Finite Group Databasebeta

← D19⋊C3×C3⋊AGL(1,𝔽11) #49178508

Subgroups — D19⋊C3×C3⋊AGL(1,𝔽11) #49178508

Order 37620.

176 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C19⋊C3×C3⋊AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
2C3⋊((C11⋊C5)⋊(D19⋊C3))C211yesmaximal, characteristic, complemented
3C3×C11⋊C5×D19⋊C3C211yesmaximal, characteristic, complemented
4D19×C3⋊AGL(1,𝔽11)C311yesmaximal, characteristic, complemented
5AGL(1,𝔽11)×D19⋊C3—31nomaximal
6C3×C11⋊C5×C19⋊C3C2211yescharacteristic, complemented, Hall
7D33×D19⋊C3C511yesmaximal, characteristic, complemented, Hall
8(C11⋊C5)⋊(D19⋊C3)—31no—
9C19⋊C3×AGL(1,𝔽11)—31no—
10C11⋊C5×D19⋊C3—21no—
11C11⋊C5×D19⋊C3D311yescharacteristic, complemented
12C3⋊(C19⋊AGL(1,𝔽11))C2×C311yescharacteristic, complemented
13C19×C3⋊AGL(1,𝔽11)C2×C311yescharacteristic, complemented
14C3×D19×C11⋊C5C2×C311yescharacteristic, complemented
15D19×AGL(1,𝔽11)—31noHall
16C19⋊C3×D33C2×C511yescharacteristic, complemented
17C3⋊(C11⋊(D19⋊C3))C2×C511yescharacteristic, complemented
18C3×C11×D19⋊C3C2×C511yescharacteristic, complemented
19C5×D3×D19⋊C3—111nomaximal, Hall
20C11⋊C5×C19⋊C3—21no—
21C11⋊C5×C19⋊C3C2×D311yescharacteristic, complemented
22C3×C19×C11⋊C5C22×C311yescharacteristic, complemented
23D19×D33C3×C511yescharacteristic, complemented
24D11×D19⋊C3—31no—
25C19⋊AGL(1,𝔽11)—31no—
26C19×AGL(1,𝔽11)—31no—
27D19×C11⋊C5C3×D311yescharacteristic, complemented
28C2×C3×C3⋊AGL(1,𝔽11)—191nomaximal, Hall
29C3×C11×C19⋊C3C22×C511yescharacteristic, complemented, Hall
30C5×C3⋊(D19⋊C3)—111no—
31C5×D3×C19⋊C3—111no—
32C3×C5×D19⋊C3—111no—
33D627C2×C3×C511yescharacteristic, complemented
34C19×D33C2×C3×C511yescharacteristic, complemented
35C3×C11×D19C2×C3×C511yescharacteristic, complemented
36C11⋊(D19⋊C3)—31no—
37D11×C19⋊C3—31no—
38C11×D19⋊C3—21no—
39C11×D19⋊C3C5×D311yescharacteristic, complemented
40C5×D3×D19—111no—
41C2×C5×D19⋊C3—331no—
42C19×C11⋊C5C2×C3×D311yescharacteristic, complemented, Hall
43C2×C32×C11⋊C5—191no—
44C3×C3⋊AGL(1,𝔽11)—191no—
45C3×C3⋊AGL(1,𝔽11)—191no—
46C3×C5×C19⋊C3—111noHall
47D11×D19—31noHall
48D3×D19⋊C3—111noHall
49C2×C3⋊AGL(1,𝔽11)—191no—
50C2×C3×AGL(1,𝔽11)—571no—
51C3×C11×C19C22×C3×C511yescharacteristic, complemented
52C11×C19⋊C3—21no—
53C11×C19⋊C3C2×C5×D311yescharacteristic, complemented
54C5×D57—111no—
55C5×D3×C19—111no—
56C3×C5×D19—111no—
57C2×C5×C19⋊C3—331no—
58C5×D19⋊C3—111no—
59C5×D19⋊C3—221no—
60C5×D19⋊C3—331no—
61C32×C11⋊C5—191noHall
62D209—31no—
63C11×D19C3×C5×D311yescharacteristic, complemented
64C19×D11—31no—
65C2×C3×D33—191noHall
66C2×C5×D19—331noHall
67C3⋊(D19⋊C3)—111no—
68D3×C19⋊C3—111no—
69C3×D19⋊C3AGL(1,𝔽11)11yescharacteristic, complemented
70C2×C3×C11⋊C5—191no—
71C2×C3×C11⋊C5—191no—
72C2×C3×C11⋊C5—381no—
73C3⋊AGL(1,𝔽11)—191no—
74C3⋊AGL(1,𝔽11)D19⋊C311yescharacteristic, direct product factor
75C3×AGL(1,𝔽11)—571no—
76C3×AGL(1,𝔽11)—571no—
77C3×C5×C19—111no—
78C5×C19⋊C3—111no—
79C5×C19⋊C3—221no—
80D3×D19—111no—
81C2×D19⋊C3—331no—
82C2×AGL(1,𝔽11)—571noHall
83C11×C19C2×C3×C5×D311yescharacteristic, complemented, Hall
84C2×C32×C11—191no—
85C3×D33—191no—
86C3×D33—191no—
87C2×C5×C19—331no—
88C5×D19—111no—
89C5×D19—331no—
90C2×C3×C5×D3—2091noHall
91C3×C19⋊C3C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
92C3×C11⋊C5—191no—
93C3×C11⋊C5—381no—
94C3×C11⋊C5C2×D19⋊C311yescharacteristic, complemented
95C2×D33—191no—
96C2×C3×D11—571no—
97D57—111no—
98C3×D19C3×AGL(1,𝔽11)11yescharacteristic, complemented
99D3×C19—111no—
100C2×C19⋊C3—331no—
101D19⋊C3—21no—
102D19⋊C3—331no—
103D19⋊C3C3⋊AGL(1,𝔽11)11yescharacteristic, direct product factor
104C2×C11⋊C5—191no—
105AGL(1,𝔽11)—31no—
106AGL(1,𝔽11)—571no—
107C32×C11—191noHall
108C5×C19—111noHall
109C2×C32×C5—2091no—
110C3×C5×D3—2091no—
111C3×C5×D3—2091no—
112C2×D19—331noHall
113C2×C3×C11—191no—
114C2×C3×C11—191no—
115C2×C3×C11—381no—
116D33—191no—
117D33C5×D19⋊C311yescharacteristic, complemented
118C3×D11—571no—
119C3×D11—571no—
120C22×C3×C5—6271no—
121C2×C5×D3—2091no—
122C3×C19C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
123C19⋊C3—21no—
124C19⋊C3C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
125C11⋊C5D3×D19⋊C311yescharacteristic, complemented, Hall
126C32×C5—2091noHall
127C2×D11—571noHall
128C2×C19—331no—
129D19—331no—
130D19C3×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
131C2×C3×D3—2091noHall
132C3×C11—191no—
133C3×C11—381no—
134C3×C11C2×C5×D19⋊C311yescharacteristic, complemented
135C2×C3×C5—6271no—
136C2×C3×C5—6271no—
137C2×C3×C5—4181no—
138C2×C3×C5—2091no—
139C2×C3×C5—2091no—
140C5×D3—111no—
141C5×D3—2091no—
142C2×C11—191no—
143D11—31no—
144D11—571no—
145C22×C5—6271noHall
146C19C2×C3×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
147C2×C32—191no—
148C3×D3—2091no—
149C3×D3—2091no—
150C3×C5—111no—
151C3×C5—4181no—
152C3×C5—2091no—
153C22×C3—6271no—
154C2×D3—2091no—
155C11C5×D3×D19⋊C311yescharacteristic, complemented, Sylow
156C2×C5—331no—
157C2×C5—6271no—
158C2×C5—2091no—
159C32—191noSylow
160C2×C3—191no—
161C2×C3—191no—
162C2×C3—381no—
163C2×C3—6271no—
164C2×C3—6271no—
165D3—111no—
166D3—2091no—
167C5—111noSylow
168C22—6271noSylow
169C3—191no—
170C3—381no—
171C3AGL(1,𝔽11)×D19⋊C311yescharacteristic, complemented
172C2—191no—
173C2—331no—
174C2—6271no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C19C22×C3×C5
LCSG ▷ C3×C11×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C19⋊C3×C3⋊AGL(1,𝔽11)C2semidirect
2. C3⋊((C11⋊C5)⋊(D19⋊C3))C2semidirect
3. C3×C11⋊C5×D19⋊C3C2semidirect
4. D19×C3⋊AGL(1,𝔽11)C3semidirect
6. C3×C11⋊C5×C19⋊C3C22semidirect
7. D33×D19⋊C3C5semidirect
11. C11⋊C5×D19⋊C3D3semidirect
12. C3⋊(C19⋊AGL(1,𝔽11))C2×C3semidirect
13. C19×C3⋊AGL(1,𝔽11)C2×C3semidirect
14. C3×D19×C11⋊C5C2×C3semidirect
16. C19⋊C3×D33C2×C5semidirect
17. C3⋊(C11⋊(D19⋊C3))C2×C5semidirect
18. C3×C11×D19⋊C3C2×C5semidirect
21. C11⋊C5×C19⋊C3C2×D3semidirect
22. C3×C19×C11⋊C5C22×C3semidirect
23. D19×D33C3×C5semidirect
27. D19×C11⋊C5C3×D3semidirect
29. C3×C11×C19⋊C3C22×C5semidirect
33. D627C2×C3×C5semidirect
34. C19×D33C2×C3×C5semidirect
35. C3×C11×D19C2×C3×C5semidirect
39. C11×D19⋊C3C5×D3semidirect
42. C19×C11⋊C5C2×C3×D3semidirect
51. C3×C11×C19C22×C3×C5semidirect
53. C11×C19⋊C3C2×C5×D3semidirect
63. C11×D19C3×C5×D3semidirect
69. C3×D19⋊C3AGL(1,𝔽11)semidirect
74. C3⋊AGL(1,𝔽11)D19⋊C3direct (N × H)
83. C11×C19C2×C3×C5×D3semidirect
91. C3×C19⋊C3C2×AGL(1,𝔽11)semidirect
94. C3×C11⋊C5C2×D19⋊C3semidirect
98. C3×D19C3×AGL(1,𝔽11)semidirect
103. D19⋊C3C3⋊AGL(1,𝔽11)direct (N × H)
117. D33C5×D19⋊C3semidirect
122. C3×C19C2×C3×AGL(1,𝔽11)semidirect
124. C19⋊C3C2×C3⋊AGL(1,𝔽11)semidirect
125. C11⋊C5D3×D19⋊C3semidirect
130. D19C3×C3⋊AGL(1,𝔽11)semidirect
134. C3×C11C2×C5×D19⋊C3semidirect
146. C19C2×C3×C3⋊AGL(1,𝔽11)semidirect
155. C11C5×D3×D19⋊C3semidirect
171. C3AGL(1,𝔽11)×D19⋊C3semidirect

Maximal subgroups

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

subgroupindex
C19⋊C3×C3⋊AGL(1,𝔽11)2
C3⋊((C11⋊C5)⋊(D19⋊C3))2
C3×C11⋊C5×D19⋊C32
D19×C3⋊AGL(1,𝔽11)3
AGL(1,𝔽11)×D19⋊C33
D33×D19⋊C35
C5×D3×D19⋊C311
C2×C3×C3⋊AGL(1,𝔽11)19