Finite Group Databasebeta

← C3×D143⋊D21 #49114915

Subgroups — C3×D143⋊D21 #49114915

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
1C32×C7×D143C211yesmaximal, characteristic, complemented
2C3×C11×D273C211yesmaximal, characteristic, complemented
3C3×C13×D231C211yesmaximal, characteristic, complemented
4D143⋊D21C311yesmaximal, characteristic, direct product factor
5C3×D77⋊D13—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C13×D231C2×C311yescharacteristic, complemented
8C11×D273C2×C311yescharacteristic, complemented
9C3×C13×D77—31no—
10C3×C11×D91—31no—
11C3×C7×D143—21no—
12C3×C7×D143D311yescharacteristic, complemented
13C3×C7×D143C2×C311yescharacteristic, complemented
14C3×D33⋊D13—71nomaximal, Hall
15D77⋊D13—31noHall
16C3×D13×D21—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D11×D21—131nomaximal, Hall
21C3×C13×D33—71no—
22C3×C11×D39—71no—
23C32×D143D711yescharacteristic, complemented
24C13×D77—31no—
25C11×D91—31no—
26C7×D143C3×D311yescharacteristic, complemented
27D33⋊D13—71no—
28C3×D11×D13—211no—
29C3×D273D1111yescharacteristic, complemented
30C3×C13×D21—111no—
31C32×C7×D13—111no—
32C3×D231D1311yescharacteristic, complemented
33C3×C11×D21—131no—
34C32×C7×D11—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D13×D21—111no—
37C3×D7×D13—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D11×D21—131no—
40C3×D7×D11—391no—
41C13×D33—71no—
42C11×D39—71no—
43C3×D143—21no—
44C3×D143C3×D711yescharacteristic, complemented
45C3×D143D2111yescharacteristic, complemented
46C3×C13×D11—211no—
47C3×C11×D13—211no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50D11×D13—211noHall
51D273C3×D1111yescharacteristic, complemented
52C13×D21—111no—
53C3×D91—31no—
54C3×C13×D7—331no—
55C3×C7×D13—111no—
56C3×C7×D13—111no—
57C3×C7×D13—221no—
58C3×D3×D13—771noHall
59D231C3×D1311yescharacteristic, complemented
60C11×D21—131no—
61C3×D77—31no—
62C3×C11×D7—391no—
63C3×C7×D11—131no—
64C3×C7×D11—131no—
65C3×C7×D11—261no—
66C3×C11×C13—21no—
67C3×C11×C13C2×C3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69C3×D3×D11—911noHall
70D7×D13—331noHall
71D7×D11—391noHall
72D143C3×D2111yescharacteristic, complemented
73C11×D13—211no—
74C13×D11—211no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×C3×D1111yescharacteristic, complemented
78C2×C3×D21—1431noHall
79C3×D39—71no—
80C3×D3×C13—771no—
81C32×D13—111no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×C3×D1311yescharacteristic, complemented
85C3×D33—71no—
86C3×D3×C11—911no—
87C32×D11—131no—
88D91—31no—
89C7×D13—111no—
90C13×D7—331no—
91C2×C3×D13—2311no—
92D3×D13—771no—
93D77—31no—
94C7×D11—131no—
95C11×D7—391no—
96C11×C13C2×C3×D2111yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11—911no—
99C2×C32×C7—1431no—
100C3×D21—111no—
101C3×D21—131no—
102C32×C13D7×D1111yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105C2×D21—1431no—
106C2×C3×D7—4291no—
107C2×C3×C13—2311no—
108D39—71no—
109C3×D13—111no—
110C3×D13—111no—
111C3×D13—211no—
112C3×D13—221no—
113D3×C13—771no—
114C7×C11C3×D3×D1311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33—71no—
117C3×D11—131no—
118C3×D11—131no—
119C3×D11—211no—
120C3×D11—261no—
121D3×C11—911no—
122C32×C7D11×D1311yescharacteristic, complemented, Hall
123C2×D13—2311noHall
124C2×D11—2731noHall
125C2×C3×C7—2861no—
126C2×C3×C7—1431no—
127C2×C3×C7—1431no—
128D21—111no—
129D21—131no—
130C3×D7—331no—
131C3×D7—391no—
132C3×C13—21no—
133C3×C13C3×D7×D1111yescharacteristic, complemented
134C3×C13D11×D2111yescharacteristic, complemented
135C2×C3×D3—10011noHall
136C3×C11—21no—
137C3×C11C3×D7×D1311yescharacteristic, complemented
138C3×C11D13×D2111yescharacteristic, complemented
139C2×D7—4291noHall
140C2×C13—2311no—
141D13—111no—
142D13—211no—
143C2×C11—2731no—
144D11—131no—
145D11—211no—
146C3×C7—21no—
147C3×C7C3×D11×D1311yescharacteristic, complemented
148C3×C7D33⋊D1311yescharacteristic, complemented
149C2×C32—1431no—
150C3×D3—771no—
151C3×D3—911no—
152C2×C7—1431no—
153D7—331no—
154D7—391no—
155C13C3×D11×D2111yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—10011no—
158C11C3×D13×D2111yescharacteristic, complemented, Sylow
159C32D77⋊D1311yescharacteristic, complemented, Sylow
160C7C3×D33⋊D1311yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—2861no—
163C2×C3—1431no—
164C2×C3—1431no—
165C2×C3—2311no—
166D3—771no—
167D3—911no—
168C22—30031noSylow
169C3—21no—
170C3C3×D77⋊D1311yescharacteristic, complemented
171C3D143⋊D2111yescharacteristic, direct product factor
172C2—2731no—
173C2—1431no—
174C2—2311no—
subgroupG/H
center, hypercenterC3D143⋊D21
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×C7×D143C2semidirect
2. C3×C11×D273C2semidirect
3. C3×C13×D231C2semidirect
4. D143⋊D21C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. C13×D231C2×C3semidirect
8. C11×D273C2×C3semidirect
12. C3×C7×D143D3semidirect
13. C3×C7×D143C2×C3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
23. C32×D143D7semidirect
26. C7×D143C3×D3semidirect
29. C3×D273D11semidirect
32. C3×D231D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13C2×C3×D3semidirect
44. C3×D143C3×D7semidirect
45. C3×D143D21semidirect
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
51. D273C3×D11semidirect
59. D231C3×D13semidirect
67. C3×C11×C13C2×C3×D7semidirect
68. C3×C11×C13C2×D21semidirect
72. D143C3×D21semidirect
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13C2×C3×D11semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×C3×D13semidirect
96. C11×C13C2×C3×D21semidirect
102. C32×C13D7×D11semidirect
103. C32×C11D7×D13semidirect
104. C7×C13C3×D3×D11semidirect
114. C7×C11C3×D3×D13semidirect
122. C32×C7D11×D13semidirect
133. C3×C13C3×D7×D11semidirect
134. C3×C13D11×D21semidirect
137. C3×C11C3×D7×D13semidirect
138. C3×C11D13×D21semidirect
147. C3×C7C3×D11×D13semidirect
148. C3×C7D33⋊D13semidirect
155. C13C3×D11×D21semidirect
158. C11C3×D13×D21semidirect
159. C32D77⋊D13semidirect
160. C7C3×D33⋊D13semidirect
170. C3C3×D77⋊D13semidirect
171. C3D143⋊D21direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D1432
C3×C11×D2732
C3×C13×D2312
D143⋊D213
C3×D77⋊D133
C3×D33⋊D137
C3×D13×D2111
C3×D11×D2113