Finite Group Databasebeta

← #49114963

Subgroups — #49114963

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×C11×D273C211yesmaximal, characteristic, complemented
2C3×D3003C211yesmaximal, characteristic, complemented
3C7×C13×C3⋊D33C211yesmaximal, characteristic, complemented
4D33⋊D91—31nomaximal
5D33×D91—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7D3003D311yescharacteristic, complemented
8C11×D273D311yescharacteristic, complemented
9C7×C13×D33—31no—
10C7×C13×D33—31no—
11C7×C13×D33—61no—
12C3×D1001—31no—
13C3×C11×D91—31no—
14D39⋊D33—71nomaximal, Hall
15D11×D91—91noHall
16(C3⋊D3)⋊D91—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⋊D33D711yescharacteristic, complemented
22C3×D429—71no—
23C3×C11×D39—71no—
24D1001—31no—
25C11×D91—31no—
26C7×C13×D11—91no—
27D33⋊D13—211no—
28D13×D33—211no—
29C7×C13×C3⋊D3—111no—
30C3×D273—111no—
31C3×D273D1111yescharacteristic, complemented
32C7×C3⋊D33D1311yescharacteristic, complemented
33C3×D231—131no—
34C3×C11×D21—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D3×D91—331no—
37D3×D91—331no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39D21⋊D11—391no—
40D7×D33—391no—
41D429—71no—
42C13×D33—31no—
43C13×D33—31no—
44C13×D33—61no—
45C11×D39—71no—
46C3×D143—211no—
47C3×C11×D13—211no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50D11×D13—631noHall
51D273—111no—
52D273D3311yescharacteristic, complemented
53D3×C7×C13—331no—
54D3×C7×C13—331no—
55D3×C7×C13—661no—
56C3×D91—31no—
57C3×D91—331no—
58(C3⋊D3)⋊D13—771noHall
59D231—131no—
60C11×D21—131no—
61C7×D33—31no—
62C7×D33—31no—
63C7×D33—61no—
64C3×D77—391no—
65C3×C11×D7—391no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13D3×D711yescharacteristic, complemented
69D3×D33—911noHall
70C2×D91—991noHall
71D7×D11—1171noHall
72D143—211no—
73C11×D13—211no—
74C13×D11—91no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×D3311yescharacteristic, complemented
78(C3⋊D3)⋊D7—1431noHall
79C13×C3⋊D3—111no—
80C3×D39—71no—
81C3×D39—771no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11D3×D1311yescharacteristic, complemented
85C3⋊D33D9111yescharacteristic, complemented
86C3×D33—911no—
87C3×D3×C11—911no—
88C2×C7×C13—991no—
89D91—31no—
90D91—331no—
91D3×D13—2311no—
92D3×D13—2311no—
93D77—391no—
94C7×D11—91no—
95C11×D7—391no—
96C11×C13(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
97C2×D33—2731no—
98D3×D11—2731no—
99C7×C3⋊D3—111no—
100C3×D21—131no—
101C3×D21—1431no—
102C32×C13D7×D1111yescharacteristic, complemented, Hall
103C32×C11C2×D9111yescharacteristic, complemented, Hall
104C7×C13D3×D3311yescharacteristic, complemented, Hall
105D3×D7—4291no—
106D3×D7—4291no—
107D39—71no—
108D39—771no—
109C3×D13—211no—
110C3×D13—2311no—
111D3×C13—331no—
112D3×C13—331no—
113D3×C13—661no—
114C7×C11(C3⋊D3)⋊D1311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33—31no—
117D33—31no—
118D33—61no—
119D33—911no—
120C3×D11—2731no—
121D3×C11—911no—
122C32×C7D11×D1311yescharacteristic, complemented, Hall
123C2×D13—6931noHall
124C2×D11—8191noHall
125D21—131no—
126D21—1431no—
127C3×D7—391no—
128C3×D7—4291no—
129D3×C7—331no—
130D3×C7—331no—
131D3×C7—661no—
132C3×C13—21no—
133C3×C13D7×D3311yescharacteristic, complemented
134C3×C13D21⋊D1111yescharacteristic, complemented
135D32—10011noHall
136C3×C11—21no—
137C3×C11D3×D9111yescharacteristic, complemented
138C3×C11D3×D9111yescharacteristic, complemented
139C2×D7—12871noHall
140C2×C13—991no—
141D13—211no—
142D13—2311no—
143C2×C11—2731no—
144D11—91no—
145D11—2731no—
146C3×C7—21no—
147C3×C7D13×D3311yescharacteristic, complemented
148C3×C7D33⋊D1311yescharacteristic, complemented
149C3⋊D3—111no—
150C3×D3—911no—
151C3×D3—10011no—
152C2×C7—991no—
153D7—391no—
154D7—4291no—
155C13D21⋊D3311yescharacteristic, complemented, Sylow
156C2×D3—30031no—
157C2×D3—30031no—
158C11(C3⋊D3)⋊D9111yescharacteristic, complemented, Sylow
159C32D11×D9111yescharacteristic, complemented, Sylow
160C7D39⋊D3311yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—30031no—
163D3—331no—
164D3—331no—
165D3—661no—
166D3—911no—
167D3—10011no—
168C22—90091noSylow
169C3—21no—
170C3D33×D9111yescharacteristic, complemented
171C3D33⋊D9111yescharacteristic, complemented
172C2—2731no—
173C2—991no—
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×C11×D273C2semidirect
2. C3×D3003C2semidirect
3. C7×C13×C3⋊D33C2semidirect
6. C32×C7×C11×C13C22semidirect
7. D3003D3semidirect
8. C11×D273D3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
21. C13×C3⋊D33D7semidirect
31. C3×D273D11semidirect
32. C7×C3⋊D33D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
52. D273D33semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13D3×D7semidirect
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13C2×D33semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11D3×D13semidirect
85. C3⋊D33D91semidirect
96. C11×C13(C3⋊D3)⋊D7semidirect
102. C32×C13D7×D11semidirect
103. C32×C11C2×D91semidirect
104. C7×C13D3×D33semidirect
114. C7×C11(C3⋊D3)⋊D13semidirect
122. C32×C7D11×D13semidirect
133. C3×C13D7×D33semidirect
134. C3×C13D21⋊D11semidirect
137. C3×C11D3×D91semidirect
138. C3×C11D3×D91semidirect
147. C3×C7D13×D33semidirect
148. C3×C7D33⋊D13semidirect
155. C13D21⋊D33semidirect
158. C11(C3⋊D3)⋊D91semidirect
159. C32D11×D91semidirect
160. C7D39⋊D33semidirect
170. C3D33×D91semidirect
171. C3D33⋊D91semidirect

Maximal subgroups

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

subgroupindex
C3×C11×D2732
C3×D30032
C7×C13×C3⋊D332
D33⋊D913
D33×D913
D39⋊D337
(C3⋊D3)⋊D9111
D21⋊D3313