Finite Group Databasebeta

← C3×C11×D13×D21 #49114909

Subgroups — C3×C11×D13×D21 #49114909

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×C7×C11×D13C211yesmaximal, characteristic, complemented
2C3×C11×C13×D21C211yesmaximal, characteristic, complemented
3C3×C11×D273C211yesmaximal, characteristic, complemented
4C11×D13×D21C311yesmaximal, characteristic, direct product factor
5C3×C11×D7×D13—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C11×D273C2×C311yescharacteristic, complemented
8C11×C13×D21C2×C311yescharacteristic, complemented
9C3×C11×D91—31no—
10C3×C11×C13×D7—31no—
11C3×C7×C11×D13—21no—
12C3×C7×C11×D13D311yescharacteristic, complemented
13C3×C7×C11×D13C2×C311yescharacteristic, complemented
14C3×D3×C11×D13—71nomaximal, Hall
15C11×D7×D13—31noHall
16C3×D13×D21C1111yesmaximal, characteristic, direct product factor, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C2×C3×C11×D21—131nomaximal, Hall
21C3×C11×D39—71no—
22C3×D3×C11×C13—71no—
23C32×C11×D13D711yescharacteristic, complemented
24C11×D91—31no—
25C11×C13×D7—31no—
26C7×C11×D13C3×D311yescharacteristic, complemented
27C2×C3×C11×D13—211no—
28D3×C11×D13—71no—
29C3×D273C2×C1111yescharacteristic, complemented
30C3×C13×D21C2×C1111yescharacteristic, complemented
31C32×C7×D13C2×C1111yescharacteristic, complemented
32C2×C32×C7×C11—131no—
33C3×C11×D21—131no—
34C3×C11×D21D1311yescharacteristic, direct product factor
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D13×D21C3×C1111yescharacteristic, direct product factor
37C3×D7×D13—31no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C11×D21—131no—
40C2×C3×C11×D7—391no—
41C2×C3×C11×C13—211no—
42C11×D39—71no—
43D3×C11×C13—71no—
44C3×C11×D13—21no—
45C3×C11×D13—211no—
46C3×C11×D13C3×D711yescharacteristic, complemented
47C3×C11×D13D2111yescharacteristic, direct product factor
48C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×C11×D13—211noHall
51D273C2×C3×C1111yescharacteristic, complemented
52C13×D21C2×C3×C1111yescharacteristic, complemented
53C3×D91—31no—
54C3×C13×D7—31no—
55C3×C7×D13—21no—
56C3×C7×D13D3×C1111yescharacteristic, complemented
57C3×C7×D13C2×C3×C1111yescharacteristic, complemented
58C3×D3×D13—71noHall
59C2×C3×C7×C11—131no—
60C2×C3×C7×C11—131no—
61C2×C3×C7×C11—261no—
62C11×D21—131no—
63C11×D21C3×D1311yescharacteristic, direct product factor
64C3×C11×D7—31no—
65C3×C11×D7—391no—
66C3×C11×C13—21no—
67C3×C11×C13C2×C3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69C2×C3×D3×C11—911noHall
70D7×D13—31noHall
71C2×C11×D7—391noHall
72C2×C11×C13—211no—
73C11×D13—211no—
74C11×D13C3×D2111yescharacteristic, direct product factor
75C3×C7×C13—21no—
76C3×C7×C13C2×D3×C1111yescharacteristic, complemented
77C3×C7×C13C22×C3×C1111yescharacteristic, complemented
78C2×C3×D21—131noHall
79C3×D39—71no—
80C3×D3×C13—71no—
81C32×D13C11×D711yescharacteristic, complemented
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×C3×D1311yescharacteristic, complemented
85C2×C32×C11—131no—
86C3×D3×C11—71no—
87C3×D3×C11—911no—
88D91—31no—
89C7×D13C3×D3×C1111yescharacteristic, complemented
90C13×D7—31no—
91C2×C3×D13—211no—
92D3×D13—71no—
93C2×C7×C11—131no—
94C11×D7—31no—
95C11×D7—391no—
96C11×C13C2×C3×D2111yescharacteristic, complemented, Hall
97C22×C3×C11—2731no—
98C2×D3×C11—911no—
99C2×C32×C7—131no—
100C3×D21—131no—
101C3×D21C11×D1311yescharacteristic, direct product factor
102C32×C13C2×C11×D711yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
105C2×D21—131no—
106C2×C3×D7—391no—
107C2×C3×C13—211no—
108D39—71no—
109C3×D13—21no—
110C3×D13—211no—
111C3×D13C3×C11×D711yescharacteristic, complemented
112C3×D13C11×D2111yescharacteristic, direct product factor
113D3×C13—71no—
114C7×C11C3×D3×D1311yescharacteristic, complemented, Hall
115C2×C3×C11—131no—
116C2×C3×C11—131no—
117C2×C3×C11—2731no—
118C2×C3×C11—211no—
119C2×C3×C11—261no—
120D3×C11—71no—
121D3×C11—911no—
122C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
123C2×D13—211noHall
124C22×C11—2731noHall
125C2×C3×C7—131no—
126C2×C3×C7—131no—
127C2×C3×C7—261no—
128D21—131no—
129D21C3×C11×D1311yescharacteristic, direct product factor
130C3×D7—31no—
131C3×D7—391no—
132C3×C13—21no—
133C3×C13C2×C3×C11×D711yescharacteristic, complemented
134C3×C13C2×C11×D2111yescharacteristic, complemented
135C2×C3×D3—911noHall
136C3×C11—21no—
137C3×C11C3×D7×D1311yescharacteristic, complemented
138C3×C11D13×D2111yescharacteristic, direct product factor
139C2×D7—391noHall
140C2×C13—211no—
141D13—211no—
142D13C3×C11×D2111yescharacteristic, direct product factor
143C2×C11—131no—
144C2×C11—2731no—
145C2×C11—211no—
146C3×C7—21no—
147C3×C7D3×C11×D1311yescharacteristic, complemented
148C3×C7C2×C3×C11×D1311yescharacteristic, complemented
149C2×C32—131no—
150C3×D3—71no—
151C3×D3—911no—
152C2×C7—131no—
153D7—31no—
154D7—391no—
155C13C2×C3×C11×D2111yescharacteristic, complemented, Sylow
156C22×C3—2731no—
157C2×D3—911no—
158C11C3×D13×D2111yescharacteristic, direct product factor, Sylow
159C32C11×D7×D1311yescharacteristic, complemented, Sylow
160C7C3×D3×C11×D1311yescharacteristic, complemented, Sylow
161C2×C3—131no—
162C2×C3—131no—
163C2×C3—2731no—
164C2×C3—211no—
165C2×C3—261no—
166D3—71no—
167D3—911no—
168C22—2731noSylow
169C3—21no—
170C3C3×C11×D7×D1311yescharacteristic, complemented
171C3C11×D13×D2111yescharacteristic, direct product factor
172C2—131no—
173C2—2731no—
174C2—211no—
subgroupG/H
center, hypercenterC3×C11D13×D21
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×C7×C11×D13C2semidirect
2. C3×C11×C13×D21C2semidirect
3. C3×C11×D273C2semidirect
4. C11×D13×D21C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. C11×D273C2×C3semidirect
8. C11×C13×D21C2×C3semidirect
12. C3×C7×C11×D13D3semidirect
13. C3×C7×C11×D13C2×C3semidirect
16. C3×D13×D21C11direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
23. C32×C11×D13D7semidirect
26. C7×C11×D13C3×D3semidirect
29. C3×D273C2×C11semidirect
30. C3×C13×D21C2×C11semidirect
31. C32×C7×D13C2×C11semidirect
34. C3×C11×D21D13direct (N × H)
35. C32×C11×C13C2×D7semidirect
36. D13×D21C3×C11direct (N × H)
38. C7×C11×C13C2×C3×D3semidirect
46. C3×C11×D13C3×D7semidirect
47. C3×C11×D13D21direct (N × H)
48. C32×C7×C13C22×C11semidirect
49. C32×C7×C11C2×D13semidirect
51. D273C2×C3×C11semidirect
52. C13×D21C2×C3×C11semidirect
56. C3×C7×D13D3×C11semidirect
57. C3×C7×D13C2×C3×C11semidirect
63. C11×D21C3×D13direct (N × H)
67. C3×C11×C13C2×C3×D7semidirect
68. C3×C11×C13C2×D21semidirect
74. C11×D13C3×D21direct (N × H)
76. C3×C7×C13C2×D3×C11semidirect
77. C3×C7×C13C22×C3×C11semidirect
81. C32×D13C11×D7semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×C3×D13semidirect
89. C7×D13C3×D3×C11semidirect
96. C11×C13C2×C3×D21semidirect
101. C3×D21C11×D13direct (N × H)
102. C32×C13C2×C11×D7semidirect
103. C32×C11D7×D13semidirect
104. C7×C13C2×C3×D3×C11semidirect
111. C3×D13C3×C11×D7semidirect
112. C3×D13C11×D21direct (N × H)
114. C7×C11C3×D3×D13semidirect
122. C32×C7C2×C11×D13semidirect
129. D21C3×C11×D13direct (N × H)
133. C3×C13C2×C3×C11×D7semidirect
134. C3×C13C2×C11×D21semidirect
137. C3×C11C3×D7×D13semidirect
138. C3×C11D13×D21direct (N × H)
142. D13C3×C11×D21direct (N × H)
147. C3×C7D3×C11×D13semidirect
148. C3×C7C2×C3×C11×D13semidirect
155. C13C2×C3×C11×D21semidirect
158. C11C3×D13×D21direct (N × H)
159. C32C11×D7×D13semidirect
160. C7C3×D3×C11×D13semidirect
170. C3C3×C11×D7×D13semidirect
171. C3C11×D13×D21direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C3×C11×C13×D212
C3×C11×D2732
C11×D13×D213
C3×C11×D7×D133
C3×D3×C11×D137
C3×D13×D2111
C2×C3×C11×D2113