Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
11989 conjugacy classes of subgroups.
The subgroup lattice has 392 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C3×#1007 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10596689 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #10596688 | C2 | 1 | 16 | yes | maximal, complemented |
| 5 | #10596687 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | D3×#1007 | C2 | 1 | 16 | yes | maximal, complemented |
| 7 | #10596669 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | #87571 | — | 3 | 2 | no | maximal |
| 9 | C22×C32×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #64364 | C22 | 1 | 16 | yes | complemented |
| 11 | C2×#3832 | C22 | 1 | 4 | yes | complemented |
| 12 | C2×Q8×C3⋊D3 | C22 | 1 | 4 | yes | complemented |
| 13 | C2×#3828 | C22 | 1 | 6 | yes | complemented |
| 14 | C3×#1007 | C22 | 1 | 16 | yes | complemented |
| 15 | C3×#1007 | C22 | 1 | 16 | yes | complemented |
| 16 | C2×C3×#239 | C22 | 1 | 8 | yes | complemented |
| 17 | C2×C3×D3×Q8 | C22 | 1 | 8 | yes | complemented |
| 18 | C2×C3×#235 | C22 | 1 | 12 | yes | complemented |
| 19 | #64330 | C22 | 1 | 16 | yes | complemented |
| 20 | #64320 | C22 | 1 | 32 | yes | complemented |
| 21 | #64319 | C22 | 1 | 32 | yes | complemented |
| 22 | D3×#239 | C22 | 1 | 64 | yes | complemented |
| 23 | D32×Q8 | C22 | 1 | 32 | yes | complemented |
| 24 | #64316 | C22 | 1 | 32 | yes | complemented |
| 25 | #64315 | C22 | 1 | 64 | yes | complemented |
| 26 | #64308 | C22 | 1 | 24 | yes | complemented |
| 27 | #64307 | C22 | 1 | 48 | yes | complemented |
| 28 | #64306 | C22 | 1 | 48 | yes | complemented |
| 29 | D3×#235 | C22 | 1 | 96 | yes | complemented |
| 30 | #64298 | C22 | 1 | 24 | yes | complemented |
| 31 | #64297 | C22 | 1 | 48 | yes | complemented |
| 32 | C2×C3×2−1+4 | — | 3 | 2 | no | — |
| 33 | #5968 | — | 3 | 16 | no | — |
| 34 | #5968 | — | 3 | 16 | no | — |
| 35 | D3×2−1+4 | — | 3 | 16 | no | — |
| 36 | D3×2−1+4 | — | 3 | 16 | no | — |
| 37 | #5964 | — | 3 | 16 | no | — |
| 38 | #5964 | — | 3 | 24 | no | — |
| 39 | C2×#1007 | — | 3 | 2 | no | — |
| 40 | C2×#1007 | — | 3 | 16 | no | — |
| 41 | C2×#1007 | — | 6 | 1 | no | — |
| 42 | C2×#1007 | D3 | 1 | 2 | yes | complemented |
| 43 | C2×C32×Q8 | C23 | 1 | 8 | yes | — |
| 44 | C2×C32×Q8 | C23 | 1 | 4 | yes | — |
| 45 | C22×C32×C4 | C23 | 1 | 3 | yes | — |
| 46 | C2×#638 | C23 | 1 | 4 | yes | — |
| 47 | #3832 | C23 | 1 | 32 | yes | — |
| 48 | Q8×C3⋊D3 | C23 | 1 | 32 | yes | — |
| 49 | #3828 | C23 | 1 | 48 | yes | — |
| 50 | C2×C4⋊(C3⋊D3) | C23 | 1 | 6 | yes | — |
| 51 | C2×C4×C3⋊D3 | C23 | 1 | 12 | yes | — |
| 52 | C2×#634 | C23 | 1 | 6 | yes | — |
| 53 | C2×C3×#67 | C23 | 1 | 8 | yes | — |
| 54 | C3×#239 | C23 | 1 | 64 | yes | — |
| 55 | C3×D3×Q8 | C23 | 1 | 64 | yes | — |
| 56 | C3×#235 | C23 | 1 | 48 | yes | — |
| 57 | C3×#235 | C23 | 1 | 48 | yes | — |
| 58 | C2×C3×D12 | C23 | 1 | 12 | yes | — |
| 59 | C2×C3×C4×D3 | C23 | 1 | 24 | yes | — |
| 60 | C2×C3×Dic6 | C23 | 1 | 12 | yes | — |
| 61 | #3811 | C23 | 1 | 32 | yes | — |
| 62 | D3×#67 | C23 | 1 | 64 | yes | — |
| 63 | #3805 | C23 | 1 | 32 | yes | — |
| 64 | #3804 | C23 | 1 | 64 | yes | — |
| 65 | #3802 | C23 | 1 | 48 | yes | — |
| 66 | D3×D12 | C23 | 1 | 96 | yes | — |
| 67 | C4×D32 | C23 | 1 | 96 | yes | — |
| 68 | #3799 | C23 | 1 | 96 | yes | — |
| 69 | #3798 | C23 | 1 | 96 | yes | — |
| 70 | #3797 | C23 | 1 | 48 | yes | — |
| 71 | #3796 | C23 | 1 | 96 | yes | — |
| 72 | #3795 | C23 | 1 | 96 | yes | — |
| 73 | D3×Dic6 | C23 | 1 | 96 | yes | — |
| 74 | 2−1+6 | — | 9 | 1 | no | Sylow |
| 75 | C3×2−1+4 | — | 3 | 16 | no | — |
| 76 | C3×2−1+4 | — | 3 | 16 | no | — |
| 77 | C2×C3×#41 | — | 3 | 8 | no | — |
| 78 | C2×C3×#41 | — | 3 | 12 | no | — |
| 79 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 80 | C22×C3×Q8 | — | 3 | 8 | no | — |
| 81 | C22×C3×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 82 | #1010 | — | 3 | 64 | no | — |
| 83 | #1010 | — | 3 | 48 | no | — |
| 84 | #1010 | — | 3 | 48 | no | — |
| 85 | #1009 | — | 3 | 64 | no | — |
| 86 | #1009 | — | 3 | 48 | no | — |
| 87 | #1009 | — | 3 | 48 | no | — |
| 88 | D3×#41 | — | 3 | 64 | no | — |
| 89 | D3×#41 | — | 3 | 64 | no | — |
| 90 | D3×#41 | — | 3 | 96 | no | — |
| 91 | D3×#41 | — | 3 | 96 | no | — |
| 92 | #1007 | — | 3 | 16 | no | — |
| 93 | #1007 | — | 3 | 16 | no | — |
| 94 | #1007 | — | 3 | 64 | no | — |
| 95 | #1007 | — | 3 | 64 | no | — |
| 96 | #1007 | — | 3 | 48 | no | — |
| 97 | #1007 | — | 6 | 16 | no | — |
| 98 | #1007 | C2×D3 | 1 | 16 | yes | complemented |
| 99 | #1007 | C2×D3 | 1 | 16 | yes | complemented |
| 100 | C2×#239 | — | 3 | 8 | no | — |
| 101 | C2×#239 | — | 3 | 64 | no | — |
| 102 | C2×#239 | — | 6 | 4 | no | — |
| 103 | C2×#239 | C2×D3 | 1 | 8 | yes | complemented |
| 104 | C2×D3×Q8 | — | 3 | 8 | no | — |
| 105 | C2×D3×Q8 | — | 3 | 64 | no | — |
| 106 | C2×D3×Q8 | — | 6 | 4 | no | — |
| 107 | C2×D3×Q8 | C2×D3 | 1 | 8 | yes | complemented |
| 108 | #1004 | — | 3 | 32 | no | — |
| 109 | #1004 | — | 3 | 48 | no | — |
| 110 | C2×#235 | — | 3 | 12 | no | — |
| 111 | C2×#235 | — | 3 | 96 | no | — |
| 112 | C2×#235 | — | 6 | 6 | no | — |
| 113 | C2×#235 | C2×D3 | 1 | 12 | yes | complemented |
| 114 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 115 | C22×C3⋊D3 | C24 | 1 | 4 | yes | — |
| 116 | C22×C3×D3 | C24 | 1 | 8 | yes | — |
| 117 | C2×D32 | C24 | 1 | 32 | yes | — |
| 118 | C32×Q8 | C24 | 1 | 16 | yes | — |
| 119 | C2×C32×C4 | C24 | 1 | 12 | yes | — |
| 120 | C2×C32×C4 | C24 | 1 | 6 | yes | — |
| 121 | #638 | C24 | 1 | 16 | yes | — |
| 122 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 123 | C4⋊(C3⋊D3) | C24 | 1 | 24 | yes | — |
| 124 | C4×C3⋊D3 | C24 | 1 | 48 | yes | — |
| 125 | #634 | C24 | 1 | 24 | yes | — |
| 126 | C3×#67 | C24 | 1 | 16 | yes | — |
| 127 | C3×#67 | C24 | 1 | 16 | yes | — |
| 128 | C2×C3×Dic3 | C24 | 1 | 8 | yes | — |
| 129 | C3×D12 | C24 | 1 | 48 | yes | — |
| 130 | C3×C4×D3 | C24 | 1 | 96 | yes | — |
| 131 | C3×Dic6 | C24 | 1 | 48 | yes | — |
| 132 | #627 | C24 | 1 | 32 | yes | — |
| 133 | #626 | C24 | 1 | 64 | yes | — |
| 134 | #625 | C24 | 1 | 32 | yes | — |
| 135 | #624 | C24 | 1 | 32 | yes | — |
| 136 | D3×Dic3 | C24 | 1 | 64 | yes | — |
| 137 | #585 | — | 9 | 12 | no | — |
| 138 | #585 | — | 9 | 16 | no | — |
| 139 | #585 | — | 9 | 8 | no | — |
| 140 | C2×2−1+4 | — | 3 | 2 | no | — |
| 141 | C2×2−1+4 | — | 9 | 16 | no | — |
| 142 | C2×2−1+4 | — | 9 | 8 | no | — |
| 143 | C2×2−1+4 | — | 9 | 1 | no | — |
| 144 | C3×#41 | — | 3 | 64 | no | — |
| 145 | C3×#41 | — | 3 | 48 | no | — |
| 146 | C3×#41 | — | 3 | 48 | no | — |
| 147 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 148 | C2×C3×Q8 | — | 2 | 8 | no | — |
| 149 | C2×C3×Q8 | — | 3 | 64 | no | — |
| 150 | C2×C3×Q8 | — | 3 | 12 | no | — |
| 151 | C2×C3×Q8 | C22×D3 | 1 | 8 | yes | — |
| 152 | C2×C3×Q8 | C22×D3 | 1 | 8 | yes | — |
| 153 | C2×C3×Q8 | C22×D3 | 1 | 8 | yes | — |
| 154 | C2×C3×D4 | — | 3 | 8 | no | — |
| 155 | C2×C3×D4 | — | 3 | 12 | no | — |
| 156 | C22×C3×C4 | — | 2 | 3 | no | — |
| 157 | C22×C3×C4 | — | 3 | 24 | no | — |
| 158 | C22×C3×C4 | C22×D3 | 1 | 6 | yes | — |
| 159 | C2×#67 | — | 3 | 8 | no | — |
| 160 | C2×#67 | — | 3 | 64 | no | — |
| 161 | C2×#67 | — | 6 | 4 | no | — |
| 162 | C2×#67 | C22×D3 | 1 | 8 | yes | — |
| 163 | #239 | — | 3 | 64 | no | — |
| 164 | #239 | — | 3 | 96 | no | — |
| 165 | #239 | — | 3 | 96 | no | — |
| 166 | #239 | — | 6 | 32 | no | — |
| 167 | #239 | C22×D3 | 1 | 64 | yes | — |
| 168 | D3×Q8 | — | 3 | 64 | no | — |
| 169 | D3×Q8 | — | 3 | 96 | no | — |
| 170 | D3×Q8 | — | 3 | 96 | no | — |
| 171 | D3×Q8 | — | 6 | 32 | no | — |
| 172 | D3×Q8 | C22×D3 | 1 | 64 | yes | — |
| 173 | #237 | — | 3 | 64 | no | — |
| 174 | #237 | — | 3 | 64 | no | — |
| 175 | #237 | — | 3 | 96 | no | — |
| 176 | #237 | — | 3 | 96 | no | — |
| 177 | D3×D4 | — | 3 | 64 | no | — |
| 178 | D3×D4 | — | 3 | 64 | no | — |
| 179 | D3×D4 | — | 3 | 96 | no | — |
| 180 | D3×D4 | — | 3 | 96 | no | — |
| 181 | #235 | — | 3 | 48 | no | — |
| 182 | #235 | — | 3 | 48 | no | — |
| 183 | #235 | — | 3 | 64 | no | — |
| 184 | #235 | — | 3 | 96 | no | — |
| 185 | #235 | — | 3 | 192 | no | — |
| 186 | #235 | — | 3 | 96 | no | — |
| 187 | #235 | — | 6 | 48 | no | — |
| 188 | #235 | C22×D3 | 1 | 48 | yes | — |
| 189 | #235 | C22×D3 | 1 | 48 | yes | — |
| 190 | C2×D12 | — | 3 | 12 | no | — |
| 191 | C2×D12 | — | 3 | 96 | no | — |
| 192 | C2×D12 | — | 6 | 6 | no | — |
| 193 | C2×D12 | C22×D3 | 1 | 12 | yes | — |
| 194 | C2×C4×D3 | — | 3 | 24 | no | — |
| 195 | C2×C4×D3 | — | 3 | 192 | no | — |
| 196 | C2×C4×D3 | — | 6 | 12 | no | — |
| 197 | C2×C4×D3 | C22×D3 | 1 | 24 | yes | — |
| 198 | C2×Dic6 | — | 3 | 12 | no | — |
| 199 | C2×Dic6 | — | 3 | 96 | no | — |
| 200 | C2×Dic6 | — | 6 | 6 | no | — |
| 201 | C2×Dic6 | C22×D3 | 1 | 12 | yes | — |
| 202 | C22×C32 | — | 4 | 1 | no | — |
| 203 | C22×C32 | C25 | 1 | 2 | yes | — |
| 204 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 205 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 206 | C2×C3⋊D3 | C25 | 1 | 8 | yes | — |
| 207 | C2×C3×D3 | — | 4 | 8 | no | — |
| 208 | C2×C3×D3 | C25 | 1 | 16 | yes | — |
| 209 | D32 | — | 4 | 32 | no | — |
| 210 | C32×C4 | C25 | 1 | 12 | yes | — |
| 211 | C3⋊Dic3 | C25 | 1 | 8 | yes | — |
| 212 | C3×Dic3 | C25 | 1 | 16 | yes | — |
| 213 | 2−1+4 | — | 3 | 16 | no | — |
| 214 | 2−1+4 | — | 3 | 16 | no | — |
| 215 | 2−1+4 | — | 9 | 32 | no | — |
| 216 | 2−1+4 | — | 9 | 64 | no | — |
| 217 | 2−1+4 | — | 9 | 48 | no | — |
| 218 | 2−1+4 | — | 9 | 24 | no | — |
| 219 | 2−1+4 | — | 9 | 16 | no | — |
| 220 | H(5,𝔽2) | — | 9 | 16 | no | — |
| 221 | H(5,𝔽2) | — | 9 | 48 | no | — |
| 222 | H(5,𝔽2) | — | 9 | 32 | no | — |
| 223 | H(5,𝔽2) | — | 9 | 24 | no | — |
| 224 | C2×#41 | — | 3 | 8 | no | — |
| 225 | C2×#41 | — | 3 | 12 | no | — |
| 226 | C2×#41 | — | 9 | 96 | no | — |
| 227 | C2×#41 | — | 9 | 64 | no | — |
| 228 | C2×#41 | — | 9 | 32 | no | — |
| 229 | C2×#41 | — | 9 | 48 | no | — |
| 230 | C2×#41 | — | 9 | 4 | no | — |
| 231 | C2×#41 | — | 9 | 6 | no | — |
| 232 | C22×Q8 | — | 3 | 8 | no | — |
| 233 | C22×Q8 | — | 9 | 32 | no | — |
| 234 | C22×Q8 | — | 9 | 4 | no | — |
| 235 | C22×Q8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 236 | C23×C3 | — | 2 | 1 | no | — |
| 237 | C23×C3 | — | 3 | 8 | no | — |
| 238 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 239 | C22×D3 | — | 3 | 8 | no | — |
| 240 | C22×D3 | — | 3 | 64 | no | — |
| 241 | C22×D3 | — | 6 | 4 | no | — |
| 242 | C22×D3 | C23×D3 | 1 | 8 | yes | — |
| 243 | C3×Q8 | — | 2 | 16 | no | — |
| 244 | C3×Q8 | — | 3 | 48 | no | — |
| 245 | C3×Q8 | C23×D3 | 1 | 32 | yes | — |
| 246 | C3×D4 | — | 3 | 16 | no | — |
| 247 | C3×D4 | — | 3 | 16 | no | — |
| 248 | C3×D4 | — | 3 | 48 | no | — |
| 249 | C2×C3×C4 | — | 2 | 6 | no | — |
| 250 | C2×C3×C4 | — | 2 | 12 | no | — |
| 251 | C2×C3×C4 | — | 3 | 8 | no | — |
| 252 | C2×C3×C4 | — | 3 | 96 | no | — |
| 253 | C2×C3×C4 | C23×D3 | 1 | 12 | yes | — |
| 254 | C2×C3×C4 | C23×D3 | 1 | 12 | yes | — |
| 255 | C2×C3×C4 | C23×D3 | 1 | 12 | yes | — |
| 256 | #67 | — | 3 | 16 | no | — |
| 257 | #67 | — | 3 | 16 | no | — |
| 258 | #67 | — | 3 | 64 | no | — |
| 259 | #67 | — | 3 | 64 | no | — |
| 260 | #67 | — | 6 | 16 | no | — |
| 261 | #67 | C23×D3 | 1 | 16 | yes | — |
| 262 | #67 | C23×D3 | 1 | 16 | yes | — |
| 263 | C2×Dic3 | — | 3 | 8 | no | — |
| 264 | C2×Dic3 | — | 3 | 64 | no | — |
| 265 | C2×Dic3 | — | 6 | 4 | no | — |
| 266 | C2×Dic3 | C23×D3 | 1 | 8 | yes | — |
| 267 | D12 | — | 3 | 64 | no | — |
| 268 | D12 | — | 3 | 48 | no | — |
| 269 | D12 | — | 6 | 24 | no | — |
| 270 | D12 | C23×D3 | 1 | 48 | yes | — |
| 271 | C4×D3 | — | 3 | 64 | no | — |
| 272 | C4×D3 | — | 3 | 96 | no | — |
| 273 | C4×D3 | — | 3 | 64 | no | — |
| 274 | C4×D3 | — | 6 | 48 | no | — |
| 275 | C4×D3 | C23×D3 | 1 | 96 | yes | — |
| 276 | Dic6 | — | 3 | 48 | no | — |
| 277 | Dic6 | — | 3 | 64 | no | — |
| 278 | Dic6 | — | 6 | 24 | no | — |
| 279 | Dic6 | C23×D3 | 1 | 48 | yes | — |
| 280 | C2×C32 | — | 2 | 1 | no | — |
| 281 | C2×C32 | — | 2 | 2 | no | — |
| 282 | C2×C32 | C26 | 1 | 1 | yes | characteristic |
| 283 | C3⋊D3 | — | 2 | 8 | no | — |
| 284 | C3×D3 | — | 2 | 16 | no | — |
| 285 | #41 | — | 3 | 64 | no | — |
| 286 | #41 | — | 3 | 48 | no | — |
| 287 | #41 | — | 3 | 48 | no | — |
| 288 | #41 | — | 9 | 96 | no | — |
| 289 | #41 | — | 9 | 64 | no | — |
| 290 | #41 | — | 9 | 96 | no | — |
| 291 | #41 | — | 9 | 96 | no | — |
| 292 | #41 | — | 9 | 32 | no | — |
| 293 | #41 | — | 9 | 96 | no | — |
| 294 | #41 | — | 9 | 32 | no | — |
| 295 | #41 | — | 9 | 48 | no | — |
| 296 | C2×Q8 | — | 3 | 64 | no | — |
| 297 | C2×Q8 | — | 3 | 12 | no | — |
| 298 | C2×Q8 | — | 9 | 96 | no | — |
| 299 | C2×Q8 | — | 9 | 48 | no | — |
| 300 | C2×Q8 | — | 9 | 32 | no | — |
| 301 | C2×Q8 | — | 9 | 6 | no | — |
| 302 | C2×Q8 | C2×D32 | 1 | 8 | yes | — |
| 303 | C2×Q8 | C2×D32 | 1 | 4 | yes | — |
| 304 | C2×D4 | — | 3 | 8 | no | — |
| 305 | C2×D4 | — | 3 | 12 | no | — |
| 306 | C2×D4 | — | 9 | 96 | no | — |
| 307 | C2×D4 | — | 9 | 32 | no | — |
| 308 | C2×D4 | — | 9 | 48 | no | — |
| 309 | C2×D4 | — | 9 | 64 | no | — |
| 310 | C2×D4 | — | 9 | 4 | no | — |
| 311 | C2×D4 | — | 9 | 6 | no | — |
| 312 | C22×C4 | — | 3 | 24 | no | — |
| 313 | C22×C4 | — | 9 | 96 | no | — |
| 314 | C22×C4 | — | 9 | 12 | no | — |
| 315 | C22×C4 | C2×D32 | 1 | 3 | yes | — |
| 316 | C22×C3 | — | 2 | 1 | no | — |
| 317 | C22×C3 | — | 2 | 2 | no | — |
| 318 | C22×C3 | — | 3 | 16 | no | — |
| 319 | C22×C3 | — | 4 | 2 | no | — |
| 320 | C22×C3 | — | 4 | 2 | no | — |
| 321 | C22×C3 | — | 12 | 8 | no | — |
| 322 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 323 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 324 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 325 | C2×D3 | — | 3 | 16 | no | — |
| 326 | C2×D3 | — | 4 | 8 | no | — |
| 327 | C2×D3 | — | 6 | 8 | no | — |
| 328 | C2×D3 | — | 12 | 64 | no | — |
| 329 | C2×D3 | — | 12 | 8 | no | — |
| 330 | C2×D3 | — | 12 | 8 | no | — |
| 331 | C2×D3 | C24×D3 | 1 | 16 | yes | — |
| 332 | C3×C4 | — | 2 | 12 | no | — |
| 333 | C3×C4 | — | 3 | 16 | no | — |
| 334 | C3×C4 | C24×D3 | 1 | 24 | yes | — |
| 335 | Dic3 | — | 3 | 16 | no | — |
| 336 | Dic3 | — | 6 | 8 | no | — |
| 337 | Dic3 | C24×D3 | 1 | 16 | yes | — |
| 338 | C32 | 2−1+6 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 339 | C23 | — | 3 | 8 | no | — |
| 340 | C23 | — | 9 | 32 | no | — |
| 341 | C23 | — | 9 | 4 | no | — |
| 342 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 343 | Q8 | — | 3 | 48 | no | — |
| 344 | Q8 | — | 9 | 32 | no | — |
| 345 | Q8 | — | 9 | 24 | no | — |
| 346 | Q8 | C22×D32 | 1 | 16 | yes | — |
| 347 | D4 | — | 3 | 16 | no | — |
| 348 | D4 | — | 3 | 16 | no | — |
| 349 | D4 | — | 3 | 48 | no | — |
| 350 | D4 | — | 9 | 64 | no | — |
| 351 | D4 | — | 9 | 32 | no | — |
| 352 | D4 | — | 9 | 16 | no | — |
| 353 | D4 | — | 9 | 24 | no | — |
| 354 | C2×C4 | — | 3 | 8 | no | — |
| 355 | C2×C4 | — | 3 | 96 | no | — |
| 356 | C2×C4 | — | 9 | 32 | no | — |
| 357 | C2×C4 | — | 9 | 64 | no | — |
| 358 | C2×C4 | — | 9 | 4 | no | — |
| 359 | C2×C4 | — | 9 | 48 | no | — |
| 360 | C2×C4 | C22×D32 | 1 | 12 | yes | — |
| 361 | C2×C4 | C22×D32 | 1 | 6 | yes | — |
| 362 | C2×C3 | — | 2 | 2 | no | — |
| 363 | C2×C3 | — | 2 | 2 | no | — |
| 364 | C2×C3 | — | 2 | 2 | no | — |
| 365 | C2×C3 | — | 2 | 2 | no | — |
| 366 | C2×C3 | — | 2 | 1 | no | — |
| 367 | C2×C3 | — | 4 | 2 | no | — |
| 368 | C2×C3 | — | 6 | 16 | no | — |
| 369 | C2×C3 | C25×D3 | 1 | 2 | yes | — |
| 370 | D3 | — | 2 | 16 | no | — |
| 371 | D3 | — | 6 | 16 | no | — |
| 372 | D3 | — | 12 | 8 | no | — |
| 373 | C22 | — | 3 | 16 | no | — |
| 374 | C22 | — | 4 | 1 | no | — |
| 375 | C22 | — | 9 | 8 | no | — |
| 376 | C22 | — | 12 | 8 | no | — |
| 377 | C22 | — | 36 | 4 | no | — |
| 378 | C22 | — | 36 | 32 | no | — |
| 379 | C22 | C23×D32 | 1 | 2 | yes | — |
| 380 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 381 | C4 | — | 3 | 16 | no | — |
| 382 | C4 | — | 9 | 8 | no | — |
| 383 | C4 | C23×D32 | 1 | 12 | yes | — |
| 384 | C3 | — | 2 | 1 | no | — |
| 385 | C3 | #87571 | 1 | 2 | yes | complemented |
| 386 | C2 | — | 2 | 2 | no | — |
| 387 | C2 | — | 2 | 1 | no | — |
| 388 | C2 | — | 6 | 16 | no | — |
| 389 | C2 | — | 18 | 8 | no | — |
| 390 | C2 | C24×D32 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D32 |
| commutator, socle, cosocle | C2×C32 | C26 |
| Fitting | C22×C32×Q8 | C22 |
| hypercenter | C22×Q8 | D32 |
| hypocenter | C32 | 2−1+6 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64364 | C2 | semidirect |
| 2. C2×C3×#1007 | C2 | semidirect |
| 3. #10596689 | C2 | semidirect |
| 4. #10596688 | C2 | semidirect |
| 5. #10596687 | C2 | semidirect |
| 6. D3×#1007 | C2 | semidirect |
| 7. #10596669 | C2 | semidirect |
| 9. C22×C32×Q8 | C22 | semidirect |
| 10. #64364 | C22 | semidirect |
| 11. C2×#3832 | C22 | semidirect |
| 12. C2×Q8×C3⋊D3 | C22 | semidirect |
| 13. C2×#3828 | C22 | semidirect |
| 14. C3×#1007 | C22 | semidirect |
| 15. C3×#1007 | C22 | semidirect |
| 16. C2×C3×#239 | C22 | semidirect |
| 17. C2×C3×D3×Q8 | C22 | semidirect |
| 18. C2×C3×#235 | C22 | semidirect |
| 19. #64330 | C22 | semidirect |
| 20. #64320 | C22 | semidirect |
| 21. #64319 | C22 | semidirect |
| 22. D3×#239 | C22 | semidirect |
| 23. D32×Q8 | C22 | semidirect |
| 24. #64316 | C22 | semidirect |
| 25. #64315 | C22 | semidirect |
| 26. #64308 | C22 | semidirect |
| 27. #64307 | C22 | semidirect |
| 28. #64306 | C22 | semidirect |
| 29. D3×#235 | C22 | semidirect |
| 30. #64298 | C22 | semidirect |
| 31. #64297 | C22 | semidirect |
| 42. C2×#1007 | D3 | semidirect |
| 81. C22×C3×Q8 | C2×D3 | semidirect |
| 98. #1007 | C2×D3 | semidirect |
| 99. #1007 | C2×D3 | semidirect |
| 103. C2×#239 | C2×D3 | semidirect |
| 107. C2×D3×Q8 | C2×D3 | semidirect |
| 113. C2×#235 | C2×D3 | semidirect |
| 235. C22×Q8 | D32 | semidirect |
| 338. C32 | 2−1+6 | semidirect |
| 385. C3 | #87571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64364 | 2 |
| C2×C3×#1007 | 2 |
| #10596689 | 2 |
| #10596688 | 2 |
| #10596687 | 2 |
| D3×#1007 | 2 |
| #10596669 | 2 |
| #87571 | 3 |