Finite Group Databasebeta

← D33⋊#10587723 #49114752

Subgroups — D33⋊#10587723 #49114752

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
1D33×#63271C211yesmaximal, characteristic, complemented
2C11×C3⋊#10587723C211yesmaximal, characteristic, complemented
3C3×C11⋊#10587723C211yesmaximal, characteristic, complemented
4D33⋊D91C311yesmaximal, characteristic, complemented
5D11×#10587723—31nomaximal
6C3×C11×#63271C2211yescharacteristic, complemented, Hall
7C11⋊#10587723—21no—
8C11⋊#10587723D311yescharacteristic, complemented
9C11×#10587723—31no—
10D11×#63271—31no—
11C11×D273C2×C311yescharacteristic, complemented
12C7×C13×D33C2×C311yescharacteristic, complemented
13C3×D1001C2×C311yescharacteristic, complemented
14D33⋊(D13⋊C3)—71nomaximal, Hall
15D11×D91—31noHall
16D3×#10587723—111nomaximal, Hall
17C11×#63271—21no—
18C11×#63271C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20D33⋊AGL(1,𝔽7)—131nomaximal, Hall
21C13⋊C3×D33—71no—
22C11×C3⋊(D13⋊C3)—71no—
23C3×C11⋊(D13⋊C3)—71no—
24D1001C3×D311yescharacteristic, complemented
25C11×D91—31no—
26C7×C13×D11—31no—
27D33⋊D13—71no—
28D11×D13⋊C3—211no—
29C3⋊#10587723D1111yescharacteristic, complemented
30D3×#63271—111no—
31C3×#10587723—111no—
32C11×C3⋊AGL(1,𝔽7)—131no—
33ΓL(1,𝔽8)×D33—131no—
34C3×C11⋊AGL(1,𝔽7)—131no—
35C3×C11×C13⋊C3—71noHall
36D3×D91—111no—
37C2×#10587723—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D21⋊D11—131no—
40D11×AGL(1,𝔽7)—391no—
41C13×D33AGL(1,𝔽7)11yescharacteristic, complemented
42C11×D39—71no—
43C3×D143—71no—
44C11⋊(D13⋊C3)—71no—
45C11⋊(D13⋊C3)—141no—
46D11×C13⋊C3—211no—
47C11×D13⋊C3—211no—
48C3×#63271C2×D1111yescharacteristic, complemented, Hall
49C3×C11×ΓL(1,𝔽8)—131noHall
50D11×D13—211noHall
51D273C3×D1111yescharacteristic, complemented
52D3×C7×C13—111no—
53C3×D91—111no—
54C2×#63271—331no—
55#10587723—31no—
56#10587723—111no—
57#10587723—221no—
58D3×D13⋊C3—771noHall
59C11×D21—131no—
60C7×D33D13⋊C311yescharacteristic, complemented
61C3×D77—131no—
62C11⋊AGL(1,𝔽7)—131no—
63C11⋊AGL(1,𝔽7)—261no—
64C11×AGL(1,𝔽7)—391no—
65ΓL(1,𝔽8)×D11—391no—
66C3×C11×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C11×C13⋊C3—71no—
68C11×C13⋊C3—141no—
69C3×D3×D11—911noHall
70C2×D91—331noHall
71D7×D11—391noHall
72D143—71no—
73C11×D13—211no—
74C13×D11—31no—
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76#63271—21no—
77#63271D3×D1111yescharacteristic, complemented
78D3×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—
88C2×C7×C13—331no—
89D91—31no—
90D91—111no—
91D3×D13—771no—
92C2×D13⋊C3—2311no—
93D77—131no—
94C7×D11—31no—
95C11×D7—391no—
96C11×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11—911no—
99C3⋊AGL(1,𝔽7)—131no—
100D3×ΓL(1,𝔽8)—1431no—
101C3×AGL(1,𝔽7)—1431no—
102C3×C13⋊C3—71noHall
103C32×C11—911noHall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105D3×D7—1431no—
106C2×AGL(1,𝔽7)—4291no—
107D39—71no—
108C3×D13—771no—
109D3×C13—111no—
110C2×C13⋊C3—2311no—
111D13⋊C3—211no—
112D13⋊C3—771no—
113D13⋊C3—1541no—
114C7×C11D3×D13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33#1058772311yescharacteristic, complemented
117C3×D11—2731no—
118C3×D11—911no—
119C3×D11—911no—
120C3×D11—1821no—
121D3×C11—911no—
122C3×ΓL(1,𝔽8)—131noHall
123C2×D13—2311noHall
124C2×D11—2731noHall
125D21—131no—
126C3×D7—1431no—
127D3×C7—111no—
128C2×ΓL(1,𝔽8)—4291no—
129AGL(1,𝔽7)—2861no—
130AGL(1,𝔽7)—391no—
131AGL(1,𝔽7)—1431no—
132C3×C13D11×AGL(1,𝔽7)11yescharacteristic, complemented
133C13⋊C3—71no—
134C13⋊C3—141no—
135C2×C3×D3—10011noHall
136C3×C11—911no—
137C3×C11—1821no—
138C3×C11C2×#1058772311yescharacteristic, complemented
139C2×D7—4291noHall
140C2×C13—331no—
141D13—211no—
142D13—771no—
143C2×C11—2731no—
144D11—31no—
145D11—911no—
146C3×C7D11×D13⋊C311yescharacteristic, complemented
147ΓL(1,𝔽8)—131no—
148ΓL(1,𝔽8)—261no—
149C2×C32—10011no—
150C3×D3—911no—
151C3×D3—10011no—
152C2×C7—331no—
153D7—391no—
154D7—1431no—
155C13D33⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—10011no—
158C11D3×#1058772311yescharacteristic, complemented, Sylow
159C32—911noSylow
160C7D33⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
161C2×C3—2731no—
162C2×C3—30031no—
163C2×C3—20021no—
164C2×C3—10011no—
165C2×C3—10011no—
166D3—111no—
167D3—911no—
168C22—30031noSylow
169C3—911no—
170C3—1821no—
171C3D11×#1058772311yescharacteristic, complemented
172C2—2731no—
173C2—331no—
174C2—10011no—
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. D33×#63271C2semidirect
2. C11×C3⋊#10587723C2semidirect
3. C3×C11⋊#10587723C2semidirect
4. D33⋊D91C3semidirect
6. C3×C11×#63271C22semidirect
8. C11⋊#10587723D3semidirect
11. C11×D273C2×C3semidirect
12. C7×C13×D33C2×C3semidirect
13. C3×D1001C2×C3semidirect
18. C11×#63271C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
24. D1001C3×D3semidirect
29. C3⋊#10587723D11semidirect
38. C7×C11×C13C2×C3×D3semidirect
41. C13×D33AGL(1,𝔽7)semidirect
48. C3×#63271C2×D11semidirect
51. D273C3×D11semidirect
60. C7×D33D13⋊C3semidirect
66. C3×C11×C13C2×AGL(1,𝔽7)semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. #63271D3×D11semidirect
82. C3×C7×C11C2×D13⋊C3semidirect
96. C11×C13D3×AGL(1,𝔽7)semidirect
104. C7×C13C3×D3×D11semidirect
114. C7×C11D3×D13⋊C3semidirect
116. D33#10587723semidirect
132. C3×C13D11×AGL(1,𝔽7)semidirect
138. C3×C11C2×#10587723semidirect
146. C3×C7D11×D13⋊C3semidirect
155. C13D33⋊AGL(1,𝔽7)semidirect
158. C11D3×#10587723semidirect
160. C7D33⋊(D13⋊C3)semidirect
171. C3D11×#10587723semidirect

Maximal subgroups

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

subgroupindex
D33×#632712
C11×C3⋊#105877232
C3×C11⋊#105877232
D33⋊D913
D11×#105877233
D33⋊(D13⋊C3)7
D3×#1058772311
D33⋊AGL(1,𝔽7)13