Finite Group Databasebeta

← C11×C3⋊(#63118⋊C3) #38788091

Subgroups — C11×C3⋊(#63118⋊C3) #38788091

Order 25740.

112 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C3×C5×C11×D13⋊C3C211yesmaximal, characteristic
2C11×C3⋊#63118C311yesmaximal, characteristic, complemented
3C11×#63118⋊C3—31nomaximal
4C3×C5×C11×C13⋊C3C411yescharacteristic, complemented, Hall
5C11×C3⋊AGL(1,𝔽13)—51nomaximal, Hall
6C5×C11×D13⋊C3—21no—
7C5×C11×D13⋊C3D311yescharacteristic
8C3×C5×C11×D13C2×C311yescharacteristic
9C11×#63118—31noHall
10C3×C11×D13⋊C3D511yescharacteristic
11C3⋊(#63118⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
12C5×C11×C13⋊C3—21no—
13C5×C11×C13⋊C3Dic311yescharacteristic, complemented
14C3×C5×C11×C13C3×C411yescharacteristic, complemented
15C3×C11×Dic15—131nomaximal, Hall
16C11×C3⋊#261—51no—
17C11×AGL(1,𝔽13)—151no—
18C5×C11×D13C3×D311yescharacteristic
19C3×C11×C13⋊C3Dic511yescharacteristic, complemented, Hall
20C3×C5×D13⋊C3C2×C1111yescharacteristic
21C2×C32×C5×C11—131no—
22C3×C11×D13C3×D511yescharacteristic
23C11×D13⋊C3—21no—
24C11×D13⋊C3D1511yescharacteristic
25C3⋊#63118C3×C1111yescharacteristic, complemented
26#63118⋊C3—31no—
27C5×C11×C13C3×Dic311yescharacteristic, complemented, Hall
28C11×Dic15—131no—
29C3×C11×Dic5—391no—
30C3×C5×C13⋊C3C4×C1111yescharacteristic, complemented, Hall
31C11×#261—151noHall
32C32×C5×C11—131noHall
33C3⋊AGL(1,𝔽13)—51noHall
34C3×C11×C13C3×Dic511yescharacteristic, complemented
35C11×C13⋊C3—21no—
36C11×C13⋊C3Dic1511yescharacteristic, complemented
37C3×C11×Dic3—651noHall
38C3×C5×D13C2×C3×C1111yescharacteristic
39C5×D13⋊C3—21no—
40C5×D13⋊C3D3×C1111yescharacteristic
41C2×C3×C5×C11—131no—
42C2×C3×C5×C11—131no—
43C2×C3×C5×C11—261no—
44C11×D13C3×D1511yescharacteristic
45#63118—31noHall
46C3×D13⋊C3D5×C1111yescharacteristic
47C11×Dic5—391noHall
48C2×C32×C11—131no—
49C3×C5×C13C3×C4×C1111yescharacteristic, complemented
50C5×C13⋊C3—21no—
51C5×C13⋊C3C11×Dic311yescharacteristic, complemented
52C3×Dic15—131noHall
53C3×C5×C11—131no—
54C3×C5×C11—261no—
55C3×C5×C11AGL(1,𝔽13)11yescharacteristic, complemented
56C3⋊#261—51no—
57AGL(1,𝔽13)—151no—
58C11×C13C3×Dic1511yescharacteristic, complemented, Hall
59C3×C4×C11—1951no—
60C11×Dic3—651no—
61C5×D13C3×D3×C1111yescharacteristic
62C3×C13⋊C3C11×Dic511yescharacteristic, complemented, Hall
63C2×C5×C11—131no—
64C32×C11—131noHall
65C2×C32×C5—131no—
66C3×D13C3×D5×C1111yescharacteristic
67D13⋊C3—21no—
68D13⋊C3C11×D1511yescharacteristic
69C2×C3×C11—131no—
70C2×C3×C11—131no—
71C2×C3×C11—261no—
72C5×C13C3×C11×Dic311yescharacteristic, complemented, Hall
73Dic15—131no—
74C3×Dic5—391no—
75C5×C11C3⋊AGL(1,𝔽13)11yescharacteristic, complemented, Hall
76#261—151noHall
77C32×C5—131noHall
78C4×C11—1951noHall
79C3×C13C3×C11×Dic511yescharacteristic, complemented
80C13⋊C3—21no—
81C13⋊C3C11×Dic1511yescharacteristic, complemented
82C3×Dic3—651noHall
83C3×C11—131no—
84C3×C11—261no—
85C3×C11#63118⋊C311yescharacteristic, complemented
86C2×C3×C5—131no—
87C2×C3×C5—131no—
88C2×C3×C5—261no—
89D13C3×C11×D1511yescharacteristic
90C2×C11—131no—
91Dic5—391noHall
92C2×C32—131no—
93C3×C5—131no—
94C3×C5—261no—
95C3×C5C11×AGL(1,𝔽13)11yescharacteristic, complemented
96C13C3×C11×Dic1511yescharacteristic, complemented, Sylow
97C3×C4—1951no—
98Dic3—651no—
99C11C3⋊(#63118⋊C3)11yescharacteristic, direct product factor, Sylow
100C2×C5—131no—
101C32—131noSylow
102C2×C3—131no—
103C2×C3—131no—
104C2×C3—261no—
105C5C11×C3⋊AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
106C4—1951noSylow
107C3—131no—
108C3—261no—
109C3C11×#63118⋊C311yescharacteristic, complemented
110C2—131no—
subgroupG/H
center, hypercenterC11C3⋊(#63118⋊C3)
commutator, hypocenterC3×C5×C13C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C3×C4
prime radicalC3×C5×C11×D13⋊C3C2
cosocleC3×C5×D13C2×C3×C11
LCSG ▷ C3×C5×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
2. C11×C3⋊#63118C3semidirect
4. C3×C5×C11×C13⋊C3C4semidirect
11. C3⋊(#63118⋊C3)C11direct (N × H)
13. C5×C11×C13⋊C3Dic3semidirect
14. C3×C5×C11×C13C3×C4semidirect
19. C3×C11×C13⋊C3Dic5semidirect
25. C3⋊#63118C3×C11semidirect
27. C5×C11×C13C3×Dic3semidirect
30. C3×C5×C13⋊C3C4×C11semidirect
34. C3×C11×C13C3×Dic5semidirect
36. C11×C13⋊C3Dic15semidirect
49. C3×C5×C13C3×C4×C11semidirect
51. C5×C13⋊C3C11×Dic3semidirect
55. C3×C5×C11AGL(1,𝔽13)semidirect
58. C11×C13C3×Dic15semidirect
62. C3×C13⋊C3C11×Dic5semidirect
72. C5×C13C3×C11×Dic3semidirect
75. C5×C11C3⋊AGL(1,𝔽13)semidirect
79. C3×C13C3×C11×Dic5semidirect
81. C13⋊C3C11×Dic15semidirect
85. C3×C11#63118⋊C3semidirect
95. C3×C5C11×AGL(1,𝔽13)semidirect
96. C13C3×C11×Dic15semidirect
99. C11C3⋊(#63118⋊C3)direct (N × H)
105. C5C11×C3⋊AGL(1,𝔽13)semidirect
109. C3C11×#63118⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C11×D13⋊C32
C11×C3⋊#631183
C11×#63118⋊C33
C11×C3⋊AGL(1,𝔽13)5
C3⋊(#63118⋊C3)11
C3×C11×Dic1513