Finite Group Databasebeta

← #95×D97 #20260578

Subgroups — #95×D97 #20260578

Order 6208.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D97C213yesmaximal
2#15690717C213yesmaximal, complemented
3#95×C97C211yesmaximal, characteristic, complemented
4C23×D97C2211yescharacteristic
5C22×Dic97C2213yes—
6C2×C4×D97—212no—
7C2×C4×D97C4112yescomplemented
8C22×C4×C97C2213yes—
9C23×C97C2311yescharacteristic
10C22×D97C2×C416yes—
11C22×D97D416yes—
12C22×D97Q812yes—
13C2×C4×C97—26no—
14C2×C4×C97C2×C416yescomplemented
15C2×Dic97—26no—
16C2×Dic97C2×C416yescomplemented
17C4×D97—224no—
18C22×C97C22×C413yes—
19C22×C97C2×D413yes—
20C22×C97C2×Q811yescharacteristic
21C2×D97C4214yes—
22C2×D97C22⋊C4112yes—
23C2×D97C4⋊C4112yes—
24C4×C97—26no—
25Dic97—26no—
26C2×C97C2×C4211yescharacteristic
27C2×C97C2×C22⋊C413yes—
28C2×C97C2×C4⋊C413yes—
29D97#9518yesdirect product factor
30C97C2×#9511yescharacteristic, complemented, Sylow
31C2×#95—971nomaximal, Sylow
32C23×C4—973no—
33#95—973no—
34#95D9711yescharacteristic, direct product factor
35C24—971no—
36C22×C4—973no—
37C22×C4—9712no—
38C22×C4—19412no—
39C22×C4C2×D9713yes—
40C23—976no—
41C23—976no—
42C23—972no—
43C23C22×D9711yescharacteristic
44C2×C4—26no—
45C2×C4—976no—
46C2×C4—19424no—
47C2×C4—1946no—
48C2×C4C4×D9716yescomplemented
49C22—974no—
50C22—9712no—
51C22—9712no—
52C22C2×C4×D9713yes—
53C22D4×D9713yes—
54C22Q8×D9711yescharacteristic
55C4—26no—
56C4—1946no—
57C2—978no—
58C2C42×D9711yescharacteristic
59C2C22⋊C4×D9713yes—
60C2C4⋊C4×D9713yes—
subgroupG/H
center, FrattiniC23C22×D97
commutatorC2×C97C2×C42
Fitting#95×C97C2
socleC23×C97C23
hypercenter#95D97
hypocenterC97C2×#95
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #15690717C2semidirect
3. #95×C97C2semidirect
7. C2×C4×D97C4semidirect
14. C2×C4×C97C2×C4semidirect
16. C2×Dic97C2×C4semidirect
29. D97#95direct (N × H)
30. C97C2×#95semidirect
34. #95D97direct (N × H)
48. C2×C4C4×D97semidirect