Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2981 conjugacy classes of subgroups.
The subgroup lattice has 636 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596698 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3⋊D3×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5751 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595445 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10595444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10594723 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10594720 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10594718 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C2×#63809 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #10594686 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #10594684 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #87206 | — | 3 | 2 | no | maximal |
| 13 | #41×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#1010 | C22 | 1 | 2 | yes | complemented |
| 15 | C3×#1009 | C22 | 1 | 2 | yes | complemented |
| 16 | D3×#239 | — | 2 | 2 | no | — |
| 17 | #64315 | — | 2 | 2 | no | — |
| 18 | #64314 | — | 2 | 6 | no | — |
| 19 | D3×#237 | — | 2 | 6 | no | — |
| 20 | #64307 | C22 | 1 | 6 | yes | complemented |
| 21 | #64306 | C22 | 1 | 6 | yes | complemented |
| 22 | #64297 | C22 | 1 | 6 | yes | complemented |
| 23 | C2×#3796 | C22 | 1 | 6 | yes | complemented |
| 24 | C32×#131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #64157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #64116 | C22 | 1 | 3 | yes | complemented |
| 27 | M16×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 28 | #64110 | C22 | 1 | 3 | yes | complemented |
| 29 | C2×C8×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 30 | C3×#909 | C22 | 1 | 6 | yes | complemented |
| 31 | C3×#908 | C22 | 1 | 6 | yes | complemented |
| 32 | C3×#904 | C22 | 1 | 6 | yes | complemented |
| 33 | C2×C3×#204 | C22 | 1 | 6 | yes | complemented |
| 34 | C2×#3718 | C22 | 1 | 3 | yes | complemented |
| 35 | #63827 | C22 | 1 | 6 | yes | complemented |
| 36 | #63823 | C22 | 1 | 6 | yes | complemented |
| 37 | #63822 | C22 | 1 | 3 | yes | complemented |
| 38 | #63822 | C22 | 1 | 3 | yes | complemented |
| 39 | C2×#3713 | C22 | 1 | 3 | yes | complemented |
| 40 | #63811 | C22 | 1 | 12 | yes | complemented |
| 41 | #63810 | C22 | 1 | 6 | yes | complemented |
| 42 | #63809 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #63809 | C22 | 1 | 3 | yes | complemented |
| 44 | #63809 | C22 | 1 | 6 | yes | complemented |
| 45 | #63809 | C22 | 1 | 6 | yes | complemented |
| 46 | #63809 | C22 | 1 | 6 | yes | complemented |
| 47 | #63802 | C22 | 1 | 3 | yes | complemented |
| 48 | #63798 | C22 | 1 | 12 | yes | complemented |
| 49 | #63797 | C22 | 1 | 3 | yes | complemented |
| 50 | #63796 | C22 | 1 | 6 | yes | complemented |
| 51 | #5968 | — | 3 | 2 | no | — |
| 52 | #5966 | — | 3 | 2 | no | — |
| 53 | C3×#577 | — | 3 | 2 | no | — |
| 54 | #5838 | — | 3 | 2 | no | — |
| 55 | #5835 | — | 3 | 2 | no | — |
| 56 | #5779 | — | 3 | 6 | no | — |
| 57 | #5777 | — | 3 | 6 | no | — |
| 58 | #5774 | — | 3 | 6 | no | — |
| 59 | #5773 | — | 3 | 6 | no | — |
| 60 | #5770 | — | 3 | 6 | no | — |
| 61 | D3×#135 | — | 3 | 6 | no | — |
| 62 | #5762 | — | 3 | 6 | no | — |
| 63 | C2×#916 | — | 3 | 6 | no | — |
| 64 | #5751 | D3 | 1 | 2 | yes | complemented |
| 65 | D3×#131 | — | 3 | 2 | no | — |
| 66 | D3×#131 | — | 6 | 1 | no | — |
| 67 | C32×#41 | C23 | 1 | 1 | yes | characteristic |
| 68 | #3832 | D4 | 1 | 1 | yes | characteristic |
| 69 | Q8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 70 | #3830 | D4 | 1 | 3 | yes | — |
| 71 | D4×C3⋊D3 | D4 | 1 | 3 | yes | — |
| 72 | #3828 | C23 | 1 | 3 | yes | — |
| 73 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 74 | C3×#239 | — | 2 | 2 | no | — |
| 75 | C3×D3×Q8 | — | 2 | 2 | no | — |
| 76 | C3×#237 | — | 2 | 6 | no | — |
| 77 | C3×D3×D4 | — | 2 | 6 | no | — |
| 78 | C3×#235 | C23 | 1 | 6 | yes | — |
| 79 | C3×#235 | C23 | 1 | 6 | yes | — |
| 80 | C2×C3×D12 | C23 | 1 | 6 | yes | — |
| 81 | C2×C3×Dic6 | C23 | 1 | 6 | yes | — |
| 82 | #3811 | — | 2 | 6 | no | — |
| 83 | D3×#67 | — | 2 | 12 | no | — |
| 84 | C2×#626 | — | 2 | 6 | no | — |
| 85 | #3805 | — | 2 | 6 | no | — |
| 86 | #3804 | — | 2 | 12 | no | — |
| 87 | C2×D3×Dic3 | — | 2 | 6 | no | — |
| 88 | #3802 | C23 | 1 | 6 | yes | — |
| 89 | D3×D12 | — | 2 | 6 | no | — |
| 90 | C4×D32 | — | 2 | 6 | no | — |
| 91 | #3799 | — | 2 | 6 | no | — |
| 92 | #3798 | — | 2 | 6 | no | — |
| 93 | #3797 | C23 | 1 | 6 | yes | — |
| 94 | #3796 | — | 2 | 6 | no | — |
| 95 | #3796 | — | 2 | 6 | no | — |
| 96 | #3796 | C23 | 1 | 6 | yes | — |
| 97 | #3796 | C23 | 1 | 12 | yes | — |
| 98 | #3796 | C23 | 1 | 2 | yes | — |
| 99 | #3795 | — | 2 | 6 | no | — |
| 100 | D3×Dic6 | — | 2 | 6 | no | — |
| 101 | C32×M16 | C23 | 1 | 3 | yes | — |
| 102 | C2×C32×C8 | C23 | 1 | 3 | yes | — |
| 103 | #3748 | C23 | 1 | 3 | yes | — |
| 104 | C2×C3⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 105 | #3743 | C23 | 1 | 6 | yes | — |
| 106 | C8×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 107 | C8×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 108 | C8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 109 | C8×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 110 | C3×Dic12 | C23 | 1 | 6 | yes | — |
| 111 | C3×D24 | C23 | 1 | 6 | yes | — |
| 112 | C3×#204 | C23 | 1 | 6 | yes | — |
| 113 | C3×#204 | C23 | 1 | 12 | yes | — |
| 114 | C3×#204 | C23 | 1 | 2 | yes | — |
| 115 | #3718 | C23 | 1 | 1 | yes | characteristic |
| 116 | #3718 | C23 | 1 | 3 | yes | — |
| 117 | #3718 | C23 | 1 | 6 | yes | — |
| 118 | #3715 | C23 | 1 | 6 | yes | — |
| 119 | #3715 | C23 | 1 | 6 | yes | — |
| 120 | #3713 | C23 | 1 | 1 | yes | characteristic |
| 121 | #3713 | C23 | 1 | 3 | yes | — |
| 122 | #3713 | C23 | 1 | 6 | yes | — |
| 123 | #3584 | — | 9 | 1 | no | Sylow |
| 124 | C3×2−1+4 | — | 3 | 2 | no | — |
| 125 | C3×H(5,𝔽2) | — | 3 | 2 | no | — |
| 126 | #1010 | — | 3 | 6 | no | — |
| 127 | #1010 | — | 6 | 2 | no | — |
| 128 | #1010 | C2×D3 | 1 | 2 | yes | complemented |
| 129 | #1009 | — | 3 | 6 | no | — |
| 130 | #1009 | — | 6 | 6 | no | — |
| 131 | #1009 | C2×D3 | 1 | 2 | yes | complemented |
| 132 | D3×#41 | — | 3 | 2 | no | — |
| 133 | D3×#41 | — | 3 | 6 | no | — |
| 134 | D3×#41 | — | 3 | 6 | no | — |
| 135 | D3×#41 | — | 6 | 1 | no | — |
| 136 | D3×#41 | — | 6 | 6 | no | — |
| 137 | D3×#41 | — | 6 | 2 | no | — |
| 138 | #1007 | — | 3 | 6 | no | — |
| 139 | #1007 | — | 6 | 2 | no | — |
| 140 | C2×#239 | — | 3 | 6 | no | — |
| 141 | C2×#239 | — | 6 | 2 | no | — |
| 142 | #1004 | — | 3 | 6 | no | — |
| 143 | #1004 | — | 6 | 6 | no | — |
| 144 | C2×#237 | — | 3 | 6 | no | — |
| 145 | C2×#237 | — | 6 | 6 | no | — |
| 146 | C3×#137 | — | 3 | 6 | no | — |
| 147 | C3×AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 148 | C3×#135 | — | 3 | 6 | no | — |
| 149 | C2×C3×SD16 | — | 3 | 6 | no | — |
| 150 | C3×#131 | — | 2 | 1 | no | — |
| 151 | C3×#131 | C2×D3 | 1 | 2 | yes | complemented |
| 152 | #951 | — | 3 | 6 | no | — |
| 153 | #950 | — | 3 | 6 | no | — |
| 154 | #950 | — | 3 | 6 | no | — |
| 155 | #949 | — | 3 | 6 | no | — |
| 156 | #948 | — | 3 | 2 | no | — |
| 157 | #948 | — | 6 | 1 | no | — |
| 158 | C2×#216 | — | 3 | 6 | no | — |
| 159 | #942 | — | 3 | 6 | no | — |
| 160 | #932 | — | 3 | 6 | no | — |
| 161 | C2×#213 | — | 3 | 6 | no | — |
| 162 | #919 | — | 3 | 6 | no | — |
| 163 | #918 | — | 3 | 12 | no | — |
| 164 | D3×Q16 | — | 3 | 6 | no | — |
| 165 | #916 | — | 3 | 6 | no | — |
| 166 | #916 | — | 3 | 12 | no | — |
| 167 | #916 | — | 3 | 12 | no | — |
| 168 | #916 | — | 3 | 12 | no | — |
| 169 | #916 | — | 3 | 2 | no | — |
| 170 | #915 | — | 3 | 12 | no | — |
| 171 | #914 | — | 3 | 12 | no | — |
| 172 | D3×SD16 | — | 3 | 6 | no | — |
| 173 | D3×SD16 | — | 3 | 6 | no | — |
| 174 | #912 | — | 3 | 6 | no | — |
| 175 | #911 | — | 3 | 12 | no | — |
| 176 | D3×D8 | — | 3 | 6 | no | — |
| 177 | #909 | C2×D3 | 1 | 6 | yes | complemented |
| 178 | #908 | C2×D3 | 1 | 6 | yes | complemented |
| 179 | #907 | — | 3 | 6 | no | — |
| 180 | #907 | — | 6 | 3 | no | — |
| 181 | D3×M16 | — | 3 | 6 | no | — |
| 182 | D3×M16 | — | 6 | 3 | no | — |
| 183 | #904 | C2×D3 | 1 | 6 | yes | complemented |
| 184 | C2×#204 | C2×D3 | 1 | 6 | yes | complemented |
| 185 | #901 | — | 3 | 6 | no | — |
| 186 | #901 | — | 6 | 3 | no | — |
| 187 | C2×D3×C8 | — | 3 | 6 | no | — |
| 188 | C2×D3×C8 | — | 6 | 3 | no | — |
| 189 | C22×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 190 | C22×C3×D3 | — | 2 | 6 | no | — |
| 191 | C2×D32 | — | 2 | 6 | no | — |
| 192 | C32×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C32×D4 | C2×D4 | 1 | 3 | yes | — |
| 194 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 195 | #638 | C2×D4 | 1 | 6 | yes | — |
| 196 | C2×C3⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 197 | C4⋊(C3⋊D3) | C2×D4 | 1 | 3 | yes | — |
| 198 | C4×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 199 | C4×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 200 | C4×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 201 | C4×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 202 | #634 | C2×D4 | 1 | 3 | yes | — |
| 203 | C3×#67 | — | 2 | 6 | no | — |
| 204 | C3×#67 | — | 2 | 6 | no | — |
| 205 | C2×C3×Dic3 | — | 2 | 6 | no | — |
| 206 | C3×D12 | — | 2 | 6 | no | — |
| 207 | C3×D12 | C24 | 1 | 6 | yes | — |
| 208 | C3×D12 | C24 | 1 | 2 | yes | — |
| 209 | C3×C4×D3 | — | 2 | 6 | no | — |
| 210 | C3×C4×D3 | — | 2 | 6 | no | — |
| 211 | C3×Dic6 | — | 2 | 6 | no | — |
| 212 | C3×Dic6 | C24 | 1 | 2 | yes | — |
| 213 | C3×Dic6 | C24 | 1 | 6 | yes | — |
| 214 | #627 | — | 2 | 6 | no | — |
| 215 | #626 | — | 2 | 6 | no | — |
| 216 | #626 | — | 2 | 12 | no | — |
| 217 | #626 | — | 2 | 2 | no | — |
| 218 | #625 | — | 2 | 6 | no | — |
| 219 | #624 | — | 2 | 6 | no | — |
| 220 | D3×Dic3 | — | 2 | 12 | no | — |
| 221 | D3×Dic3 | — | 2 | 6 | no | — |
| 222 | D3×Dic3 | — | 2 | 2 | no | — |
| 223 | C32×C8 | C24 | 1 | 1 | yes | characteristic |
| 224 | C32×C8 | C24 | 1 | 3 | yes | — |
| 225 | C3⋊(C3⋊C8) | C24 | 1 | 1 | yes | characteristic |
| 226 | C3⋊(C3⋊C8) | C24 | 1 | 3 | yes | — |
| 227 | #585 | — | 9 | 2 | no | — |
| 228 | #578 | — | 9 | 3 | no | — |
| 229 | #578 | — | 9 | 1 | no | — |
| 230 | #577 | — | 3 | 2 | no | — |
| 231 | #577 | — | 9 | 6 | no | — |
| 232 | #576 | — | 9 | 3 | no | — |
| 233 | #576 | — | 9 | 1 | no | — |
| 234 | #575 | — | 9 | 6 | no | — |
| 235 | C2×#135 | — | 9 | 3 | no | — |
| 236 | C2×#135 | — | 9 | 3 | no | — |
| 237 | C2×#131 | — | 9 | 1 | no | — |
| 238 | C3×#41 | — | 2 | 1 | no | — |
| 239 | C3×#41 | — | 3 | 6 | no | — |
| 240 | C3×#41 | — | 3 | 6 | no | — |
| 241 | C3×#41 | — | 6 | 2 | no | — |
| 242 | C3×#41 | — | 6 | 6 | no | — |
| 243 | C3×#41 | C22×D3 | 1 | 2 | yes | — |
| 244 | C2×C3×Q8 | — | 3 | 6 | no | — |
| 245 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 246 | C2×C3×D4 | — | 3 | 6 | no | — |
| 247 | C2×C3×D4 | — | 6 | 6 | no | — |
| 248 | C2×#67 | — | 6 | 6 | no | — |
| 249 | C2×#67 | — | 6 | 12 | no | — |
| 250 | C22×Dic3 | — | 6 | 6 | no | — |
| 251 | #239 | — | 2 | 2 | no | — |
| 252 | #239 | — | 3 | 2 | no | — |
| 253 | #239 | — | 3 | 12 | no | — |
| 254 | #239 | — | 3 | 6 | no | — |
| 255 | #239 | — | 3 | 2 | no | — |
| 256 | #239 | — | 6 | 1 | no | — |
| 257 | #239 | — | 6 | 6 | no | — |
| 258 | #239 | — | 6 | 6 | no | — |
| 259 | #239 | — | 6 | 6 | no | — |
| 260 | D3×Q8 | — | 2 | 2 | no | — |
| 261 | D3×Q8 | — | 3 | 2 | no | — |
| 262 | D3×Q8 | — | 3 | 6 | no | — |
| 263 | D3×Q8 | — | 3 | 6 | no | — |
| 264 | D3×Q8 | — | 6 | 1 | no | — |
| 265 | D3×Q8 | — | 6 | 6 | no | — |
| 266 | #237 | — | 2 | 6 | no | — |
| 267 | #237 | — | 3 | 6 | no | — |
| 268 | #237 | — | 3 | 12 | no | — |
| 269 | #237 | — | 3 | 2 | no | — |
| 270 | #237 | — | 3 | 6 | no | — |
| 271 | #237 | — | 6 | 3 | no | — |
| 272 | #237 | — | 6 | 6 | no | — |
| 273 | #237 | — | 6 | 6 | no | — |
| 274 | #237 | — | 6 | 6 | no | — |
| 275 | #237 | — | 6 | 12 | no | — |
| 276 | #237 | — | 6 | 6 | no | — |
| 277 | #237 | — | 6 | 6 | no | — |
| 278 | D3×D4 | — | 2 | 6 | no | — |
| 279 | D3×D4 | — | 3 | 6 | no | — |
| 280 | D3×D4 | — | 3 | 6 | no | — |
| 281 | D3×D4 | — | 3 | 6 | no | — |
| 282 | D3×D4 | — | 6 | 3 | no | — |
| 283 | D3×D4 | — | 6 | 6 | no | — |
| 284 | D3×D4 | — | 6 | 6 | no | — |
| 285 | D3×D4 | — | 6 | 6 | no | — |
| 286 | D3×D4 | — | 6 | 12 | no | — |
| 287 | #235 | — | 3 | 6 | no | — |
| 288 | #235 | — | 6 | 3 | no | — |
| 289 | #235 | — | 6 | 6 | no | — |
| 290 | #235 | — | 6 | 6 | no | — |
| 291 | #235 | — | 6 | 6 | no | — |
| 292 | #235 | — | 6 | 6 | no | — |
| 293 | #235 | — | 6 | 12 | no | — |
| 294 | #235 | C22×D3 | 1 | 6 | yes | — |
| 295 | #235 | C22×D3 | 1 | 6 | yes | — |
| 296 | C2×D12 | — | 6 | 6 | no | — |
| 297 | C2×D12 | — | 6 | 6 | no | — |
| 298 | C2×D12 | C22×D3 | 1 | 6 | yes | — |
| 299 | C2×C4×D3 | — | 3 | 6 | no | — |
| 300 | C2×C4×D3 | — | 6 | 3 | no | — |
| 301 | C2×C4×D3 | — | 6 | 6 | no | — |
| 302 | C2×C4×D3 | — | 6 | 6 | no | — |
| 303 | C2×C4×D3 | — | 6 | 6 | no | — |
| 304 | C2×Dic6 | — | 6 | 6 | no | — |
| 305 | C2×Dic6 | C22×D3 | 1 | 6 | yes | — |
| 306 | C3×Q16 | — | 3 | 6 | no | — |
| 307 | C3×SD16 | — | 3 | 2 | no | — |
| 308 | C3×SD16 | — | 3 | 6 | no | — |
| 309 | C3×SD16 | — | 3 | 12 | no | — |
| 310 | C3×D8 | — | 3 | 6 | no | — |
| 311 | C3×M16 | — | 2 | 3 | no | — |
| 312 | C3×M16 | C22×D3 | 1 | 6 | yes | — |
| 313 | C2×C3×C8 | — | 2 | 3 | no | — |
| 314 | C2×C3×C8 | C22×D3 | 1 | 6 | yes | — |
| 315 | #216 | — | 3 | 12 | no | — |
| 316 | #216 | — | 3 | 6 | no | — |
| 317 | #216 | — | 3 | 2 | no | — |
| 318 | #215 | — | 3 | 6 | no | — |
| 319 | #215 | — | 3 | 6 | no | — |
| 320 | #214 | — | 3 | 6 | no | — |
| 321 | #214 | — | 3 | 6 | no | — |
| 322 | #213 | — | 3 | 2 | no | — |
| 323 | #213 | — | 3 | 6 | no | — |
| 324 | #213 | — | 3 | 12 | no | — |
| 325 | #208 | — | 3 | 6 | no | — |
| 326 | #208 | — | 6 | 3 | no | — |
| 327 | C2×C3⋊C8 | — | 3 | 6 | no | — |
| 328 | C2×C3⋊C8 | — | 6 | 3 | no | — |
| 329 | Dic12 | C22×D3 | 1 | 6 | yes | — |
| 330 | D24 | C22×D3 | 1 | 6 | yes | — |
| 331 | #204 | C22×D3 | 1 | 6 | yes | — |
| 332 | #204 | C22×D3 | 1 | 12 | yes | — |
| 333 | #204 | C22×D3 | 1 | 2 | yes | — |
| 334 | ΓL(1,𝔽25) | — | 3 | 12 | no | — |
| 335 | ΓL(1,𝔽25) | — | 6 | 6 | no | — |
| 336 | D3×C8 | — | 3 | 2 | no | — |
| 337 | D3×C8 | — | 3 | 6 | no | — |
| 338 | D3×C8 | — | 3 | 6 | no | — |
| 339 | D3×C8 | — | 3 | 6 | no | — |
| 340 | D3×C8 | — | 6 | 1 | no | — |
| 341 | D3×C8 | — | 6 | 3 | no | — |
| 342 | D3×C8 | — | 6 | 3 | no | — |
| 343 | D3×C8 | — | 6 | 3 | no | — |
| 344 | C22×C32 | C22×D4 | 1 | 3 | yes | — |
| 345 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 346 | C2×C3⋊D3 | C22×D4 | 1 | 3 | yes | — |
| 347 | C2×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 348 | C2×C3×D3 | — | 2 | 6 | no | — |
| 349 | C2×C3×D3 | — | 2 | 2 | no | — |
| 350 | C2×C3×D3 | — | 8 | 6 | no | — |
| 351 | D32 | — | 8 | 6 | no | — |
| 352 | C32×C4 | C22×D4 | 1 | 3 | yes | — |
| 353 | C32×C4 | C25 | 1 | 1 | yes | characteristic |
| 354 | C3⋊Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 355 | C3⋊Dic3 | C22×D4 | 1 | 3 | yes | — |
| 356 | C3×Dic3 | — | 2 | 6 | no | — |
| 357 | C3×Dic3 | — | 2 | 2 | no | — |
| 358 | 2−1+4 | — | 3 | 2 | no | — |
| 359 | 2−1+4 | — | 9 | 6 | no | — |
| 360 | 2−1+4 | — | 18 | 2 | no | — |
| 361 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 362 | H(5,𝔽2) | — | 9 | 6 | no | — |
| 363 | H(5,𝔽2) | — | 18 | 6 | no | — |
| 364 | C2×#41 | — | 9 | 1 | no | — |
| 365 | C2×#41 | — | 9 | 6 | no | — |
| 366 | C2×#41 | — | 9 | 6 | no | — |
| 367 | C2×#41 | — | 18 | 6 | no | — |
| 368 | C2×#41 | — | 18 | 2 | no | — |
| 369 | #137 | — | 3 | 6 | no | — |
| 370 | #137 | — | 9 | 12 | no | — |
| 371 | #137 | — | 9 | 6 | no | — |
| 372 | AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 373 | AGL(1,ℤ/8) | — | 9 | 12 | no | — |
| 374 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 375 | #135 | — | 3 | 6 | no | — |
| 376 | #135 | — | 9 | 6 | no | — |
| 377 | #135 | — | 9 | 3 | no | — |
| 378 | #135 | — | 9 | 1 | no | — |
| 379 | #135 | — | 9 | 6 | no | — |
| 380 | #135 | — | 9 | 6 | no | — |
| 381 | #135 | — | 9 | 6 | no | — |
| 382 | #135 | — | 9 | 3 | no | — |
| 383 | #135 | — | 9 | 3 | no | — |
| 384 | C2×Q16 | — | 9 | 3 | no | — |
| 385 | C2×Q16 | — | 9 | 3 | no | — |
| 386 | C2×SD16 | — | 3 | 6 | no | — |
| 387 | C2×SD16 | — | 9 | 6 | no | — |
| 388 | C2×D8 | — | 9 | 3 | no | — |
| 389 | C2×D8 | — | 9 | 3 | no | — |
| 390 | #131 | — | 9 | 1 | no | — |
| 391 | #131 | — | 9 | 3 | no | — |
| 392 | #131 | — | 9 | 3 | no | — |
| 393 | #131 | D32 | 1 | 1 | yes | characteristic, complemented |
| 394 | C2×M16 | — | 9 | 3 | no | — |
| 395 | C22×C8 | — | 9 | 3 | no | — |
| 396 | C23×C3 | — | 6 | 6 | no | — |
| 397 | C22×D3 | — | 2 | 6 | no | — |
| 398 | C22×D3 | — | 3 | 6 | no | — |
| 399 | C22×D3 | — | 6 | 3 | no | — |
| 400 | C22×D3 | — | 6 | 6 | no | — |
| 401 | C22×D3 | — | 6 | 6 | no | — |
| 402 | C3×Q8 | — | 2 | 1 | no | — |
| 403 | C3×Q8 | — | 3 | 2 | no | — |
| 404 | C3×Q8 | — | 3 | 6 | no | — |
| 405 | C3×Q8 | — | 6 | 6 | no | — |
| 406 | C3×Q8 | D3×D4 | 1 | 2 | yes | — |
| 407 | C3×D4 | — | 2 | 3 | no | — |
| 408 | C3×D4 | — | 3 | 6 | no | — |
| 409 | C3×D4 | — | 3 | 2 | no | — |
| 410 | C3×D4 | — | 6 | 6 | no | — |
| 411 | C3×D4 | — | 6 | 6 | no | — |
| 412 | C3×D4 | — | 6 | 6 | no | — |
| 413 | C3×D4 | D3×D4 | 1 | 6 | yes | — |
| 414 | C2×C3×C4 | — | 2 | 3 | no | — |
| 415 | C2×C3×C4 | — | 6 | 6 | no | — |
| 416 | C2×C3×C4 | — | 6 | 6 | no | — |
| 417 | C2×C3×C4 | — | 6 | 6 | no | — |
| 418 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 419 | #67 | — | 2 | 6 | no | — |
| 420 | #67 | — | 2 | 6 | no | — |
| 421 | #67 | — | 3 | 12 | no | — |
| 422 | #67 | — | 6 | 6 | no | — |
| 423 | #67 | — | 6 | 2 | no | — |
| 424 | #67 | — | 6 | 6 | no | — |
| 425 | #67 | — | 6 | 12 | no | — |
| 426 | #67 | — | 6 | 6 | no | — |
| 427 | #67 | — | 6 | 6 | no | — |
| 428 | C2×Dic3 | — | 2 | 6 | no | — |
| 429 | C2×Dic3 | — | 3 | 6 | no | — |
| 430 | C2×Dic3 | — | 6 | 3 | no | — |
| 431 | C2×Dic3 | — | 6 | 12 | no | — |
| 432 | C2×Dic3 | — | 6 | 2 | no | — |
| 433 | C2×Dic3 | — | 6 | 6 | no | — |
| 434 | D12 | — | 2 | 6 | no | — |
| 435 | D12 | — | 3 | 6 | no | — |
| 436 | D12 | — | 6 | 3 | no | — |
| 437 | D12 | — | 6 | 6 | no | — |
| 438 | D12 | — | 6 | 12 | no | — |
| 439 | D12 | — | 6 | 2 | no | — |
| 440 | D12 | C23×D3 | 1 | 6 | yes | — |
| 441 | D12 | C23×D3 | 1 | 2 | yes | — |
| 442 | C4×D3 | — | 2 | 6 | no | — |
| 443 | C4×D3 | — | 2 | 6 | no | — |
| 444 | C4×D3 | — | 3 | 6 | no | — |
| 445 | C4×D3 | — | 3 | 6 | no | — |
| 446 | C4×D3 | — | 3 | 2 | no | — |
| 447 | C4×D3 | — | 3 | 6 | no | — |
| 448 | C4×D3 | — | 6 | 3 | no | — |
| 449 | C4×D3 | — | 6 | 3 | no | — |
| 450 | C4×D3 | — | 6 | 1 | no | — |
| 451 | C4×D3 | — | 6 | 3 | no | — |
| 452 | C4×D3 | — | 6 | 6 | no | — |
| 453 | C4×D3 | — | 6 | 6 | no | — |
| 454 | C4×D3 | — | 6 | 2 | no | — |
| 455 | C4×D3 | — | 6 | 6 | no | — |
| 456 | C4×D3 | — | 6 | 12 | no | — |
| 457 | Dic6 | — | 2 | 6 | no | — |
| 458 | Dic6 | — | 3 | 6 | no | — |
| 459 | Dic6 | — | 6 | 3 | no | — |
| 460 | Dic6 | — | 6 | 6 | no | — |
| 461 | Dic6 | — | 6 | 6 | no | — |
| 462 | Dic6 | C23×D3 | 1 | 6 | yes | — |
| 463 | Dic6 | C23×D3 | 1 | 2 | yes | — |
| 464 | C3×C8 | — | 2 | 1 | no | — |
| 465 | C3×C8 | — | 2 | 3 | no | — |
| 466 | C3×C8 | C23×D3 | 1 | 2 | yes | — |
| 467 | C3×C8 | C23×D3 | 1 | 6 | yes | — |
| 468 | C3⋊C8 | — | 3 | 2 | no | — |
| 469 | C3⋊C8 | — | 3 | 6 | no | — |
| 470 | C3⋊C8 | — | 6 | 1 | no | — |
| 471 | C3⋊C8 | — | 6 | 3 | no | — |
| 472 | C2×C32 | — | 2 | 3 | no | — |
| 473 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 474 | C3⋊D3 | — | 2 | 1 | no | — |
| 475 | C3⋊D3 | — | 2 | 3 | no | — |
| 476 | C3×D3 | — | 4 | 2 | no | — |
| 477 | C3×D3 | — | 4 | 6 | no | — |
| 478 | #41 | — | 3 | 6 | no | — |
| 479 | #41 | — | 3 | 6 | no | — |
| 480 | #41 | — | 6 | 2 | no | — |
| 481 | #41 | — | 6 | 6 | no | — |
| 482 | #41 | — | 9 | 1 | no | — |
| 483 | #41 | — | 9 | 3 | no | — |
| 484 | #41 | — | 9 | 3 | no | — |
| 485 | #41 | — | 9 | 2 | no | — |
| 486 | #41 | — | 9 | 6 | no | — |
| 487 | #41 | — | 9 | 12 | no | — |
| 488 | #41 | — | 18 | 6 | no | — |
| 489 | #41 | — | 18 | 12 | no | — |
| 490 | #41 | — | 18 | 6 | no | — |
| 491 | #41 | — | 18 | 6 | no | — |
| 492 | #41 | — | 18 | 6 | no | — |
| 493 | #41 | — | 18 | 6 | no | — |
| 494 | #41 | — | 18 | 6 | no | — |
| 495 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 496 | C2×Q8 | — | 3 | 6 | no | — |
| 497 | C2×Q8 | — | 6 | 2 | no | — |
| 498 | C2×Q8 | — | 9 | 1 | no | — |
| 499 | C2×Q8 | — | 9 | 6 | no | — |
| 500 | C2×Q8 | — | 18 | 6 | no | — |
| 501 | C2×D4 | — | 3 | 6 | no | — |
| 502 | C2×D4 | — | 6 | 6 | no | — |
| 503 | C2×D4 | — | 9 | 6 | no | — |
| 504 | C2×D4 | — | 9 | 3 | no | — |
| 505 | C2×D4 | — | 18 | 6 | no | — |
| 506 | C2×D4 | — | 18 | 6 | no | — |
| 507 | C2×D4 | — | 18 | 6 | no | — |
| 508 | C2×D4 | — | 18 | 12 | no | — |
| 509 | C22×C4 | — | 9 | 3 | no | — |
| 510 | C22×C4 | — | 18 | 6 | no | — |
| 511 | C22×C4 | — | 18 | 6 | no | — |
| 512 | Q16 | — | 3 | 6 | no | — |
| 513 | Q16 | — | 9 | 3 | no | — |
| 514 | Q16 | — | 9 | 1 | no | — |
| 515 | Q16 | — | 9 | 6 | no | — |
| 516 | SD16 | — | 3 | 6 | no | — |
| 517 | SD16 | — | 3 | 12 | no | — |
| 518 | SD16 | — | 3 | 2 | no | — |
| 519 | SD16 | — | 9 | 6 | no | — |
| 520 | SD16 | — | 9 | 6 | no | — |
| 521 | D8 | — | 3 | 6 | no | — |
| 522 | D8 | — | 9 | 1 | no | — |
| 523 | D8 | — | 9 | 3 | no | — |
| 524 | D8 | — | 9 | 6 | no | — |
| 525 | M16 | — | 9 | 3 | no | — |
| 526 | M16 | — | 9 | 6 | no | — |
| 527 | M16 | C2×D32 | 1 | 3 | yes | — |
| 528 | C2×C8 | — | 9 | 3 | no | — |
| 529 | C2×C8 | — | 9 | 1 | no | — |
| 530 | C2×C8 | — | 9 | 3 | no | — |
| 531 | C2×C8 | — | 9 | 3 | no | — |
| 532 | C2×C8 | — | 9 | 3 | no | — |
| 533 | C2×C8 | C2×D32 | 1 | 3 | yes | — |
| 534 | C22×C3 | — | 2 | 3 | no | — |
| 535 | C22×C3 | — | 6 | 6 | no | — |
| 536 | C22×C3 | — | 6 | 2 | no | — |
| 537 | C22×C3 | — | 24 | 6 | no | — |
| 538 | C22×C3 | C2×D3×D4 | 1 | 6 | yes | — |
| 539 | C2×D3 | — | 2 | 2 | no | — |
| 540 | C2×D3 | — | 2 | 6 | no | — |
| 541 | C2×D3 | — | 3 | 2 | no | — |
| 542 | C2×D3 | — | 3 | 6 | no | — |
| 543 | C2×D3 | — | 6 | 1 | no | — |
| 544 | C2×D3 | — | 6 | 3 | no | — |
| 545 | C2×D3 | — | 8 | 6 | no | — |
| 546 | C2×D3 | — | 12 | 6 | no | — |
| 547 | C2×D3 | — | 12 | 6 | no | — |
| 548 | C2×D3 | — | 24 | 6 | no | — |
| 549 | C2×D3 | — | 24 | 6 | no | — |
| 550 | C3×C4 | — | 2 | 3 | no | — |
| 551 | C3×C4 | — | 2 | 1 | no | — |
| 552 | C3×C4 | — | 6 | 2 | no | — |
| 553 | C3×C4 | — | 6 | 6 | no | — |
| 554 | C3×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 555 | C3×C4 | C24×D3 | 1 | 2 | yes | — |
| 556 | Dic3 | — | 2 | 6 | no | — |
| 557 | Dic3 | — | 2 | 2 | no | — |
| 558 | Dic3 | — | 3 | 6 | no | — |
| 559 | Dic3 | — | 3 | 2 | no | — |
| 560 | Dic3 | — | 6 | 3 | no | — |
| 561 | Dic3 | — | 6 | 1 | no | — |
| 562 | C32 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 563 | C23 | — | 6 | 6 | no | — |
| 564 | C23 | — | 9 | 3 | no | — |
| 565 | C23 | — | 18 | 6 | no | — |
| 566 | Q8 | — | 3 | 6 | no | — |
| 567 | Q8 | — | 3 | 2 | no | — |
| 568 | Q8 | — | 6 | 6 | no | — |
| 569 | Q8 | — | 9 | 3 | no | — |
| 570 | Q8 | — | 18 | 6 | no | — |
| 571 | Q8 | #3802 | 1 | 1 | yes | characteristic |
| 572 | D4 | — | 3 | 2 | no | — |
| 573 | D4 | — | 3 | 6 | no | — |
| 574 | D4 | — | 6 | 6 | no | — |
| 575 | D4 | — | 6 | 6 | no | — |
| 576 | D4 | — | 6 | 6 | no | — |
| 577 | D4 | — | 9 | 6 | no | — |
| 578 | D4 | — | 9 | 3 | no | — |
| 579 | D4 | — | 18 | 2 | no | — |
| 580 | D4 | — | 18 | 6 | no | — |
| 581 | D4 | — | 18 | 12 | no | — |
| 582 | D4 | — | 18 | 6 | no | — |
| 583 | D4 | #3802 | 1 | 3 | yes | — |
| 584 | C2×C4 | — | 6 | 6 | no | — |
| 585 | C2×C4 | — | 6 | 6 | no | — |
| 586 | C2×C4 | — | 6 | 6 | no | — |
| 587 | C2×C4 | — | 9 | 3 | no | — |
| 588 | C2×C4 | — | 9 | 3 | no | — |
| 589 | C2×C4 | — | 9 | 3 | no | — |
| 590 | C2×C4 | — | 9 | 1 | no | — |
| 591 | C2×C4 | — | 9 | 3 | no | — |
| 592 | C2×C4 | — | 18 | 6 | no | — |
| 593 | C2×C4 | — | 18 | 2 | no | — |
| 594 | C2×C4 | — | 18 | 6 | no | — |
| 595 | C2×C4 | — | 18 | 12 | no | — |
| 596 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 597 | C8 | — | 9 | 1 | no | — |
| 598 | C8 | — | 9 | 3 | no | — |
| 599 | C8 | C22×D32 | 1 | 1 | yes | characteristic |
| 600 | C8 | C22×D32 | 1 | 3 | yes | — |
| 601 | C2×C3 | — | 2 | 6 | no | — |
| 602 | C2×C3 | — | 2 | 1 | no | — |
| 603 | C2×C3 | — | 4 | 3 | no | — |
| 604 | C2×C3 | — | 12 | 2 | no | — |
| 605 | C2×C3 | — | 12 | 6 | no | — |
| 606 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 607 | D3 | — | 4 | 6 | no | — |
| 608 | D3 | — | 4 | 2 | no | — |
| 609 | D3 | — | 6 | 2 | no | — |
| 610 | D3 | — | 6 | 2 | no | — |
| 611 | D3 | — | 6 | 6 | no | — |
| 612 | D3 | — | 12 | 3 | no | — |
| 613 | C22 | — | 6 | 2 | no | — |
| 614 | C22 | — | 6 | 6 | no | — |
| 615 | C22 | — | 9 | 1 | no | — |
| 616 | C22 | — | 9 | 3 | no | — |
| 617 | C22 | — | 24 | 6 | no | — |
| 618 | C22 | — | 36 | 3 | no | — |
| 619 | C22 | — | 72 | 6 | no | — |
| 620 | C22 | C2×#3802 | 1 | 3 | yes | — |
| 621 | C4 | — | 6 | 2 | no | — |
| 622 | C4 | — | 6 | 6 | no | — |
| 623 | C4 | — | 9 | 1 | no | — |
| 624 | C4 | — | 9 | 3 | no | — |
| 625 | C4 | C2×#3802 | 1 | 3 | yes | — |
| 626 | C4 | C23×D32 | 1 | 1 | yes | characteristic |
| 627 | C3 | — | 2 | 1 | no | — |
| 628 | C3 | #87206 | 1 | 2 | yes | complemented |
| 629 | C2 | — | 2 | 3 | no | — |
| 630 | C2 | — | 12 | 6 | no | — |
| 631 | C2 | — | 12 | 2 | no | — |
| 632 | C2 | — | 18 | 1 | no | — |
| 633 | C2 | — | 18 | 3 | no | — |
| 634 | 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 | #3584 |
| 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. #10596698 | C2 | semidirect |
| 2. C3⋊D3×#131 | C2 | semidirect |
| 3. C3×#5751 | C2 | semidirect |
| 4. #10595445 | C2 | semidirect |
| 5. #10595444 | C2 | semidirect |
| 6. #10594723 | C2 | semidirect |
| 7. #10594720 | C2 | semidirect |
| 8. #10594718 | C2 | semidirect |
| 9. C2×#63809 | C2 | semidirect |
| 10. #10594686 | C2 | semidirect |
| 11. #10594684 | C2 | semidirect |
| 14. C3×#1010 | C22 | semidirect |
| 15. C3×#1009 | C22 | semidirect |
| 20. #64307 | C22 | semidirect |
| 21. #64306 | C22 | semidirect |
| 22. #64297 | C22 | semidirect |
| 23. C2×#3796 | C22 | semidirect |
| 24. C32×#131 | C22 | semidirect |
| 25. #64157 | C22 | semidirect |
| 26. #64116 | C22 | semidirect |
| 27. M16×C3⋊D3 | C22 | semidirect |
| 28. #64110 | C22 | semidirect |
| 29. C2×C8×C3⋊D3 | C22 | semidirect |
| 30. C3×#909 | C22 | semidirect |
| 31. C3×#908 | C22 | semidirect |
| 32. C3×#904 | C22 | semidirect |
| 33. C2×C3×#204 | C22 | semidirect |
| 34. C2×#3718 | C22 | semidirect |
| 35. #63827 | C22 | semidirect |
| 36. #63823 | C22 | semidirect |
| 37. #63822 | C22 | semidirect |
| 38. #63822 | C22 | semidirect |
| 39. C2×#3713 | C22 | semidirect |
| 40. #63811 | C22 | semidirect |
| 41. #63810 | C22 | semidirect |
| 42. #63809 | C22 | semidirect |
| 43. #63809 | C22 | semidirect |
| 44. #63809 | C22 | semidirect |
| 45. #63809 | C22 | semidirect |
| 46. #63809 | C22 | semidirect |
| 47. #63802 | C22 | semidirect |
| 48. #63798 | C22 | semidirect |
| 49. #63797 | C22 | semidirect |
| 50. #63796 | C22 | semidirect |
| 64. #5751 | D3 | semidirect |
| 128. #1010 | C2×D3 | semidirect |
| 131. #1009 | C2×D3 | semidirect |
| 151. C3×#131 | C2×D3 | semidirect |
| 177. #909 | C2×D3 | semidirect |
| 178. #908 | C2×D3 | semidirect |
| 183. #904 | C2×D3 | semidirect |
| 184. C2×#204 | C2×D3 | semidirect |
| 393. #131 | D32 | semidirect |
| 562. C32 | #3584 | semidirect |
| 628. C3 | #87206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596698 | 2 |
| C3⋊D3×#131 | 2 |
| C3×#5751 | 2 |
| #10595445 | 2 |
| #10595444 | 2 |
| #10594723 | 2 |
| #10594720 | 2 |
| #10594718 | 2 |
| C2×#63809 | 2 |
| #10594686 | 2 |
| #10594684 | 2 |
| #87206 | 3 |