Finite Group Databasebeta

← C3×C7×D11×D13⋊C3 #49114638

Subgroups — C3×C7×D11×D13⋊C3 #49114638

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
1C3×C7×D11×C13⋊C3C211yesmaximal, characteristic, complemented
2C3×C7×C11⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C7×C11×D13⋊C3C211yesmaximal, characteristic, complemented
4C3×C7×D11×D13C311yesmaximal, characteristic, complemented
5C7×D11×D13⋊C3C313yesmaximal, direct product factor
6C3×C7×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C7×C11⋊(D13⋊C3)C2×C313yescomplemented
8C7×D11×C13⋊C3C2×C313yescomplemented
9C7×C11×D13⋊C3C2×C313yescomplemented
10C3×C7×D143C2×C311yescharacteristic, complemented
11C3×C7×C13×D11C2×C311yescharacteristic, complemented
12C3×C7×C11×D13C2×C311yescharacteristic, complemented
13C3×D11×D13⋊C3C711yesmaximal, characteristic, direct product factor, Hall
14C7×D11×D13C3211yescharacteristic, complemented, Hall
15C2×C3×C7×D13⋊C3—111nomaximal, Hall
16C7×C11×C13⋊C3C22×C313yescomplemented
17C3×C7×C11×C13C22×C311yescharacteristic, complemented
18C2×C32×C7×D11—131nomaximal, Hall
19C3×D11×C13⋊C3C2×C711yescharacteristic, complemented
20C3×C11⋊(D13⋊C3)C2×C711yescharacteristic, complemented
21C3×C11×D13⋊C3C2×C711yescharacteristic, complemented
22C7×D143C2×C3211yescharacteristic, complemented
23C7×C13×D11C2×C3211yescharacteristic, complemented
24C7×C11×D13C2×C3211yescharacteristic, complemented
25C3×D11×D13C3×C711yescharacteristic, complemented
26D11×D13⋊C3C3×C713yesdirect product factor
27C2×C3×C7×C13⋊C3—111no—
28C3×C7×D13⋊C3—111no—
29C3×C7×D13⋊C3D1111yescharacteristic, direct product factor
30C2×C32×C7×C11—131no—
31C32×C7×D11—131no—
32C32×C7×D11—131no—
33C3×C11×C13⋊C3C22×C711yescharacteristic, complemented, Hall
34C2×C3×C7×D13—111no—
35C2×C7×D13⋊C3—113no—
36C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
37C2×C3×C7×D11—133no—
38C2×C3×C7×D11—131no—
39C3×D143C2×C3×C711yescharacteristic, complemented
40C3×C13×D11C2×C3×C711yescharacteristic, complemented
41C3×C11×D13C2×C3×C711yescharacteristic, complemented
42C11⋊(D13⋊C3)C2×C3×C713yescomplemented
43D11×C13⋊C3C2×C3×C713yescomplemented
44C11×D13⋊C3C2×C3×C713yescomplemented
45C3×C7×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
46C32×C7×C11—131noHall
47D11×D13C32×C711yescharacteristic, complemented, Hall
48C2×C3×C7×C13—111no—
49C3×C7×D13—111no—
50C3×C7×D13C3×D1111yescharacteristic, complemented
51C2×C7×C13⋊C3—113no—
52C7×D13⋊C3—113no—
53C7×D13⋊C3C3×D1113yesdirect product factor
54C2×C3×D13⋊C3—111noHall
55C2×C3×C7×C11—133no—
56C2×C3×C7×C11—131no—
57C3×C7×D11—133no—
58C3×C7×D11—131no—
59C3×C7×D11—133no—
60C3×C7×D11D13⋊C311yescharacteristic, direct product factor
61C3×C11×C13C22×C3×C711yescharacteristic, complemented
62C11×C13⋊C3C22×C3×C713yescomplemented
63C2×C32×D11—131noHall
64C2×C7×D13—111noHall
65C2×C7×D11—131noHall
66D143C2×C32×C711yescharacteristic, complemented
67C11×D13C2×C32×C711yescharacteristic, complemented
68C13×D11C2×C32×C711yescharacteristic, complemented
69C3×C7×C13C2×C3×D1111yescharacteristic, complemented
70C7×C13⋊C3C2×C3×D1113yescomplemented
71C22×C32×C7—1431noHall
72C2×C3×C13⋊C3—111no—
73C3×D13⋊C3—111no—
74C3×D13⋊C3C7×D1111yescharacteristic, direct product factor
75C3×C7×C11—133no—
76C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
77C2×C32×C11—131no—
78C32×D11—131no—
79C32×D11—131no—
80C2×C7×C13—111no—
81C7×D13—111no—
82C7×D13C32×D1111yescharacteristic, complemented
83C2×C3×D13—111no—
84C2×D13⋊C3—113no—
85C2×C7×C11—131no—
86C7×D11—131no—
87C7×D11C3×D13⋊C311yescharacteristic, direct product factor
88C11×C13C22×C32×C711yescharacteristic, complemented, Hall
89C2×C3×D11—133no—
90C2×C3×D11—131no—
91C2×C32×C7—131no—
92C2×C32×C7—1431no—
93C2×C32×C7—1431no—
94C3×C13⋊C3C2×C7×D1111yescharacteristic, complemented, Hall
95C32×C11—131noHall
96C7×C13C2×C32×D1111yescharacteristic, complemented, Hall
97C22×C3×C7—1431no—
98C22×C3×C7—1433no—
99C2×C3×C13—111no—
100C3×D13—111no—
101C3×D13C3×C7×D1111yescharacteristic, complemented
102C2×C13⋊C3—113no—
103D13⋊C3—113no—
104D13⋊C3C3×C7×D1113yesdirect product factor
105C7×C11C2×C3×D13⋊C311yescharacteristic, complemented, Hall
106C2×C3×C11—133no—
107C2×C3×C11—131no—
108C3×D11—133no—
109C3×D11—131no—
110C3×D11—133no—
111C3×D11C7×D13⋊C311yescharacteristic, direct product factor
112C32×C7—131noHall
113C2×D13—111noHall
114C2×D11—131noHall
115C2×C3×C7—111no—
116C2×C3×C7—133no—
117C2×C3×C7—131no—
118C2×C3×C7—1433no—
119C2×C3×C7—1433no—
120C2×C3×C7—1431no—
121C3×C13C2×C3×C7×D1111yescharacteristic, complemented
122C13⋊C3C2×C3×C7×D1113yescomplemented
123C22×C32—1431noHall
124C3×C11—133no—
125C3×C11C2×C7×D13⋊C311yescharacteristic, complemented
126C22×C7—1431noHall
127C2×C13—111no—
128D13—111no—
129D13C32×C7×D1111yescharacteristic, complemented
130C2×C11—131no—
131D11—131no—
132D11C3×C7×D13⋊C311yescharacteristic, direct product factor
133C3×C7—133no—
134C3×C7D11×D13⋊C311yescharacteristic, direct product factor
135C2×C32—131no—
136C2×C32—1431no—
137C2×C32—1431no—
138C2×C7—111no—
139C2×C7—131no—
140C2×C7—1431no—
141C13C2×C32×C7×D1111yescharacteristic, complemented, Sylow
142C22×C3—1431no—
143C22×C3—1433no—
144C11C2×C3×C7×D13⋊C311yescharacteristic, complemented, Sylow
145C32—131noSylow
146C7C3×D11×D13⋊C311yescharacteristic, direct product factor, Sylow
147C2×C3—111no—
148C2×C3—133no—
149C2×C3—131no—
150C2×C3—1433no—
151C2×C3—1433no—
152C2×C3—1431no—
153C22—1431noSylow
154C3—133no—
155C3C7×D11×D13⋊C311yescharacteristic, direct product factor
156C2—111no—
157C2—131no—
158C2—1431no—
subgroupG/H
center, hypercenterC3×C7D11×D13⋊C3
commutator, cosocle, hypocenterC11×C13C22×C32×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22×C3
LCSG ▷ C11×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×D11×C13⋊C3C2semidirect
2. C3×C7×C11⋊(D13⋊C3)C2semidirect
3. C3×C7×C11×D13⋊C3C2semidirect
4. C3×C7×D11×D13C3semidirect
5. C7×D11×D13⋊C3C3direct (N × H)
6. C3×C7×C11×C13⋊C3C22semidirect
7. C7×C11⋊(D13⋊C3)C2×C3semidirect
8. C7×D11×C13⋊C3C2×C3semidirect
9. C7×C11×D13⋊C3C2×C3semidirect
10. C3×C7×D143C2×C3semidirect
11. C3×C7×C13×D11C2×C3semidirect
12. C3×C7×C11×D13C2×C3semidirect
13. C3×D11×D13⋊C3C7direct (N × H)
14. C7×D11×D13C32semidirect
16. C7×C11×C13⋊C3C22×C3semidirect
17. C3×C7×C11×C13C22×C3semidirect
19. C3×D11×C13⋊C3C2×C7semidirect
20. C3×C11⋊(D13⋊C3)C2×C7semidirect
21. C3×C11×D13⋊C3C2×C7semidirect
22. C7×D143C2×C32semidirect
23. C7×C13×D11C2×C32semidirect
24. C7×C11×D13C2×C32semidirect
25. C3×D11×D13C3×C7semidirect
26. D11×D13⋊C3C3×C7direct (N × H)
29. C3×C7×D13⋊C3D11direct (N × H)
33. C3×C11×C13⋊C3C22×C7semidirect
36. C7×C11×C13C22×C32semidirect
39. C3×D143C2×C3×C7semidirect
40. C3×C13×D11C2×C3×C7semidirect
41. C3×C11×D13C2×C3×C7semidirect
42. C11⋊(D13⋊C3)C2×C3×C7semidirect
43. D11×C13⋊C3C2×C3×C7semidirect
44. C11×D13⋊C3C2×C3×C7semidirect
45. C3×C7×C13⋊C3C2×D11semidirect
47. D11×D13C32×C7semidirect
50. C3×C7×D13C3×D11semidirect
53. C7×D13⋊C3C3×D11direct (N × H)
60. C3×C7×D11D13⋊C3direct (N × H)
61. C3×C11×C13C22×C3×C7semidirect
62. C11×C13⋊C3C22×C3×C7semidirect
66. D143C2×C32×C7semidirect
67. C11×D13C2×C32×C7semidirect
68. C13×D11C2×C32×C7semidirect
69. C3×C7×C13C2×C3×D11semidirect
70. C7×C13⋊C3C2×C3×D11semidirect
74. C3×D13⋊C3C7×D11direct (N × H)
76. C3×C7×C11C2×D13⋊C3semidirect
82. C7×D13C32×D11semidirect
87. C7×D11C3×D13⋊C3direct (N × H)
88. C11×C13C22×C32×C7semidirect
94. C3×C13⋊C3C2×C7×D11semidirect
96. C7×C13C2×C32×D11semidirect
101. C3×D13C3×C7×D11semidirect
104. D13⋊C3C3×C7×D11direct (N × H)
105. C7×C11C2×C3×D13⋊C3semidirect
111. C3×D11C7×D13⋊C3direct (N × H)
121. C3×C13C2×C3×C7×D11semidirect
122. C13⋊C3C2×C3×C7×D11semidirect
125. C3×C11C2×C7×D13⋊C3semidirect
129. D13C32×C7×D11semidirect
132. D11C3×C7×D13⋊C3direct (N × H)
134. C3×C7D11×D13⋊C3direct (N × H)
141. C13C2×C32×C7×D11semidirect
144. C11C2×C3×C7×D13⋊C3semidirect
146. C7C3×D11×D13⋊C3direct (N × H)
155. C3C7×D11×D13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×D11×C13⋊C32
C3×C7×C11⋊(D13⋊C3)2
C3×C7×C11×D13⋊C32
C3×C7×D11×D133
C7×D11×D13⋊C33
C3×D11×D13⋊C37
C2×C3×C7×D13⋊C311
C2×C32×C7×D1113