Finite Group Databasebeta

← C3×D21×D143 #49114914

Subgroups — C3×D21×D143 #49114914

Order 36036.

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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×C13×D21C211yesmaximal, characteristic, complemented
3C3×D3003C211yesmaximal, characteristic, complemented
4D21×D143C311yesmaximal, characteristic, direct product factor
5C3×D7×D143—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7D3003C2×C311yescharacteristic, complemented
8C11×C13×D21C2×C311yescharacteristic, complemented
9C3×D1001—31no—
10C3×C11×C13×D7—31no—
11C3×C7×D143—21no—
12C3×C7×D143D311yescharacteristic, complemented
13C3×C7×D143C2×C311yescharacteristic, complemented
14C3×D3×D143—71nomaximal, Hall
15D7×D143—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×D429—71no—
22C3×D3×C11×C13—71no—
23C32×D143D711yescharacteristic, complemented
24D1001—31no—
25C11×C13×D7—31no—
26C7×D143C3×D311yescharacteristic, complemented
27C2×C3×D143—211no—
28D3×D143—71no—
29C3×D273—111no—
30C3×C13×D21D1111yescharacteristic, complemented
31C32×C7×D13—111no—
32C3×D231—131no—
33C3×C11×D21D1311yescharacteristic, complemented
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—
41C2×C3×C11×C13—211no—
42D429—71no—
43D3×C11×C13—71no—
44C3×D143—21no—
45C3×D143—211no—
46C3×D143C3×D711yescharacteristic, complemented
47C3×D143D2111yescharacteristic, direct product factor
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×D143—211noHall
51D273—111no—
52C13×D21C3×D1111yescharacteristic, complemented
53C3×D91—331no—
54C3×C13×D7—31no—
55C3×C7×D13—111no—
56C3×C7×D13—111no—
57C3×C7×D13—221no—
58C3×D3×D13—771noHall
59D231—131no—
60C11×D21C3×D1311yescharacteristic, complemented
61C3×D77—391no—
62C3×C11×D7—31no—
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
72C2×C11×C13—211no—
73D143—211no—
74D143C3×D2111yescharacteristic, direct product factor
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×C3×D1111yescharacteristic, complemented
78C2×C3×D21—1431noHall
79C3×D39—771no—
80C3×D3×C13—71no—
81C32×D13—111no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×C3×D1311yescharacteristic, complemented
85C3×D33—911no—
86C3×D3×C11—71no—
87C32×D11—131no—
88D91—331no—
89C7×D13—111no—
90C13×D7—31no—
91C2×C3×D13—2311no—
92D3×D13—771no—
93D77—391no—
94C7×D11—131no—
95C11×D7—31no—
96C11×C13C2×C3×D2111yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11—911no—
99C2×C32×C7—1431no—
100C3×D21—1431no—
101C3×D21D14311yescharacteristic, direct product factor
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—211no—
108D39—771no—
109C3×D13—111no—
110C3×D13—111no—
111C3×D13—221no—
112C3×D13—2311no—
113D3×C13—71no—
114C7×C11C3×D3×D1311yescharacteristic, complemented, Hall
115C2×C3×C11—211no—
116D33—911no—
117C3×D11—131no—
118C3×D11—131no—
119C3×D11—2731no—
120C3×D11—261no—
121D3×C11—71no—
122C32×C7C2×D14311yescharacteristic, complemented, Hall
123C2×D13—2311noHall
124C2×D11—2731noHall
125C2×C3×C7—2861no—
126C2×C3×C7—1431no—
127C2×C3×C7—1431no—
128D21—1431no—
129D21C3×D14311yescharacteristic, direct product factor
130C3×D7—31no—
131C3×D7—4291no—
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—211no—
141D13—111no—
142D13—2311no—
143C2×C11—211no—
144D11—131no—
145D11—2731no—
146C3×C7—21no—
147C3×C7D3×D14311yescharacteristic, complemented
148C3×C7C2×C3×D14311yescharacteristic, complemented
149C2×C32—1431no—
150C3×D3—71no—
151C3×D3—10011no—
152C2×C7—1431no—
153D7—31no—
154D7—4291no—
155C13C3×D11×D2111yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—10011no—
158C11C3×D13×D2111yescharacteristic, complemented, Sylow
159C32D7×D14311yescharacteristic, complemented, Sylow
160C7C3×D3×D14311yescharacteristic, complemented, Sylow
161C2×C3—211no—
162C2×C3—2861no—
163C2×C3—1431no—
164C2×C3—1431no—
165C2×C3—30031no—
166D3—71no—
167D3—10011no—
168C22—30031noSylow
169C3—21no—
170C3C3×D7×D14311yescharacteristic, complemented
171C3D21×D14311yescharacteristic, direct product factor
172C2—211no—
173C2—1431no—
174C2—30031no—
subgroupG/H
center, hypercenterC3D21×D143
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×C13×D21C2semidirect
3. C3×D3003C2semidirect
4. D21×D143C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. D3003C2×C3semidirect
8. C11×C13×D21C2×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
30. C3×C13×D21D11semidirect
33. C3×C11×D21D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13C2×C3×D3semidirect
46. C3×D143C3×D7semidirect
47. C3×D143D21direct (N × H)
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
52. C13×D21C3×D11semidirect
60. C11×D21C3×D13semidirect
67. C3×C11×C13C2×C3×D7semidirect
68. C3×C11×C13C2×D21semidirect
74. D143C3×D21direct (N × H)
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
101. C3×D21D143direct (N × H)
102. C32×C13D7×D11semidirect
103. C32×C11D7×D13semidirect
104. C7×C13C3×D3×D11semidirect
114. C7×C11C3×D3×D13semidirect
122. C32×C7C2×D143semidirect
129. D21C3×D143direct (N × H)
133. C3×C13C3×D7×D11semidirect
134. C3×C13D11×D21semidirect
137. C3×C11C3×D7×D13semidirect
138. C3×C11D13×D21semidirect
147. C3×C7D3×D143semidirect
148. C3×C7C2×C3×D143semidirect
155. C13C3×D11×D21semidirect
158. C11C3×D13×D21semidirect
159. C32D7×D143semidirect
160. C7C3×D3×D143semidirect
170. C3C3×D7×D143semidirect
171. C3D21×D143direct (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×C13×D212
C3×D30032
D21×D1433
C3×D7×D1433
C3×D3×D1437
C3×D13×D2111
C3×D11×D2113