Finite Group Databasebeta

← C3×C11×D7×D39 #49114917

Subgroups — C3×C11×D7×D39 #49114917

Order 36036.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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×C11×C13×D7C211yesmaximal, characteristic, complemented
2C3×C7×C11×D39C211yesmaximal, characteristic, complemented
3C3×C11×D273C211yesmaximal, characteristic, complemented
4C11×D7×D39C311yesmaximal, characteristic, direct product factor
5C3×C11×D7×D13—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C11×D273C2×C311yescharacteristic, complemented
8C7×C11×D39C2×C311yescharacteristic, complemented
9C3×C11×D91—31no—
10C3×C11×C13×D7—21no—
11C3×C11×C13×D7D311yescharacteristic, complemented
12C3×C11×C13×D7C2×C311yescharacteristic, complemented
13C3×C7×C11×D13—31no—
14C2×C3×C11×D39—71nomaximal, Hall
15C11×D7×D13—31noHall
16C3×D7×D39C1111yesmaximal, characteristic, direct product factor, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D3×C11×D7—131nomaximal, Hall
21C3×C11×D39—71no—
22C3×C11×D39D711yescharacteristic, direct product factor
23C2×C32×C11×C13—71no—
24C11×D91—31no—
25C11×C13×D7C3×D311yescharacteristic, complemented
26C7×C11×D13—31no—
27C2×C11×D39—71no—
28C2×C3×C11×D13—211no—
29C3×D273C2×C1111yescharacteristic, complemented
30C3×C7×D39C2×C1111yescharacteristic, complemented
31C32×C13×D7C2×C1111yescharacteristic, complemented
32C3×C11×D21—131no—
33C3×D3×C7×C11—131no—
34C32×C11×D7D1311yescharacteristic, complemented
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D7×D39C3×C1111yescharacteristic, direct product factor
37C3×D7×D13—31no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C3×C11×D7—391no—
40D3×C11×D7—131no—
41C2×C3×C11×C13—71no—
42C2×C3×C11×C13—71no—
43C2×C3×C11×C13—141no—
44C11×D39—71no—
45C11×D39C3×D711yescharacteristic, direct product factor
46C3×C11×D13—31no—
47C3×C11×D13—211no—
48C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×C11×D13—211noHall
51D273C2×C3×C1111yescharacteristic, complemented
52C7×D39C2×C3×C1111yescharacteristic, complemented
53C3×D91—31no—
54C3×C13×D7—21no—
55C3×C13×D7D3×C1111yescharacteristic, complemented
56C3×C13×D7C2×C3×C1111yescharacteristic, complemented
57C3×C7×D13—31no—
58C2×C3×D39—71noHall
59C2×C3×C7×C11—391no—
60C11×D21—131no—
61D3×C7×C11—131no—
62C3×C11×D7—21no—
63C3×C11×D7—391no—
64C3×C11×D7C3×D1311yescharacteristic, complemented
65C3×C11×D7D3911yescharacteristic, direct product factor
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×C3×D711yescharacteristic, complemented
69C2×C3×D3×C11—911noHall
70D7×D13—31noHall
71C2×C11×D7—391noHall
72C2×C11×C13—71no—
73C11×D13—31no—
74C11×D13—211no—
75C3×C7×C13—21no—
76C3×C7×C13C2×D3×C1111yescharacteristic, complemented
77C3×C7×C13C22×C3×C1111yescharacteristic, complemented
78C3×D3×D7—131noHall
79C2×C32×C13—71no—
80C3×D39—71no—
81C3×D39C11×D711yescharacteristic, direct product factor
82C3×C7×C11—21no—
83C3×C7×C11C2×C3×D1311yescharacteristic, complemented
84C3×C7×C11C2×D3911yescharacteristic, complemented
85C2×C32×C11—71no—
86C3×D3×C11—131no—
87C3×D3×C11—911no—
88D91—31no—
89C7×D13—31no—
90C13×D7C3×D3×C1111yescharacteristic, complemented
91C2×D39—71no—
92C2×C3×D13—211no—
93C2×C7×C11—391no—
94C11×D7—391no—
95C11×D7C3×D3911yescharacteristic, direct product factor
96C11×C13C3×D3×D711yescharacteristic, complemented, Hall
97C22×C3×C11—2731no—
98C2×D3×C11—911no—
99C3×D21—131no—
100C3×D3×C7—131no—
101C32×D7C11×D1311yescharacteristic, complemented
102C32×C13C2×C11×D711yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
105C2×C3×D7—391no—
106D3×D7—131no—
107C2×C3×C13—71no—
108C2×C3×C13—71no—
109C2×C3×C13—141no—
110D39—71no—
111D39C3×C11×D711yescharacteristic, direct product factor
112C3×D13—31no—
113C3×D13—211no—
114C7×C11C2×C3×D3911yescharacteristic, complemented, Hall
115C2×C3×C11—71no—
116C2×C3×C11—71no—
117C2×C3×C11—141no—
118C2×C3×C11—2731no—
119C2×C3×C11—391no—
120D3×C11—131no—
121D3×C11—911no—
122C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
123C2×D13—211noHall
124C22×C11—2731noHall
125C2×C3×C7—391no—
126D21—131no—
127C3×D7—21no—
128C3×D7—391no—
129C3×D7C3×C11×D1311yescharacteristic, complemented
130C3×D7C11×D3911yescharacteristic, direct product factor
131D3×C7—131no—
132C3×C13—21no—
133C3×C13D3×C11×D711yescharacteristic, complemented
134C3×C13C2×C3×C11×D711yescharacteristic, complemented
135C2×C3×D3—911noHall
136C3×C11—21no—
137C3×C11C3×D7×D1311yescharacteristic, complemented
138C3×C11D7×D3911yescharacteristic, direct product factor
139C2×D7—391noHall
140C2×C13—71no—
141D13—31no—
142D13—211no—
143C2×C11—71no—
144C2×C11—2731no—
145C2×C11—391no—
146C3×C7—21no—
147C3×C7C2×C3×C11×D1311yescharacteristic, complemented
148C3×C7C2×C11×D3911yescharacteristic, complemented
149C2×C32—71no—
150C3×D3—131no—
151C3×D3—911no—
152C2×C7—391no—
153D7—391no—
154D7C3×C11×D3911yescharacteristic, direct product factor
155C13C3×D3×C11×D711yescharacteristic, complemented, Sylow
156C22×C3—2731no—
157C2×D3—911no—
158C11C3×D7×D3911yescharacteristic, direct product factor, Sylow
159C32C11×D7×D1311yescharacteristic, complemented, Sylow
160C7C2×C3×C11×D3911yescharacteristic, complemented, Sylow
161C2×C3—71no—
162C2×C3—71no—
163C2×C3—141no—
164C2×C3—2731no—
165C2×C3—391no—
166D3—131no—
167D3—911no—
168C22—2731noSylow
169C3—21no—
170C3C3×C11×D7×D1311yescharacteristic, complemented
171C3C11×D7×D3911yescharacteristic, direct product factor
172C2—71no—
173C2—2731no—
174C2—391no—
subgroupG/H
center, hypercenterC3×C11D7×D39
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C3×C7×C13
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×C13×D7C2semidirect
2. C3×C7×C11×D39C2semidirect
3. C3×C11×D273C2semidirect
4. C11×D7×D39C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. C11×D273C2×C3semidirect
8. C7×C11×D39C2×C3semidirect
11. C3×C11×C13×D7D3semidirect
12. C3×C11×C13×D7C2×C3semidirect
16. C3×D7×D39C11direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
22. C3×C11×D39D7direct (N × H)
25. C11×C13×D7C3×D3semidirect
29. C3×D273C2×C11semidirect
30. C3×C7×D39C2×C11semidirect
31. C32×C13×D7C2×C11semidirect
34. C32×C11×D7D13semidirect
35. C32×C11×C13C2×D7semidirect
36. D7×D39C3×C11direct (N × H)
38. C7×C11×C13C2×C3×D3semidirect
45. C11×D39C3×D7direct (N × H)
48. C32×C7×C13C22×C11semidirect
49. C32×C7×C11C2×D13semidirect
51. D273C2×C3×C11semidirect
52. C7×D39C2×C3×C11semidirect
55. C3×C13×D7D3×C11semidirect
56. C3×C13×D7C2×C3×C11semidirect
64. C3×C11×D7C3×D13semidirect
65. C3×C11×D7D39direct (N × H)
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×C3×D7semidirect
76. C3×C7×C13C2×D3×C11semidirect
77. C3×C7×C13C22×C3×C11semidirect
81. C3×D39C11×D7direct (N × H)
83. C3×C7×C11C2×C3×D13semidirect
84. C3×C7×C11C2×D39semidirect
90. C13×D7C3×D3×C11semidirect
95. C11×D7C3×D39direct (N × H)
96. C11×C13C3×D3×D7semidirect
101. C32×D7C11×D13semidirect
102. C32×C13C2×C11×D7semidirect
103. C32×C11D7×D13semidirect
104. C7×C13C2×C3×D3×C11semidirect
111. D39C3×C11×D7direct (N × H)
114. C7×C11C2×C3×D39semidirect
122. C32×C7C2×C11×D13semidirect
129. C3×D7C3×C11×D13semidirect
130. C3×D7C11×D39direct (N × H)
133. C3×C13D3×C11×D7semidirect
134. C3×C13C2×C3×C11×D7semidirect
137. C3×C11C3×D7×D13semidirect
138. C3×C11D7×D39direct (N × H)
147. C3×C7C2×C3×C11×D13semidirect
148. C3×C7C2×C11×D39semidirect
154. D7C3×C11×D39direct (N × H)
155. C13C3×D3×C11×D7semidirect
158. C11C3×D7×D39direct (N × H)
159. C32C11×D7×D13semidirect
160. C7C2×C3×C11×D39semidirect
170. C3C3×C11×D7×D13semidirect
171. C3C11×D7×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×C13×D72
C3×C7×C11×D392
C3×C11×D2732
C11×D7×D393
C3×C11×D7×D133
C2×C3×C11×D397
C3×D7×D3911
C3×D3×C11×D713