Finite Group Databasebeta

← D77×C3⋊(D13⋊C3) #49114800

Subgroups — D77×C3⋊(D13⋊C3) #49114800

Order 36036.

176 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 42 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⋊(C11⋊((C13⋊C3)⋊D7))C211yesmaximal, characteristic, complemented
2C7×C11×C3⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C13⋊C3×D77C211yesmaximal, characteristic, complemented
4D39×D77C311yesmaximal, characteristic, complemented
5D13⋊C3×D77—31nomaximal
6C3×C7×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C11⋊((C13⋊C3)⋊D7)—31no—
8C13⋊C3×D77—21no—
9C13⋊C3×D77D311yescharacteristic, complemented
10C7×C11×D13⋊C3—31no—
11D3003C2×C311yescharacteristic, complemented
12C7×C11×D39C2×C311yescharacteristic, complemented
13C3×C13×D77C2×C311yescharacteristic, complemented
14D11×C3⋊(D13⋊C3)—71nomaximal, Hall
15D13×D77—31noHall
16D7×C3⋊(D13⋊C3)—111nomaximal, Hall
17C7×C11×C13⋊C3—21no—
18C7×C11×C13⋊C3C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D3×D77—131nomaximal, Hall
21C3⋊(C11⋊(D13⋊C3))—71no—
22C11×C3⋊(D13⋊C3)D711yescharacteristic, complemented
23C3×D11×C13⋊C3—71no—
24D1001—31no—
25C13×D77C3×D311yescharacteristic, complemented
26C7×C11×D13—31no—
27D11×D39—71no—
28D11×D13⋊C3—211no—
29C3⋊((C13⋊C3)⋊D7)—111no—
30C7×C3⋊(D13⋊C3)D1111yescharacteristic, complemented
31C3×D7×C13⋊C3—111no—
32C3×D231—131no—
33C3×D3×C7×C11—131no—
34C32×D77—131no—
35C3×C11×C13⋊C3C2×D711yescharacteristic, complemented, Hall
36D7×D39—111no—
37D7×D13⋊C3—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C3×D77—391no—
40D3×D77—131no—
41D429—71no—
42C11×D39C3×D711yescharacteristic, complemented
43C3×C13×D11—71no—
44C11⋊(D13⋊C3)—211no—
45D11×C13⋊C3—71no—
46D11×C13⋊C3—141no—
47C11×D13⋊C3—31no—
48C3×C7×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11—131noHall
50D11×D13—211noHall
51D273—111no—
52C7×D39C3×D1111yescharacteristic, complemented
53C3×C13×D7—111no—
54(C13⋊C3)⋊D7—331no—
55D7×C13⋊C3—111no—
56D7×C13⋊C3—221no—
57C7×D13⋊C3—31no—
58C2×C3⋊(D13⋊C3)—771noHall
59C2×C3×C7×C11—391no—
60D231—131no—
61D3×C7×C11—131no—
62C3×D77—131no—
63C3×D77—261no—
64C3×D77—391no—
65C3×D77D13⋊C311yescharacteristic, complemented
66C3×C11×C13C2×C3×D711yescharacteristic, complemented
67C11×C13⋊C3—21no—
68C11×C13⋊C3D3×D711yescharacteristic, complemented
69C3×D3×D11—911noHall
70D7×D13—331noHall
71C2×D77—391noHall
72D143—211no—
73C11×D13—31no—
74C13×D11—71no—
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76C7×C13⋊C3—21no—
77C7×C13⋊C3D3×D1111yescharacteristic, complemented
78C3×D3×D7—1431noHall
79C2×C3×C13⋊C3—771no—
80C3⋊(D13⋊C3)—771no—
81C3⋊(D13⋊C3)D7711yescharacteristic, direct product factor
82C3×C7×C11—131no—
83C3×C7×C11—261no—
84C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
85C3×D33—911no—
86C3×D3×C11—131no—
87C32×D11—911no—
88D91—331no—
89C7×D13—31no—
90C13×D7—111no—
91C2×D39—771no—
92C2×D13⋊C3—2311no—
93C2×C7×C11—391no—
94D77—391no—
95D77C3⋊(D13⋊C3)11yescharacteristic, direct product factor
96C11×C13C3×D3×D711yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11—911no—
99C3×D21—1431no—
100C3×D3×C7—131no—
101C32×D7—1431no—
102C3×C13⋊C3C2×D7711yescharacteristic, complemented, Hall
103C32×C11—131noHall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105C2×C3×D7—4291no—
106D3×D7—1431no—
107C2×C3×C13—771no—
108D39—771no—
109D39C3×D7711yescharacteristic, complemented
110C2×C13⋊C3—771no—
111C2×C13⋊C3—1541no—
112D13⋊C3—31no—
113D13⋊C3—2311no—
114C7×C11C2×C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
115C2×C3×C11—391no—
116D33—911no—
117C3×D11—71no—
118C3×D11—2731no—
119C3×D11—911no—
120C3×D11—1821no—
121D3×C11—131no—
122C32×C7—131noHall
123C2×D13—2311noHall
124C2×D11—2731noHall
125C2×C3×C7—391no—
126D21—1431no—
127C3×D7—111no—
128C3×D7—2861no—
129C3×D7—1431no—
130C3×D7—4291no—
131D3×C7—131no—
132C3×C13C2×C3×D7711yescharacteristic, complemented
133C13⋊C3—21no—
134C13⋊C3D3×D7711yescharacteristic, complemented
135C2×C3×D3—10011noHall
136C3×C11—131no—
137C3×C11—261no—
138C3×C11D7×D13⋊C311yescharacteristic, complemented
139C2×D7—4291noHall
140C2×C13—771no—
141D13—31no—
142D13—2311no—
143C2×C11—391no—
144D11—71no—
145D11—2731no—
146C3×C7—131no—
147C3×C7—261no—
148C3×C7D11×D13⋊C311yescharacteristic, complemented
149C2×C32—10011no—
150C3×D3—131no—
151C3×D3—10011no—
152C2×C7—391no—
153D7—111no—
154D7—4291no—
155C13C3×D3×D7711yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—10011no—
158C11D7×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
159C32—131noSylow
160C7D11×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
161C2×C3—391no—
162C2×C3—771no—
163C2×C3—30031no—
164C2×C3—20021no—
165C2×C3—10011no—
166D3—131no—
167D3—10011no—
168C22—30031noSylow
169C3—131no—
170C3—261no—
171C3D13⋊C3×D7711yescharacteristic, complemented
172C2—391no—
173C2—771no—
174C2—30031no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C22×C3
LCSG ▷ C3×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C11⋊((C13⋊C3)⋊D7))C2semidirect
2. C7×C11×C3⋊(D13⋊C3)C2semidirect
3. C3×C13⋊C3×D77C2semidirect
4. D39×D77C3semidirect
6. C3×C7×C11×C13⋊C3C22semidirect
9. C13⋊C3×D77D3semidirect
11. D3003C2×C3semidirect
12. C7×C11×D39C2×C3semidirect
13. C3×C13×D77C2×C3semidirect
18. C7×C11×C13⋊C3C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
22. C11×C3⋊(D13⋊C3)D7semidirect
25. C13×D77C3×D3semidirect
30. C7×C3⋊(D13⋊C3)D11semidirect
35. C3×C11×C13⋊C3C2×D7semidirect
38. C7×C11×C13C2×C3×D3semidirect
42. C11×D39C3×D7semidirect
48. C3×C7×C13⋊C3C2×D11semidirect
52. C7×D39C3×D11semidirect
65. C3×D77D13⋊C3semidirect
66. C3×C11×C13C2×C3×D7semidirect
68. C11×C13⋊C3D3×D7semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. C7×C13⋊C3D3×D11semidirect
81. C3⋊(D13⋊C3)D77direct (N × H)
84. C3×C7×C11C2×D13⋊C3semidirect
95. D77C3⋊(D13⋊C3)direct (N × H)
96. C11×C13C3×D3×D7semidirect
102. C3×C13⋊C3C2×D77semidirect
104. C7×C13C3×D3×D11semidirect
109. D39C3×D77semidirect
114. C7×C11C2×C3⋊(D13⋊C3)semidirect
132. C3×C13C2×C3×D77semidirect
134. C13⋊C3D3×D77semidirect
138. C3×C11D7×D13⋊C3semidirect
148. C3×C7D11×D13⋊C3semidirect
155. C13C3×D3×D77semidirect
158. C11D7×C3⋊(D13⋊C3)semidirect
160. C7D11×C3⋊(D13⋊C3)semidirect
171. C3D13⋊C3×D77semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C11⋊((C13⋊C3)⋊D7))2
C7×C11×C3⋊(D13⋊C3)2
C3×C13⋊C3×D772
D39×D773
D13⋊C3×D773
D11×C3⋊(D13⋊C3)7
D7×C3⋊(D13⋊C3)11
C3×D3×D7713