Finite Group Databasebeta

← #20301009

Subgroups — #20301009

Order 7328.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16814667C211yesmaximal, characteristic, complemented
2#16814665C211yesmaximal, characteristic, complemented
3#16814656C211yesmaximal, characteristic, complemented
4#16814655C211yesmaximal, characteristic, complemented
5#16814651C211yesmaximal, characteristic, complemented
6C8×D229C211yesmaximal, characteristic, complemented
7SD16×C229C211yesmaximal, characteristic, complemented
8Dic458C2211yescharacteristic
9D916—21no—
10D916C2211yescharacteristic
11C22⋊D229—21no—
12C2×Dic229—21no—
13C4×D229—21no—
14C4×D229C2211yescharacteristic
15#14270080C2211yescharacteristic
16Q8×C229C2211yescharacteristic
17D4×C229C2211yescharacteristic
18C8×C229C2211yescharacteristic
19C22×C229—21no—
20C2×D229—21no—
21C2×D229D411yescharacteristic
22C4×C229—21no—
23C4×C229C2311yescharacteristic
24Dic229—21no—
25Dic229D411yescharacteristic
26C2×C229—41no—
27C2×C229C2×D411yescharacteristic
28D229—21no—
29D229—41no—
30C229#13511yescharacteristic, complemented, Sylow
31#135—2291nomaximal, Sylow
32#41—2291no—
33#41—2291no—
34Q16—2291no—
35SD16—2291no—
36SD16D22911yescharacteristic, complemented
37D8—2291no—
38C2×C8—2291no—
39Q8—2291no—
40Q8C2×D22911yescharacteristic
41D4—4581no—
42D4—4581no—
43D4—2291no—
44D4C2×D22911yescharacteristic
45C2×C4—4581no—
46C2×C4—4581no—
47C2×C4—2291no—
48C8—2291no—
49C8C2×D22911yescharacteristic
50C22—21no—
51C22—4581no—
52C22—2291no—
53C4—21no—
54C4—4581no—
55C4—2291no—
56C4C22×D22911yescharacteristic
57C2—41no—
58C2—9161no—
59C2—4581no—
60C2D4×D22911yescharacteristic
subgroupG/H
centerC2D4×D229
commutatorC4×C229C23
FrattiniC4C22×D229
FittingSD16×C229C2
socleC2×C229C2×D4
hypercenterSD16D229
hypocenterC229#135
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #16814667C2semidirect
2. #16814665C2semidirect
3. #16814656C2semidirect
4. #16814655C2semidirect
5. #16814651C2semidirect
6. C8×D229C2semidirect
7. SD16×C229C2semidirect
30. C229#135semidirect
36. SD16D229semidirect