← #16755056
Subgroups — #16755056
Order 3328.
2114 conjugacy classes of subgroups.
The subgroup lattice has 524 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13128655 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #41×D52 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13127818 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13127479 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13126702 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | D4×#6095 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #13126153 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #13125763 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #13124845 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C2×#11718502 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C13×#2988 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#41×D13 | — | 2 | 1 | no | — |
| 13 | C4×C13×#41 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11719532 | — | 2 | 1 | no | — |
| 15 | C22×#6095 | C22 | 1 | 6 | yes | — |
| 16 | #11719282 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11719281 | — | 2 | 1 | no | — |
| 18 | Q8×D52 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11719275 | C22 | 1 | 2 | yes | complemented |
| 20 | Q8×Dic26 | — | 2 | 1 | no | — |
| 21 | #11719260 | C22 | 1 | 3 | yes | — |
| 22 | #11719259 | — | 2 | 3 | no | — |
| 23 | D4×D52 | C22 | 1 | 3 | yes | — |
| 24 | #11719248 | — | 2 | 3 | no | — |
| 25 | D4×Dic26 | C22 | 1 | 6 | yes | complemented |
| 26 | #11719229 | — | 2 | 3 | no | — |
| 27 | #11719224 | — | 2 | 3 | no | — |
| 28 | #11719182 | C22 | 1 | 3 | yes | — |
| 29 | C2×C4×D52 | C22 | 1 | 3 | yes | — |
| 30 | #11719175 | C22 | 1 | 3 | yes | complemented |
| 31 | C2×#88123 | C22 | 1 | 3 | yes | complemented |
| 32 | C8×Q8×C13 | C22 | 1 | 2 | yes | complemented |
| 33 | C8×D4×C13 | C22 | 1 | 6 | yes | complemented |
| 34 | C13×#431 | C22 | 1 | 3 | yes | complemented |
| 35 | C2×C13×C4⋊C8 | C22 | 1 | 3 | yes | complemented |
| 36 | #11718775 | C22 | 1 | 12 | yes | complemented |
| 37 | C2×#88056 | C22 | 1 | 6 | yes | complemented |
| 38 | #11718512 | C22 | 1 | 6 | yes | complemented |
| 39 | #11718509 | C22 | 1 | 6 | yes | complemented |
| 40 | #11718503 | C22 | 1 | 1 | yes | characteristic |
| 41 | #11718503 | C22 | 1 | 3 | yes | complemented |
| 42 | #11718502 | C22 | 1 | 6 | yes | — |
| 43 | #11718502 | C22 | 1 | 3 | yes | — |
| 44 | #11718502 | C22 | 1 | 6 | yes | complemented |
| 45 | #11718502 | C22 | 1 | 6 | yes | complemented |
| 46 | #11718502 | C22 | 1 | 3 | yes | complemented |
| 47 | #11718399 | C22 | 1 | 12 | yes | complemented |
| 48 | #11718392 | C22 | 1 | 6 | yes | — |
| 49 | #11718382 | C22 | 1 | 6 | yes | complemented |
| 50 | #11718354 | C22 | 1 | 6 | yes | complemented |
| 51 | C4×#6095 | C22 | 1 | 6 | yes | — |
| 52 | C4×#6095 | C22 | 1 | 6 | yes | complemented |
| 53 | #11718342 | C22 | 1 | 6 | yes | complemented |
| 54 | C2×C13×#41 | D4 | 1 | 1 | yes | characteristic |
| 55 | #41×D13 | — | 4 | 8 | no | — |
| 56 | C2×#6131 | — | 2 | 1 | no | — |
| 57 | C2×Q8×D13 | — | 2 | 1 | no | — |
| 58 | C2×#6129 | — | 2 | 3 | no | — |
| 59 | C2×D4×D13 | — | 2 | 3 | no | — |
| 60 | C2×#6127 | — | 2 | 3 | no | — |
| 61 | C22×D52 | C23 | 1 | 3 | yes | — |
| 62 | C22×C4×D13 | — | 2 | 3 | no | — |
| 63 | C22×Dic26 | C23 | 1 | 6 | yes | — |
| 64 | C22×C8×C13 | C23 | 1 | 6 | yes | — |
| 65 | C4×Q8×C13 | D4 | 1 | 1 | yes | characteristic |
| 66 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 67 | C4×D4×C13 | D4 | 1 | 3 | yes | — |
| 68 | C4×D4×C13 | C23 | 1 | 3 | yes | — |
| 69 | C13×#117 | D4 | 1 | 3 | yes | — |
| 70 | C2×C42×C13 | C23 | 1 | 3 | yes | — |
| 71 | Q8×Dic13 | — | 2 | 2 | no | — |
| 72 | D4×Dic13 | — | 2 | 6 | no | — |
| 73 | #88184 | — | 2 | 3 | no | — |
| 74 | #88184 | C23 | 1 | 6 | yes | — |
| 75 | C2×#6103 | — | 2 | 3 | no | — |
| 76 | #88180 | — | 2 | 3 | no | — |
| 77 | C2×C4⋊Dic13 | — | 2 | 3 | no | — |
| 78 | C2×C4⋊Dic13 | — | 2 | 3 | no | — |
| 79 | C2×C4⋊Dic13 | C23 | 1 | 3 | yes | — |
| 80 | #88178 | — | 2 | 3 | no | — |
| 81 | #88178 | C23 | 1 | 6 | yes | — |
| 82 | C2×#6095 | — | 4 | 12 | no | — |
| 83 | C2×#6095 | C23 | 1 | 6 | yes | — |
| 84 | C2×#6095 | C23 | 1 | 12 | yes | — |
| 85 | C2×#6095 | C23 | 1 | 6 | yes | — |
| 86 | #88151 | — | 2 | 3 | no | — |
| 87 | #88151 | — | 2 | 3 | no | — |
| 88 | #88149 | — | 2 | 3 | no | — |
| 89 | #88149 | — | 2 | 3 | no | — |
| 90 | #88144 | — | 2 | 6 | no | — |
| 91 | #88142 | — | 2 | 6 | no | — |
| 92 | #88140 | — | 2 | 6 | no | — |
| 93 | #88136 | — | 2 | 6 | no | — |
| 94 | #88132 | — | 2 | 12 | no | — |
| 95 | #88129 | — | 2 | 3 | no | — |
| 96 | #88128 | C23 | 1 | 3 | yes | — |
| 97 | C4×D52 | — | 2 | 3 | no | — |
| 98 | C4×D52 | — | 2 | 3 | no | — |
| 99 | C4×D52 | — | 2 | 3 | no | — |
| 100 | C4×D52 | C23 | 1 | 1 | yes | characteristic |
| 101 | C4×D52 | C23 | 1 | 3 | yes | — |
| 102 | C4×D52 | C23 | 1 | 3 | yes | — |
| 103 | C4×D52 | C23 | 1 | 3 | yes | — |
| 104 | #88124 | — | 2 | 3 | no | — |
| 105 | #88123 | — | 2 | 3 | no | — |
| 106 | #88123 | — | 2 | 3 | no | — |
| 107 | #88123 | C23 | 1 | 3 | yes | — |
| 108 | #88123 | C23 | 1 | 6 | yes | — |
| 109 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 110 | #88123 | C23 | 1 | 3 | yes | — |
| 111 | C4×Dic26 | — | 2 | 3 | no | — |
| 112 | C4×Dic26 | C23 | 1 | 6 | yes | — |
| 113 | C13×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 114 | C13×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 115 | C13×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 116 | C13×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 117 | C4×C8×C13 | C23 | 1 | 6 | yes | — |
| 118 | #88061 | C23 | 1 | 2 | yes | — |
| 119 | #88061 | C23 | 1 | 6 | yes | — |
| 120 | #88057 | C23 | 1 | 2 | yes | — |
| 121 | #88057 | C23 | 1 | 6 | yes | — |
| 122 | #88056 | C23 | 1 | 6 | yes | — |
| 123 | #88056 | C23 | 1 | 12 | yes | — |
| 124 | #88056 | C23 | 1 | 6 | yes | — |
| 125 | #61948 | — | 13 | 1 | no | maximal, Sylow |
| 126 | C23×D13 | — | 2 | 3 | no | — |
| 127 | C13×#41 | SD16 | 1 | 8 | yes | complemented |
| 128 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×D4×C13 | C2×D4 | 1 | 3 | yes | — |
| 130 | C22×C4×C13 | C2×D4 | 1 | 3 | yes | — |
| 131 | C22×C4×C13 | C2×D4 | 1 | 3 | yes | — |
| 132 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 133 | C2×C22⋊D13 | — | 2 | 6 | no | — |
| 134 | C22×Dic13 | — | 2 | 3 | no | — |
| 135 | C22×Dic13 | — | 2 | 6 | no | — |
| 136 | #6131 | — | 4 | 4 | no | — |
| 137 | Q8×D13 | — | 4 | 4 | no | — |
| 138 | #6129 | — | 4 | 12 | no | — |
| 139 | D4×D13 | — | 4 | 12 | no | — |
| 140 | #6127 | — | 4 | 12 | no | — |
| 141 | C2×D52 | — | 2 | 6 | no | — |
| 142 | C2×D52 | — | 2 | 3 | no | — |
| 143 | C2×D52 | — | 2 | 3 | no | — |
| 144 | C2×D52 | — | 2 | 3 | no | — |
| 145 | C2×D52 | — | 4 | 3 | no | — |
| 146 | C2×D52 | C24 | 1 | 3 | yes | — |
| 147 | C2×D52 | C24 | 1 | 1 | yes | characteristic |
| 148 | C2×C4×D13 | — | 2 | 1 | no | — |
| 149 | C2×C4×D13 | — | 2 | 3 | no | — |
| 150 | C2×C4×D13 | — | 2 | 3 | no | — |
| 151 | C2×C4×D13 | — | 2 | 3 | no | — |
| 152 | C2×C4×D13 | — | 4 | 12 | no | — |
| 153 | C2×Dic26 | — | 2 | 1 | no | — |
| 154 | C2×Dic26 | — | 2 | 3 | no | — |
| 155 | C2×Dic26 | — | 2 | 6 | no | — |
| 156 | C2×Dic26 | — | 4 | 6 | no | — |
| 157 | C2×Dic26 | — | 4 | 6 | no | — |
| 158 | C2×Dic26 | C24 | 1 | 6 | yes | — |
| 159 | C2×C8×C13 | — | 4 | 6 | no | — |
| 160 | C2×C8×C13 | C24 | 1 | 2 | yes | — |
| 161 | C2×C8×C13 | C24 | 1 | 6 | yes | — |
| 162 | C13×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 163 | C13×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 164 | C13×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 165 | C42×C13 | C2×D4 | 1 | 3 | yes | — |
| 166 | C42×C13 | C2×D4 | 1 | 3 | yes | — |
| 167 | C42×C13 | C24 | 1 | 3 | yes | — |
| 168 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 169 | C22⋊Dic13 | — | 2 | 6 | no | — |
| 170 | #6103 | — | 2 | 1 | no | — |
| 171 | #6103 | — | 2 | 3 | no | — |
| 172 | #6103 | — | 2 | 3 | no | — |
| 173 | #6103 | — | 2 | 3 | no | — |
| 174 | #6103 | — | 2 | 6 | no | — |
| 175 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 176 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 177 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 178 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 179 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 180 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 181 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 182 | C4⋊Dic13 | C24 | 1 | 2 | yes | — |
| 183 | C4⋊Dic13 | C24 | 1 | 3 | yes | — |
| 184 | C4⋊Dic13 | C24 | 1 | 1 | yes | characteristic |
| 185 | #6101 | — | 2 | 6 | no | — |
| 186 | #6101 | — | 2 | 6 | no | — |
| 187 | C4×Dic13 | — | 2 | 6 | no | — |
| 188 | #6095 | — | 2 | 12 | no | — |
| 189 | #6095 | — | 4 | 12 | no | — |
| 190 | #6095 | — | 4 | 6 | no | — |
| 191 | #3503 | — | 13 | 1 | no | — |
| 192 | D4×#41 | — | 13 | 1 | no | — |
| 193 | #3392 | — | 13 | 2 | no | — |
| 194 | #3359 | — | 13 | 2 | no | — |
| 195 | #3298 | — | 13 | 6 | no | — |
| 196 | D4×SD16 | — | 13 | 6 | no | — |
| 197 | #3246 | — | 13 | 3 | no | — |
| 198 | #3206 | — | 13 | 3 | no | — |
| 199 | #3101 | — | 13 | 3 | no | — |
| 200 | C2×#461 | — | 13 | 3 | no | — |
| 201 | #2988 | D13 | 1 | 1 | yes | characteristic, complemented |
| 202 | C23×C13 | C22×D4 | 1 | 3 | yes | — |
| 203 | C22×D13 | — | 2 | 1 | no | — |
| 204 | C22×D13 | — | 2 | 3 | no | — |
| 205 | C22×D13 | — | 4 | 6 | no | — |
| 206 | C22×D13 | — | 4 | 6 | no | — |
| 207 | C22×D13 | — | 8 | 3 | no | — |
| 208 | Q8×C13 | C2×SD16 | 1 | 4 | yes | complemented |
| 209 | D4×C13 | C2×SD16 | 1 | 12 | yes | complemented |
| 210 | C2×C4×C13 | — | 2 | 3 | no | — |
| 211 | C2×C4×C13 | — | 2 | 3 | no | — |
| 212 | C2×C4×C13 | — | 4 | 3 | no | — |
| 213 | C2×C4×C13 | C2×SD16 | 1 | 12 | yes | complemented |
| 214 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 215 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 216 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 218 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 220 | C22⋊D13 | — | 4 | 12 | no | — |
| 221 | C2×Dic13 | — | 2 | 2 | no | — |
| 222 | C2×Dic13 | — | 2 | 6 | no | — |
| 223 | C2×Dic13 | — | 2 | 3 | no | — |
| 224 | C2×Dic13 | — | 2 | 1 | no | — |
| 225 | C2×Dic13 | — | 4 | 6 | no | — |
| 226 | C2×Dic13 | — | 8 | 6 | no | — |
| 227 | D52 | — | 2 | 3 | no | — |
| 228 | D52 | — | 2 | 1 | no | — |
| 229 | D52 | — | 2 | 3 | no | — |
| 230 | D52 | — | 4 | 6 | no | — |
| 231 | D52 | — | 4 | 6 | no | — |
| 232 | D52 | — | 8 | 3 | no | — |
| 233 | D52 | H(5,𝔽2) | 1 | 2 | yes | — |
| 234 | C4×D13 | — | 4 | 2 | no | — |
| 235 | C4×D13 | — | 4 | 6 | no | — |
| 236 | C4×D13 | — | 4 | 6 | no | — |
| 237 | C4×D13 | — | 4 | 6 | no | — |
| 238 | Dic26 | — | 2 | 6 | no | — |
| 239 | Dic26 | — | 2 | 6 | no | — |
| 240 | Dic26 | — | 4 | 2 | no | — |
| 241 | Dic26 | — | 4 | 6 | no | — |
| 242 | Dic26 | — | 8 | 6 | no | — |
| 243 | C8×C13 | — | 2 | 6 | no | — |
| 244 | C8×C13 | — | 2 | 2 | no | — |
| 245 | C22×#41 | — | 26 | 1 | no | — |
| 246 | C22×SD16 | — | 13 | 6 | no | — |
| 247 | Q82 | — | 26 | 1 | no | — |
| 248 | #557 | — | 13 | 2 | no | — |
| 249 | #554 | — | 26 | 3 | no | — |
| 250 | #550 | — | 13 | 1 | no | — |
| 251 | D4×Q8 | — | 13 | 1 | no | — |
| 252 | D4×Q8 | — | 13 | 6 | no | — |
| 253 | #548 | — | 26 | 1 | no | — |
| 254 | #547 | — | 13 | 3 | no | — |
| 255 | #546 | — | 26 | 3 | no | — |
| 256 | D42 | — | 13 | 3 | no | — |
| 257 | #544 | — | 26 | 3 | no | — |
| 258 | #533 | — | 13 | 3 | no | — |
| 259 | #532 | — | 13 | 3 | no | — |
| 260 | C2×C4⋊Q8 | — | 13 | 3 | no | — |
| 261 | #525 | — | 26 | 3 | no | — |
| 262 | #520 | — | 26 | 1 | no | — |
| 263 | C4×#41 | C2×D13 | 1 | 1 | yes | characteristic |
| 264 | C2×C4×D4 | — | 13 | 3 | no | — |
| 265 | #492 | — | 13 | 6 | no | — |
| 266 | #487 | — | 13 | 6 | no | — |
| 267 | #483 | — | 13 | 6 | no | — |
| 268 | #476 | — | 13 | 1 | no | — |
| 269 | #476 | — | 13 | 3 | no | — |
| 270 | #475 | — | 13 | 6 | no | — |
| 271 | #465 | — | 13 | 12 | no | — |
| 272 | #461 | — | 13 | 3 | no | — |
| 273 | #461 | — | 13 | 3 | no | — |
| 274 | #461 | — | 13 | 6 | no | — |
| 275 | #461 | — | 13 | 6 | no | — |
| 276 | #461 | — | 13 | 6 | no | — |
| 277 | #460 | — | 13 | 6 | no | — |
| 278 | #450 | — | 13 | 6 | no | — |
| 279 | #448 | — | 13 | 12 | no | — |
| 280 | C8×Q8 | C2×D13 | 1 | 2 | yes | complemented |
| 281 | C4×SD16 | — | 13 | 6 | no | — |
| 282 | C4×SD16 | — | 13 | 6 | no | — |
| 283 | C8×D4 | C2×D13 | 1 | 6 | yes | complemented |
| 284 | #431 | C2×D13 | 1 | 3 | yes | complemented |
| 285 | C2×C4⋊C8 | C2×D13 | 1 | 3 | yes | complemented |
| 286 | C2×#103 | — | 13 | 6 | no | — |
| 287 | C22×C13 | — | 2 | 3 | no | — |
| 288 | C22×C13 | — | 2 | 3 | no | — |
| 289 | C22×C13 | C22×SD16 | 1 | 6 | yes | — |
| 290 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×D13 | — | 2 | 2 | no | — |
| 292 | C2×D13 | — | 4 | 1 | no | — |
| 293 | C2×D13 | — | 4 | 1 | no | — |
| 294 | C2×D13 | — | 4 | 3 | no | — |
| 295 | C2×D13 | — | 4 | 3 | no | — |
| 296 | C2×D13 | — | 4 | 3 | no | — |
| 297 | C2×D13 | — | 8 | 12 | no | — |
| 298 | C4×C13 | — | 2 | 1 | no | — |
| 299 | C4×C13 | — | 2 | 3 | no | — |
| 300 | C4×C13 | — | 2 | 3 | no | — |
| 301 | C4×C13 | C22×SD16 | 1 | 6 | yes | — |
| 302 | C4×C13 | C22×SD16 | 1 | 2 | yes | — |
| 303 | C4×C13 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 304 | C4×C13 | #585 | 1 | 1 | yes | characteristic |
| 305 | Dic13 | — | 4 | 2 | no | — |
| 306 | Dic13 | — | 4 | 6 | no | — |
| 307 | Dic13 | — | 4 | 3 | no | — |
| 308 | Dic13 | — | 4 | 1 | no | — |
| 309 | C2×#41 | — | 26 | 1 | no | — |
| 310 | C2×#41 | — | 26 | 3 | no | — |
| 311 | C2×#41 | — | 26 | 3 | no | — |
| 312 | C2×#41 | — | 52 | 8 | no | — |
| 313 | C2×#41 | D52 | 1 | 1 | yes | characteristic |
| 314 | C22×Q8 | — | 13 | 6 | no | — |
| 315 | C22×Q8 | — | 26 | 1 | no | — |
| 316 | C22×D4 | — | 13 | 3 | no | — |
| 317 | C22×D4 | — | 26 | 3 | no | — |
| 318 | C23×C4 | — | 26 | 3 | no | — |
| 319 | C2×SD16 | — | 13 | 6 | no | — |
| 320 | C2×SD16 | — | 13 | 12 | no | — |
| 321 | C2×SD16 | — | 13 | 6 | no | — |
| 322 | C2×SD16 | — | 52 | 12 | no | — |
| 323 | C22×C8 | C22×D13 | 1 | 6 | yes | — |
| 324 | C4⋊Q8 | — | 13 | 3 | no | — |
| 325 | C4⋊Q8 | — | 13 | 1 | no | — |
| 326 | C4⋊Q8 | — | 13 | 3 | no | — |
| 327 | C4⋊Q8 | — | 13 | 6 | no | — |
| 328 | C4⋊Q8 | — | 26 | 6 | no | — |
| 329 | C4⋊Q8 | — | 26 | 3 | no | — |
| 330 | C4⋊Q8 | — | 26 | 3 | no | — |
| 331 | #127 | — | 13 | 3 | no | — |
| 332 | #125 | — | 26 | 6 | no | — |
| 333 | #125 | — | 26 | 3 | no | — |
| 334 | #124 | — | 26 | 3 | no | — |
| 335 | #123 | — | 26 | 6 | no | — |
| 336 | C22⋊Q8 | — | 13 | 6 | no | — |
| 337 | C22⋊Q8 | — | 26 | 3 | no | — |
| 338 | C22⋊Q8 | — | 26 | 3 | no | — |
| 339 | C22⋊Q8 | — | 26 | 3 | no | — |
| 340 | C22⋊Q8 | — | 26 | 12 | no | — |
| 341 | #121 | — | 13 | 6 | no | — |
| 342 | #121 | — | 26 | 3 | no | — |
| 343 | #121 | — | 26 | 3 | no | — |
| 344 | #121 | — | 26 | 3 | no | — |
| 345 | #120 | — | 26 | 6 | no | — |
| 346 | C4×Q8 | — | 13 | 6 | no | — |
| 347 | C4×Q8 | — | 26 | 2 | no | — |
| 348 | C4×Q8 | — | 26 | 3 | no | — |
| 349 | C4×Q8 | D52 | 1 | 1 | yes | characteristic |
| 350 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 351 | C4×D4 | — | 13 | 1 | no | — |
| 352 | C4×D4 | — | 13 | 3 | no | — |
| 353 | C4×D4 | — | 13 | 3 | no | — |
| 354 | C4×D4 | — | 13 | 3 | no | — |
| 355 | C4×D4 | — | 26 | 6 | no | — |
| 356 | C4×D4 | — | 26 | 3 | no | — |
| 357 | C4×D4 | — | 26 | 3 | no | — |
| 358 | C4×D4 | — | 26 | 3 | no | — |
| 359 | C4×D4 | D52 | 1 | 3 | yes | — |
| 360 | C4×D4 | C22×D13 | 1 | 3 | yes | — |
| 361 | #117 | — | 26 | 3 | no | — |
| 362 | #117 | D52 | 1 | 3 | yes | — |
| 363 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 364 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 365 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 366 | C2×C22⋊C4 | — | 26 | 3 | no | — |
| 367 | C2×C42 | C22×D13 | 1 | 3 | yes | — |
| 368 | #106 | — | 13 | 2 | no | — |
| 369 | #106 | — | 13 | 6 | no | — |
| 370 | C4⋊C8 | C22×D13 | 1 | 3 | yes | — |
| 371 | C4⋊C8 | C22×D13 | 1 | 6 | yes | — |
| 372 | C4⋊C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 373 | #103 | — | 13 | 6 | no | — |
| 374 | #103 | — | 13 | 12 | no | — |
| 375 | #103 | — | 13 | 6 | no | — |
| 376 | #102 | — | 13 | 2 | no | — |
| 377 | #102 | — | 13 | 6 | no | — |
| 378 | C22⋊C8 | C22×D13 | 1 | 6 | yes | — |
| 379 | C4×C8 | C22×D13 | 1 | 6 | yes | — |
| 380 | C2×C13 | — | 2 | 6 | no | — |
| 381 | C2×C13 | #3488 | 1 | 1 | yes | characteristic |
| 382 | C2×C13 | C23×SD16 | 1 | 1 | yes | characteristic |
| 383 | C2×C13 | #3586 | 1 | 1 | yes | characteristic |
| 384 | D13 | — | 4 | 2 | no | — |
| 385 | D13 | — | 8 | 3 | no | — |
| 386 | C24 | — | 26 | 3 | no | — |
| 387 | #41 | — | 52 | 4 | no | — |
| 388 | #41 | — | 52 | 12 | no | — |
| 389 | #41 | — | 52 | 12 | no | — |
| 390 | #41 | #6095 | 1 | 8 | yes | complemented |
| 391 | C2×Q8 | — | 13 | 6 | no | — |
| 392 | C2×Q8 | — | 26 | 1 | no | — |
| 393 | C2×Q8 | — | 26 | 3 | no | — |
| 394 | C2×Q8 | — | 26 | 6 | no | — |
| 395 | C2×Q8 | — | 52 | 6 | no | — |
| 396 | C2×Q8 | — | 52 | 6 | no | — |
| 397 | C2×Q8 | — | 52 | 4 | no | — |
| 398 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic |
| 399 | C2×D4 | — | 13 | 1 | no | — |
| 400 | C2×D4 | — | 13 | 3 | no | — |
| 401 | C2×D4 | — | 26 | 6 | no | — |
| 402 | C2×D4 | — | 26 | 6 | no | — |
| 403 | C2×D4 | — | 26 | 3 | no | — |
| 404 | C2×D4 | — | 26 | 3 | no | — |
| 405 | C2×D4 | — | 26 | 3 | no | — |
| 406 | C2×D4 | — | 52 | 3 | no | — |
| 407 | C2×D4 | — | 52 | 12 | no | — |
| 408 | C2×D4 | C2×D52 | 1 | 3 | yes | — |
| 409 | C22×C4 | — | 26 | 3 | no | — |
| 410 | C22×C4 | — | 26 | 6 | no | — |
| 411 | C22×C4 | — | 26 | 1 | no | — |
| 412 | C22×C4 | — | 26 | 3 | no | — |
| 413 | C22×C4 | — | 26 | 3 | no | — |
| 414 | C22×C4 | — | 26 | 3 | no | — |
| 415 | C22×C4 | — | 52 | 12 | no | — |
| 416 | C22×C4 | C2×D52 | 1 | 3 | yes | — |
| 417 | C22×C4 | C2×D52 | 1 | 3 | yes | — |
| 418 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 419 | SD16 | — | 26 | 12 | no | — |
| 420 | SD16 | — | 52 | 12 | no | — |
| 421 | SD16 | — | 52 | 6 | no | — |
| 422 | C2×C8 | — | 4 | 6 | no | — |
| 423 | C2×C8 | C23×D13 | 1 | 2 | yes | — |
| 424 | C2×C8 | C23×D13 | 1 | 6 | yes | — |
| 425 | C4⋊C4 | — | 13 | 2 | no | — |
| 426 | C4⋊C4 | — | 13 | 1 | no | — |
| 427 | C4⋊C4 | — | 13 | 3 | no | — |
| 428 | C4⋊C4 | — | 26 | 3 | no | — |
| 429 | C4⋊C4 | — | 26 | 3 | no | — |
| 430 | C4⋊C4 | — | 26 | 3 | no | — |
| 431 | C4⋊C4 | — | 26 | 6 | no | — |
| 432 | C4⋊C4 | — | 26 | 6 | no | — |
| 433 | C4⋊C4 | — | 26 | 1 | no | — |
| 434 | C4⋊C4 | — | 26 | 3 | no | — |
| 435 | C4⋊C4 | — | 26 | 6 | no | — |
| 436 | C4⋊C4 | — | 26 | 6 | no | — |
| 437 | C4⋊C4 | C2×D52 | 1 | 3 | yes | — |
| 438 | C4⋊C4 | C2×D52 | 1 | 3 | yes | — |
| 439 | C22⋊C4 | — | 26 | 6 | no | — |
| 440 | C22⋊C4 | — | 26 | 1 | no | — |
| 441 | C22⋊C4 | — | 26 | 3 | no | — |
| 442 | C22⋊C4 | — | 26 | 3 | no | — |
| 443 | C22⋊C4 | — | 26 | 3 | no | — |
| 444 | C22⋊C4 | — | 26 | 6 | no | — |
| 445 | C22⋊C4 | C2×D52 | 1 | 6 | yes | — |
| 446 | C42 | — | 26 | 6 | no | — |
| 447 | C42 | C2×D52 | 1 | 3 | yes | — |
| 448 | C42 | C2×D52 | 1 | 3 | yes | — |
| 449 | C42 | C23×D13 | 1 | 3 | yes | — |
| 450 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 451 | C13 | #61948 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 452 | C23 | — | 26 | 1 | no | — |
| 453 | C23 | — | 26 | 3 | no | — |
| 454 | C23 | — | 52 | 6 | no | — |
| 455 | C23 | — | 52 | 6 | no | — |
| 456 | C23 | — | 104 | 3 | no | — |
| 457 | C23 | C22×D52 | 1 | 3 | yes | — |
| 458 | Q8 | — | 26 | 6 | no | — |
| 459 | Q8 | — | 26 | 6 | no | — |
| 460 | Q8 | — | 52 | 2 | no | — |
| 461 | Q8 | — | 52 | 6 | no | — |
| 462 | Q8 | — | 104 | 6 | no | — |
| 463 | Q8 | C2×#6095 | 1 | 4 | yes | complemented |
| 464 | D4 | — | 13 | 2 | no | — |
| 465 | D4 | — | 26 | 3 | no | — |
| 466 | D4 | — | 26 | 1 | no | — |
| 467 | D4 | — | 26 | 3 | no | — |
| 468 | D4 | — | 52 | 6 | no | — |
| 469 | D4 | — | 52 | 12 | no | — |
| 470 | D4 | — | 52 | 6 | no | — |
| 471 | D4 | — | 104 | 3 | no | — |
| 472 | D4 | C2×#6095 | 1 | 12 | yes | complemented |
| 473 | C2×C4 | — | 2 | 3 | no | — |
| 474 | C2×C4 | — | 2 | 3 | no | — |
| 475 | C2×C4 | — | 4 | 3 | no | — |
| 476 | C2×C4 | — | 26 | 2 | no | — |
| 477 | C2×C4 | — | 26 | 6 | no | — |
| 478 | C2×C4 | — | 26 | 1 | no | — |
| 479 | C2×C4 | — | 26 | 3 | no | — |
| 480 | C2×C4 | — | 52 | 6 | no | — |
| 481 | C2×C4 | — | 52 | 2 | no | — |
| 482 | C2×C4 | — | 52 | 6 | no | — |
| 483 | C2×C4 | — | 52 | 6 | no | — |
| 484 | C2×C4 | — | 52 | 6 | no | — |
| 485 | C2×C4 | — | 104 | 6 | no | — |
| 486 | C2×C4 | C2×#6095 | 1 | 12 | yes | complemented |
| 487 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 488 | C2×C4 | C22×D52 | 1 | 3 | yes | — |
| 489 | C2×C4 | C22×D52 | 1 | 3 | yes | — |
| 490 | C2×C4 | C22×D52 | 1 | 3 | yes | — |
| 491 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 492 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 493 | C8 | — | 2 | 6 | no | — |
| 494 | C8 | — | 2 | 2 | no | — |
| 495 | C22 | — | 2 | 3 | no | — |
| 496 | C22 | — | 2 | 3 | no | — |
| 497 | C22 | — | 26 | 2 | no | — |
| 498 | C22 | — | 52 | 1 | no | — |
| 499 | C22 | — | 52 | 1 | no | — |
| 500 | C22 | — | 52 | 3 | no | — |
| 501 | C22 | — | 52 | 3 | no | — |
| 502 | C22 | — | 52 | 3 | no | — |
| 503 | C22 | — | 104 | 12 | no | — |
| 504 | C22 | C22×#6095 | 1 | 6 | yes | — |
| 505 | C22 | C23×D52 | 1 | 1 | yes | characteristic |
| 506 | C4 | — | 2 | 3 | no | — |
| 507 | C4 | — | 2 | 1 | no | — |
| 508 | C4 | — | 2 | 3 | no | — |
| 509 | C4 | — | 52 | 6 | no | — |
| 510 | C4 | — | 52 | 1 | no | — |
| 511 | C4 | — | 52 | 3 | no | — |
| 512 | C4 | — | 52 | 2 | no | — |
| 513 | C4 | C22×#6095 | 1 | 2 | yes | — |
| 514 | C4 | C22×#6095 | 1 | 6 | yes | — |
| 515 | C4 | D13×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 516 | C4 | #11719652 | 1 | 1 | yes | characteristic |
| 517 | C2 | — | 2 | 6 | no | — |
| 518 | C2 | — | 52 | 2 | no | — |
| 519 | C2 | — | 104 | 3 | no | — |
| 520 | C2 | #13128506 | 1 | 1 | yes | characteristic |
| 521 | C2 | C23×#6095 | 1 | 1 | yes | characteristic |
| 522 | C2 | #13129624 | 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