← #10576183
Subgroups — #10576183
Order 512.
10179 conjugacy classes of subgroups.
The subgroup lattice has 543 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #63092 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #61111 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #61110 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #61107 | C2 | 1 | 24 | yes | maximal, complemented |
| 5 | #61105 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#3291 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #60646 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #60470 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #60391 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #60388 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #60183 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | 2−1+6 | C22 | 1 | 2 | yes | complemented |
| 13 | H(7,𝔽2) | C22 | 1 | 2 | yes | complemented |
| 14 | #3586 | — | 2 | 16 | no | — |
| 15 | #3586 | C22 | 1 | 4 | yes | complemented |
| 16 | #3586 | C22 | 1 | 24 | yes | complemented |
| 17 | #3585 | — | 2 | 16 | no | — |
| 18 | #3585 | C22 | 1 | 4 | yes | complemented |
| 19 | #3585 | C22 | 1 | 24 | yes | complemented |
| 20 | #3584 | — | 2 | 16 | no | — |
| 21 | #3584 | C22 | 1 | 2 | yes | — |
| 22 | #3584 | C22 | 1 | 24 | yes | complemented |
| 23 | C2×#577 | — | 2 | 16 | no | — |
| 24 | C2×#577 | C22 | 1 | 4 | yes | complemented |
| 25 | C2×#577 | C22 | 1 | 24 | yes | complemented |
| 26 | #3573 | C22 | 1 | 4 | yes | complemented |
| 27 | #3499 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #3498 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #3293 | C22 | 1 | 12 | yes | complemented |
| 30 | #3292 | C22 | 1 | 12 | yes | complemented |
| 31 | #3291 | C22 | 1 | 12 | yes | complemented |
| 32 | #3291 | C22 | 1 | 48 | yes | complemented |
| 33 | #3291 | C22 | 1 | 24 | yes | complemented |
| 34 | #3291 | C22 | 1 | 4 | yes | complemented |
| 35 | #3290 | C22 | 1 | 48 | yes | complemented |
| 36 | #3289 | C22 | 1 | 48 | yes | complemented |
| 37 | #3288 | C22 | 1 | 48 | yes | complemented |
| 38 | #3154 | C22 | 1 | 12 | yes | complemented |
| 39 | #3152 | C22 | 1 | 3 | yes | complemented |
| 40 | #3151 | C22 | 1 | 3 | yes | complemented |
| 41 | #3147 | C22 | 1 | 3 | yes | complemented |
| 42 | C2×#492 | C22 | 1 | 3 | yes | complemented |
| 43 | #3069 | C22 | 1 | 24 | yes | complemented |
| 44 | #3068 | C22 | 1 | 24 | yes | complemented |
| 45 | #3067 | C22 | 1 | 24 | yes | complemented |
| 46 | C2×#471 | C22 | 1 | 24 | yes | complemented |
| 47 | #3022 | C22 | 1 | 12 | yes | complemented |
| 48 | #3021 | C22 | 1 | 12 | yes | complemented |
| 49 | #3020 | C22 | 1 | 12 | yes | complemented |
| 50 | #3019 | C22 | 1 | 12 | yes | complemented |
| 51 | #3018 | C22 | 1 | 12 | yes | complemented |
| 52 | #3018 | C22 | 1 | 12 | yes | complemented |
| 53 | C2×#456 | C22 | 1 | 12 | yes | complemented |
| 54 | C2×#453 | C22 | 1 | 12 | yes | complemented |
| 55 | #2957 | C22 | 1 | 12 | yes | complemented |
| 56 | #2956 | C22 | 1 | 12 | yes | complemented |
| 57 | #2955 | C22 | 1 | 12 | yes | complemented |
| 58 | C2×#443 | C22 | 1 | 12 | yes | complemented |
| 59 | #2916 | C22 | 1 | 2 | yes | complemented |
| 60 | #2901 | C22 | 1 | 4 | yes | complemented |
| 61 | #2889 | C22 | 1 | 2 | yes | complemented |
| 62 | #2888 | C22 | 1 | 2 | yes | complemented |
| 63 | C4×#131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #585 | — | 2 | 16 | no | — |
| 65 | #585 | — | 2 | 16 | no | — |
| 66 | #585 | — | 4 | 6 | no | — |
| 67 | #585 | — | 4 | 2 | no | — |
| 68 | #585 | C23 | 1 | 12 | yes | — |
| 69 | #585 | C23 | 1 | 4 | yes | — |
| 70 | #585 | C23 | 1 | 12 | yes | complemented |
| 71 | C2×2−1+4 | — | 2 | 16 | no | — |
| 72 | C2×2−1+4 | — | 4 | 2 | no | — |
| 73 | C2×2−1+4 | C23 | 1 | 12 | yes | — |
| 74 | C2×2−1+4 | C23 | 1 | 2 | yes | — |
| 75 | C2×H(5,𝔽2) | — | 2 | 16 | no | — |
| 76 | C2×H(5,𝔽2) | — | 4 | 6 | no | — |
| 77 | C2×H(5,𝔽2) | C23 | 1 | 2 | yes | — |
| 78 | C2×H(5,𝔽2) | C23 | 1 | 12 | yes | complemented |
| 79 | #578 | — | 2 | 16 | no | — |
| 80 | #578 | — | 2 | 48 | no | — |
| 81 | #578 | — | 2 | 24 | no | — |
| 82 | #578 | D4 | 1 | 8 | yes | complemented |
| 83 | #578 | C23 | 1 | 48 | yes | complemented |
| 84 | #577 | — | 2 | 16 | no | — |
| 85 | #577 | — | 2 | 16 | no | — |
| 86 | #577 | — | 2 | 48 | no | — |
| 87 | #577 | — | 2 | 48 | no | — |
| 88 | #577 | — | 2 | 48 | no | — |
| 89 | #577 | — | 2 | 48 | no | — |
| 90 | #577 | — | 2 | 24 | no | — |
| 91 | #577 | — | 2 | 24 | no | — |
| 92 | #577 | — | 2 | 16 | no | — |
| 93 | #577 | — | 2 | 16 | no | — |
| 94 | #577 | D4 | 1 | 16 | yes | complemented |
| 95 | #577 | C23 | 1 | 16 | yes | complemented |
| 96 | #577 | C23 | 1 | 48 | yes | complemented |
| 97 | #577 | C23 | 1 | 96 | yes | complemented |
| 98 | #576 | — | 2 | 16 | no | — |
| 99 | #576 | — | 2 | 48 | no | — |
| 100 | #576 | — | 2 | 24 | no | — |
| 101 | #576 | D4 | 1 | 8 | yes | complemented |
| 102 | #576 | C23 | 1 | 48 | yes | complemented |
| 103 | #575 | — | 2 | 48 | no | — |
| 104 | #575 | — | 2 | 48 | no | — |
| 105 | #575 | — | 2 | 48 | no | — |
| 106 | #575 | C23 | 1 | 24 | yes | — |
| 107 | #575 | C23 | 1 | 12 | yes | — |
| 108 | #575 | C23 | 1 | 24 | yes | complemented |
| 109 | C2×#137 | — | 2 | 48 | no | — |
| 110 | C2×#137 | — | 2 | 24 | no | — |
| 111 | C2×#137 | C23 | 1 | 24 | yes | complemented |
| 112 | C2×#137 | C23 | 1 | 12 | yes | complemented |
| 113 | C2×AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 114 | C2×AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 115 | C2×AGL(1,ℤ/8) | C23 | 1 | 24 | yes | — |
| 116 | C2×AGL(1,ℤ/8) | C23 | 1 | 12 | yes | complemented |
| 117 | C2×#135 | — | 2 | 48 | no | — |
| 118 | C2×#135 | — | 2 | 24 | no | — |
| 119 | C2×#135 | C23 | 1 | 12 | yes | — |
| 120 | C2×#135 | C23 | 1 | 12 | yes | complemented |
| 121 | C22×SD16 | — | 2 | 24 | no | — |
| 122 | C22×SD16 | C23 | 1 | 12 | yes | complemented |
| 123 | #568 | — | 2 | 16 | no | — |
| 124 | #568 | C23 | 1 | 4 | yes | — |
| 125 | #568 | C23 | 1 | 24 | yes | complemented |
| 126 | C2×#131 | — | 2 | 16 | no | — |
| 127 | C2×#131 | C23 | 1 | 2 | yes | — |
| 128 | C2×#131 | C23 | 1 | 24 | yes | complemented |
| 129 | #550 | — | 4 | 1 | no | — |
| 130 | D4×Q8 | — | 4 | 1 | no | — |
| 131 | #547 | — | 4 | 3 | no | — |
| 132 | D42 | — | 4 | 3 | no | — |
| 133 | #536 | C23 | 1 | 6 | yes | complemented |
| 134 | #535 | C23 | 1 | 6 | yes | — |
| 135 | #532 | C23 | 1 | 3 | yes | — |
| 136 | #532 | C23 | 1 | 3 | yes | complemented |
| 137 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | complemented |
| 138 | C2×#127 | C23 | 1 | 3 | yes | — |
| 139 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 140 | #497 | C23 | 1 | 12 | yes | complemented |
| 141 | #496 | C23 | 1 | 12 | yes | complemented |
| 142 | #495 | C23 | 1 | 12 | yes | complemented |
| 143 | #494 | C23 | 1 | 3 | yes | complemented |
| 144 | #493 | C23 | 1 | 3 | yes | complemented |
| 145 | #492 | C23 | 1 | 3 | yes | complemented |
| 146 | #492 | C23 | 1 | 6 | yes | complemented |
| 147 | #492 | C23 | 1 | 12 | yes | complemented |
| 148 | #492 | C23 | 1 | 1 | yes | characteristic, complemented |
| 149 | #473 | C23 | 1 | 48 | yes | complemented |
| 150 | #472 | C23 | 1 | 48 | yes | complemented |
| 151 | #471 | C23 | 1 | 96 | yes | complemented |
| 152 | #471 | C23 | 1 | 16 | yes | complemented |
| 153 | #471 | C23 | 1 | 48 | yes | complemented |
| 154 | #456 | C23 | 1 | 24 | yes | complemented |
| 155 | #456 | C23 | 1 | 48 | yes | complemented |
| 156 | #456 | C23 | 1 | 8 | yes | complemented |
| 157 | #455 | C23 | 1 | 24 | yes | complemented |
| 158 | #455 | C23 | 1 | 24 | yes | complemented |
| 159 | #454 | C23 | 1 | 24 | yes | complemented |
| 160 | #454 | C23 | 1 | 24 | yes | complemented |
| 161 | #453 | C23 | 1 | 24 | yes | complemented |
| 162 | #453 | C23 | 1 | 48 | yes | complemented |
| 163 | #453 | C23 | 1 | 8 | yes | complemented |
| 164 | #444 | C23 | 1 | 48 | yes | complemented |
| 165 | #443 | C23 | 1 | 8 | yes | complemented |
| 166 | #443 | C23 | 1 | 24 | yes | complemented |
| 167 | #443 | C23 | 1 | 24 | yes | complemented |
| 168 | #443 | C23 | 1 | 24 | yes | complemented |
| 169 | #430 | C23 | 1 | 12 | yes | complemented |
| 170 | C2×#108 | C23 | 1 | 12 | yes | complemented |
| 171 | #421 | C23 | 1 | 24 | yes | complemented |
| 172 | C2×#104 | C23 | 1 | 24 | yes | complemented |
| 173 | #413 | C23 | 1 | 12 | yes | complemented |
| 174 | #413 | C23 | 1 | 12 | yes | complemented |
| 175 | C2×#101 | C23 | 1 | 12 | yes | complemented |
| 176 | C2×#100 | C23 | 1 | 12 | yes | complemented |
| 177 | #405 | C23 | 1 | 6 | yes | complemented |
| 178 | C4×M16 | C23 | 1 | 3 | yes | complemented |
| 179 | C2×C4×C8 | C23 | 1 | 3 | yes | complemented |
| 180 | 2−1+4 | — | 2 | 4 | no | — |
| 181 | 2−1+4 | — | 2 | 48 | no | — |
| 182 | 2−1+4 | — | 2 | 16 | no | — |
| 183 | 2−1+4 | — | 2 | 24 | no | — |
| 184 | 2−1+4 | — | 2 | 24 | no | — |
| 185 | 2−1+4 | — | 4 | 8 | no | — |
| 186 | 2−1+4 | — | 4 | 12 | no | — |
| 187 | 2−1+4 | — | 4 | 16 | no | — |
| 188 | 2−1+4 | — | 4 | 24 | no | — |
| 189 | 2−1+4 | C2×D4 | 1 | 16 | yes | — |
| 190 | 2−1+4 | C24 | 1 | 24 | yes | — |
| 191 | 2−1+4 | C24 | 1 | 8 | yes | — |
| 192 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 193 | H(5,𝔽2) | — | 2 | 16 | no | — |
| 194 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 195 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 196 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 197 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 198 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 199 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 200 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 201 | H(5,𝔽2) | — | 4 | 48 | no | — |
| 202 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 203 | H(5,𝔽2) | C2×D4 | 1 | 16 | yes | — |
| 204 | H(5,𝔽2) | C24 | 1 | 8 | yes | — |
| 205 | H(5,𝔽2) | C24 | 1 | 24 | yes | — |
| 206 | C2×#41 | — | 2 | 16 | no | — |
| 207 | C2×#41 | — | 2 | 2 | no | — |
| 208 | C2×#41 | — | 2 | 6 | no | — |
| 209 | C2×#41 | — | 2 | 48 | no | — |
| 210 | C2×#41 | — | 2 | 48 | no | — |
| 211 | C2×#41 | — | 2 | 24 | no | — |
| 212 | C2×#41 | — | 2 | 24 | no | — |
| 213 | C2×#41 | — | 4 | 12 | no | — |
| 214 | C2×#41 | — | 4 | 12 | no | — |
| 215 | C2×#41 | — | 4 | 12 | no | — |
| 216 | C2×#41 | — | 4 | 48 | no | — |
| 217 | C2×#41 | — | 4 | 16 | no | — |
| 218 | C2×#41 | — | 4 | 24 | no | — |
| 219 | C2×#41 | — | 4 | 8 | no | — |
| 220 | C2×#41 | C24 | 1 | 24 | yes | — |
| 221 | C2×#41 | C24 | 1 | 6 | yes | — |
| 222 | C2×#41 | C24 | 1 | 6 | yes | — |
| 223 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 224 | C22×Q8 | — | 2 | 2 | no | — |
| 225 | C22×Q8 | — | 2 | 24 | no | — |
| 226 | C22×Q8 | — | 4 | 8 | no | — |
| 227 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 228 | C22×D4 | — | 2 | 24 | no | — |
| 229 | C22×D4 | — | 2 | 6 | no | — |
| 230 | C22×D4 | — | 4 | 3 | no | — |
| 231 | C22×D4 | — | 4 | 12 | no | — |
| 232 | C22×D4 | — | 4 | 24 | no | — |
| 233 | C22×D4 | C24 | 1 | 6 | yes | — |
| 234 | #137 | — | 2 | 48 | no | — |
| 235 | #137 | — | 2 | 24 | no | — |
| 236 | #137 | — | 2 | 24 | no | — |
| 237 | #137 | — | 2 | 96 | no | — |
| 238 | #137 | — | 2 | 48 | no | — |
| 239 | #137 | — | 2 | 16 | no | — |
| 240 | #137 | — | 2 | 48 | no | — |
| 241 | #137 | — | 2 | 48 | no | — |
| 242 | #137 | — | 2 | 48 | no | — |
| 243 | #137 | C2×D4 | 1 | 48 | yes | complemented |
| 244 | #137 | C24 | 1 | 48 | yes | — |
| 245 | #137 | C24 | 1 | 16 | yes | — |
| 246 | AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 247 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 248 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 249 | AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 250 | AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 251 | AGL(1,ℤ/8) | — | 2 | 96 | no | — |
| 252 | AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 253 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 254 | AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 255 | AGL(1,ℤ/8) | C2×D4 | 1 | 48 | yes | complemented |
| 256 | AGL(1,ℤ/8) | C24 | 1 | 48 | yes | — |
| 257 | AGL(1,ℤ/8) | C24 | 1 | 16 | yes | — |
| 258 | #135 | — | 2 | 48 | no | — |
| 259 | #135 | — | 2 | 48 | no | — |
| 260 | #135 | — | 2 | 48 | no | — |
| 261 | #135 | — | 2 | 48 | no | — |
| 262 | #135 | — | 2 | 16 | no | — |
| 263 | #135 | — | 2 | 96 | no | — |
| 264 | #135 | — | 2 | 48 | no | — |
| 265 | #135 | — | 2 | 24 | no | — |
| 266 | #135 | — | 2 | 24 | no | — |
| 267 | #135 | C2×D4 | 1 | 24 | yes | complemented |
| 268 | #135 | C2×D4 | 1 | 24 | yes | complemented |
| 269 | #135 | C24 | 1 | 8 | yes | — |
| 270 | #135 | C24 | 1 | 24 | yes | — |
| 271 | C2×Q16 | — | 2 | 24 | no | — |
| 272 | C2×Q16 | — | 2 | 48 | no | — |
| 273 | C2×Q16 | C2×D4 | 1 | 12 | yes | complemented |
| 274 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 275 | C2×SD16 | — | 2 | 24 | no | — |
| 276 | C2×SD16 | — | 2 | 24 | no | — |
| 277 | C2×SD16 | — | 2 | 48 | no | — |
| 278 | C2×SD16 | — | 2 | 96 | no | — |
| 279 | C2×SD16 | — | 2 | 16 | no | — |
| 280 | C2×SD16 | — | 2 | 24 | no | — |
| 281 | C2×SD16 | — | 2 | 24 | no | — |
| 282 | C2×SD16 | C2×D4 | 1 | 24 | yes | complemented |
| 283 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 284 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 285 | C2×SD16 | C24 | 1 | 4 | yes | — |
| 286 | C2×D8 | — | 2 | 24 | no | — |
| 287 | C2×D8 | — | 2 | 48 | no | — |
| 288 | C2×D8 | C2×D4 | 1 | 12 | yes | complemented |
| 289 | C2×D8 | C24 | 1 | 12 | yes | — |
| 290 | #131 | — | 2 | 16 | no | — |
| 291 | #131 | — | 2 | 48 | no | — |
| 292 | #131 | — | 2 | 24 | no | — |
| 293 | #131 | — | 2 | 24 | no | — |
| 294 | #131 | C2×D4 | 1 | 8 | yes | — |
| 295 | #131 | C2×D4 | 1 | 8 | yes | — |
| 296 | #131 | C24 | 1 | 16 | yes | — |
| 297 | #131 | C24 | 1 | 48 | yes | — |
| 298 | C2×M16 | — | 2 | 48 | no | — |
| 299 | C2×M16 | — | 2 | 24 | no | — |
| 300 | C2×M16 | C24 | 1 | 24 | yes | — |
| 301 | C2×M16 | C24 | 1 | 6 | yes | — |
| 302 | C22×C8 | — | 2 | 24 | no | — |
| 303 | C22×C8 | C24 | 1 | 6 | yes | — |
| 304 | C4⋊Q8 | — | 4 | 3 | no | — |
| 305 | C4⋊Q8 | C24 | 1 | 3 | yes | — |
| 306 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 307 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 308 | #127 | — | 4 | 3 | no | — |
| 309 | #127 | C24 | 1 | 3 | yes | — |
| 310 | #127 | C24 | 1 | 6 | yes | — |
| 311 | #127 | C24 | 1 | 1 | yes | characteristic |
| 312 | #124 | C24 | 1 | 6 | yes | — |
| 313 | #124 | C24 | 1 | 6 | yes | — |
| 314 | #123 | — | 4 | 6 | no | — |
| 315 | C22⋊Q8 | — | 4 | 6 | no | — |
| 316 | #121 | — | 4 | 6 | no | — |
| 317 | #121 | — | 4 | 3 | no | — |
| 318 | #121 | — | 4 | 3 | no | — |
| 319 | #120 | — | 4 | 6 | no | — |
| 320 | C4×Q8 | — | 2 | 1 | no | — |
| 321 | C4×D4 | — | 2 | 3 | no | — |
| 322 | C4×D4 | — | 4 | 3 | no | — |
| 323 | C4×D4 | — | 4 | 3 | no | — |
| 324 | #117 | C24 | 1 | 3 | yes | — |
| 325 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 326 | C2×C42 | C24 | 1 | 3 | yes | — |
| 327 | #108 | C24 | 1 | 8 | yes | — |
| 328 | #108 | C24 | 1 | 24 | yes | — |
| 329 | #104 | C24 | 1 | 16 | yes | — |
| 330 | #104 | C24 | 1 | 48 | yes | — |
| 331 | #101 | C24 | 1 | 24 | yes | — |
| 332 | #101 | C24 | 1 | 8 | yes | — |
| 333 | #100 | C24 | 1 | 24 | yes | — |
| 334 | #100 | C24 | 1 | 8 | yes | — |
| 335 | #97 | C24 | 1 | 6 | yes | — |
| 336 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 337 | C4×C8 | C24 | 1 | 3 | yes | — |
| 338 | C4×C8 | C24 | 1 | 6 | yes | — |
| 339 | C24 | — | 2 | 6 | no | — |
| 340 | C24 | — | 4 | 12 | no | — |
| 341 | #41 | — | 2 | 16 | no | — |
| 342 | #41 | — | 2 | 48 | no | — |
| 343 | #41 | — | 2 | 24 | no | — |
| 344 | #41 | — | 2 | 24 | no | — |
| 345 | #41 | — | 2 | 16 | no | — |
| 346 | #41 | — | 2 | 48 | no | — |
| 347 | #41 | — | 2 | 48 | no | — |
| 348 | #41 | — | 2 | 16 | no | — |
| 349 | #41 | — | 2 | 24 | no | — |
| 350 | #41 | — | 2 | 24 | no | — |
| 351 | #41 | — | 4 | 24 | no | — |
| 352 | #41 | — | 4 | 24 | no | — |
| 353 | #41 | — | 4 | 8 | no | — |
| 354 | #41 | — | 4 | 24 | no | — |
| 355 | #41 | — | 4 | 48 | no | — |
| 356 | #41 | — | 4 | 48 | no | — |
| 357 | #41 | — | 4 | 48 | no | — |
| 358 | #41 | — | 4 | 48 | no | — |
| 359 | #41 | — | 4 | 48 | no | — |
| 360 | #41 | — | 4 | 24 | no | — |
| 361 | #41 | — | 4 | 24 | no | — |
| 362 | #41 | — | 4 | 8 | no | — |
| 363 | #41 | — | 4 | 24 | no | — |
| 364 | #41 | C22×D4 | 1 | 48 | yes | — |
| 365 | #41 | C22×D4 | 1 | 8 | yes | — |
| 366 | #41 | C25 | 1 | 16 | yes | — |
| 367 | C2×Q8 | — | 2 | 16 | no | — |
| 368 | C2×Q8 | — | 2 | 6 | no | — |
| 369 | C2×Q8 | — | 2 | 48 | no | — |
| 370 | C2×Q8 | — | 2 | 16 | no | — |
| 371 | C2×Q8 | — | 2 | 24 | no | — |
| 372 | C2×Q8 | — | 4 | 12 | no | — |
| 373 | C2×Q8 | — | 4 | 48 | no | — |
| 374 | C2×Q8 | — | 4 | 12 | no | — |
| 375 | C2×Q8 | — | 4 | 12 | no | — |
| 376 | C2×Q8 | — | 4 | 8 | no | — |
| 377 | C2×Q8 | C22×D4 | 1 | 24 | yes | — |
| 378 | C2×Q8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 379 | C2×Q8 | C25 | 1 | 2 | yes | — |
| 380 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 381 | C2×D4 | — | 2 | 24 | no | — |
| 382 | C2×D4 | — | 2 | 48 | no | — |
| 383 | C2×D4 | — | 2 | 16 | no | — |
| 384 | C2×D4 | — | 2 | 48 | no | — |
| 385 | C2×D4 | — | 2 | 6 | no | — |
| 386 | C2×D4 | — | 2 | 6 | no | — |
| 387 | C2×D4 | — | 2 | 24 | no | — |
| 388 | C2×D4 | — | 2 | 6 | no | — |
| 389 | C2×D4 | — | 4 | 48 | no | — |
| 390 | C2×D4 | — | 4 | 24 | no | — |
| 391 | C2×D4 | — | 4 | 1 | no | — |
| 392 | C2×D4 | — | 4 | 3 | no | — |
| 393 | C2×D4 | — | 4 | 6 | no | — |
| 394 | C2×D4 | — | 4 | 24 | no | — |
| 395 | C2×D4 | — | 4 | 8 | no | — |
| 396 | C2×D4 | — | 4 | 48 | no | — |
| 397 | C2×D4 | — | 4 | 12 | no | — |
| 398 | C2×D4 | — | 4 | 12 | no | — |
| 399 | C2×D4 | — | 4 | 48 | no | — |
| 400 | C2×D4 | — | 4 | 48 | no | — |
| 401 | C2×D4 | — | 4 | 12 | no | — |
| 402 | C2×D4 | — | 4 | 24 | no | — |
| 403 | C2×D4 | — | 16 | 6 | no | — |
| 404 | C2×D4 | C22×D4 | 1 | 24 | yes | — |
| 405 | C2×D4 | H(5,𝔽2) | 1 | 3 | yes | — |
| 406 | C2×D4 | C25 | 1 | 2 | yes | — |
| 407 | C2×D4 | C25 | 1 | 6 | yes | — |
| 408 | C22×C4 | — | 2 | 24 | no | — |
| 409 | C22×C4 | — | 2 | 3 | no | — |
| 410 | C22×C4 | — | 2 | 6 | no | — |
| 411 | C22×C4 | — | 2 | 6 | no | — |
| 412 | C22×C4 | — | 2 | 6 | no | — |
| 413 | C22×C4 | — | 4 | 12 | no | — |
| 414 | C22×C4 | — | 4 | 24 | no | — |
| 415 | C22×C4 | — | 4 | 24 | no | — |
| 416 | C22×C4 | — | 4 | 24 | no | — |
| 417 | C22×C4 | C25 | 1 | 3 | yes | — |
| 418 | Q16 | — | 2 | 48 | no | — |
| 419 | Q16 | — | 2 | 16 | no | — |
| 420 | Q16 | — | 2 | 24 | no | — |
| 421 | Q16 | C22×D4 | 1 | 24 | yes | — |
| 422 | Q16 | C22×D4 | 1 | 8 | yes | — |
| 423 | SD16 | — | 2 | 48 | no | — |
| 424 | SD16 | — | 2 | 16 | no | — |
| 425 | SD16 | — | 2 | 48 | no | — |
| 426 | SD16 | — | 2 | 16 | no | — |
| 427 | SD16 | — | 2 | 12 | no | — |
| 428 | SD16 | — | 2 | 4 | no | — |
| 429 | SD16 | — | 2 | 48 | no | — |
| 430 | SD16 | — | 2 | 12 | no | — |
| 431 | SD16 | — | 2 | 4 | no | — |
| 432 | SD16 | C22×D4 | 1 | 16 | yes | — |
| 433 | SD16 | C22×D4 | 1 | 48 | yes | — |
| 434 | D8 | — | 2 | 16 | no | — |
| 435 | D8 | — | 2 | 48 | no | — |
| 436 | D8 | — | 2 | 24 | no | — |
| 437 | D8 | C22×D4 | 1 | 24 | yes | — |
| 438 | D8 | C22×D4 | 1 | 8 | yes | — |
| 439 | M16 | — | 2 | 24 | no | — |
| 440 | M16 | — | 2 | 48 | no | — |
| 441 | M16 | — | 2 | 16 | no | — |
| 442 | M16 | C22×D4 | 1 | 24 | yes | — |
| 443 | M16 | C25 | 1 | 16 | yes | — |
| 444 | C2×C8 | — | 2 | 24 | no | — |
| 445 | C2×C8 | — | 2 | 16 | no | — |
| 446 | C2×C8 | — | 2 | 48 | no | — |
| 447 | C2×C8 | C22×D4 | 1 | 12 | yes | — |
| 448 | C2×C8 | C22×D4 | 1 | 12 | yes | — |
| 449 | C2×C8 | C25 | 1 | 2 | yes | — |
| 450 | C2×C8 | C25 | 1 | 6 | yes | — |
| 451 | C4⋊C4 | — | 2 | 3 | no | — |
| 452 | C4⋊C4 | — | 4 | 3 | no | — |
| 453 | C4⋊C4 | — | 4 | 6 | no | — |
| 454 | C4⋊C4 | — | 4 | 1 | no | — |
| 455 | C22⋊C4 | — | 2 | 3 | no | — |
| 456 | C22⋊C4 | — | 4 | 6 | no | — |
| 457 | C22⋊C4 | — | 4 | 6 | no | — |
| 458 | C42 | — | 2 | 3 | no | — |
| 459 | C42 | C25 | 1 | 1 | yes | characteristic |
| 460 | C42 | C25 | 1 | 3 | yes | — |
| 461 | C23 | — | 2 | 24 | no | — |
| 462 | C23 | — | 2 | 2 | no | — |
| 463 | C23 | — | 2 | 6 | no | — |
| 464 | C23 | — | 4 | 8 | no | — |
| 465 | C23 | — | 4 | 24 | no | — |
| 466 | C23 | — | 4 | 12 | no | — |
| 467 | C23 | — | 16 | 6 | no | — |
| 468 | C23 | — | 32 | 12 | no | — |
| 469 | C23 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 470 | Q8 | — | 2 | 24 | no | — |
| 471 | Q8 | — | 2 | 12 | no | — |
| 472 | Q8 | — | 2 | 4 | no | — |
| 473 | Q8 | — | 4 | 24 | no | — |
| 474 | Q8 | — | 4 | 8 | no | — |
| 475 | Q8 | — | 4 | 12 | no | — |
| 476 | Q8 | D42 | 1 | 4 | yes | — |
| 477 | Q8 | C23×D4 | 1 | 16 | yes | — |
| 478 | D4 | — | 2 | 16 | no | — |
| 479 | D4 | — | 2 | 48 | no | — |
| 480 | D4 | — | 2 | 4 | no | — |
| 481 | D4 | — | 2 | 12 | no | — |
| 482 | D4 | — | 2 | 24 | no | — |
| 483 | D4 | — | 4 | 48 | no | — |
| 484 | D4 | — | 4 | 16 | no | — |
| 485 | D4 | — | 4 | 8 | no | — |
| 486 | D4 | — | 4 | 24 | no | — |
| 487 | D4 | — | 4 | 12 | no | — |
| 488 | D4 | — | 4 | 12 | no | — |
| 489 | D4 | — | 4 | 12 | no | — |
| 490 | D4 | — | 8 | 2 | no | — |
| 491 | D4 | — | 8 | 6 | no | — |
| 492 | D4 | — | 16 | 6 | no | — |
| 493 | D4 | D42 | 1 | 12 | yes | — |
| 494 | D4 | C23×D4 | 1 | 16 | yes | — |
| 495 | C2×C4 | — | 2 | 1 | no | — |
| 496 | C2×C4 | — | 2 | 24 | no | — |
| 497 | C2×C4 | — | 2 | 16 | no | — |
| 498 | C2×C4 | — | 2 | 48 | no | — |
| 499 | C2×C4 | — | 2 | 3 | no | — |
| 500 | C2×C4 | — | 2 | 2 | no | — |
| 501 | C2×C4 | — | 2 | 6 | no | — |
| 502 | C2×C4 | — | 4 | 24 | no | — |
| 503 | C2×C4 | — | 4 | 8 | no | — |
| 504 | C2×C4 | — | 4 | 16 | no | — |
| 505 | C2×C4 | — | 4 | 48 | no | — |
| 506 | C2×C4 | — | 4 | 6 | no | — |
| 507 | C2×C4 | — | 4 | 12 | no | — |
| 508 | C2×C4 | — | 4 | 12 | no | — |
| 509 | C2×C4 | — | 4 | 12 | no | — |
| 510 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 511 | C2×C4 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 512 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 513 | C8 | — | 2 | 16 | no | — |
| 514 | C8 | C23×D4 | 1 | 2 | yes | — |
| 515 | C8 | C23×D4 | 1 | 12 | yes | — |
| 516 | C8 | C23×D4 | 1 | 2 | yes | — |
| 517 | C22 | — | 2 | 16 | no | — |
| 518 | C22 | — | 4 | 3 | no | — |
| 519 | C22 | — | 4 | 2 | no | — |
| 520 | C22 | — | 4 | 6 | no | — |
| 521 | C22 | — | 8 | 24 | no | — |
| 522 | C22 | — | 8 | 6 | no | — |
| 523 | C22 | — | 8 | 2 | no | — |
| 524 | C22 | — | 16 | 12 | no | — |
| 525 | C22 | — | 16 | 8 | no | — |
| 526 | C22 | — | 16 | 24 | no | — |
| 527 | C22 | C2×D42 | 1 | 6 | yes | — |
| 528 | C22 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 529 | C4 | — | 2 | 2 | no | — |
| 530 | C4 | — | 2 | 16 | no | — |
| 531 | C4 | — | 4 | 3 | no | — |
| 532 | C4 | — | 4 | 2 | no | — |
| 533 | C4 | — | 4 | 6 | no | — |
| 534 | C4 | C2×D42 | 1 | 6 | yes | — |
| 535 | C4 | C24×D4 | 1 | 2 | yes | — |
| 536 | C2 | — | 2 | 1 | no | — |
| 537 | C2 | — | 2 | 6 | no | — |
| 538 | C2 | — | 4 | 16 | no | — |
| 539 | C2 | — | 8 | 2 | no | — |
| 540 | C2 | — | 8 | 6 | no | — |
| 541 | C2 | C22×D42 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta