Finite Group Databasebeta

← #10587721⋊D33 #49114726

Subgroups — #10587721⋊D33 #49114726

Order 36036.

176 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 39 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⋊#10587717)C211yesmaximal, characteristic, complemented
2C3⋊(C11⋊#10587723)C211yesmaximal, characteristic, complemented
3C3×C11×#10587721C211yesmaximal, characteristic, complemented
4D7×D429C311yesmaximal, characteristic, complemented
5#10587721⋊D11—31nomaximal
6C3×C11×#63271C2211yescharacteristic, complemented, Hall
7C11⋊#10587723—31no—
8C11×#10587721—21no—
9C11×#10587721D311yescharacteristic, complemented
10C11⋊#10587717—31no—
11D3003C2×C311yescharacteristic, complemented
12C7×D429C2×C311yescharacteristic, complemented
13C3×C11×C13×D7C2×C311yescharacteristic, complemented
14C2×C3⋊(C11⋊(D13⋊C3))—71nomaximal, Hall
15D7×D143—31noHall
16#10587721⋊D3—111nomaximal, Hall
17C11×#63271—21no—
18C11×#63271C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20AGL(1,𝔽7)×D33—131nomaximal, Hall
21C2×C3×C11×C13⋊C3—71no—
22C3⋊(C11⋊(D13⋊C3))—71no—
23C3⋊(C11⋊(D13⋊C3))—71no—
24D1001—31no—
25C11×C13×D7C3×D311yescharacteristic, complemented
26C7×D143—31no—
27C2×D429—71no—
28C2×C11⋊(D13⋊C3)—211no—
29C3⋊#10587723—111no—
30C3⋊#10587717—111no—
31C3×#10587721D1111yescharacteristic, complemented
32C3⋊(C11⋊AGL(1,𝔽7))—131no—
33ΓL(1,𝔽8)×D33—131no—
34C3×C11×AGL(1,𝔽7)—131no—
35C3×C11×C13⋊C3—71noHall
36D7×D39—111no—
37#10587717⋊C2—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D7×D33—131no—
40D11×AGL(1,𝔽7)—391no—
41C2×C3×C11×C13—71no—
42D429—71no—
43D429AGL(1,𝔽7)11yescharacteristic, complemented
44C2×C11×C13⋊C3—71no—
45C2×C11×C13⋊C3—141no—
46C11⋊(D13⋊C3)—211no—
47C11⋊(D13⋊C3)—211no—
48C3×#63271C2×D1111yescharacteristic, complemented, Hall
49C3×C11×ΓL(1,𝔽8)—131noHall
50C2×D143—211noHall
51D273—111no—
52C7×D39—111no—
53C3×C13×D7C3×D1111yescharacteristic, complemented
54#10587723—331no—
55#10587721—21no—
56#10587721D3311yescharacteristic, complemented
57#10587717—331no—
58C2×C3⋊(D13⋊C3)—771noHall
59D231—131no—
60C7×D33—131no—
61C3×C11×D7D13⋊C311yescharacteristic, complemented
62C11⋊AGL(1,𝔽7)—391no—
63C11×AGL(1,𝔽7)—131no—
64C11×AGL(1,𝔽7)—261no—
65ΓL(1,𝔽8)×D11—391no—
66C3×C11×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C11×C13⋊C3—71no—
68C11×C13⋊C3—141no—
69C2×C3×D33—911noHall
70D7×D13—331noHall
71D7×D11—391noHall
72C2×C11×C13—71no—
73D143—31no—
74D143—211no—
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76#63271—21no—
77#63271C2×D3311yescharacteristic, complemented
78D3×AGL(1,𝔽7)—1431noHall
79C2×C3×C13⋊C3—71no—
80C3⋊(D13⋊C3)—771no—
81C3⋊(D13⋊C3)—771no—
82C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
83C11×ΓL(1,𝔽8)—131no—
84C11×ΓL(1,𝔽8)—261no—
85C2×C32×C11—911no—
86C3×D33—911no—
87C3×D33—911no—
88D91—331no—
89C7×D13—331no—
90C13×D7C3×D3311yescharacteristic, complemented
91C2×D39—771no—
92C2×D13⋊C3—2311no—
93D77—391no—
94C7×D11—391no—
95C11×D7C3⋊(D13⋊C3)11yescharacteristic, complemented
96C11×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
97C2×D33—911no—
98C2×C3×D11—2731no—
99C3⋊AGL(1,𝔽7)—1431no—
100D3×ΓL(1,𝔽8)—1431no—
101C3×AGL(1,𝔽7)—131no—
102C3×C13⋊C3—71noHall
103C32×C11—911noHall
104C7×C13C2×C3×D3311yescharacteristic, complemented, Hall
105D3×D7—1431no—
106C2×AGL(1,𝔽7)—4291no—
107C2×C3×C13—71no—
108D39—111no—
109D39—771no—
110C2×C13⋊C3—71no—
111C2×C13⋊C3—141no—
112D13⋊C3—2311no—
113D13⋊C3—2311no—
114C7×C11C2×C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
115C2×C3×C11—71no—
116C2×C3×C11—911no—
117C2×C3×C11—1821no—
118D33—131no—
119D33—911no—
120C3×D11—2731no—
121C3×D11—2731no—
122C3×ΓL(1,𝔽8)—131noHall
123C2×D13—2311noHall
124C2×D11—2731noHall
125D21—1431no—
126C3×D7C11⋊(D13⋊C3)11yescharacteristic, complemented
127D3×C7—1431no—
128C2×ΓL(1,𝔽8)—4291no—
129AGL(1,𝔽7)—131no—
130AGL(1,𝔽7)—261no—
131AGL(1,𝔽7)—4291no—
132C3×C13D11×AGL(1,𝔽7)11yescharacteristic, complemented
133C13⋊C3—71no—
134C13⋊C3—141no—
135C2×C3×D3—10011noHall
136C3×C11—911no—
137C3×C11—1821no—
138C3×C11#10587717⋊C211yescharacteristic, complemented
139C2×D7—4291noHall
140C2×C13—71no—
141D13—331no—
142D13—2311no—
143C2×C11—71no—
144D11—2731no—
145D11—391no—
146C3×C7C2×C11⋊(D13⋊C3)11yescharacteristic, complemented
147ΓL(1,𝔽8)—131no—
148ΓL(1,𝔽8)—261no—
149C2×C32—911no—
150C3×D3—10011no—
151C3×D3—10011no—
152C2×C7—4291no—
153D7—4291no—
154D7C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented
155C13AGL(1,𝔽7)×D3311yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—10011no—
158C11#10587721⋊D311yescharacteristic, complemented, Sylow
159C32—911noSylow
160C7C2×C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented, Sylow
161C2×C3—71no—
162C2×C3—911no—
163C2×C3—1821no—
164C2×C3—30031no—
165C2×C3—30031no—
166D3—1431no—
167D3—10011no—
168C22—30031noSylow
169C3—911no—
170C3—1821no—
171C3#10587721⋊D1111yescharacteristic, complemented
172C2—71no—
173C2—4291no—
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⋊#10587717)C2semidirect
2. C3⋊(C11⋊#10587723)C2semidirect
3. C3×C11×#10587721C2semidirect
4. D7×D429C3semidirect
6. C3×C11×#63271C22semidirect
9. C11×#10587721D3semidirect
11. D3003C2×C3semidirect
12. C7×D429C2×C3semidirect
13. C3×C11×C13×D7C2×C3semidirect
18. C11×#63271C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
25. C11×C13×D7C3×D3semidirect
31. C3×#10587721D11semidirect
38. C7×C11×C13C2×C3×D3semidirect
43. D429AGL(1,𝔽7)semidirect
48. C3×#63271C2×D11semidirect
53. C3×C13×D7C3×D11semidirect
56. #10587721D33semidirect
61. C3×C11×D7D13⋊C3semidirect
66. C3×C11×C13C2×AGL(1,𝔽7)semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. #63271C2×D33semidirect
82. C3×C7×C11C2×D13⋊C3semidirect
90. C13×D7C3×D33semidirect
95. C11×D7C3⋊(D13⋊C3)semidirect
96. C11×C13D3×AGL(1,𝔽7)semidirect
104. C7×C13C2×C3×D33semidirect
114. C7×C11C2×C3⋊(D13⋊C3)semidirect
126. C3×D7C11⋊(D13⋊C3)semidirect
132. C3×C13D11×AGL(1,𝔽7)semidirect
138. C3×C11#10587717⋊C2semidirect
146. C3×C7C2×C11⋊(D13⋊C3)semidirect
154. D7C3⋊(C11⋊(D13⋊C3))semidirect
155. C13AGL(1,𝔽7)×D33semidirect
158. C11#10587721⋊D3semidirect
160. C7C2×C3⋊(C11⋊(D13⋊C3))semidirect
171. C3#10587721⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C11⋊#10587717)2
C3⋊(C11⋊#10587723)2
C3×C11×#105877212
D7×D4293
#10587721⋊D113
C2×C3⋊(C11⋊(D13⋊C3))7
#10587721⋊D311
AGL(1,𝔽7)×D3313