Finite Group Databasebeta

← C7×C11×D9×D11 #44478957

Subgroups — C7×C11×D9×D11 #44478957

Order 30492.

180 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×D99C211yesmaximal, characteristic, complemented
2C7×C112×D9C211yesmaximal, characteristic, complemented
3C7×C9×C11×D11C211yesmaximal, characteristic, complemented
4D3×C7×C11×D11—31nomaximal
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C7×C11×D33—31no—
7D3×C7×C112—31no—
8C3×C7×C11×D11D311yescharacteristic
9C11×D9×D11C711yesmaximal, characteristic, direct product factor, Hall
10C2×C7×C11×D11—91noHall
11C2×C7×C11×D9—111nomaximal
12C7×D9×D11C1111yesmaximal, characteristic, direct product factor
13C3×C7×C112C2×D311yescharacteristic
14C11×D99C2×C711yescharacteristic, complemented
15C112×D9C2×C711yescharacteristic, complemented
16C9×C11×D11C2×C711yescharacteristic, complemented
17C2×C7×C112—91no—
18C7×C11×D11—91no—
19C7×C11×D11D911yescharacteristic, direct product factor
20D3×C11×D11—31no—
21C2×C7×C9×C11—111no—
22C7×D99C2×C1111yescharacteristic, complemented
23C7×C11×D9—25no—
24C7×C11×D9—111no—
25C7×C11×D9D1111yescharacteristic, direct product factor
26C7×C11×D9C2×C1111yescharacteristic, complemented
27C7×C9×D11C2×C1111yescharacteristic, complemented
28C9×C112C22×C711yescharacteristic, complemented, Hall
29C2×D3×C7×C11—331no—
30D3×C7×D11—31no—
31C7×C112C2×D911yescharacteristic, complemented, Hall
32C11×D33—31no—
33D3×C112—31no—
34C3×C11×D11D3×C711yescharacteristic
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C22×C1111yescharacteristic, complemented
38C2×C11×D11—91noHall
39C2×C3×C7×C11—111no—
40C7×D33—31no—
41D3×C7×C11—31no—
42D3×C7×C11—31no—
43D3×C7×C11—65no—
44D3×C7×C11—331no—
45C3×C7×D11D3×C1111yescharacteristic
46C2×C11×D9—111no—
47D9×D11C7×C1111yescharacteristic, direct product factor
48C3×C112C2×D3×C711yescharacteristic
49C22×C7×C11—991no—
50C2×C7×D11—91no—
51C2×C7×D9—111noHall
52C2×C112—91no—
53C11×D11—91no—
54C11×D11C7×D911yescharacteristic, direct product factor
55C3×C7×C11—25no—
56C3×C7×C11D3×D1111yescharacteristic
57C3×C7×C11C2×D3×C1111yescharacteristic
58C2×C9×C11—111no—
59D99C2×C7×C1111yescharacteristic, complemented
60C9×D11C2×C7×C1111yescharacteristic, complemented
61C11×D9—25no—
62C11×D9—111no—
63C11×D9C7×D1111yescharacteristic, direct product factor
64C11×D9C2×C7×C1111yescharacteristic, complemented
65C2×C7×C11—91no—
66C2×C7×C11—91no—
67C2×C7×C11—111no—
68C2×C7×C11—185no—
69C2×C7×C11—991no—
70C7×D11—91no—
71C7×D11C11×D911yescharacteristic, direct product factor
72C2×D3×C11—331no—
73D3×D11—31no—
74C2×C7×C9—111no—
75C7×D9—111no—
76C7×D9C11×D1111yescharacteristic, direct product factor
77C112C2×C7×D911yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11C2×C7×D1111yescharacteristic, complemented
80C9×C11C22×C7×C1111yescharacteristic, complemented
81C2×D3×C7—331no—
82C7×C11—25no—
83C7×C11D9×D1111yescharacteristic, direct product factor
84C7×C11C2×C11×D911yescharacteristic, complemented
85C2×C3×C11—111no—
86D33—31no—
87C3×D11D3×C7×C1111yescharacteristic
88D3×C11—31no—
89D3×C11—31no—
90D3×C11—65no—
91D3×C11—331no—
92C7×C9C2×C11×D1111yescharacteristic, complemented, Hall
93C22×C11—991no—
94C2×D11—91no—
95C2×C3×C7—111no—
96D3×C7—31no—
97D3×C7—331no—
98C2×D9—111noHall
99C3×C11—25no—
100C3×C11D3×C7×D1111yescharacteristic
101C3×C11C2×D3×C7×C1111yescharacteristic
102C22×C7—991noHall
103C2×C11—91no—
104C2×C11—91no—
105C2×C11—111no—
106C2×C11—185no—
107C2×C11—991no—
108D11—91no—
109D11C7×C11×D911yescharacteristic, direct product factor
110C3×C7D3×C11×D1111yescharacteristic
111C2×C9—111no—
112D9—111no—
113D9C7×C11×D1111yescharacteristic, direct product factor
114C2×C7—91no—
115C2×C7—111no—
116C2×C7—991no—
117C2×D3—331no—
118C11—25no—
119C11C7×D9×D1111yescharacteristic, direct product factor
120C11C2×C7×C11×D911yescharacteristic, complemented
121C9C2×C7×C11×D1111yescharacteristic, complemented, Sylow
122C7C11×D9×D1111yescharacteristic, direct product factor, Sylow
123C2×C3—111no—
124D3—31no—
125D3—331no—
126C22—991noSylow
127C3D3×C7×C11×D1111yescharacteristic
128C2—91no—
129C2—111no—
130C2—991no—
subgroupG/H
center, hypercenterC7×C11D9×D11
commutator, cosocle, hypocenterC9×C11C22×C7×C11
FrattiniC3D3×C7×C11×D11
FittingC7×C9×C112C22
socleC3×C7×C112C2×D3
LCSG ▷ C9×C11
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
1. C7×C11×D99C2semidirect
2. C7×C112×D9C2semidirect
3. C7×C9×C11×D11C2semidirect
5. C7×C9×C112C22semidirect
9. C11×D9×D11C7direct (N × H)
12. C7×D9×D11C11direct (N × H)
14. C11×D99C2×C7semidirect
15. C112×D9C2×C7semidirect
16. C9×C11×D11C2×C7semidirect
19. C7×C11×D11D9direct (N × H)
22. C7×D99C2×C11semidirect
25. C7×C11×D9D11direct (N × H)
26. C7×C11×D9C2×C11semidirect
27. C7×C9×D11C2×C11semidirect
28. C9×C112C22×C7semidirect
31. C7×C112C2×D9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C22×C11semidirect
47. D9×D11C7×C11direct (N × H)
54. C11×D11C7×D9direct (N × H)
59. D99C2×C7×C11semidirect
60. C9×D11C2×C7×C11semidirect
63. C11×D9C7×D11direct (N × H)
64. C11×D9C2×C7×C11semidirect
71. C7×D11C11×D9direct (N × H)
76. C7×D9C11×D11direct (N × H)
77. C112C2×C7×D9semidirect
79. C9×C11C2×C7×D11semidirect
80. C9×C11C22×C7×C11semidirect
83. C7×C11D9×D11direct (N × H)
84. C7×C11C2×C11×D9semidirect
92. C7×C9C2×C11×D11semidirect
109. D11C7×C11×D9direct (N × H)
113. D9C7×C11×D11direct (N × H)
119. C11C7×D9×D11direct (N × H)
120. C11C2×C7×C11×D9semidirect
121. C9C2×C7×C11×D11semidirect
122. C7C11×D9×D11direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C11×D992
C7×C112×D92
C7×C9×C11×D112
D3×C7×C11×D113
C11×D9×D117
C2×C7×C11×D911
C7×D9×D1111