Finite Group Databasebeta

← C2×C3⋊(C11⋊((C13⋊C3)⋊D7)) #49114875

Subgroups — C2×C3⋊(C11⋊((C13⋊C3)⋊D7)) #49114875

Order 36036.

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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×C7×C11×C13⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(C11⋊((C13⋊C3)⋊D7))C212yesmaximal, direct product factor
3C2×D3003C311yesmaximal, characteristic, complemented
4C2×C11⋊((C13⋊C3)⋊D7)—31nomaximal
5C3×C7×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
6C11⋊((C13⋊C3)⋊D7)—32no—
7D3003C2×C312yescomplemented
8C2×C7×C11×C13⋊C3—21no—
9C2×C7×C11×C13⋊C3D311yescharacteristic, complemented
10C2×C3×C7×C11×C13C2×C311yescharacteristic, complemented
11C2×C3⋊(C11⋊(D13⋊C3))—71nomaximal, Hall
12C2×D1001—31noHall
13C2×C3⋊((C13⋊C3)⋊D7)—111nomaximal, Hall
14C7×C11×C13⋊C3—21no—
15C7×C11×C13⋊C3C2×D311yescharacteristic, complemented
16C3×C7×C11×C13C22×C311yescharacteristic, complemented
17C2×C3×D231—131nomaximal, Hall
18C2×C3×C11×C13⋊C3D711yescharacteristic, complemented
19C3⋊(C11⋊(D13⋊C3))—72no—
20D1001—32no—
21C2×C7×C11×C13C3×D311yescharacteristic, complemented
22C2×D429—71no—
23C2×C11⋊(D13⋊C3)—211no—
24C2×C3×C7×C13⋊C3D1111yescharacteristic, complemented
25C3⋊((C13⋊C3)⋊D7)—112no—
26C2×C32×C7×C11—131no—
27C3×D231—132no—
28C3×C11×C13⋊C3C2×D711yescharacteristic, complemented, Hall
29C2×D273—111no—
30C2×(C13⋊C3)⋊D7—331no—
31C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
32C2×D231—131no—
33C2×C3×D77—391no—
34C2×C3×C11×C13C3×D711yescharacteristic, complemented
35D429—72no—
36C2×C11×C13⋊C3—21no—
37C2×C11×C13⋊C3D2111yescharacteristic, complemented
38C11⋊(D13⋊C3)—212no—
39C3×C7×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
40C32×C7×C11—131noHall
41C2×D143—211noHall
42C2×C3×C7×C13C3×D1111yescharacteristic, complemented
43D273—112no—
44C2×C7×C13⋊C3—21no—
45C2×C7×C13⋊C3D3311yescharacteristic, complemented
46(C13⋊C3)⋊D7—332no—
47C2×C3⋊(D13⋊C3)—771noHall
48C2×C3×C7×C11—131no—
49C2×C3×C7×C11—261no—
50C2×C3×C7×C11D13⋊C311yescharacteristic, complemented
51D231—132no—
52C3×D77—392no—
53C3×C11×C13C2×C3×D711yescharacteristic, complemented
54C11×C13⋊C3—21no—
55C11×C13⋊C3C2×D2111yescharacteristic, complemented
56C2×C3×D33—911noHall
57C2×D91—331noHall
58C2×D77—391noHall
59C2×C11×C13C3×D2111yescharacteristic, complemented
60D143—212no—
61C3×C7×C13C2×C3×D1111yescharacteristic, complemented
62C7×C13⋊C3—21no—
63C7×C13⋊C3C2×D3311yescharacteristic, complemented
64C2×C3×D21—1431noHall
65C2×C3×C13⋊C3D7711yescharacteristic, complemented
66C3⋊(D13⋊C3)—772no—
67C3×C7×C11—131no—
68C3×C7×C11—261no—
69C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
70C2×C32×C11—131no—
71C3×D33—912no—
72C2×C7×C13C3×D3311yescharacteristic, complemented
73D91—332no—
74C2×D39—771no—
75C2×D13⋊C3—2311no—
76C2×C7×C11C3⋊(D13⋊C3)11yescharacteristic, complemented
77D77—392no—
78C11×C13C2×C3×D2111yescharacteristic, complemented, Hall
79C2×D33—911no—
80C2×C3×D11—2731no—
81C2×C32×C7—131no—
82C3×D21—1432no—
83C3×C13⋊C3C2×D7711yescharacteristic, complemented, Hall
84C32×C11—131noHall
85C7×C13C2×C3×D3311yescharacteristic, complemented, Hall
86C2×D21—1431no—
87C2×C3×D7—4291no—
88C2×C3×C13C3×D7711yescharacteristic, complemented
89D39—772no—
90C2×C13⋊C3—21no—
91C2×C13⋊C3D23111yescharacteristic, complemented
92D13⋊C3—2312no—
93C7×C11C2×C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
94C2×C3×C11—131no—
95C2×C3×C11—261no—
96C2×C3×C11(C13⋊C3)⋊D711yescharacteristic, complemented
97D33—912no—
98C3×D11—2732no—
99C32×C7—131noHall
100C2×D13—2311noHall
101C2×D11—2731noHall
102C2×C3×C7—131no—
103C2×C3×C7—261no—
104C2×C3×C7C11⋊(D13⋊C3)11yescharacteristic, complemented
105D21—1432no—
106C3×D7—4292no—
107C3×C13C2×C3×D7711yescharacteristic, complemented
108C13⋊C3—21no—
109C13⋊C3C2×D23111yescharacteristic, complemented
110C2×C3×D3—10011noHall
111C3×C11—131no—
112C3×C11—261no—
113C3×C11C2×(C13⋊C3)⋊D711yescharacteristic, complemented
114C2×D7—4291noHall
115C2×C13C3×D23111yescharacteristic, complemented
116D13—2312no—
117C2×C11C3⋊((C13⋊C3)⋊D7)11yescharacteristic, complemented
118D11—2732no—
119C3×C7—131no—
120C3×C7—261no—
121C3×C7C2×C11⋊(D13⋊C3)11yescharacteristic, complemented
122C2×C32—131no—
123C3×D3—10012no—
124C2×C7C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented
125D7—4292no—
126C13C2×C3×D23111yescharacteristic, complemented, Sylow
127C22×C3—30031no—
128C2×D3—10011no—
129C11C2×C3⋊((C13⋊C3)⋊D7)11yescharacteristic, complemented, Sylow
130C32—131noSylow
131C7C2×C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented, Sylow
132C2×C3—131no—
133C2×C3—261no—
134C2×C3—30032no—
135C2×C3C11⋊((C13⋊C3)⋊D7)11yescharacteristic, complemented
136D3—10012no—
137C22—30031noSylow
138C3—131no—
139C3—261no—
140C3C2×C11⋊((C13⋊C3)⋊D7)11yescharacteristic, complemented
141C2—30032no—
142C2C3⋊(C11⋊((C13⋊C3)⋊D7))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C11⋊((C13⋊C3)⋊D7))
commutator, cosocle, hypocenterC3×C7×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C11×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C7×C11×C13⋊C3C2semidirect
2. C3⋊(C11⋊((C13⋊C3)⋊D7))C2direct (N × H)
3. C2×D3003C3semidirect
5. C3×C7×C11×C13⋊C3C22semidirect
7. D3003C2×C3semidirect
9. C2×C7×C11×C13⋊C3D3semidirect
10. C2×C3×C7×C11×C13C2×C3semidirect
15. C7×C11×C13⋊C3C2×D3semidirect
16. C3×C7×C11×C13C22×C3semidirect
18. C2×C3×C11×C13⋊C3D7semidirect
21. C2×C7×C11×C13C3×D3semidirect
24. C2×C3×C7×C13⋊C3D11semidirect
28. C3×C11×C13⋊C3C2×D7semidirect
31. C7×C11×C13C2×C3×D3semidirect
34. C2×C3×C11×C13C3×D7semidirect
37. C2×C11×C13⋊C3D21semidirect
39. C3×C7×C13⋊C3C2×D11semidirect
42. C2×C3×C7×C13C3×D11semidirect
45. C2×C7×C13⋊C3D33semidirect
50. C2×C3×C7×C11D13⋊C3semidirect
53. C3×C11×C13C2×C3×D7semidirect
55. C11×C13⋊C3C2×D21semidirect
59. C2×C11×C13C3×D21semidirect
61. C3×C7×C13C2×C3×D11semidirect
63. C7×C13⋊C3C2×D33semidirect
65. C2×C3×C13⋊C3D77semidirect
69. C3×C7×C11C2×D13⋊C3semidirect
72. C2×C7×C13C3×D33semidirect
76. C2×C7×C11C3⋊(D13⋊C3)semidirect
78. C11×C13C2×C3×D21semidirect
83. C3×C13⋊C3C2×D77semidirect
85. C7×C13C2×C3×D33semidirect
88. C2×C3×C13C3×D77semidirect
91. C2×C13⋊C3D231semidirect
93. C7×C11C2×C3⋊(D13⋊C3)semidirect
96. C2×C3×C11(C13⋊C3)⋊D7semidirect
104. C2×C3×C7C11⋊(D13⋊C3)semidirect
107. C3×C13C2×C3×D77semidirect
109. C13⋊C3C2×D231semidirect
113. C3×C11C2×(C13⋊C3)⋊D7semidirect
115. C2×C13C3×D231semidirect
117. C2×C11C3⋊((C13⋊C3)⋊D7)semidirect
121. C3×C7C2×C11⋊(D13⋊C3)semidirect
124. C2×C7C3⋊(C11⋊(D13⋊C3))semidirect
126. C13C2×C3×D231semidirect
129. C11C2×C3⋊((C13⋊C3)⋊D7)semidirect
131. C7C2×C3⋊(C11⋊(D13⋊C3))semidirect
135. C2×C3C11⋊((C13⋊C3)⋊D7)semidirect
140. C3C2×C11⋊((C13⋊C3)⋊D7)semidirect
142. C2C3⋊(C11⋊((C13⋊C3)⋊D7))direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C7×C11×C13⋊C32
C3⋊(C11⋊((C13⋊C3)⋊D7))2
C2×D30033
C2×C11⋊((C13⋊C3)⋊D7)3
C2×C3⋊(C11⋊(D13⋊C3))7
C2×C3⋊((C13⋊C3)⋊D7)11
C2×C3×D23113