Finite Group Databasebeta

← C3×D7×D429 #49114921

Subgroups — C3×D7×D429 #49114921

Order 36036.

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C32×C11×C13×D7C211yesmaximal, characteristic, complemented
2C3×C7×D429C211yesmaximal, characteristic, complemented
3C3×D3003C211yesmaximal, characteristic, complemented
4D7×D429C311yesmaximal, characteristic, direct product factor
5C3×D7×D143—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7D3003C2×C311yescharacteristic, complemented
8C7×D429C2×C311yescharacteristic, complemented
9C3×D1001—31no—
10C3×C11×C13×D7—21no—
11C3×C11×C13×D7D311yescharacteristic, complemented
12C3×C11×C13×D7C2×C311yescharacteristic, complemented
13C3×C7×D143—31no—
14C2×C3×D429—71nomaximal, Hall
15D7×D143—31noHall
16C3×D7×D39—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D7×D33—131nomaximal, Hall
21C3×D429—71no—
22C3×D429D711yescharacteristic, direct product factor
23C2×C32×C11×C13—71no—
24D1001—31no—
25C11×C13×D7C3×D311yescharacteristic, complemented
26C7×D143—31no—
27C2×D429—71no—
28C2×C3×D143—211no—
29C3×D273—111no—
30C3×C7×D39—111no—
31C32×C13×D7D1111yescharacteristic, complemented
32C3×D231—131no—
33C3×C7×D33—131no—
34C32×C11×D7D1311yescharacteristic, complemented
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D7×D39—111no—
37C3×D7×D13—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D7×D33—131no—
40C3×D7×D11—391no—
41C2×C3×C11×C13—71no—
42C2×C3×C11×C13—71no—
43C2×C3×C11×C13—141no—
44D429—71no—
45D429C3×D711yescharacteristic, direct product factor
46C3×D143—31no—
47C3×D143—211no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×D143—211noHall
51D273—111no—
52C7×D39—111no—
53C3×D91—331no—
54C3×C13×D7—21no—
55C3×C13×D7C3×D1111yescharacteristic, complemented
56C3×C13×D7D3311yescharacteristic, complemented
57C3×C7×D13—331no—
58C2×C3×D39—771noHall
59D231—131no—
60C7×D33—131no—
61C3×D77—391no—
62C3×C11×D7—21no—
63C3×C11×D7C3×D1311yescharacteristic, complemented
64C3×C11×D7D3911yescharacteristic, complemented
65C3×C7×D11—391no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×C3×D711yescharacteristic, complemented
69C2×C3×D33—911noHall
70D7×D13—331noHall
71D7×D11—391noHall
72C2×C11×C13—71no—
73D143—31no—
74D143—211no—
75C3×C7×C13—21no—
76C3×C7×C13C2×C3×D1111yescharacteristic, complemented
77C3×C7×C13C2×D3311yescharacteristic, complemented
78C3×D3×D7—1431noHall
79C2×C32×C13—71no—
80C3×D39—111no—
81C3×D39—771no—
82C3×C7×C11—21no—
83C3×C7×C11C2×C3×D1311yescharacteristic, complemented
84C3×C7×C11C2×D3911yescharacteristic, complemented
85C2×C32×C11—71no—
86C3×D33—131no—
87C3×D33—911no—
88D91—331no—
89C7×D13—331no—
90C13×D7C3×D3311yescharacteristic, complemented
91C2×D39—771no—
92C2×C3×D13—2311no—
93D77—391no—
94C7×D11—391no—
95C11×D7C3×D3911yescharacteristic, complemented
96C11×C13C3×D3×D711yescharacteristic, complemented, Hall
97C2×D33—911no—
98C2×C3×D11—2731no—
99C3×D21—1431no—
100C3×D3×C7—1431no—
101C32×D7D14311yescharacteristic, complemented
102C32×C13D7×D1111yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13C2×C3×D3311yescharacteristic, complemented, Hall
105C2×C3×D7—4291no—
106D3×D7—1431no—
107C2×C3×C13—71no—
108C2×C3×C13—71no—
109C2×C3×C13—141no—
110D39—111no—
111D39—771no—
112C3×D13—331no—
113C3×D13—2311no—
114C7×C11C2×C3×D3911yescharacteristic, complemented, Hall
115C2×C3×C11—71no—
116C2×C3×C11—71no—
117C2×C3×C11—141no—
118D33—131no—
119D33—911no—
120C3×D11—2731no—
121C3×D11—391no—
122C32×C7C2×D14311yescharacteristic, complemented, Hall
123C2×D13—2311noHall
124C2×D11—2731noHall
125C2×C3×C7—4291no—
126D21—1431no—
127C3×D7—21no—
128C3×D7—4291no—
129C3×D7C3×D14311yescharacteristic, complemented
130C3×D7D42911yescharacteristic, direct product factor
131D3×C7—1431no—
132C3×C13—21no—
133C3×C13C3×D7×D1111yescharacteristic, complemented
134C3×C13D7×D3311yescharacteristic, complemented
135C2×C3×D3—10011noHall
136C3×C11—21no—
137C3×C11C3×D7×D1311yescharacteristic, complemented
138C3×C11D7×D3911yescharacteristic, complemented
139C2×D7—4291noHall
140C2×C13—71no—
141D13—331no—
142D13—2311no—
143C2×C11—71no—
144D11—2731no—
145D11—391no—
146C3×C7—21no—
147C3×C7C2×C3×D14311yescharacteristic, complemented
148C3×C7C2×D42911yescharacteristic, complemented
149C2×C32—71no—
150C3×D3—1431no—
151C3×D3—10011no—
152C2×C7—4291no—
153D7—4291no—
154D7C3×D42911yescharacteristic, direct product factor
155C13C3×D7×D3311yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—10011no—
158C11C3×D7×D3911yescharacteristic, complemented, Sylow
159C32D7×D14311yescharacteristic, complemented, Sylow
160C7C2×C3×D42911yescharacteristic, complemented, Sylow
161C2×C3—71no—
162C2×C3—71no—
163C2×C3—141no—
164C2×C3—4291no—
165C2×C3—30031no—
166D3—1431no—
167D3—10011no—
168C22—30031noSylow
169C3—21no—
170C3C3×D7×D14311yescharacteristic, complemented
171C3D7×D42911yescharacteristic, direct product factor
172C2—71no—
173C2—4291no—
174C2—30031no—
subgroupG/H
center, hypercenterC3D7×D429
commutator, cosocle, hypocenterC3×C7×C11×C13C22×C3
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C3×C7×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C11×C13×D7C2semidirect
2. C3×C7×D429C2semidirect
3. C3×D3003C2semidirect
4. D7×D429C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. D3003C2×C3semidirect
8. C7×D429C2×C3semidirect
11. C3×C11×C13×D7D3semidirect
12. C3×C11×C13×D7C2×C3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
22. C3×D429D7direct (N × H)
25. C11×C13×D7C3×D3semidirect
31. C32×C13×D7D11semidirect
34. C32×C11×D7D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13C2×C3×D3semidirect
45. D429C3×D7direct (N × H)
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
55. C3×C13×D7C3×D11semidirect
56. C3×C13×D7D33semidirect
63. C3×C11×D7C3×D13semidirect
64. C3×C11×D7D39semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×C3×D7semidirect
76. C3×C7×C13C2×C3×D11semidirect
77. C3×C7×C13C2×D33semidirect
83. C3×C7×C11C2×C3×D13semidirect
84. C3×C7×C11C2×D39semidirect
90. C13×D7C3×D33semidirect
95. C11×D7C3×D39semidirect
96. C11×C13C3×D3×D7semidirect
101. C32×D7D143semidirect
102. C32×C13D7×D11semidirect
103. C32×C11D7×D13semidirect
104. C7×C13C2×C3×D33semidirect
114. C7×C11C2×C3×D39semidirect
122. C32×C7C2×D143semidirect
129. C3×D7C3×D143semidirect
130. C3×D7D429direct (N × H)
133. C3×C13C3×D7×D11semidirect
134. C3×C13D7×D33semidirect
137. C3×C11C3×D7×D13semidirect
138. C3×C11D7×D39semidirect
147. C3×C7C2×C3×D143semidirect
148. C3×C7C2×D429semidirect
154. D7C3×D429direct (N × H)
155. C13C3×D7×D33semidirect
158. C11C3×D7×D39semidirect
159. C32D7×D143semidirect
160. C7C2×C3×D429semidirect
170. C3C3×D7×D143semidirect
171. C3D7×D429direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×C13×D72
C3×C7×D4292
C3×D30032
D7×D4293
C3×D7×D1433
C2×C3×D4297
C3×D7×D3911
C3×D7×D3313