Finite Group Databasebeta

← C11×(C3⋊(D13⋊C3))⋊D7 #49114794

Subgroups — C11×(C3⋊(D13⋊C3))⋊D7 #49114794

Order 36036.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C11×C13⋊C3×D21C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C11×(C13⋊C3)⋊D7C211yesmaximal, characteristic, complemented
4C11×D21⋊D13C311yesmaximal, characteristic, complemented
5C11×D7×D13⋊C3—31nomaximal
6C3×C7×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C11×(C13⋊C3)⋊D7—21no—
8C11×(C13⋊C3)⋊D7D311yescharacteristic, complemented
9C11×D7×C13⋊C3—31no—
10C7×C11×D13⋊C3—31no—
11C11×C13×D21C2×C311yescharacteristic, complemented
12C7×C11×D39C2×C311yescharacteristic, complemented
13C3×C11×D91C2×C311yescharacteristic, complemented
14D3×C11×D13⋊C3—71nomaximal, Hall
15C11×D7×D13—31noHall
16(C3⋊(D13⋊C3))⋊D7C1111yesmaximal, characteristic, direct product factor, Hall
17C7×C11×C13⋊C3—21no—
18C7×C11×C13⋊C3C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D3×C11×D7—131nomaximal, Hall
21D3×C11×C13⋊C3—71no—
22C11×C3⋊(D13⋊C3)D711yescharacteristic, complemented
23C3×C11×D13⋊C3—71no—
24C11×D91C3×D311yescharacteristic, complemented
25C11×C13×D7—31no—
26C7×C11×D13—31no—
27D3×C11×D13—71no—
28C2×C11×D13⋊C3—211no—
29C13⋊C3×D21C2×C1111yescharacteristic, complemented
30C7×C3⋊(D13⋊C3)C2×C1111yescharacteristic, complemented
31C3×(C13⋊C3)⋊D7C2×C1111yescharacteristic, complemented
32C3×C11×D21—131no—
33C3×D3×C7×C11—131no—
34C32×C11×D7—131no—
35C3×C11×C13⋊C3C2×D711yescharacteristic, complemented, Hall
36D21⋊D13C3×C1111yescharacteristic, complemented
37D7×D13⋊C3—31no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C3×C11×D7—391no—
40D3×C11×D7—131no—
41C11×D39C3×D711yescharacteristic, complemented
42D3×C11×C13—71no—
43C3×C11×D13—71no—
44C2×C11×C13⋊C3—211no—
45C11×D13⋊C3—31no—
46C11×D13⋊C3—71no—
47C11×D13⋊C3—141no—
48C3×C7×C13⋊C3C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11—131noHall
50C2×C11×D13—211noHall
51C13×D21C2×C3×C1111yescharacteristic, complemented
52C7×D39C2×C3×C1111yescharacteristic, complemented
53C3×D91C2×C3×C1111yescharacteristic, complemented
54(C13⋊C3)⋊D7—21no—
55(C13⋊C3)⋊D7D3×C1111yescharacteristic, complemented
56D7×C13⋊C3—31no—
57C7×D13⋊C3—31no—
58D3×D13⋊C3—71noHall
59C2×C3×C7×C11—391no—
60C11×D21D13⋊C311yescharacteristic, complemented
61D3×C7×C11—131no—
62C3×C11×D7—131no—
63C3×C11×D7—131no—
64C3×C11×D7—261no—
65C3×C11×D7—391no—
66C3×C11×C13C2×C3×D711yescharacteristic, complemented
67C11×C13⋊C3—21no—
68C11×C13⋊C3D3×D711yescharacteristic, complemented
69C2×C3×D3×C11—911noHall
70D7×D13—31noHall
71C2×C11×D7—391noHall
72C2×C11×C13—211no—
73C11×D13—31no—
74C11×D13—71no—
75C3×C7×C13C22×C3×C1111yescharacteristic, complemented
76C7×C13⋊C3—21no—
77C7×C13⋊C3C2×D3×C1111yescharacteristic, complemented
78C3×D3×D7—131noHall
79C3⋊(D13⋊C3)C11×D711yescharacteristic, complemented
80D3×C13⋊C3—71no—
81C3×D13⋊C3—71no—
82C3×C7×C11—131no—
83C3×C7×C11—261no—
84C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
85C2×C32×C11—911no—
86C3×D3×C11—131no—
87C3×D3×C11—911no—
88D91C3×D3×C1111yescharacteristic, complemented
89C7×D13—31no—
90C13×D7—31no—
91D3×D13—71no—
92C2×D13⋊C3—211no—
93C2×C7×C11—391no—
94C11×D7—31no—
95C11×D7—131no—
96C11×C13C3×D3×D711yescharacteristic, complemented, Hall
97C22×C3×C11—2731no—
98C2×D3×C11—911no—
99C3×D21—131no—
100C3×D3×C7—131no—
101C32×D7—131no—
102C3×C13⋊C3C2×C11×D711yescharacteristic, complemented, Hall
103C32×C11—131noHall
104C7×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
105C2×C3×D7—391no—
106D3×D7—131no—
107D39C3×C11×D711yescharacteristic, complemented
108C3×D13—71no—
109D3×C13—71no—
110C2×C13⋊C3—211no—
111D13⋊C3—31no—
112D13⋊C3—71no—
113D13⋊C3—141no—
114C7×C11D3×D13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116C2×C3×C11—391no—
117C2×C3×C11—911no—
118C2×C3×C11—911no—
119C2×C3×C11—1821no—
120D3×C11—71no—
121D3×C11—131no—
122C32×C7—131noHall
123C2×D13—211noHall
124C22×C11—2731noHall
125C2×C3×C7—391no—
126D21C11×D13⋊C311yescharacteristic, complemented
127C3×D7—131no—
128C3×D7—131no—
129C3×D7—261no—
130C3×D7—391no—
131D3×C7—131no—
132C3×C13C2×C3×C11×D711yescharacteristic, complemented
133C13⋊C3—21no—
134C13⋊C3D3×C11×D711yescharacteristic, complemented
135C2×C3×D3—911noHall
136C3×C11—131no—
137C3×C11—261no—
138C3×C11D7×D13⋊C311yescharacteristic, complemented
139C2×D7—391noHall
140C2×C13—211no—
141D13—31no—
142D13—71no—
143C2×C11—211no—
144C2×C11—391no—
145C2×C11—911no—
146C3×C7—131no—
147C3×C7—261no—
148C3×C7C2×C11×D13⋊C311yescharacteristic, complemented
149C2×C32—911no—
150C3×D3—131no—
151C3×D3—911no—
152C2×C7—391no—
153D7—31no—
154D7—131no—
155C13C3×D3×C11×D711yescharacteristic, complemented, Sylow
156C22×C3—2731no—
157C2×D3—911no—
158C11(C3⋊(D13⋊C3))⋊D711yescharacteristic, direct product factor, Sylow
159C32—131noSylow
160C7D3×C11×D13⋊C311yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—391no—
163C2×C3—911no—
164C2×C3—911no—
165C2×C3—1821no—
166D3—71no—
167D3—131no—
168C22—2731noSylow
169C3—131no—
170C3—261no—
171C3C11×D7×D13⋊C311yescharacteristic, complemented
172C2—211no—
173C2—391no—
174C2—911no—
subgroupG/H
center, hypercenterC11(C3⋊(D13⋊C3))⋊D7
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×C13⋊C3×D21C2semidirect
2. C7×C11×C3⋊(D13⋊C3)C2semidirect
3. C3×C11×(C13⋊C3)⋊D7C2semidirect
4. C11×D21⋊D13C3semidirect
6. C3×C7×C11×C13⋊C3C22semidirect
8. C11×(C13⋊C3)⋊D7D3semidirect
11. C11×C13×D21C2×C3semidirect
12. C7×C11×D39C2×C3semidirect
13. C3×C11×D91C2×C3semidirect
16. (C3⋊(D13⋊C3))⋊D7C11direct (N × H)
18. C7×C11×C13⋊C3C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
22. C11×C3⋊(D13⋊C3)D7semidirect
24. C11×D91C3×D3semidirect
29. C13⋊C3×D21C2×C11semidirect
30. C7×C3⋊(D13⋊C3)C2×C11semidirect
31. C3×(C13⋊C3)⋊D7C2×C11semidirect
35. C3×C11×C13⋊C3C2×D7semidirect
36. D21⋊D13C3×C11semidirect
38. C7×C11×C13C2×C3×D3semidirect
41. C11×D39C3×D7semidirect
48. C3×C7×C13⋊C3C22×C11semidirect
51. C13×D21C2×C3×C11semidirect
52. C7×D39C2×C3×C11semidirect
53. C3×D91C2×C3×C11semidirect
55. (C13⋊C3)⋊D7D3×C11semidirect
60. C11×D21D13⋊C3semidirect
66. C3×C11×C13C2×C3×D7semidirect
68. C11×C13⋊C3D3×D7semidirect
75. C3×C7×C13C22×C3×C11semidirect
77. C7×C13⋊C3C2×D3×C11semidirect
79. C3⋊(D13⋊C3)C11×D7semidirect
84. C3×C7×C11C2×D13⋊C3semidirect
88. D91C3×D3×C11semidirect
96. C11×C13C3×D3×D7semidirect
102. C3×C13⋊C3C2×C11×D7semidirect
104. C7×C13C2×C3×D3×C11semidirect
107. D39C3×C11×D7semidirect
114. C7×C11D3×D13⋊C3semidirect
126. D21C11×D13⋊C3semidirect
132. C3×C13C2×C3×C11×D7semidirect
134. C13⋊C3D3×C11×D7semidirect
138. C3×C11D7×D13⋊C3semidirect
148. C3×C7C2×C11×D13⋊C3semidirect
155. C13C3×D3×C11×D7semidirect
158. C11(C3⋊(D13⋊C3))⋊D7direct (N × H)
160. C7D3×C11×D13⋊C3semidirect
171. C3C11×D7×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11×C13⋊C3×D212
C7×C11×C3⋊(D13⋊C3)2
C3×C11×(C13⋊C3)⋊D72
C11×D21⋊D133
C11×D7×D13⋊C33
D3×C11×D13⋊C37
(C3⋊(D13⋊C3))⋊D711
C3×D3×C11×D713