Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1100 conjugacy classes of subgroups.
The subgroup lattice has 629 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7622628 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #151895 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #150071 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #150071 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#7389 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#7389 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #134661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #62635 | C4 | 1 | 1 | yes | characteristic |
| 9 | #60183 | — | 2 | 1 | no | — |
| 10 | #33465 | — | 2 | 2 | no | — |
| 11 | #33465 | C4 | 1 | 1 | yes | characteristic |
| 12 | #33465 | C4 | 1 | 1 | yes | characteristic |
| 13 | #33464 | — | 2 | 2 | no | — |
| 14 | #33464 | — | 2 | 1 | no | — |
| 15 | #33463 | — | 2 | 2 | no | — |
| 16 | #33463 | — | 2 | 1 | no | — |
| 17 | C2×#2179 | — | 2 | 2 | no | — |
| 18 | C2×#2179 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#2179 | C22 | 1 | 1 | yes | characteristic |
| 20 | #33414 | C4 | 1 | 1 | yes | characteristic |
| 21 | #33385 | — | 2 | 1 | no | — |
| 22 | #33326 | C22 | 1 | 1 | yes | characteristic |
| 23 | #13558 | — | 2 | 1 | no | — |
| 24 | C2×#1398 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#1398 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #11999 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#1368 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #8604 | — | 2 | 1 | no | — |
| 29 | #7469 | — | 2 | 1 | no | — |
| 30 | #7389 | — | 2 | 2 | no | — |
| 31 | #7389 | — | 2 | 2 | no | — |
| 32 | #7389 | — | 2 | 2 | no | — |
| 33 | #7389 | — | 2 | 2 | no | — |
| 34 | #7158 | — | 2 | 1 | no | — |
| 35 | #3584 | — | 2 | 1 | no | — |
| 36 | #3573 | — | 4 | 1 | no | — |
| 37 | #3417 | — | 2 | 1 | no | — |
| 38 | #3417 | C8 | 1 | 2 | yes | complemented |
| 39 | #3416 | — | 2 | 2 | no | — |
| 40 | #3416 | — | 2 | 2 | no | — |
| 41 | #3415 | — | 2 | 1 | no | — |
| 42 | #3415 | C8 | 1 | 2 | yes | complemented |
| 43 | #3414 | — | 2 | 2 | no | — |
| 44 | #3414 | — | 2 | 1 | no | — |
| 45 | C2×#508 | — | 2 | 2 | no | — |
| 46 | C2×#508 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C2×#508 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×#504 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×#504 | D4 | 1 | 1 | yes | characteristic |
| 50 | #2957 | — | 2 | 4 | no | — |
| 51 | #2957 | — | 2 | 1 | no | — |
| 52 | #2957 | — | 2 | 1 | no | — |
| 53 | #2956 | — | 4 | 2 | no | — |
| 54 | #2956 | — | 4 | 1 | no | — |
| 55 | #2955 | — | 4 | 2 | no | — |
| 56 | #2955 | — | 4 | 1 | no | — |
| 57 | C2×#443 | — | 2 | 4 | no | — |
| 58 | C2×#443 | — | 2 | 1 | no | — |
| 59 | C2×#443 | — | 2 | 1 | no | — |
| 60 | #2916 | — | 2 | 1 | no | — |
| 61 | #2901 | — | 4 | 1 | no | — |
| 62 | C4×#131 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×M64 | — | 2 | 1 | no | — |
| 64 | C2×M64 | — | 2 | 1 | no | — |
| 65 | #2179 | — | 2 | 4 | no | — |
| 66 | #2179 | — | 2 | 4 | no | — |
| 67 | #2179 | — | 2 | 2 | no | — |
| 68 | #2179 | — | 2 | 2 | no | — |
| 69 | #2179 | — | 2 | 1 | no | — |
| 70 | #2179 | — | 2 | 1 | no | — |
| 71 | #2179 | — | 2 | 1 | no | — |
| 72 | #2179 | — | 2 | 1 | no | — |
| 73 | #2179 | D4 | 1 | 2 | yes | — |
| 74 | #2179 | D4 | 1 | 2 | yes | — |
| 75 | #2179 | D4 | 1 | 2 | yes | — |
| 76 | #2179 | D4 | 1 | 2 | yes | — |
| 77 | #2178 | — | 2 | 4 | no | — |
| 78 | #2178 | — | 2 | 4 | no | — |
| 79 | #2178 | — | 2 | 2 | no | — |
| 80 | #2178 | — | 2 | 2 | no | — |
| 81 | #2161 | — | 2 | 1 | no | — |
| 82 | #2161 | — | 2 | 2 | no | — |
| 83 | C2×#368 | — | 2 | 2 | no | — |
| 84 | C2×#368 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C2×#368 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | #2143 | — | 2 | 4 | no | — |
| 87 | #2143 | — | 2 | 1 | no | — |
| 88 | #2143 | — | 2 | 1 | no | — |
| 89 | C2×#359 | — | 2 | 4 | no | — |
| 90 | C2×#359 | — | 2 | 1 | no | — |
| 91 | C2×#359 | — | 2 | 1 | no | — |
| 92 | #2108 | — | 2 | 1 | no | — |
| 93 | #2108 | — | 2 | 1 | no | — |
| 94 | #2108 | C2×C4 | 1 | 1 | yes | characteristic |
| 95 | #2108 | D4 | 1 | 1 | yes | characteristic |
| 96 | C4×M32 | — | 2 | 1 | no | — |
| 97 | C4×M32 | D4 | 1 | 1 | yes | characteristic |
| 98 | C2×#346 | — | 2 | 1 | no | — |
| 99 | C2×#346 | C23 | 1 | 1 | yes | characteristic |
| 100 | #1564 | — | 2 | 1 | no | — |
| 101 | C2×#334 | — | 2 | 1 | no | — |
| 102 | #1477 | — | 4 | 1 | no | — |
| 103 | #1401 | — | 2 | 4 | no | — |
| 104 | #1398 | — | 2 | 1 | no | — |
| 105 | #1398 | — | 2 | 1 | no | — |
| 106 | #1398 | — | 2 | 1 | no | — |
| 107 | #1398 | — | 2 | 1 | no | — |
| 108 | #1368 | — | 2 | 1 | no | — |
| 109 | #1368 | — | 2 | 1 | no | — |
| 110 | #1368 | — | 2 | 1 | no | — |
| 111 | #1368 | — | 2 | 1 | no | — |
| 112 | #1283 | — | 4 | 1 | no | — |
| 113 | #585 | — | 4 | 1 | no | — |
| 114 | #578 | — | 2 | 2 | no | — |
| 115 | #578 | — | 2 | 2 | no | — |
| 116 | #577 | — | 4 | 2 | no | — |
| 117 | #577 | — | 4 | 2 | no | — |
| 118 | #576 | — | 2 | 2 | no | — |
| 119 | #576 | — | 2 | 2 | no | — |
| 120 | #575 | — | 4 | 2 | no | — |
| 121 | #575 | — | 4 | 1 | no | — |
| 122 | C2×#135 | — | 2 | 4 | no | — |
| 123 | C2×#135 | — | 2 | 1 | no | — |
| 124 | C2×#135 | — | 2 | 1 | no | — |
| 125 | #568 | — | 4 | 4 | no | — |
| 126 | #568 | — | 4 | 1 | no | — |
| 127 | #568 | — | 4 | 1 | no | — |
| 128 | #568 | — | 4 | 1 | no | — |
| 129 | #568 | — | 8 | 2 | no | — |
| 130 | #568 | — | 8 | 2 | no | — |
| 131 | C2×#131 | — | 4 | 4 | no | — |
| 132 | C2×#131 | — | 4 | 1 | no | — |
| 133 | C2×#131 | — | 4 | 1 | no | — |
| 134 | C2×#131 | — | 8 | 2 | no | — |
| 135 | C2×#131 | — | 8 | 2 | no | — |
| 136 | C2×#131 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 137 | C2×#131 | SD16 | 1 | 1 | yes | characteristic |
| 138 | C4×#41 | D8 | 1 | 1 | yes | characteristic |
| 139 | #510 | — | 2 | 2 | no | — |
| 140 | #510 | — | 2 | 4 | no | — |
| 141 | #510 | — | 2 | 4 | no | — |
| 142 | #510 | — | 2 | 2 | no | — |
| 143 | #509 | — | 2 | 2 | no | — |
| 144 | #509 | — | 2 | 4 | no | — |
| 145 | #509 | — | 2 | 4 | no | — |
| 146 | #509 | — | 2 | 2 | no | — |
| 147 | #508 | — | 2 | 4 | no | — |
| 148 | #508 | — | 2 | 4 | no | — |
| 149 | #508 | — | 2 | 2 | no | — |
| 150 | #508 | — | 2 | 2 | no | — |
| 151 | #508 | — | 2 | 1 | no | — |
| 152 | #508 | — | 2 | 1 | no | — |
| 153 | #508 | — | 2 | 1 | no | — |
| 154 | #508 | — | 2 | 1 | no | — |
| 155 | #508 | C22⋊C4 | 1 | 2 | yes | — |
| 156 | #508 | C22⋊C4 | 1 | 2 | yes | — |
| 157 | #508 | C2×C8 | 1 | 2 | yes | — |
| 158 | #508 | M16 | 1 | 2 | yes | — |
| 159 | C2×Q32 | — | 2 | 2 | no | — |
| 160 | C2×Q32 | C2×C8 | 1 | 1 | yes | characteristic |
| 161 | C2×Q32 | M16 | 1 | 1 | yes | characteristic |
| 162 | C2×SD32 | — | 2 | 4 | no | — |
| 163 | C2×SD32 | — | 2 | 1 | no | — |
| 164 | C2×SD32 | — | 2 | 1 | no | — |
| 165 | C2×D16 | — | 2 | 2 | no | — |
| 166 | C2×D16 | C2×C8 | 1 | 1 | yes | characteristic |
| 167 | C2×D16 | M16 | 1 | 1 | yes | characteristic |
| 168 | #504 | — | 2 | 1 | no | — |
| 169 | #504 | — | 2 | 1 | no | — |
| 170 | #504 | — | 2 | 2 | no | — |
| 171 | #504 | — | 4 | 1 | no | — |
| 172 | #504 | C2×C8 | 1 | 2 | yes | — |
| 173 | #504 | M16 | 1 | 2 | yes | — |
| 174 | C2×M32 | — | 2 | 1 | no | — |
| 175 | C2×M32 | — | 2 | 1 | no | — |
| 176 | C2×M32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 177 | C2×M32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 178 | C22×C16 | — | 2 | 1 | no | — |
| 179 | C22×C16 | — | 2 | 1 | no | — |
| 180 | C22×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 181 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | #444 | — | 4 | 2 | no | — |
| 183 | #444 | — | 4 | 2 | no | — |
| 184 | #444 | — | 4 | 4 | no | — |
| 185 | #444 | — | 4 | 4 | no | — |
| 186 | #443 | — | 2 | 4 | no | — |
| 187 | #443 | — | 2 | 4 | no | — |
| 188 | #443 | — | 2 | 2 | no | — |
| 189 | #443 | — | 2 | 2 | no | — |
| 190 | #443 | — | 2 | 2 | no | — |
| 191 | #443 | — | 2 | 2 | no | — |
| 192 | #443 | — | 4 | 4 | no | — |
| 193 | #443 | — | 4 | 4 | no | — |
| 194 | #443 | — | 4 | 1 | no | — |
| 195 | #443 | — | 4 | 1 | no | — |
| 196 | #443 | — | 4 | 1 | no | — |
| 197 | #443 | — | 4 | 1 | no | — |
| 198 | #431 | — | 4 | 1 | no | — |
| 199 | #430 | — | 4 | 2 | no | — |
| 200 | #430 | — | 4 | 1 | no | — |
| 201 | C2×#108 | — | 2 | 4 | no | — |
| 202 | C2×#108 | — | 2 | 1 | no | — |
| 203 | C2×#108 | — | 2 | 1 | no | — |
| 204 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 205 | #421 | — | 4 | 4 | no | — |
| 206 | #421 | — | 4 | 1 | no | — |
| 207 | #421 | — | 4 | 1 | no | — |
| 208 | C2×#104 | — | 4 | 4 | no | — |
| 209 | C2×#104 | — | 4 | 1 | no | — |
| 210 | C2×#104 | — | 4 | 1 | no | — |
| 211 | #405 | — | 2 | 1 | no | — |
| 212 | #405 | — | 2 | 1 | no | — |
| 213 | #405 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 214 | #405 | SD16 | 1 | 1 | yes | characteristic |
| 215 | C4×M16 | — | 2 | 1 | no | — |
| 216 | C4×M16 | D8 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C8 | — | 2 | 1 | no | — |
| 218 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | M64 | — | 2 | 2 | no | — |
| 220 | M64 | — | 4 | 1 | no | — |
| 221 | M64 | — | 4 | 1 | no | — |
| 222 | M64 | — | 4 | 1 | no | — |
| 223 | C2×C32 | — | 2 | 2 | no | — |
| 224 | C2×C32 | — | 4 | 1 | no | — |
| 225 | #368 | — | 2 | 4 | no | — |
| 226 | #368 | — | 2 | 1 | no | — |
| 227 | #368 | — | 2 | 1 | no | — |
| 228 | #368 | C22⋊C4 | 1 | 2 | yes | — |
| 229 | #368 | C22⋊C4 | 1 | 2 | yes | — |
| 230 | #359 | — | 2 | 4 | no | — |
| 231 | #359 | — | 2 | 4 | no | — |
| 232 | #359 | — | 2 | 2 | no | — |
| 233 | #359 | — | 2 | 2 | no | — |
| 234 | #359 | — | 2 | 2 | no | — |
| 235 | #359 | — | 2 | 2 | no | — |
| 236 | #346 | — | 2 | 1 | no | — |
| 237 | #346 | — | 2 | 1 | no | — |
| 238 | #346 | — | 2 | 1 | no | — |
| 239 | #346 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | #346 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | #346 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | #346 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C4×C16 | — | 2 | 1 | no | — |
| 244 | C4×C16 | — | 2 | 1 | no | — |
| 245 | C4×C16 | — | 2 | 1 | no | — |
| 246 | #335 | — | 4 | 1 | no | — |
| 247 | #334 | — | 4 | 1 | no | — |
| 248 | #334 | — | 4 | 1 | no | — |
| 249 | #334 | — | 4 | 1 | no | — |
| 250 | Q8⋊C8 | — | 8 | 1 | no | — |
| 251 | D4⋊C8 | — | 8 | 1 | no | — |
| 252 | 2−1+4 | — | 4 | 2 | no | — |
| 253 | 2−1+4 | — | 4 | 2 | no | — |
| 254 | 2−1+4 | — | 8 | 1 | no | — |
| 255 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 256 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 257 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 258 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 259 | C2×#41 | — | 4 | 4 | no | — |
| 260 | C2×#41 | — | 4 | 1 | no | — |
| 261 | C2×#41 | — | 4 | 1 | no | — |
| 262 | C2×#41 | — | 8 | 2 | no | — |
| 263 | C2×#41 | — | 8 | 2 | no | — |
| 264 | C2×#41 | #102 | 1 | 1 | yes | characteristic |
| 265 | #137 | — | 4 | 2 | no | — |
| 266 | #137 | — | 4 | 4 | no | — |
| 267 | #137 | — | 4 | 4 | no | — |
| 268 | #137 | — | 4 | 2 | no | — |
| 269 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 270 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 271 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 272 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 273 | #135 | — | 2 | 4 | no | — |
| 274 | #135 | — | 2 | 4 | no | — |
| 275 | #135 | — | 2 | 2 | no | — |
| 276 | #135 | — | 2 | 2 | no | — |
| 277 | #135 | — | 2 | 2 | no | — |
| 278 | #135 | — | 2 | 2 | no | — |
| 279 | #135 | — | 4 | 4 | no | — |
| 280 | #135 | — | 4 | 4 | no | — |
| 281 | #135 | — | 4 | 1 | no | — |
| 282 | #135 | — | 4 | 1 | no | — |
| 283 | #135 | — | 4 | 1 | no | — |
| 284 | #135 | — | 4 | 1 | no | — |
| 285 | C2×Q16 | — | 2 | 4 | no | — |
| 286 | C2×Q16 | — | 2 | 1 | no | — |
| 287 | C2×Q16 | — | 2 | 1 | no | — |
| 288 | C2×SD16 | — | 4 | 4 | no | — |
| 289 | C2×SD16 | — | 4 | 1 | no | — |
| 290 | C2×SD16 | — | 4 | 1 | no | — |
| 291 | C2×D8 | — | 2 | 4 | no | — |
| 292 | C2×D8 | — | 2 | 1 | no | — |
| 293 | C2×D8 | — | 2 | 1 | no | — |
| 294 | #131 | — | 2 | 2 | no | — |
| 295 | #131 | — | 2 | 2 | no | — |
| 296 | #131 | — | 2 | 1 | no | — |
| 297 | #131 | — | 2 | 1 | no | — |
| 298 | #131 | — | 4 | 4 | no | — |
| 299 | #131 | — | 4 | 4 | no | — |
| 300 | #131 | — | 4 | 2 | no | — |
| 301 | #131 | — | 4 | 2 | no | — |
| 302 | #131 | — | 4 | 2 | no | — |
| 303 | #131 | — | 4 | 2 | no | — |
| 304 | #131 | — | 8 | 4 | no | — |
| 305 | #131 | — | 8 | 1 | no | — |
| 306 | #131 | — | 8 | 1 | no | — |
| 307 | #131 | — | 8 | 4 | no | — |
| 308 | #131 | — | 8 | 1 | no | — |
| 309 | #131 | — | 8 | 1 | no | — |
| 310 | #131 | — | 8 | 4 | no | — |
| 311 | #131 | — | 8 | 4 | no | — |
| 312 | #131 | — | 8 | 2 | no | — |
| 313 | #131 | — | 8 | 2 | no | — |
| 314 | #131 | — | 8 | 2 | no | — |
| 315 | #131 | — | 8 | 2 | no | — |
| 316 | #131 | C22⋊C8 | 1 | 2 | yes | — |
| 317 | #131 | #104 | 1 | 2 | yes | — |
| 318 | C2×M16 | — | 2 | 1 | no | — |
| 319 | C2×M16 | — | 2 | 1 | no | — |
| 320 | C2×M16 | — | 4 | 4 | no | — |
| 321 | C2×M16 | — | 4 | 1 | no | — |
| 322 | C2×M16 | — | 4 | 1 | no | — |
| 323 | C2×M16 | — | 8 | 4 | no | — |
| 324 | C2×M16 | — | 8 | 1 | no | — |
| 325 | C2×M16 | — | 8 | 1 | no | — |
| 326 | C2×M16 | — | 8 | 4 | no | — |
| 327 | C2×M16 | — | 8 | 4 | no | — |
| 328 | C2×M16 | — | 8 | 2 | no | — |
| 329 | C2×M16 | — | 8 | 2 | no | — |
| 330 | C2×M16 | #102 | 1 | 1 | yes | characteristic |
| 331 | C2×M16 | #102 | 1 | 1 | yes | characteristic |
| 332 | C22×C8 | — | 2 | 1 | no | — |
| 333 | C22×C8 | — | 2 | 1 | no | — |
| 334 | C22×C8 | — | 8 | 4 | no | — |
| 335 | C22×C8 | — | 8 | 1 | no | — |
| 336 | C22×C8 | — | 8 | 1 | no | — |
| 337 | C22×C8 | — | 8 | 1 | no | — |
| 338 | C22×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 339 | C22×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 340 | C4×Q8 | — | 2 | 1 | no | — |
| 341 | C4×D4 | — | 2 | 1 | no | — |
| 342 | C4×D4 | — | 4 | 1 | no | — |
| 343 | #117 | — | 2 | 1 | no | — |
| 344 | #117 | #102 | 1 | 1 | yes | characteristic |
| 345 | C2×C42 | — | 2 | 1 | no | — |
| 346 | C2×C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 347 | Q32 | — | 2 | 4 | no | — |
| 348 | Q32 | — | 2 | 1 | no | — |
| 349 | Q32 | — | 2 | 1 | no | — |
| 350 | Q32 | C22⋊C8 | 1 | 2 | yes | — |
| 351 | Q32 | C22⋊C8 | 1 | 2 | yes | — |
| 352 | SD32 | — | 2 | 4 | no | — |
| 353 | SD32 | — | 2 | 4 | no | — |
| 354 | SD32 | — | 2 | 2 | no | — |
| 355 | SD32 | — | 2 | 2 | no | — |
| 356 | SD32 | — | 2 | 2 | no | — |
| 357 | SD32 | — | 2 | 2 | no | — |
| 358 | D16 | — | 2 | 4 | no | — |
| 359 | D16 | — | 2 | 1 | no | — |
| 360 | D16 | — | 2 | 1 | no | — |
| 361 | D16 | C22⋊C8 | 1 | 2 | yes | — |
| 362 | D16 | C22⋊C8 | 1 | 2 | yes | — |
| 363 | M32 | — | 2 | 1 | no | — |
| 364 | M32 | — | 2 | 2 | no | — |
| 365 | M32 | — | 2 | 2 | no | — |
| 366 | M32 | — | 2 | 1 | no | — |
| 367 | M32 | — | 2 | 1 | no | — |
| 368 | M32 | — | 4 | 2 | no | — |
| 369 | M32 | C22⋊C8 | 1 | 2 | yes | — |
| 370 | C2×C16 | — | 2 | 1 | no | — |
| 371 | C2×C16 | — | 2 | 1 | no | — |
| 372 | C2×C16 | — | 2 | 1 | no | — |
| 373 | C2×C16 | — | 2 | 2 | no | — |
| 374 | C2×C16 | — | 2 | 2 | no | — |
| 375 | C2×C16 | — | 2 | 1 | no | — |
| 376 | C2×C16 | — | 4 | 2 | no | — |
| 377 | C2×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 378 | C2×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 379 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 380 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 381 | C2×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 382 | C2×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 383 | C2×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 384 | C2×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 385 | #108 | — | 2 | 2 | no | — |
| 386 | #108 | — | 2 | 2 | no | — |
| 387 | #108 | — | 4 | 4 | no | — |
| 388 | #108 | — | 4 | 1 | no | — |
| 389 | #108 | — | 4 | 1 | no | — |
| 390 | C4⋊C8 | — | 8 | 1 | no | — |
| 391 | C4⋊C8 | — | 8 | 1 | no | — |
| 392 | C4⋊C8 | — | 8 | 1 | no | — |
| 393 | #104 | — | 4 | 4 | no | — |
| 394 | #104 | — | 4 | 4 | no | — |
| 395 | #104 | — | 4 | 2 | no | — |
| 396 | #104 | — | 4 | 2 | no | — |
| 397 | #104 | — | 4 | 2 | no | — |
| 398 | #104 | — | 4 | 2 | no | — |
| 399 | C22⋊C8 | — | 8 | 1 | no | — |
| 400 | #97 | — | 2 | 1 | no | — |
| 401 | #97 | — | 2 | 1 | no | — |
| 402 | #97 | — | 2 | 1 | no | — |
| 403 | C4×C8 | — | 2 | 1 | no | — |
| 404 | C4×C8 | — | 2 | 1 | no | — |
| 405 | C4×C8 | — | 2 | 1 | no | — |
| 406 | C4×C8 | — | 8 | 1 | no | — |
| 407 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 408 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 409 | C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 410 | C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 411 | C32 | — | 4 | 2 | no | — |
| 412 | C32 | — | 4 | 2 | no | — |
| 413 | #41 | — | 2 | 1 | no | — |
| 414 | #41 | — | 2 | 1 | no | — |
| 415 | #41 | — | 4 | 4 | no | — |
| 416 | #41 | — | 4 | 4 | no | — |
| 417 | #41 | — | 4 | 2 | no | — |
| 418 | #41 | — | 4 | 2 | no | — |
| 419 | #41 | — | 4 | 2 | no | — |
| 420 | #41 | — | 4 | 2 | no | — |
| 421 | #41 | — | 8 | 4 | no | — |
| 422 | #41 | — | 8 | 4 | no | — |
| 423 | #41 | — | 8 | 4 | no | — |
| 424 | #41 | — | 8 | 4 | no | — |
| 425 | #41 | — | 8 | 2 | no | — |
| 426 | #41 | — | 8 | 2 | no | — |
| 427 | #41 | — | 8 | 2 | no | — |
| 428 | #41 | — | 8 | 2 | no | — |
| 429 | #41 | — | 8 | 1 | no | — |
| 430 | #41 | — | 8 | 1 | no | — |
| 431 | #41 | — | 8 | 1 | no | — |
| 432 | #41 | — | 8 | 1 | no | — |
| 433 | #41 | D4⋊C8 | 1 | 2 | yes | — |
| 434 | #41 | #361 | 1 | 2 | yes | — |
| 435 | C2×Q8 | — | 4 | 4 | no | — |
| 436 | C2×Q8 | — | 4 | 1 | no | — |
| 437 | C2×Q8 | — | 4 | 1 | no | — |
| 438 | C2×Q8 | — | 8 | 2 | no | — |
| 439 | C2×Q8 | — | 8 | 2 | no | — |
| 440 | C2×Q8 | #360 | 1 | 1 | yes | characteristic |
| 441 | C2×D4 | — | 2 | 1 | no | — |
| 442 | C2×D4 | — | 4 | 4 | no | — |
| 443 | C2×D4 | — | 4 | 1 | no | — |
| 444 | C2×D4 | — | 4 | 1 | no | — |
| 445 | C2×D4 | — | 8 | 4 | no | — |
| 446 | C2×D4 | — | 8 | 4 | no | — |
| 447 | C2×D4 | — | 8 | 2 | no | — |
| 448 | C2×D4 | — | 8 | 4 | no | — |
| 449 | C2×D4 | — | 8 | 1 | no | — |
| 450 | C2×D4 | — | 8 | 1 | no | — |
| 451 | C2×D4 | — | 8 | 2 | no | — |
| 452 | C2×D4 | #360 | 1 | 1 | yes | characteristic |
| 453 | C22×C4 | — | 2 | 1 | no | — |
| 454 | C22×C4 | — | 2 | 1 | no | — |
| 455 | C22×C4 | — | 4 | 1 | no | — |
| 456 | C22×C4 | — | 8 | 4 | no | — |
| 457 | C22×C4 | — | 8 | 1 | no | — |
| 458 | C22×C4 | — | 8 | 1 | no | — |
| 459 | C22×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 460 | Q16 | — | 2 | 2 | no | — |
| 461 | Q16 | — | 2 | 2 | no | — |
| 462 | Q16 | — | 4 | 4 | no | — |
| 463 | Q16 | — | 4 | 1 | no | — |
| 464 | Q16 | — | 4 | 1 | no | — |
| 465 | SD16 | — | 4 | 4 | no | — |
| 466 | SD16 | — | 4 | 4 | no | — |
| 467 | SD16 | — | 4 | 2 | no | — |
| 468 | SD16 | — | 4 | 2 | no | — |
| 469 | SD16 | — | 4 | 2 | no | — |
| 470 | SD16 | — | 4 | 2 | no | — |
| 471 | D8 | — | 2 | 2 | no | — |
| 472 | D8 | — | 2 | 2 | no | — |
| 473 | D8 | — | 4 | 4 | no | — |
| 474 | D8 | — | 4 | 1 | no | — |
| 475 | D8 | — | 4 | 1 | no | — |
| 476 | M16 | — | 2 | 4 | no | — |
| 477 | M16 | — | 2 | 1 | no | — |
| 478 | M16 | — | 2 | 1 | no | — |
| 479 | M16 | — | 2 | 2 | no | — |
| 480 | M16 | — | 2 | 2 | no | — |
| 481 | M16 | — | 4 | 2 | no | — |
| 482 | M16 | — | 4 | 2 | no | — |
| 483 | M16 | — | 8 | 2 | no | — |
| 484 | M16 | — | 8 | 2 | no | — |
| 485 | M16 | — | 8 | 4 | no | — |
| 486 | M16 | — | 8 | 4 | no | — |
| 487 | M16 | — | 8 | 2 | no | — |
| 488 | M16 | — | 8 | 2 | no | — |
| 489 | M16 | — | 8 | 4 | no | — |
| 490 | M16 | — | 8 | 1 | no | — |
| 491 | M16 | — | 8 | 1 | no | — |
| 492 | M16 | D4⋊C8 | 1 | 2 | yes | — |
| 493 | M16 | #361 | 1 | 2 | yes | — |
| 494 | C2×C8 | — | 2 | 4 | no | — |
| 495 | C2×C8 | — | 2 | 1 | no | — |
| 496 | C2×C8 | — | 2 | 1 | no | — |
| 497 | C2×C8 | — | 2 | 1 | no | — |
| 498 | C2×C8 | — | 2 | 1 | no | — |
| 499 | C2×C8 | — | 2 | 2 | no | — |
| 500 | C2×C8 | — | 2 | 2 | no | — |
| 501 | C2×C8 | — | 8 | 2 | no | — |
| 502 | C2×C8 | — | 8 | 2 | no | — |
| 503 | C2×C8 | — | 8 | 4 | no | — |
| 504 | C2×C8 | — | 8 | 4 | no | — |
| 505 | C2×C8 | — | 8 | 2 | no | — |
| 506 | C2×C8 | — | 8 | 2 | no | — |
| 507 | C2×C8 | — | 8 | 4 | no | — |
| 508 | C2×C8 | — | 8 | 1 | no | — |
| 509 | C2×C8 | — | 8 | 1 | no | — |
| 510 | C2×C8 | — | 16 | 1 | no | — |
| 511 | C2×C8 | — | 16 | 1 | no | — |
| 512 | C2×C8 | — | 32 | 1 | no | — |
| 513 | C2×C8 | #379 | 1 | 1 | yes | characteristic |
| 514 | C2×C8 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 515 | C2×C8 | #407 | 1 | 1 | yes | characteristic |
| 516 | C2×C8 | #418 | 1 | 1 | yes | characteristic |
| 517 | C2×C8 | C2×#104 | 1 | 1 | yes | characteristic |
| 518 | C2×C8 | #421 | 1 | 1 | yes | characteristic |
| 519 | C2×C8 | #450 | 1 | 1 | yes | characteristic |
| 520 | C2×C8 | #450 | 1 | 1 | yes | characteristic |
| 521 | C4⋊C4 | — | 2 | 1 | no | — |
| 522 | C4⋊C4 | — | 4 | 1 | no | — |
| 523 | C22⋊C4 | — | 2 | 1 | no | — |
| 524 | C22⋊C4 | — | 4 | 1 | no | — |
| 525 | C42 | — | 2 | 1 | no | — |
| 526 | C42 | — | 2 | 1 | no | — |
| 527 | C42 | — | 4 | 1 | no | — |
| 528 | C42 | #447 | 1 | 1 | yes | characteristic |
| 529 | C42 | #447 | 1 | 1 | yes | characteristic |
| 530 | C16 | — | 2 | 2 | no | — |
| 531 | C16 | — | 2 | 1 | no | — |
| 532 | C16 | — | 2 | 1 | no | — |
| 533 | C16 | — | 4 | 1 | no | — |
| 534 | C16 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 535 | C16 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 536 | C16 | #407 | 1 | 1 | yes | characteristic |
| 537 | C16 | #407 | 1 | 1 | yes | characteristic |
| 538 | C23 | — | 2 | 1 | no | — |
| 539 | C23 | — | 8 | 4 | no | — |
| 540 | C23 | — | 8 | 1 | no | — |
| 541 | C23 | — | 8 | 1 | no | — |
| 542 | C23 | #2145 | 1 | 1 | yes | characteristic |
| 543 | Q8 | — | 2 | 1 | no | — |
| 544 | Q8 | — | 4 | 2 | no | — |
| 545 | Q8 | — | 4 | 2 | no | — |
| 546 | Q8 | — | 8 | 4 | no | — |
| 547 | Q8 | — | 8 | 1 | no | — |
| 548 | Q8 | — | 8 | 1 | no | — |
| 549 | Q8 | #1333 | 1 | 2 | yes | — |
| 550 | D4 | — | 2 | 2 | no | — |
| 551 | D4 | — | 2 | 2 | no | — |
| 552 | D4 | — | 2 | 1 | no | — |
| 553 | D4 | — | 4 | 2 | no | — |
| 554 | D4 | — | 4 | 2 | no | — |
| 555 | D4 | — | 8 | 4 | no | — |
| 556 | D4 | — | 8 | 4 | no | — |
| 557 | D4 | — | 8 | 4 | no | — |
| 558 | D4 | — | 8 | 2 | no | — |
| 559 | D4 | — | 8 | 2 | no | — |
| 560 | D4 | — | 8 | 2 | no | — |
| 561 | D4 | — | 8 | 2 | no | — |
| 562 | D4 | — | 8 | 1 | no | — |
| 563 | D4 | — | 8 | 1 | no | — |
| 564 | D4 | #1333 | 1 | 2 | yes | — |
| 565 | C2×C4 | — | 2 | 1 | no | — |
| 566 | C2×C4 | — | 2 | 2 | no | — |
| 567 | C2×C4 | — | 2 | 2 | no | — |
| 568 | C2×C4 | — | 2 | 1 | no | — |
| 569 | C2×C4 | — | 2 | 1 | no | — |
| 570 | C2×C4 | — | 4 | 1 | no | — |
| 571 | C2×C4 | — | 8 | 4 | no | — |
| 572 | C2×C4 | — | 8 | 4 | no | — |
| 573 | C2×C4 | — | 8 | 1 | no | — |
| 574 | C2×C4 | — | 8 | 4 | no | — |
| 575 | C2×C4 | — | 8 | 1 | no | — |
| 576 | C2×C4 | — | 8 | 1 | no | — |
| 577 | C2×C4 | — | 8 | 2 | no | — |
| 578 | C2×C4 | — | 8 | 2 | no | — |
| 579 | C2×C4 | — | 8 | 2 | no | — |
| 580 | C2×C4 | — | 8 | 2 | no | — |
| 581 | C2×C4 | — | 16 | 1 | no | — |
| 582 | C2×C4 | C2×D4⋊C8 | 1 | 1 | yes | characteristic |
| 583 | C2×C4 | #1486 | 1 | 1 | yes | characteristic |
| 584 | C2×C4 | #1786 | 1 | 1 | yes | characteristic |
| 585 | C2×C4 | C2×#360 | 1 | 1 | yes | characteristic |
| 586 | C2×C4 | C2×#361 | 1 | 1 | yes | characteristic |
| 587 | C2×C4 | C2×#361 | 1 | 1 | yes | characteristic |
| 588 | C8 | — | 2 | 2 | no | — |
| 589 | C8 | — | 2 | 1 | no | — |
| 590 | C8 | — | 2 | 2 | no | — |
| 591 | C8 | — | 2 | 1 | no | — |
| 592 | C8 | — | 8 | 2 | no | — |
| 593 | C8 | — | 8 | 2 | no | — |
| 594 | C8 | — | 32 | 1 | no | — |
| 595 | C8 | — | 32 | 1 | no | — |
| 596 | C8 | #1478 | 1 | 1 | yes | characteristic |
| 597 | C8 | #1490 | 1 | 1 | yes | characteristic |
| 598 | C8 | #1779 | 1 | 1 | yes | characteristic |
| 599 | C8 | #1789 | 1 | 1 | yes | characteristic |
| 600 | C22 | — | 2 | 2 | no | — |
| 601 | C22 | — | 4 | 1 | no | — |
| 602 | C22 | — | 8 | 1 | no | — |
| 603 | C22 | — | 8 | 2 | no | — |
| 604 | C22 | — | 8 | 2 | no | — |
| 605 | C22 | — | 32 | 1 | no | — |
| 606 | C22 | — | 32 | 1 | no | — |
| 607 | C22 | — | 32 | 4 | no | — |
| 608 | C22 | #11599 | 1 | 1 | yes | characteristic |
| 609 | C22 | #11667 | 1 | 1 | yes | characteristic |
| 610 | C22 | #12735 | 1 | 1 | yes | characteristic |
| 611 | C4 | — | 2 | 2 | no | — |
| 612 | C4 | — | 4 | 1 | no | — |
| 613 | C4 | — | 4 | 1 | no | — |
| 614 | C4 | — | 8 | 1 | no | — |
| 615 | C4 | — | 8 | 2 | no | — |
| 616 | C4 | — | 8 | 2 | no | — |
| 617 | C4 | #8310 | 1 | 1 | yes | characteristic |
| 618 | C4 | C2×#1333 | 1 | 1 | yes | characteristic |
| 619 | C4 | #11663 | 1 | 1 | yes | characteristic |
| 620 | C4 | #12736 | 1 | 1 | yes | characteristic |
| 621 | C2 | — | 2 | 1 | no | — |
| 622 | C2 | — | 2 | 1 | no | — |
| 623 | C2 | — | 2 | 1 | no | — |
| 624 | C2 | — | 4 | 2 | no | — |
| 625 | C2 | — | 16 | 2 | no | — |
| 626 | C2 | — | 16 | 2 | no | — |
| 627 | C2 | #129503 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #129503 |
| commutator | C2×C16 | C22×C8 |
| Frattini, cosocle | C2×#346 | C23 |
| prime radical | #62635 | C4 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C4×#131 ◁ #33326 ◁ G | |
| LECS | G ▷ C2×#346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #151895 | C2 | semidirect |
| 3. #150071 | C2 | semidirect |
| 4. #150071 | C2 | semidirect |
| 5. C2×#7389 | C2 | semidirect |
| 6. C2×#7389 | C2 | semidirect |
| 7. #134661 | C2 | semidirect |
| 24. C2×#1398 | C22 | semidirect |
| 25. C2×#1398 | C22 | semidirect |
| 26. #11999 | C22 | semidirect |
| 27. C2×#1368 | C22 | semidirect |
| 38. #3417 | C8 | semidirect |
| 42. #3415 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7622628 | 2 |
| #151895 | 2 |
| #150071 | 2 |
| C2×#7389 | 2 |
| #134661 | 2 |