Finite Group Databasebeta

← C11×D9×D77 #44478969

Subgroups — C11×D9×D77 #44478969

Order 30492.

180 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 42 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
2C7×C112×D9C211yesmaximal, characteristic, complemented
3C9×C11×D77C211yesmaximal, characteristic, complemented
4D3×C11×D77—31nomaximal
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C11×D231—31no—
7D3×C7×C112—31no—
8C3×C11×D77D311yescharacteristic
9C11×D9×D11—71nomaximal, Hall
10C2×C11×D77—91noHall
11D9×D77C1111yesmaximal, characteristic, direct product factor
12C11×D7×D9—111nomaximal
13C3×C7×C112C2×D311yescharacteristic
14C11×D99—71no—
15C112×D9D711yescharacteristic, complemented
16C9×C11×D11—71no—
17C2×C7×C112—91no—
18C11×D77—91no—
19C11×D77D911yescharacteristic, direct product factor
20D3×C11×D11—211no—
21D693C2×C1111yescharacteristic, complemented
22C11×D63—111no—
23C7×C11×D9—25no—
24C7×C11×D9D1111yescharacteristic, complemented
25C7×C11×D9C2×C1111yescharacteristic, complemented
26C9×D77C2×C1111yescharacteristic, complemented
27C9×C11×D7—111no—
28C9×C112C2×D711yescharacteristic, complemented, Hall
29D3×D77—31no—
30D3×C11×D7—331no—
31C7×C112C2×D911yescharacteristic, complemented, Hall
32C11×D33—211no—
33D3×C112—31no—
34C3×C11×D11—71no—
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C22×C1111yescharacteristic, complemented
38C2×C11×D11—631noHall
39D231—31no—
40C11×D21—331no—
41D3×C7×C11—31no—
42D3×C7×C11—31no—
43D3×C7×C11—65no—
44C3×D77D3×C1111yescharacteristic
45C3×C11×D7—111no—
46C2×C11×D9—771no—
47D9×D11—71no—
48C3×C112D3×D711yescharacteristic
49C2×D77—91no—
50C2×C11×D7—991no—
51D7×D9—111noHall
52C2×C112—91no—
53C11×D11—71no—
54C11×D11—631no—
55C3×C7×C11—25no—
56C3×C7×C11D3×D1111yescharacteristic
57C3×C7×C11C2×D3×C1111yescharacteristic
58C2×C9×C11—771no—
59D99—71no—
60C9×D11—71no—
61C11×D9—25no—
62C11×D9—771no—
63C11×D9C11×D711yescharacteristic, complemented
64C11×D9D7711yescharacteristic, direct product factor
65C2×C7×C11—91no—
66C2×C7×C11—91no—
67C2×C7×C11—185no—
68D77—91no—
69D77C11×D911yescharacteristic, direct product factor
70C11×D7—111no—
71C11×D7—991no—
72C2×D3×C11—2311no—
73D3×D11—211no—
74D63—111no—
75C9×D7—111no—
76C7×D9C11×D1111yescharacteristic, complemented
77C112D7×D911yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11C2×C11×D711yescharacteristic, complemented
80C9×C11C2×D7711yescharacteristic, complemented
81D3×D7—331no—
82C7×C11—25no—
83C7×C11D9×D1111yescharacteristic, complemented
84C7×C11C2×C11×D911yescharacteristic, complemented
85C2×C3×C11—771no—
86D33—211no—
87C3×D11—71no—
88D3×C11—31no—
89D3×C11—31no—
90D3×C11—65no—
91D3×C11—2311no—
92C7×C9C2×C11×D1111yescharacteristic, complemented, Hall
93C22×C11—6931no—
94C2×D11—631no—
95D21—331no—
96C3×D7—111no—
97D3×C7—31no—
98C2×D9—771noHall
99C3×C11—25no—
100C3×C11D3×C11×D711yescharacteristic
101C3×C11D3×D7711yescharacteristic
102C2×D7—991noHall
103C2×C11—91no—
104C2×C11—91no—
105C2×C11—185no—
106C2×C11—771no—
107C2×C11—6931no—
108D11—71no—
109D11—631no—
110C3×C7D3×C11×D1111yescharacteristic
111C2×C9—771no—
112D9—771no—
113D9C11×D7711yescharacteristic, direct product factor
114C2×C7—91no—
115D7—111no—
116D7—991no—
117C2×D3—2311no—
118C11—25no—
119C11C11×D7×D911yescharacteristic, complemented
120C11D9×D7711yescharacteristic, direct product factor
121C9C2×C11×D7711yescharacteristic, complemented, Sylow
122C7C11×D9×D1111yescharacteristic, complemented, Sylow
123C2×C3—771no—
124D3—31no—
125D3—2311no—
126C22—6931noSylow
127C3D3×C11×D7711yescharacteristic
128C2—91no—
129C2—771no—
130C2—6931no—
subgroupG/H
center, hypercenterC11D9×D77
commutator, cosocle, hypocenterC7×C9×C11C22×C11
FrattiniC3D3×C11×D77
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. C7×C112×D9C2semidirect
3. C9×C11×D77C2semidirect
5. C7×C9×C112C22semidirect
11. D9×D77C11direct (N × H)
15. C112×D9D7semidirect
19. C11×D77D9direct (N × H)
21. D693C2×C11semidirect
24. C7×C11×D9D11semidirect
25. C7×C11×D9C2×C11semidirect
26. C9×D77C2×C11semidirect
28. C9×C112C2×D7semidirect
31. C7×C112C2×D9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C22×C11semidirect
63. C11×D9C11×D7semidirect
64. C11×D9D77direct (N × H)
69. D77C11×D9direct (N × H)
76. C7×D9C11×D11semidirect
77. C112D7×D9semidirect
79. C9×C11C2×C11×D7semidirect
80. C9×C11C2×D77semidirect
83. C7×C11D9×D11semidirect
84. C7×C11C2×C11×D9semidirect
92. C7×C9C2×C11×D11semidirect
113. D9C11×D77direct (N × H)
119. C11C11×D7×D9semidirect
120. C11D9×D77direct (N × H)
121. C9C2×C11×D77semidirect
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
C7×C112×D92
C9×C11×D772
D3×C11×D773
C11×D9×D117
D9×D7711
C11×D7×D911