Finite Group Databasebeta

← D21×D429 #49114957

Subgroups — D21×D429 #49114957

Order 36036.

176 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 46 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×C7×D429C211yesmaximal, characteristic, complemented
2C3×C11×C13×D21C211yesmaximal, characteristic, complemented
3C3⋊D3003C211yesmaximal, characteristic, complemented
4D7×D429—31nomaximal
5D21×D143—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7D3003—31no—
8D3003—31no—
9D3003—61no—
10C11×C13×D21D311yescharacteristic, complemented
11C7×D429D311yescharacteristic, complemented
12C3×C11×C13×D7—31no—
13C3×C7×D143—31no—
14D3×D429—71nomaximal, Hall
15D7×D143—91noHall
16D21×D39—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D21×D33—131nomaximal, Hall
21C3⋊D429—71no—
22C3×D429D711yescharacteristic, complemented
23C3×D3×C11×C13—71no—
24D1001—91no—
25C11×C13×D7—31no—
26C7×D143—31no—
27C2×D429—211no—
28D3×D143—211no—
29C3⋊D273—111no—
30C3×C13×D21D1111yescharacteristic, complemented
31C3×C7×D39—111no—
32C3⋊D231—131no—
33C3×C11×D21D1311yescharacteristic, complemented
34C3×C7×D33—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D7×D39—331no—
37D13×D21—331no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39D7×D33—391no—
40D11×D21—391no—
41C2×C3×C11×C13—211no—
42D429—211no—
43D429—211no—
44D429—421no—
45D429D2111yescharacteristic, direct product factor
46D3×C11×C13—71no—
47C3×D143—31no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×D143—631noHall
51D273—331no—
52D273—331no—
53D273—661no—
54C13×D21D3311yescharacteristic, complemented
55C7×D39—111no—
56C3×C13×D7—31no—
57C3×C7×D13—331no—
58D3×D39—771noHall
59D231—391no—
60D231—391no—
61D231—781no—
62C11×D21D3911yescharacteristic, complemented
63C7×D33—131no—
64C3×C11×D7—31no—
65C3×C7×D11—391no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69D3×D33—911noHall
70D7×D13—991noHall
71D7×D11—1171noHall
72C2×C11×C13—211no—
73D143—31no—
74D143—631no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×D3311yescharacteristic, complemented
78D3×D21—1431noHall
79C3⋊D39—771no—
80C3×D39—111no—
81C3×D3×C13—71no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×D3911yescharacteristic, complemented
85C3⋊D33—911no—
86C3×D33—131no—
87C3×D3×C11—71no—
88D91—991no—
89C7×D13—331no—
90C13×D7—31no—
91C2×D39—2311no—
92D3×D13—2311no—
93D77—1171no—
94C7×D11—391no—
95C11×D7—31no—
96C11×C13D3×D2111yescharacteristic, complemented, Hall
97C2×D33—2731no—
98D3×D11—2731no—
99C3⋊D21—1431no—
100C3×D21D14311yescharacteristic, complemented
101C3×D3×C7—1431no—
102C32×C13D7×D1111yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13D3×D3311yescharacteristic, complemented, Hall
105C2×D21—4291no—
106D3×D7—4291no—
107C2×C3×C13—211no—
108D39—111no—
109D39—4621no—
110D39—2311no—
111D39—2311no—
112C3×D13—331no—
113D3×C13—71no—
114C7×C11D3×D3911yescharacteristic, complemented, Hall
115C2×C3×C11—211no—
116D33—131no—
117D33—2731no—
118D33—2731no—
119D33—5461no—
120C3×D11—391no—
121D3×C11—71no—
122C32×C7C2×D14311yescharacteristic, complemented, Hall
123C2×D13—6931noHall
124C2×D11—8191noHall
125C2×C3×C7—4291no—
126D21—8581no—
127D21—4291no—
128D21—4291no—
129D21D42911yescharacteristic, direct product factor
130C3×D7—31no—
131D3×C7—1431no—
132C3×C13—21no—
133C3×C13D11×D2111yescharacteristic, complemented
134C3×C13D7×D3311yescharacteristic, complemented
135D32—10011noHall
136C3×C11—21no—
137C3×C11D13×D2111yescharacteristic, complemented
138C3×C11D7×D3911yescharacteristic, complemented
139C2×D7—12871noHall
140C2×C13—211no—
141D13—331no—
142D13—6931no—
143C2×C11—211no—
144D11—391no—
145D11—8191no—
146C3×C7—21no—
147C3×C7D3×D14311yescharacteristic, complemented
148C3×C7C2×D42911yescharacteristic, complemented
149C3⋊D3—10011no—
150C3×D3—71no—
151C3×D3—1431no—
152C2×C7—4291no—
153D7—31no—
154D7—12871no—
155C13D21×D3311yescharacteristic, complemented, Sylow
156C2×D3—30031no—
157C2×D3—30031no—
158C11D21×D3911yescharacteristic, complemented, Sylow
159C32D7×D14311yescharacteristic, complemented, Sylow
160C7D3×D42911yescharacteristic, complemented, Sylow
161C2×C3—211no—
162C2×C3—4291no—
163D3—71no—
164D3—60061no—
165D3—1431no—
166D3—30031no—
167D3—30031no—
168C22—90091noSylow
169C3—21no—
170C3D21×D14311yescharacteristic, complemented
171C3D7×D42911yescharacteristic, complemented
172C2—211no—
173C2—90091no—
174C2—4291no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×D429C2semidirect
2. C3×C11×C13×D21C2semidirect
3. C3⋊D3003C2semidirect
6. C32×C7×C11×C13C22semidirect
10. C11×C13×D21D3semidirect
11. C7×D429D3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
22. C3×D429D7semidirect
30. C3×C13×D21D11semidirect
33. C3×C11×D21D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
45. D429D21direct (N × H)
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
54. C13×D21D33semidirect
62. C11×D21D39semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×D21semidirect
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13C2×D33semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×D39semidirect
96. C11×C13D3×D21semidirect
100. C3×D21D143semidirect
102. C32×C13D7×D11semidirect
103. C32×C11D7×D13semidirect
104. C7×C13D3×D33semidirect
114. C7×C11D3×D39semidirect
122. C32×C7C2×D143semidirect
129. D21D429direct (N × H)
133. C3×C13D11×D21semidirect
134. C3×C13D7×D33semidirect
137. C3×C11D13×D21semidirect
138. C3×C11D7×D39semidirect
147. C3×C7D3×D143semidirect
148. C3×C7C2×D429semidirect
155. C13D21×D33semidirect
158. C11D21×D39semidirect
159. C32D7×D143semidirect
160. C7D3×D429semidirect
170. C3D21×D143semidirect
171. C3D7×D429semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D4292
C3×C11×C13×D212
C3⋊D30032
D7×D4293
D21×D1433
D3×D4297
D21×D3911
D21×D3313