Finite Group Databasebeta

← C2×C3⋊(C11⋊#10587717) #49114869

Subgroups — C2×C3⋊(C11⋊#10587717) #49114869

Order 36036.

176 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 49 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×C11×#63271C211yesmaximal, characteristic, complemented
2C3⋊(C11⋊#10587717)C212yesmaximal, direct product factor
3C2×C7×D429C311yesmaximal, characteristic, complemented
4C2×C11⋊#10587717—31nomaximal
5C3×C11×#63271C2211yescharacteristic, complemented, Hall
6C11⋊#10587717—32no—
7C7×D429C2×C312yescomplemented
8C2×C11×#63271—21no—
9C2×C11×#63271D311yescharacteristic, complemented
10C2×C3×C7×C11×C13C2×C311yescharacteristic, complemented
11C2×C3⋊(C11⋊(D13⋊C3))—71nomaximal, Hall
12C2×C7×D143—31noHall
13C2×C3⋊#10587717—111nomaximal, Hall
14C11×#63271—21no—
15C11×#63271C2×D311yescharacteristic, complemented
16C3×C7×C11×C13C22×C311yescharacteristic, complemented
17C2×ΓL(1,𝔽8)×D33—131nomaximal, Hall
18C2×C3×C11×C13⋊C3—71no—
19C3⋊(C11⋊(D13⋊C3))—72no—
20C7×D143—32no—
21C2×C7×C11×C13C3×D311yescharacteristic, complemented
22C2×D429ΓL(1,𝔽8)11yescharacteristic, complemented
23C2×C11⋊(D13⋊C3)—211no—
24C2×C3×#63271D1111yescharacteristic, complemented
25C3⋊#10587717—112no—
26C2×C3×C11×ΓL(1,𝔽8)—131no—
27ΓL(1,𝔽8)×D33—132no—
28C3×C11×C13⋊C3—71noHall
29C2×C7×D39—111no—
30C2×#10587717—331no—
31C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
32C2×C7×D33—131no—
33C2×ΓL(1,𝔽8)×D11—391no—
34C2×C3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented
35D429C2×ΓL(1,𝔽8)12yescomplemented
36C2×C11×C13⋊C3—71no—
37C2×C11×C13⋊C3—141no—
38C11⋊(D13⋊C3)—212no—
39C3×#63271C2×D1111yescharacteristic, complemented, Hall
40C3×C11×ΓL(1,𝔽8)—131noHall
41C2×D143—31noHall
42C2×C3×C7×C13C3×D1111yescharacteristic, complemented
43C7×D39—112no—
44C2×#63271—21no—
45C2×#63271D3311yescharacteristic, complemented
46#10587717—332no—
47C2×C3⋊(D13⋊C3)—771noHall
48C2×C3×C7×C11D13⋊C311yescharacteristic, complemented
49C7×D33—132no—
50C2×C11×ΓL(1,𝔽8)—131no—
51C2×C11×ΓL(1,𝔽8)—261no—
52ΓL(1,𝔽8)×D11—392no—
53C3×C11×C13C22×ΓL(1,𝔽8)11yescharacteristic, complemented
54C11×C13⋊C3—71no—
55C11×C13⋊C3—141no—
56C2×C3×D33—911noHall
57C2×C7×D13—331noHall
58C2×C7×D11—391noHall
59C2×C11×C13D3×ΓL(1,𝔽8)11yescharacteristic, complemented
60D143—32no—
61C3×C7×C13C2×C3×D1111yescharacteristic, complemented
62#63271—21no—
63#63271C2×D3311yescharacteristic, complemented
64C2×D3×ΓL(1,𝔽8)—1431noHall
65C2×C3×C13⋊C3—71no—
66C3⋊(D13⋊C3)—772no—
67C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
68C11×ΓL(1,𝔽8)—131no—
69C11×ΓL(1,𝔽8)—261no—
70C2×C32×C11—911no—
71C3×D33—912no—
72C2×C7×C13C3×D3311yescharacteristic, complemented
73C7×D13—332no—
74C2×D39—111no—
75C2×D13⋊C3—2311no—
76C2×C7×C11C3⋊(D13⋊C3)11yescharacteristic, complemented
77C7×D11—392no—
78C11×C13C2×D3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
79C2×D33—131no—
80C2×C3×D11—2731no—
81C2×C3×ΓL(1,𝔽8)—131no—
82D3×ΓL(1,𝔽8)—1432no—
83C3×C13⋊C3—71noHall
84C32×C11—911noHall
85C7×C13C2×C3×D3311yescharacteristic, complemented, Hall
86C2×D3×C7—1431no—
87C22×ΓL(1,𝔽8)—4291no—
88C2×C3×C13ΓL(1,𝔽8)×D1111yescharacteristic, complemented
89D39—112no—
90C2×C13⋊C3—71no—
91C2×C13⋊C3—141no—
92D13⋊C3—2312no—
93C7×C11C2×C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
94C2×C3×C11—911no—
95C2×C3×C11—1821no—
96C2×C3×C11#1058771711yescharacteristic, complemented
97D33—132no—
98C3×D11—2732no—
99C3×ΓL(1,𝔽8)—131noHall
100C2×D13—331noHall
101C2×D11—391noHall
102C2×C3×C7C11⋊(D13⋊C3)11yescharacteristic, complemented
103D3×C7—1432no—
104C2×ΓL(1,𝔽8)—131no—
105C2×ΓL(1,𝔽8)—261no—
106C2×ΓL(1,𝔽8)—4292no—
107C3×C13C2×ΓL(1,𝔽8)×D1111yescharacteristic, complemented
108C13⋊C3—71no—
109C13⋊C3—141no—
110C2×C3×D3—10011noHall
111C3×C11—911no—
112C3×C11—1821no—
113C3×C11C2×#1058771711yescharacteristic, complemented
114C22×C7—4291noHall
115C2×C13ΓL(1,𝔽8)×D3311yescharacteristic, complemented
116D13—332no—
117C2×C11C3⋊#1058771711yescharacteristic, complemented
118D11—392no—
119C3×C7C2×C11⋊(D13⋊C3)11yescharacteristic, complemented
120ΓL(1,𝔽8)—131no—
121ΓL(1,𝔽8)—261no—
122C2×C32—911no—
123C3×D3—10012no—
124C2×C7—4292no—
125C2×C7C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented
126C13C2×ΓL(1,𝔽8)×D3311yescharacteristic, complemented, Sylow
127C22×C3—30031no—
128C2×D3—1431no—
129C11C2×C3⋊#1058771711yescharacteristic, complemented, Sylow
130C32—911noSylow
131C7C2×C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented, Sylow
132C2×C3—911no—
133C2×C3—1821no—
134C2×C3—30032no—
135C2×C3C11⋊#1058771711yescharacteristic, complemented
136D3—1432no—
137C22—4291noSylow
138C3—911no—
139C3—1821no—
140C3C2×C11⋊#1058771711yescharacteristic, complemented
141C2—4292no—
142C2C3⋊(C11⋊#10587717)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C11⋊#10587717)
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×C11×#63271C2semidirect
2. C3⋊(C11⋊#10587717)C2direct (N × H)
3. C2×C7×D429C3semidirect
5. C3×C11×#63271C22semidirect
7. C7×D429C2×C3semidirect
9. C2×C11×#63271D3semidirect
10. C2×C3×C7×C11×C13C2×C3semidirect
15. C11×#63271C2×D3semidirect
16. C3×C7×C11×C13C22×C3semidirect
21. C2×C7×C11×C13C3×D3semidirect
22. C2×D429ΓL(1,𝔽8)semidirect
24. C2×C3×#63271D11semidirect
31. C7×C11×C13C2×C3×D3semidirect
34. C2×C3×C11×C13C2×ΓL(1,𝔽8)semidirect
35. D429C2×ΓL(1,𝔽8)semidirect
39. C3×#63271C2×D11semidirect
42. C2×C3×C7×C13C3×D11semidirect
45. C2×#63271D33semidirect
48. C2×C3×C7×C11D13⋊C3semidirect
53. C3×C11×C13C22×ΓL(1,𝔽8)semidirect
59. C2×C11×C13D3×ΓL(1,𝔽8)semidirect
61. C3×C7×C13C2×C3×D11semidirect
63. #63271C2×D33semidirect
67. C3×C7×C11C2×D13⋊C3semidirect
72. C2×C7×C13C3×D33semidirect
76. C2×C7×C11C3⋊(D13⋊C3)semidirect
78. C11×C13C2×D3×ΓL(1,𝔽8)semidirect
85. C7×C13C2×C3×D33semidirect
88. C2×C3×C13ΓL(1,𝔽8)×D11semidirect
93. C7×C11C2×C3⋊(D13⋊C3)semidirect
96. C2×C3×C11#10587717semidirect
102. C2×C3×C7C11⋊(D13⋊C3)semidirect
107. C3×C13C2×ΓL(1,𝔽8)×D11semidirect
113. C3×C11C2×#10587717semidirect
115. C2×C13ΓL(1,𝔽8)×D33semidirect
117. C2×C11C3⋊#10587717semidirect
119. C3×C7C2×C11⋊(D13⋊C3)semidirect
125. C2×C7C3⋊(C11⋊(D13⋊C3))semidirect
126. C13C2×ΓL(1,𝔽8)×D33semidirect
129. C11C2×C3⋊#10587717semidirect
131. C7C2×C3⋊(C11⋊(D13⋊C3))semidirect
135. C2×C3C11⋊#10587717semidirect
140. C3C2×C11⋊#10587717semidirect
142. C2C3⋊(C11⋊#10587717)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×C11×#632712
C3⋊(C11⋊#10587717)2
C2×C7×D4293
C2×C11⋊#105877173
C2×C3⋊(C11⋊(D13⋊C3))7
C2×C3⋊#1058771711
C2×ΓL(1,𝔽8)×D3313