Finite Group Databasebeta

← C11×D11×D63 #44478962

Subgroups — C11×D11×D63 #44478962

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
1C11×D693C211yesmaximal, characteristic, complemented
2C112×D63C211yesmaximal, characteristic, complemented
3C7×C9×C11×D11C211yesmaximal, characteristic, complemented
4C11×D11×D21—31nomaximal
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C11×D231—31no—
7C112×D21—31no—
8C3×C7×C11×D11D311yescharacteristic
9C11×D9×D11—71nomaximal, Hall
10C11×D7×D11—91noHall
11C2×C11×D63—111nomaximal
12D11×D63C1111yesmaximal, characteristic, direct product factor
13C3×C7×C112C2×D311yescharacteristic
14C11×D99—71no—
15C112×D9—71no—
16C9×C11×D11D711yescharacteristic, complemented
17C11×D77—91no—
18C112×D7—91no—
19C7×C11×D11D911yescharacteristic, complemented
20D3×C11×D11—211no—
21C2×C7×C9×C11—111no—
22D693C2×C1111yescharacteristic, complemented
23C11×D63—25no—
24C11×D63—111no—
25C11×D63D1111yescharacteristic, direct product factor
26C11×D63C2×C1111yescharacteristic, complemented
27C7×C9×D11C2×C1111yescharacteristic, complemented
28C9×C112C2×D711yescharacteristic, complemented, Hall
29C2×C11×D21—331no—
30D11×D21—31no—
31C7×C112C2×D911yescharacteristic, complemented, Hall
32C11×D33—211no—
33D3×C112—211no—
34C3×C11×D11D2111yescharacteristic
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C22×C1111yescharacteristic, complemented
38C2×C11×D11—631noHall
39C2×C3×C7×C11—111no—
40D231—31no—
41C11×D21—31no—
42C11×D21—31no—
43C11×D21—65no—
44C11×D21—331no—
45C3×C7×D11D3×C1111yescharacteristic
46C2×C11×D9—771no—
47D9×D11—71no—
48C3×C112C2×D2111yescharacteristic
49C2×C11×D7—991no—
50D7×D11—91no—
51C2×D63—111noHall
52C2×C112—631no—
53C11×D11—631no—
54C11×D11D6311yescharacteristic, direct product factor
55C3×C7×C11—25no—
56C3×C7×C11D3×D1111yescharacteristic
57C3×C7×C11C2×D3×C1111yescharacteristic
58C2×C9×C11—111no—
59D99—71no—
60C9×D11C11×D711yescharacteristic, complemented
61C11×D9—71no—
62C11×D9—71no—
63C11×D9—145no—
64C11×D9—771no—
65C2×C7×C11—111no—
66D77—91no—
67C7×D11C11×D911yescharacteristic, complemented
68C11×D7—91no—
69C11×D7—91no—
70C11×D7—185no—
71C11×D7—991no—
72C2×D3×C11—2311no—
73D3×D11—211no—
74C2×C7×C9—111no—
75D63—111no—
76D63C11×D1111yescharacteristic, direct product factor
77C112C2×D6311yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11D7×D1111yescharacteristic, complemented
80C9×C11C2×C11×D711yescharacteristic, complemented
81C2×D21—331no—
82C7×C11—25no—
83C7×C11D9×D1111yescharacteristic, complemented
84C7×C11C2×C11×D911yescharacteristic, complemented
85C2×C3×C11—111no—
86D33—211no—
87C3×D11C11×D2111yescharacteristic
88D3×C11—211no—
89D3×C11—211no—
90D3×C11—425no—
91D3×C11—2311no—
92C7×C9C2×C11×D1111yescharacteristic, complemented, Hall
93C22×C11—6931no—
94C2×D11—631no—
95C2×C3×C7—111no—
96D21—31no—
97D21—331no—
98C2×D9—771noHall
99C3×C11—25no—
100C3×C11D11×D2111yescharacteristic
101C3×C11C2×C11×D2111yescharacteristic
102C2×D7—991noHall
103C2×C11—111no—
104C2×C11—631no—
105C2×C11—631no—
106C2×C11—1265no—
107C2×C11—6931no—
108D11—631no—
109D11C11×D6311yescharacteristic, direct product factor
110C3×C7D3×C11×D1111yescharacteristic
111C2×C9—111no—
112D9—71no—
113D9—771no—
114C2×C7—111no—
115D7—91no—
116D7—991no—
117C2×D3—2311no—
118C11—25no—
119C11D11×D6311yescharacteristic, direct product factor
120C11C2×C11×D6311yescharacteristic, complemented
121C9C11×D7×D1111yescharacteristic, complemented, Sylow
122C7C11×D9×D1111yescharacteristic, complemented, Sylow
123C2×C3—111no—
124D3—211no—
125D3—2311no—
126C22—6931noSylow
127C3C11×D11×D2111yescharacteristic
128C2—111no—
129C2—631no—
130C2—6931no—
subgroupG/H
center, hypercenterC11D11×D63
commutator, cosocle, hypocenterC7×C9×C11C22×C11
FrattiniC3C11×D11×D21
FittingC7×C9×C112C22
socleC3×C7×C112C2×D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D693C2semidirect
2. C112×D63C2semidirect
3. C7×C9×C11×D11C2semidirect
5. C7×C9×C112C22semidirect
12. D11×D63C11direct (N × H)
16. C9×C11×D11D7semidirect
19. C7×C11×D11D9semidirect
22. D693C2×C11semidirect
25. C11×D63D11direct (N × H)
26. C11×D63C2×C11semidirect
27. C7×C9×D11C2×C11semidirect
28. C9×C112C2×D7semidirect
31. C7×C112C2×D9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C22×C11semidirect
54. C11×D11D63direct (N × H)
60. C9×D11C11×D7semidirect
67. C7×D11C11×D9semidirect
76. D63C11×D11direct (N × H)
77. C112C2×D63semidirect
79. C9×C11D7×D11semidirect
80. C9×C11C2×C11×D7semidirect
83. C7×C11D9×D11semidirect
84. C7×C11C2×C11×D9semidirect
92. C7×C9C2×C11×D11semidirect
109. D11C11×D63direct (N × H)
119. C11D11×D63direct (N × H)
120. C11C2×C11×D63semidirect
121. C9C11×D7×D11semidirect
122. C7C11×D9×D11semidirect

Maximal subgroups

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

subgroupindex
C11×D6932
C112×D632
C7×C9×C11×D112
C11×D11×D213
C11×D9×D117
C2×C11×D6311
D11×D6311