Finite Group Databasebeta

← C7×(C2×D9)⋊C4 #11758913

Subgroups — C7×(C2×D9)⋊C4 #11758913

Order 1008.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×D9C211yesmaximal, characteristic
2C2×C4×C7×C9C211yesmaximal, characteristic, complemented
3C2×C7×Dic9C211yesmaximal, characteristic, complemented
4C7×(C2×D3)⋊C4—31nomaximal
5C22×C7×C9C2211yescharacteristic
6C2×C7×D9—21no—
7C2×C7×D9—21no—
8C2×C7×D9C412yescomplemented
9C4×C7×C9—21no—
10C7×Dic9—21no—
11C22×D3×C7—31no—
12C2×C3×C4×C7D311yescharacteristic
13C2×C7×Dic3—31no—
14(C2×D9)⋊C4C711yesmaximal, characteristic, direct product factor, Hall
15C2×C7×C9C2×C411yescharacteristic
16C2×C7×C9D411yescharacteristic
17C2×C7×C9D411yescharacteristic
18C7×D9—22no—
19C7×C22⋊C4—91noHall
20C22×C3×C7C2×D311yescharacteristic
21C2×D3×C7—32no—
22C2×D3×C7—61no—
23C2×D3×C7—61no—
24C3×C4×C7—21no—
25C7×Dic3—61no—
26C22×D9C2×C711yescharacteristic
27C2×C4×C9C2×C711yescharacteristic, complemented
28C2×Dic9C2×C711yescharacteristic, complemented
29C7×C9C22⋊C411yescharacteristic, complemented, Hall
30C23×C7—91no—
31C2×C4×C7—91no—
32C2×C4×C7D911yescharacteristic, complemented
33(C2×D3)⋊C4—31no—
34C2×C3×C7C4×D311yescharacteristic
35C2×C3×C7D1211yescharacteristic
36C2×C3×C7#6711yescharacteristic
37D3×C7—62no—
38C22×C9C22×C711yescharacteristic
39C2×D9—21no—
40C2×D9—21no—
41C2×D9C4×C712yescomplemented
42C4×C9—21no—
43Dic9—21no—
44C22×C7—92no—
45C22×C7—181no—
46C22×C7—181no—
47C22×C7C2×D911yescharacteristic
48C4×C7—21no—
49C4×C7—181no—
50C22×D3—31no—
51C2×C3×C4D3×C711yescharacteristic
52C2×Dic3—31no—
53C3×C7(C2×D3)⋊C411yescharacteristic
54C2×C9C2×C4×C711yescharacteristic
55C2×C9C7×D411yescharacteristic
56C2×C9C7×D411yescharacteristic
57D9—22no—
58C22⋊C4—91noSylow
59C2×C7—182no—
60C2×C7C4×D911yescharacteristic
61C2×C7D3611yescharacteristic
62C2×C7#61111yescharacteristic
63C22×C3C2×D3×C711yescharacteristic
64C2×D3—32no—
65C2×D3—61no—
66C2×D3—61no—
67C3×C4—21no—
68Dic3—61no—
69C9C7×C22⋊C411yescharacteristic, complemented, Sylow
70C23—91no—
71C2×C4—91no—
72C2×C4C7×D911yescharacteristic, complemented
73C7(C2×D9)⋊C411yescharacteristic, direct product factor, Sylow
74C2×C3C4×D3×C711yescharacteristic
75C2×C3C7×D1211yescharacteristic
76C2×C3C7×#6711yescharacteristic
77D3—62no—
78C22—92no—
79C22—181no—
80C22—181no—
81C22C2×C7×D911yescharacteristic
82C4—21no—
83C4—181no—
84C3C7×(C2×D3)⋊C411yescharacteristic
85C2—182no—
86C2C4×C7×D911yescharacteristic
87C2C7×D3611yescharacteristic
88C2C7×#61111yescharacteristic
subgroupG/H
centerC22×C7C2×D9
commutatorC2×C9C2×C4×C7
FrattiniC22×C3C2×D3×C7
FittingC2×C4×C7×C9C2
socleC22×C3×C7C2×D3
prime radicalC22×C7×D9C2
cosocleC22×C9C22×C7
hypercenterC2×C4×C7D9
hypocenterC9C7×C22⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C7 ◁ C2×C4×C7

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C9C2semidirect
3. C2×C7×Dic9C2semidirect
8. C2×C7×D9C4semidirect
14. (C2×D9)⋊C4C7direct (N × H)
27. C2×C4×C9C2×C7semidirect
28. C2×Dic9C2×C7semidirect
29. C7×C9C22⋊C4semidirect
32. C2×C4×C7D9semidirect
41. C2×D9C4×C7semidirect
69. C9C7×C22⋊C4semidirect
72. C2×C4C7×D9semidirect
73. C7(C2×D9)⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×D92
C2×C4×C7×C92
C2×C7×Dic92
C7×(C2×D3)⋊C43
(C2×D9)⋊C47