Finite Group Databasebeta

← #564×D173 #36367705

Subgroups — #564×D173 #36367705

Order 22144.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C173⋊#564C2115yesmaximal, complemented
2#125×D173C2115yesmaximal
3#564×C173C211yesmaximal, characteristic, complemented
4#19149671C22115yes—
5#19149670C22130yes—
6#19149669C22160yes—
7C4⋊C4×D173C22130yes—
8C42×D173C2215yes—
9#125×C173C22115yes—
10C2×C4×D173C23115yes—
11C4⋊Dic173C23130yes—
12#14583805C23160yes—
13C4×Dic173C23115yes—
14C4⋊C4×C173C23130yes—
15C42×C173C2315yes—
16C22×D173C2411yescharacteristic
17C2×Dic173C24115yes—
18C4×D173—230no—
19C2×C4×C173C24115yes—
20C22×C173C2511yescharacteristic
21C2×D1732−1+416yes—
22C4×C173—215no—
23Dic173—215no—
24C2×C173C2×2−1+413yes—
25D173#56414yesdirect product factor
26C173C2×#56411yescharacteristic, complemented, Sylow
27C2×#564—1731nomaximal, Sylow
28#564—17315no—
29#564D17311yescharacteristic, direct product factor
30C2×#125—17315no—
31#125—17360no—
32#125—17330no—
33#125—17315no—
34#125C2×D173115yes—
35C2×C4⋊C4—17330no—
36C2×C42—1735no—
37C22×C4—17315no—
38C4⋊C4—17360no—
39C4⋊C4—17330no—
40C4⋊C4C22×D173130yes—
41C42—17315no—
42C42C22×D17315yes—
43C23—1731no—
44C2×C4—34630no—
45C2×C4—17315no—
46C2×C4C23×D173115yes—
47C22—1736no—
48C22C24×D17311yescharacteristic
49C4—215no—
50C4—34615no—
51C2—1734no—
52C22−1+4×D17313yes—
subgroupG/H
center, FrattiniC22C24×D173
commutator, socle, cosocleC22×C173C25
Fitting#564×C173C2
prime radicalC22×D173C24
hypercenter#564D173
hypocenterC173C2×#564
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C173⋊#564C2semidirect
3. #564×C173C2semidirect
25. D173#564direct (N × H)
26. C173C2×#564semidirect
29. #564D173direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C173⋊#5642
#125×D1732
#564×C1732
C2×#564173