Finite Group Databasebeta

← C11×#10587717⋊D3 #49114690

Subgroups — C11×#10587717⋊D3 #49114690

Order 36036.

176 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C11×C3⋊#10587721C211yesmaximal, characteristic, complemented
2C11×C3⋊#10587723C211yesmaximal, characteristic, complemented
3C3×C11×#10587717C211yesmaximal, characteristic, complemented
4C11×D13×D21C311yesmaximal, characteristic, complemented
5C11×#10587717⋊C2—31nomaximal
6C3×C11×#63271C2211yescharacteristic, complemented, Hall
7C11×#10587723—31no—
8C11×#10587721—31no—
9C11×#10587717—21no—
10C11×#10587717D311yescharacteristic, complemented
11C11×D273C2×C311yescharacteristic, complemented
12C11×C13×D21C2×C311yescharacteristic, complemented
13C3×C7×C11×D13C2×C311yescharacteristic, complemented
14D3×C11×D13⋊C3—71nomaximal, Hall
15C11×D7×D13—31noHall
16#10587717⋊D3C1111yesmaximal, characteristic, direct product factor, Hall
17C11×#63271—21no—
18C11×#63271C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C2×C11×C3⋊AGL(1,𝔽7)—131nomaximal, Hall
21D3×C11×C13⋊C3—71no—
22C11×C3⋊(D13⋊C3)—71no—
23C3×C11×D13⋊C3—71no—
24C11×D91—31no—
25C11×C13×D7—31no—
26C7×C11×D13C3×D311yescharacteristic, complemented
27D3×C11×D13—71no—
28C2×C11×D13⋊C3—211no—
29C3⋊#10587723C2×C1111yescharacteristic, complemented
30C3⋊#10587721C2×C1111yescharacteristic, complemented
31C3×#10587717C2×C1111yescharacteristic, complemented
32C2×C3×C11×ΓL(1,𝔽8)—131no—
33C11×C3⋊AGL(1,𝔽7)—131no—
34C11×C3⋊AGL(1,𝔽7)—131no—
35C3×C11×C13⋊C3—71noHall
36D13×D21C3×C1111yescharacteristic, complemented
37#10587717⋊C2—31no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C11×D21—131no—
40C2×C11×AGL(1,𝔽7)—391no—
41C11×D39—71no—
42D3×C11×C13—71no—
43C3×C11×D13AGL(1,𝔽7)11yescharacteristic, complemented
44C2×C11×C13⋊C3—211no—
45C11×D13⋊C3—71no—
46C11×D13⋊C3—141no—
47C11×D13⋊C3—211no—
48C3×#63271C22×C1111yescharacteristic, complemented, Hall
49C3×C11×ΓL(1,𝔽8)—131noHall
50C2×C11×D13—211noHall
51D273C2×C3×C1111yescharacteristic, complemented
52C13×D21C2×C3×C1111yescharacteristic, complemented
53C3×C7×D13C2×C3×C1111yescharacteristic, complemented
54#10587723—31no—
55#10587721—31no—
56#10587717—21no—
57#10587717D3×C1111yescharacteristic, complemented
58D3×D13⋊C3—71noHall
59C2×C3×C7×C11—131no—
60C11×D21—131no—
61C11×D21D13⋊C311yescharacteristic, complemented
62C2×C11×ΓL(1,𝔽8)—131no—
63C2×C11×ΓL(1,𝔽8)—261no—
64C11×AGL(1,𝔽7)—391no—
65C11×AGL(1,𝔽7)—391no—
66C3×C11×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C11×C13⋊C3—71no—
68C11×C13⋊C3—141no—
69C2×C3×D3×C11—911noHall
70D7×D13—31noHall
71C2×C11×D7—391noHall
72C2×C11×C13—211no—
73C11×D13—211no—
74C11×D13C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
75C3×C7×C13C22×C3×C1111yescharacteristic, complemented
76#63271—21no—
77#63271C2×D3×C1111yescharacteristic, complemented
78C2×C3⋊AGL(1,𝔽7)—131noHall
79C3⋊(D13⋊C3)—71no—
80D3×C13⋊C3—71no—
81C3×D13⋊C3—71no—
82C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
83C11×ΓL(1,𝔽8)—131no—
84C11×ΓL(1,𝔽8)—261no—
85C2×C32×C11—911no—
86C3×D3×C11—911no—
87C3×D3×C11—911no—
88D91—31no—
89C7×D13C3×D3×C1111yescharacteristic, complemented
90C13×D7—31no—
91D3×D13—71no—
92C2×D13⋊C3—211no—
93C2×C7×C11—131no—
94C11×D7—31no—
95C11×D7—391no—
96C11×C13C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Hall
97C22×C3×C11—2731no—
98C2×D3×C11—911no—
99C2×C3×ΓL(1,𝔽8)—131no—
100C3⋊AGL(1,𝔽7)—131no—
101C3⋊AGL(1,𝔽7)—131no—
102C3×C13⋊C3—71noHall
103C32×C11—911noHall
104C7×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
105C2×D21—131no—
106C2×AGL(1,𝔽7)—391no—
107D39—71no—
108C3×D13C11×AGL(1,𝔽7)11yescharacteristic, complemented
109D3×C13—71no—
110C2×C13⋊C3—211no—
111D13⋊C3—71no—
112D13⋊C3—141no—
113D13⋊C3—211no—
114C7×C11D3×D13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—131no—
116C2×C3×C11—2731no—
117C2×C3×C11—2731no—
118C2×C3×C11—911no—
119C2×C3×C11—1821no—
120D3×C11—71no—
121D3×C11—911no—
122C3×ΓL(1,𝔽8)—131noHall
123C2×D13—211noHall
124C22×C11—2731noHall
125C2×C3×C7—131no—
126D21—131no—
127D21C11×D13⋊C311yescharacteristic, complemented
128C2×ΓL(1,𝔽8)—131no—
129C2×ΓL(1,𝔽8)—261no—
130AGL(1,𝔽7)—391no—
131AGL(1,𝔽7)—391no—
132C3×C13C2×C11×AGL(1,𝔽7)11yescharacteristic, complemented
133C13⋊C3—71no—
134C13⋊C3—141no—
135C2×C3×D3—911noHall
136C3×C11—911no—
137C3×C11—1821no—
138C3×C11#10587717⋊C211yescharacteristic, complemented
139C2×D7—391noHall
140C2×C13—211no—
141D13—211no—
142D13C11×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
143C2×C11—131no—
144C2×C11—2731no—
145C2×C11—211no—
146C3×C7C2×C11×D13⋊C311yescharacteristic, complemented
147ΓL(1,𝔽8)—131no—
148ΓL(1,𝔽8)—261no—
149C2×C32—911no—
150C3×D3—911no—
151C3×D3—911no—
152C2×C7—131no—
153D7—31no—
154D7—391no—
155C13C2×C11×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
156C22×C3—2731no—
157C2×D3—911no—
158C11#10587717⋊D311yescharacteristic, direct product factor, Sylow
159C32—911noSylow
160C7D3×C11×D13⋊C311yescharacteristic, complemented, Sylow
161C2×C3—131no—
162C2×C3—2731no—
163C2×C3—2731no—
164C2×C3—911no—
165C2×C3—1821no—
166D3—71no—
167D3—911no—
168C22—2731noSylow
169C3—911no—
170C3—1821no—
171C3C11×#10587717⋊C211yescharacteristic, complemented
172C2—131no—
173C2—2731no—
174C2—211no—
subgroupG/H
center, hypercenterC11#10587717⋊D3
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×C3⋊#10587721C2semidirect
2. C11×C3⋊#10587723C2semidirect
3. C3×C11×#10587717C2semidirect
4. C11×D13×D21C3semidirect
6. C3×C11×#63271C22semidirect
10. C11×#10587717D3semidirect
11. C11×D273C2×C3semidirect
12. C11×C13×D21C2×C3semidirect
13. C3×C7×C11×D13C2×C3semidirect
16. #10587717⋊D3C11direct (N × H)
18. C11×#63271C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
26. C7×C11×D13C3×D3semidirect
29. C3⋊#10587723C2×C11semidirect
30. C3⋊#10587721C2×C11semidirect
31. C3×#10587717C2×C11semidirect
36. D13×D21C3×C11semidirect
38. C7×C11×C13C2×C3×D3semidirect
43. C3×C11×D13AGL(1,𝔽7)semidirect
48. C3×#63271C22×C11semidirect
51. D273C2×C3×C11semidirect
52. C13×D21C2×C3×C11semidirect
53. C3×C7×D13C2×C3×C11semidirect
57. #10587717D3×C11semidirect
61. C11×D21D13⋊C3semidirect
66. C3×C11×C13C2×AGL(1,𝔽7)semidirect
74. C11×D13C3⋊AGL(1,𝔽7)semidirect
75. C3×C7×C13C22×C3×C11semidirect
77. #63271C2×D3×C11semidirect
82. C3×C7×C11C2×D13⋊C3semidirect
89. C7×D13C3×D3×C11semidirect
96. C11×C13C2×C3⋊AGL(1,𝔽7)semidirect
104. C7×C13C2×C3×D3×C11semidirect
108. C3×D13C11×AGL(1,𝔽7)semidirect
114. C7×C11D3×D13⋊C3semidirect
127. D21C11×D13⋊C3semidirect
132. C3×C13C2×C11×AGL(1,𝔽7)semidirect
138. C3×C11#10587717⋊C2semidirect
142. D13C11×C3⋊AGL(1,𝔽7)semidirect
146. C3×C7C2×C11×D13⋊C3semidirect
155. C13C2×C11×C3⋊AGL(1,𝔽7)semidirect
158. C11#10587717⋊D3direct (N × H)
160. C7D3×C11×D13⋊C3semidirect
171. C3C11×#10587717⋊C2semidirect

Maximal subgroups

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

subgroupindex
C11×C3⋊#105877212
C11×C3⋊#105877232
C3×C11×#105877172
C11×D13×D213
C11×#10587717⋊C23
D3×C11×D13⋊C37
#10587717⋊D311
C2×C11×C3⋊AGL(1,𝔽7)13