Finite Group Databasebeta

← #49114966

Subgroups — #49114966

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×C13×D231C211yesmaximal, characteristic, complemented
2C3×D3003C211yesmaximal, characteristic, complemented
3C7×C11×C3⋊D39C211yesmaximal, characteristic, complemented
4D39⋊D77—31nomaximal
5D39×D77—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7D3003D311yescharacteristic, complemented
8C13×D231D311yescharacteristic, complemented
9C7×C11×D39—31no—
10C7×C11×D39—31no—
11C7×C11×D39—61no—
12C3×D1001—31no—
13C3×C13×D77—31no—
14D33⋊D39—71nomaximal, Hall
15D13×D77—91noHall
16D21⋊D39—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20(C3⋊D3)⋊D77—131nomaximal, Hall
21C11×C3⋊D39D711yescharacteristic, complemented
22C3×D429—71no—
23C3×C13×D33—71no—
24D1001—31no—
25C13×D77—31no—
26C7×C11×D13—91no—
27D33⋊D13—211no—
28D11×D39—211no—
29C7×C3⋊D39D1111yescharacteristic, complemented
30C3×D273—111no—
31C3×C13×D21—111no—
32C7×C11×C3⋊D3—131no—
33C3×D231—131no—
34C3×D231D1311yescharacteristic, complemented
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D21⋊D13—331no—
37D7×D39—331no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39D3×D77—391no—
40D3×D77—391no—
41D429—71no—
42C13×D33—71no—
43C11×D39—31no—
44C11×D39—31no—
45C11×D39—61no—
46C3×D143—211no—
47C3×C13×D11—211no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50D11×D13—631noHall
51D273—111no—
52C13×D21—111no—
53C7×D39—31no—
54C7×D39—31no—
55C7×D39—61no—
56C3×D91—331no—
57C3×C13×D7—331no—
58D3×D39—771noHall
59D231—131no—
60D231D3911yescharacteristic, complemented
61D3×C7×C11—391no—
62D3×C7×C11—391no—
63D3×C7×C11—781no—
64C3×D77—31no—
65C3×D77—391no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13D3×D711yescharacteristic, complemented
69(C3⋊D3)⋊D11—911noHall
70D7×D13—991noHall
71C2×D77—1171noHall
72D143—211no—
73C11×D13—91no—
74C13×D11—211no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13D3×D1111yescharacteristic, complemented
78(C3⋊D3)⋊D7—1431noHall
79C3⋊D39D7711yescharacteristic, complemented
80C3×D39—771no—
81C3×D3×C13—771no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×D3911yescharacteristic, complemented
85C11×C3⋊D3—131no—
86C3×D33—71no—
87C3×D33—911no—
88D91—331no—
89C7×D13—91no—
90C13×D7—331no—
91C2×D39—2311no—
92D3×D13—2311no—
93C2×C7×C11—1171no—
94D77—31no—
95D77—391no—
96C11×C13(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
97D3×D11—2731no—
98D3×D11—2731no—
99C7×C3⋊D3—131no—
100C3×D21—111no—
101C3×D21—1431no—
102C32×C13C2×D7711yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13(C3⋊D3)⋊D1111yescharacteristic, complemented, Hall
105D3×D7—4291no—
106D3×D7—4291no—
107C2×C3×C13—2311no—
108D39—31no—
109D39—31no—
110D39—61no—
111D39—771no—
112C3×D13—2311no—
113D3×C13—771no—
114C7×C11D3×D3911yescharacteristic, complemented, Hall
115D33—71no—
116D33—911no—
117C3×D11—2731no—
118C3×D11—211no—
119D3×C11—391no—
120D3×C11—391no—
121D3×C11—781no—
122C32×C7D11×D1311yescharacteristic, complemented, Hall
123C2×D13—6931noHall
124C2×D11—8191noHall
125D21—111no—
126D21—1431no—
127C3×D7—331no—
128C3×D7—4291no—
129D3×C7—391no—
130D3×C7—391no—
131D3×C7—781no—
132C3×C13—21no—
133C3×C13D3×D7711yescharacteristic, complemented
134C3×C13D3×D7711yescharacteristic, complemented
135D32—10011noHall
136C3×C11—21no—
137C3×C11D7×D3911yescharacteristic, complemented
138C3×C11D21⋊D1311yescharacteristic, complemented
139C2×D7—12871noHall
140C2×C13—2311no—
141D13—91no—
142D13—2311no—
143C2×C11—1171no—
144D11—2731no—
145D11—211no—
146C3×C7—21no—
147C3×C7D11×D3911yescharacteristic, complemented
148C3×C7D33⋊D1311yescharacteristic, complemented
149C3⋊D3—131no—
150C3×D3—771no—
151C3×D3—10011no—
152C2×C7—1171no—
153D7—331no—
154D7—4291no—
155C13(C3⋊D3)⋊D7711yescharacteristic, complemented, Sylow
156C2×D3—30031no—
157C2×D3—30031no—
158C11D21⋊D3911yescharacteristic, complemented, Sylow
159C32D13×D7711yescharacteristic, complemented, Sylow
160C7D33⋊D3911yescharacteristic, complemented, Sylow
161C2×C3—30031no—
162C2×C3—2311no—
163D3—391no—
164D3—391no—
165D3—771no—
166D3—781no—
167D3—10011no—
168C22—90091noSylow
169C3—21no—
170C3D39×D7711yescharacteristic, complemented
171C3D39⋊D7711yescharacteristic, complemented
172C2—1171no—
173C2—30031no—
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×C13×D231C2semidirect
2. C3×D3003C2semidirect
3. C7×C11×C3⋊D39C2semidirect
6. C32×C7×C11×C13C22semidirect
7. D3003D3semidirect
8. C13×D231D3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
21. C11×C3⋊D39D7semidirect
29. C7×C3⋊D39D11semidirect
34. C3×D231D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
60. D231D39semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13D3×D7semidirect
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13D3×D11semidirect
79. C3⋊D39D77semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×D39semidirect
96. C11×C13(C3⋊D3)⋊D7semidirect
102. C32×C13C2×D77semidirect
103. C32×C11D7×D13semidirect
104. C7×C13(C3⋊D3)⋊D11semidirect
114. C7×C11D3×D39semidirect
122. C32×C7D11×D13semidirect
133. C3×C13D3×D77semidirect
134. C3×C13D3×D77semidirect
137. C3×C11D7×D39semidirect
138. C3×C11D21⋊D13semidirect
147. C3×C7D11×D39semidirect
148. C3×C7D33⋊D13semidirect
155. C13(C3⋊D3)⋊D77semidirect
158. C11D21⋊D39semidirect
159. C32D13×D77semidirect
160. C7D33⋊D39semidirect
170. C3D39×D77semidirect
171. C3D39⋊D77semidirect

Maximal subgroups

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

subgroupindex
C3×C13×D2312
C3×D30032
C7×C11×C3⋊D392
D39⋊D773
D39×D773
D33⋊D397
D21⋊D3911
(C3⋊D3)⋊D7713