Finite Group Databasebeta

← #49114706

Subgroups — #49114706

Order 36036.

176 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 35 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⋊#10587720)C211yesmaximal, characteristic, complemented
2C11×C3⋊#10587722C211yesmaximal, characteristic, complemented
3C3×C11⋊#10587716C211yesmaximal, characteristic, complemented
4D143⋊D21C311yesmaximal, characteristic, complemented
5#10587722⋊D11—31nomaximal
6C3×C11×#63270C2211yescharacteristic, complemented, Hall
7C11⋊#10587720—31no—
8C11×#10587722—31no—
9C11⋊#10587716—21no—
10C11⋊#10587716D311yescharacteristic, complemented
11C13×D231C2×C311yescharacteristic, complemented
12C11×D273C2×C311yescharacteristic, complemented
13C3×C7×D143C2×C311yescharacteristic, complemented
14D33⋊(D13⋊C3)—71nomaximal, Hall
15D77⋊D13—31noHall
16#10587716⋊D3—111nomaximal, Hall
17C11×#63270—21no—
18C11×#63270C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20D11×C3⋊AGL(1,𝔽7)—131nomaximal, Hall
21C13⋊C3×D33—71no—
22C11×C3⋊(D13⋊C3)—71no—
23C3×C11⋊(D13⋊C3)—71no—
24C13×D77—31no—
25C11×D91—31no—
26C7×D143C3×D311yescharacteristic, complemented
27D33⋊D13—71no—
28D11×D13⋊C3—211no—
29C3⋊#10587722D1111yescharacteristic, complemented
30C3⋊#10587720—111no—
31C3×#10587716—111no—
32C3⋊(C11⋊AGL(1,𝔽7))—131no—
33C11×C3⋊AGL(1,𝔽7)—131no—
34C3×ΓL(1,𝔽8)×D11—131no—
35C3×C11×C13⋊C3—71noHall
36D13×D21—111no—
37#10587716⋊C2—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D11×D21—131no—
40D11×AGL(1,𝔽7)—391no—
41C13×D33—71no—
42C11×D39—71no—
43C3×D143AGL(1,𝔽7)11yescharacteristic, complemented
44C11⋊(D13⋊C3)—71no—
45C11⋊(D13⋊C3)—141no—
46D11×C13⋊C3—211no—
47C11×D13⋊C3—211no—
48C3×#63270C2×D1111yescharacteristic, complemented, Hall
49C3×C11×ΓL(1,𝔽8)—131noHall
50D11×D13—211noHall
51D273C3×D1111yescharacteristic, complemented
52C13×D21—111no—
53C3×C7×D13—111no—
54#10587722—31no—
55#10587720—331no—
56#10587716—111no—
57#10587716—221no—
58D3×D13⋊C3—771noHall
59D231D13⋊C311yescharacteristic, complemented
60C11×D21—131no—
61C3×C7×D11—131no—
62C11⋊AGL(1,𝔽7)—391no—
63C11×AGL(1,𝔽7)—391no—
64ΓL(1,𝔽8)×D11—131no—
65ΓL(1,𝔽8)×D11—261no—
66C3×C11×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C11×C13⋊C3—71no—
68C11×C13⋊C3—141no—
69C3×D3×D11—911noHall
70D7×D13—331noHall
71D7×D11—391noHall
72D143C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
73C11×D13—211no—
74C13×D11—211no—
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76#63270—21no—
77#63270D3×D1111yescharacteristic, complemented
78C2×C3⋊AGL(1,𝔽7)—1431noHall
79C3⋊(D13⋊C3)—71no—
80D3×C13⋊C3—771no—
81C3×D13⋊C3—771no—
82C3×C7×C11C2×D13⋊C311yescharacteristic, complemented
83C11×ΓL(1,𝔽8)—131no—
84C11×ΓL(1,𝔽8)—261no—
85C3×D33—911no—
86C3×D3×C11—911no—
87C32×D11—911no—
88D91—31no—
89C7×D13—111no—
90C13×D7—331no—
91D3×D13—771no—
92C2×D13⋊C3—2311no—
93D77—31no—
94C7×D11—131no—
95C11×D7—391no—
96C11×C13C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11—911no—
99C2×C3×ΓL(1,𝔽8)—1431no—
100C3⋊AGL(1,𝔽7)—131no—
101C3⋊AGL(1,𝔽7)—1431no—
102C3×C13⋊C3—71noHall
103C32×C11—911noHall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105C2×D21—1431no—
106C2×AGL(1,𝔽7)—4291no—
107D39—71no—
108C3×D13—111no—
109D3×C13—771no—
110C2×C13⋊C3—2311no—
111D13⋊C3—211no—
112D13⋊C3—771no—
113D13⋊C3—1541no—
114C7×C11D3×D13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33—71no—
117C3×D11—131no—
118C3×D11—2731no—
119C3×D11—911no—
120C3×D11—1821no—
121D3×C11—911no—
122C3×ΓL(1,𝔽8)—131noHall
123C2×D13—2311noHall
124C2×D11—2731noHall
125C2×C3×C7—1431no—
126D21—111no—
127D21—131no—
128C2×ΓL(1,𝔽8)—2861no—
129C2×ΓL(1,𝔽8)—1431no—
130AGL(1,𝔽7)—391no—
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#10587716⋊C211yescharacteristic, complemented
139C2×D7—4291noHall
140C2×C13—2311no—
141D13—111no—
142D13—211no—
143C2×C11—2731no—
144D11—131no—
145D11—211no—
146C3×C7D11×D13⋊C311yescharacteristic, complemented
147ΓL(1,𝔽8)—131no—
148ΓL(1,𝔽8)—261no—
149C2×C32—10011no—
150C3×D3—911no—
151C3×D3—10011no—
152C2×C7—1431no—
153D7—331no—
154D7—391no—
155C13D11×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—10011no—
158C11#10587716⋊D311yescharacteristic, complemented, Sylow
159C32—911noSylow
160C7D33⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—1431no—
163C2×C3—30031no—
164C2×C3—20021no—
165C2×C3—10011no—
166D3—771no—
167D3—911no—
168C22—30031noSylow
169C3—911no—
170C3—1821no—
171C3#10587722⋊D1111yescharacteristic, complemented
172C2—2731no—
173C2—1431no—
174C2—2311no—
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⋊#10587720)C2semidirect
2. C11×C3⋊#10587722C2semidirect
3. C3×C11⋊#10587716C2semidirect
4. D143⋊D21C3semidirect
6. C3×C11×#63270C22semidirect
10. C11⋊#10587716D3semidirect
11. C13×D231C2×C3semidirect
12. C11×D273C2×C3semidirect
13. C3×C7×D143C2×C3semidirect
18. C11×#63270C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
26. C7×D143C3×D3semidirect
29. C3⋊#10587722D11semidirect
38. C7×C11×C13C2×C3×D3semidirect
43. C3×D143AGL(1,𝔽7)semidirect
48. C3×#63270C2×D11semidirect
51. D273C3×D11semidirect
59. D231D13⋊C3semidirect
66. C3×C11×C13C2×AGL(1,𝔽7)semidirect
72. D143C3⋊AGL(1,𝔽7)semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. #63270D3×D11semidirect
82. C3×C7×C11C2×D13⋊C3semidirect
96. C11×C13C2×C3⋊AGL(1,𝔽7)semidirect
104. C7×C13C3×D3×D11semidirect
114. C7×C11D3×D13⋊C3semidirect
132. C3×C13D11×AGL(1,𝔽7)semidirect
138. C3×C11#10587716⋊C2semidirect
146. C3×C7D11×D13⋊C3semidirect
155. C13D11×C3⋊AGL(1,𝔽7)semidirect
158. C11#10587716⋊D3semidirect
160. C7D33⋊(D13⋊C3)semidirect
171. C3#10587722⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C11⋊#10587720)2
C11×C3⋊#105877222
C3×C11⋊#105877162
D143⋊D213
#10587722⋊D113
D33⋊(D13⋊C3)7
#10587716⋊D311
D11×C3⋊AGL(1,𝔽7)13