Finite Group Databasebeta

← #49114952

Subgroups — #49114952

Order 36036.

176 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 43 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×D3003C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4D21⋊D143—31nomaximal
5D21×D143—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7D3003D311yescharacteristic, complemented
8C11×C13×D21—31no—
9C11×C13×D21—31no—
10C11×C13×D21—61no—
11C7×D429D311yescharacteristic, complemented
12C3×D1001—31no—
13C3×C7×D143—31no—
14(C3⋊D3)⋊D143—71nomaximal, Hall
15D7×D143—91noHall
16D39⋊D21—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D33⋊D21—131nomaximal, Hall
21C11×C13×C3⋊D3—71no—
22C3×D429—71no—
23C3×D429D711yescharacteristic, complemented
24D1001—31no—
25C11×C13×D7—91no—
26C7×D143—31no—
27D3×D143—211no—
28D3×D143—211no—
29C13×C3⋊D21D1111yescharacteristic, complemented
30C3×D273—111no—
31C3×C7×D39—111no—
32C11×C3⋊D21D1311yescharacteristic, complemented
33C3×D231—131no—
34C3×C7×D33—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D21⋊D13—331no—
37D13×D21—331no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39D21⋊D11—391no—
40D11×D21—391no—
41D429—71no—
42D429D2111yescharacteristic, complemented
43D3×C11×C13—211no—
44D3×C11×C13—211no—
45D3×C11×C13—421no—
46C3×D143—31no—
47C3×D143—211no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×D143—631noHall
51D273—111no—
52C13×D21—31no—
53C13×D21—31no—
54C13×D21—61no—
55C7×D39—111no—
56C3×D91—331no—
57C3×C7×D13—331no—
58(C3⋊D3)⋊D13—771noHall
59D231—131no—
60C11×D21—31no—
61C11×D21—31no—
62C11×D21—61no—
63C7×D33—131no—
64C3×D77—391no—
65C3×C7×D11—391no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69(C3⋊D3)⋊D11—911noHall
70D7×D13—991noHall
71D7×D11—1171noHall
72C2×C11×C13—631no—
73D143—31no—
74D143—211no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13D3×D1111yescharacteristic, complemented
78D3×D21—1431noHall
79C13×C3⋊D3—71no—
80C3×D39—111no—
81C3×D39—771no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11D3×D1311yescharacteristic, complemented
85C11×C3⋊D3—71no—
86C3×D33—131no—
87C3×D33—911no—
88D91—331no—
89C7×D13—331no—
90C13×D7—91no—
91D3×D13—2311no—
92D3×D13—2311no—
93D77—391no—
94C7×D11—391no—
95C11×D7—91no—
96C11×C13D3×D2111yescharacteristic, complemented, Hall
97D3×D11—2731no—
98D3×D11—2731no—
99C3⋊D21D14311yescharacteristic, complemented
100C3×D21—1431no—
101C3×D3×C7—1431no—
102C32×C13D7×D1111yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13(C3⋊D3)⋊D1111yescharacteristic, complemented, Hall
105C2×D21—4291no—
106D3×D7—4291no—
107D39—111no—
108D39—771no—
109C3×D13—331no—
110C3×D13—2311no—
111D3×C13—211no—
112D3×C13—211no—
113D3×C13—421no—
114C7×C11(C3⋊D3)⋊D1311yescharacteristic, complemented, Hall
115D33—131no—
116D33—911no—
117C3×D11—2731no—
118C3×D11—391no—
119D3×C11—211no—
120D3×C11—211no—
121D3×C11—421no—
122C32×C7C2×D14311yescharacteristic, complemented, Hall
123C2×D13—6931noHall
124C2×D11—8191noHall
125C2×C3×C7—4291no—
126D21—31no—
127D21—31no—
128D21—61no—
129D21—1431no—
130C3×D7—4291no—
131D3×C7—1431no—
132C3×C13—21no—
133C3×C13D11×D2111yescharacteristic, complemented
134C3×C13D21⋊D1111yescharacteristic, complemented
135D32—10011noHall
136C3×C11—21no—
137C3×C11D13×D2111yescharacteristic, complemented
138C3×C11D21⋊D1311yescharacteristic, complemented
139C2×D7—12871noHall
140C2×C13—631no—
141D13—331no—
142D13—2311no—
143C2×C11—631no—
144D11—2731no—
145D11—391no—
146C3×C7—21no—
147C3×C7D3×D14311yescharacteristic, complemented
148C3×C7D3×D14311yescharacteristic, complemented
149C3⋊D3—71no—
150C3×D3—1431no—
151C3×D3—10011no—
152C2×C7—4291no—
153D7—91no—
154D7—4291no—
155C13D33⋊D2111yescharacteristic, complemented, Sylow
156C2×D3—30031no—
157C2×D3—30031no—
158C11D39⋊D2111yescharacteristic, complemented, Sylow
159C32D7×D14311yescharacteristic, complemented, Sylow
160C7(C3⋊D3)⋊D14311yescharacteristic, complemented, Sylow
161C2×C3—4291no—
162C2×C3—30031no—
163D3—211no—
164D3—211no—
165D3—421no—
166D3—1431no—
167D3—10011no—
168C22—90091noSylow
169C3—21no—
170C3D21×D14311yescharacteristic, complemented
171C3D21⋊D14311yescharacteristic, complemented
172C2—631no—
173C2—4291no—
174C2—30031no—
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×D3003C2semidirect
3. C11×C13×C3⋊D21C2semidirect
6. C32×C7×C11×C13C22semidirect
7. D3003D3semidirect
11. C7×D429D3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
23. C3×D429D7semidirect
29. C13×C3⋊D21D11semidirect
32. C11×C3⋊D21D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
42. D429D21semidirect
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×D21semidirect
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13D3×D11semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11D3×D13semidirect
96. C11×C13D3×D21semidirect
99. C3⋊D21D143semidirect
102. C32×C13D7×D11semidirect
103. C32×C11D7×D13semidirect
104. C7×C13(C3⋊D3)⋊D11semidirect
114. C7×C11(C3⋊D3)⋊D13semidirect
122. C32×C7C2×D143semidirect
133. C3×C13D11×D21semidirect
134. C3×C13D21⋊D11semidirect
137. C3×C11D13×D21semidirect
138. C3×C11D21⋊D13semidirect
147. C3×C7D3×D143semidirect
148. C3×C7D3×D143semidirect
155. C13D33⋊D21semidirect
158. C11D39⋊D21semidirect
159. C32D7×D143semidirect
160. C7(C3⋊D3)⋊D143semidirect
170. C3D21×D143semidirect
171. C3D21⋊D143semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D4292
C3×D30032
C11×C13×C3⋊D212
D21⋊D1433
D21×D1433
(C3⋊D3)⋊D1437
D39⋊D2111
D33⋊D2113