Finite Group Databasebeta

← C11×D39⋊D21 #49114944

Subgroups — C11×D39⋊D21 #49114944

Order 36036.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3×C7×C11×D39C211yesmaximal, characteristic, complemented
2C3×C11×D273C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4C11×D21⋊D13—31nomaximal
5C11×D13×D21—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C11×D273D311yescharacteristic, complemented
8C11×C13×D21—31no—
9C11×C13×D21—31no—
10C11×C13×D21—61no—
11C7×C11×D39D311yescharacteristic, complemented
12C3×C11×D91—31no—
13C3×C7×C11×D13—31no—
14C11×(C3⋊D3)⋊D13—71nomaximal, Hall
15C11×D7×D13—91noHall
16D39⋊D21C1111yesmaximal, characteristic, direct product factor, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D3×C11×D21—131nomaximal, Hall
21C11×C13×C3⋊D3—71no—
22C3×C11×D39—71no—
23C3×C11×D39D711yescharacteristic, complemented
24C11×D91—31no—
25C11×C13×D7—91no—
26C7×C11×D13—31no—
27D3×C11×D13—211no—
28D3×C11×D13—211no—
29C13×C3⋊D21C2×C1111yescharacteristic, complemented
30C3×D273C2×C1111yescharacteristic, complemented
31C3×C7×D39C2×C1111yescharacteristic, complemented
32C11×C3⋊D21D1311yescharacteristic, complemented
33C3×C11×D21—131no—
34C3×D3×C7×C11—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D21⋊D13—31no—
37D13×D21—31no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39C2×C11×D21—391no—
40D3×C11×D7—391no—
41C11×D39—71no—
42C11×D39D2111yescharacteristic, complemented
43D3×C11×C13—211no—
44D3×C11×C13—211no—
45D3×C11×C13—421no—
46C3×C11×D13—31no—
47C3×C11×D13—211no—
48C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×C11×D13—631noHall
51D273D3×C1111yescharacteristic, complemented
52C13×D21—31no—
53C13×D21—31no—
54C13×D21—61no—
55C7×D39D3×C1111yescharacteristic, complemented
56C3×D91—31no—
57C3×C7×D13—31no—
58(C3⋊D3)⋊D13—71noHall
59C2×C3×C7×C11—391no—
60C11×D21—31no—
61C11×D21—31no—
62C11×D21—61no—
63C11×D21—131no—
64D3×C7×C11—131no—
65C3×C11×D7—391no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69D32×C11—911noHall
70D7×D13—91noHall
71C2×C11×D7—1171noHall
72C2×C11×C13—631no—
73C11×D13—31no—
74C11×D13—211no—
75C3×C7×C13—21no—
76C3×C7×C13C2×D3×C1111yescharacteristic, complemented
77C3×C7×C13C2×D3×C1111yescharacteristic, complemented
78D3×D21—131noHall
79C13×C3⋊D3—71no—
80C3×D39—71no—
81C3×D39C11×D711yescharacteristic, complemented
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11D3×D1311yescharacteristic, complemented
85C11×C3⋊D3—71no—
86C3×D3×C11—131no—
87C3×D3×C11—911no—
88D91—31no—
89C7×D13—31no—
90C13×D7—91no—
91D3×D13—211no—
92D3×D13—211no—
93C2×C7×C11—391no—
94C11×D7—91no—
95C11×D7—391no—
96C11×C13D3×D2111yescharacteristic, complemented, Hall
97C2×D3×C11—2731no—
98C2×D3×C11—2731no—
99C3⋊D21C11×D1311yescharacteristic, complemented
100C3×D21—131no—
101C3×D3×C7—131no—
102C32×C13C2×C11×D711yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13D32×C1111yescharacteristic, complemented, Hall
105C2×D21—391no—
106D3×D7—391no—
107D39—71no—
108D39C11×D2111yescharacteristic, complemented
109C3×D13—31no—
110C3×D13—211no—
111D3×C13—211no—
112D3×C13—211no—
113D3×C13—421no—
114C7×C11(C3⋊D3)⋊D1311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116C2×C3×C11—391no—
117D3×C11—131no—
118D3×C11—211no—
119D3×C11—211no—
120D3×C11—421no—
121D3×C11—911no—
122C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
123C2×D13—631noHall
124C22×C11—8191noHall
125C2×C3×C7—391no—
126D21—31no—
127D21—31no—
128D21—61no—
129D21—131no—
130C3×D7—391no—
131D3×C7—131no—
132C3×C13—21no—
133C3×C13D3×C11×D711yescharacteristic, complemented
134C3×C13C2×C11×D2111yescharacteristic, complemented
135D32—911noHall
136C3×C11—21no—
137C3×C11D13×D2111yescharacteristic, complemented
138C3×C11D21⋊D1311yescharacteristic, complemented
139C2×D7—1171noHall
140C2×C13—631no—
141D13—31no—
142D13—211no—
143C2×C11—2731no—
144C2×C11—391no—
145C2×C11—631no—
146C3×C7—21no—
147C3×C7D3×C11×D1311yescharacteristic, complemented
148C3×C7D3×C11×D1311yescharacteristic, complemented
149C3⋊D3—71no—
150C3×D3—131no—
151C3×D3—911no—
152C2×C7—391no—
153D7—91no—
154D7—391no—
155C13D3×C11×D2111yescharacteristic, complemented, Sylow
156C2×D3—2731no—
157C2×D3—2731no—
158C11D39⋊D2111yescharacteristic, direct product factor, Sylow
159C32C11×D7×D1311yescharacteristic, complemented, Sylow
160C7C11×(C3⋊D3)⋊D1311yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—391no—
163D3—131no—
164D3—211no—
165D3—211no—
166D3—421no—
167D3—911no—
168C22—8191noSylow
169C3—21no—
170C3C11×D13×D2111yescharacteristic, complemented
171C3C11×D21⋊D1311yescharacteristic, complemented
172C2—2731no—
173C2—391no—
174C2—631no—
subgroupG/H
center, hypercenterC11D39⋊D21
commutator, cosocle, hypocenterC32×C7×C13C22×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×D39C2semidirect
2. C3×C11×D273C2semidirect
3. C11×C13×C3⋊D21C2semidirect
6. C32×C7×C11×C13C22semidirect
7. C11×D273D3semidirect
11. C7×C11×D39D3semidirect
16. D39⋊D21C11direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
23. C3×C11×D39D7semidirect
29. C13×C3⋊D21C2×C11semidirect
30. C3×D273C2×C11semidirect
31. C3×C7×D39C2×C11semidirect
32. C11×C3⋊D21D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
42. C11×D39D21semidirect
48. C32×C7×C13C22×C11semidirect
49. C32×C7×C11C2×D13semidirect
51. D273D3×C11semidirect
55. C7×D39D3×C11semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×D21semidirect
76. C3×C7×C13C2×D3×C11semidirect
77. C3×C7×C13C2×D3×C11semidirect
81. C3×D39C11×D7semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11D3×D13semidirect
96. C11×C13D3×D21semidirect
99. C3⋊D21C11×D13semidirect
102. C32×C13C2×C11×D7semidirect
103. C32×C11D7×D13semidirect
104. C7×C13D32×C11semidirect
108. D39C11×D21semidirect
114. C7×C11(C3⋊D3)⋊D13semidirect
122. C32×C7C2×C11×D13semidirect
133. C3×C13D3×C11×D7semidirect
134. C3×C13C2×C11×D21semidirect
137. C3×C11D13×D21semidirect
138. C3×C11D21⋊D13semidirect
147. C3×C7D3×C11×D13semidirect
148. C3×C7D3×C11×D13semidirect
155. C13D3×C11×D21semidirect
158. C11D39⋊D21direct (N × H)
159. C32C11×D7×D13semidirect
160. C7C11×(C3⋊D3)⋊D13semidirect
170. C3C11×D13×D21semidirect
171. C3C11×D21⋊D13semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C11×D392
C3×C11×D2732
C11×C13×C3⋊D212
C11×D21⋊D133
C11×D13×D213
C11×(C3⋊D3)⋊D137
D39⋊D2111
D3×C11×D2113