Finite Group Databasebeta

← C3×((C2×D11)⋊C4)⋊C5 #72217172

Subgroups — C3×((C2×D11)⋊C4)⋊C5 #72217172

Order 2640.

136 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C22×C3×AGL(1,𝔽11)C211yesmaximal, characteristic
2C2×C3×C4×C11⋊C5C211yesmaximal, characteristic, complemented
3C2×C3×Dic11⋊C5C211yesmaximal, characteristic, complemented
4((C2×D11)⋊C4)⋊C5C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C11⋊C5C2211yescharacteristic
6C2×C3×AGL(1,𝔽11)—21no—
7C2×C3×AGL(1,𝔽11)—21no—
8C2×C3×AGL(1,𝔽11)C412yescomplemented
9C3×C4×C11⋊C5—21no—
10C3×Dic11⋊C5—21no—
11C3×(C2×D11)⋊C4C511yesmaximal, characteristic, complemented, Hall
12C22×AGL(1,𝔽11)C2×C311yescharacteristic
13C2×C4×C11⋊C5C2×C311yescharacteristic, complemented
14C2×Dic11⋊C5C2×C311yescharacteristic, complemented
15C2×C3×C11⋊C5C2×C411yescharacteristic
16C2×C3×C11⋊C5D411yescharacteristic
17C2×C3×C11⋊C5D411yescharacteristic
18C3×AGL(1,𝔽11)—22no—
19C22×C3×D11C2×C511yescharacteristic
20C2×C3×C4×C11C2×C511yescharacteristic, complemented
21C2×C3×Dic11C2×C511yescharacteristic, complemented
22C3×C5×C22⋊C4—111nomaximal, Hall
23C22×C11⋊C5C22×C311yescharacteristic
24C2×AGL(1,𝔽11)—21no—
25C2×AGL(1,𝔽11)—21no—
26C2×AGL(1,𝔽11)C3×C412yescomplemented
27C4×C11⋊C5—21no—
28Dic11⋊C5—21no—
29(C2×D11)⋊C4C3×C511yescharacteristic, complemented, Hall
30C3×C11⋊C5C22⋊C411yescharacteristic, complemented, Hall
31C22×C3×C11C22×C511yescharacteristic
32C2×C3×D11—21no—
33C2×C3×D11—21no—
34C2×C3×D11C4×C512yescomplemented
35C3×C4×C11—21no—
36C3×Dic11—21no—
37C23×C3×C5—111no—
38C2×C3×C4×C5—111no—
39C2×C3×C4×C5—111no—
40C2×C11⋊C5C2×C3×C411yescharacteristic
41C2×C11⋊C5C3×D411yescharacteristic
42C2×C11⋊C5C3×D411yescharacteristic
43AGL(1,𝔽11)—22no—
44C22×D11C2×C3×C511yescharacteristic
45C2×C4×C11C2×C3×C511yescharacteristic, complemented
46C2×Dic11C2×C3×C511yescharacteristic, complemented
47C5×C22⋊C4—111noHall
48C2×C3×C11C2×C4×C511yescharacteristic
49C2×C3×C11C5×D411yescharacteristic
50C2×C3×C11C5×D411yescharacteristic
51C3×D11—22no—
52C22×C3×C5—112no—
53C22×C3×C5—111no—
54C22×C3×C5—221no—
55C22×C3×C5—221no—
56C3×C4×C5—221no—
57C3×C4×C5—221no—
58C11⋊C5C3×C22⋊C411yescharacteristic, complemented, Hall
59C3×C22⋊C4—111noHall
60C22×C11C22×C3×C511yescharacteristic
61C2×D11—21no—
62C2×D11—21no—
63C2×D11C3×C4×C512yescomplemented
64C4×C11—21no—
65Dic11—21no—
66C23×C5—111no—
67C2×C4×C5—111no—
68C2×C4×C5—111no—
69C3×C11C5×C22⋊C411yescharacteristic, complemented, Hall
70C2×C3×C5—111no—
71C2×C3×C5—111no—
72C2×C3×C5—111no—
73C2×C3×C5—222no—
74C23×C3—111no—
75C2×C3×C4—111no—
76C2×C3×C4AGL(1,𝔽11)11yescharacteristic, complemented
77C2×C11C2×C3×C4×C511yescharacteristic
78C2×C11C3×C5×D411yescharacteristic
79C2×C11C3×C5×D411yescharacteristic
80D11—22no—
81C22×C5—112no—
82C22×C5—111no—
83C22×C5—221no—
84C22×C5—221no—
85C4×C5—221no—
86C4×C5—221no—
87C22⋊C4—111noSylow
88C3×C5—111noHall
89C22×C3—112no—
90C22×C3—221no—
91C22×C3—221no—
92C22×C3C2×AGL(1,𝔽11)11yescharacteristic
93C3×C4—21no—
94C3×C4—221no—
95C11C3×C5×C22⋊C411yescharacteristic, complemented, Sylow
96C2×C5—111no—
97C2×C5—111no—
98C2×C5—111no—
99C2×C5—222no—
100C23—111no—
101C2×C4—111no—
102C2×C4C3×AGL(1,𝔽11)11yescharacteristic, complemented
103C2×C3—222no—
104C2×C3C4×AGL(1,𝔽11)11yescharacteristic
105C2×C3C4⋊AGL(1,𝔽11)11yescharacteristic
106C2×C3C22⋊AGL(1,𝔽11)11yescharacteristic
107C5—111noSylow
108C22—112no—
109C22—221no—
110C22—221no—
111C22C2×C3×AGL(1,𝔽11)11yescharacteristic
112C4—21no—
113C4—221no—
114C3((C2×D11)⋊C4)⋊C511yescharacteristic, direct product factor, Sylow
115C2—222no—
116C2C3×C4×AGL(1,𝔽11)11yescharacteristic
117C2C3×C4⋊AGL(1,𝔽11)11yescharacteristic
118C2C3×C22⋊AGL(1,𝔽11)11yescharacteristic
subgroupG/H
centerC22×C3C2×AGL(1,𝔽11)
commutatorC2×C11C2×C3×C4×C5
FrattiniC22C2×C3×AGL(1,𝔽11)
FittingC2×C3×C4×C11C2×C5
socleC22×C3×C11C22×C5
prime radicalC22×C3×AGL(1,𝔽11)C2
cosocleC22×C11C22×C3×C5
hypercenterC2×C3×C4AGL(1,𝔽11)
hypocenterC11C3×C5×C22⋊C4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C11⋊C5C2semidirect
3. C2×C3×Dic11⋊C5C2semidirect
4. ((C2×D11)⋊C4)⋊C5C3direct (N × H)
8. C2×C3×AGL(1,𝔽11)C4semidirect
11. C3×(C2×D11)⋊C4C5semidirect
13. C2×C4×C11⋊C5C2×C3semidirect
14. C2×Dic11⋊C5C2×C3semidirect
20. C2×C3×C4×C11C2×C5semidirect
21. C2×C3×Dic11C2×C5semidirect
26. C2×AGL(1,𝔽11)C3×C4semidirect
29. (C2×D11)⋊C4C3×C5semidirect
30. C3×C11⋊C5C22⋊C4semidirect
34. C2×C3×D11C4×C5semidirect
45. C2×C4×C11C2×C3×C5semidirect
46. C2×Dic11C2×C3×C5semidirect
58. C11⋊C5C3×C22⋊C4semidirect
63. C2×D11C3×C4×C5semidirect
69. C3×C11C5×C22⋊C4semidirect
76. C2×C3×C4AGL(1,𝔽11)semidirect
95. C11C3×C5×C22⋊C4semidirect
102. C2×C4C3×AGL(1,𝔽11)semidirect
114. C3((C2×D11)⋊C4)⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AGL(1,𝔽11)2
C2×C3×C4×C11⋊C52
C2×C3×Dic11⋊C52
((C2×D11)⋊C4)⋊C53
C3×(C2×D11)⋊C45
C3×C5×C22⋊C411