Finite Group Databasebeta

← C2×C3×C11×#10587720 #49114824

Subgroups — C2×C3×C11×#10587720 #49114824

Order 36036.

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 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×#63270C211yesmaximal, characteristic, complemented
2C3×C11×#10587720C212yesmaximal, direct product factor
3C2×C3×C11×C13×D7C311yesmaximal, characteristic, complemented
4C2×C11×#10587720C313yesmaximal, direct product factor
5C3×C11×#63270C2211yescharacteristic, complemented, Hall
6C11×#10587720C2×C316yesdirect product factor
7C3×C11×C13×D7C2×C312yescomplemented
8C2×C11×#63270C2×C313yescomplemented
9C2×C3×C7×C11×C13C2×C311yescharacteristic, complemented
10C22×C3×C11×C13⋊C3—71nomaximal, Hall
11C2×C11×C13×D7C3211yescharacteristic, complemented, Hall
12C2×C3×#10587720C1111yesmaximal, characteristic, direct product factor, Hall
13C11×#63270C22×C313yescomplemented
14C3×C7×C11×C13C22×C311yescharacteristic, complemented
15C2×C3×C11×AGL(1,𝔽7)—131nomaximal, Hall
16C2×C3×C11×C13⋊C3—72no—
17C2×C3×C11×C13⋊C3—71no—
18C11×C13×D7C2×C3212yescomplemented
19C2×C7×C11×C13C2×C3211yescharacteristic, complemented
20C22×C3×C11×C13—71no—
21C22×C11×C13⋊C3—73no—
22C2×C3×#63270C2×C1111yescharacteristic, complemented
23C3×#10587720C2×C1112yesdirect product factor
24C2×C3×C11×ΓL(1,𝔽8)—131no—
25C3×C11×AGL(1,𝔽7)—132no—
26C3×C11×C13⋊C3—71noHall
27C2×C3×C13×D7C3×C1111yescharacteristic, complemented
28C2×#10587720C3×C1113yesdirect product factor
29C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
30C2×C3×C11×D7C13⋊C311yescharacteristic, complemented
31C2×C11×AGL(1,𝔽7)—133no—
32C2×C3×C11×C13—72no—
33C2×C3×C11×C13AGL(1,𝔽7)11yescharacteristic, complemented
34C2×C11×C13⋊C3—76no—
35C2×C11×C13⋊C3—73no—
36C3×#63270C22×C1111yescharacteristic, complemented, Hall
37C3×C11×ΓL(1,𝔽8)—131noHall
38C22×C11×C13—71noHall
39C2×C3×C7×C13C2×C3×C1111yescharacteristic, complemented
40C3×C13×D7C2×C3×C1112yescomplemented
41C2×#63270C2×C3×C1113yescomplemented
42#10587720C2×C3×C1116yesdirect product factor
43C22×C3×C13⋊C3—71noHall
44C2×C3×C7×C11C2×C13⋊C311yescharacteristic, complemented
45C3×C11×D7C2×C13⋊C312yescomplemented
46C2×C11×ΓL(1,𝔽8)—133no—
47C11×AGL(1,𝔽7)—136no—
48C3×C11×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
49C11×C13⋊C3—73no—
50C22×C32×C11—911noHall
51C2×C13×D7C32×C1111yescharacteristic, complemented, Hall
52C2×C11×D7C3×C13⋊C311yescharacteristic, complemented, Hall
53C2×C11×C13—72no—
54C2×C11×C13C3×AGL(1,𝔽7)11yescharacteristic, complemented
55C3×C7×C13C22×C3×C1111yescharacteristic, complemented
56#63270C22×C3×C1113yescomplemented
57C2×C3×AGL(1,𝔽7)—131noHall
58C2×C3×C13⋊C3—72no—
59C2×C3×C13⋊C3—71no—
60C3×C7×C11C22×C13⋊C311yescharacteristic, complemented
61C11×ΓL(1,𝔽8)—133no—
62C2×C32×C11—912no—
63C2×C32×C11—911no—
64C2×C7×C13C2×C32×C1111yescharacteristic, complemented
65C13×D7C2×C32×C1112yescomplemented
66C22×C3×C13—71no—
67C22×C13⋊C3—73no—
68C2×C7×C11C2×C3×C13⋊C311yescharacteristic, complemented
69C11×D7C2×C3×C13⋊C312yescomplemented
70C11×C13C2×C3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
71C22×C3×C11—71no—
72C22×C3×C11—913no—
73C2×C3×ΓL(1,𝔽8)—131no—
74C3×AGL(1,𝔽7)—132no—
75C3×C13⋊C3—71noHall
76C32×C11—911noHall
77C7×C13C22×C32×C1111yescharacteristic, complemented, Hall
78C2×C3×D7C11×C13⋊C311yescharacteristic, complemented
79C2×AGL(1,𝔽7)—133no—
80C2×C3×C13—72no—
81C2×C3×C13C11×AGL(1,𝔽7)11yescharacteristic, complemented
82C2×C13⋊C3—76no—
83C2×C13⋊C3—73no—
84C7×C11C22×C3×C13⋊C311yescharacteristic, complemented, Hall
85C2×C3×C11—72no—
86C2×C3×C11—916no—
87C2×C3×C11—913no—
88C2×C3×C11#1058772011yescharacteristic, direct product factor
89C3×ΓL(1,𝔽8)—131noHall
90C22×C13—71noHall
91C22×C11—71noHall
92C2×C3×C7C2×C11×C13⋊C311yescharacteristic, complemented
93C3×D7C2×C11×C13⋊C312yescomplemented
94C2×ΓL(1,𝔽8)—133no—
95AGL(1,𝔽7)—136no—
96C3×C13C2×C11×AGL(1,𝔽7)11yescharacteristic, complemented
97C13⋊C3—73no—
98C22×C32—911noHall
99C3×C11—913no—
100C3×C11C2×#1058772011yescharacteristic, direct product factor
101C2×D7C3×C11×C13⋊C311yescharacteristic, complemented, Hall
102C2×C13—72no—
103C2×C13C3×C11×AGL(1,𝔽7)11yescharacteristic, complemented
104C2×C11—72no—
105C2×C11C3×#1058772011yescharacteristic, direct product factor
106C3×C7C22×C11×C13⋊C311yescharacteristic, complemented
107ΓL(1,𝔽8)—133no—
108C2×C32—912no—
109C2×C32—911no—
110C2×C7C2×C3×C11×C13⋊C311yescharacteristic, complemented
111D7C2×C3×C11×C13⋊C312yescomplemented
112C13C2×C3×C11×AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
113C22×C3—71no—
114C22×C3—913no—
115C11C2×C3×#1058772011yescharacteristic, direct product factor, Sylow
116C32—911noSylow
117C7C22×C3×C11×C13⋊C311yescharacteristic, complemented, Sylow
118C2×C3—72no—
119C2×C3—916no—
120C2×C3—913no—
121C2×C3C11×#1058772011yescharacteristic, direct product factor
122C22—71noSylow
123C3—913no—
124C3C2×C11×#1058772011yescharacteristic, direct product factor
125C2—72no—
126C2C3×C11×#1058772011yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11#10587720
commutator, cosocle, hypocenterC7×C13C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C2×C3×C11×#63270C2semidirect
2. C3×C11×#10587720C2direct (N × H)
3. C2×C3×C11×C13×D7C3semidirect
4. C2×C11×#10587720C3direct (N × H)
5. C3×C11×#63270C22semidirect
6. C11×#10587720C2×C3direct (N × H)
7. C3×C11×C13×D7C2×C3semidirect
8. C2×C11×#63270C2×C3semidirect
9. C2×C3×C7×C11×C13C2×C3semidirect
11. C2×C11×C13×D7C32semidirect
12. C2×C3×#10587720C11direct (N × H)
13. C11×#63270C22×C3semidirect
14. C3×C7×C11×C13C22×C3semidirect
18. C11×C13×D7C2×C32semidirect
19. C2×C7×C11×C13C2×C32semidirect
22. C2×C3×#63270C2×C11semidirect
23. C3×#10587720C2×C11direct (N × H)
27. C2×C3×C13×D7C3×C11semidirect
28. C2×#10587720C3×C11direct (N × H)
29. C7×C11×C13C22×C32semidirect
30. C2×C3×C11×D7C13⋊C3semidirect
33. C2×C3×C11×C13AGL(1,𝔽7)semidirect
36. C3×#63270C22×C11semidirect
39. C2×C3×C7×C13C2×C3×C11semidirect
40. C3×C13×D7C2×C3×C11semidirect
41. C2×#63270C2×C3×C11semidirect
42. #10587720C2×C3×C11direct (N × H)
44. C2×C3×C7×C11C2×C13⋊C3semidirect
45. C3×C11×D7C2×C13⋊C3semidirect
48. C3×C11×C13C2×AGL(1,𝔽7)semidirect
51. C2×C13×D7C32×C11semidirect
52. C2×C11×D7C3×C13⋊C3semidirect
54. C2×C11×C13C3×AGL(1,𝔽7)semidirect
55. C3×C7×C13C22×C3×C11semidirect
56. #63270C22×C3×C11semidirect
60. C3×C7×C11C22×C13⋊C3semidirect
64. C2×C7×C13C2×C32×C11semidirect
65. C13×D7C2×C32×C11semidirect
68. C2×C7×C11C2×C3×C13⋊C3semidirect
69. C11×D7C2×C3×C13⋊C3semidirect
70. C11×C13C2×C3×AGL(1,𝔽7)semidirect
77. C7×C13C22×C32×C11semidirect
78. C2×C3×D7C11×C13⋊C3semidirect
81. C2×C3×C13C11×AGL(1,𝔽7)semidirect
84. C7×C11C22×C3×C13⋊C3semidirect
88. C2×C3×C11#10587720direct (N × H)
92. C2×C3×C7C2×C11×C13⋊C3semidirect
93. C3×D7C2×C11×C13⋊C3semidirect
96. C3×C13C2×C11×AGL(1,𝔽7)semidirect
100. C3×C11C2×#10587720direct (N × H)
101. C2×D7C3×C11×C13⋊C3semidirect
103. C2×C13C3×C11×AGL(1,𝔽7)semidirect
105. C2×C11C3×#10587720direct (N × H)
106. C3×C7C22×C11×C13⋊C3semidirect
110. C2×C7C2×C3×C11×C13⋊C3semidirect
111. D7C2×C3×C11×C13⋊C3semidirect
112. C13C2×C3×C11×AGL(1,𝔽7)semidirect
115. C11C2×C3×#10587720direct (N × H)
117. C7C22×C3×C11×C13⋊C3semidirect
121. C2×C3C11×#10587720direct (N × H)
124. C3C2×C11×#10587720direct (N × H)
126. C2C3×C11×#10587720direct (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×#632702
C3×C11×#105877202
C2×C3×C11×C13×D73
C2×C11×#105877203
C22×C3×C11×C13⋊C37
C2×C3×#1058772011
C2×C3×C11×AGL(1,𝔽7)13