Finite Group Databasebeta

← D17×#564 #14542926

Subgroups — D17×#564 #14542926

Order 2176.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17⋊#564C2115yesmaximal, complemented
2#125×D17C2115yesmaximal
3C17×#564C211yesmaximal, characteristic, complemented
4C17×#125C22115yes—
5C4⋊C4×D17C22130yes—
6#10587576C22130yes—
7#10587575C22160yes—
8C42×D17C2215yes—
9#10587556C22115yes—
10C2×C4×D17C23115yes—
11C4⋊C4×C17C23130yes—
12C42×C17C2315yes—
13C4⋊Dic17C23130yes—
14#63225C23160yes—
15C4×Dic17C23115yes—
16C22×D17C2411yescharacteristic
17C2×C4×C17C24115yes—
18C2×Dic17C24115yes—
19C4×D17—230no—
20C2×#564—171nomaximal, Sylow
21C22×C17C2511yescharacteristic
22C2×D172−1+416yes—
23C4×C17—215no—
24Dic17—215no—
25#564—1715no—
26#564D1711yescharacteristic, direct product factor
27C2×#125—1715no—
28C2×C17C2×2−1+413yes—
29D17#56414yesdirect product factor
30#125—1760no—
31#125—1730no—
32#125—1715no—
33#125C2×D17115yes—
34C2×C4⋊C4—1730no—
35C2×C42—175no—
36C17C2×#56411yescharacteristic, complemented, Sylow
37C22×C4—1715no—
38C4⋊C4—1760no—
39C4⋊C4—1730no—
40C4⋊C4C22×D17130yes—
41C42—1715no—
42C42C22×D1715yes—
43C23—171no—
44C2×C4—1715no—
45C2×C4—3430no—
46C2×C4C23×D17115yes—
47C22—176no—
48C22C24×D1711yescharacteristic
49C4—215no—
50C4—3415no—
51C2—174no—
52C22−1+4×D1713yes—
subgroupG/H
center, FrattiniC22C24×D17
commutator, socle, cosocleC22×C17C25
FittingC17×#564C2
prime radicalC22×D17C24
hypercenter#564D17
hypocenterC17C2×#564
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C17⋊#564C2semidirect
3. C17×#564C2semidirect
26. #564D17direct (N × H)
29. D17#564direct (N × H)
36. C17C2×#564semidirect

Maximal subgroups

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

subgroupindex
C17⋊#5642
#125×D172
C17×#5642
C2×#56417