Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2562 conjugacy classes of subgroups.
The subgroup lattice has 457 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3291 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #61080 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #31071 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #31070 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #28247 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #28242 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #24292 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #24225 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #24222 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #21710 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #21692 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#577 | C22 | 1 | 8 | yes | complemented |
| 13 | #3497 | C22 | 1 | 2 | yes | — |
| 14 | #3496 | C22 | 1 | 2 | yes | complemented |
| 15 | #3291 | — | 2 | 16 | no | — |
| 16 | #3269 | — | 2 | 8 | no | — |
| 17 | #3268 | — | 2 | 8 | no | — |
| 18 | #3266 | — | 2 | 8 | no | — |
| 19 | #3265 | — | 2 | 8 | no | — |
| 20 | #3150 | C22 | 1 | 2 | yes | — |
| 21 | C2×#492 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#471 | C22 | 1 | 8 | yes | complemented |
| 23 | #3061 | C22 | 1 | 8 | yes | complemented |
| 24 | #3037 | C22 | 1 | 4 | yes | complemented |
| 25 | #3036 | C22 | 1 | 4 | yes | — |
| 26 | C2×#456 | C22 | 1 | 4 | yes | complemented |
| 27 | C2×#453 | C22 | 1 | 4 | yes | — |
| 28 | #3013 | C22 | 1 | 8 | yes | complemented |
| 29 | #3012 | C22 | 1 | 8 | yes | complemented |
| 30 | C2×#444 | C22 | 1 | 4 | yes | complemented |
| 31 | C2×#443 | C22 | 1 | 4 | yes | complemented |
| 32 | C2×#440 | C22 | 1 | 4 | yes | complemented |
| 33 | #2932 | C22 | 1 | 4 | yes | complemented |
| 34 | C4×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C4×#127 | C22 | 1 | 1 | yes | characteristic |
| 36 | #2052 | C22 | 1 | 8 | yes | complemented |
| 37 | #2051 | C22 | 1 | 8 | yes | complemented |
| 38 | #2039 | C22 | 1 | 4 | yes | complemented |
| 39 | #2039 | C22 | 1 | 4 | yes | complemented |
| 40 | #2007 | C22 | 1 | 4 | yes | complemented |
| 41 | #2006 | C22 | 1 | 4 | yes | — |
| 42 | #1975 | C22 | 1 | 4 | yes | complemented |
| 43 | #1974 | C22 | 1 | 4 | yes | complemented |
| 44 | #1973 | C22 | 1 | 4 | yes | complemented |
| 45 | #1962 | C22 | 1 | 4 | yes | complemented |
| 46 | #1957 | C22 | 1 | 1 | yes | characteristic |
| 47 | #1956 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #1849 | C22 | 1 | 2 | yes | complemented |
| 49 | #1845 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #1816 | C22 | 1 | 8 | yes | complemented |
| 51 | #1801 | C22 | 1 | 2 | yes | complemented |
| 52 | #1800 | C22 | 1 | 2 | yes | complemented |
| 53 | #1793 | C22 | 1 | 4 | yes | complemented |
| 54 | #1792 | C22 | 1 | 4 | yes | complemented |
| 55 | C4×#97 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×2−1+4 | C23 | 1 | 4 | yes | — |
| 57 | C2×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 58 | #577 | — | 2 | 32 | no | — |
| 59 | #577 | — | 4 | 16 | no | — |
| 60 | C2×#137 | — | 2 | 8 | no | — |
| 61 | C2×#137 | C23 | 1 | 8 | yes | — |
| 62 | C2×AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 63 | C2×AGL(1,ℤ/8) | C23 | 1 | 8 | yes | — |
| 64 | C2×#135 | — | 2 | 8 | no | — |
| 65 | C2×#135 | C23 | 1 | 4 | yes | — |
| 66 | C2×#135 | C23 | 1 | 4 | yes | — |
| 67 | C22×SD16 | — | 2 | 8 | no | — |
| 68 | C22×SD16 | C23 | 1 | 4 | yes | — |
| 69 | C2×#131 | C23 | 1 | 8 | yes | — |
| 70 | #550 | — | 2 | 4 | no | — |
| 71 | D4×Q8 | — | 2 | 4 | no | — |
| 72 | #548 | — | 2 | 8 | no | — |
| 73 | #547 | — | 2 | 4 | no | — |
| 74 | #546 | — | 2 | 8 | no | — |
| 75 | D42 | — | 2 | 4 | no | — |
| 76 | #537 | — | 4 | 2 | no | — |
| 77 | #537 | C23 | 1 | 4 | yes | — |
| 78 | #537 | C23 | 1 | 4 | yes | — |
| 79 | #534 | — | 4 | 2 | no | — |
| 80 | #532 | — | 4 | 2 | no | — |
| 81 | #532 | C23 | 1 | 4 | yes | — |
| 82 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#121 | — | 4 | 2 | no | — |
| 85 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 86 | C2×C4×D4 | — | 4 | 1 | no | — |
| 87 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 88 | #497 | D4 | 1 | 8 | yes | complemented |
| 89 | #496 | D4 | 1 | 8 | yes | complemented |
| 90 | #492 | D4 | 1 | 8 | yes | complemented |
| 91 | #471 | — | 2 | 32 | no | — |
| 92 | #468 | — | 2 | 8 | no | — |
| 93 | #468 | — | 2 | 8 | no | — |
| 94 | #467 | — | 2 | 8 | no | — |
| 95 | #466 | — | 2 | 8 | no | — |
| 96 | #464 | — | 2 | 8 | no | — |
| 97 | #463 | — | 2 | 8 | no | — |
| 98 | #462 | — | 2 | 4 | no | — |
| 99 | #461 | — | 2 | 4 | no | — |
| 100 | #460 | — | 2 | 4 | no | — |
| 101 | #459 | — | 2 | 4 | no | — |
| 102 | #456 | — | 2 | 16 | no | — |
| 103 | #453 | — | 2 | 16 | no | — |
| 104 | #452 | — | 2 | 8 | no | — |
| 105 | #452 | — | 2 | 8 | no | — |
| 106 | #451 | — | 2 | 8 | no | — |
| 107 | #450 | — | 2 | 8 | no | — |
| 108 | #449 | — | 2 | 8 | no | — |
| 109 | #449 | — | 2 | 8 | no | — |
| 110 | #448 | — | 2 | 8 | no | — |
| 111 | #447 | — | 2 | 8 | no | — |
| 112 | #444 | — | 4 | 8 | no | — |
| 113 | #443 | — | 2 | 16 | no | — |
| 114 | #440 | — | 2 | 8 | no | — |
| 115 | #440 | — | 2 | 8 | no | — |
| 116 | #435 | — | 2 | 8 | no | — |
| 117 | #435 | — | 2 | 8 | no | — |
| 118 | C2×#108 | C23 | 1 | 4 | yes | — |
| 119 | C2×#108 | C23 | 1 | 4 | yes | — |
| 120 | C2×#107 | C23 | 1 | 4 | yes | — |
| 121 | #423 | C23 | 1 | 4 | yes | — |
| 122 | C2×#104 | C23 | 1 | 8 | yes | — |
| 123 | C2×#104 | C23 | 1 | 8 | yes | — |
| 124 | #417 | C23 | 1 | 8 | yes | — |
| 125 | #417 | C23 | 1 | 8 | yes | — |
| 126 | C2×#103 | C23 | 1 | 4 | yes | — |
| 127 | C2×#102 | C23 | 1 | 4 | yes | — |
| 128 | C2×#101 | C23 | 1 | 4 | yes | — |
| 129 | C2×#100 | C23 | 1 | 4 | yes | — |
| 130 | #408 | C23 | 1 | 8 | yes | — |
| 131 | C2×#97 | C23 | 1 | 2 | yes | — |
| 132 | C2×#97 | C23 | 1 | 2 | yes | — |
| 133 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 135 | #391 | C23 | 1 | 2 | yes | — |
| 136 | #390 | — | 4 | 1 | no | — |
| 137 | #390 | C23 | 1 | 2 | yes | — |
| 138 | #389 | — | 4 | 1 | no | — |
| 139 | #384 | C23 | 1 | 1 | yes | characteristic |
| 140 | #384 | C23 | 1 | 1 | yes | characteristic |
| 141 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 142 | C43 | C23 | 1 | 1 | yes | characteristic |
| 143 | #343 | C23 | 1 | 4 | yes | — |
| 144 | #343 | C23 | 1 | 4 | yes | — |
| 145 | 2−1+4 | — | 2 | 8 | no | — |
| 146 | 2−1+4 | — | 4 | 8 | no | — |
| 147 | 2−1+4 | — | 4 | 4 | no | — |
| 148 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 149 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 150 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 151 | C2×#41 | — | 2 | 8 | no | — |
| 152 | C2×#41 | — | 2 | 8 | no | — |
| 153 | C2×#41 | — | 4 | 4 | no | — |
| 154 | C2×#41 | C24 | 1 | 8 | yes | — |
| 155 | C22×Q8 | — | 2 | 8 | no | — |
| 156 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 157 | C22×D4 | — | 2 | 8 | no | — |
| 158 | C22×D4 | — | 4 | 1 | no | — |
| 159 | C22×D4 | — | 4 | 4 | no | — |
| 160 | C22×D4 | — | 4 | 2 | no | — |
| 161 | C22×D4 | C24 | 1 | 2 | yes | — |
| 162 | C23×C4 | — | 2 | 2 | no | — |
| 163 | #137 | — | 2 | 16 | no | — |
| 164 | #137 | — | 4 | 8 | no | — |
| 165 | #137 | — | 4 | 32 | no | — |
| 166 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 167 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 168 | AGL(1,ℤ/8) | — | 4 | 32 | no | — |
| 169 | #135 | — | 2 | 8 | no | — |
| 170 | #135 | — | 2 | 8 | no | — |
| 171 | #135 | — | 4 | 4 | no | — |
| 172 | #135 | — | 4 | 4 | no | — |
| 173 | #135 | — | 4 | 32 | no | — |
| 174 | C2×Q16 | — | 2 | 8 | no | — |
| 175 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 176 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 177 | C2×SD16 | — | 2 | 8 | no | — |
| 178 | C2×SD16 | — | 2 | 8 | no | — |
| 179 | C2×SD16 | — | 2 | 8 | no | — |
| 180 | C2×SD16 | — | 2 | 8 | no | — |
| 181 | C2×SD16 | — | 4 | 32 | no | — |
| 182 | C2×SD16 | C2×D4 | 1 | 8 | yes | — |
| 183 | C2×SD16 | C2×D4 | 1 | 8 | yes | — |
| 184 | C2×SD16 | C2×D4 | 1 | 16 | yes | complemented |
| 185 | C2×D8 | — | 2 | 8 | no | — |
| 186 | C2×D8 | C2×D4 | 1 | 4 | yes | — |
| 187 | C2×D8 | C2×D4 | 1 | 4 | yes | — |
| 188 | #131 | — | 2 | 16 | no | — |
| 189 | #131 | — | 2 | 16 | no | — |
| 190 | C2×M16 | — | 2 | 8 | no | — |
| 191 | C2×M16 | C24 | 1 | 8 | yes | — |
| 192 | C22×C8 | — | 2 | 8 | no | — |
| 193 | C22×C8 | C24 | 1 | 2 | yes | — |
| 194 | C22×C8 | C24 | 1 | 2 | yes | — |
| 195 | C4⋊Q8 | — | 4 | 1 | no | — |
| 196 | C4⋊Q8 | — | 4 | 2 | no | — |
| 197 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 198 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | complemented |
| 199 | #127 | — | 4 | 1 | no | — |
| 200 | #127 | — | 4 | 2 | no | — |
| 201 | #127 | C2×D4 | 1 | 4 | yes | — |
| 202 | #127 | C2×D4 | 1 | 4 | yes | — |
| 203 | #124 | — | 4 | 4 | no | — |
| 204 | #124 | C2×D4 | 1 | 8 | yes | — |
| 205 | #123 | — | 4 | 8 | no | — |
| 206 | C22⋊Q8 | — | 2 | 8 | no | — |
| 207 | C22⋊Q8 | — | 2 | 8 | no | — |
| 208 | C22⋊Q8 | — | 4 | 8 | no | — |
| 209 | #121 | — | 2 | 4 | no | — |
| 210 | #121 | — | 2 | 4 | no | — |
| 211 | #121 | — | 2 | 8 | no | — |
| 212 | #121 | — | 2 | 8 | no | — |
| 213 | #121 | — | 4 | 4 | no | — |
| 214 | #121 | — | 4 | 8 | no | — |
| 215 | #121 | — | 4 | 4 | no | — |
| 216 | #121 | — | 4 | 4 | no | — |
| 217 | #121 | — | 4 | 4 | no | — |
| 218 | #120 | — | 4 | 8 | no | — |
| 219 | C4×Q8 | — | 2 | 4 | no | — |
| 220 | C4×Q8 | — | 2 | 4 | no | — |
| 221 | C4×D4 | — | 2 | 4 | no | — |
| 222 | C4×D4 | — | 2 | 4 | no | — |
| 223 | C4×D4 | — | 2 | 4 | no | — |
| 224 | C4×D4 | — | 2 | 4 | no | — |
| 225 | C4×D4 | — | 4 | 4 | no | — |
| 226 | C4×D4 | — | 4 | 4 | no | — |
| 227 | C4×D4 | — | 8 | 4 | no | — |
| 228 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 229 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 230 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 231 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 232 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 233 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 234 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 235 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 236 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 237 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 238 | C2×C42 | — | 2 | 1 | no | — |
| 239 | C2×C42 | — | 2 | 2 | no | — |
| 240 | C2×C42 | — | 2 | 1 | no | — |
| 241 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 242 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 243 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 244 | #108 | — | 2 | 8 | no | — |
| 245 | #108 | — | 4 | 4 | no | — |
| 246 | #107 | — | 2 | 8 | no | — |
| 247 | C4⋊C8 | — | 2 | 4 | no | — |
| 248 | C4⋊C8 | — | 2 | 4 | no | — |
| 249 | #104 | — | 2 | 16 | no | — |
| 250 | #104 | — | 4 | 8 | no | — |
| 251 | #103 | — | 2 | 8 | no | — |
| 252 | #103 | — | 2 | 8 | no | — |
| 253 | #103 | — | 2 | 8 | no | — |
| 254 | #102 | — | 2 | 8 | no | — |
| 255 | #102 | — | 2 | 8 | no | — |
| 256 | #102 | — | 2 | 8 | no | — |
| 257 | #101 | — | 2 | 8 | no | — |
| 258 | #100 | — | 2 | 8 | no | — |
| 259 | C22⋊C8 | — | 2 | 8 | no | — |
| 260 | C22⋊C8 | — | 2 | 8 | no | — |
| 261 | #97 | — | 2 | 4 | no | — |
| 262 | #97 | C2×D4 | 1 | 8 | yes | — |
| 263 | C4×C8 | — | 4 | 1 | no | — |
| 264 | C4×C8 | C2×D4 | 1 | 4 | yes | complemented |
| 265 | #95 | — | 4 | 2 | no | — |
| 266 | C24 | — | 2 | 2 | no | — |
| 267 | C24 | — | 4 | 4 | no | — |
| 268 | #41 | — | 2 | 8 | no | — |
| 269 | #41 | — | 2 | 8 | no | — |
| 270 | #41 | — | 2 | 8 | no | — |
| 271 | #41 | — | 2 | 8 | no | — |
| 272 | #41 | — | 4 | 16 | no | — |
| 273 | #41 | — | 4 | 16 | no | — |
| 274 | #41 | — | 8 | 8 | no | — |
| 275 | #41 | — | 8 | 8 | no | — |
| 276 | #41 | — | 8 | 8 | no | — |
| 277 | #41 | — | 8 | 8 | no | — |
| 278 | C2×Q8 | — | 2 | 2 | no | — |
| 279 | C2×Q8 | — | 2 | 4 | no | — |
| 280 | C2×Q8 | — | 2 | 4 | no | — |
| 281 | C2×Q8 | — | 4 | 4 | no | — |
| 282 | C2×Q8 | — | 4 | 16 | no | — |
| 283 | C2×Q8 | — | 8 | 8 | no | — |
| 284 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 285 | C2×Q8 | C22×D4 | 1 | 8 | yes | — |
| 286 | C2×D4 | — | 2 | 8 | no | — |
| 287 | C2×D4 | — | 2 | 4 | no | — |
| 288 | C2×D4 | — | 2 | 4 | no | — |
| 289 | C2×D4 | — | 2 | 4 | no | — |
| 290 | C2×D4 | — | 2 | 4 | no | — |
| 291 | C2×D4 | — | 2 | 2 | no | — |
| 292 | C2×D4 | — | 4 | 4 | no | — |
| 293 | C2×D4 | — | 4 | 8 | no | — |
| 294 | C2×D4 | — | 4 | 16 | no | — |
| 295 | C2×D4 | — | 4 | 4 | no | — |
| 296 | C2×D4 | — | 4 | 4 | no | — |
| 297 | C2×D4 | — | 4 | 4 | no | — |
| 298 | C2×D4 | — | 8 | 2 | no | — |
| 299 | C2×D4 | — | 8 | 2 | no | — |
| 300 | C2×D4 | — | 8 | 8 | no | — |
| 301 | C2×D4 | — | 8 | 8 | no | — |
| 302 | C2×D4 | — | 8 | 8 | no | — |
| 303 | C2×D4 | — | 16 | 4 | no | — |
| 304 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 305 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 306 | C22×C4 | — | 2 | 1 | no | — |
| 307 | C22×C4 | — | 2 | 2 | no | — |
| 308 | C22×C4 | — | 2 | 8 | no | — |
| 309 | C22×C4 | — | 2 | 1 | no | — |
| 310 | C22×C4 | — | 2 | 2 | no | — |
| 311 | C22×C4 | — | 2 | 2 | no | — |
| 312 | C22×C4 | — | 4 | 4 | no | — |
| 313 | C22×C4 | — | 4 | 8 | no | — |
| 314 | C22×C4 | — | 4 | 2 | no | — |
| 315 | C22×C4 | — | 4 | 2 | no | — |
| 316 | C22×C4 | — | 8 | 4 | no | — |
| 317 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 318 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 319 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 320 | Q16 | — | 2 | 8 | no | — |
| 321 | Q16 | — | 4 | 4 | no | — |
| 322 | Q16 | — | 4 | 16 | no | — |
| 323 | SD16 | — | 2 | 32 | no | — |
| 324 | SD16 | — | 2 | 16 | no | — |
| 325 | SD16 | — | 4 | 8 | no | — |
| 326 | SD16 | — | 4 | 16 | no | — |
| 327 | SD16 | — | 4 | 16 | no | — |
| 328 | D8 | — | 2 | 8 | no | — |
| 329 | D8 | — | 4 | 4 | no | — |
| 330 | D8 | — | 4 | 16 | no | — |
| 331 | M16 | — | 2 | 8 | no | — |
| 332 | M16 | — | 2 | 8 | no | — |
| 333 | M16 | — | 4 | 16 | no | — |
| 334 | C2×C8 | — | 2 | 2 | no | — |
| 335 | C2×C8 | — | 2 | 2 | no | — |
| 336 | C2×C8 | — | 2 | 8 | no | — |
| 337 | C2×C8 | — | 4 | 16 | no | — |
| 338 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 339 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 340 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 341 | C2×C8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 342 | C4⋊C4 | — | 2 | 4 | no | — |
| 343 | C4⋊C4 | — | 2 | 4 | no | — |
| 344 | C4⋊C4 | — | 2 | 4 | no | — |
| 345 | C4⋊C4 | — | 2 | 4 | no | — |
| 346 | C4⋊C4 | — | 4 | 4 | no | — |
| 347 | C4⋊C4 | — | 4 | 4 | no | — |
| 348 | C4⋊C4 | — | 4 | 4 | no | — |
| 349 | C4⋊C4 | — | 4 | 4 | no | — |
| 350 | C4⋊C4 | — | 8 | 2 | no | — |
| 351 | C4⋊C4 | — | 8 | 2 | no | — |
| 352 | C22⋊C4 | — | 2 | 8 | no | — |
| 353 | C22⋊C4 | — | 2 | 8 | no | — |
| 354 | C22⋊C4 | — | 4 | 8 | no | — |
| 355 | C22⋊C4 | — | 4 | 8 | no | — |
| 356 | C22⋊C4 | — | 4 | 4 | no | — |
| 357 | C22⋊C4 | — | 8 | 4 | no | — |
| 358 | C42 | — | 2 | 1 | no | — |
| 359 | C42 | — | 2 | 2 | no | — |
| 360 | C42 | — | 4 | 2 | no | — |
| 361 | C42 | — | 4 | 2 | no | — |
| 362 | C42 | — | 4 | 2 | no | — |
| 363 | C42 | — | 4 | 2 | no | — |
| 364 | C42 | C22×D4 | 1 | 2 | yes | — |
| 365 | C42 | C22×D4 | 1 | 4 | yes | — |
| 366 | C23 | — | 2 | 8 | no | — |
| 367 | C23 | — | 2 | 4 | no | — |
| 368 | C23 | — | 4 | 2 | no | — |
| 369 | C23 | — | 4 | 2 | no | — |
| 370 | C23 | — | 8 | 2 | no | — |
| 371 | C23 | — | 8 | 2 | no | — |
| 372 | C23 | — | 8 | 8 | no | — |
| 373 | C23 | — | 16 | 4 | no | — |
| 374 | C23 | — | 16 | 4 | no | — |
| 375 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 376 | Q8 | — | 2 | 8 | no | — |
| 377 | Q8 | — | 2 | 8 | no | — |
| 378 | Q8 | — | 2 | 8 | no | — |
| 379 | Q8 | — | 4 | 4 | no | — |
| 380 | Q8 | — | 8 | 8 | no | — |
| 381 | D4 | — | 2 | 8 | no | — |
| 382 | D4 | — | 2 | 8 | no | — |
| 383 | D4 | — | 2 | 8 | no | — |
| 384 | D4 | — | 4 | 8 | no | — |
| 385 | D4 | — | 4 | 8 | no | — |
| 386 | D4 | — | 4 | 4 | no | — |
| 387 | D4 | — | 8 | 4 | no | — |
| 388 | D4 | — | 8 | 4 | no | — |
| 389 | D4 | — | 8 | 8 | no | — |
| 390 | D4 | — | 8 | 16 | no | — |
| 391 | D4 | — | 8 | 8 | no | — |
| 392 | D4 | — | 16 | 4 | no | — |
| 393 | D4 | — | 16 | 4 | no | — |
| 394 | C2×C4 | — | 2 | 2 | no | — |
| 395 | C2×C4 | — | 2 | 2 | no | — |
| 396 | C2×C4 | — | 2 | 2 | no | — |
| 397 | C2×C4 | — | 2 | 8 | no | — |
| 398 | C2×C4 | — | 2 | 4 | no | — |
| 399 | C2×C4 | — | 4 | 1 | no | — |
| 400 | C2×C4 | — | 4 | 1 | no | — |
| 401 | C2×C4 | — | 4 | 2 | no | — |
| 402 | C2×C4 | — | 4 | 2 | no | — |
| 403 | C2×C4 | — | 4 | 8 | no | — |
| 404 | C2×C4 | — | 4 | 8 | no | — |
| 405 | C2×C4 | — | 4 | 1 | no | — |
| 406 | C2×C4 | — | 4 | 1 | no | — |
| 407 | C2×C4 | — | 4 | 2 | no | — |
| 408 | C2×C4 | — | 4 | 2 | no | — |
| 409 | C2×C4 | — | 4 | 1 | no | — |
| 410 | C2×C4 | — | 8 | 4 | no | — |
| 411 | C2×C4 | — | 8 | 8 | no | — |
| 412 | C2×C4 | — | 8 | 16 | no | — |
| 413 | C2×C4 | — | 8 | 2 | no | — |
| 414 | C2×C4 | — | 8 | 2 | no | — |
| 415 | C2×C4 | — | 16 | 2 | no | — |
| 416 | C2×C4 | D42 | 1 | 2 | yes | — |
| 417 | C2×C4 | D42 | 1 | 2 | yes | — |
| 418 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 420 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 421 | C2×C4 | #585 | 1 | 1 | yes | characteristic |
| 422 | C8 | — | 2 | 4 | no | — |
| 423 | C8 | — | 4 | 8 | no | — |
| 424 | C8 | D42 | 1 | 8 | yes | — |
| 425 | C22 | — | 2 | 1 | no | — |
| 426 | C22 | — | 2 | 1 | no | — |
| 427 | C22 | — | 4 | 8 | no | — |
| 428 | C22 | — | 4 | 4 | no | — |
| 429 | C22 | — | 4 | 8 | no | — |
| 430 | C22 | — | 4 | 8 | no | — |
| 431 | C22 | — | 8 | 4 | no | — |
| 432 | C22 | — | 8 | 2 | no | — |
| 433 | C22 | — | 8 | 2 | no | — |
| 434 | C22 | — | 16 | 2 | no | — |
| 435 | C22 | — | 32 | 8 | no | — |
| 436 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 437 | C22 | #3496 | 1 | 1 | yes | characteristic |
| 438 | C22 | #3549 | 1 | 1 | yes | characteristic |
| 439 | C4 | — | 2 | 4 | no | — |
| 440 | C4 | — | 2 | 2 | no | — |
| 441 | C4 | — | 2 | 2 | no | — |
| 442 | C4 | — | 4 | 8 | no | — |
| 443 | C4 | — | 4 | 4 | no | — |
| 444 | C4 | — | 8 | 1 | no | — |
| 445 | C4 | — | 8 | 2 | no | — |
| 446 | C4 | — | 8 | 2 | no | — |
| 447 | C4 | C2×D42 | 1 | 2 | yes | — |
| 448 | C4 | #3496 | 1 | 2 | yes | — |
| 449 | C2 | — | 2 | 1 | no | — |
| 450 | C2 | — | 2 | 1 | no | — |
| 451 | C2 | — | 8 | 8 | no | — |
| 452 | C2 | — | 8 | 4 | no | — |
| 453 | C2 | #59816 | 1 | 1 | yes | characteristic |
| 454 | C2 | #61110 | 1 | 1 | yes | characteristic |
| 455 | C2 | #61111 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3291 | C2 | semidirect |
| 2. #61080 | C2 | semidirect |
| 3. #31071 | C2 | semidirect |
| 4. #31070 | C2 | semidirect |
| 5. #28247 | C2 | semidirect |
| 6. #28242 | C2 | semidirect |
| 7. #24292 | C2 | semidirect |
| 8. #24225 | C2 | semidirect |
| 9. #24222 | C2 | semidirect |
| 10. #21710 | C2 | semidirect |
| 11. #21692 | C2 | semidirect |
| 12. C2×#577 | C22 | semidirect |
| 14. #3496 | C22 | semidirect |
| 22. C2×#471 | C22 | semidirect |
| 23. #3061 | C22 | semidirect |
| 24. #3037 | C22 | semidirect |
| 26. C2×#456 | C22 | semidirect |
| 28. #3013 | C22 | semidirect |
| 29. #3012 | C22 | semidirect |
| 30. C2×#444 | C22 | semidirect |
| 31. C2×#443 | C22 | semidirect |
| 32. C2×#440 | C22 | semidirect |
| 33. #2932 | C22 | semidirect |
| 34. C4×C4⋊Q8 | C22 | semidirect |
| 36. #2052 | C22 | semidirect |
| 37. #2051 | C22 | semidirect |
| 38. #2039 | C22 | semidirect |
| 39. #2039 | C22 | semidirect |
| 40. #2007 | C22 | semidirect |
| 42. #1975 | C22 | semidirect |
| 43. #1974 | C22 | semidirect |
| 44. #1973 | C22 | semidirect |
| 45. #1962 | C22 | semidirect |
| 47. #1956 | C22 | semidirect |
| 48. #1849 | C22 | semidirect |
| 49. #1845 | C22 | semidirect |
| 50. #1816 | C22 | semidirect |
| 51. #1801 | C22 | semidirect |
| 52. #1800 | C22 | semidirect |
| 53. #1793 | C22 | semidirect |
| 54. #1792 | C22 | semidirect |
| 55. C4×#97 | C22 | semidirect |
| 88. #497 | D4 | semidirect |
| 89. #496 | D4 | semidirect |
| 90. #492 | D4 | semidirect |
| 184. C2×SD16 | C2×D4 | semidirect |
| 198. C4⋊Q8 | C2×D4 | semidirect |
| 264. C4×C8 | C2×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3291 | 2 |
| #61080 | 2 |
| #31071 | 2 |
| #31070 | 2 |
| #28247 | 2 |
| #28242 | 2 |
| #24292 | 2 |
| #24225 | 2 |
| #24222 | 2 |
| #21710 | 2 |
| #21692 | 2 |