Finite Group Databasebeta

← C11×C3⋊((C11⋊C5)⋊Dic5) #49137266

Subgroups — C11×C3⋊((C11⋊C5)⋊Dic5) #49137266

Order 36300.

136 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C2×C3×C5×C11×C11⋊C5C211yesmaximal, characteristic
2C11×(C11⋊C5)⋊Dic5—31nomaximal, Hall
3C3×C5×C11×C11⋊C5C411yescharacteristic, complemented, Hall
4C11×Dic165C511yesmaximal, characteristic, complemented
5C11×C3⋊(Dic11⋊C5)—51nomaximal
6C2×C5×C11×C11⋊C5D311yescharacteristic
7C2×C3×C11×C11⋊C5—22no—
8C2×C3×C11×C11⋊C5D511yescharacteristic
9C2×C3×C5×C112C2×C511yescharacteristic
10C5×C11×Dic15—111nomaximal
11C3⋊((C11⋊C5)⋊Dic5)C1111yesmaximal, characteristic, direct product factor
12C5×C11×C11⋊C5Dic311yescharacteristic, complemented, Hall
13C11×Dic55—31no—
14C11×Dic11⋊C5—151no—
15C3×C5×C112C4×C511yescharacteristic, complemented
16C3×C11×C11⋊C5—22no—
17C3×C11×C11⋊C5Dic511yescharacteristic, complemented
18C2×C3×C52×C11—221no—
19C2×C3×C5×C11⋊C5C2×C1111yescharacteristic
20C11×Dic33—51noHall
21C2×C5×C112C5×D311yescharacteristic
22C2×C11×C11⋊C5—22no—
23C2×C11×C11⋊C5D1511yescharacteristic
24C5×C11×Dic5—331no—
25(C11⋊C5)⋊Dic5—31no—
26C3×C52×C11—221no—
27C3×C5×C11⋊C5C4×C1111yescharacteristic, complemented
28C2×C3×C112C5×D511yescharacteristic
29Dic165C5×C1111yescharacteristic, complemented
30C11×Dic15—111no—
31C5×C11×Dic3—551no—
32C3⋊(Dic11⋊C5)—51no—
33C5×C112C5×Dic311yescharacteristic, complemented
34C11×C11⋊C5—22no—
35C11×C11⋊C5Dic1511yescharacteristic, complemented
36C2×C52×C11—221no—
37C2×C5×C11⋊C5D3×C1111yescharacteristic
38C11×Dic11—151noHall
39C3×C112C5×Dic511yescharacteristic, complemented, Hall
40C2×C3×C5×C11—101no—
41C2×C3×C5×C11—222no—
42C2×C3×C5×C11—221no—
43C2×C3×C5×C11AGL(1,𝔽11)11yescharacteristic
44C2×C3×C5×C11C2×C5×C1111yescharacteristic
45C2×C3×C11⋊C5—22no—
46C2×C3×C11⋊C5D5×C1111yescharacteristic
47C5×Dic15—111noHall
48C52×C11—221no—
49C5×C11⋊C5C11×Dic311yescharacteristic, complemented
50C2×C112C5×D1511yescharacteristic
51C4×C5×C11—1651no—
52Dic55—31no—
53C11×Dic5—331no—
54Dic11⋊C5—151no—
55C3×C5×C11—101no—
56C3×C5×C11—222no—
57C3×C5×C11—221no—
58C3×C5×C11Dic11⋊C511yescharacteristic, complemented
59C3×C5×C11C4×C5×C1111yescharacteristic, complemented
60C3×C11⋊C5—22no—
61C3×C11⋊C5C11×Dic511yescharacteristic, complemented
62C2×C3×C52—221no—
63Dic33—51no—
64C11×Dic3—551no—
65C112C5×Dic1511yescharacteristic, complemented, Sylow
66C2×C5×C11—101no—
67C2×C5×C11—222no—
68C2×C5×C11—221no—
69C2×C5×C11C3⋊AGL(1,𝔽11)11yescharacteristic
70C2×C5×C11C5×D3×C1111yescharacteristic
71C2×C11⋊C5—22no—
72C2×C11⋊C5C11×D1511yescharacteristic
73C5×Dic5—331noHall
74C3×C52—221noHall
75C2×C3×C11—101no—
76C2×C3×C11C5⋊AGL(1,𝔽11)11yescharacteristic
77C2×C3×C11C5×D5×C1111yescharacteristic
78Dic15—111no—
79C5×Dic3—551no—
80C5×C11—101no—
81C5×C11—222no—
82C5×C11—221no—
83C5×C11C3⋊(Dic11⋊C5)11yescharacteristic, complemented
84C5×C11C5×C11×Dic311yescharacteristic, complemented
85C11⋊C5—22no—
86C11⋊C5C11×Dic1511yescharacteristic, complemented
87C2×C52—111no—
88C4×C11—1651no—
89Dic11—151no—
90C3×C11—101no—
91C3×C11(C11⋊C5)⋊Dic511yescharacteristic, complemented
92C3×C11C5×C11×Dic511yescharacteristic, complemented
93C2×C3×C5—221no—
94C2×C3×C5—222no—
95C2×C3×C5C11×AGL(1,𝔽11)11yescharacteristic
96C52—111noSylow
97C2×C11—101no—
98C2×C11C3⋊(C5⋊AGL(1,𝔽11))11yescharacteristic
99C2×C11C5×C11×D1511yescharacteristic
100C4×C5—1651no—
101Dic5—331no—
102C3×C5—222no—
103C3×C5—221no—
104C3×C5C11×Dic11⋊C511yescharacteristic, complemented
105Dic3—551noHall
106C11—101no—
107C11C3⋊((C11⋊C5)⋊Dic5)11yescharacteristic, direct product factor
108C11C5×C11×Dic1511yescharacteristic, complemented
109C2×C5—221no—
110C2×C5—222no—
111C2×C5C11×C3⋊AGL(1,𝔽11)11yescharacteristic
112C2×C3C11×C5⋊AGL(1,𝔽11)11yescharacteristic
113C5—222no—
114C5—221no—
115C5C11×C3⋊(Dic11⋊C5)11yescharacteristic, complemented
116C4—1651noSylow
117C3C11×(C11⋊C5)⋊Dic511yescharacteristic, complemented, Sylow
118C2C11×C3⋊(C5⋊AGL(1,𝔽11))11yescharacteristic
subgroupG/H
center, hypercenterC2×C11C3⋊(C5⋊AGL(1,𝔽11))
commutator, hypocenterC3×C5×C11C4×C5×C11
FrattiniC2C11×C3⋊(C5⋊AGL(1,𝔽11))
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×C11×C11⋊C5C2
cosocleC2×C3×C5×C11C2×C5×C11
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
3. C3×C5×C11×C11⋊C5C4semidirect
4. C11×Dic165C5semidirect
11. C3⋊((C11⋊C5)⋊Dic5)C11direct (N × H)
12. C5×C11×C11⋊C5Dic3semidirect
15. C3×C5×C112C4×C5semidirect
17. C3×C11×C11⋊C5Dic5semidirect
27. C3×C5×C11⋊C5C4×C11semidirect
29. Dic165C5×C11semidirect
33. C5×C112C5×Dic3semidirect
35. C11×C11⋊C5Dic15semidirect
39. C3×C112C5×Dic5semidirect
49. C5×C11⋊C5C11×Dic3semidirect
58. C3×C5×C11Dic11⋊C5semidirect
59. C3×C5×C11C4×C5×C11semidirect
61. C3×C11⋊C5C11×Dic5semidirect
65. C112C5×Dic15semidirect
83. C5×C11C3⋊(Dic11⋊C5)semidirect
84. C5×C11C5×C11×Dic3semidirect
86. C11⋊C5C11×Dic15semidirect
91. C3×C11(C11⋊C5)⋊Dic5semidirect
92. C3×C11C5×C11×Dic5semidirect
104. C3×C5C11×Dic11⋊C5semidirect
107. C11C3⋊((C11⋊C5)⋊Dic5)direct (N × H)
108. C11C5×C11×Dic15semidirect
115. C5C11×C3⋊(Dic11⋊C5)semidirect
117. C3C11×(C11⋊C5)⋊Dic5semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×C11×C11⋊C52
C11×(C11⋊C5)⋊Dic53
C11×Dic1655
C11×C3⋊(Dic11⋊C5)5
C5×C11×Dic1511
C3⋊((C11⋊C5)⋊Dic5)11