Finite Group Databasebeta

← #20261815

Subgroups — #20261815

Order 6208.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690898C218yesmaximal, complemented
2D97⋊M16C216yesmaximal, complemented
3C2×#13095512C211yesmaximal, characteristic
4#13095521C22112yescomplemented
5#13095520C2214yes—
6#13095519C22112yescomplemented
7#13095512C414yes—
8#13095512C2214yes—
9C2×D388C413yes—
10C2×C4×D97C2213yes—
11C2×Q8×C97C411yescharacteristic
12C22×D97C2×C413yes—
13Q8×C97C2×C414yes—
14C2×C4×C97C2×C413yes—
15C2×Dic97C2311yescharacteristic
16D388C2×C4112yes—
17C4×D97C2×C416yes—
18C4×D97C2316yes—
19#11715897C2318yes—
20C22×C97C22×C411yescharacteristic
21C2×D97—43no—
22C2×D97C22×C416yes—
23C4×C97C22×C416yes—
24Dic97C22×C411yescharacteristic
25Dic97C2411yescharacteristic
26C2×C97—21no—
27C2×C97C23×C411yescharacteristic
28D97—26no—
29C97#56811yescharacteristic, complemented, Sylow
30#568—971nomaximal, Sylow
31C2×#41—971no—
32#131—978no—
33C2×M16—976no—
34#41—974no—
35#41—974no—
36C2×Q8#8760411yescharacteristic
37C2×D4—973no—
38C22×C4—973no—
39M16—974no—
40M16—9712no—
41C2×C8—9712no—
42C23—973no—
43Q8C2×#8760414yes—
44D4—9712no—
45C2×C4—971no—
46C2×C4—976no—
47C2×C4—976no—
48C2×C4C2×#8760413yes—
49C8—978no—
50C22—976no—
51C22—3883no—
52C22C22×#8760411yescharacteristic
53C4—971no—
54C4—971no—
55C4C22×#8760416yes—
56C2—21no—
57C2—1946no—
58C2C23×#8760411yescharacteristic
subgroupG/H
center, FrattiniC2C23×#87604
commutator, socleC2×C97C23×C4
FittingC2×Q8×C97C4
hypercenterC2×Q8#87604
hypocenterC97#568
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #15690898C2semidirect
2. D97⋊M16C2semidirect
4. #13095521C22semidirect
6. #13095519C22semidirect
29. C97#568semidirect