Finite Group Databasebeta

← C3×C11×D21⋊D13 #49114919

Subgroups — C3×C11×D21⋊D13 #49114919

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×C11×D91C211yesmaximal, characteristic, complemented
2C3×C7×C11×D39C211yesmaximal, characteristic, complemented
3C3×C11×C13×D21C211yesmaximal, characteristic, complemented
4C11×D21⋊D13C311yesmaximal, characteristic, direct product factor
5C3×C11×D7×D13—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C11×C13×D21C2×C311yescharacteristic, complemented
8C7×C11×D39C2×C311yescharacteristic, complemented
9C3×C11×D91—21no—
10C3×C11×D91D311yescharacteristic, complemented
11C3×C11×D91C2×C311yescharacteristic, complemented
12C3×C11×C13×D7—31no—
13C3×C7×C11×D13—31no—
14C3×D3×C11×D13—71nomaximal, Hall
15C11×D7×D13—31noHall
16C3×D21⋊D13C1111yesmaximal, 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×D39D711yescharacteristic, complemented
22C3×D3×C11×C13—71no—
23C32×C11×D13—71no—
24C11×D91C3×D311yescharacteristic, complemented
25C11×C13×D7—31no—
26C7×C11×D13—31no—
27C2×C3×C11×D13—211no—
28D3×C11×D13—71no—
29C3×C13×D21C2×C1111yescharacteristic, complemented
30C3×C7×D39C2×C1111yescharacteristic, complemented
31C32×D91C2×C1111yescharacteristic, complemented
32C3×C11×D21D1311yescharacteristic, complemented
33C3×D3×C7×C11—131no—
34C32×C11×D7—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D21⋊D13C3×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—211no—
42C11×D39C3×D711yescharacteristic, complemented
43D3×C11×C13—71no—
44C3×C11×D13—31no—
45C3×C11×D13—71no—
46C3×C11×D13—71no—
47C3×C11×D13—141no—
48C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×C11×D13—211noHall
51C13×D21C2×C3×C1111yescharacteristic, complemented
52C7×D39C2×C3×C1111yescharacteristic, complemented
53C3×D91—21no—
54C3×D91D3×C1111yescharacteristic, complemented
55C3×D91C2×C3×C1111yescharacteristic, complemented
56C3×C13×D7—31no—
57C3×C7×D13—31no—
58C3×D3×D13—71noHall
59C2×C3×C7×C11—391no—
60C11×D21C3×D1311yescharacteristic, complemented
61D3×C7×C11—131no—
62C3×C11×D7—31no—
63C3×C11×D7—131no—
64C3×C11×D7—131no—
65C3×C11×D7—261no—
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—211no—
73C11×D13—31no—
74C11×D13—71no—
75C3×C7×C13—21no—
76C3×C7×C13C2×D3×C1111yescharacteristic, complemented
77C3×C7×C13C22×C3×C1111yescharacteristic, complemented
78C3×D3×D7—131noHall
79C3×D39C11×D711yescharacteristic, complemented
80C3×D3×C13—71no—
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—71no—
87C3×D3×C11—131no—
88D91C3×D3×C1111yescharacteristic, complemented
89C7×D13—31no—
90C13×D7—31no—
91C2×C3×D13—211no—
92D3×D13—71no—
93C2×C7×C11—391no—
94C11×D7—31no—
95C11×D7—131no—
96C11×C13C3×D3×D711yescharacteristic, complemented, Hall
97C22×C3×C11—2731no—
98C2×D3×C11—911no—
99C3×D21C11×D1311yescharacteristic, complemented
100C3×D3×C7—131no—
101C32×D7—131no—
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—211no—
108D39C3×C11×D711yescharacteristic, complemented
109C3×D13—31no—
110C3×D13—71no—
111C3×D13—71no—
112C3×D13—141no—
113D3×C13—71no—
114C7×C11C3×D3×D1311yescharacteristic, complemented, Hall
115C2×C3×C11—211no—
116C2×C3×C11—391no—
117C2×C3×C11—911no—
118C2×C3×C11—911no—
119C2×C3×C11—1821no—
120D3×C11—71no—
121D3×C11—131no—
122C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
123C2×D13—211noHall
124C22×C11—2731noHall
125C2×C3×C7—391no—
126D21C3×C11×D1311yescharacteristic, complemented
127C3×D7—31no—
128C3×D7—131no—
129C3×D7—131no—
130C3×D7—261no—
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×C11D21⋊D1311yescharacteristic, direct product factor
139C2×D7—391noHall
140C2×C13—211no—
141D13—31no—
142D13—71no—
143C2×C11—211no—
144C2×C11—391no—
145C2×C11—911no—
146C3×C7—21no—
147C3×C7D3×C11×D1311yescharacteristic, complemented
148C3×C7C2×C3×C11×D1311yescharacteristic, complemented
149C2×C32—911no—
150C3×D3—71no—
151C3×D3—131no—
152C2×C7—391no—
153D7—31no—
154D7—131no—
155C13C3×D3×C11×D711yescharacteristic, complemented, Sylow
156C22×C3—2731no—
157C2×D3—911no—
158C11C3×D21⋊D1311yescharacteristic, direct product factor, Sylow
159C32C11×D7×D1311yescharacteristic, complemented, Sylow
160C7C3×D3×C11×D1311yescharacteristic, complemented, Sylow
161C2×C3—211no—
162C2×C3—391no—
163C2×C3—911no—
164C2×C3—911no—
165C2×C3—1821no—
166D3—71no—
167D3—131no—
168C22—2731noSylow
169C3—21no—
170C3C3×C11×D7×D1311yescharacteristic, complemented
171C3C11×D21⋊D1311yescharacteristic, direct product factor
172C2—211no—
173C2—391no—
174C2—911no—
subgroupG/H
center, hypercenterC3×C11D21⋊D13
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×C7×C11×D39C2semidirect
3. C3×C11×C13×D21C2semidirect
4. C11×D21⋊D13C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. C11×C13×D21C2×C3semidirect
8. C7×C11×D39C2×C3semidirect
10. C3×C11×D91D3semidirect
11. C3×C11×D91C2×C3semidirect
16. C3×D21⋊D13C11direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
21. C3×C11×D39D7semidirect
24. C11×D91C3×D3semidirect
29. C3×C13×D21C2×C11semidirect
30. C3×C7×D39C2×C11semidirect
31. C32×D91C2×C11semidirect
32. C3×C11×D21D13semidirect
35. C32×C11×C13C2×D7semidirect
36. D21⋊D13C3×C11direct (N × H)
38. C7×C11×C13C2×C3×D3semidirect
42. C11×D39C3×D7semidirect
48. C32×C7×C13C22×C11semidirect
49. C32×C7×C11C2×D13semidirect
51. C13×D21C2×C3×C11semidirect
52. C7×D39C2×C3×C11semidirect
54. C3×D91D3×C11semidirect
55. C3×D91C2×C3×C11semidirect
60. C11×D21C3×D13semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×C3×D7semidirect
76. C3×C7×C13C2×D3×C11semidirect
77. C3×C7×C13C22×C3×C11semidirect
79. C3×D39C11×D7semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×C3×D13semidirect
88. D91C3×D3×C11semidirect
96. C11×C13C3×D3×D7semidirect
99. C3×D21C11×D13semidirect
102. C32×C13C2×C11×D7semidirect
103. C32×C11D7×D13semidirect
104. C7×C13C2×C3×D3×C11semidirect
108. D39C3×C11×D7semidirect
114. C7×C11C3×D3×D13semidirect
122. C32×C7C2×C11×D13semidirect
126. D21C3×C11×D13semidirect
133. C3×C13D3×C11×D7semidirect
134. C3×C13C2×C3×C11×D7semidirect
137. C3×C11C3×D7×D13semidirect
138. C3×C11D21⋊D13direct (N × H)
147. C3×C7D3×C11×D13semidirect
148. C3×C7C2×C3×C11×D13semidirect
155. C13C3×D3×C11×D7semidirect
158. C11C3×D21⋊D13direct (N × H)
159. C32C11×D7×D13semidirect
160. C7C3×D3×C11×D13semidirect
170. C3C3×C11×D7×D13semidirect
171. C3C11×D21⋊D13direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×D912
C3×C7×C11×D392
C3×C11×C13×D212
C11×D21⋊D133
C3×C11×D7×D133
C3×D3×C11×D137
C3×D21⋊D1311
C3×D3×C11×D713