Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2949 conjugacy classes of subgroups.
The subgroup lattice has 477 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596694 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3⋊D3×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5753 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595445 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10594723 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #10594717 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10594703 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×#63802 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10594684 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | D3×#578 | — | 3 | 2 | no | maximal |
| 11 | #41×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#1010 | C22 | 1 | 4 | yes | complemented |
| 13 | D32×Q8 | — | 2 | 2 | no | — |
| 14 | #64316 | — | 2 | 2 | no | — |
| 15 | #64312 | — | 2 | 6 | no | — |
| 16 | #64309 | — | 2 | 6 | no | — |
| 17 | #64306 | C22 | 1 | 6 | yes | — |
| 18 | C2×#3797 | C22 | 1 | 6 | yes | — |
| 19 | #64297 | C22 | 1 | 12 | yes | complemented |
| 20 | C32×#131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #64157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #64116 | C22 | 1 | 3 | yes | complemented |
| 23 | M16×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 24 | #64110 | C22 | 1 | 3 | yes | complemented |
| 25 | C2×C8×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 26 | C3×#909 | C22 | 1 | 12 | yes | complemented |
| 27 | C2×C3×Dic12 | C22 | 1 | 6 | yes | complemented |
| 28 | C3×#904 | C22 | 1 | 6 | yes | complemented |
| 29 | C2×#3718 | C22 | 1 | 6 | yes | complemented |
| 30 | #63827 | C22 | 1 | 12 | yes | complemented |
| 31 | #63822 | C22 | 1 | 6 | yes | complemented |
| 32 | #63811 | C22 | 1 | 24 | yes | complemented |
| 33 | #63810 | C22 | 1 | 6 | yes | complemented |
| 34 | #63809 | C22 | 1 | 6 | yes | complemented |
| 35 | #63802 | C22 | 1 | 3 | yes | — |
| 36 | #63802 | C22 | 1 | 6 | yes | — |
| 37 | #63802 | C22 | 1 | 6 | yes | complemented |
| 38 | #63802 | C22 | 1 | 6 | yes | complemented |
| 39 | #63797 | C22 | 1 | 1 | yes | characteristic |
| 40 | #63796 | C22 | 1 | 6 | yes | — |
| 41 | D3×2−1+4 | — | 3 | 4 | no | — |
| 42 | C3×#578 | — | 3 | 2 | no | — |
| 43 | #5838 | — | 3 | 4 | no | — |
| 44 | #5779 | — | 3 | 12 | no | — |
| 45 | D3×#137 | — | 3 | 12 | no | — |
| 46 | #5771 | — | 3 | 6 | no | — |
| 47 | D3×#135 | — | 3 | 6 | no | — |
| 48 | #5766 | — | 3 | 6 | no | — |
| 49 | C2×D3×Q16 | — | 3 | 6 | no | — |
| 50 | #5753 | D3 | 1 | 2 | yes | complemented |
| 51 | D3×#131 | — | 3 | 2 | no | — |
| 52 | D3×#131 | — | 6 | 1 | no | — |
| 53 | C32×#41 | C23 | 1 | 1 | yes | characteristic |
| 54 | #3832 | D4 | 1 | 1 | yes | characteristic |
| 55 | Q8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 56 | #3830 | D4 | 1 | 3 | yes | — |
| 57 | D4×C3⋊D3 | D4 | 1 | 3 | yes | — |
| 58 | #3828 | C23 | 1 | 3 | yes | — |
| 59 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 60 | C3×D3×Q8 | — | 2 | 4 | no | — |
| 61 | C3×#237 | — | 2 | 12 | no | — |
| 62 | C3×#235 | C23 | 1 | 12 | yes | — |
| 63 | C2×C3×Dic6 | C23 | 1 | 12 | yes | — |
| 64 | #3811 | — | 2 | 6 | no | — |
| 65 | C2×#627 | — | 2 | 6 | no | — |
| 66 | C2×#624 | — | 2 | 6 | no | — |
| 67 | #3805 | — | 2 | 6 | no | — |
| 68 | #3804 | — | 2 | 24 | no | — |
| 69 | #3802 | C23 | 1 | 2 | yes | — |
| 70 | C4×D32 | — | 2 | 6 | no | — |
| 71 | #3799 | — | 2 | 12 | no | — |
| 72 | #3798 | — | 2 | 6 | no | — |
| 73 | #3797 | — | 2 | 6 | no | — |
| 74 | #3797 | — | 2 | 6 | no | — |
| 75 | #3797 | C23 | 1 | 12 | yes | — |
| 76 | #3797 | C23 | 1 | 6 | yes | — |
| 77 | #3796 | C23 | 1 | 12 | yes | — |
| 78 | D3×Dic6 | — | 2 | 12 | no | — |
| 79 | C32×M16 | C23 | 1 | 3 | yes | — |
| 80 | C2×C32×C8 | C23 | 1 | 3 | yes | — |
| 81 | #3748 | C23 | 1 | 3 | yes | — |
| 82 | C2×C3⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 83 | #3743 | C23 | 1 | 6 | yes | — |
| 84 | C8×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 85 | C8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 86 | C8×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 87 | C8×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 88 | C3×Dic12 | C23 | 1 | 6 | yes | — |
| 89 | C3×Dic12 | C23 | 1 | 12 | yes | — |
| 90 | C3×D24 | C23 | 1 | 2 | yes | — |
| 91 | C3×#204 | C23 | 1 | 12 | yes | — |
| 92 | #3718 | C23 | 1 | 6 | yes | — |
| 93 | #3718 | C23 | 1 | 12 | yes | — |
| 94 | #3715 | C23 | 1 | 12 | yes | — |
| 95 | #3713 | C23 | 1 | 2 | yes | — |
| 96 | C2×#578 | — | 9 | 1 | no | Sylow |
| 97 | C3×2−1+4 | — | 3 | 4 | no | — |
| 98 | #1010 | — | 3 | 12 | no | — |
| 99 | #1010 | — | 6 | 12 | no | — |
| 100 | #1010 | C2×D3 | 1 | 4 | yes | complemented |
| 101 | D3×#41 | — | 3 | 2 | no | — |
| 102 | D3×#41 | — | 3 | 12 | no | — |
| 103 | D3×#41 | — | 6 | 1 | no | — |
| 104 | D3×#41 | — | 6 | 12 | no | — |
| 105 | #1007 | — | 3 | 12 | no | — |
| 106 | #1007 | — | 6 | 4 | no | — |
| 107 | C2×D3×Q8 | — | 3 | 12 | no | — |
| 108 | C2×D3×Q8 | — | 6 | 4 | no | — |
| 109 | C3×#137 | — | 3 | 12 | no | — |
| 110 | C3×#135 | — | 3 | 6 | no | — |
| 111 | C2×C3×Q16 | — | 3 | 6 | no | — |
| 112 | C3×#131 | — | 2 | 1 | no | — |
| 113 | C3×#131 | C2×D3 | 1 | 2 | yes | complemented |
| 114 | #951 | — | 3 | 12 | no | — |
| 115 | #950 | — | 3 | 12 | no | — |
| 116 | #948 | — | 3 | 2 | no | — |
| 117 | #948 | — | 6 | 1 | no | — |
| 118 | C2×#216 | — | 3 | 12 | no | — |
| 119 | #942 | — | 3 | 12 | no | — |
| 120 | #919 | — | 3 | 6 | no | — |
| 121 | #918 | — | 3 | 24 | no | — |
| 122 | D3×Q16 | — | 3 | 6 | no | — |
| 123 | D3×Q16 | — | 3 | 12 | no | — |
| 124 | D3×Q16 | — | 3 | 12 | no | — |
| 125 | D3×Q16 | — | 3 | 12 | no | — |
| 126 | #916 | — | 3 | 12 | no | — |
| 127 | #915 | — | 3 | 24 | no | — |
| 128 | D3×SD16 | — | 3 | 12 | no | — |
| 129 | #912 | — | 3 | 6 | no | — |
| 130 | D3×D8 | — | 3 | 2 | no | — |
| 131 | #909 | C2×D3 | 1 | 12 | yes | complemented |
| 132 | #907 | — | 3 | 6 | no | — |
| 133 | #907 | — | 6 | 3 | no | — |
| 134 | D3×M16 | — | 3 | 6 | no | — |
| 135 | D3×M16 | — | 6 | 3 | no | — |
| 136 | C2×Dic12 | C2×D3 | 1 | 6 | yes | complemented |
| 137 | #904 | C2×D3 | 1 | 6 | yes | complemented |
| 138 | #901 | — | 3 | 6 | no | — |
| 139 | #901 | — | 6 | 3 | no | — |
| 140 | C2×D3×C8 | — | 3 | 6 | no | — |
| 141 | C2×D3×C8 | — | 6 | 3 | no | — |
| 142 | C22×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 143 | C2×D32 | — | 2 | 2 | no | — |
| 144 | C32×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C32×D4 | C2×D4 | 1 | 3 | yes | — |
| 146 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 147 | #638 | C2×D4 | 1 | 6 | yes | — |
| 148 | C2×C3⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 149 | C4⋊(C3⋊D3) | C2×D4 | 1 | 3 | yes | — |
| 150 | C4×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 151 | C4×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 152 | C4×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 153 | C4×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 154 | #634 | C2×D4 | 1 | 3 | yes | — |
| 155 | C3×#67 | — | 2 | 12 | no | — |
| 156 | C2×C3×Dic3 | — | 2 | 12 | no | — |
| 157 | C3×D12 | C24 | 1 | 4 | yes | — |
| 158 | C3×C4×D3 | — | 2 | 12 | no | — |
| 159 | C3×Dic6 | — | 2 | 12 | no | — |
| 160 | C3×Dic6 | C24 | 1 | 12 | yes | — |
| 161 | #627 | — | 2 | 12 | no | — |
| 162 | #627 | — | 2 | 6 | no | — |
| 163 | #626 | — | 2 | 12 | no | — |
| 164 | #625 | — | 2 | 2 | no | — |
| 165 | #624 | — | 2 | 6 | no | — |
| 166 | #624 | — | 2 | 12 | no | — |
| 167 | D3×Dic3 | — | 2 | 12 | no | — |
| 168 | C32×C8 | C24 | 1 | 3 | yes | — |
| 169 | C32×C8 | C24 | 1 | 1 | yes | characteristic |
| 170 | C3⋊(C3⋊C8) | C24 | 1 | 1 | yes | characteristic |
| 171 | C3⋊(C3⋊C8) | C24 | 1 | 3 | yes | — |
| 172 | C2×2−1+4 | — | 9 | 2 | no | — |
| 173 | #578 | — | 3 | 2 | no | — |
| 174 | #578 | — | 9 | 6 | no | — |
| 175 | #578 | — | 9 | 6 | no | — |
| 176 | #578 | — | 9 | 2 | no | — |
| 177 | C2×#137 | — | 9 | 6 | no | — |
| 178 | C2×#135 | — | 9 | 3 | no | — |
| 179 | C22×Q16 | — | 9 | 3 | no | — |
| 180 | C2×#131 | — | 9 | 1 | no | — |
| 181 | C3×#41 | — | 2 | 1 | no | — |
| 182 | C3×#41 | — | 3 | 12 | no | — |
| 183 | C3×#41 | — | 6 | 12 | no | — |
| 184 | C3×#41 | C22×D3 | 1 | 2 | yes | — |
| 185 | C2×C3×Q8 | — | 3 | 12 | no | — |
| 186 | C2×C3×Q8 | — | 6 | 4 | no | — |
| 187 | #239 | — | 3 | 2 | no | — |
| 188 | #239 | — | 3 | 12 | no | — |
| 189 | #239 | — | 6 | 1 | no | — |
| 190 | #239 | — | 6 | 12 | no | — |
| 191 | D3×Q8 | — | 2 | 4 | no | — |
| 192 | D3×Q8 | — | 3 | 2 | no | — |
| 193 | D3×Q8 | — | 3 | 12 | no | — |
| 194 | D3×Q8 | — | 3 | 24 | no | — |
| 195 | D3×Q8 | — | 6 | 1 | no | — |
| 196 | D3×Q8 | — | 6 | 12 | no | — |
| 197 | D3×Q8 | — | 6 | 12 | no | — |
| 198 | D3×Q8 | — | 6 | 12 | no | — |
| 199 | #237 | — | 2 | 12 | no | — |
| 200 | #237 | — | 3 | 6 | no | — |
| 201 | #237 | — | 3 | 12 | no | — |
| 202 | #237 | — | 6 | 3 | no | — |
| 203 | #237 | — | 6 | 24 | no | — |
| 204 | #237 | — | 6 | 12 | no | — |
| 205 | D3×D4 | — | 3 | 6 | no | — |
| 206 | D3×D4 | — | 3 | 4 | no | — |
| 207 | D3×D4 | — | 6 | 3 | no | — |
| 208 | D3×D4 | — | 6 | 12 | no | — |
| 209 | #235 | — | 3 | 6 | no | — |
| 210 | #235 | — | 6 | 3 | no | — |
| 211 | #235 | — | 6 | 12 | no | — |
| 212 | #235 | — | 6 | 12 | no | — |
| 213 | #235 | — | 6 | 24 | no | — |
| 214 | #235 | C22×D3 | 1 | 12 | yes | — |
| 215 | C2×C4×D3 | — | 3 | 6 | no | — |
| 216 | C2×C4×D3 | — | 6 | 3 | no | — |
| 217 | C2×C4×D3 | — | 6 | 12 | no | — |
| 218 | C2×C4×D3 | — | 6 | 12 | no | — |
| 219 | C2×Dic6 | — | 6 | 12 | no | — |
| 220 | C2×Dic6 | — | 6 | 12 | no | — |
| 221 | C2×Dic6 | C22×D3 | 1 | 12 | yes | — |
| 222 | C3×Q16 | — | 3 | 6 | no | — |
| 223 | C3×Q16 | — | 3 | 12 | no | — |
| 224 | C3×SD16 | — | 3 | 12 | no | — |
| 225 | C3×D8 | — | 3 | 2 | no | — |
| 226 | C3×M16 | — | 2 | 3 | no | — |
| 227 | C3×M16 | C22×D3 | 1 | 6 | yes | — |
| 228 | C2×C3×C8 | — | 2 | 3 | no | — |
| 229 | C2×C3×C8 | C22×D3 | 1 | 6 | yes | — |
| 230 | #216 | — | 3 | 24 | no | — |
| 231 | #216 | — | 3 | 12 | no | — |
| 232 | #215 | — | 3 | 12 | no | — |
| 233 | #214 | — | 3 | 12 | no | — |
| 234 | #213 | — | 3 | 4 | no | — |
| 235 | #208 | — | 3 | 6 | no | — |
| 236 | #208 | — | 6 | 3 | no | — |
| 237 | C2×C3⋊C8 | — | 3 | 6 | no | — |
| 238 | C2×C3⋊C8 | — | 6 | 3 | no | — |
| 239 | Dic12 | C22×D3 | 1 | 6 | yes | — |
| 240 | Dic12 | C22×D3 | 1 | 12 | yes | — |
| 241 | D24 | C22×D3 | 1 | 2 | yes | — |
| 242 | #204 | C22×D3 | 1 | 12 | yes | — |
| 243 | ΓL(1,𝔽25) | — | 3 | 12 | no | — |
| 244 | ΓL(1,𝔽25) | — | 6 | 6 | no | — |
| 245 | D3×C8 | — | 3 | 2 | no | — |
| 246 | D3×C8 | — | 3 | 6 | no | — |
| 247 | D3×C8 | — | 3 | 6 | no | — |
| 248 | D3×C8 | — | 3 | 6 | no | — |
| 249 | D3×C8 | — | 6 | 1 | no | — |
| 250 | D3×C8 | — | 6 | 3 | no | — |
| 251 | D3×C8 | — | 6 | 3 | no | — |
| 252 | D3×C8 | — | 6 | 3 | no | — |
| 253 | C22×C32 | C22×D4 | 1 | 3 | yes | — |
| 254 | C2×C3⋊D3 | — | 2 | 6 | no | — |
| 255 | C2×C3⋊D3 | C22×D4 | 1 | 3 | yes | — |
| 256 | C2×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×C3×D3 | — | 2 | 4 | no | — |
| 258 | D32 | — | 4 | 4 | no | — |
| 259 | C32×C4 | C22×D4 | 1 | 3 | yes | — |
| 260 | C32×C4 | C25 | 1 | 1 | yes | characteristic |
| 261 | C3⋊Dic3 | C22×D4 | 1 | 3 | yes | — |
| 262 | C3⋊Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 263 | C3×Dic3 | — | 2 | 12 | no | — |
| 264 | 2−1+4 | — | 3 | 4 | no | — |
| 265 | 2−1+4 | — | 9 | 12 | no | — |
| 266 | 2−1+4 | — | 18 | 2 | no | — |
| 267 | 2−1+4 | — | 18 | 6 | no | — |
| 268 | C2×#41 | — | 9 | 1 | no | — |
| 269 | C2×#41 | — | 9 | 6 | no | — |
| 270 | C2×#41 | — | 18 | 6 | no | — |
| 271 | C22×Q8 | — | 9 | 6 | no | — |
| 272 | C22×Q8 | — | 18 | 2 | no | — |
| 273 | #137 | — | 3 | 12 | no | — |
| 274 | #137 | — | 9 | 24 | no | — |
| 275 | #137 | — | 9 | 12 | no | — |
| 276 | #135 | — | 3 | 6 | no | — |
| 277 | #135 | — | 9 | 6 | no | — |
| 278 | #135 | — | 9 | 6 | no | — |
| 279 | #135 | — | 9 | 6 | no | — |
| 280 | C2×Q16 | — | 3 | 6 | no | — |
| 281 | C2×Q16 | — | 9 | 3 | no | — |
| 282 | C2×Q16 | — | 9 | 6 | no | — |
| 283 | C2×Q16 | — | 9 | 6 | no | — |
| 284 | C2×Q16 | — | 9 | 6 | no | — |
| 285 | C2×Q16 | — | 9 | 6 | no | — |
| 286 | C2×SD16 | — | 9 | 6 | no | — |
| 287 | C2×D8 | — | 9 | 1 | no | — |
| 288 | #131 | — | 9 | 1 | no | — |
| 289 | #131 | — | 9 | 3 | no | — |
| 290 | #131 | — | 9 | 3 | no | — |
| 291 | #131 | D32 | 1 | 1 | yes | characteristic, complemented |
| 292 | C2×M16 | — | 9 | 3 | no | — |
| 293 | C22×C8 | — | 9 | 3 | no | — |
| 294 | C22×D3 | — | 3 | 6 | no | — |
| 295 | C22×D3 | — | 6 | 3 | no | — |
| 296 | C22×D3 | — | 6 | 4 | no | — |
| 297 | C3×Q8 | — | 2 | 1 | no | — |
| 298 | C3×Q8 | — | 3 | 12 | no | — |
| 299 | C3×Q8 | — | 6 | 12 | no | — |
| 300 | C3×Q8 | D3×D4 | 1 | 2 | yes | — |
| 301 | C3×D4 | — | 2 | 3 | no | — |
| 302 | C3×D4 | — | 3 | 4 | no | — |
| 303 | C3×D4 | — | 6 | 12 | no | — |
| 304 | C3×D4 | D3×D4 | 1 | 6 | yes | — |
| 305 | C2×C3×C4 | — | 2 | 3 | no | — |
| 306 | C2×C3×C4 | — | 6 | 12 | no | — |
| 307 | C2×C3×C4 | — | 6 | 12 | no | — |
| 308 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 309 | #67 | — | 2 | 12 | no | — |
| 310 | #67 | — | 3 | 12 | no | — |
| 311 | #67 | — | 6 | 6 | no | — |
| 312 | #67 | — | 6 | 12 | no | — |
| 313 | #67 | — | 6 | 4 | no | — |
| 314 | C2×Dic3 | — | 2 | 12 | no | — |
| 315 | C2×Dic3 | — | 3 | 6 | no | — |
| 316 | C2×Dic3 | — | 6 | 3 | no | — |
| 317 | C2×Dic3 | — | 6 | 12 | no | — |
| 318 | D12 | — | 3 | 6 | no | — |
| 319 | D12 | — | 6 | 3 | no | — |
| 320 | D12 | — | 6 | 12 | no | — |
| 321 | D12 | C23×D3 | 1 | 4 | yes | — |
| 322 | C4×D3 | — | 2 | 12 | no | — |
| 323 | C4×D3 | — | 3 | 6 | no | — |
| 324 | C4×D3 | — | 3 | 6 | no | — |
| 325 | C4×D3 | — | 3 | 2 | no | — |
| 326 | C4×D3 | — | 3 | 6 | no | — |
| 327 | C4×D3 | — | 6 | 3 | no | — |
| 328 | C4×D3 | — | 6 | 3 | no | — |
| 329 | C4×D3 | — | 6 | 1 | no | — |
| 330 | C4×D3 | — | 6 | 3 | no | — |
| 331 | C4×D3 | — | 6 | 12 | no | — |
| 332 | C4×D3 | — | 6 | 24 | no | — |
| 333 | C4×D3 | — | 6 | 12 | no | — |
| 334 | Dic6 | — | 2 | 12 | no | — |
| 335 | Dic6 | — | 3 | 6 | no | — |
| 336 | Dic6 | — | 6 | 3 | no | — |
| 337 | Dic6 | — | 6 | 24 | no | — |
| 338 | Dic6 | — | 6 | 12 | no | — |
| 339 | Dic6 | C23×D3 | 1 | 12 | yes | — |
| 340 | C3×C8 | — | 2 | 1 | no | — |
| 341 | C3×C8 | — | 2 | 3 | no | — |
| 342 | C3×C8 | C23×D3 | 1 | 2 | yes | — |
| 343 | C3×C8 | C23×D3 | 1 | 6 | yes | — |
| 344 | C3⋊C8 | — | 3 | 2 | no | — |
| 345 | C3⋊C8 | — | 3 | 6 | no | — |
| 346 | C3⋊C8 | — | 6 | 1 | no | — |
| 347 | C3⋊C8 | — | 6 | 3 | no | — |
| 348 | C2×C32 | — | 2 | 3 | no | — |
| 349 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 350 | C3⋊D3 | — | 2 | 3 | no | — |
| 351 | C3⋊D3 | #578 | 1 | 2 | yes | complemented |
| 352 | C3×D3 | — | 4 | 4 | no | — |
| 353 | #41 | — | 3 | 12 | no | — |
| 354 | #41 | — | 6 | 12 | no | — |
| 355 | #41 | — | 9 | 1 | no | — |
| 356 | #41 | — | 9 | 3 | no | — |
| 357 | #41 | — | 9 | 3 | no | — |
| 358 | #41 | — | 9 | 12 | no | — |
| 359 | #41 | — | 18 | 6 | no | — |
| 360 | #41 | — | 18 | 24 | no | — |
| 361 | #41 | — | 18 | 12 | no | — |
| 362 | #41 | — | 18 | 6 | no | — |
| 363 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 364 | C2×Q8 | — | 3 | 12 | no | — |
| 365 | C2×Q8 | — | 6 | 4 | no | — |
| 366 | C2×Q8 | — | 9 | 1 | no | — |
| 367 | C2×Q8 | — | 9 | 6 | no | — |
| 368 | C2×Q8 | — | 9 | 12 | no | — |
| 369 | C2×Q8 | — | 18 | 6 | no | — |
| 370 | C2×Q8 | — | 18 | 12 | no | — |
| 371 | C2×Q8 | — | 18 | 6 | no | — |
| 372 | C2×Q8 | — | 18 | 6 | no | — |
| 373 | C2×D4 | — | 9 | 2 | no | — |
| 374 | C2×D4 | — | 9 | 3 | no | — |
| 375 | C2×D4 | — | 18 | 6 | no | — |
| 376 | C22×C4 | — | 9 | 3 | no | — |
| 377 | C22×C4 | — | 18 | 6 | no | — |
| 378 | C22×C4 | — | 18 | 6 | no | — |
| 379 | Q16 | — | 3 | 6 | no | — |
| 380 | Q16 | — | 3 | 12 | no | — |
| 381 | Q16 | — | 9 | 6 | no | — |
| 382 | Q16 | — | 9 | 12 | no | — |
| 383 | SD16 | — | 3 | 12 | no | — |
| 384 | SD16 | — | 9 | 12 | no | — |
| 385 | D8 | — | 3 | 2 | no | — |
| 386 | D8 | — | 9 | 2 | no | — |
| 387 | M16 | — | 9 | 3 | no | — |
| 388 | M16 | — | 9 | 6 | no | — |
| 389 | M16 | C2×D32 | 1 | 3 | yes | — |
| 390 | C2×C8 | — | 9 | 3 | no | — |
| 391 | C2×C8 | — | 9 | 1 | no | — |
| 392 | C2×C8 | — | 9 | 3 | no | — |
| 393 | C2×C8 | — | 9 | 3 | no | — |
| 394 | C2×C8 | — | 9 | 3 | no | — |
| 395 | C2×C8 | C2×D32 | 1 | 3 | yes | — |
| 396 | C22×C3 | — | 2 | 3 | no | — |
| 397 | C22×C3 | — | 6 | 4 | no | — |
| 398 | C22×C3 | C2×D3×D4 | 1 | 6 | yes | — |
| 399 | C2×D3 | — | 2 | 4 | no | — |
| 400 | C2×D3 | — | 3 | 2 | no | — |
| 401 | C2×D3 | — | 3 | 6 | no | — |
| 402 | C2×D3 | — | 6 | 1 | no | — |
| 403 | C2×D3 | — | 6 | 3 | no | — |
| 404 | C2×D3 | — | 6 | 12 | no | — |
| 405 | C2×D3 | — | 12 | 6 | no | — |
| 406 | C2×D3 | — | 12 | 8 | no | — |
| 407 | C3×C4 | — | 2 | 3 | no | — |
| 408 | C3×C4 | — | 2 | 1 | no | — |
| 409 | C3×C4 | — | 6 | 12 | no | — |
| 410 | C3×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 411 | C3×C4 | C24×D3 | 1 | 2 | yes | — |
| 412 | Dic3 | — | 2 | 12 | no | — |
| 413 | Dic3 | — | 3 | 6 | no | — |
| 414 | Dic3 | — | 3 | 2 | no | — |
| 415 | Dic3 | — | 6 | 3 | no | — |
| 416 | Dic3 | — | 6 | 1 | no | — |
| 417 | C32 | C2×#578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 418 | C23 | — | 9 | 3 | no | — |
| 419 | C23 | — | 18 | 2 | no | — |
| 420 | Q8 | — | 3 | 12 | no | — |
| 421 | Q8 | — | 6 | 12 | no | — |
| 422 | Q8 | — | 9 | 3 | no | — |
| 423 | Q8 | — | 18 | 6 | no | — |
| 424 | Q8 | — | 18 | 12 | no | — |
| 425 | Q8 | #3802 | 1 | 1 | yes | characteristic |
| 426 | D4 | — | 3 | 4 | no | — |
| 427 | D4 | — | 6 | 12 | no | — |
| 428 | D4 | — | 9 | 6 | no | — |
| 429 | D4 | — | 9 | 3 | no | — |
| 430 | D4 | — | 18 | 12 | no | — |
| 431 | D4 | — | 18 | 2 | no | — |
| 432 | D4 | #3802 | 1 | 3 | yes | — |
| 433 | C2×C4 | — | 6 | 12 | no | — |
| 434 | C2×C4 | — | 6 | 12 | no | — |
| 435 | C2×C4 | — | 9 | 3 | no | — |
| 436 | C2×C4 | — | 9 | 3 | no | — |
| 437 | C2×C4 | — | 9 | 3 | no | — |
| 438 | C2×C4 | — | 9 | 1 | no | — |
| 439 | C2×C4 | — | 9 | 3 | no | — |
| 440 | C2×C4 | — | 18 | 6 | no | — |
| 441 | C2×C4 | — | 18 | 12 | no | — |
| 442 | C2×C4 | — | 18 | 12 | no | — |
| 443 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 444 | C8 | — | 9 | 1 | no | — |
| 445 | C8 | — | 9 | 3 | no | — |
| 446 | C8 | C22×D32 | 1 | 1 | yes | characteristic |
| 447 | C8 | C22×D32 | 1 | 3 | yes | — |
| 448 | C2×C3 | — | 2 | 6 | no | — |
| 449 | C2×C3 | — | 2 | 1 | no | — |
| 450 | C2×C3 | — | 4 | 3 | no | — |
| 451 | C2×C3 | — | 12 | 4 | no | — |
| 452 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 453 | D3 | — | 3 | 4 | no | — |
| 454 | D3 | — | 4 | 4 | no | — |
| 455 | D3 | — | 6 | 2 | no | — |
| 456 | D3 | — | 6 | 6 | no | — |
| 457 | D3 | — | 12 | 3 | no | — |
| 458 | C22 | — | 6 | 4 | no | — |
| 459 | C22 | — | 9 | 1 | no | — |
| 460 | C22 | — | 9 | 3 | no | — |
| 461 | C22 | — | 18 | 6 | no | — |
| 462 | C22 | — | 36 | 4 | no | — |
| 463 | C22 | C2×#3802 | 1 | 3 | yes | — |
| 464 | C4 | — | 6 | 12 | no | — |
| 465 | C4 | — | 9 | 1 | no | — |
| 466 | C4 | — | 9 | 3 | no | — |
| 467 | C4 | C2×#3802 | 1 | 3 | yes | — |
| 468 | C4 | C23×D32 | 1 | 1 | yes | characteristic |
| 469 | C3 | — | 2 | 1 | no | — |
| 470 | C3 | D3×#578 | 1 | 2 | yes | complemented |
| 471 | C2 | — | 2 | 3 | no | — |
| 472 | C2 | — | 9 | 2 | no | — |
| 473 | C2 | — | 12 | 4 | no | — |
| 474 | C2 | — | 18 | 3 | no | — |
| 475 | C2 | C22×#3802 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#3802 |
| commutator, cosocle | C32×C4 | C25 |
| Frattini | C4 | C23×D32 |
| Fitting | C32×#131 | C22 |
| socle | C2×C32 | C23×D4 |
| hypercenter | #131 | D32 |
| hypocenter | C32 | C2×#578 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596694 | C2 | semidirect |
| 2. C3⋊D3×#131 | C2 | semidirect |
| 3. C3×#5753 | C2 | semidirect |
| 4. #10595445 | C2 | semidirect |
| 5. #10594723 | C2 | semidirect |
| 6. #10594717 | C2 | semidirect |
| 7. #10594703 | C2 | semidirect |
| 8. C2×#63802 | C2 | semidirect |
| 9. #10594684 | C2 | semidirect |
| 12. C3×#1010 | C22 | semidirect |
| 19. #64297 | C22 | semidirect |
| 20. C32×#131 | C22 | semidirect |
| 21. #64157 | C22 | semidirect |
| 22. #64116 | C22 | semidirect |
| 24. #64110 | C22 | semidirect |
| 26. C3×#909 | C22 | semidirect |
| 27. C2×C3×Dic12 | C22 | semidirect |
| 28. C3×#904 | C22 | semidirect |
| 29. C2×#3718 | C22 | semidirect |
| 30. #63827 | C22 | semidirect |
| 31. #63822 | C22 | semidirect |
| 32. #63811 | C22 | semidirect |
| 33. #63810 | C22 | semidirect |
| 34. #63809 | C22 | semidirect |
| 37. #63802 | C22 | semidirect |
| 38. #63802 | C22 | semidirect |
| 50. #5753 | D3 | semidirect |
| 100. #1010 | C2×D3 | semidirect |
| 113. C3×#131 | C2×D3 | semidirect |
| 131. #909 | C2×D3 | semidirect |
| 136. C2×Dic12 | C2×D3 | semidirect |
| 137. #904 | C2×D3 | semidirect |
| 291. #131 | D32 | semidirect |
| 351. C3⋊D3 | #578 | semidirect |
| 417. C32 | C2×#578 | semidirect |
| 470. C3 | D3×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596694 | 2 |
| C3⋊D3×#131 | 2 |
| C3×#5753 | 2 |
| #10595445 | 2 |
| #10594723 | 2 |
| #10594717 | 2 |
| #10594703 | 2 |
| C2×#63802 | 2 |
| #10594684 | 2 |
| D3×#578 | 3 |