Finite Group Databasebeta

← #564×D107 #28350603

Subgroups — #564×D107 #28350603

Order 13696.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107⋊#564C2115yesmaximal, complemented
2#125×D107C2115yesmaximal
3#564×C107C211yesmaximal, characteristic, complemented
4#16812101C22115yes—
5#16812100C22130yes—
6#16812099C22160yes—
7C4⋊C4×D107C22130yes—
8C42×D107C2215yes—
9#125×C107C22115yes—
10C2×C4×D107C23115yes—
11C4⋊Dic107C23130yes—
12Dic107⋊C4C23160yes—
13C4×Dic107C23115yes—
14C4⋊C4×C107C23130yes—
15C42×C107C2315yes—
16C22×D107C2411yescharacteristic
17C2×C4×C107C24115yes—
18C2×Dic107C24115yes—
19C4×D107—230no—
20C22×C107C2511yescharacteristic
21C2×D1072−1+416yes—
22C4×C107—215no—
23Dic107—215no—
24C2×C107C2×2−1+413yes—
25D107#56414yesdirect product factor
26C2×#564—1071nomaximal, Sylow
27C107C2×#56411yescharacteristic, complemented, Sylow
28#564—10715no—
29#564D10711yescharacteristic, direct product factor
30C2×#125—10715no—
31#125—10760no—
32#125—10730no—
33#125—10715no—
34#125C2×D107115yes—
35C2×C4⋊C4—10730no—
36C2×C42—1075no—
37C22×C4—10715no—
38C4⋊C4—10760no—
39C4⋊C4—10730no—
40C4⋊C4C22×D107130yes—
41C42—10715no—
42C42C22×D10715yes—
43C23—1071no—
44C2×C4—10715no—
45C2×C4—21430no—
46C2×C4C23×D107115yes—
47C22—1076no—
48C22C24×D10711yescharacteristic
49C4—215no—
50C4—21415no—
51C2—1074no—
52C22−1+4×D10713yes—
subgroupG/H
center, FrattiniC22C24×D107
commutator, socle, cosocleC22×C107C25
Fitting#564×C107C2
prime radicalC22×D107C24
hypercenter#564D107
hypocenterC107C2×#564
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C107⋊#564C2semidirect
3. #564×C107C2semidirect
25. D107#564direct (N × H)
27. C107C2×#564semidirect
29. #564D107direct (N × H)

Maximal subgroups

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

subgroupindex
C107⋊#5642
#125×D1072
#564×C1072
C2×#564107