Finite Group Databasebeta

← C11×D63⋊D11 #44478970

Subgroups — C11×D63⋊D11 #44478970

Order 30492.

180 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C112×D63C211yesmaximal, characteristic, complemented
2C7×C11×D99C211yesmaximal, characteristic, complemented
3C9×C11×D77C211yesmaximal, characteristic, complemented
4C11×D21⋊D11—31nomaximal
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C112×D21—31no—
7C7×C11×D33—31no—
8C3×C11×D77D311yescharacteristic
9C11×D9×D11—71nomaximal, Hall
10C11×D7×D11—91noHall
11D63⋊D11C1111yesmaximal, characteristic, direct product factor
12C11×D7×D9—111nomaximal
13C3×C7×C112C2×D311yescharacteristic
14C11×D99D711yescharacteristic, complemented
15C112×D9—71no—
16C9×C11×D11—71no—
17C11×D77D911yescharacteristic, complemented
18C112×D7—91no—
19C7×C11×D11—91no—
20D3×C11×D11—211no—
21C11×D63—25no—
22C11×D63D1111yescharacteristic, complemented
23C11×D63C2×C1111yescharacteristic, complemented
24C7×D99C2×C1111yescharacteristic, complemented
25C7×C11×D9—111no—
26C9×D77C2×C1111yescharacteristic, complemented
27C9×C11×D7—111no—
28C9×C112C2×D711yescharacteristic, complemented, Hall
29D21⋊D11—31no—
30D3×C11×D7—331no—
31C7×C112C2×D911yescharacteristic, complemented, Hall
32C11×D33—31no—
33D3×C112—211no—
34C3×C11×D11—71no—
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C22×C1111yescharacteristic, complemented
38C2×C11×D11—631noHall
39C11×D21—31no—
40C11×D21—31no—
41C11×D21—65no—
42C7×D33—31no—
43D3×C7×C11—331no—
44C3×D77D3×C1111yescharacteristic
45C3×C11×D7—111no—
46C2×C11×D9—771no—
47D9×D11—71no—
48C3×C112D3×D711yescharacteristic
49C2×C11×D7—991no—
50D7×D11—91no—
51D7×D9—111noHall
52C2×C112—631no—
53C11×D11—71no—
54C11×D11—91no—
55C3×C7×C11—25no—
56C3×C7×C11D3×D1111yescharacteristic
57C3×C7×C11C2×D3×C1111yescharacteristic
58C2×C9×C11—771no—
59D99C11×D711yescharacteristic, complemented
60C9×D11—71no—
61C11×D9—71no—
62C11×D9—71no—
63C11×D9—111no—
64C11×D9—145no—
65C2×C7×C11—991no—
66D77C11×D911yescharacteristic, complemented
67C7×D11—91no—
68C11×D7—91no—
69C11×D7—91no—
70C11×D7—111no—
71C11×D7—185no—
72C2×D3×C11—2311no—
73D3×D11—211no—
74D63C11×D1111yescharacteristic, complemented
75C9×D7—111no—
76C7×D9—111no—
77C112D7×D911yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11D7×D1111yescharacteristic, complemented
80C9×C11C2×C11×D711yescharacteristic, complemented
81D3×D7—331no—
82C7×C11—25no—
83C7×C11D9×D1111yescharacteristic, complemented
84C7×C11C2×C11×D911yescharacteristic, complemented
85C2×C3×C11—771no—
86D33—31no—
87C3×D11—71no—
88D3×C11—211no—
89D3×C11—211no—
90D3×C11—331no—
91D3×C11—425no—
92C7×C9C2×C11×D1111yescharacteristic, complemented, Hall
93C22×C11—6931no—
94C2×D11—631no—
95D21—31no—
96C3×D7—111no—
97D3×C7—331no—
98C2×D9—771noHall
99C3×C11—25no—
100C3×C11D3×C11×D711yescharacteristic
101C3×C11D21⋊D1111yescharacteristic
102C2×D7—991noHall
103C2×C11—631no—
104C2×C11—631no—
105C2×C11—771no—
106C2×C11—991no—
107C2×C11—1265no—
108D11—71no—
109D11—91no—
110C3×C7D3×C11×D1111yescharacteristic
111C2×C9—771no—
112D9—71no—
113D9—111no—
114C2×C7—991no—
115D7—91no—
116D7—111no—
117C2×D3—2311no—
118C11—25no—
119C11C11×D7×D911yescharacteristic, complemented
120C11D63⋊D1111yescharacteristic, direct product factor
121C9C11×D7×D1111yescharacteristic, complemented, Sylow
122C7C11×D9×D1111yescharacteristic, complemented, Sylow
123C2×C3—771no—
124D3—211no—
125D3—331no—
126C22—6931noSylow
127C3C11×D21⋊D1111yescharacteristic
128C2—631no—
129C2—771no—
130C2—991no—
subgroupG/H
center, hypercenterC11D63⋊D11
commutator, cosocle, hypocenterC7×C9×C11C22×C11
FrattiniC3C11×D21⋊D11
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. C112×D63C2semidirect
2. C7×C11×D99C2semidirect
3. C9×C11×D77C2semidirect
5. C7×C9×C112C22semidirect
11. D63⋊D11C11direct (N × H)
14. C11×D99D7semidirect
17. C11×D77D9semidirect
22. C11×D63D11semidirect
23. C11×D63C2×C11semidirect
24. C7×D99C2×C11semidirect
26. C9×D77C2×C11semidirect
28. C9×C112C2×D7semidirect
31. C7×C112C2×D9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C22×C11semidirect
59. D99C11×D7semidirect
66. D77C11×D9semidirect
74. D63C11×D11semidirect
77. C112D7×D9semidirect
79. C9×C11D7×D11semidirect
80. C9×C11C2×C11×D7semidirect
83. C7×C11D9×D11semidirect
84. C7×C11C2×C11×D9semidirect
92. C7×C9C2×C11×D11semidirect
119. C11C11×D7×D9semidirect
120. C11D63⋊D11direct (N × H)
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
C112×D632
C7×C11×D992
C9×C11×D772
C11×D21⋊D113
C11×D9×D117
D63⋊D1111
C11×D7×D911