Finite Group Databasebeta

← D33×#10587721 #49114732

Subgroups — D33×#10587721 #49114732

Order 36036.

176 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 43 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
2C3⋊(C11⋊#10587721)C211yesmaximal, characteristic, complemented
3C3×C11×#10587721C211yesmaximal, characteristic, complemented
4C13×D7×D33C311yesmaximal, characteristic, complemented
5D11×#10587721—31nomaximal
6C3×C11×#63271C2211yescharacteristic, complemented, Hall
7C11⋊#10587721—31no—
8C11×#10587721—21no—
9C11×#10587721D311yescharacteristic, complemented
10D11×#63271—31no—
11C13×D231C2×C311yescharacteristic, complemented
12C7×C13×D33C2×C311yescharacteristic, complemented
13C3×C11×C13×D7C2×C311yescharacteristic, complemented
14C2×C13⋊C3×D33—71nomaximal, Hall
15C13×D7×D11—31noHall
16D3×#10587721—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—
22C13⋊C3×D33—71no—
23C13⋊C3×D33—71no—
24C13×D77—31no—
25C11×C13×D7C3×D311yescharacteristic, complemented
26C7×C13×D11—31no—
27C2×C13×D33—71no—
28C2×D11×C13⋊C3—211no—
29C3⋊#10587721—111no—
30D3×#63271—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
36D3×C13×D7—111no—
37C2×#10587721—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D7×D33C13⋊C311yescharacteristic, complemented
40D11×AGL(1,𝔽7)—391no—
41C2×C3×C11×C13—71no—
42C13×D33—71no—
43C13×D33AGL(1,𝔽7)11yescharacteristic, complemented
44C2×C11×C13⋊C3—71no—
45C2×C11×C13⋊C3—141no—
46D11×C13⋊C3—211no—
47D11×C13⋊C3—211no—
48C3×#63271C2×D1111yescharacteristic, complemented, Hall
49C3×C11×ΓL(1,𝔽8)—131noHall
50C2×C13×D11—211noHall
51C13×D21—111no—
52D3×C7×C13—111no—
53C3×C13×D7C3×D1111yescharacteristic, complemented
54C2×#63271—331no—
55#10587721—21no—
56#10587721—331no—
57#10587721D3311yescharacteristic, direct product factor
58C2×D3×C13⋊C3—771noHall
59D231C2×C13⋊C311yescharacteristic, complemented
60C7×D33C2×C13⋊C311yescharacteristic, complemented
61C3×C11×D7C2×C13⋊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
70C2×C13×D7—331noHall
71D7×D11—31noHall
72C2×C11×C13—71no—
73C13×D11—31no—
74C13×D11—211no—
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76#63271—21no—
77#63271C2×D3311yescharacteristic, complemented
78D3×AGL(1,𝔽7)—1431noHall
79C2×C3×C13⋊C3—71no—
80D3×C13⋊C3—771no—
81D3×C13⋊C3—771no—
82C3×C7×C11C22×C13⋊C311yescharacteristic, complemented
83C11×ΓL(1,𝔽8)—131no—
84C11×ΓL(1,𝔽8)—261no—
85C2×C32×C11—911no—
86C3×D33—911no—
87C3×D33—911no—
88C2×C7×C13—331no—
89C13×D7—331no—
90C13×D7C3×D3311yescharacteristic, complemented
91C2×D3×C13—771no—
92C22×C13⋊C3—2311no—
93D77—31no—
94C7×D11—31no—
95C11×D7D3×C13⋊C311yescharacteristic, complemented
96C11×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
97C2×D33—71no—
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—111no—
106C2×AGL(1,𝔽7)—4291no—
107C2×C3×C13—71no—
108D3×C13—111no—
109D3×C13—771no—
110C2×C13⋊C3—71no—
111C2×C13⋊C3—141no—
112C2×C13⋊C3—2311no—
113C2×C13⋊C3—2311no—
114C7×C11C2×D3×C13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—71no—
116C2×C3×C11—911no—
117C2×C3×C11—1821no—
118D33—71no—
119D33#1058772111yescharacteristic, direct product factor
120C3×D11—2731no—
121C3×D11—2731no—
122C3×ΓL(1,𝔽8)—131noHall
123C22×C13—2311noHall
124C2×D11—211noHall
125D21—111no—
126C3×D7D11×C13⋊C311yescharacteristic, complemented
127D3×C7—111no—
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×C11C2×#1058772111yescharacteristic, complemented
139C2×D7—331noHall
140C2×C13—71no—
141C2×C13—331no—
142C2×C13—2311no—
143C2×C11—71no—
144D11—31no—
145D11—211no—
146C3×C7C2×D11×C13⋊C311yescharacteristic, complemented
147ΓL(1,𝔽8)—131no—
148ΓL(1,𝔽8)—261no—
149C2×C32—911no—
150C3×D3—10011no—
151C3×D3—10011no—
152C2×C7—331no—
153D7—331no—
154D7C13⋊C3×D3311yescharacteristic, complemented
155C13AGL(1,𝔽7)×D3311yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—771no—
158C11D3×#1058772111yescharacteristic, complemented, Sylow
159C32—911noSylow
160C7C2×C13⋊C3×D3311yescharacteristic, complemented, Sylow
161C2×C3—71no—
162C2×C3—911no—
163C2×C3—1821no—
164C2×C3—30031no—
165C2×C3—30031no—
166D3—111no—
167D3—771no—
168C22—2311noSylow
169C3—911no—
170C3—1821no—
171C3D11×#1058772111yescharacteristic, complemented
172C2—71no—
173C2—331no—
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. D33×#63271C2semidirect
2. C3⋊(C11⋊#10587721)C2semidirect
3. C3×C11×#10587721C2semidirect
4. C13×D7×D33C3semidirect
6. C3×C11×#63271C22semidirect
9. C11×#10587721D3semidirect
11. C13×D231C2×C3semidirect
12. C7×C13×D33C2×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
39. D7×D33C13⋊C3semidirect
43. C13×D33AGL(1,𝔽7)semidirect
48. C3×#63271C2×D11semidirect
53. C3×C13×D7C3×D11semidirect
57. #10587721D33direct (N × H)
59. D231C2×C13⋊C3semidirect
60. C7×D33C2×C13⋊C3semidirect
61. C3×C11×D7C2×C13⋊C3semidirect
66. C3×C11×C13C2×AGL(1,𝔽7)semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. #63271C2×D33semidirect
82. C3×C7×C11C22×C13⋊C3semidirect
90. C13×D7C3×D33semidirect
95. C11×D7D3×C13⋊C3semidirect
96. C11×C13D3×AGL(1,𝔽7)semidirect
104. C7×C13C2×C3×D33semidirect
114. C7×C11C2×D3×C13⋊C3semidirect
119. D33#10587721direct (N × H)
126. C3×D7D11×C13⋊C3semidirect
132. C3×C13D11×AGL(1,𝔽7)semidirect
138. C3×C11C2×#10587721semidirect
146. C3×C7C2×D11×C13⋊C3semidirect
154. D7C13⋊C3×D33semidirect
155. C13AGL(1,𝔽7)×D33semidirect
158. C11D3×#10587721semidirect
160. C7C2×C13⋊C3×D33semidirect
171. C3D11×#10587721semidirect

Maximal subgroups

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

subgroupindex
D33×#632712
C3⋊(C11⋊#10587721)2
C3×C11×#105877212
C13×D7×D333
D11×#105877213
C2×C13⋊C3×D337
D3×#1058772111
AGL(1,𝔽7)×D3313