Finite Group Databasebeta

← #564×D71 #22602482

Subgroups — #564×D71 #22602482

Order 9088.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71⋊#564C2115yesmaximal, complemented
2#125×D71C2115yesmaximal
3#564×C71C211yesmaximal, characteristic, complemented
4#14556120C22115yes—
5#14556119C22130yes—
6#14556118C22160yes—
7C4⋊C4×D71C22130yes—
8C42×D71C2215yes—
9#125×C71C22115yes—
10C2×C4×D71C23115yes—
11C4⋊Dic71C23130yes—
12Dic71⋊C4C23160yes—
13C4×Dic71C23115yes—
14C4⋊C4×C71C23130yes—
15C42×C71C2315yes—
16C22×D71C2411yescharacteristic
17C2×C4×C71C24115yes—
18C2×Dic71C24115yes—
19C4×D71—230no—
20C22×C71C2511yescharacteristic
21C2×D712−1+416yes—
22C4×C71—215no—
23Dic71—215no—
24C2×C71C2×2−1+413yes—
25D71#56414yesdirect product factor
26C2×#564—711nomaximal, Sylow
27C71C2×#56411yescharacteristic, complemented, Sylow
28#564—7115no—
29#564D7111yescharacteristic, direct product factor
30C2×#125—7115no—
31#125—7160no—
32#125—7130no—
33#125—7115no—
34#125C2×D71115yes—
35C2×C4⋊C4—7130no—
36C2×C42—715no—
37C22×C4—7115no—
38C4⋊C4—7160no—
39C4⋊C4—7130no—
40C4⋊C4C22×D71130yes—
41C42—7115no—
42C42C22×D7115yes—
43C23—711no—
44C2×C4—7115no—
45C2×C4—14230no—
46C2×C4C23×D71115yes—
47C22—716no—
48C22C24×D7111yescharacteristic
49C4—215no—
50C4—14215no—
51C2—714no—
52C22−1+4×D7113yes—
subgroupG/H
center, FrattiniC22C24×D71
commutator, socleC22×C71C25
Fitting#564×C71C2
hypercenter#564D71
hypocenterC71C2×#564
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #564

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C71⋊#564C2semidirect
3. #564×C71C2semidirect
25. D71#564direct (N × H)
27. C71C2×#564semidirect
29. #564D71direct (N × H)