Finite Group Databasebeta

← #20300960

Subgroups — #20300960

Order 7328.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊D229C211yesmaximal, characteristic, complemented
2C2×C22⋊D229C211yesmaximal, characteristic, complemented
3C22×Dic229C211yesmaximal, characteristic, complemented
4#16814645C211yesmaximal, characteristic, complemented
5C22⋊Dic229C211yesmaximal, characteristic, complemented
6#16814643C211yesmaximal, characteristic, complemented
7C2×D4×C229C211yesmaximal, characteristic, complemented
8C22×D229C2211yescharacteristic
9C22⋊D229—22no—
10C22⋊D229—22no—
11C2×Dic229—22no—
12C2×Dic229C2211yescharacteristic
13C2×Dic229C2211yescharacteristic
14C2×Dic229C2211yescharacteristic
15C23×C229C2211yescharacteristic
16C23×C229C2211yescharacteristic
17D4×C229—22no—
18C2×C4×C229C2211yescharacteristic
19C22×C229—21no—
20C22×C229—21no—
21C22×C229—21no—
22C22×C229—21no—
23C22×C229—21no—
24C22×C229D412yescomplemented
25C22×C229C2311yescharacteristic
26C2×D229—21no—
27C2×D229—21no—
28C2×D229—21no—
29C4×C229—21no—
30Dic229—21no—
31Dic229—21no—
32Dic229D412yescomplemented
33C2×C229—22no—
34C2×C229—41no—
35C2×C229C2×D411yescharacteristic
36C2×C229C2×D411yescharacteristic
37C2×C229#4111yescharacteristic
38D229—41no—
39C229#12111yescharacteristic, complemented, Sylow
40#121—2291nomaximal, Sylow
41C2×D4—2291no—
42C2×D4—2291no—
43C2×D4D22911yescharacteristic, complemented
44C22×C4—2291no—
45C4⋊C4—2291no—
46C22⋊C4—2291no—
47C22⋊C4—2291no—
48C23—2291no—
49C23C2×D22911yescharacteristic
50C23C2×D22911yescharacteristic
51D4—22no—
52D4—4582no—
53D4—4582no—
54C2×C4—4582no—
55C2×C4—2291no—
56C2×C4—2291no—
57C2×C4—2291no—
58C2×C4C2×D22911yescharacteristic
59C22—21no—
60C22—21no—
61C22—21no—
62C22—21no—
63C22—21no—
64C22—4581no—
65C22—4581no—
66C22—4581no—
67C22C22⋊D22912yescomplemented
68C22C22×D22911yescharacteristic
69C4—21no—
70C4—4581no—
71C4—4581no—
72C4—2292no—
73C2—22no—
74C2—41no—
75C2—9161no—
76C2D4×D22911yescharacteristic
77C2C2×C22⋊D22911yescharacteristic
78C2#1681466511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D229
commutator, socleC22×C229C23
FittingC2×D4×C229C2
hypercenterC2×D4D229
hypocenterC229#121
LCSG ▷ C22×C229 ▷ C229
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊D229C2semidirect
2. C2×C22⋊D229C2semidirect
3. C22×Dic229C2semidirect
4. #16814645C2semidirect
5. C22⋊Dic229C2semidirect
6. #16814643C2semidirect
7. C2×D4×C229C2semidirect
24. C22×C229D4semidirect
32. Dic229D4semidirect
39. C229#121semidirect
43. C2×D4D229semidirect
67. C22C22⋊D229semidirect