Finite Group Databasebeta

← C3×D3×C11×D91 #49114918

Subgroups — C3×D3×C11×D91 #49114918

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×D91C211yesmaximal, characteristic, complemented
2C3×D3×C7×C11×C13C211yesmaximal, characteristic, complemented
3C3×C11×D273C211yesmaximal, characteristic, complemented
4C2×C3×C11×D91—31nomaximal
5D3×C11×D91C311yesmaximal, characteristic, direct product factor
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C11×D273C2×C311yescharacteristic, complemented
8D3×C7×C11×C13C2×C311yescharacteristic, complemented
9C3×C11×D91—21no—
10C3×C11×D91—31no—
11C3×C11×D91D311yescharacteristic, direct product factor
12C3×C11×D91C2×C311yescharacteristic, complemented
13C2×C3×C7×C11×C13—31no—
14C3×D3×C11×D13—71nomaximal, Hall
15C2×C11×D91—31noHall
16C3×D3×D91C1111yesmaximal, 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×D3×C11×C13D711yescharacteristic, complemented
23C32×C11×D13—71no—
24C11×D91—31no—
25C11×D91C3×D311yescharacteristic, direct product factor
26C2×C7×C11×C13—31no—
27C2×C3×C11×D13—211no—
28D3×C11×D13—71no—
29C3×D273C2×C1111yescharacteristic, complemented
30C3×D3×C7×C13C2×C1111yescharacteristic, complemented
31C32×D91C2×C1111yescharacteristic, complemented
32C3×C11×D21—131no—
33C3×D3×C7×C11D1311yescharacteristic, complemented
34C32×C11×D7—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36C2×C3×D91—31no—
37D3×D91C3×C1111yescharacteristic, direct product factor
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C3×C11×D7—391no—
40D3×C11×D7—131no—
41C2×C3×C11×C13—31no—
42C11×D39—71no—
43D3×C11×C13C3×D711yescharacteristic, complemented
44C3×C11×D13—71no—
45C3×C11×D13—71no—
46C3×C11×D13—141no—
47C3×C11×D13—211no—
48C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×C11×D13—211noHall
51C2×C3×C7×C13—31no—
52D273C2×C3×C1111yescharacteristic, complemented
53D3×C7×C13C2×C3×C1111yescharacteristic, complemented
54C3×D91—21no—
55C3×D91—31no—
56C3×D91D3×C1111yescharacteristic, direct product factor
57C3×D91C2×C3×C1111yescharacteristic, complemented
58C3×D3×D13—71noHall
59C2×C3×C7×C11—31no—
60C11×D21—131no—
61D3×C7×C11C3×D1311yescharacteristic, complemented
62C3×C11×D7—131no—
63C3×C11×D7—131no—
64C3×C11×D7—261no—
65C3×C11×D7—391no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×C3×D711yescharacteristic, complemented
69C2×C3×D3×C11—911noHall
70C2×D91—31noHall
71C2×C11×D7—391noHall
72C2×C11×C13—31no—
73C11×D13—71no—
74C11×D13—211no—
75C3×C7×C13—21no—
76C3×C7×C13C2×D3×C1111yescharacteristic, complemented
77C3×C7×C13C22×C3×C1111yescharacteristic, complemented
78C3×D3×D7—131noHall
79C3×D39—71no—
80C3×D3×C13C11×D711yescharacteristic, complemented
81C32×D13—71no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×C3×D1311yescharacteristic, complemented
85C2×C32×C11—911no—
86C3×D3×C11—911no—
87C3×D3×C11D9111yescharacteristic, direct product factor
88C2×C7×C13—31no—
89D91—31no—
90D91C3×D3×C1111yescharacteristic, direct product factor
91C2×C3×D13—211no—
92D3×D13—71no—
93C2×C7×C11—31no—
94C11×D7—131no—
95C11×D7—391no—
96C11×C13C3×D3×D711yescharacteristic, complemented, Hall
97C22×C3×C11—2731no—
98C2×D3×C11—911no—
99C3×D21—131no—
100C3×D3×C7C11×D1311yescharacteristic, complemented
101C32×D7—131no—
102C32×C13C2×C11×D711yescharacteristic, complemented, Hall
103C32×C11C2×D9111yescharacteristic, complemented, Hall
104C7×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
105C2×C3×D7—391no—
106D3×D7—131no—
107C2×C3×C13—31no—
108D39—71no—
109C3×D13—71no—
110C3×D13—71no—
111C3×D13—141no—
112C3×D13—211no—
113D3×C13C3×C11×D711yescharacteristic, complemented
114C7×C11C3×D3×D1311yescharacteristic, complemented, Hall
115C2×C3×C11—31no—
116C2×C3×C11—2731no—
117C2×C3×C11—911no—
118C2×C3×C11—911no—
119C2×C3×C11—1821no—
120D3×C11—911no—
121D3×C11C3×D9111yescharacteristic, direct product factor
122C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
123C2×D13—211noHall
124C22×C11—2731noHall
125C2×C3×C7—31no—
126D21—131no—
127C3×D7—131no—
128C3×D7—131no—
129C3×D7—261no—
130C3×D7—391no—
131D3×C7C3×C11×D1311yescharacteristic, complemented
132C3×C13—21no—
133C3×C13D3×C11×D711yescharacteristic, complemented
134C3×C13C2×C3×C11×D711yescharacteristic, complemented
135C2×C3×D3—911noHall
136C3×C11—21no—
137C3×C11D3×D9111yescharacteristic, direct product factor
138C3×C11C2×C3×D9111yescharacteristic, complemented
139C2×D7—391noHall
140C2×C13—31no—
141D13—71no—
142D13—211no—
143C2×C11—31no—
144C2×C11—2731no—
145C2×C11—911no—
146C3×C7—21no—
147C3×C7D3×C11×D1311yescharacteristic, complemented
148C3×C7C2×C3×C11×D1311yescharacteristic, complemented
149C2×C32—911no—
150C3×D3—911no—
151C3×D3C11×D9111yescharacteristic, direct product factor
152C2×C7—31no—
153D7—131no—
154D7—391no—
155C13C3×D3×C11×D711yescharacteristic, complemented, Sylow
156C22×C3—2731no—
157C2×D3—911no—
158C11C3×D3×D9111yescharacteristic, direct product factor, Sylow
159C32C2×C11×D9111yescharacteristic, complemented, Sylow
160C7C3×D3×C11×D1311yescharacteristic, complemented, Sylow
161C2×C3—31no—
162C2×C3—2731no—
163C2×C3—911no—
164C2×C3—911no—
165C2×C3—1821no—
166D3—911no—
167D3C3×C11×D9111yescharacteristic, direct product factor
168C22—2731noSylow
169C3—21no—
170C3D3×C11×D9111yescharacteristic, direct product factor
171C3C2×C3×C11×D9111yescharacteristic, complemented
172C2—31no—
173C2—2731no—
174C2—911no—
subgroupG/H
center, hypercenterC3×C11D3×D91
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×D91C2semidirect
2. C3×D3×C7×C11×C13C2semidirect
3. C3×C11×D273C2semidirect
5. D3×C11×D91C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. C11×D273C2×C3semidirect
8. D3×C7×C11×C13C2×C3semidirect
11. C3×C11×D91D3direct (N × H)
12. C3×C11×D91C2×C3semidirect
16. C3×D3×D91C11direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
22. C3×D3×C11×C13D7semidirect
25. C11×D91C3×D3direct (N × H)
29. C3×D273C2×C11semidirect
30. C3×D3×C7×C13C2×C11semidirect
31. C32×D91C2×C11semidirect
33. C3×D3×C7×C11D13semidirect
35. C32×C11×C13C2×D7semidirect
37. D3×D91C3×C11direct (N × H)
38. C7×C11×C13C2×C3×D3semidirect
43. D3×C11×C13C3×D7semidirect
48. C32×C7×C13C22×C11semidirect
49. C32×C7×C11C2×D13semidirect
52. D273C2×C3×C11semidirect
53. D3×C7×C13C2×C3×C11semidirect
56. C3×D91D3×C11direct (N × H)
57. C3×D91C2×C3×C11semidirect
61. D3×C7×C11C3×D13semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×C3×D7semidirect
76. C3×C7×C13C2×D3×C11semidirect
77. C3×C7×C13C22×C3×C11semidirect
80. C3×D3×C13C11×D7semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×C3×D13semidirect
87. C3×D3×C11D91direct (N × H)
90. D91C3×D3×C11direct (N × H)
96. C11×C13C3×D3×D7semidirect
100. C3×D3×C7C11×D13semidirect
102. C32×C13C2×C11×D7semidirect
103. C32×C11C2×D91semidirect
104. C7×C13C2×C3×D3×C11semidirect
113. D3×C13C3×C11×D7semidirect
114. C7×C11C3×D3×D13semidirect
121. D3×C11C3×D91direct (N × H)
122. C32×C7C2×C11×D13semidirect
131. D3×C7C3×C11×D13semidirect
133. C3×C13D3×C11×D7semidirect
134. C3×C13C2×C3×C11×D7semidirect
137. C3×C11D3×D91direct (N × H)
138. C3×C11C2×C3×D91semidirect
147. C3×C7D3×C11×D13semidirect
148. C3×C7C2×C3×C11×D13semidirect
151. C3×D3C11×D91direct (N × H)
155. C13C3×D3×C11×D7semidirect
158. C11C3×D3×D91direct (N × H)
159. C32C2×C11×D91semidirect
160. C7C3×D3×C11×D13semidirect
167. D3C3×C11×D91direct (N × H)
170. C3D3×C11×D91direct (N × H)
171. C3C2×C3×C11×D91semidirect

Maximal subgroups

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

subgroupindex
C32×C11×D912
C3×D3×C7×C11×C132
C3×C11×D2732
C2×C3×C11×D913
D3×C11×D913
C3×D3×C11×D137
C3×D3×D9111
C3×D3×C11×D713