Finite Group Databasebeta

← C3×C7×D33⋊D13 #49114907

Subgroups — C3×C7×D33⋊D13 #49114907

Order 36036.

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C32×C7×D143C211yesmaximal, characteristic, complemented
2C3×C7×C11×D39C211yesmaximal, characteristic, complemented
3C3×C7×C13×D33C211yesmaximal, characteristic, complemented
4C7×D33⋊D13C311yesmaximal, characteristic, direct product factor
5C3×C7×D11×D13—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C7×C13×D33C2×C311yescharacteristic, complemented
8C7×C11×D39C2×C311yescharacteristic, complemented
9C3×C7×D143—21no—
10C3×C7×D143D311yescharacteristic, complemented
11C3×C7×D143C2×C311yescharacteristic, complemented
12C3×C7×C13×D11—31no—
13C3×C7×C11×D13—31no—
14C3×D33⋊D13C711yesmaximal, characteristic, direct product factor, Hall
15C7×D11×D13—31noHall
16C3×D3×C7×D13—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D3×C7×D11—131nomaximal, Hall
21C3×C13×D33C2×C711yescharacteristic, complemented
22C3×C11×D39C2×C711yescharacteristic, complemented
23C32×D143C2×C711yescharacteristic, complemented
24C7×D143C3×D311yescharacteristic, complemented
25C7×C13×D11—31no—
26C7×C11×D13—31no—
27D33⋊D13C3×C711yescharacteristic, direct product factor
28C3×D11×D13—31no—
29C3×C7×D39D1111yescharacteristic, complemented
30C3×D3×C7×C13—111no—
31C32×C7×D13—111no—
32C3×C7×D33D1311yescharacteristic, complemented
33C3×D3×C7×C11—131no—
34C32×C7×D11—131no—
35C32×C11×C13C22×C711yescharacteristic, complemented, Hall
36C2×C3×C7×D13—331no—
37D3×C7×D13—111no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C3×C7×D11—391no—
40D3×C7×D11—131no—
41C13×D33C2×C3×C711yescharacteristic, complemented
42C11×D39C2×C3×C711yescharacteristic, complemented
43C3×D143—21no—
44C3×D143D3×C711yescharacteristic, complemented
45C3×D143C2×C3×C711yescharacteristic, complemented
46C3×C13×D11—31no—
47C3×C11×D13—31no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50D11×D13—31noHall
51C2×C3×C7×C13—331no—
52C7×D39C3×D1111yescharacteristic, complemented
53D3×C7×C13—111no—
54C3×C7×D13—31no—
55C3×C7×D13—111no—
56C3×C7×D13—111no—
57C3×C7×D13—221no—
58C3×D3×D13—111noHall
59C2×C3×C7×C11—391no—
60C7×D33C3×D1311yescharacteristic, complemented
61D3×C7×C11—131no—
62C3×C7×D11—31no—
63C3×C7×D11—131no—
64C3×C7×D11—131no—
65C3×C7×D11—261no—
66C3×C11×C13—21no—
67C3×C11×C13C2×D3×C711yescharacteristic, complemented
68C3×C11×C13C22×C3×C711yescharacteristic, complemented
69C3×D3×D11—131noHall
70C2×C7×D13—331noHall
71C2×C7×D11—391noHall
72D143C3×D3×C711yescharacteristic, complemented
73C11×D13—31no—
74C13×D11—31no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×C3×D1111yescharacteristic, complemented
78C2×C3×D3×C7—1431noHall
79C3×D39C7×D1111yescharacteristic, complemented
80C3×D3×C13—111no—
81C32×D13—111no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×C3×D1311yescharacteristic, complemented
85C3×D33C7×D1311yescharacteristic, complemented
86C3×D3×C11—131no—
87C32×D11—131no—
88C2×C7×C13—331no—
89C7×D13—31no—
90C7×D13—111no—
91C2×C3×D13—331no—
92D3×D13—111no—
93C2×C7×C11—391no—
94C7×D11—31no—
95C7×D11—131no—
96C11×C13C2×C3×D3×C711yescharacteristic, complemented, Hall
97C2×C3×D11—391no—
98D3×D11—131no—
99C2×C32×C7—1431no—
100C3×D3×C7—111no—
101C3×D3×C7—131no—
102C32×C13C2×C7×D1111yescharacteristic, complemented, Hall
103C32×C11C2×C7×D1311yescharacteristic, complemented, Hall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105C22×C3×C7—4291no—
106C2×D3×C7—1431no—
107C2×C3×C13—331no—
108D39C3×C7×D1111yescharacteristic, complemented
109C3×D13—31no—
110C3×D13—111no—
111C3×D13—111no—
112C3×D13—221no—
113D3×C13—111no—
114C7×C11C3×D3×D1311yescharacteristic, complemented, Hall
115C2×C3×C11—391no—
116D33C3×C7×D1311yescharacteristic, complemented
117C3×D11—31no—
118C3×D11—131no—
119C3×D11—131no—
120C3×D11—261no—
121D3×C11—131no—
122C32×C7D11×D1311yescharacteristic, complemented, Hall
123C2×D13—331noHall
124C2×D11—391noHall
125C2×C3×C7—2861no—
126C2×C3×C7—331no—
127C2×C3×C7—391no—
128C2×C3×C7—1431no—
129C2×C3×C7—1431no—
130D3×C7—111no—
131D3×C7—131no—
132C3×C13—21no—
133C3×C13D3×C7×D1111yescharacteristic, complemented
134C3×C13C2×C3×C7×D1111yescharacteristic, complemented
135C2×C3×D3—1431noHall
136C3×C11—21no—
137C3×C11D3×C7×D1311yescharacteristic, complemented
138C3×C11C2×C3×C7×D1311yescharacteristic, complemented
139C22×C7—4291noHall
140C2×C13—331no—
141D13—31no—
142D13—111no—
143C2×C11—391no—
144D11—31no—
145D11—131no—
146C3×C7—21no—
147C3×C7C3×D11×D1311yescharacteristic, complemented
148C3×C7D33⋊D1311yescharacteristic, direct product factor
149C2×C32—1431no—
150C3×D3—111no—
151C3×D3—131no—
152C2×C7—331no—
153C2×C7—391no—
154C2×C7—1431no—
155C13C3×D3×C7×D1111yescharacteristic, complemented, Sylow
156C22×C3—4291no—
157C2×D3—1431no—
158C11C3×D3×C7×D1311yescharacteristic, complemented, Sylow
159C32C7×D11×D1311yescharacteristic, complemented, Sylow
160C7C3×D33⋊D1311yescharacteristic, direct product factor, Sylow
161C2×C3—2861no—
162C2×C3—331no—
163C2×C3—391no—
164C2×C3—1431no—
165C2×C3—1431no—
166D3—111no—
167D3—131no—
168C22—4291noSylow
169C3—21no—
170C3C3×C7×D11×D1311yescharacteristic, complemented
171C3C7×D33⋊D1311yescharacteristic, direct product factor
172C2—331no—
173C2—391no—
174C2—1431no—
subgroupG/H
center, hypercenterC3×C7D33⋊D13
commutator, cosocle, hypocenterC3×C11×C13C22×C3×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C3×C11×C13
UCSC1 ◁ C3×C7

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×C7×D143C2semidirect
2. C3×C7×C11×D39C2semidirect
3. C3×C7×C13×D33C2semidirect
4. C7×D33⋊D13C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. C7×C13×D33C2×C3semidirect
8. C7×C11×D39C2×C3semidirect
10. C3×C7×D143D3semidirect
11. C3×C7×D143C2×C3semidirect
14. C3×D33⋊D13C7direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
21. C3×C13×D33C2×C7semidirect
22. C3×C11×D39C2×C7semidirect
23. C32×D143C2×C7semidirect
24. C7×D143C3×D3semidirect
27. D33⋊D13C3×C7direct (N × H)
29. C3×C7×D39D11semidirect
32. C3×C7×D33D13semidirect
35. C32×C11×C13C22×C7semidirect
38. C7×C11×C13C2×C3×D3semidirect
41. C13×D33C2×C3×C7semidirect
42. C11×D39C2×C3×C7semidirect
44. C3×D143D3×C7semidirect
45. C3×D143C2×C3×C7semidirect
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C2×D13semidirect
52. C7×D39C3×D11semidirect
60. C7×D33C3×D13semidirect
67. C3×C11×C13C2×D3×C7semidirect
68. C3×C11×C13C22×C3×C7semidirect
72. D143C3×D3×C7semidirect
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13C2×C3×D11semidirect
79. C3×D39C7×D11semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×C3×D13semidirect
85. C3×D33C7×D13semidirect
96. C11×C13C2×C3×D3×C7semidirect
102. C32×C13C2×C7×D11semidirect
103. C32×C11C2×C7×D13semidirect
104. C7×C13C3×D3×D11semidirect
108. D39C3×C7×D11semidirect
114. C7×C11C3×D3×D13semidirect
116. D33C3×C7×D13semidirect
122. C32×C7D11×D13semidirect
133. C3×C13D3×C7×D11semidirect
134. C3×C13C2×C3×C7×D11semidirect
137. C3×C11D3×C7×D13semidirect
138. C3×C11C2×C3×C7×D13semidirect
147. C3×C7C3×D11×D13semidirect
148. C3×C7D33⋊D13direct (N × H)
155. C13C3×D3×C7×D11semidirect
158. C11C3×D3×C7×D13semidirect
159. C32C7×D11×D13semidirect
160. C7C3×D33⋊D13direct (N × H)
170. C3C3×C7×D11×D13semidirect
171. C3C7×D33⋊D13direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D1432
C3×C7×C11×D392
C3×C7×C13×D332
C7×D33⋊D133
C3×C7×D11×D133
C3×D33⋊D137
C3×D3×C7×D1311
C3×D3×C7×D1113