Finite Group Databasebeta

← D21×C11⋊(D13⋊C3) #49114789

Subgroups — D21×C11⋊(D13⋊C3) #49114789

Order 36036.

176 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 42 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⋊(C11⋊((C13⋊C3)⋊D7))C211yesmaximal, characteristic, complemented
2C11×C13⋊C3×D21C211yesmaximal, characteristic, complemented
3C3×C7×C11⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
4D21×D143C311yesmaximal, characteristic, complemented
5D7×C11⋊(D13⋊C3)—31nomaximal
6C3×C7×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C11⋊((C13⋊C3)⋊D7)—31no—
8C11×D7×C13⋊C3—31no—
9C7×C11⋊(D13⋊C3)—21no—
10C7×C11⋊(D13⋊C3)D311yescharacteristic, complemented
11D3003C2×C311yescharacteristic, complemented
12C11×C13×D21C2×C311yescharacteristic, complemented
13C3×C7×D143C2×C311yescharacteristic, complemented
14D3×C11⋊(D13⋊C3)—71nomaximal, Hall
15D7×D143—31noHall
16D21×D13⋊C3—111nomaximal, Hall
17C7×C11×C13⋊C3—21no—
18C7×C11×C13⋊C3C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D11×D21—131nomaximal, Hall
21C3⋊(C11⋊(D13⋊C3))—71no—
22D3×C11×C13⋊C3—71no—
23C3×C11⋊(D13⋊C3)D711yescharacteristic, complemented
24D1001—31no—
25C11×C13×D7—31no—
26C7×D143C3×D311yescharacteristic, complemented
27D3×D143—71no—
28C2×C11⋊(D13⋊C3)—211no—
29C3⋊((C13⋊C3)⋊D7)—111no—
30C13⋊C3×D21D1111yescharacteristic, complemented
31C3×C7×D13⋊C3—111no—
32C3×D231—131no—
33C3×C11×D21—131no—
34C32×C7×D11—131no—
35C3×C11×C13⋊C3C2×D711yescharacteristic, complemented, Hall
36D13×D21—111no—
37D7×D13⋊C3—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D11×D21—131no—
40C3×D7×D11—391no—
41D429—71no—
42D3×C11×C13—71no—
43C3×D143C3×D711yescharacteristic, complemented
44C2×C11×C13⋊C3—211no—
45C11⋊(D13⋊C3)—21no—
46C11⋊(D13⋊C3)—211no—
47C11⋊(D13⋊C3)D2111yescharacteristic, direct product factor
48C3×C7×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11—131noHall
50C2×D143—211noHall
51D273—111no—
52C13×D21C3×D1111yescharacteristic, complemented
53C3×C7×D13—111no—
54(C13⋊C3)⋊D7—331no—
55D7×C13⋊C3—31no—
56C7×D13⋊C3—111no—
57C7×D13⋊C3—221no—
58D3×D13⋊C3—771noHall
59D231—131no—
60C11×D21D13⋊C311yescharacteristic, complemented
61C3×D77—391no—
62C3×C11×D7—391no—
63C3×C7×D11—131no—
64C3×C7×D11—131no—
65C3×C7×D11—261no—
66C3×C11×C13C2×C3×D711yescharacteristic, complemented
67C11×C13⋊C3—21no—
68C11×C13⋊C3C2×D2111yescharacteristic, complemented
69C3×D3×D11—911noHall
70D7×D13—331noHall
71D7×D11—391noHall
72C2×C11×C13—211no—
73D143—211no—
74D143C3×D2111yescharacteristic, complemented
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76C7×C13⋊C3—21no—
77C7×C13⋊C3D3×D1111yescharacteristic, complemented
78C2×C3×D21—1431noHall
79C3⋊(D13⋊C3)—771no—
80D3×C13⋊C3—71no—
81C3×D13⋊C3—111no—
82C3×C7×C11—131no—
83C3×C7×C11—261no—
84C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
85C3×D33—911no—
86C3×D3×C11—911no—
87C32×D11—131no—
88D91—331no—
89C7×D13—111no—
90C13×D7—31no—
91D3×D13—771no—
92C2×D13⋊C3—2311no—
93D77—391no—
94C7×D11—131no—
95C11×D7—31no—
96C11×C13C2×C3×D2111yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11—911no—
99C2×C32×C7—1431no—
100C3×D21—131no—
101C3×D21—1431no—
102C3×C13⋊C3D7×D1111yescharacteristic, complemented, Hall
103C32×C11—131noHall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105C2×D21—1431no—
106C2×C3×D7—4291no—
107D39—771no—
108C3×D13—111no—
109D3×C13—71no—
110C2×C13⋊C3—211no—
111D13⋊C3—111no—
112D13⋊C3—221no—
113D13⋊C3—2311no—
114C7×C11D3×D13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33—911no—
117C3×D11—131no—
118C3×D11—131no—
119C3×D11—2731no—
120C3×D11—261no—
121D3×C11—71no—
122C32×C7—131noHall
123C2×D13—2311noHall
124C2×D11—2731noHall
125C2×C3×C7—2861no—
126C2×C3×C7—1431no—
127C2×C3×C7—1431no—
128D21—1431no—
129D21C11⋊(D13⋊C3)11yescharacteristic, direct product factor
130C3×D7—391no—
131C3×D7—4291no—
132C3×C13C3×D7×D1111yescharacteristic, complemented
133C13⋊C3—21no—
134C13⋊C3D11×D2111yescharacteristic, complemented
135C2×C3×D3—10011noHall
136C3×C11—131no—
137C3×C11—261no—
138C3×C11D7×D13⋊C311yescharacteristic, complemented
139C2×D7—4291noHall
140C2×C13—211no—
141D13—111no—
142D13—2311no—
143C2×C11—211no—
144D11—131no—
145D11—2731no—
146C3×C7—131no—
147C3×C7—261no—
148C3×C7C2×C11⋊(D13⋊C3)11yescharacteristic, complemented
149C2×C32—1431no—
150C3×D3—911no—
151C3×D3—10011no—
152C2×C7—1431no—
153D7—31no—
154D7—4291no—
155C13C3×D11×D2111yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—10011no—
158C11D21×D13⋊C311yescharacteristic, complemented, Sylow
159C32—131noSylow
160C7D3×C11⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—2861no—
163C2×C3—1431no—
164C2×C3—1431no—
165C2×C3—30031no—
166D3—71no—
167D3—10011no—
168C22—30031noSylow
169C3—131no—
170C3—261no—
171C3D7×C11⋊(D13⋊C3)11yescharacteristic, complemented
172C2—211no—
173C2—1431no—
174C2—30031no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C22×C3
LCSG ▷ C3×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C11⋊((C13⋊C3)⋊D7))C2semidirect
2. C11×C13⋊C3×D21C2semidirect
3. C3×C7×C11⋊(D13⋊C3)C2semidirect
4. D21×D143C3semidirect
6. C3×C7×C11×C13⋊C3C22semidirect
10. C7×C11⋊(D13⋊C3)D3semidirect
11. D3003C2×C3semidirect
12. C11×C13×D21C2×C3semidirect
13. C3×C7×D143C2×C3semidirect
18. C7×C11×C13⋊C3C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
23. C3×C11⋊(D13⋊C3)D7semidirect
26. C7×D143C3×D3semidirect
30. C13⋊C3×D21D11semidirect
35. C3×C11×C13⋊C3C2×D7semidirect
38. C7×C11×C13C2×C3×D3semidirect
43. C3×D143C3×D7semidirect
47. C11⋊(D13⋊C3)D21direct (N × H)
48. C3×C7×C13⋊C3C2×D11semidirect
52. C13×D21C3×D11semidirect
60. C11×D21D13⋊C3semidirect
66. C3×C11×C13C2×C3×D7semidirect
68. C11×C13⋊C3C2×D21semidirect
74. D143C3×D21semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. C7×C13⋊C3D3×D11semidirect
84. C3×C7×C11C2×D13⋊C3semidirect
96. C11×C13C2×C3×D21semidirect
102. C3×C13⋊C3D7×D11semidirect
104. C7×C13C3×D3×D11semidirect
114. C7×C11D3×D13⋊C3semidirect
129. D21C11⋊(D13⋊C3)direct (N × H)
132. C3×C13C3×D7×D11semidirect
134. C13⋊C3D11×D21semidirect
138. C3×C11D7×D13⋊C3semidirect
148. C3×C7C2×C11⋊(D13⋊C3)semidirect
155. C13C3×D11×D21semidirect
158. C11D21×D13⋊C3semidirect
160. C7D3×C11⋊(D13⋊C3)semidirect
171. C3D7×C11⋊(D13⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C11⋊((C13⋊C3)⋊D7))2
C11×C13⋊C3×D212
C3×C7×C11⋊(D13⋊C3)2
D21×D1433
D7×C11⋊(D13⋊C3)3
D3×C11⋊(D13⋊C3)7
D21×D13⋊C311
C3×D11×D2113