Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
6509 conjugacy classes of subgroups.
The subgroup lattice has 682 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10585848 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #7622976 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #6629044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#32948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #511968 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #511966 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #494664 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×#13074 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #493820 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C2×#3573 | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #62624 | — | 2 | 12 | no | — |
| 13 | #62624 | C22 | 1 | 8 | yes | complemented |
| 14 | C2×#3407 | — | 2 | 12 | no | — |
| 15 | C2×#3407 | C22 | 1 | 3 | yes | — |
| 16 | C2×#3407 | C22 | 1 | 3 | yes | — |
| 17 | #60450 | C22 | 1 | 3 | yes | — |
| 18 | C2×#3058 | C22 | 1 | 3 | yes | — |
| 19 | #60398 | — | 2 | 1 | no | — |
| 20 | C2×#3027 | — | 2 | 1 | no | — |
| 21 | #33612 | — | 2 | 12 | no | — |
| 22 | #33609 | C22 | 1 | 12 | yes | complemented |
| 23 | #33607 | C22 | 1 | 12 | yes | complemented |
| 24 | #33605 | — | 2 | 12 | no | — |
| 25 | #33409 | C22 | 1 | 3 | yes | complemented |
| 26 | #33380 | C22 | 1 | 3 | yes | complemented |
| 27 | C2×#2140 | C22 | 1 | 3 | yes | complemented |
| 28 | #32949 | C22 | 1 | 4 | yes | complemented |
| 29 | #32948 | — | 2 | 4 | no | — |
| 30 | #32948 | C22 | 1 | 8 | yes | — |
| 31 | #32948 | C22 | 1 | 4 | yes | complemented |
| 32 | #32947 | — | 2 | 4 | no | — |
| 33 | #21009 | — | 2 | 3 | no | — |
| 34 | C2×#1910 | — | 2 | 3 | no | — |
| 35 | C2×#1812 | C22 | 1 | 3 | yes | — |
| 36 | C2×#1812 | C22 | 1 | 3 | yes | — |
| 37 | #13075 | C22 | 1 | 12 | yes | complemented |
| 38 | #13074 | C22 | 1 | 24 | yes | complemented |
| 39 | #13074 | C22 | 1 | 12 | yes | complemented |
| 40 | #12839 | C22 | 1 | 24 | yes | complemented |
| 41 | C2×#1384 | C22 | 1 | 6 | yes | complemented |
| 42 | C2×#585 | D4 | 1 | 1 | yes | characteristic |
| 43 | C22×#135 | C23 | 1 | 1 | yes | characteristic |
| 44 | C23×D8 | C23 | 1 | 1 | yes | characteristic |
| 45 | #3573 | — | 2 | 6 | no | — |
| 46 | #3573 | — | 2 | 6 | no | — |
| 47 | #3573 | D4 | 1 | 4 | yes | — |
| 48 | #3573 | C23 | 1 | 4 | yes | — |
| 49 | C2×#568 | — | 2 | 6 | no | — |
| 50 | C2×#568 | D4 | 1 | 3 | yes | — |
| 51 | C22×#131 | — | 2 | 6 | no | — |
| 52 | C22×#131 | C23 | 1 | 3 | yes | — |
| 53 | #3449 | — | 2 | 3 | no | — |
| 54 | C2×#535 | — | 2 | 3 | no | — |
| 55 | C2×#509 | — | 2 | 6 | no | — |
| 56 | C2×#509 | — | 2 | 6 | no | — |
| 57 | C22×SD32 | C23 | 1 | 2 | yes | complemented |
| 58 | C22×D16 | C23 | 1 | 2 | yes | complemented |
| 59 | #3407 | — | 2 | 16 | no | — |
| 60 | #3407 | — | 2 | 48 | no | — |
| 61 | #3407 | — | 2 | 12 | no | — |
| 62 | #3407 | — | 2 | 12 | no | — |
| 63 | #3407 | — | 2 | 12 | no | — |
| 64 | #3407 | — | 2 | 48 | no | — |
| 65 | #3407 | — | 2 | 6 | no | — |
| 66 | #3407 | C23 | 1 | 12 | yes | — |
| 67 | C2×#504 | — | 2 | 48 | no | — |
| 68 | C2×#504 | — | 2 | 12 | no | — |
| 69 | C2×#504 | — | 2 | 48 | no | — |
| 70 | C2×#504 | D4 | 1 | 12 | yes | complemented |
| 71 | C2×#504 | C23 | 1 | 12 | yes | — |
| 72 | C22×M32 | — | 2 | 16 | no | — |
| 73 | C22×M32 | — | 2 | 6 | no | — |
| 74 | C22×M32 | D4 | 1 | 12 | yes | complemented |
| 75 | C22×M32 | C23 | 1 | 3 | yes | — |
| 76 | C22×M32 | C23 | 1 | 1 | yes | characteristic |
| 77 | #3061 | — | 2 | 6 | no | — |
| 78 | #3060 | — | 2 | 6 | no | — |
| 79 | #3059 | C23 | 1 | 6 | yes | — |
| 80 | #3058 | — | 2 | 6 | no | — |
| 81 | #3058 | — | 2 | 6 | no | — |
| 82 | #3058 | — | 2 | 6 | no | — |
| 83 | #3058 | C23 | 1 | 12 | yes | — |
| 84 | #3058 | C23 | 1 | 6 | yes | — |
| 85 | #3057 | — | 2 | 6 | no | — |
| 86 | #3054 | — | 2 | 6 | no | — |
| 87 | C2×#469 | — | 2 | 6 | no | — |
| 88 | #3050 | — | 2 | 6 | no | — |
| 89 | C2×#466 | — | 2 | 6 | no | — |
| 90 | #3028 | — | 2 | 4 | no | — |
| 91 | #3027 | — | 2 | 4 | no | — |
| 92 | #3027 | — | 2 | 8 | no | — |
| 93 | #3027 | — | 4 | 4 | no | — |
| 94 | #3026 | — | 4 | 4 | no | — |
| 95 | #3025 | — | 4 | 4 | no | — |
| 96 | C2×B(4,𝔽2) | — | 4 | 4 | no | — |
| 97 | C2×#427 | C23 | 1 | 3 | yes | — |
| 98 | C2×#427 | C23 | 1 | 3 | yes | — |
| 99 | #2896 | — | 2 | 3 | no | — |
| 100 | C2×#418 | — | 2 | 3 | no | — |
| 101 | C2×#410 | — | 2 | 3 | no | — |
| 102 | C2×#410 | — | 2 | 3 | no | — |
| 103 | #2220 | — | 2 | 24 | no | — |
| 104 | #2218 | — | 2 | 24 | no | — |
| 105 | #2217 | — | 2 | 24 | no | — |
| 106 | #2215 | — | 2 | 24 | no | — |
| 107 | #2159 | — | 2 | 6 | no | — |
| 108 | #2159 | — | 2 | 6 | no | — |
| 109 | #2158 | C23 | 1 | 12 | yes | complemented |
| 110 | #2141 | C23 | 1 | 6 | yes | complemented |
| 111 | #2140 | — | 2 | 6 | no | — |
| 112 | #2140 | C23 | 1 | 6 | yes | complemented |
| 113 | #2140 | C23 | 1 | 12 | yes | complemented |
| 114 | #2139 | — | 2 | 6 | no | — |
| 115 | #2138 | — | 2 | 6 | no | — |
| 116 | C2×#357 | — | 2 | 6 | no | — |
| 117 | #1910 | — | 2 | 24 | no | — |
| 118 | #1910 | — | 2 | 12 | no | — |
| 119 | #1909 | — | 2 | 12 | no | — |
| 120 | #1812 | — | 2 | 6 | no | — |
| 121 | #1812 | — | 2 | 6 | no | — |
| 122 | #1812 | C23 | 1 | 12 | yes | — |
| 123 | #1812 | C23 | 1 | 12 | yes | — |
| 124 | C2×H(3,ℤ/4) | — | 2 | 3 | no | — |
| 125 | C2×H(3,ℤ/4) | — | 2 | 3 | no | — |
| 126 | #1384 | C23 | 1 | 24 | yes | complemented |
| 127 | #585 | — | 2 | 6 | no | — |
| 128 | #585 | — | 2 | 6 | no | — |
| 129 | #585 | D8 | 1 | 4 | yes | — |
| 130 | #585 | C2×D4 | 1 | 4 | yes | — |
| 131 | C2×2−1+4 | — | 2 | 3 | no | — |
| 132 | C2×H(5,𝔽2) | — | 2 | 3 | no | — |
| 133 | C2×H(5,𝔽2) | D8 | 1 | 4 | yes | — |
| 134 | C22×#41 | — | 2 | 6 | no | — |
| 135 | C22×#41 | — | 2 | 1 | no | — |
| 136 | C22×#41 | C2×D4 | 1 | 3 | yes | — |
| 137 | C23×D4 | — | 2 | 1 | no | — |
| 138 | C2×#135 | — | 2 | 3 | no | — |
| 139 | C2×#135 | — | 2 | 3 | no | — |
| 140 | C2×#135 | — | 2 | 3 | no | — |
| 141 | C2×#135 | — | 2 | 3 | no | — |
| 142 | C22×Q16 | C24 | 1 | 1 | yes | characteristic |
| 143 | C22×SD16 | — | 2 | 1 | no | — |
| 144 | C22×D8 | — | 2 | 3 | no | — |
| 145 | C22×D8 | — | 2 | 3 | no | — |
| 146 | C22×D8 | — | 2 | 1 | no | — |
| 147 | C22×D8 | — | 2 | 3 | no | — |
| 148 | C22×D8 | — | 2 | 3 | no | — |
| 149 | C22×D8 | C24 | 1 | 1 | yes | characteristic |
| 150 | C22×D8 | C24 | 1 | 2 | yes | — |
| 151 | #568 | — | 2 | 48 | no | — |
| 152 | #568 | — | 2 | 6 | no | — |
| 153 | #568 | — | 2 | 24 | no | — |
| 154 | #568 | — | 2 | 12 | no | — |
| 155 | #568 | — | 2 | 24 | no | — |
| 156 | #568 | C2×D4 | 1 | 12 | yes | — |
| 157 | C2×#131 | — | 2 | 24 | no | — |
| 158 | C2×#131 | — | 2 | 4 | no | — |
| 159 | C2×#131 | — | 2 | 12 | no | — |
| 160 | C2×#131 | — | 2 | 24 | no | — |
| 161 | C2×#131 | — | 2 | 12 | no | — |
| 162 | C2×#131 | — | 2 | 24 | no | — |
| 163 | C2×#131 | — | 2 | 24 | no | — |
| 164 | C2×#131 | — | 2 | 6 | no | — |
| 165 | C2×#131 | — | 2 | 6 | no | — |
| 166 | C2×#131 | — | 2 | 6 | no | — |
| 167 | C2×#131 | — | 2 | 6 | no | — |
| 168 | C2×#131 | C2×D4 | 1 | 6 | yes | — |
| 169 | C2×#131 | C2×D4 | 1 | 6 | yes | — |
| 170 | C2×#131 | #41 | 1 | 6 | yes | — |
| 171 | C2×#131 | C24 | 1 | 6 | yes | — |
| 172 | C22×M16 | — | 2 | 12 | no | — |
| 173 | C22×M16 | — | 2 | 6 | no | — |
| 174 | C22×M16 | C2×D4 | 1 | 3 | yes | — |
| 175 | C22×M16 | #41 | 1 | 6 | yes | — |
| 176 | C23×C8 | — | 2 | 4 | no | — |
| 177 | C23×C8 | C2×D4 | 1 | 6 | yes | — |
| 178 | C23×C8 | C24 | 1 | 1 | yes | characteristic |
| 179 | #537 | — | 4 | 6 | no | — |
| 180 | #536 | — | 2 | 6 | no | — |
| 181 | #536 | — | 4 | 3 | no | — |
| 182 | #535 | — | 2 | 12 | no | — |
| 183 | #535 | — | 2 | 6 | no | — |
| 184 | #535 | — | 4 | 6 | no | — |
| 185 | #535 | — | 4 | 6 | no | — |
| 186 | #535 | — | 4 | 6 | no | — |
| 187 | #535 | — | 4 | 3 | no | — |
| 188 | #534 | — | 4 | 6 | no | — |
| 189 | #532 | — | 4 | 6 | no | — |
| 190 | C2×#127 | — | 4 | 3 | no | — |
| 191 | C2×#124 | — | 4 | 3 | no | — |
| 192 | #525 | — | 4 | 6 | no | — |
| 193 | #525 | — | 4 | 6 | no | — |
| 194 | C2×#121 | — | 4 | 6 | no | — |
| 195 | C2×#120 | — | 4 | 6 | no | — |
| 196 | C2×#117 | — | 2 | 3 | no | — |
| 197 | C2×#117 | — | 2 | 3 | no | — |
| 198 | #509 | — | 4 | 4 | no | — |
| 199 | #509 | — | 4 | 12 | no | — |
| 200 | C2×SD32 | — | 2 | 12 | no | — |
| 201 | C2×D16 | — | 2 | 12 | no | — |
| 202 | #504 | — | 2 | 48 | no | — |
| 203 | #504 | — | 2 | 96 | no | — |
| 204 | #504 | — | 2 | 32 | no | — |
| 205 | #504 | — | 2 | 48 | no | — |
| 206 | #504 | — | 2 | 48 | no | — |
| 207 | #504 | — | 2 | 48 | no | — |
| 208 | C2×M32 | — | 2 | 24 | no | — |
| 209 | C2×M32 | — | 2 | 96 | no | — |
| 210 | C2×M32 | — | 2 | 12 | no | — |
| 211 | C2×M32 | — | 2 | 6 | no | — |
| 212 | C2×M32 | — | 2 | 24 | no | — |
| 213 | C2×M32 | — | 2 | 6 | no | — |
| 214 | C2×M32 | — | 2 | 24 | no | — |
| 215 | C2×M32 | — | 2 | 24 | no | — |
| 216 | C2×M32 | C2×D4 | 1 | 6 | yes | — |
| 217 | C2×M32 | C2×D4 | 1 | 6 | yes | — |
| 218 | C2×M32 | C2×D4 | 1 | 6 | yes | — |
| 219 | C2×M32 | C2×D4 | 1 | 24 | yes | complemented |
| 220 | C2×M32 | C24 | 1 | 6 | yes | — |
| 221 | C22×C16 | — | 2 | 12 | no | — |
| 222 | C22×C16 | — | 2 | 32 | no | — |
| 223 | C22×C16 | C2×D4 | 1 | 6 | yes | — |
| 224 | C22×C16 | C2×D4 | 1 | 24 | yes | complemented |
| 225 | C22×C16 | C24 | 1 | 2 | yes | — |
| 226 | #470 | — | 2 | 12 | no | — |
| 227 | #469 | — | 2 | 24 | no | — |
| 228 | #469 | — | 2 | 12 | no | — |
| 229 | #469 | — | 4 | 12 | no | — |
| 230 | #468 | — | 4 | 12 | no | — |
| 231 | #467 | — | 2 | 12 | no | — |
| 232 | #466 | — | 2 | 12 | no | — |
| 233 | #466 | — | 2 | 24 | no | — |
| 234 | #466 | — | 4 | 12 | no | — |
| 235 | #465 | — | 4 | 12 | no | — |
| 236 | #458 | — | 4 | 16 | no | — |
| 237 | B(4,𝔽2) | — | 4 | 32 | no | — |
| 238 | B(4,𝔽2) | — | 4 | 16 | no | — |
| 239 | #427 | — | 2 | 3 | no | — |
| 240 | #427 | — | 2 | 3 | no | — |
| 241 | #427 | — | 2 | 3 | no | — |
| 242 | #427 | — | 2 | 3 | no | — |
| 243 | #427 | — | 2 | 3 | no | — |
| 244 | #427 | — | 2 | 3 | no | — |
| 245 | #427 | C24 | 1 | 6 | yes | — |
| 246 | #427 | C24 | 1 | 6 | yes | — |
| 247 | C2×#107 | — | 2 | 3 | no | — |
| 248 | C2×#107 | — | 2 | 3 | no | — |
| 249 | C2×#106 | — | 2 | 3 | no | — |
| 250 | C2×#106 | — | 2 | 3 | no | — |
| 251 | #419 | — | 2 | 6 | no | — |
| 252 | #418 | — | 2 | 12 | no | — |
| 253 | #418 | — | 2 | 6 | no | — |
| 254 | #418 | — | 4 | 6 | no | — |
| 255 | #417 | — | 4 | 6 | no | — |
| 256 | #416 | — | 4 | 6 | no | — |
| 257 | C2×#102 | — | 4 | 6 | no | — |
| 258 | #410 | — | 2 | 12 | no | — |
| 259 | #410 | — | 2 | 12 | no | — |
| 260 | #410 | — | 4 | 6 | no | — |
| 261 | #410 | — | 4 | 6 | no | — |
| 262 | C2×#99 | — | 4 | 6 | no | — |
| 263 | C2×#99 | — | 4 | 6 | no | — |
| 264 | #367 | — | 2 | 12 | no | — |
| 265 | #366 | — | 2 | 12 | no | — |
| 266 | #358 | — | 2 | 12 | no | — |
| 267 | #357 | — | 2 | 24 | no | — |
| 268 | #357 | — | 2 | 12 | no | — |
| 269 | H(3,ℤ/4) | — | 2 | 12 | no | — |
| 270 | H(3,ℤ/4) | — | 2 | 12 | no | — |
| 271 | C25 | — | 4 | 1 | no | — |
| 272 | 2−1+4 | — | 2 | 24 | no | — |
| 273 | 2−1+4 | — | 2 | 12 | no | — |
| 274 | 2−1+4 | — | 2 | 12 | no | — |
| 275 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 276 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 277 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 278 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 279 | H(5,𝔽2) | C2×D8 | 1 | 16 | yes | — |
| 280 | C2×#41 | — | 2 | 4 | no | — |
| 281 | C2×#41 | — | 2 | 24 | no | — |
| 282 | C2×#41 | — | 2 | 12 | no | — |
| 283 | C2×#41 | — | 2 | 24 | no | — |
| 284 | C2×#41 | — | 2 | 6 | no | — |
| 285 | C2×#41 | — | 2 | 24 | no | — |
| 286 | C2×#41 | — | 2 | 6 | no | — |
| 287 | C2×#41 | — | 2 | 6 | no | — |
| 288 | C2×#41 | — | 2 | 6 | no | — |
| 289 | C2×#41 | — | 2 | 12 | no | — |
| 290 | C2×#41 | — | 2 | 24 | no | — |
| 291 | C2×#41 | — | 4 | 3 | no | — |
| 292 | C2×#41 | — | 4 | 3 | no | — |
| 293 | C2×#41 | — | 4 | 3 | no | — |
| 294 | C2×#41 | — | 4 | 3 | no | — |
| 295 | C2×#41 | #121 | 1 | 6 | yes | — |
| 296 | C2×#41 | C2×D8 | 1 | 6 | yes | — |
| 297 | C2×#41 | #135 | 1 | 6 | yes | — |
| 298 | C2×#41 | C22×D4 | 1 | 6 | yes | — |
| 299 | C22×Q8 | — | 2 | 6 | no | — |
| 300 | C22×Q8 | — | 2 | 1 | no | — |
| 301 | C22×Q8 | #135 | 1 | 3 | yes | — |
| 302 | C22×D4 | — | 2 | 6 | no | — |
| 303 | C22×D4 | — | 2 | 12 | no | — |
| 304 | C22×D4 | — | 2 | 2 | no | — |
| 305 | C22×D4 | — | 2 | 1 | no | — |
| 306 | C22×D4 | — | 4 | 1 | no | — |
| 307 | C22×D4 | — | 4 | 3 | no | — |
| 308 | C22×D4 | — | 4 | 3 | no | — |
| 309 | C22×D4 | — | 4 | 1 | no | — |
| 310 | C22×D4 | — | 4 | 3 | no | — |
| 311 | C22×D4 | — | 4 | 3 | no | — |
| 312 | C22×D4 | — | 8 | 6 | no | — |
| 313 | C22×D4 | C2×D8 | 1 | 6 | yes | — |
| 314 | C22×D4 | #135 | 1 | 3 | yes | — |
| 315 | C23×C4 | — | 2 | 4 | no | — |
| 316 | C23×C4 | — | 4 | 1 | no | — |
| 317 | C23×C4 | #121 | 1 | 6 | yes | — |
| 318 | C23×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 319 | #135 | — | 4 | 3 | no | — |
| 320 | #135 | — | 4 | 1 | no | — |
| 321 | #135 | — | 4 | 3 | no | — |
| 322 | #135 | — | 4 | 3 | no | — |
| 323 | #135 | — | 4 | 6 | no | — |
| 324 | C2×Q16 | — | 2 | 3 | no | — |
| 325 | C2×Q16 | — | 2 | 3 | no | — |
| 326 | C2×SD16 | — | 4 | 3 | no | — |
| 327 | C2×SD16 | — | 4 | 3 | no | — |
| 328 | C2×D8 | — | 2 | 6 | no | — |
| 329 | C2×D8 | — | 2 | 3 | no | — |
| 330 | C2×D8 | — | 2 | 6 | no | — |
| 331 | C2×D8 | — | 2 | 3 | no | — |
| 332 | C2×D8 | — | 4 | 3 | no | — |
| 333 | C2×D8 | — | 4 | 1 | no | — |
| 334 | C2×D8 | — | 4 | 3 | no | — |
| 335 | C2×D8 | — | 4 | 3 | no | — |
| 336 | C2×D8 | — | 4 | 3 | no | — |
| 337 | C2×D8 | — | 4 | 3 | no | — |
| 338 | C2×D8 | — | 4 | 6 | no | — |
| 339 | #131 | — | 2 | 16 | no | — |
| 340 | #131 | — | 2 | 16 | no | — |
| 341 | #131 | — | 2 | 48 | no | — |
| 342 | #131 | — | 2 | 48 | no | — |
| 343 | #131 | — | 2 | 48 | no | — |
| 344 | #131 | — | 2 | 12 | no | — |
| 345 | #131 | — | 2 | 12 | no | — |
| 346 | #131 | — | 2 | 48 | no | — |
| 347 | #131 | — | 2 | 12 | no | — |
| 348 | #131 | — | 2 | 12 | no | — |
| 349 | #131 | — | 2 | 12 | no | — |
| 350 | #131 | — | 2 | 12 | no | — |
| 351 | #131 | — | 2 | 12 | no | — |
| 352 | #131 | — | 2 | 12 | no | — |
| 353 | C2×M16 | — | 2 | 12 | no | — |
| 354 | C2×M16 | — | 2 | 24 | no | — |
| 355 | C2×M16 | — | 2 | 48 | no | — |
| 356 | C2×M16 | — | 2 | 48 | no | — |
| 357 | C2×M16 | — | 2 | 6 | no | — |
| 358 | C2×M16 | — | 2 | 24 | no | — |
| 359 | C2×M16 | — | 2 | 6 | no | — |
| 360 | C2×M16 | — | 2 | 12 | no | — |
| 361 | C2×M16 | — | 2 | 12 | no | — |
| 362 | C2×M16 | #121 | 1 | 6 | yes | — |
| 363 | C2×M16 | #121 | 1 | 12 | yes | — |
| 364 | C2×M16 | C22×D4 | 1 | 6 | yes | — |
| 365 | C2×M16 | C2×#41 | 1 | 12 | yes | — |
| 366 | C22×C8 | — | 2 | 12 | no | — |
| 367 | C22×C8 | — | 2 | 16 | no | — |
| 368 | C22×C8 | — | 2 | 16 | no | — |
| 369 | C22×C8 | — | 2 | 6 | no | — |
| 370 | C22×C8 | — | 2 | 6 | no | — |
| 371 | C22×C8 | — | 2 | 6 | no | — |
| 372 | C22×C8 | — | 2 | 6 | no | — |
| 373 | C22×C8 | #121 | 1 | 6 | yes | — |
| 374 | C22×C8 | #121 | 1 | 12 | yes | — |
| 375 | C22×C8 | C22×D4 | 1 | 12 | yes | — |
| 376 | C22×C8 | C22×D4 | 1 | 3 | yes | — |
| 377 | C22×C8 | C22×D4 | 1 | 3 | yes | — |
| 378 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 379 | C22×C8 | C2×#41 | 1 | 3 | yes | — |
| 380 | C22×C8 | C2×#41 | 1 | 3 | yes | — |
| 381 | C22×C8 | C25 | 1 | 1 | yes | characteristic |
| 382 | C4⋊Q8 | — | 4 | 6 | no | — |
| 383 | #127 | — | 4 | 12 | no | — |
| 384 | #127 | — | 4 | 6 | no | — |
| 385 | #127 | — | 8 | 6 | no | — |
| 386 | #124 | — | 4 | 12 | no | — |
| 387 | #124 | — | 4 | 6 | no | — |
| 388 | #124 | — | 4 | 6 | no | — |
| 389 | #124 | — | 8 | 6 | no | — |
| 390 | #123 | — | 4 | 12 | no | — |
| 391 | #123 | — | 8 | 6 | no | — |
| 392 | C22⋊Q8 | — | 4 | 12 | no | — |
| 393 | C22⋊Q8 | — | 8 | 6 | no | — |
| 394 | #121 | — | 4 | 24 | no | — |
| 395 | #121 | — | 4 | 12 | no | — |
| 396 | #121 | — | 8 | 6 | no | — |
| 397 | #121 | — | 8 | 12 | no | — |
| 398 | #121 | — | 8 | 12 | no | — |
| 399 | #120 | — | 4 | 24 | no | — |
| 400 | #120 | — | 4 | 12 | no | — |
| 401 | #120 | — | 8 | 6 | no | — |
| 402 | #120 | — | 8 | 12 | no | — |
| 403 | C4×D4 | — | 8 | 12 | no | — |
| 404 | #117 | — | 2 | 6 | no | — |
| 405 | #117 | — | 2 | 6 | no | — |
| 406 | #117 | — | 4 | 3 | no | — |
| 407 | #117 | — | 4 | 3 | no | — |
| 408 | #117 | — | 4 | 3 | no | — |
| 409 | #117 | — | 4 | 3 | no | — |
| 410 | #117 | — | 4 | 3 | no | — |
| 411 | #117 | — | 4 | 3 | no | — |
| 412 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 413 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 414 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 415 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 416 | C2×C22⋊C4 | — | 8 | 6 | no | — |
| 417 | C2×C42 | — | 4 | 3 | no | — |
| 418 | C2×C42 | — | 4 | 3 | no | — |
| 419 | SD32 | — | 4 | 8 | no | — |
| 420 | D16 | — | 4 | 8 | no | — |
| 421 | M32 | — | 2 | 48 | no | — |
| 422 | M32 | — | 2 | 6 | no | — |
| 423 | M32 | — | 2 | 6 | no | — |
| 424 | M32 | — | 2 | 12 | no | — |
| 425 | M32 | — | 2 | 48 | no | — |
| 426 | M32 | #120 | 1 | 4 | yes | — |
| 427 | M32 | #120 | 1 | 12 | yes | — |
| 428 | C2×C16 | — | 2 | 48 | no | — |
| 429 | C2×C16 | — | 2 | 12 | no | — |
| 430 | C2×C16 | — | 2 | 48 | no | — |
| 431 | C2×C16 | C22×D4 | 1 | 12 | yes | — |
| 432 | C2×C16 | C22×D4 | 1 | 12 | yes | — |
| 433 | #107 | — | 2 | 6 | no | — |
| 434 | #107 | — | 2 | 6 | no | — |
| 435 | #107 | — | 4 | 3 | no | — |
| 436 | #107 | — | 4 | 3 | no | — |
| 437 | #106 | — | 2 | 6 | no | — |
| 438 | #106 | — | 2 | 6 | no | — |
| 439 | #106 | — | 4 | 3 | no | — |
| 440 | #106 | — | 4 | 3 | no | — |
| 441 | #103 | — | 4 | 12 | no | — |
| 442 | #102 | — | 4 | 24 | no | — |
| 443 | #102 | — | 4 | 12 | no | — |
| 444 | #99 | — | 4 | 24 | no | — |
| 445 | #99 | — | 4 | 24 | no | — |
| 446 | C24 | — | 2 | 4 | no | — |
| 447 | C24 | — | 4 | 1 | no | — |
| 448 | C24 | — | 4 | 2 | no | — |
| 449 | C24 | — | 8 | 3 | no | — |
| 450 | C24 | — | 8 | 3 | no | — |
| 451 | C24 | — | 32 | 2 | no | — |
| 452 | C24 | #466 | 1 | 6 | yes | — |
| 453 | C24 | C22×D8 | 1 | 1 | yes | characteristic |
| 454 | #41 | — | 2 | 16 | no | — |
| 455 | #41 | — | 2 | 16 | no | — |
| 456 | #41 | — | 2 | 48 | no | — |
| 457 | #41 | — | 2 | 48 | no | — |
| 458 | #41 | — | 2 | 48 | no | — |
| 459 | #41 | — | 2 | 12 | no | — |
| 460 | #41 | — | 2 | 12 | no | — |
| 461 | #41 | — | 2 | 12 | no | — |
| 462 | #41 | — | 2 | 48 | no | — |
| 463 | #41 | — | 2 | 12 | no | — |
| 464 | #41 | — | 2 | 12 | no | — |
| 465 | #41 | — | 2 | 12 | no | — |
| 466 | #41 | — | 2 | 12 | no | — |
| 467 | #41 | — | 2 | 12 | no | — |
| 468 | #41 | — | 8 | 1 | no | — |
| 469 | #41 | — | 8 | 3 | no | — |
| 470 | #41 | — | 8 | 3 | no | — |
| 471 | #41 | — | 8 | 3 | no | — |
| 472 | #41 | — | 8 | 6 | no | — |
| 473 | C2×Q8 | — | 2 | 4 | no | — |
| 474 | C2×Q8 | — | 2 | 24 | no | — |
| 475 | C2×Q8 | — | 2 | 24 | no | — |
| 476 | C2×Q8 | — | 2 | 6 | no | — |
| 477 | C2×Q8 | — | 2 | 6 | no | — |
| 478 | C2×Q8 | — | 4 | 3 | no | — |
| 479 | C2×Q8 | — | 4 | 3 | no | — |
| 480 | C2×Q8 | #466 | 1 | 6 | yes | — |
| 481 | C2×Q8 | C2×#135 | 1 | 6 | yes | — |
| 482 | C2×D4 | — | 2 | 12 | no | — |
| 483 | C2×D4 | — | 2 | 48 | no | — |
| 484 | C2×D4 | — | 2 | 24 | no | — |
| 485 | C2×D4 | — | 2 | 24 | no | — |
| 486 | C2×D4 | — | 2 | 12 | no | — |
| 487 | C2×D4 | — | 2 | 48 | no | — |
| 488 | C2×D4 | — | 2 | 12 | no | — |
| 489 | C2×D4 | — | 2 | 6 | no | — |
| 490 | C2×D4 | — | 2 | 6 | no | — |
| 491 | C2×D4 | — | 4 | 6 | no | — |
| 492 | C2×D4 | — | 4 | 3 | no | — |
| 493 | C2×D4 | — | 4 | 6 | no | — |
| 494 | C2×D4 | — | 4 | 3 | no | — |
| 495 | C2×D4 | — | 8 | 3 | no | — |
| 496 | C2×D4 | — | 8 | 3 | no | — |
| 497 | C2×D4 | — | 8 | 12 | no | — |
| 498 | C2×D4 | — | 8 | 24 | no | — |
| 499 | C2×D4 | — | 8 | 1 | no | — |
| 500 | C2×D4 | — | 8 | 3 | no | — |
| 501 | C2×D4 | — | 8 | 3 | no | — |
| 502 | C2×D4 | — | 8 | 3 | no | — |
| 503 | C2×D4 | — | 8 | 3 | no | — |
| 504 | C2×D4 | — | 8 | 3 | no | — |
| 505 | C2×D4 | — | 8 | 6 | no | — |
| 506 | C2×D4 | — | 32 | 12 | no | — |
| 507 | C2×D4 | #466 | 1 | 12 | yes | — |
| 508 | C2×D4 | #466 | 1 | 6 | yes | — |
| 509 | C2×D4 | C22×D8 | 1 | 12 | yes | — |
| 510 | C2×D4 | C2×#135 | 1 | 6 | yes | — |
| 511 | C22×C4 | — | 2 | 16 | no | — |
| 512 | C22×C4 | — | 2 | 12 | no | — |
| 513 | C22×C4 | — | 2 | 16 | no | — |
| 514 | C22×C4 | — | 2 | 6 | no | — |
| 515 | C22×C4 | — | 2 | 6 | no | — |
| 516 | C22×C4 | — | 2 | 6 | no | — |
| 517 | C22×C4 | — | 2 | 6 | no | — |
| 518 | C22×C4 | — | 4 | 1 | no | — |
| 519 | C22×C4 | — | 8 | 3 | no | — |
| 520 | C22×C4 | — | 8 | 3 | no | — |
| 521 | C22×C4 | — | 8 | 3 | no | — |
| 522 | C22×C4 | — | 8 | 3 | no | — |
| 523 | C22×C4 | #466 | 1 | 6 | yes | — |
| 524 | C22×C4 | #466 | 1 | 12 | yes | — |
| 525 | C22×C4 | C2×#121 | 1 | 12 | yes | — |
| 526 | C22×C4 | C2×#121 | 1 | 3 | yes | — |
| 527 | C22×C4 | C2×#121 | 1 | 3 | yes | — |
| 528 | C22×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 529 | C22×C4 | C2×#135 | 1 | 3 | yes | — |
| 530 | C22×C4 | C2×#135 | 1 | 3 | yes | — |
| 531 | C22×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 532 | Q16 | — | 4 | 1 | no | — |
| 533 | Q16 | — | 4 | 3 | no | — |
| 534 | SD16 | — | 8 | 1 | no | — |
| 535 | SD16 | — | 8 | 3 | no | — |
| 536 | D8 | — | 4 | 1 | no | — |
| 537 | D8 | — | 4 | 2 | no | — |
| 538 | D8 | — | 4 | 6 | no | — |
| 539 | D8 | — | 4 | 3 | no | — |
| 540 | D8 | — | 8 | 1 | no | — |
| 541 | D8 | — | 8 | 3 | no | — |
| 542 | M16 | — | 2 | 48 | no | — |
| 543 | M16 | — | 2 | 12 | no | — |
| 544 | M16 | — | 2 | 12 | no | — |
| 545 | M16 | — | 2 | 24 | no | — |
| 546 | M16 | — | 2 | 24 | no | — |
| 547 | C2×C8 | — | 2 | 48 | no | — |
| 548 | C2×C8 | — | 2 | 6 | no | — |
| 549 | C2×C8 | — | 2 | 6 | no | — |
| 550 | C2×C8 | — | 2 | 12 | no | — |
| 551 | C2×C8 | — | 2 | 12 | no | — |
| 552 | C2×C8 | — | 2 | 12 | no | — |
| 553 | C2×C8 | — | 2 | 12 | no | — |
| 554 | C2×C8 | C2×#120 | 1 | 3 | yes | — |
| 555 | C2×C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 556 | C2×C8 | C2×#121 | 1 | 12 | yes | — |
| 557 | C2×C8 | C2×#121 | 1 | 3 | yes | — |
| 558 | C2×C8 | C2×#121 | 1 | 3 | yes | — |
| 559 | C2×C8 | #525 | 1 | 3 | yes | — |
| 560 | C2×C8 | #525 | 1 | 3 | yes | — |
| 561 | C2×C8 | #525 | 1 | 6 | yes | — |
| 562 | C2×C8 | C23×D4 | 1 | 3 | yes | — |
| 563 | C2×C8 | C22×#41 | 1 | 3 | yes | — |
| 564 | C4⋊C4 | — | 4 | 6 | no | — |
| 565 | C4⋊C4 | — | 4 | 6 | no | — |
| 566 | C4⋊C4 | — | 8 | 3 | no | — |
| 567 | C4⋊C4 | — | 8 | 3 | no | — |
| 568 | C4⋊C4 | — | 8 | 12 | no | — |
| 569 | C22⋊C4 | — | 4 | 6 | no | — |
| 570 | C22⋊C4 | — | 4 | 6 | no | — |
| 571 | C22⋊C4 | — | 8 | 3 | no | — |
| 572 | C22⋊C4 | — | 8 | 3 | no | — |
| 573 | C22⋊C4 | — | 8 | 12 | no | — |
| 574 | C22⋊C4 | — | 8 | 24 | no | — |
| 575 | C22⋊C4 | — | 8 | 12 | no | — |
| 576 | C42 | — | 4 | 6 | no | — |
| 577 | C42 | — | 4 | 6 | no | — |
| 578 | C42 | — | 8 | 3 | no | — |
| 579 | C42 | — | 8 | 3 | no | — |
| 580 | C16 | — | 2 | 12 | no | — |
| 581 | C16 | C2×#120 | 1 | 8 | yes | — |
| 582 | C23 | — | 2 | 16 | no | — |
| 583 | C23 | — | 2 | 6 | no | — |
| 584 | C23 | — | 2 | 6 | no | — |
| 585 | C23 | — | 8 | 1 | no | — |
| 586 | C23 | — | 8 | 6 | no | — |
| 587 | C23 | — | 8 | 3 | no | — |
| 588 | C23 | — | 8 | 6 | no | — |
| 589 | C23 | — | 16 | 12 | no | — |
| 590 | C23 | — | 16 | 4 | no | — |
| 591 | C23 | — | 16 | 1 | no | — |
| 592 | C23 | — | 16 | 3 | no | — |
| 593 | C23 | — | 32 | 1 | no | — |
| 594 | C23 | — | 32 | 2 | no | — |
| 595 | C23 | — | 32 | 6 | no | — |
| 596 | C23 | C2×#466 | 1 | 12 | yes | — |
| 597 | C23 | C2×#466 | 1 | 3 | yes | — |
| 598 | C23 | C2×#466 | 1 | 3 | yes | — |
| 599 | C23 | C23×D8 | 1 | 1 | yes | characteristic |
| 600 | Q8 | — | 2 | 16 | no | — |
| 601 | Q8 | — | 2 | 12 | no | — |
| 602 | Q8 | — | 2 | 12 | no | — |
| 603 | Q8 | — | 8 | 1 | no | — |
| 604 | Q8 | — | 8 | 3 | no | — |
| 605 | D4 | — | 2 | 48 | no | — |
| 606 | D4 | — | 2 | 24 | no | — |
| 607 | D4 | — | 2 | 24 | no | — |
| 608 | D4 | — | 2 | 12 | no | — |
| 609 | D4 | — | 2 | 12 | no | — |
| 610 | D4 | — | 8 | 2 | no | — |
| 611 | D4 | — | 8 | 1 | no | — |
| 612 | D4 | — | 8 | 6 | no | — |
| 613 | D4 | — | 8 | 3 | no | — |
| 614 | D4 | — | 16 | 1 | no | — |
| 615 | D4 | — | 16 | 3 | no | — |
| 616 | D4 | — | 16 | 1 | no | — |
| 617 | D4 | — | 16 | 3 | no | — |
| 618 | D4 | — | 32 | 12 | no | — |
| 619 | D4 | — | 32 | 24 | no | — |
| 620 | C2×C4 | — | 2 | 48 | no | — |
| 621 | C2×C4 | — | 2 | 6 | no | — |
| 622 | C2×C4 | — | 2 | 6 | no | — |
| 623 | C2×C4 | — | 2 | 12 | no | — |
| 624 | C2×C4 | — | 2 | 12 | no | — |
| 625 | C2×C4 | — | 2 | 12 | no | — |
| 626 | C2×C4 | — | 2 | 12 | no | — |
| 627 | C2×C4 | — | 8 | 6 | no | — |
| 628 | C2×C4 | — | 8 | 6 | no | — |
| 629 | C2×C4 | — | 8 | 3 | no | — |
| 630 | C2×C4 | — | 16 | 6 | no | — |
| 631 | C2×C4 | — | 16 | 1 | no | — |
| 632 | C2×C4 | — | 16 | 3 | no | — |
| 633 | C2×C4 | — | 32 | 3 | no | — |
| 634 | C2×C4 | #2847 | 1 | 1 | yes | characteristic |
| 635 | C2×C4 | #2847 | 1 | 3 | yes | — |
| 636 | C2×C4 | C2×#466 | 1 | 12 | yes | — |
| 637 | C2×C4 | C2×#466 | 1 | 3 | yes | — |
| 638 | C2×C4 | C2×#466 | 1 | 3 | yes | — |
| 639 | C2×C4 | #3050 | 1 | 3 | yes | — |
| 640 | C2×C4 | #3050 | 1 | 3 | yes | — |
| 641 | C2×C4 | #3050 | 1 | 6 | yes | — |
| 642 | C2×C4 | C22×#121 | 1 | 3 | yes | — |
| 643 | C2×C4 | C22×#135 | 1 | 3 | yes | — |
| 644 | C8 | — | 2 | 12 | no | — |
| 645 | C8 | #2847 | 1 | 1 | yes | characteristic |
| 646 | C8 | #2847 | 1 | 3 | yes | — |
| 647 | C8 | C22×#120 | 1 | 1 | yes | characteristic |
| 648 | C8 | C2×#525 | 1 | 3 | yes | — |
| 649 | C22 | — | 2 | 12 | no | — |
| 650 | C22 | — | 4 | 3 | no | — |
| 651 | C22 | — | 4 | 3 | no | — |
| 652 | C22 | — | 4 | 1 | no | — |
| 653 | C22 | — | 4 | 12 | no | — |
| 654 | C22 | — | 8 | 6 | no | — |
| 655 | C22 | — | 8 | 6 | no | — |
| 656 | C22 | — | 8 | 16 | no | — |
| 657 | C22 | — | 16 | 12 | no | — |
| 658 | C22 | — | 16 | 6 | no | — |
| 659 | C22 | — | 16 | 1 | no | — |
| 660 | C22 | — | 16 | 2 | no | — |
| 661 | C22 | — | 32 | 2 | no | — |
| 662 | C22 | — | 32 | 6 | no | — |
| 663 | C22 | #32930 | 1 | 1 | yes | characteristic |
| 664 | C22 | #32930 | 1 | 3 | yes | — |
| 665 | C22 | C22×#466 | 1 | 3 | yes | — |
| 666 | C4 | — | 2 | 12 | no | — |
| 667 | C4 | — | 16 | 6 | no | — |
| 668 | C4 | — | 16 | 6 | no | — |
| 669 | C4 | — | 16 | 1 | no | — |
| 670 | C4 | #32930 | 1 | 1 | yes | characteristic |
| 671 | C4 | #32930 | 1 | 3 | yes | — |
| 672 | C4 | C2×#2847 | 1 | 1 | yes | characteristic |
| 673 | C4 | C2×#3050 | 1 | 3 | yes | — |
| 674 | C2 | — | 2 | 3 | no | — |
| 675 | C2 | — | 2 | 1 | no | — |
| 676 | C2 | — | 2 | 3 | no | — |
| 677 | C2 | — | 4 | 12 | no | — |
| 678 | C2 | — | 32 | 1 | no | — |
| 679 | C2 | — | 32 | 2 | no | — |
| 680 | C2 | C2×#32930 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×#32930 |
| commutator, Frattini, cosocle | C22×C8 | C25 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C23×C4 ◁ C2×#3573 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10585848 | C2 | semidirect |
| 2. #7622976 | C2 | semidirect |
| 3. #6629044 | C2 | semidirect |
| 4. C2×#32948 | C2 | semidirect |
| 5. #511968 | C2 | semidirect |
| 6. #511966 | C2 | semidirect |
| 7. #494664 | C2 | semidirect |
| 8. C2×#13074 | C2 | semidirect |
| 9. #493820 | C2 | semidirect |
| 11. C22×#509 | C22 | semidirect |
| 13. #62624 | C22 | semidirect |
| 22. #33609 | C22 | semidirect |
| 23. #33607 | C22 | semidirect |
| 25. #33409 | C22 | semidirect |
| 26. #33380 | C22 | semidirect |
| 27. C2×#2140 | C22 | semidirect |
| 28. #32949 | C22 | semidirect |
| 31. #32948 | C22 | semidirect |
| 37. #13075 | C22 | semidirect |
| 38. #13074 | C22 | semidirect |
| 39. #13074 | C22 | semidirect |
| 40. #12839 | C22 | semidirect |
| 41. C2×#1384 | C22 | semidirect |
| 57. C22×SD32 | C23 | semidirect |
| 58. C22×D16 | C23 | semidirect |
| 70. C2×#504 | D4 | semidirect |
| 74. C22×M32 | D4 | semidirect |
| 109. #2158 | C23 | semidirect |
| 110. #2141 | C23 | semidirect |
| 112. #2140 | C23 | semidirect |
| 113. #2140 | C23 | semidirect |
| 126. #1384 | C23 | semidirect |
| 219. C2×M32 | C2×D4 | semidirect |
| 224. C22×C16 | C2×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10585848 | 2 |
| #7622976 | 2 |
| #6629044 | 2 |
| C2×#32948 | 2 |
| #511968 | 2 |
| #511966 | 2 |
| #494664 | 2 |
| C2×#13074 | 2 |
| #493820 | 2 |