Finite Group Databasebeta

← C7×D11×D99 #44478959

Subgroups — C7×D11×D99 #44478959

Order 30492.

180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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×C9⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
2C7×C11×D99C211yesmaximal, characteristic, complemented
3C7×C9×C11×D11C211yesmaximal, characteristic, complemented
4C7×D11×D33—31nomaximal
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C7×C3⋊(C11⋊D11)—31no—
7C7×C11×D33—31no—
8C3×C7×C11×D11D311yescharacteristic
9D11×D99C711yesmaximal, characteristic, direct product factor, Hall
10C7×D112—91noHall
11C2×C7×D99—111nomaximal
12C7×D9×D11—111nomaximal
13C3×C7×C112C2×D311yescharacteristic
14C9⋊(C11⋊D11)C2×C711yescharacteristic, complemented
15C11×D99C2×C711yescharacteristic, complemented
16C9×C11×D11C2×C711yescharacteristic, complemented
17C7×C11⋊D11—91no—
18C7×C11×D11—91no—
19C7×C11×D11D911yescharacteristic, complemented
20D11×D33—31no—
21C2×C7×C9×C11—111no—
22C7×D99—111no—
23C7×D99—111no—
24C7×D99—225no—
25C7×D99D1111yescharacteristic, direct product factor
26C7×C11×D9—111no—
27C7×C9×D11D1111yescharacteristic, complemented
28C9×C112C22×C711yescharacteristic, complemented, Hall
29C2×C7×D33—331no—
30D3×C7×D11—331no—
31C7×C112C2×D911yescharacteristic, complemented, Hall
32C3⋊(C11⋊D11)—31no—
33C11×D33—31no—
34C3×C11×D11D3×C711yescharacteristic
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C2×D1111yescharacteristic, complemented
38D112—91noHall
39C2×C3×C7×C11—111no—
40C7×D33—31no—
41C7×D33—331no—
42C7×D33—331no—
43C7×D33—665no—
44D3×C7×C11—331no—
45C3×C7×D11D3311yescharacteristic
46C2×D99—111no—
47D9×D11—111no—
48C3×C112C2×D3×C711yescharacteristic
49C2×C7×D11—991no—
50C2×C7×D11—991no—
51C2×C7×D9—1211noHall
52C11⋊D11—91no—
53C11×D11—91no—
54C11×D11C7×D911yescharacteristic, complemented
55C3×C7×C11—25no—
56C3×C7×C11D3×D1111yescharacteristic
57C3×C7×C11C2×D3311yescharacteristic
58C2×C9×C11—111no—
59D99—111no—
60D99—111no—
61D99—225no—
62D99C7×D1111yescharacteristic, direct product factor
63C9×D11C7×D1111yescharacteristic, complemented
64C11×D9—111no—
65C2×C7×C11—111no—
66C2×C7×C11—991no—
67C7×D11—91no—
68C7×D11—991no—
69C7×D11—991no—
70C7×D11—1985no—
71C7×D11D9911yescharacteristic, direct product factor
72C2×D33—331no—
73D3×D11—331no—
74C2×C7×C9—111no—
75C7×D9—111no—
76C7×D9—1211no—
77C112C2×C7×D911yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11C2×C7×D1111yescharacteristic, complemented
80C9×C11C2×C7×D1111yescharacteristic, complemented
81C2×D3×C7—3631no—
82C7×C11—25no—
83C7×C11D9×D1111yescharacteristic, complemented
84C7×C11C2×D9911yescharacteristic, complemented
85C2×C3×C11—111no—
86D33—31no—
87D33—331no—
88D33—331no—
89D33—665no—
90C3×D11C7×D3311yescharacteristic
91D3×C11—331no—
92C7×C9D11211yescharacteristic, complemented, Hall
93C2×D11—991no—
94C2×D11—991no—
95C2×C3×C7—111no—
96D3×C7—331no—
97D3×C7—3631no—
98C2×D9—1211noHall
99C3×C11—25no—
100C3×C11D3×C7×D1111yescharacteristic
101C3×C11C2×C7×D3311yescharacteristic
102C22×C7—10891noHall
103C2×C11—111no—
104C2×C11—991no—
105D11—91no—
106D11—991no—
107D11—991no—
108D11—1985no—
109D11C7×D9911yescharacteristic, direct product factor
110C3×C7D11×D3311yescharacteristic
111C2×C9—111no—
112D9—111no—
113D9—1211no—
114C2×C7—111no—
115C2×C7—10891no—
116C2×C7—991no—
117C2×D3—3631no—
118C11—25no—
119C11C7×D9×D1111yescharacteristic, complemented
120C11C2×C7×D9911yescharacteristic, complemented
121C9C7×D11211yescharacteristic, complemented, Sylow
122C7D11×D9911yescharacteristic, direct product factor, Sylow
123C2×C3—111no—
124D3—331no—
125D3—3631no—
126C22—10891noSylow
127C3C7×D11×D3311yescharacteristic
128C2—111no—
129C2—10891no—
130C2—991no—
subgroupG/H
center, hypercenterC7D11×D99
commutator, cosocle, hypocenterC9×C112C22×C7
FrattiniC3C7×D11×D33
FittingC7×C9×C112C22
socleC3×C7×C112C2×D3
LCSG ▷ C9×C112
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×C9⋊(C11⋊D11)C2semidirect
2. C7×C11×D99C2semidirect
3. C7×C9×C11×D11C2semidirect
5. C7×C9×C112C22semidirect
9. D11×D99C7direct (N × H)
14. C9⋊(C11⋊D11)C2×C7semidirect
15. C11×D99C2×C7semidirect
16. C9×C11×D11C2×C7semidirect
19. C7×C11×D11D9semidirect
25. C7×D99D11direct (N × H)
27. C7×C9×D11D11semidirect
28. C9×C112C22×C7semidirect
31. C7×C112C2×D9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C2×D11semidirect
54. C11×D11C7×D9semidirect
62. D99C7×D11direct (N × H)
63. C9×D11C7×D11semidirect
71. C7×D11D99direct (N × H)
77. C112C2×C7×D9semidirect
79. C9×C11C2×C7×D11semidirect
80. C9×C11C2×C7×D11semidirect
83. C7×C11D9×D11semidirect
84. C7×C11C2×D99semidirect
92. C7×C9D112semidirect
109. D11C7×D99direct (N × H)
119. C11C7×D9×D11semidirect
120. C11C2×C7×D99semidirect
121. C9C7×D112semidirect
122. C7D11×D99direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C9⋊(C11⋊D11)2
C7×C11×D992
C7×C9×C11×D112
C7×D11×D333
D11×D997
C2×C7×D9911
C7×D9×D1111