Finite Group Databasebeta

← #49114956

Subgroups — #49114956

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×C11×D273C211yesmaximal, characteristic, complemented
3C13×C3⋊D231C211yesmaximal, characteristic, complemented
4D91⋊D33—31nomaximal
5D143⋊D21—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C13×D231—31no—
8C13×D231—31no—
9C13×D231—61no—
10C11×D273D311yescharacteristic, complemented
11C7×D429D311yescharacteristic, complemented
12C3×C11×D91—31no—
13C3×C7×D143—31no—
14D39⋊D33—71nomaximal, Hall
15D77⋊D13—91noHall
16D39⋊D21—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D21×D33—131nomaximal, Hall
21C13×C3⋊D33—71no—
22C3×D429D711yescharacteristic, complemented
23C3×C11×D39—71no—
24C13×D77—91no—
25C11×D91—31no—
26C7×D143—31no—
27D33⋊D13—211no—
28D13×D33—211no—
29C13×C3⋊D21—111no—
30C3×D273D1111yescharacteristic, complemented
31C3×C7×D39—111no—
32C3⋊D231D1311yescharacteristic, complemented
33C3×C11×D21—131no—
34C3×C7×D33—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D21⋊D13—331no—
37D13×D21—331no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39D7×D33—391no—
40D11×D21—391no—
41D429D2111yescharacteristic, complemented
42C13×D33—211no—
43C13×D33—211no—
44C13×D33—421no—
45C11×D39—71no—
46C3×D143—31no—
47C3×C11×D13—211no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50D11×D13—631noHall
51D273D3311yescharacteristic, complemented
52C13×D21—331no—
53C13×D21—331no—
54C13×D21—661no—
55C7×D39—111no—
56C3×D91—31no—
57C3×C7×D13—331no—
58(C3⋊D3)⋊D13—771noHall
59D231—31no—
60D231—31no—
61D231—61no—
62C11×D21—131no—
63C7×D33—131no—
64C3×C11×D7—391no—
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
72D143—31no—
73C11×D13—211no—
74C13×D11—631no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×D3311yescharacteristic, complemented
78D3×D21—1431noHall
79C13×C3⋊D3—771no—
80C3×D39—71no—
81C3×D39—111no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11D3×D1311yescharacteristic, complemented
85C3⋊D33—71no—
86C3×D33—131no—
87C3×D3×C11—911no—
88D91—31no—
89C7×D13—331no—
90C13×D7—991no—
91D3×D13—2311no—
92D3×D13—2311no—
93D77—91no—
94C7×D11—391no—
95C11×D7—391no—
96C11×C13D3×D2111yescharacteristic, complemented, Hall
97C2×D33—2731no—
98D3×D11—2731no—
99C3⋊D21—111no—
100C3×D21—131no—
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—
107D39—71no—
108D39—111no—
109C3×D13—211no—
110C3×D13—331no—
111D3×C13—4621no—
112D3×C13—2311no—
113D3×C13—2311no—
114C7×C11(C3⋊D3)⋊D1311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33—131no—
117D33—211no—
118D33—211no—
119D33—421no—
120C3×D11—391no—
121D3×C11—911no—
122C32×C7D11×D1311yescharacteristic, complemented, Hall
123C2×D13—6931noHall
124C2×D11—8191noHall
125C2×C3×C7—4291no—
126D21—131no—
127D21—331no—
128D21—331no—
129D21—661no—
130C3×D7—391no—
131D3×C7—1431no—
132C3×C13—21no—
133C3×C13D11×D2111yescharacteristic, complemented
134C3×C13D7×D3311yescharacteristic, complemented
135D32—10011noHall
136C3×C11—21no—
137C3×C11D13×D2111yescharacteristic, complemented
138C3×C11D21⋊D1311yescharacteristic, complemented
139C2×D7—12871noHall
140C2×C13—6931no—
141D13—211no—
142D13—331no—
143C2×C11—2731no—
144D11—391no—
145D11—631no—
146C3×C7—21no—
147C3×C7D13×D3311yescharacteristic, complemented
148C3×C7D33⋊D1311yescharacteristic, complemented
149C3⋊D3—771no—
150C3×D3—911no—
151C3×D3—1431no—
152C2×C7—4291no—
153D7—391no—
154D7—991no—
155C13D21×D3311yescharacteristic, complemented, Sylow
156C2×D3—30031no—
157C2×D3—30031no—
158C11D39⋊D2111yescharacteristic, complemented, Sylow
159C32D77⋊D1311yescharacteristic, complemented, Sylow
160C7D39⋊D3311yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—4291no—
163D3—911no—
164D3—1431no—
165D3—4621no—
166D3—2311no—
167D3—2311no—
168C22—90091noSylow
169C3—21no—
170C3D143⋊D2111yescharacteristic, complemented
171C3D91⋊D3311yescharacteristic, complemented
172C2—2731no—
173C2—4291no—
174C2—6931no—
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×D273C2semidirect
3. C13×C3⋊D231C2semidirect
6. C32×C7×C11×C13C22semidirect
10. C11×D273D3semidirect
11. C7×D429D3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
22. C3×D429D7semidirect
30. C3×D273D11semidirect
32. C3⋊D231D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
41. D429D21semidirect
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
51. D273D33semidirect
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×C11D3×D13semidirect
96. C11×C13D3×D21semidirect
102. C32×C13D7×D11semidirect
103. C32×C11D7×D13semidirect
104. C7×C13D3×D33semidirect
114. C7×C11(C3⋊D3)⋊D13semidirect
122. C32×C7D11×D13semidirect
133. C3×C13D11×D21semidirect
134. C3×C13D7×D33semidirect
137. C3×C11D13×D21semidirect
138. C3×C11D21⋊D13semidirect
147. C3×C7D13×D33semidirect
148. C3×C7D33⋊D13semidirect
155. C13D21×D33semidirect
158. C11D39⋊D21semidirect
159. C32D77⋊D13semidirect
160. C7D39⋊D33semidirect
170. C3D143⋊D21semidirect
171. C3D91⋊D33semidirect

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×D2732
C13×C3⋊D2312
D91⋊D333
D143⋊D213
D39⋊D337
D39⋊D2111
D21×D3313