Finite Group Databasebeta

← #72217178

Subgroups — #72217178

Order 2640.

136 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 46 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⋊C5)C211yesmaximal, characteristic, complemented
4((C2×D11)⋊C4)⋊C5—31nomaximal, 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—
11#10587203C511yesmaximal, characteristic, complemented, Hall
12C22×AGL(1,𝔽11)—31no—
13C2×C4×C11⋊C5D311yescharacteristic, complemented
14C2×Dic11⋊C5—31no—
15C2×C3×C11⋊C5C2×C411yescharacteristic
16C2×C3×C11⋊C5D411yescharacteristic
17C2×C3×C11⋊C5D411yescharacteristic
18C3⋊AGL(1,𝔽11)—22no—
19C22×D33C2×C511yescharacteristic
20C2×C3×C4×C11C2×C511yescharacteristic, complemented
21C2×Dic33C2×C511yescharacteristic, complemented
22C5×(C2×D3)⋊C4—111nomaximal, Hall
23C22×C11⋊C5C2×D311yescharacteristic
24C2×AGL(1,𝔽11)—32no—
25C2×AGL(1,𝔽11)—61no—
26C2×AGL(1,𝔽11)—61no—
27C4×C11⋊C5—21no—
28Dic11⋊C5—61no—
29(C2×D11)⋊C4—31noHall
30C3×C11⋊C5C22⋊C411yescharacteristic, complemented, Hall
31C22×C3×C11C22×C511yescharacteristic
32C2×D33—21no—
33C2×D33—21no—
34C2×D33C4×C512yescomplemented
35C3×C4×C11—21no—
36Dic33—21no—
37C22×C5×D3—111no—
38C2×C3×C4×C5—111no—
39C2×C5×Dic3—111no—
40C2×C11⋊C5C4×D311yescharacteristic
41C2×C11⋊C5D1211yescharacteristic
42C2×C11⋊C5#6711yescharacteristic
43AGL(1,𝔽11)—62no—
44C22×D11—31no—
45C2×C4×C11C5×D311yescharacteristic, complemented
46C2×Dic11—31no—
47C5×C22⋊C4—331noHall
48C2×C3×C11C2×C4×C511yescharacteristic
49C2×C3×C11C5×D411yescharacteristic
50C2×C3×C11C5×D411yescharacteristic
51D33—22no—
52C22×C3×C5—111no—
53C2×C5×D3—112no—
54C2×C5×D3—221no—
55C2×C5×D3—221no—
56C3×C4×C5—221no—
57C5×Dic3—221no—
58C11⋊C5(C2×D3)⋊C411yescharacteristic, complemented, Hall
59(C2×D3)⋊C4—111noHall
60C22×C11C2×C5×D311yescharacteristic
61C2×D11—32no—
62C2×D11—61no—
63C2×D11—61no—
64C4×C11—21no—
65Dic11—61no—
66C23×C5—331no—
67C2×C4×C5—111no—
68C2×C4×C5—331no—
69C3×C11C5×C22⋊C411yescharacteristic, complemented, Hall
70C2×C3×C5—111no—
71C2×C3×C5—111no—
72C2×C3×C5—111no—
73C5×D3—222no—
74C22×D3—111no—
75C2×C3×C4AGL(1,𝔽11)11yescharacteristic, complemented
76C2×Dic3—111no—
77C2×C11C4×C5×D311yescharacteristic
78C2×C11C5×D1211yescharacteristic
79C2×C11C5×#6711yescharacteristic
80D11—62no—
81C22×C5—111no—
82C22×C5—332no—
83C22×C5—661no—
84C22×C5—661no—
85C4×C5—221no—
86C4×C5—661no—
87C22⋊C4—331noSylow
88C3×C5—111noHall
89C22×C3C2×AGL(1,𝔽11)11yescharacteristic
90C2×D3—112no—
91C2×D3—221no—
92C2×D3—221no—
93C3×C4—21no—
94Dic3—221no—
95C11C5×(C2×D3)⋊C411yescharacteristic, complemented, Sylow
96C2×C5—111no—
97C2×C5—111no—
98C2×C5—111no—
99C2×C5—662no—
100C23—331no—
101C2×C4—331no—
102C2×C4C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
103C2×C3C4×AGL(1,𝔽11)11yescharacteristic
104C2×C3C4⋊AGL(1,𝔽11)11yescharacteristic
105C2×C3C22⋊AGL(1,𝔽11)11yescharacteristic
106D3—222no—
107C5—111noSylow
108C22—332no—
109C22—661no—
110C22—661no—
111C22C2×C3⋊AGL(1,𝔽11)11yescharacteristic
112C4—21no—
113C4—661no—
114C3((C2×D11)⋊C4)⋊C511yescharacteristic, complemented, Sylow
115C2—662no—
116C2C4×C3⋊AGL(1,𝔽11)11yescharacteristic
117C2C4⋊(C3⋊AGL(1,𝔽11))11yescharacteristic
118C2#63159⋊C511yescharacteristic
subgroupG/H
center, FrattiniC22C2×C3⋊AGL(1,𝔽11)
commutatorC2×C3×C11C2×C4×C5
FittingC2×C3×C4×C11C2×C5
socle, cosocleC22×C3×C11C22×C5
prime radicalC22×C3⋊AGL(1,𝔽11)C2
hypercenterC2×C4C3⋊AGL(1,𝔽11)
hypocenterC3×C11C5×C22⋊C4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C22 ◁ C2×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⋊C5)C2semidirect
8. C2×C3⋊AGL(1,𝔽11)C4semidirect
11. #10587203C5semidirect
13. C2×C4×C11⋊C5D3semidirect
20. C2×C3×C4×C11C2×C5semidirect
21. C2×Dic33C2×C5semidirect
30. C3×C11⋊C5C22⋊C4semidirect
34. C2×D33C4×C5semidirect
45. C2×C4×C11C5×D3semidirect
58. C11⋊C5(C2×D3)⋊C4semidirect
69. C3×C11C5×C22⋊C4semidirect
75. C2×C3×C4AGL(1,𝔽11)semidirect
95. C11C5×(C2×D3)⋊C4semidirect
102. C2×C4C3⋊AGL(1,𝔽11)semidirect
114. C3((C2×D11)⋊C4)⋊C5semidirect

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⋊C5)2
((C2×D11)⋊C4)⋊C53
#105872035
C5×(C2×D3)⋊C411