Finite Group Databasebeta

← C2×C3×C11×#10587716 #49114832

Subgroups — C2×C3×C11×#10587716 #49114832

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×#10587716C212yesmaximal, direct product factor
3C2×C3×C7×C11×D13C311yesmaximal, characteristic, complemented
4C2×C11×#10587716C313yesmaximal, direct product factor
5C3×C11×#63270C2211yescharacteristic, complemented, Hall
6C11×#10587716C2×C316yesdirect product factor
7C3×C7×C11×D13C2×C312yescomplemented
8C2×C11×#63270C2×C313yescomplemented
9C2×C3×C7×C11×C13C2×C311yescharacteristic, complemented
10C2×C3×C11×D13⋊C3—71nomaximal, Hall
11C2×C7×C11×D13C3211yescharacteristic, complemented, Hall
12C2×C3×#10587716C1111yesmaximal, characteristic, direct product factor, Hall
13C11×#63270C22×C313yescomplemented
14C3×C7×C11×C13C22×C311yescharacteristic, complemented
15C22×C3×C11×ΓL(1,𝔽8)—131nomaximal, Hall
16C2×C3×C11×C13⋊C3—71no—
17C3×C11×D13⋊C3—72no—
18C7×C11×D13C2×C3212yescomplemented
19C2×C7×C11×C13C2×C3211yescharacteristic, complemented
20C2×C3×C11×D13ΓL(1,𝔽8)11yescharacteristic, complemented
21C2×C11×D13⋊C3—73no—
22C2×C3×#63270C2×C1111yescharacteristic, complemented
23C3×#10587716C2×C1112yesdirect product factor
24C2×C3×C11×ΓL(1,𝔽8)—132no—
25C2×C3×C11×ΓL(1,𝔽8)—131no—
26C3×C11×C13⋊C3—71noHall
27C2×C3×C7×D13C3×C1111yescharacteristic, complemented
28C2×#10587716C3×C1113yesdirect product factor
29C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
30C22×C3×C7×C11—131no—
31C22×C11×ΓL(1,𝔽8)—133no—
32C2×C3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented
33C3×C11×D13C2×ΓL(1,𝔽8)12yescomplemented
34C2×C11×C13⋊C3—73no—
35C11×D13⋊C3—76no—
36C3×#63270C22×C1111yescharacteristic, complemented, Hall
37C3×C11×ΓL(1,𝔽8)—131noHall
38C2×C11×D13C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
39C2×C3×C7×C13C2×C3×C1111yescharacteristic, complemented
40C3×C7×D13C2×C3×C1112yescomplemented
41C2×#63270C2×C3×C1113yescomplemented
42#10587716C2×C3×C1116yesdirect product factor
43C2×C3×D13⋊C3—71noHall
44C2×C3×C7×C11—132no—
45C2×C3×C7×C11D13⋊C311yescharacteristic, complemented
46C2×C11×ΓL(1,𝔽8)—136no—
47C2×C11×ΓL(1,𝔽8)—133no—
48C3×C11×C13C22×ΓL(1,𝔽8)11yescharacteristic, complemented
49C11×C13⋊C3—73no—
50C22×C32×C11—911noHall
51C2×C7×D13C32×C1111yescharacteristic, complemented, Hall
52C22×C7×C11—131noHall
53C2×C11×C13C2×C3×ΓL(1,𝔽8)11yescharacteristic, complemented
54C11×D13C2×C3×ΓL(1,𝔽8)12yescomplemented
55C3×C7×C13C22×C3×C1111yescharacteristic, complemented
56#63270C22×C3×C1113yescomplemented
57C22×C3×ΓL(1,𝔽8)—131noHall
58C2×C3×C13⋊C3—71no—
59C3×D13⋊C3—72no—
60C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
61C11×ΓL(1,𝔽8)—133no—
62C2×C32×C11—912no—
63C2×C32×C11—911no—
64C2×C7×C13C2×C32×C1111yescharacteristic, complemented
65C7×D13C2×C32×C1112yescomplemented
66C2×C3×D13C11×ΓL(1,𝔽8)11yescharacteristic, complemented
67C2×D13⋊C3—73no—
68C2×C7×C11—132no—
69C2×C7×C11C3×D13⋊C311yescharacteristic, complemented
70C11×C13C22×C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
71C22×C3×C11—131no—
72C22×C3×C11—913no—
73C2×C3×ΓL(1,𝔽8)—132no—
74C2×C3×ΓL(1,𝔽8)—131no—
75C3×C13⋊C3—71noHall
76C32×C11—911noHall
77C7×C13C22×C32×C1111yescharacteristic, complemented, Hall
78C22×C3×C7—131no—
79C22×ΓL(1,𝔽8)—133no—
80C2×C3×C13C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
81C3×D13C2×C11×ΓL(1,𝔽8)12yescomplemented
82C2×C13⋊C3—73no—
83D13⋊C3—76no—
84C7×C11C2×C3×D13⋊C311yescharacteristic, complemented, Hall
85C2×C3×C11—132no—
86C2×C3×C11—916no—
87C2×C3×C11—913no—
88C2×C3×C11#1058771611yescharacteristic, direct product factor
89C3×ΓL(1,𝔽8)—131noHall
90C2×D13C3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
91C22×C11—131noHall
92C2×C3×C7—132no—
93C2×C3×C7C11×D13⋊C311yescharacteristic, complemented
94C2×ΓL(1,𝔽8)—136no—
95C2×ΓL(1,𝔽8)—133no—
96C3×C13C22×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
97C13⋊C3—73no—
98C22×C32—911noHall
99C3×C11—913no—
100C3×C11C2×#1058771611yescharacteristic, direct product factor
101C22×C7—131noHall
102C2×C13C2×C3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
103D13C2×C3×C11×ΓL(1,𝔽8)12yescomplemented
104C2×C11—132no—
105C2×C11C3×#1058771611yescharacteristic, direct product factor
106C3×C7C2×C11×D13⋊C311yescharacteristic, complemented
107ΓL(1,𝔽8)—133no—
108C2×C32—912no—
109C2×C32—911no—
110C2×C7—132no—
111C2×C7C3×C11×D13⋊C311yescharacteristic, complemented
112C13C22×C3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
113C22×C3—131no—
114C22×C3—913no—
115C11C2×C3×#1058771611yescharacteristic, direct product factor, Sylow
116C32—911noSylow
117C7C2×C3×C11×D13⋊C311yescharacteristic, complemented, Sylow
118C2×C3—132no—
119C2×C3—916no—
120C2×C3—913no—
121C2×C3C11×#1058771611yescharacteristic, direct product factor
122C22—131noSylow
123C3—913no—
124C3C2×C11×#1058771611yescharacteristic, direct product factor
125C2—132no—
126C2C3×C11×#1058771611yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11#10587716
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×#10587716C2direct (N × H)
3. C2×C3×C7×C11×D13C3semidirect
4. C2×C11×#10587716C3direct (N × H)
5. C3×C11×#63270C22semidirect
6. C11×#10587716C2×C3direct (N × H)
7. C3×C7×C11×D13C2×C3semidirect
8. C2×C11×#63270C2×C3semidirect
9. C2×C3×C7×C11×C13C2×C3semidirect
11. C2×C7×C11×D13C32semidirect
12. C2×C3×#10587716C11direct (N × H)
13. C11×#63270C22×C3semidirect
14. C3×C7×C11×C13C22×C3semidirect
18. C7×C11×D13C2×C32semidirect
19. C2×C7×C11×C13C2×C32semidirect
20. C2×C3×C11×D13ΓL(1,𝔽8)semidirect
22. C2×C3×#63270C2×C11semidirect
23. C3×#10587716C2×C11direct (N × H)
27. C2×C3×C7×D13C3×C11semidirect
28. C2×#10587716C3×C11direct (N × H)
29. C7×C11×C13C22×C32semidirect
32. C2×C3×C11×C13C2×ΓL(1,𝔽8)semidirect
33. C3×C11×D13C2×ΓL(1,𝔽8)semidirect
36. C3×#63270C22×C11semidirect
38. C2×C11×D13C3×ΓL(1,𝔽8)semidirect
39. C2×C3×C7×C13C2×C3×C11semidirect
40. C3×C7×D13C2×C3×C11semidirect
41. C2×#63270C2×C3×C11semidirect
42. #10587716C2×C3×C11direct (N × H)
45. C2×C3×C7×C11D13⋊C3semidirect
48. C3×C11×C13C22×ΓL(1,𝔽8)semidirect
51. C2×C7×D13C32×C11semidirect
53. C2×C11×C13C2×C3×ΓL(1,𝔽8)semidirect
54. C11×D13C2×C3×ΓL(1,𝔽8)semidirect
55. C3×C7×C13C22×C3×C11semidirect
56. #63270C22×C3×C11semidirect
60. C3×C7×C11C2×D13⋊C3semidirect
64. C2×C7×C13C2×C32×C11semidirect
65. C7×D13C2×C32×C11semidirect
66. C2×C3×D13C11×ΓL(1,𝔽8)semidirect
69. C2×C7×C11C3×D13⋊C3semidirect
70. C11×C13C22×C3×ΓL(1,𝔽8)semidirect
77. C7×C13C22×C32×C11semidirect
80. C2×C3×C13C2×C11×ΓL(1,𝔽8)semidirect
81. C3×D13C2×C11×ΓL(1,𝔽8)semidirect
84. C7×C11C2×C3×D13⋊C3semidirect
88. C2×C3×C11#10587716direct (N × H)
90. C2×D13C3×C11×ΓL(1,𝔽8)semidirect
93. C2×C3×C7C11×D13⋊C3semidirect
96. C3×C13C22×C11×ΓL(1,𝔽8)semidirect
100. C3×C11C2×#10587716direct (N × H)
102. C2×C13C2×C3×C11×ΓL(1,𝔽8)semidirect
103. D13C2×C3×C11×ΓL(1,𝔽8)semidirect
105. C2×C11C3×#10587716direct (N × H)
106. C3×C7C2×C11×D13⋊C3semidirect
111. C2×C7C3×C11×D13⋊C3semidirect
112. C13C22×C3×C11×ΓL(1,𝔽8)semidirect
115. C11C2×C3×#10587716direct (N × H)
117. C7C2×C3×C11×D13⋊C3semidirect
121. C2×C3C11×#10587716direct (N × H)
124. C3C2×C11×#10587716direct (N × H)
126. C2C3×C11×#10587716direct (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×#105877162
C2×C3×C7×C11×D133
C2×C11×#105877163
C2×C3×C11×D13⋊C37
C2×C3×#1058771611
C22×C3×C11×ΓL(1,𝔽8)13