Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
984 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62636 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33595 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #33522 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #25799 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22458 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13442 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13336 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13079 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13021 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #12916 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12746 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#576 | C22 | 1 | 1 | yes | characteristic |
| 14 | #3416 | — | 2 | 4 | no | — |
| 15 | #3415 | — | 2 | 4 | no | — |
| 16 | #3414 | — | 2 | 2 | no | — |
| 17 | #3414 | C22 | 1 | 2 | yes | — |
| 18 | C2×#509 | — | 2 | 2 | no | — |
| 19 | C2×#509 | C22 | 1 | 2 | yes | — |
| 20 | C2×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C22×D16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #3407 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3155 | C22 | 1 | 2 | yes | complemented |
| 24 | #3058 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3027 | — | 2 | 1 | no | — |
| 26 | #3021 | — | 2 | 1 | no | — |
| 27 | #2957 | C22 | 1 | 2 | yes | complemented |
| 28 | #2888 | — | 2 | 1 | no | — |
| 29 | #2213 | — | 2 | 4 | no | — |
| 30 | #2212 | — | 2 | 4 | no | — |
| 31 | #2186 | — | 2 | 2 | no | — |
| 32 | #2184 | — | 2 | 2 | no | — |
| 33 | #2153 | C22 | 1 | 2 | yes | complemented |
| 34 | #2148 | C22 | 1 | 2 | yes | complemented |
| 35 | C2×#361 | C22 | 1 | 2 | yes | complemented |
| 36 | C2×#359 | C22 | 1 | 2 | yes | complemented |
| 37 | #2140 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #2138 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #2113 | C22 | 1 | 1 | yes | characteristic |
| 40 | #2008 | — | 2 | 2 | no | — |
| 41 | #1978 | C22 | 1 | 2 | yes | complemented |
| 42 | #1976 | C22 | 1 | 2 | yes | complemented |
| 43 | #1903 | — | 2 | 2 | no | — |
| 44 | #1813 | C22 | 1 | 1 | yes | characteristic |
| 45 | #1795 | — | 2 | 1 | no | — |
| 46 | #1757 | C22 | 1 | 1 | yes | characteristic |
| 47 | #1389 | C22 | 1 | 2 | yes | complemented |
| 48 | #1379 | C22 | 1 | 2 | yes | complemented |
| 49 | #585 | — | 2 | 1 | no | — |
| 50 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 51 | #578 | — | 2 | 2 | no | — |
| 52 | #577 | — | 4 | 2 | no | — |
| 53 | #576 | — | 2 | 4 | no | — |
| 54 | #576 | — | 2 | 2 | no | — |
| 55 | #576 | — | 4 | 2 | no | — |
| 56 | #575 | — | 2 | 1 | no | — |
| 57 | #575 | — | 2 | 2 | no | — |
| 58 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 59 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 60 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 61 | C2×#135 | — | 2 | 2 | no | — |
| 62 | C2×#135 | D4 | 1 | 2 | yes | complemented |
| 63 | C2×#135 | C23 | 1 | 2 | yes | — |
| 64 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 65 | C22×D8 | D4 | 1 | 2 | yes | complemented |
| 66 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 68 | #568 | — | 2 | 2 | no | — |
| 69 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 70 | #535 | — | 2 | 1 | no | — |
| 71 | #535 | — | 2 | 2 | no | — |
| 72 | #510 | — | 2 | 4 | no | — |
| 73 | #510 | — | 2 | 2 | no | — |
| 74 | #510 | D4 | 1 | 4 | yes | complemented |
| 75 | #509 | — | 2 | 8 | no | — |
| 76 | #509 | — | 2 | 4 | no | — |
| 77 | #509 | — | 2 | 2 | no | — |
| 78 | #509 | — | 2 | 4 | no | — |
| 79 | #509 | — | 2 | 4 | no | — |
| 80 | #509 | — | 2 | 4 | no | — |
| 81 | #509 | D4 | 1 | 4 | yes | complemented |
| 82 | #508 | — | 2 | 8 | no | — |
| 83 | #508 | — | 2 | 4 | no | — |
| 84 | C2×SD32 | — | 2 | 4 | no | — |
| 85 | C2×SD32 | — | 2 | 2 | no | — |
| 86 | C2×SD32 | — | 2 | 1 | no | — |
| 87 | C2×D16 | — | 2 | 4 | no | — |
| 88 | C2×D16 | — | 2 | 2 | no | — |
| 89 | C2×D16 | — | 2 | 2 | no | — |
| 90 | C2×D16 | — | 2 | 1 | no | — |
| 91 | C2×D16 | — | 4 | 2 | no | — |
| 92 | #504 | — | 2 | 4 | no | — |
| 93 | C2×M32 | — | 2 | 2 | no | — |
| 94 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×M32 | C23 | 1 | 2 | yes | — |
| 96 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 97 | #496 | — | 4 | 2 | no | — |
| 98 | #495 | — | 2 | 2 | no | — |
| 99 | #493 | — | 2 | 2 | no | — |
| 100 | #469 | — | 2 | 2 | no | — |
| 101 | #466 | — | 2 | 2 | no | — |
| 102 | B(4,𝔽2) | — | 4 | 4 | no | — |
| 103 | #454 | — | 4 | 2 | no | — |
| 104 | #453 | — | 4 | 2 | no | — |
| 105 | #444 | — | 4 | 2 | no | — |
| 106 | #443 | — | 2 | 4 | no | — |
| 107 | C2×#108 | C23 | 1 | 2 | yes | — |
| 108 | #427 | C23 | 1 | 1 | yes | characteristic |
| 109 | #421 | — | 2 | 2 | no | — |
| 110 | #421 | — | 2 | 2 | no | — |
| 111 | #418 | — | 2 | 1 | no | — |
| 112 | #418 | — | 2 | 2 | no | — |
| 113 | #413 | — | 2 | 1 | no | — |
| 114 | #413 | — | 4 | 2 | no | — |
| 115 | #413 | D4 | 1 | 1 | yes | characteristic |
| 116 | C2×#100 | — | 2 | 2 | no | — |
| 117 | C2×#100 | — | 4 | 2 | no | — |
| 118 | #410 | — | 2 | 2 | no | — |
| 119 | #410 | D4 | 1 | 1 | yes | characteristic |
| 120 | #405 | C23 | 1 | 2 | yes | — |
| 121 | #364 | — | 2 | 4 | no | — |
| 122 | #362 | — | 2 | 2 | no | — |
| 123 | #361 | — | 2 | 2 | no | — |
| 124 | #361 | — | 2 | 4 | no | — |
| 125 | #359 | — | 4 | 2 | no | — |
| 126 | #358 | — | 2 | 1 | no | — |
| 127 | #357 | — | 2 | 1 | no | — |
| 128 | #357 | — | 2 | 2 | no | — |
| 129 | C22⋊C16 | — | 2 | 2 | no | — |
| 130 | #344 | D4 | 1 | 2 | yes | — |
| 131 | #338 | — | 2 | 1 | no | — |
| 132 | 2−1+4 | — | 4 | 2 | no | — |
| 133 | 2−1+4 | — | 4 | 1 | no | — |
| 134 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 135 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 136 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 137 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 138 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 139 | C2×#41 | — | 2 | 2 | no | — |
| 140 | C2×#41 | — | 2 | 1 | no | — |
| 141 | C2×#41 | — | 2 | 2 | no | — |
| 142 | C2×#41 | — | 4 | 1 | no | — |
| 143 | C2×#41 | — | 4 | 2 | no | — |
| 144 | C2×#41 | — | 8 | 2 | no | — |
| 145 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C22×D4 | — | 2 | 2 | no | — |
| 147 | C22×D4 | — | 2 | 1 | no | — |
| 148 | C22×D4 | — | 2 | 1 | no | — |
| 149 | C22×D4 | — | 4 | 1 | no | — |
| 150 | C22×D4 | — | 4 | 2 | no | — |
| 151 | #137 | — | 4 | 4 | no | — |
| 152 | #137 | — | 4 | 2 | no | — |
| 153 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 154 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 155 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 156 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 157 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 158 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 159 | #135 | — | 2 | 4 | no | — |
| 160 | #135 | — | 2 | 4 | no | — |
| 161 | #135 | — | 2 | 2 | no | — |
| 162 | #135 | — | 2 | 2 | no | — |
| 163 | #135 | — | 2 | 2 | no | — |
| 164 | #135 | — | 2 | 2 | no | — |
| 165 | #135 | — | 2 | 2 | no | — |
| 166 | #135 | — | 4 | 2 | no | — |
| 167 | #135 | — | 4 | 2 | no | — |
| 168 | #135 | — | 4 | 2 | no | — |
| 169 | #135 | C2×D4 | 1 | 4 | yes | — |
| 170 | C2×Q16 | — | 2 | 2 | no | — |
| 171 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×SD16 | — | 2 | 2 | no | — |
| 174 | C2×SD16 | — | 2 | 1 | no | — |
| 175 | C2×SD16 | — | 2 | 2 | no | — |
| 176 | C2×SD16 | — | 4 | 2 | no | — |
| 177 | C2×SD16 | — | 4 | 2 | no | — |
| 178 | C2×D8 | — | 2 | 2 | no | — |
| 179 | C2×D8 | — | 2 | 4 | no | — |
| 180 | C2×D8 | — | 2 | 2 | no | — |
| 181 | C2×D8 | — | 2 | 2 | no | — |
| 182 | C2×D8 | — | 2 | 2 | no | — |
| 183 | C2×D8 | — | 2 | 1 | no | — |
| 184 | C2×D8 | — | 2 | 1 | no | — |
| 185 | C2×D8 | — | 2 | 1 | no | — |
| 186 | C2×D8 | — | 2 | 2 | no | — |
| 187 | C2×D8 | — | 2 | 2 | no | — |
| 188 | C2×D8 | — | 4 | 2 | no | — |
| 189 | C2×D8 | — | 4 | 2 | no | — |
| 190 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 191 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 192 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | #131 | — | 2 | 2 | no | — |
| 194 | #131 | — | 2 | 2 | no | — |
| 195 | #131 | — | 4 | 4 | no | — |
| 196 | #131 | — | 8 | 2 | no | — |
| 197 | C2×M16 | — | 2 | 2 | no | — |
| 198 | C2×M16 | — | 4 | 4 | no | — |
| 199 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 200 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×M16 | #41 | 1 | 2 | yes | — |
| 202 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 203 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 204 | #127 | — | 4 | 2 | no | — |
| 205 | #127 | — | 4 | 1 | no | — |
| 206 | #124 | — | 4 | 2 | no | — |
| 207 | #124 | — | 4 | 1 | no | — |
| 208 | #121 | — | 4 | 2 | no | — |
| 209 | #121 | — | 8 | 2 | no | — |
| 210 | #120 | — | 4 | 4 | no | — |
| 211 | #120 | — | 4 | 2 | no | — |
| 212 | #117 | — | 2 | 1 | no | — |
| 213 | #117 | C2×D4 | 1 | 2 | yes | — |
| 214 | Q32 | — | 2 | 4 | no | — |
| 215 | SD32 | — | 2 | 8 | no | — |
| 216 | SD32 | — | 2 | 4 | no | — |
| 217 | SD32 | — | 2 | 4 | no | — |
| 218 | SD32 | — | 4 | 2 | no | — |
| 219 | D16 | — | 2 | 8 | no | — |
| 220 | D16 | — | 2 | 4 | no | — |
| 221 | D16 | — | 4 | 4 | no | — |
| 222 | D16 | — | 4 | 2 | no | — |
| 223 | M32 | — | 2 | 4 | no | — |
| 224 | M32 | — | 2 | 2 | no | — |
| 225 | M32 | — | 2 | 2 | no | — |
| 226 | M32 | C2×D4 | 1 | 4 | yes | — |
| 227 | C2×C16 | — | 2 | 4 | no | — |
| 228 | C2×C16 | — | 2 | 2 | no | — |
| 229 | C2×C16 | — | 2 | 1 | no | — |
| 230 | C2×C16 | — | 2 | 1 | no | — |
| 231 | C2×C16 | — | 2 | 2 | no | — |
| 232 | #108 | — | 2 | 2 | no | — |
| 233 | #108 | — | 2 | 2 | no | — |
| 234 | #107 | — | 2 | 1 | no | — |
| 235 | #106 | — | 2 | 1 | no | — |
| 236 | #104 | — | 4 | 4 | no | — |
| 237 | #104 | — | 4 | 4 | no | — |
| 238 | #102 | — | 4 | 2 | no | — |
| 239 | #102 | — | 8 | 2 | no | — |
| 240 | #101 | — | 4 | 1 | no | — |
| 241 | #101 | D8 | 1 | 2 | yes | — |
| 242 | #100 | — | 4 | 1 | no | — |
| 243 | #100 | — | 4 | 4 | no | — |
| 244 | #100 | D8 | 1 | 2 | yes | — |
| 245 | #99 | — | 2 | 2 | no | — |
| 246 | #99 | — | 4 | 4 | no | — |
| 247 | #97 | — | 2 | 2 | no | — |
| 248 | C4×C8 | — | 2 | 2 | no | — |
| 249 | C24 | — | 4 | 1 | no | — |
| 250 | C24 | — | 4 | 2 | no | — |
| 251 | C24 | — | 4 | 1 | no | — |
| 252 | #41 | — | 2 | 2 | no | — |
| 253 | #41 | — | 2 | 2 | no | — |
| 254 | #41 | — | 2 | 4 | no | — |
| 255 | #41 | — | 4 | 4 | no | — |
| 256 | #41 | — | 4 | 4 | no | — |
| 257 | #41 | — | 4 | 2 | no | — |
| 258 | #41 | — | 4 | 2 | no | — |
| 259 | #41 | — | 4 | 2 | no | — |
| 260 | #41 | — | 4 | 2 | no | — |
| 261 | #41 | — | 4 | 2 | no | — |
| 262 | #41 | — | 8 | 2 | no | — |
| 263 | #41 | — | 8 | 2 | no | — |
| 264 | #41 | — | 8 | 4 | no | — |
| 265 | #41 | — | 8 | 4 | no | — |
| 266 | #41 | — | 8 | 2 | no | — |
| 267 | #41 | — | 8 | 2 | no | — |
| 268 | #41 | — | 8 | 2 | no | — |
| 269 | C2×Q8 | — | 2 | 1 | no | — |
| 270 | C2×Q8 | — | 2 | 2 | no | — |
| 271 | C2×Q8 | — | 4 | 2 | no | — |
| 272 | C2×Q8 | — | 8 | 2 | no | — |
| 273 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 274 | C2×D4 | — | 2 | 1 | no | — |
| 275 | C2×D4 | — | 2 | 2 | no | — |
| 276 | C2×D4 | — | 2 | 2 | no | — |
| 277 | C2×D4 | — | 4 | 4 | no | — |
| 278 | C2×D4 | — | 4 | 2 | no | — |
| 279 | C2×D4 | — | 4 | 1 | no | — |
| 280 | C2×D4 | — | 4 | 2 | no | — |
| 281 | C2×D4 | — | 4 | 2 | no | — |
| 282 | C2×D4 | — | 4 | 1 | no | — |
| 283 | C2×D4 | — | 4 | 2 | no | — |
| 284 | C2×D4 | — | 4 | 2 | no | — |
| 285 | C2×D4 | — | 4 | 1 | no | — |
| 286 | C2×D4 | — | 4 | 1 | no | — |
| 287 | C2×D4 | — | 4 | 2 | no | — |
| 288 | C2×D4 | — | 4 | 2 | no | — |
| 289 | C2×D4 | — | 4 | 2 | no | — |
| 290 | C2×D4 | — | 8 | 2 | no | — |
| 291 | C2×D4 | — | 8 | 4 | no | — |
| 292 | C2×D4 | — | 8 | 4 | no | — |
| 293 | C2×D4 | — | 8 | 8 | no | — |
| 294 | C2×D4 | — | 8 | 2 | no | — |
| 295 | C2×D4 | — | 8 | 4 | no | — |
| 296 | C2×D4 | — | 8 | 2 | no | — |
| 297 | C2×D4 | — | 8 | 2 | no | — |
| 298 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 299 | C2×D4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 300 | C22×C4 | — | 4 | 1 | no | — |
| 301 | C22×C4 | — | 4 | 2 | no | — |
| 302 | C22×C4 | — | 4 | 2 | no | — |
| 303 | C22×C4 | — | 8 | 2 | no | — |
| 304 | C22×C4 | #121 | 1 | 2 | yes | — |
| 305 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 306 | Q16 | — | 2 | 2 | no | — |
| 307 | Q16 | — | 2 | 1 | no | — |
| 308 | Q16 | — | 2 | 2 | no | — |
| 309 | Q16 | — | 4 | 2 | no | — |
| 310 | Q16 | #120 | 1 | 2 | yes | — |
| 311 | SD16 | — | 2 | 4 | no | — |
| 312 | SD16 | — | 4 | 4 | no | — |
| 313 | SD16 | — | 4 | 4 | no | — |
| 314 | SD16 | — | 4 | 2 | no | — |
| 315 | SD16 | — | 4 | 2 | no | — |
| 316 | SD16 | — | 8 | 4 | no | — |
| 317 | D8 | — | 2 | 2 | no | — |
| 318 | D8 | — | 2 | 2 | no | — |
| 319 | D8 | — | 2 | 1 | no | — |
| 320 | D8 | — | 2 | 2 | no | — |
| 321 | D8 | — | 2 | 2 | no | — |
| 322 | D8 | — | 4 | 4 | no | — |
| 323 | D8 | — | 4 | 2 | no | — |
| 324 | D8 | — | 4 | 1 | no | — |
| 325 | D8 | — | 4 | 1 | no | — |
| 326 | D8 | — | 4 | 2 | no | — |
| 327 | D8 | — | 4 | 2 | no | — |
| 328 | D8 | — | 8 | 4 | no | — |
| 329 | D8 | #120 | 1 | 2 | yes | — |
| 330 | M16 | — | 2 | 2 | no | — |
| 331 | M16 | — | 2 | 2 | no | — |
| 332 | M16 | — | 2 | 4 | no | — |
| 333 | M16 | — | 4 | 2 | no | — |
| 334 | M16 | — | 4 | 2 | no | — |
| 335 | M16 | — | 8 | 4 | no | — |
| 336 | M16 | C2×D8 | 1 | 4 | yes | — |
| 337 | C2×C8 | — | 2 | 2 | no | — |
| 338 | C2×C8 | — | 2 | 2 | no | — |
| 339 | C2×C8 | — | 2 | 2 | no | — |
| 340 | C2×C8 | — | 4 | 2 | no | — |
| 341 | C2×C8 | — | 8 | 4 | no | — |
| 342 | C2×C8 | #121 | 1 | 2 | yes | — |
| 343 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 344 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 345 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 346 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 347 | C4⋊C4 | — | 2 | 2 | no | — |
| 348 | C4⋊C4 | — | 4 | 1 | no | — |
| 349 | C22⋊C4 | — | 2 | 2 | no | — |
| 350 | C22⋊C4 | — | 4 | 1 | no | — |
| 351 | C22⋊C4 | — | 8 | 4 | no | — |
| 352 | C22⋊C4 | — | 8 | 2 | no | — |
| 353 | C42 | — | 2 | 2 | no | — |
| 354 | C42 | — | 4 | 1 | no | — |
| 355 | C16 | — | 2 | 4 | no | — |
| 356 | C16 | — | 4 | 1 | no | — |
| 357 | C16 | — | 4 | 1 | no | — |
| 358 | C23 | — | 4 | 1 | no | — |
| 359 | C23 | — | 4 | 2 | no | — |
| 360 | C23 | — | 4 | 2 | no | — |
| 361 | C23 | — | 8 | 4 | no | — |
| 362 | C23 | — | 8 | 2 | no | — |
| 363 | C23 | — | 8 | 2 | no | — |
| 364 | C23 | — | 8 | 2 | no | — |
| 365 | C23 | — | 8 | 1 | no | — |
| 366 | C23 | — | 32 | 1 | no | — |
| 367 | C23 | — | 32 | 1 | no | — |
| 368 | C23 | — | 32 | 2 | no | — |
| 369 | C23 | #459 | 1 | 2 | yes | — |
| 370 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 371 | Q8 | — | 2 | 2 | no | — |
| 372 | Q8 | — | 2 | 2 | no | — |
| 373 | Q8 | — | 4 | 1 | no | — |
| 374 | Q8 | — | 4 | 2 | no | — |
| 375 | Q8 | — | 4 | 2 | no | — |
| 376 | Q8 | — | 8 | 2 | no | — |
| 377 | D4 | — | 2 | 4 | no | — |
| 378 | D4 | — | 2 | 2 | no | — |
| 379 | D4 | — | 2 | 2 | no | — |
| 380 | D4 | — | 4 | 4 | no | — |
| 381 | D4 | — | 4 | 2 | no | — |
| 382 | D4 | — | 4 | 2 | no | — |
| 383 | D4 | — | 4 | 2 | no | — |
| 384 | D4 | — | 4 | 1 | no | — |
| 385 | D4 | — | 4 | 2 | no | — |
| 386 | D4 | — | 8 | 4 | no | — |
| 387 | D4 | — | 8 | 2 | no | — |
| 388 | D4 | — | 8 | 4 | no | — |
| 389 | D4 | — | 8 | 4 | no | — |
| 390 | D4 | — | 8 | 2 | no | — |
| 391 | D4 | — | 8 | 2 | no | — |
| 392 | D4 | — | 8 | 1 | no | — |
| 393 | D4 | — | 8 | 2 | no | — |
| 394 | D4 | — | 8 | 2 | no | — |
| 395 | D4 | — | 8 | 1 | no | — |
| 396 | D4 | — | 32 | 4 | no | — |
| 397 | D4 | — | 32 | 2 | no | — |
| 398 | C2×C4 | — | 2 | 2 | no | — |
| 399 | C2×C4 | — | 2 | 2 | no | — |
| 400 | C2×C4 | — | 4 | 1 | no | — |
| 401 | C2×C4 | — | 4 | 4 | no | — |
| 402 | C2×C4 | — | 4 | 2 | no | — |
| 403 | C2×C4 | — | 4 | 2 | no | — |
| 404 | C2×C4 | — | 8 | 4 | no | — |
| 405 | C2×C4 | — | 8 | 4 | no | — |
| 406 | C2×C4 | — | 8 | 2 | no | — |
| 407 | C2×C4 | — | 8 | 2 | no | — |
| 408 | C2×C4 | — | 8 | 2 | no | — |
| 409 | C2×C4 | — | 8 | 1 | no | — |
| 410 | C2×C4 | #459 | 1 | 2 | yes | — |
| 411 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 412 | C2×C4 | D42 | 1 | 2 | yes | — |
| 413 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 414 | C2×C4 | #576 | 1 | 2 | yes | — |
| 415 | C8 | — | 2 | 2 | no | — |
| 416 | C8 | — | 2 | 4 | no | — |
| 417 | C8 | — | 8 | 2 | no | — |
| 418 | C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 419 | C8 | #534 | 1 | 1 | yes | characteristic |
| 420 | C8 | #546 | 1 | 2 | yes | — |
| 421 | C22 | — | 2 | 2 | no | — |
| 422 | C22 | — | 4 | 1 | no | — |
| 423 | C22 | — | 4 | 2 | no | — |
| 424 | C22 | — | 4 | 2 | no | — |
| 425 | C22 | — | 8 | 2 | no | — |
| 426 | C22 | — | 8 | 2 | no | — |
| 427 | C22 | — | 16 | 1 | no | — |
| 428 | C22 | — | 16 | 2 | no | — |
| 429 | C22 | — | 16 | 2 | no | — |
| 430 | C22 | — | 16 | 4 | no | — |
| 431 | C22 | — | 16 | 2 | no | — |
| 432 | C22 | — | 16 | 1 | no | — |
| 433 | C22 | — | 32 | 2 | no | — |
| 434 | C22 | — | 32 | 4 | no | — |
| 435 | C22 | — | 32 | 2 | no | — |
| 436 | C22 | C2×#459 | 1 | 1 | yes | characteristic |
| 437 | C22 | #3264 | 1 | 2 | yes | — |
| 438 | C4 | — | 2 | 2 | no | — |
| 439 | C4 | — | 4 | 2 | no | — |
| 440 | C4 | — | 8 | 2 | no | — |
| 441 | C4 | — | 8 | 2 | no | — |
| 442 | C4 | — | 16 | 1 | no | — |
| 443 | C4 | #2410 | 1 | 1 | yes | characteristic |
| 444 | C4 | #3041 | 1 | 1 | yes | characteristic |
| 445 | C4 | D4×D8 | 1 | 2 | yes | — |
| 446 | C2 | — | 2 | 2 | no | — |
| 447 | C2 | — | 2 | 1 | no | — |
| 448 | C2 | — | 4 | 2 | no | — |
| 449 | C2 | — | 8 | 2 | no | — |
| 450 | C2 | — | 16 | 2 | no | — |
| 451 | C2 | — | 16 | 2 | no | — |
| 452 | C2 | — | 32 | 1 | no | — |
| 453 | C2 | #24354 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #24354 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #1757 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62636 | C2 | semidirect |
| 2. #33595 | C2 | semidirect |
| 3. #33522 | C2 | semidirect |
| 4. #25799 | C2 | semidirect |
| 5. #22458 | C2 | semidirect |
| 6. #13442 | C2 | semidirect |
| 7. #13336 | C2 | semidirect |
| 8. #13079 | C2 | semidirect |
| 9. #13021 | C2 | semidirect |
| 10. #12916 | C2 | semidirect |
| 11. #12746 | C2 | semidirect |
| 20. C2×#509 | C22 | semidirect |
| 21. C22×D16 | C22 | semidirect |
| 23. #3155 | C22 | semidirect |
| 27. #2957 | C22 | semidirect |
| 33. #2153 | C22 | semidirect |
| 34. #2148 | C22 | semidirect |
| 35. C2×#361 | C22 | semidirect |
| 36. C2×#359 | C22 | semidirect |
| 37. #2140 | C22 | semidirect |
| 38. #2138 | C22 | semidirect |
| 41. #1978 | C22 | semidirect |
| 42. #1976 | C22 | semidirect |
| 47. #1389 | C22 | semidirect |
| 48. #1379 | C22 | semidirect |
| 62. C2×#135 | D4 | semidirect |
| 65. C22×D8 | D4 | semidirect |
| 74. #510 | D4 | semidirect |
| 81. #509 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62636 | 2 |
| #33595 | 2 |
| #33522 | 2 |
| #25799 | 2 |
| #22458 | 2 |
| #13442 | 2 |
| #13336 | 2 |
| #13079 | 2 |
| #13021 | 2 |
| #12916 | 2 |
| #12746 | 2 |