Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2981 conjugacy classes of subgroups.
The subgroup lattice has 520 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596669 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#64116 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5748 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#63822 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10594723 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10594720 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10594719 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #10594685 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10594684 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #87199 | — | 3 | 2 | no | maximal |
| 11 | C2×#3828 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×#235 | C22 | 1 | 4 | yes | complemented |
| 13 | #64330 | — | 2 | 4 | no | — |
| 14 | #64308 | — | 2 | 2 | no | — |
| 15 | #64307 | C22 | 1 | 8 | yes | complemented |
| 16 | #64306 | C22 | 1 | 8 | yes | complemented |
| 17 | D3×#235 | — | 2 | 8 | no | — |
| 18 | #64298 | — | 2 | 2 | no | — |
| 19 | #64297 | C22 | 1 | 8 | yes | complemented |
| 20 | C2×C32×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C22×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #64116 | C22 | 1 | 4 | yes | complemented |
| 23 | #64116 | C22 | 1 | 4 | yes | complemented |
| 24 | C2×#3743 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×C8×C3⋊D3 | C22 | 1 | 2 | yes | complemented |
| 26 | C3×#909 | C22 | 1 | 8 | yes | complemented |
| 27 | C3×#908 | C22 | 1 | 8 | yes | complemented |
| 28 | C3×#904 | C22 | 1 | 8 | yes | complemented |
| 29 | C2×#3718 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×#3715 | C22 | 1 | 4 | yes | complemented |
| 31 | #63822 | C22 | 1 | 4 | yes | complemented |
| 32 | #63822 | C22 | 1 | 4 | yes | complemented |
| 33 | #63822 | C22 | 1 | 4 | yes | complemented |
| 34 | #63822 | C22 | 1 | 4 | yes | complemented |
| 35 | C2×#3713 | C22 | 1 | 2 | yes | complemented |
| 36 | #63811 | C22 | 1 | 16 | yes | complemented |
| 37 | #63810 | C22 | 1 | 8 | yes | complemented |
| 38 | #63809 | C22 | 1 | 8 | yes | complemented |
| 39 | #63802 | C22 | 1 | 4 | yes | complemented |
| 40 | #63798 | C22 | 1 | 16 | yes | complemented |
| 41 | #63797 | C22 | 1 | 4 | yes | complemented |
| 42 | #63796 | C22 | 1 | 8 | yes | complemented |
| 43 | #5964 | — | 3 | 4 | no | — |
| 44 | C3×#575 | — | 3 | 2 | no | — |
| 45 | C2×#950 | — | 3 | 4 | no | — |
| 46 | #5779 | — | 3 | 8 | no | — |
| 47 | #5778 | — | 3 | 8 | no | — |
| 48 | #5775 | — | 3 | 8 | no | — |
| 49 | #5774 | — | 3 | 8 | no | — |
| 50 | #5768 | — | 3 | 8 | no | — |
| 51 | D3×#135 | — | 3 | 8 | no | — |
| 52 | #5748 | D3 | 1 | 2 | yes | complemented |
| 53 | C2×#907 | — | 3 | 2 | no | — |
| 54 | C2×#907 | — | 6 | 1 | no | — |
| 55 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#638 | D4 | 1 | 2 | yes | — |
| 57 | #3828 | D4 | 1 | 4 | yes | — |
| 58 | #3828 | C23 | 1 | 4 | yes | — |
| 59 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 61 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×C3×#67 | — | 2 | 4 | no | — |
| 63 | C3×#235 | — | 2 | 4 | no | — |
| 64 | C3×#235 | — | 2 | 4 | no | — |
| 65 | C3×#235 | C23 | 1 | 8 | yes | — |
| 66 | C3×#235 | C23 | 1 | 8 | yes | — |
| 67 | C2×C3×D12 | C23 | 1 | 4 | yes | — |
| 68 | C2×C3×C4×D3 | — | 2 | 4 | no | — |
| 69 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 70 | #3811 | — | 2 | 8 | no | — |
| 71 | D3×#67 | — | 2 | 16 | no | — |
| 72 | #3805 | — | 2 | 8 | no | — |
| 73 | #3804 | — | 2 | 16 | no | — |
| 74 | #3802 | C23 | 1 | 8 | yes | — |
| 75 | D3×D12 | — | 2 | 8 | no | — |
| 76 | C4×D32 | — | 2 | 8 | no | — |
| 77 | #3799 | — | 2 | 8 | no | — |
| 78 | #3798 | — | 2 | 8 | no | — |
| 79 | #3797 | C23 | 1 | 8 | yes | — |
| 80 | #3796 | C23 | 1 | 16 | yes | — |
| 81 | #3795 | — | 2 | 8 | no | — |
| 82 | D3×Dic6 | — | 2 | 8 | no | — |
| 83 | C32×M16 | C23 | 1 | 4 | yes | — |
| 84 | C2×C32×C8 | C23 | 1 | 2 | yes | — |
| 85 | C2×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 86 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 89 | #3743 | C23 | 1 | 8 | yes | — |
| 90 | C8×C3⋊D3 | C23 | 1 | 4 | yes | — |
| 91 | C8×C3⋊D3 | C23 | 1 | 4 | yes | — |
| 92 | C3×Dic12 | C23 | 1 | 8 | yes | — |
| 93 | C3×D24 | C23 | 1 | 8 | yes | — |
| 94 | C3×#204 | C23 | 1 | 16 | yes | — |
| 95 | #3718 | C23 | 1 | 4 | yes | — |
| 96 | #3718 | C23 | 1 | 4 | yes | — |
| 97 | #3715 | C23 | 1 | 8 | yes | — |
| 98 | #3715 | C23 | 1 | 8 | yes | — |
| 99 | #3713 | C23 | 1 | 4 | yes | — |
| 100 | #3713 | C23 | 1 | 4 | yes | — |
| 101 | #3584 | — | 9 | 1 | no | Sylow |
| 102 | C2×C3×#41 | — | 3 | 4 | no | — |
| 103 | #1010 | — | 3 | 8 | no | — |
| 104 | #1010 | — | 6 | 4 | no | — |
| 105 | #1009 | — | 3 | 8 | no | — |
| 106 | #1009 | — | 6 | 4 | no | — |
| 107 | D3×#41 | — | 3 | 16 | no | — |
| 108 | D3×#41 | — | 6 | 8 | no | — |
| 109 | #1007 | — | 3 | 8 | no | — |
| 110 | #1004 | — | 3 | 8 | no | — |
| 111 | #1004 | — | 6 | 8 | no | — |
| 112 | C2×#235 | — | 3 | 2 | no | — |
| 113 | C2×#235 | — | 6 | 1 | no | — |
| 114 | C2×#235 | — | 6 | 8 | no | — |
| 115 | C2×#235 | C2×D3 | 1 | 4 | yes | complemented |
| 116 | C3×#137 | — | 3 | 8 | no | — |
| 117 | C3×AGL(1,ℤ/8) | — | 3 | 8 | no | — |
| 118 | C3×#135 | — | 3 | 8 | no | — |
| 119 | C2×C3×M16 | — | 2 | 1 | no | — |
| 120 | C2×C3×M16 | C2×D3 | 1 | 2 | yes | complemented |
| 121 | #950 | — | 3 | 8 | no | — |
| 122 | #950 | — | 3 | 8 | no | — |
| 123 | #950 | — | 3 | 8 | no | — |
| 124 | #950 | — | 3 | 8 | no | — |
| 125 | C2×#216 | — | 3 | 4 | no | — |
| 126 | C2×#215 | — | 3 | 4 | no | — |
| 127 | C2×#214 | — | 3 | 4 | no | — |
| 128 | C2×#213 | — | 3 | 4 | no | — |
| 129 | C22×C3⋊C8 | — | 3 | 2 | no | — |
| 130 | C22×C3⋊C8 | — | 6 | 1 | no | — |
| 131 | #919 | — | 3 | 8 | no | — |
| 132 | #918 | — | 3 | 16 | no | — |
| 133 | D3×Q16 | — | 3 | 8 | no | — |
| 134 | #916 | — | 3 | 16 | no | — |
| 135 | #915 | — | 3 | 16 | no | — |
| 136 | #914 | — | 3 | 16 | no | — |
| 137 | D3×SD16 | — | 3 | 16 | no | — |
| 138 | #912 | — | 3 | 8 | no | — |
| 139 | #911 | — | 3 | 16 | no | — |
| 140 | D3×D8 | — | 3 | 8 | no | — |
| 141 | #909 | C2×D3 | 1 | 8 | yes | complemented |
| 142 | #908 | C2×D3 | 1 | 8 | yes | complemented |
| 143 | #907 | — | 3 | 8 | no | — |
| 144 | #907 | — | 3 | 8 | no | — |
| 145 | #907 | — | 6 | 4 | no | — |
| 146 | #907 | — | 6 | 4 | no | — |
| 147 | #904 | C2×D3 | 1 | 8 | yes | complemented |
| 148 | C2×ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 149 | C2×ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 150 | C2×D3×C8 | — | 3 | 4 | no | — |
| 151 | C2×D3×C8 | — | 6 | 2 | no | — |
| 152 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C22×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 154 | C22×C3×D3 | — | 2 | 4 | no | — |
| 155 | C2×D32 | — | 2 | 8 | no | — |
| 156 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 157 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 159 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 160 | #638 | C2×D4 | 1 | 8 | yes | — |
| 161 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 162 | C4⋊(C3⋊D3) | C2×D4 | 1 | 4 | yes | — |
| 163 | C4×C3⋊D3 | C2×D4 | 1 | 4 | yes | — |
| 164 | C4×C3⋊D3 | C24 | 1 | 4 | yes | — |
| 165 | #634 | C2×D4 | 1 | 4 | yes | — |
| 166 | C3×#67 | — | 2 | 8 | no | — |
| 167 | C3×#67 | — | 2 | 8 | no | — |
| 168 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 169 | C3×D12 | — | 2 | 4 | no | — |
| 170 | C3×D12 | C24 | 1 | 8 | yes | — |
| 171 | C3×C4×D3 | — | 2 | 8 | no | — |
| 172 | C3×C4×D3 | — | 2 | 8 | no | — |
| 173 | C3×Dic6 | — | 2 | 4 | no | — |
| 174 | C3×Dic6 | C24 | 1 | 8 | yes | — |
| 175 | #627 | — | 2 | 8 | no | — |
| 176 | #626 | — | 2 | 16 | no | — |
| 177 | #625 | — | 2 | 8 | no | — |
| 178 | #624 | — | 2 | 8 | no | — |
| 179 | D3×Dic3 | — | 2 | 16 | no | — |
| 180 | C32×C8 | C24 | 1 | 4 | yes | — |
| 181 | C3⋊(C3⋊C8) | C24 | 1 | 1 | yes | characteristic |
| 182 | C3⋊(C3⋊C8) | C24 | 1 | 2 | yes | — |
| 183 | C3⋊(C3⋊C8) | C24 | 1 | 1 | yes | characteristic |
| 184 | #585 | — | 9 | 2 | no | — |
| 185 | #578 | — | 9 | 4 | no | — |
| 186 | #577 | — | 9 | 8 | no | — |
| 187 | #576 | — | 9 | 4 | no | — |
| 188 | #575 | — | 3 | 2 | no | — |
| 189 | #575 | — | 9 | 4 | no | — |
| 190 | C2×#135 | — | 9 | 4 | no | — |
| 191 | C2×#135 | — | 9 | 2 | no | — |
| 192 | C2×#131 | — | 9 | 1 | no | — |
| 193 | C3×#41 | — | 3 | 8 | no | — |
| 194 | C3×#41 | — | 3 | 8 | no | — |
| 195 | C3×#41 | — | 6 | 4 | no | — |
| 196 | C3×#41 | — | 6 | 4 | no | — |
| 197 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 198 | C2×C3×D4 | — | 3 | 4 | no | — |
| 199 | C2×C3×D4 | — | 6 | 4 | no | — |
| 200 | C22×C3×C4 | — | 2 | 1 | no | — |
| 201 | C22×C3×C4 | — | 6 | 4 | no | — |
| 202 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 203 | C2×#67 | — | 2 | 4 | no | — |
| 204 | C2×#67 | — | 3 | 4 | no | — |
| 205 | C2×#67 | — | 6 | 2 | no | — |
| 206 | C2×#67 | — | 6 | 16 | no | — |
| 207 | #239 | — | 3 | 16 | no | — |
| 208 | #239 | — | 6 | 8 | no | — |
| 209 | D3×Q8 | — | 3 | 16 | no | — |
| 210 | D3×Q8 | — | 6 | 8 | no | — |
| 211 | #237 | — | 3 | 16 | no | — |
| 212 | #237 | — | 6 | 8 | no | — |
| 213 | #237 | — | 6 | 16 | no | — |
| 214 | #237 | — | 6 | 16 | no | — |
| 215 | D3×D4 | — | 3 | 16 | no | — |
| 216 | D3×D4 | — | 6 | 8 | no | — |
| 217 | D3×D4 | — | 6 | 16 | no | — |
| 218 | D3×D4 | — | 6 | 16 | no | — |
| 219 | #235 | — | 2 | 4 | no | — |
| 220 | #235 | — | 2 | 4 | no | — |
| 221 | #235 | — | 3 | 8 | no | — |
| 222 | #235 | — | 3 | 8 | no | — |
| 223 | #235 | — | 6 | 4 | no | — |
| 224 | #235 | — | 6 | 4 | no | — |
| 225 | #235 | — | 6 | 8 | no | — |
| 226 | #235 | — | 6 | 8 | no | — |
| 227 | #235 | — | 6 | 16 | no | — |
| 228 | #235 | — | 6 | 16 | no | — |
| 229 | #235 | C22×D3 | 1 | 8 | yes | — |
| 230 | #235 | C22×D3 | 1 | 8 | yes | — |
| 231 | C2×D12 | — | 3 | 2 | no | — |
| 232 | C2×D12 | — | 6 | 1 | no | — |
| 233 | C2×D12 | — | 6 | 8 | no | — |
| 234 | C2×D12 | C22×D3 | 1 | 4 | yes | — |
| 235 | C2×C4×D3 | — | 2 | 4 | no | — |
| 236 | C2×C4×D3 | — | 3 | 4 | no | — |
| 237 | C2×C4×D3 | — | 6 | 2 | no | — |
| 238 | C2×C4×D3 | — | 6 | 16 | no | — |
| 239 | C2×Dic6 | — | 3 | 2 | no | — |
| 240 | C2×Dic6 | — | 6 | 1 | no | — |
| 241 | C2×Dic6 | — | 6 | 8 | no | — |
| 242 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 243 | C3×Q16 | — | 3 | 8 | no | — |
| 244 | C3×SD16 | — | 3 | 16 | no | — |
| 245 | C3×D8 | — | 3 | 8 | no | — |
| 246 | C3×M16 | — | 2 | 4 | no | — |
| 247 | C3×M16 | C22×D3 | 1 | 8 | yes | — |
| 248 | C2×C3×C8 | — | 2 | 2 | no | — |
| 249 | C2×C3×C8 | C22×D3 | 1 | 4 | yes | — |
| 250 | #216 | — | 3 | 8 | no | — |
| 251 | #216 | — | 3 | 8 | no | — |
| 252 | #215 | — | 3 | 8 | no | — |
| 253 | #215 | — | 3 | 8 | no | — |
| 254 | #214 | — | 3 | 8 | no | — |
| 255 | #214 | — | 3 | 8 | no | — |
| 256 | #213 | — | 3 | 8 | no | — |
| 257 | #213 | — | 3 | 8 | no | — |
| 258 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 259 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 260 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 261 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 262 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 263 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 264 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 265 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 266 | Dic12 | C22×D3 | 1 | 8 | yes | — |
| 267 | D24 | C22×D3 | 1 | 8 | yes | — |
| 268 | #204 | C22×D3 | 1 | 16 | yes | — |
| 269 | ΓL(1,𝔽25) | — | 3 | 16 | no | — |
| 270 | ΓL(1,𝔽25) | — | 6 | 8 | no | — |
| 271 | D3×C8 | — | 3 | 8 | no | — |
| 272 | D3×C8 | — | 3 | 8 | no | — |
| 273 | D3×C8 | — | 6 | 4 | no | — |
| 274 | D3×C8 | — | 6 | 4 | no | — |
| 275 | C22×C32 | — | 4 | 1 | no | — |
| 276 | C22×C32 | C22×D4 | 1 | 2 | yes | — |
| 277 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 278 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 279 | C2×C3⋊D3 | C22×D4 | 1 | 4 | yes | — |
| 280 | C2×C3×D3 | — | 2 | 8 | no | — |
| 281 | C2×C3×D3 | — | 8 | 4 | no | — |
| 282 | D32 | — | 8 | 8 | no | — |
| 283 | C32×C4 | C22×D4 | 1 | 2 | yes | — |
| 284 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 285 | C32×C4 | C25 | 1 | 1 | yes | characteristic |
| 286 | C3⋊Dic3 | C22×D4 | 1 | 4 | yes | — |
| 287 | C3×Dic3 | — | 2 | 8 | no | — |
| 288 | 2−1+4 | — | 9 | 8 | no | — |
| 289 | 2−1+4 | — | 18 | 2 | no | — |
| 290 | H(5,𝔽2) | — | 9 | 8 | no | — |
| 291 | H(5,𝔽2) | — | 18 | 4 | no | — |
| 292 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 293 | C2×#41 | — | 3 | 4 | no | — |
| 294 | C2×#41 | — | 9 | 1 | no | — |
| 295 | C2×#41 | — | 9 | 8 | no | — |
| 296 | C2×#41 | — | 18 | 8 | no | — |
| 297 | #137 | — | 3 | 8 | no | — |
| 298 | #137 | — | 9 | 16 | no | — |
| 299 | AGL(1,ℤ/8) | — | 3 | 8 | no | — |
| 300 | AGL(1,ℤ/8) | — | 9 | 16 | no | — |
| 301 | #135 | — | 3 | 8 | no | — |
| 302 | #135 | — | 9 | 8 | no | — |
| 303 | #135 | — | 9 | 8 | no | — |
| 304 | #135 | — | 9 | 4 | no | — |
| 305 | #135 | — | 9 | 4 | no | — |
| 306 | #135 | — | 9 | 4 | no | — |
| 307 | #135 | — | 9 | 4 | no | — |
| 308 | C2×Q16 | — | 9 | 4 | no | — |
| 309 | C2×Q16 | — | 9 | 2 | no | — |
| 310 | C2×SD16 | — | 9 | 8 | no | — |
| 311 | C2×SD16 | — | 9 | 4 | no | — |
| 312 | C2×D8 | — | 9 | 4 | no | — |
| 313 | C2×D8 | — | 9 | 2 | no | — |
| 314 | #131 | — | 9 | 4 | no | — |
| 315 | #131 | — | 9 | 4 | no | — |
| 316 | C2×M16 | — | 9 | 2 | no | — |
| 317 | C2×M16 | D32 | 1 | 1 | yes | characteristic, complemented |
| 318 | C22×C8 | — | 9 | 1 | no | — |
| 319 | C22×C8 | — | 9 | 2 | no | — |
| 320 | C23×C3 | — | 2 | 1 | no | — |
| 321 | C23×C3 | — | 6 | 4 | no | — |
| 322 | C23×C3 | D3×D4 | 1 | 2 | yes | — |
| 323 | C22×D3 | — | 2 | 4 | no | — |
| 324 | C22×D3 | — | 3 | 4 | no | — |
| 325 | C22×D3 | — | 6 | 2 | no | — |
| 326 | C22×D3 | — | 6 | 16 | no | — |
| 327 | C3×Q8 | — | 3 | 8 | no | — |
| 328 | C3×Q8 | — | 6 | 4 | no | — |
| 329 | C3×D4 | — | 3 | 8 | no | — |
| 330 | C3×D4 | — | 6 | 8 | no | — |
| 331 | C3×D4 | — | 6 | 8 | no | — |
| 332 | C3×D4 | — | 6 | 4 | no | — |
| 333 | C2×C3×C4 | — | 2 | 1 | no | — |
| 334 | C2×C3×C4 | — | 2 | 2 | no | — |
| 335 | C2×C3×C4 | — | 2 | 1 | no | — |
| 336 | C2×C3×C4 | — | 2 | 2 | no | — |
| 337 | C2×C3×C4 | — | 6 | 4 | no | — |
| 338 | C2×C3×C4 | — | 6 | 8 | no | — |
| 339 | C2×C3×C4 | — | 6 | 8 | no | — |
| 340 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 341 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 342 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 343 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 344 | #67 | — | 2 | 8 | no | — |
| 345 | #67 | — | 2 | 8 | no | — |
| 346 | #67 | — | 3 | 16 | no | — |
| 347 | #67 | — | 6 | 8 | no | — |
| 348 | #67 | — | 6 | 16 | no | — |
| 349 | #67 | — | 6 | 16 | no | — |
| 350 | C2×Dic3 | — | 2 | 4 | no | — |
| 351 | C2×Dic3 | — | 3 | 4 | no | — |
| 352 | C2×Dic3 | — | 6 | 2 | no | — |
| 353 | C2×Dic3 | — | 6 | 16 | no | — |
| 354 | D12 | — | 2 | 4 | no | — |
| 355 | D12 | — | 3 | 8 | no | — |
| 356 | D12 | — | 6 | 4 | no | — |
| 357 | D12 | — | 6 | 16 | no | — |
| 358 | D12 | C23×D3 | 1 | 8 | yes | — |
| 359 | C4×D3 | — | 2 | 8 | no | — |
| 360 | C4×D3 | — | 2 | 8 | no | — |
| 361 | C4×D3 | — | 3 | 8 | no | — |
| 362 | C4×D3 | — | 3 | 8 | no | — |
| 363 | C4×D3 | — | 6 | 4 | no | — |
| 364 | C4×D3 | — | 6 | 4 | no | — |
| 365 | C4×D3 | — | 6 | 16 | no | — |
| 366 | C4×D3 | — | 6 | 16 | no | — |
| 367 | Dic6 | — | 2 | 4 | no | — |
| 368 | Dic6 | — | 3 | 8 | no | — |
| 369 | Dic6 | — | 6 | 4 | no | — |
| 370 | Dic6 | — | 6 | 16 | no | — |
| 371 | Dic6 | C23×D3 | 1 | 8 | yes | — |
| 372 | C3×C8 | — | 2 | 4 | no | — |
| 373 | C3×C8 | C23×D3 | 1 | 8 | yes | — |
| 374 | C3⋊C8 | — | 3 | 2 | no | — |
| 375 | C3⋊C8 | — | 3 | 2 | no | — |
| 376 | C3⋊C8 | — | 3 | 4 | no | — |
| 377 | C3⋊C8 | — | 6 | 1 | no | — |
| 378 | C3⋊C8 | — | 6 | 1 | no | — |
| 379 | C3⋊C8 | — | 6 | 2 | no | — |
| 380 | C2×C32 | — | 2 | 1 | no | — |
| 381 | C2×C32 | — | 2 | 2 | no | — |
| 382 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 383 | C3⋊D3 | — | 2 | 4 | no | — |
| 384 | C3×D3 | — | 4 | 8 | no | — |
| 385 | #41 | — | 3 | 8 | no | — |
| 386 | #41 | — | 3 | 8 | no | — |
| 387 | #41 | — | 6 | 4 | no | — |
| 388 | #41 | — | 6 | 4 | no | — |
| 389 | #41 | — | 9 | 4 | no | — |
| 390 | #41 | — | 9 | 4 | no | — |
| 391 | #41 | — | 9 | 16 | no | — |
| 392 | #41 | — | 18 | 8 | no | — |
| 393 | #41 | — | 18 | 16 | no | — |
| 394 | #41 | — | 18 | 8 | no | — |
| 395 | #41 | — | 18 | 8 | no | — |
| 396 | #41 | — | 18 | 8 | no | — |
| 397 | C2×Q8 | — | 3 | 4 | no | — |
| 398 | C2×Q8 | — | 9 | 1 | no | — |
| 399 | C2×Q8 | — | 9 | 8 | no | — |
| 400 | C2×Q8 | — | 18 | 8 | no | — |
| 401 | C2×D4 | — | 3 | 4 | no | — |
| 402 | C2×D4 | — | 6 | 4 | no | — |
| 403 | C2×D4 | — | 9 | 8 | no | — |
| 404 | C2×D4 | — | 9 | 2 | no | — |
| 405 | C2×D4 | — | 9 | 1 | no | — |
| 406 | C2×D4 | — | 18 | 8 | no | — |
| 407 | C2×D4 | — | 18 | 8 | no | — |
| 408 | C2×D4 | — | 18 | 16 | no | — |
| 409 | C22×C4 | — | 6 | 4 | no | — |
| 410 | C22×C4 | — | 9 | 2 | no | — |
| 411 | C22×C4 | — | 18 | 8 | no | — |
| 412 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 413 | Q16 | — | 3 | 8 | no | — |
| 414 | Q16 | — | 9 | 4 | no | — |
| 415 | Q16 | — | 9 | 4 | no | — |
| 416 | SD16 | — | 3 | 16 | no | — |
| 417 | SD16 | — | 9 | 8 | no | — |
| 418 | SD16 | — | 9 | 8 | no | — |
| 419 | D8 | — | 3 | 8 | no | — |
| 420 | D8 | — | 9 | 4 | no | — |
| 421 | D8 | — | 9 | 4 | no | — |
| 422 | M16 | — | 9 | 8 | no | — |
| 423 | M16 | C2×D32 | 1 | 4 | yes | — |
| 424 | C2×C8 | — | 9 | 1 | no | — |
| 425 | C2×C8 | — | 9 | 1 | no | — |
| 426 | C2×C8 | — | 9 | 2 | no | — |
| 427 | C2×C8 | — | 9 | 2 | no | — |
| 428 | C2×C8 | — | 9 | 4 | no | — |
| 429 | C2×C8 | — | 9 | 4 | no | — |
| 430 | C2×C8 | C2×D32 | 1 | 2 | yes | — |
| 431 | C22×C3 | — | 2 | 1 | no | — |
| 432 | C22×C3 | — | 2 | 2 | no | — |
| 433 | C22×C3 | — | 4 | 2 | no | — |
| 434 | C22×C3 | — | 4 | 2 | no | — |
| 435 | C22×C3 | — | 6 | 8 | no | — |
| 436 | C22×C3 | — | 24 | 4 | no | — |
| 437 | C22×C3 | C2×D3×D4 | 1 | 4 | yes | — |
| 438 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 439 | C2×D3 | — | 2 | 8 | no | — |
| 440 | C2×D3 | — | 3 | 8 | no | — |
| 441 | C2×D3 | — | 6 | 4 | no | — |
| 442 | C2×D3 | — | 8 | 4 | no | — |
| 443 | C2×D3 | — | 12 | 4 | no | — |
| 444 | C2×D3 | — | 12 | 4 | no | — |
| 445 | C2×D3 | — | 24 | 16 | no | — |
| 446 | C3×C4 | — | 2 | 2 | no | — |
| 447 | C3×C4 | — | 2 | 1 | no | — |
| 448 | C3×C4 | — | 2 | 1 | no | — |
| 449 | C3×C4 | — | 6 | 8 | no | — |
| 450 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 451 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 452 | C3×C4 | C24×D3 | 1 | 2 | yes | — |
| 453 | Dic3 | — | 2 | 8 | no | — |
| 454 | Dic3 | — | 3 | 8 | no | — |
| 455 | Dic3 | — | 6 | 4 | no | — |
| 456 | C32 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 457 | C23 | — | 6 | 4 | no | — |
| 458 | C23 | — | 9 | 2 | no | — |
| 459 | C23 | — | 18 | 8 | no | — |
| 460 | C23 | #3802 | 1 | 1 | yes | characteristic |
| 461 | Q8 | — | 3 | 8 | no | — |
| 462 | Q8 | — | 6 | 4 | no | — |
| 463 | Q8 | — | 9 | 4 | no | — |
| 464 | Q8 | — | 18 | 8 | no | — |
| 465 | D4 | — | 3 | 8 | no | — |
| 466 | D4 | — | 6 | 8 | no | — |
| 467 | D4 | — | 6 | 8 | no | — |
| 468 | D4 | — | 6 | 4 | no | — |
| 469 | D4 | — | 9 | 8 | no | — |
| 470 | D4 | — | 9 | 4 | no | — |
| 471 | D4 | — | 18 | 16 | no | — |
| 472 | D4 | — | 18 | 8 | no | — |
| 473 | C2×C4 | — | 6 | 4 | no | — |
| 474 | C2×C4 | — | 6 | 8 | no | — |
| 475 | C2×C4 | — | 6 | 8 | no | — |
| 476 | C2×C4 | — | 9 | 2 | no | — |
| 477 | C2×C4 | — | 9 | 4 | no | — |
| 478 | C2×C4 | — | 9 | 4 | no | — |
| 479 | C2×C4 | — | 18 | 8 | no | — |
| 480 | C2×C4 | — | 18 | 16 | no | — |
| 481 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 482 | C2×C4 | #3802 | 1 | 2 | yes | — |
| 483 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 484 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 485 | C8 | — | 9 | 1 | no | — |
| 486 | C8 | — | 9 | 1 | no | — |
| 487 | C8 | — | 9 | 2 | no | — |
| 488 | C8 | C22×D32 | 1 | 4 | yes | — |
| 489 | C2×C3 | — | 2 | 2 | no | — |
| 490 | C2×C3 | — | 2 | 4 | no | — |
| 491 | C2×C3 | — | 2 | 2 | no | — |
| 492 | C2×C3 | — | 2 | 1 | no | — |
| 493 | C2×C3 | — | 4 | 2 | no | — |
| 494 | C2×C3 | — | 12 | 8 | no | — |
| 495 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 496 | D3 | — | 4 | 8 | no | — |
| 497 | D3 | — | 6 | 8 | no | — |
| 498 | D3 | — | 12 | 4 | no | — |
| 499 | C22 | — | 4 | 1 | no | — |
| 500 | C22 | — | 6 | 8 | no | — |
| 501 | C22 | — | 9 | 4 | no | — |
| 502 | C22 | — | 24 | 4 | no | — |
| 503 | C22 | — | 36 | 2 | no | — |
| 504 | C22 | — | 72 | 8 | no | — |
| 505 | C22 | C2×#3802 | 1 | 2 | yes | — |
| 506 | C22 | C2×#3802 | 1 | 1 | yes | characteristic |
| 507 | C4 | — | 6 | 8 | no | — |
| 508 | C4 | — | 9 | 4 | no | — |
| 509 | C4 | C2×#3802 | 1 | 2 | yes | — |
| 510 | C4 | C2×#3802 | 1 | 1 | yes | characteristic |
| 511 | C4 | C23×D32 | 1 | 1 | yes | characteristic |
| 512 | C3 | — | 2 | 1 | no | — |
| 513 | C3 | #87199 | 1 | 2 | yes | complemented |
| 514 | C2 | — | 2 | 2 | no | — |
| 515 | C2 | — | 2 | 1 | no | — |
| 516 | C2 | — | 12 | 8 | no | — |
| 517 | C2 | — | 18 | 4 | no | — |
| 518 | C2 | C22×#3802 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596669 | C2 | semidirect |
| 2. C2×#64116 | C2 | semidirect |
| 3. C3×#5748 | C2 | semidirect |
| 4. C2×#63822 | C2 | semidirect |
| 5. #10594723 | C2 | semidirect |
| 6. #10594720 | C2 | semidirect |
| 7. #10594719 | C2 | semidirect |
| 8. #10594685 | C2 | semidirect |
| 9. #10594684 | C2 | semidirect |
| 12. C2×C3×#235 | C22 | semidirect |
| 15. #64307 | C22 | semidirect |
| 16. #64306 | C22 | semidirect |
| 19. #64297 | C22 | semidirect |
| 20. C2×C32×M16 | C22 | semidirect |
| 21. C22×C3⋊(C3⋊C8) | C22 | semidirect |
| 22. #64116 | C22 | semidirect |
| 23. #64116 | C22 | semidirect |
| 24. C2×#3743 | C22 | semidirect |
| 25. C2×C8×C3⋊D3 | C22 | semidirect |
| 26. C3×#909 | C22 | semidirect |
| 27. C3×#908 | C22 | semidirect |
| 28. C3×#904 | C22 | semidirect |
| 29. C2×#3718 | C22 | semidirect |
| 30. C2×#3715 | C22 | semidirect |
| 31. #63822 | C22 | semidirect |
| 32. #63822 | C22 | semidirect |
| 33. #63822 | C22 | semidirect |
| 34. #63822 | C22 | semidirect |
| 35. C2×#3713 | C22 | semidirect |
| 36. #63811 | C22 | semidirect |
| 37. #63810 | C22 | semidirect |
| 38. #63809 | C22 | semidirect |
| 39. #63802 | C22 | semidirect |
| 40. #63798 | C22 | semidirect |
| 41. #63797 | C22 | semidirect |
| 42. #63796 | C22 | semidirect |
| 52. #5748 | D3 | semidirect |
| 115. C2×#235 | C2×D3 | semidirect |
| 120. C2×C3×M16 | C2×D3 | semidirect |
| 141. #909 | C2×D3 | semidirect |
| 142. #908 | C2×D3 | semidirect |
| 147. #904 | C2×D3 | semidirect |
| 317. C2×M16 | D32 | semidirect |
| 456. C32 | #3584 | semidirect |
| 513. C3 | #87199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596669 | 2 |
| C2×#64116 | 2 |
| C3×#5748 | 2 |
| C2×#63822 | 2 |
| #10594723 | 2 |
| #10594720 | 2 |
| #10594719 | 2 |
| #10594685 | 2 |
| #10594684 | 2 |
| #87199 | 3 |