | — |
| 200 | D3×Q8 | — | 12 | 2 | no | — |
| 201 | #237 | — | 6 | 8 | no | — |
| 202 | #237 | — | 6 | 8 | no | — |
| 203 | #237 | — | 6 | 4 | no | — |
| 204 | #237 | — | 6 | 4 | no | — |
| 205 | D3×D4 | — | 6 | 4 | no | — |
| 206 | D3×D4 | — | 6 | 4 | no | — |
| 207 | D3×D4 | — | 6 | 8 | no | — |
| 208 | D3×D4 | — | 6 | 8 | no | — |
| 209 | #235 | — | 6 | 8 | no | — |
| 210 | #235 | — | 6 | 8 | no | — |
| 211 | #235 | — | 6 | 4 | no | — |
| 212 | #235 | — | 6 | 4 | no | — |
| 213 | C2×D12 | C4×D3 | 1 | 4 | yes | — |
| 214 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 215 | C2×C4×D3 | — | 3 | 2 | no | — |
| 216 | C2×C4×D3 | — | 3 | 2 | no | — |
| 217 | C2×C4×D3 | — | 3 | 2 | no | — |
| 218 | C2×C4×D3 | — | 3 | 4 | no | — |
| 219 | C2×C4×D3 | — | 3 | 4 | no | — |
| 220 | C2×C4×D3 | — | 3 | 4 | no | — |
| 221 | C2×C4×D3 | — | 3 | 4 | no | — |
| 222 | C2×C4×D3 | — | 3 | 4 | no | — |
| 223 | C2×C4×D3 | — | 3 | 4 | no | — |
| 224 | C2×C4×D3 | — | 6 | 1 | no | — |
| 225 | C2×C4×D3 | — | 6 | 2 | no | — |
| 226 | C2×C4×D3 | — | 6 | 4 | no | — |
| 227 | C2×C4×D3 | — | 6 | 4 | no | — |
| 228 | C2×C4×D3 | — | 6 | 4 | no | — |
| 229 | C2×C4×D3 | — | 6 | 4 | no | — |
| 230 | C2×C4×D3 | C4×D3 | 1 | 4 | yes | — |
| 231 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 232 | C2×Dic6 | — | 3 | 4 | no | — |
| 233 | C2×Dic6 | — | 3 | 2 | no | — |
| 234 | C2×Dic6 | — | 6 | 1 | no | — |
| 235 | C2×Dic6 | — | 6 | 2 | no | — |
| 236 | C3×M16 | — | 2 | 2 | no | — |
| 237 | C3×M16 | — | 3 | 4 | no | — |
| 238 | C3×M16 | — | 6 | 4 | no | — |
| 239 | C3×M16 | C22×D3 | 1 | 4 | yes | — |
| 240 | C2×C3×C8 | — | 6 | 4 | no | — |
| 241 | #208 | — | 3 | 4 | no | — |
| 242 | #208 | — | 6 | 2 | no | — |
| 243 | #208 | — | 6 | 4 | no | — |
| 244 | #208 | C22×D3 | 1 | 4 | yes | — |
| 245 | C2×C3⋊C8 | — | 6 | 4 | no | — |
| 246 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 247 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 248 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 249 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 250 | ΓL(1,𝔽25) | — | 12 | 2 | no | — |
| 251 | D3×C8 | — | 2 | 4 | no | — |
| 252 | D3×C8 | — | 6 | 4 | no | — |
| 253 | D3×C8 | — | 6 | 4 | no | — |
| 254 | D3×C8 | — | 6 | 4 | no | — |
| 255 | D3×C8 | — | 12 | 2 | no | — |
| 256 | C22×C32 | C23×C4 | 1 | 1 | yes | characteristic |
| 257 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 258 | C2×C3⋊D3 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 259 | C2×C3⋊D3 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 260 | C2×C3×D3 | — | 2 | 4 | no | — |
| 261 | C2×C3×D3 | — | 4 | 2 | no | — |
| 262 | C2×C3×D3 | — | 4 | 4 | no | — |
| 263 | C2×C3×D3 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 264 | D32 | — | 2 | 4 | no | — |
| 265 | D32 | — | 4 | 2 | no | — |
| 266 | D32 | — | 4 | 4 | no | — |
| 267 | D32 | — | 4 | 4 | no | — |
| 268 | C32×C4 | — | 2 | 2 | no | — |
| 269 | C32×C4 | C22×D4 | 1 | 2 | yes | — |
| 270 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 271 | C3⋊Dic3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 272 | C3×Dic3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 273 | C3×Dic3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 274 | C2×#41 | — | 3 | 2 | no | — |
| 275 | C2×#41 | — | 9 | 2 | no | — |
| 276 | C2×#41 | — | 9 | 4 | no | — |
| 277 | C2×#41 | — | 18 | 2 | no | — |
| 278 | C2×#41 | — | 18 | 4 | no | — |
| 279 | C2×#41 | — | 18 | 2 | no | — |
| 280 | C22×Q8 | — | 9 | 1 | no | — |
| 281 | C22×D4 | — | 9 | 1 | no | — |
| 282 | C22×D4 | — | 9 | 2 | no | — |
| 283 | C23×C4 | — | 9 | 1 | no | — |
| 284 | C23×C4 | — | 9 | 2 | no | — |
| 285 | C2×M16 | — | 3 | 4 | no | — |
| 286 | C2×M16 | — | 9 | 2 | no | — |
| 287 | C2×M16 | — | 9 | 4 | no | — |
| 288 | C2×M16 | — | 9 | 2 | no | — |
| 289 | C2×M16 | — | 18 | 4 | no | — |
| 290 | C2×M16 | — | 18 | 2 | no | — |
| 291 | C22×C8 | — | 18 | 2 | no | — |
| 292 | #101 | — | 3 | 2 | no | — |
| 293 | #101 | — | 9 | 2 | no | — |
| 294 | #101 | — | 9 | 1 | no | — |
| 295 | #101 | — | 9 | 2 | no | — |
| 296 | #101 | D32 | 1 | 1 | yes | characteristic, complemented |
| 297 | #100 | — | 3 | 4 | no | — |
| 298 | #100 | — | 9 | 4 | no | — |
| 299 | C23×C3 | — | 3 | 2 | no | — |
| 300 | C23×C3 | — | 3 | 4 | no | — |
| 301 | C22×D3 | — | 3 | 2 | no | — |
| 302 | C22×D3 | — | 3 | 4 | no | — |
| 303 | C22×D3 | — | 3 | 4 | no | — |
| 304 | C22×D3 | — | 6 | 1 | no | — |
| 305 | C22×D3 | — | 6 | 4 | no | — |
| 306 | C22×D3 | — | 6 | 4 | no | — |
| 307 | C22×D3 | — | 12 | 4 | no | — |
| 308 | C22×D3 | — | 12 | 8 | no | — |
| 309 | C22×D3 | C2×C4×D3 | 1 | 4 | yes | — |
| 310 | C22×D3 | C2×C4×D3 | 1 | 2 | yes | — |
| 311 | C3×Q8 | — | 2 | 4 | no | — |
| 312 | C3×Q8 | — | 4 | 2 | no | — |
| 313 | C3×D4 | — | 6 | 8 | no | — |
| 314 | C3×D4 | — | 6 | 4 | no | — |
| 315 | C2×C3×C4 | — | 2 | 1 | no | — |
| 316 | C2×C3×C4 | — | 2 | 2 | no | — |
| 317 | C2×C3×C4 | — | 3 | 2 | no | — |
| 318 | C2×C3×C4 | — | 3 | 4 | no | — |
| 319 | C2×C3×C4 | — | 3 | 4 | no | — |
| 320 | C2×C3×C4 | — | 6 | 4 | no | — |
| 321 | C2×C3×C4 | — | 6 | 4 | no | — |
| 322 | C2×C3×C4 | C2×C4×D3 | 1 | 4 | yes | — |
| 323 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 324 | #67 | — | 6 | 8 | no | — |
| 325 | #67 | — | 6 | 8 | no | — |
| 326 | #67 | — | 6 | 8 | no | — |
| 327 | C2×Dic3 | — | 3 | 2 | no | — |
| 328 | C2×Dic3 | — | 3 | 4 | no | — |
| 329 | C2×Dic3 | — | 3 | 4 | no | — |
| 330 | C2×Dic3 | — | 3 | 4 | no | — |
| 331 | C2×Dic3 | — | 6 | 1 | no | — |
| 332 | C2×Dic3 | — | 6 | 2 | no | — |
| 333 | C2×Dic3 | — | 6 | 4 | no | — |
| 334 | C2×Dic3 | — | 6 | 4 | no | — |
| 335 | C2×Dic3 | C2×C4×D3 | 1 | 2 | yes | — |
| 336 | D12 | — | 2 | 8 | no | — |
| 337 | D12 | — | 2 | 4 | no | — |
| 338 | C4×D3 | — | 2 | 4 | no | — |
| 339 | C4×D3 | — | 2 | 4 | no | — |
| 340 | C4×D3 | — | 3 | 4 | no | — |
| 341 | C4×D3 | — | 3 | 4 | no | — |
| 342 | C4×D3 | — | 3 | 4 | no | — |
| 343 | C4×D3 | — | 3 | 4 | no | — |
| 344 | C4×D3 | — | 3 | 2 | no | — |
| 345 | C4×D3 | — | 3 | 2 | no | — |
| 346 | C4×D3 | — | 3 | 2 | no | — |
| 347 | C4×D3 | — | 3 | 2 | no | — |
| 348 | C4×D3 | — | 6 | 2 | no | — |
| 349 | C4×D3 | — | 6 | 2 | no | — |
| 350 | C4×D3 | — | 6 | 4 | no | — |
| 351 | C4×D3 | — | 6 | 4 | no | — |
| 352 | C4×D3 | — | 6 | 4 | no | — |
| 353 | C4×D3 | — | 6 | 4 | no | — |
| 354 | C4×D3 | — | 12 | 2 | no | — |
| 355 | C4×D3 | — | 12 | 2 | no | — |
| 356 | C4×D3 | D3×D4 | 1 | 4 | yes | — |
| 357 | C4×D3 | D3×D4 | 1 | 4 | yes | — |
| 358 | Dic6 | — | 6 | 8 | no | — |
| 359 | Dic6 | — | 6 | 4 | no | — |
| 360 | Dic6 | — | 12 | 4 | no | — |
| 361 | Dic6 | — | 12 | 2 | no | — |
| 362 | C3×C8 | — | 2 | 4 | no | — |
| 363 | C3×C8 | — | 4 | 2 | no | — |
| 364 | C3×C8 | — | 6 | 4 | no | — |
| 365 | C3⋊C8 | — | 2 | 4 | no | — |
| 366 | C3⋊C8 | — | 6 | 4 | no | — |
| 367 | C3⋊C8 | — | 12 | 2 | no | — |
| 368 | C2×C32 | — | 2 | 1 | no | — |
| 369 | C2×C32 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 370 | C3⋊D3 | — | 2 | 1 | no | — |
| 371 | C3⋊D3 | #413 | 1 | 2 | yes | complemented |
| 372 | C3×D3 | — | 2 | 4 | no | — |
| 373 | C3×D3 | — | 4 | 4 | no | — |
| 374 | C24 | — | 9 | 1 | no | — |
| 375 | C24 | — | 9 | 2 | no | — |
| 376 | #41 | — | 6 | 4 | no | — |
| 377 | #41 | — | 6 | 4 | no | — |
| 378 | #41 | — | 18 | 4 | no | — |
| 379 | #41 | — | 18 | 4 | no | — |
| 380 | #41 | — | 18 | 8 | no | — |
| 381 | #41 | — | 18 | 8 | no | — |
| 382 | C2×Q8 | — | 9 | 1 | no | — |
| 383 | C2×Q8 | — | 9 | 2 | no | — |
| 384 | C2×Q8 | — | 18 | 2 | no | — |
| 385 | C2×Q8 | — | 18 | 2 | no | — |
| 386 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 387 | C2×D4 | — | 3 | 2 | no | — |
| 388 | C2×D4 | — | 3 | 4 | no | — |
| 389 | C2×D4 | — | 9 | 2 | no | — |
| 390 | C2×D4 | — | 9 | 4 | no | — |
| 391 | C2×D4 | — | 18 | 2 | no | — |
| 392 | C2×D4 | — | 18 | 2 | no | — |
| 393 | C2×D4 | — | 18 | 4 | no | — |
| 394 | C2×D4 | — | 18 | 4 | no | — |
| 395 | C22×C4 | — | 3 | 2 | no | — |
| 396 | C22×C4 | — | 3 | 4 | no | — |
| 397 | C22×C4 | — | 9 | 2 | no | — |
| 398 | C22×C4 | — | 9 | 4 | no | — |
| 399 | C22×C4 | — | 9 | 2 | no | — |
| 400 | C22×C4 | — | 9 | 1 | no | — |
| 401 | C22×C4 | — | 9 | 2 | no | — |
| 402 | C22×C4 | — | 9 | 4 | no | — |
| 403 | C22×C4 | — | 9 | 1 | no | — |
| 404 | C22×C4 | — | 9 | 2 | no | — |
| 405 | C22×C4 | — | 18 | 2 | no | — |
| 406 | C22×C4 | — | 18 | 2 | no | — |
| 407 | C22×C4 | — | 18 | 4 | no | — |
| 408 | M16 | — | 3 | 4 | no | — |
| 409 | M16 | — | 6 | 4 | no | — |
| 410 | M16 | — | 9 | 2 | no | — |
| 411 | M16 | — | 18 | 2 | no | — |
| 412 | M16 | — | 18 | 2 | no | — |
| 413 | M16 | — | 18 | 4 | no | — |
| 414 | M16 | C2×D32 | 1 | 2 | yes | — |
| 415 | C2×C8 | — | 6 | 4 | no | — |
| 416 | C2×C8 | — | 18 | 2 | no | — |
| 417 | C2×C8 | — | 18 | 2 | no | — |
| 418 | C2×C8 | — | 18 | 4 | no | — |
| 419 | C22×C3 | — | 2 | 1 | no | — |
| 420 | C22×C3 | — | 3 | 4 | no | — |
| 421 | C22×C3 | — | 6 | 4 | no | — |
| 422 | C22×C3 | — | 12 | 2 | no | — |
| 423 | C22×C3 | — | 12 | 4 | no | — |
| 424 | C22×C3 | C22×C4×D3 | 1 | 2 | yes | — |
| 425 | C2×D3 | — | 2 | 4 | no | — |
| 426 | C2×D3 | — | 3 | 2 | no | — |
| 427 | C2×D3 | — | 3 | 2 | no | — |
| 428 | C2×D3 | — | 4 | 2 | no | — |
| 429 | C2×D3 | — | 4 | 4 | no | — |
| 430 | C2×D3 | — | 6 | 1 | no | — |
| 431 | C2×D3 | — | 6 | 1 | no | — |
| 432 | C2×D3 | — | 6 | 8 | no | — |
| 433 | C2×D3 | — | 6 | 4 | no | — |
| 434 | C2×D3 | — | 12 | 2 | no | — |
| 435 | C2×D3 | — | 12 | 4 | no | — |
| 436 | C2×D3 | — | 12 | 8 | no | — |
| 437 | C2×D3 | — | 12 | 8 | no | — |
| 438 | C2×D3 | D3×C22⋊C4 | 1 | 4 | yes | — |
| 439 | C3×C4 | — | 2 | 4 | no | — |
| 440 | C3×C4 | — | 2 | 2 | no | — |
| 441 | C3×C4 | — | 3 | 2 | no | — |
| 442 | C3×C4 | — | 3 | 2 | no | — |
| 443 | C3×C4 | — | 4 | 2 | no | — |
| 444 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 445 | Dic3 | — | 3 | 4 | no | — |
| 446 | Dic3 | — | 6 | 2 | no | — |
| 447 | Dic3 | — | 6 | 4 | no | — |
| 448 | Dic3 | — | 12 | 2 | no | — |
| 449 | Dic3 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 450 | Dic3 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 451 | C32 | C2×#413 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 452 | C23 | — | 3 | 2 | no | — |
| 453 | C23 | — | 3 | 4 | no | — |
| 454 | C23 | — | 9 | 2 | no | — |
| 455 | C23 | — | 9 | 2 | no | — |
| 456 | C23 | — | 9 | 1 | no | — |
| 457 | C23 | — | 18 | 2 | no | — |
| 458 | C23 | — | 18 | 2 | no | — |
| 459 | C23 | — | 36 | 2 | no | — |
| 460 | C23 | — | 36 | 4 | no | — |
| 461 | Q8 | — | 2 | 2 | no | — |
| 462 | Q8 | — | 18 | 4 | no | — |
| 463 | Q8 | — | 18 | 2 | no | — |
| 464 | D4 | — | 6 | 8 | no | — |
| 465 | D4 | — | 6 | 4 | no | — |
| 466 | D4 | — | 18 | 4 | no | — |
| 467 | D4 | — | 18 | 8 | no | — |
| 468 | C2×C4 | — | 3 | 2 | no | — |
| 469 | C2×C4 | — | 3 | 4 | no | — |
| 470 | C2×C4 | — | 3 | 4 | no | — |
| 471 | C2×C4 | — | 6 | 4 | no | — |
| 472 | C2×C4 | — | 6 | 4 | no | — |
| 473 | C2×C4 | — | 9 | 1 | no | — |
| 474 | C2×C4 | — | 9 | 1 | no | — |
| 475 | C2×C4 | — | 9 | 2 | no | — |
| 476 | C2×C4 | — | 9 | 4 | no | — |
| 477 | C2×C4 | — | 9 | 4 | no | — |
| 478 | C2×C4 | — | 9 | 1 | no | — |
| 479 | C2×C4 | — | 9 | 2 | no | — |
| 480 | C2×C4 | — | 9 | 2 | no | — |
| 481 | C2×C4 | — | 9 | 2 | no | — |
| 482 | C2×C4 | — | 18 | 2 | no | — |
| 483 | C2×C4 | — | 18 | 2 | no | — |
| 484 | C2×C4 | — | 18 | 4 | no | — |
| 485 | C2×C4 | — | 18 | 4 | no | — |
| 486 | C2×C4 | C4×D32 | 1 | 2 | yes | — |
| 487 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 488 | C8 | — | 2 | 2 | no | — |
| 489 | C8 | — | 6 | 4 | no | — |
| 490 | C8 | — | 18 | 2 | no | — |
| 491 | C2×C3 | — | 2 | 2 | no | — |
| 492 | C2×C3 | — | 2 | 1 | no | — |
| 493 | C2×C3 | — | 4 | 1 | no | — |
| 494 | C2×C3 | — | 6 | 4 | no | — |
| 495 | C2×C3 | — | 12 | 4 | no | — |
| 496 | C2×C3 | C2×D3×C22⋊C4 | 1 | 2 | yes | — |
| 497 | D3 | — | 2 | 4 | no | — |
| 498 | D3 | — | 3 | 4 | no | — |
| 499 | D3 | — | 4 | 4 | no | — |
| 500 | D3 | — | 6 | 2 | no | — |
| 501 | D3 | — | 6 | 2 | no | — |
| 502 | D3 | — | 12 | 1 | no | — |
| 503 | C22 | — | 3 | 4 | no | — |
| 504 | C22 | — | 6 | 4 | no | — |
| 505 | C22 | — | 9 | 1 | no | — |
| 506 | C22 | — | 9 | 1 | no | — |
| 507 | C22 | — | 12 | 2 | no | — |
| 508 | C22 | — | 12 | 4 | no | — |
| 509 | C22 | — | 18 | 2 | no | — |
| 510 | C22 | — | 18 | 4 | no | — |
| 511 | C22 | — | 36 | 2 | no | — |
| 512 | C22 | — | 36 | 4 | no | — |
| 513 | C22 | — | 36 | 4 | no | — |
| 514 | C22 | C2×C4×D32 | 1 | 1 | yes | characteristic |
| 515 | C4 | — | 2 | 2 | no | — |
| 516 | C4 | — | 3 | 2 | no | — |
| 517 | C4 | — | 3 | 2 | no | — |
| 518 | C4 | — | 9 | 2 | no | — |
| 519 | C4 | — | 18 | 2 | no | — |
| 520 | C4 | D32×D4 | 1 | 2 | yes | — |
| 521 | C3 | — | 2 | 1 | no | — |
| 522 | C3 | D3×#413 | 1 | 2 | yes | complemented |
| 523 | C2 | — | 2 | 1 | no | — |
| 524 | C2 | — | 6 | 4 | no | — |
| 525 | C2 | — | 9 | 2 | no | — |
| 526 | C2 | — | 12 | 4 | no | — |
| 527 | C2 | — | 18 | 1 | no | — |
| 528 | C2 | D32×C22⋊C4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. D32×M16 | C2 | semidirect |
| 3. C3⋊D3×#101 | C2 | semidirect |
| 4. C3×#4751 | C2 | semidirect |
| 5. #10591639 | C2 | semidirect |
| 6. #10591637 | C2 | semidirect |
| 7. #10591006 | C2 | semidirect |
| 8. #10591001 | C2 | semidirect |
| 22. C3×D3×M16 | C22 | semidirect |
| 24. D3×#208 | C22 | semidirect |
| 28. C32×#101 | C22 | semidirect |
| 29. #63663 | C22 | semidirect |
| 30. #63651 | C22 | semidirect |
| 31. C3×#836 | C22 | semidirect |
| 32. C3×#823 | C22 | semidirect |
| 33. #63561 | C22 | semidirect |
| 34. #63558 | C22 | semidirect |
| 41. #4751 | D3 | semidirect |
| 117. D3×M16 | C2×D3 | semidirect |
| 122. C3×#101 | C2×D3 | semidirect |
| 126. #836 | C2×D3 | semidirect |
| 132. #823 | C2×D3 | semidirect |
| 296. #101 | D32 | semidirect |
| 371. C3⋊D3 | #413 | semidirect |
| 451. C32 | C2×#413 | semidirect |
| 522. C3 | D3×#413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64319 | 2 |
| D32×M16 | 2 |
| C3⋊D3×#101 | 2 |
| C3×#4751 | 2 |
| #10591639 | 2 |
| #10591637 | 2 |
| #10591006 | 2 |
| #10591001 | 2 |
| D3×#413 | 3 |