Finite Group Databasebeta

← #49114953

Subgroups — #49114953

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×C13×D231C211yesmaximal, characteristic, complemented
3C11×C3⋊D273C211yesmaximal, characteristic, complemented
4D77⋊D39—31nomaximal
5D143⋊D21—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C13×D231D311yescharacteristic, complemented
8C11×D273—31no—
9C11×D273—31no—
10C11×D273—61no—
11C7×D429D311yescharacteristic, complemented
12C3×C13×D77—31no—
13C3×C7×D143—31no—
14D33⋊D39—71nomaximal, Hall
15D77⋊D13—91noHall
16D21×D39—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D33⋊D21—131nomaximal, Hall
21C11×C3⋊D39—71no—
22C3×D429D711yescharacteristic, complemented
23C3×C13×D33—71no—
24C13×D77—31no—
25C11×D91—91no—
26C7×D143—31no—
27D33⋊D13—211no—
28D11×D39—211no—
29C3⋊D273D1111yescharacteristic, complemented
30C3×C13×D21—111no—
31C3×C7×D39—111no—
32C11×C3⋊D21—131no—
33C3×D231D1311yescharacteristic, complemented
34C3×C7×D33—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D7×D39—331no—
37D13×D21—331no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39D21⋊D11—391no—
40D11×D21—391no—
41D429D2111yescharacteristic, complemented
42C13×D33—71no—
43C11×D39—211no—
44C11×D39—211no—
45C11×D39—421no—
46C3×D143—31no—
47C3×C13×D11—211no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50D11×D13—631noHall
51D273—31no—
52D273—31no—
53D273—61no—
54C13×D21—111no—
55C7×D39—111no—
56C3×C13×D7—331no—
57C3×C7×D13—331no—
58D3×D39—771noHall
59D231D3911yescharacteristic, complemented
60C11×D21—391no—
61C11×D21—391no—
62C11×D21—781no—
63C7×D33—131no—
64C3×D77—31no—
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
72D143—31no—
73C11×D13—631no—
74C13×D11—211no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13D3×D1111yescharacteristic, complemented
78D3×D21—1431noHall
79C3⋊D39—71no—
80C3×D39—111no—
81C3×D3×C13—771no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×D3911yescharacteristic, complemented
85C11×C3⋊D3—911no—
86C3×D33—71no—
87C3×D33—131no—
88D91—91no—
89C7×D13—331no—
90C13×D7—331no—
91C2×D39—2311no—
92D3×D13—2311no—
93D77—31no—
94C7×D11—391no—
95C11×D7—1171no—
96C11×C13D3×D2111yescharacteristic, complemented, Hall
97D3×D11—2731no—
98D3×D11—2731no—
99C3⋊D21—131no—
100C3×D21—111no—
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—
107C2×C3×C13—2311no—
108D39—111no—
109D39—211no—
110D39—211no—
111D39—421no—
112C3×D13—331no—
113D3×C13—771no—
114C7×C11D3×D3911yescharacteristic, complemented, Hall
115D33—71no—
116D33—131no—
117C3×D11—211no—
118C3×D11—391no—
119D3×C11—2731no—
120D3×C11—2731no—
121D3×C11—5461no—
122C32×C7D11×D1311yescharacteristic, complemented, Hall
123C2×D13—6931noHall
124C2×D11—8191noHall
125C2×C3×C7—4291no—
126D21—111no—
127D21—391no—
128D21—391no—
129D21—781no—
130C3×D7—331no—
131D3×C7—1431no—
132C3×C13—21no—
133C3×C13D11×D2111yescharacteristic, complemented
134C3×C13D21⋊D1111yescharacteristic, complemented
135D32—10011noHall
136C3×C11—21no—
137C3×C11D13×D2111yescharacteristic, complemented
138C3×C11D7×D3911yescharacteristic, complemented
139C2×D7—12871noHall
140C2×C13—2311no—
141D13—331no—
142D13—631no—
143C2×C11—8191no—
144D11—211no—
145D11—391no—
146C3×C7—21no—
147C3×C7D11×D3911yescharacteristic, complemented
148C3×C7D33⋊D1311yescharacteristic, complemented
149C3⋊D3—911no—
150C3×D3—771no—
151C3×D3—1431no—
152C2×C7—4291no—
153D7—331no—
154D7—1171no—
155C13D33⋊D2111yescharacteristic, complemented, Sylow
156C2×D3—30031no—
157C2×D3—30031no—
158C11D21×D3911yescharacteristic, complemented, Sylow
159C32D77⋊D1311yescharacteristic, complemented, Sylow
160C7D33⋊D3911yescharacteristic, complemented, Sylow
161C2×C3—4291no—
162C2×C3—2311no—
163D3—2731no—
164D3—2731no—
165D3—5461no—
166D3—771no—
167D3—1431no—
168C22—90091noSylow
169C3—21no—
170C3D143⋊D2111yescharacteristic, complemented
171C3D77⋊D3911yescharacteristic, complemented
172C2—8191no—
173C2—4291no—
174C2—2311no—
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×C13×D231C2semidirect
3. C11×C3⋊D273C2semidirect
6. C32×C7×C11×C13C22semidirect
7. C13×D231D3semidirect
11. C7×D429D3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
22. C3×D429D7semidirect
29. C3⋊D273D11semidirect
33. C3×D231D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
41. D429D21semidirect
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
59. D231D39semidirect
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×C11C2×D39semidirect
96. C11×C13D3×D21semidirect
102. C32×C13D7×D11semidirect
103. C32×C11D7×D13semidirect
104. C7×C13(C3⋊D3)⋊D11semidirect
114. C7×C11D3×D39semidirect
122. C32×C7D11×D13semidirect
133. C3×C13D11×D21semidirect
134. C3×C13D21⋊D11semidirect
137. C3×C11D13×D21semidirect
138. C3×C11D7×D39semidirect
147. C3×C7D11×D39semidirect
148. C3×C7D33⋊D13semidirect
155. C13D33⋊D21semidirect
158. C11D21×D39semidirect
159. C32D77⋊D13semidirect
160. C7D33⋊D39semidirect
170. C3D143⋊D21semidirect
171. C3D77⋊D39semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D4292
C3×C13×D2312
C11×C3⋊D2732
D77⋊D393
D143⋊D213
D33⋊D397
D21×D3911
D33⋊D2113