Finite Group Databasebeta

← C2×D3×C11×#63271 #49114865

Subgroups — C2×D3×C11×#63271 #49114865

Order 36036.

176 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×C3×C11×#63271C211yesmaximal, characteristic, complemented
2D3×C11×#63271C212yesmaximal, direct product factor
3C2×D3×C7×C11×C13C311yesmaximal, characteristic, complemented
4C22×C11×#63271—31nomaximal
5C3×C11×#63271C2211yescharacteristic, complemented, Hall
6D3×C7×C11×C13C2×C312yescomplemented
7C2×C11×#63271—21no—
8C2×C11×#63271—32no—
9C2×C11×#63271D311yescharacteristic, direct product factor
10C2×C3×C7×C11×C13C2×C311yescharacteristic, complemented
11C2×D3×C11×C13⋊C3—71nomaximal, Hall
12C22×C7×C11×C13—31noHall
13C2×D3×#63271C1111yesmaximal, characteristic, direct product factor, Hall
14C11×#63271—21no—
15C11×#63271C2×D311yescharacteristic, direct product factor
16C3×C7×C11×C13C22×C311yescharacteristic, complemented
17C2×D3×C11×ΓL(1,𝔽8)—131nomaximal, Hall
18C2×C3×C11×C13⋊C3—71no—
19D3×C11×C13⋊C3—72no—
20C2×C7×C11×C13—32no—
21C2×C7×C11×C13C3×D311yescharacteristic, complemented
22C2×D3×C11×C13ΓL(1,𝔽8)11yescharacteristic, complemented
23C22×C11×C13⋊C3—211no—
24C2×C3×#63271C2×C1111yescharacteristic, complemented
25D3×#63271C2×C1112yesdirect product factor
26C2×C3×C11×ΓL(1,𝔽8)—131no—
27D3×C11×ΓL(1,𝔽8)—132no—
28C3×C11×C13⋊C3—71noHall
29C2×D3×C7×C13C3×C1111yescharacteristic, complemented
30C22×#63271—31no—
31C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
32C2×D3×C7×C11C13⋊C311yescharacteristic, complemented
33C22×C11×ΓL(1,𝔽8)—391no—
34C2×C3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented
35D3×C11×C13C2×ΓL(1,𝔽8)12yescomplemented
36C2×C11×C13⋊C3—71no—
37C2×C11×C13⋊C3—141no—
38C2×C11×C13⋊C3—212no—
39C3×#63271C22×C1111yescharacteristic, complemented, Hall
40C3×C11×ΓL(1,𝔽8)—131noHall
41C22×C11×C13—31noHall
42C2×C3×C7×C13C2×C3×C1111yescharacteristic, complemented
43D3×C7×C13C2×C3×C1112yescomplemented
44C2×#63271—21no—
45C2×#63271—32no—
46C2×#63271D3×C1111yescharacteristic, direct product factor
47C2×D3×C13⋊C3—71noHall
48C2×C3×C7×C11C2×C13⋊C311yescharacteristic, complemented
49D3×C7×C11C2×C13⋊C312yescomplemented
50C2×C11×ΓL(1,𝔽8)—131no—
51C2×C11×ΓL(1,𝔽8)—261no—
52C2×C11×ΓL(1,𝔽8)—392no—
53C3×C11×C13C22×ΓL(1,𝔽8)11yescharacteristic, complemented
54C11×C13⋊C3—71no—
55C11×C13⋊C3—141no—
56C2×C3×D3×C11—911noHall
57C22×C7×C13—31noHall
58C22×C7×C11—31noHall
59C2×C11×C13—32no—
60C2×C11×C13D3×ΓL(1,𝔽8)11yescharacteristic, complemented
61C3×C7×C13C22×C3×C1111yescharacteristic, complemented
62#63271—21no—
63#63271C2×D3×C1111yescharacteristic, direct product factor
64C2×D3×ΓL(1,𝔽8)—131noHall
65C2×C3×C13⋊C3—71no—
66D3×C13⋊C3—72no—
67C3×C7×C11C22×C13⋊C311yescharacteristic, complemented
68C11×ΓL(1,𝔽8)—131no—
69C11×ΓL(1,𝔽8)—261no—
70C2×C32×C11—911no—
71C3×D3×C11—912no—
72C2×C7×C13—32no—
73C2×C7×C13C3×D3×C1111yescharacteristic, complemented
74C2×D3×C13C11×ΓL(1,𝔽8)11yescharacteristic, complemented
75C22×C13⋊C3—211no—
76C2×C7×C11—32no—
77C2×C7×C11D3×C13⋊C311yescharacteristic, complemented
78C11×C13C2×D3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
79C22×C3×C11—2731no—
80C2×D3×C11#6327111yescharacteristic, direct product factor
81C2×C3×ΓL(1,𝔽8)—131no—
82D3×ΓL(1,𝔽8)—132no—
83C3×C13⋊C3—71noHall
84C32×C11—911noHall
85C7×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
86C2×D3×C7C11×C13⋊C311yescharacteristic, complemented
87C22×ΓL(1,𝔽8)—391no—
88C2×C3×C13C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
89D3×C13C2×C11×ΓL(1,𝔽8)12yescomplemented
90C2×C13⋊C3—71no—
91C2×C13⋊C3—141no—
92C2×C13⋊C3—212no—
93C7×C11C2×D3×C13⋊C311yescharacteristic, complemented, Hall
94C2×C3×C11—2732no—
95C2×C3×C11—911no—
96C2×C3×C11—1821no—
97C2×C3×C11C2×#6327111yescharacteristic, complemented
98D3×C11C2×#6327112yesdirect product factor
99C3×ΓL(1,𝔽8)—131noHall
100C22×C13—31noHall
101C22×C11—31noHall
102C2×C3×C7C2×C11×C13⋊C311yescharacteristic, complemented
103D3×C7C2×C11×C13⋊C312yescomplemented
104C2×ΓL(1,𝔽8)—131no—
105C2×ΓL(1,𝔽8)—261no—
106C2×ΓL(1,𝔽8)—392no—
107C3×C13C22×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
108C13⋊C3—71no—
109C13⋊C3—141no—
110C2×C3×D3—911noHall
111C3×C11—911no—
112C3×C11—1821no—
113C3×C11C22×#6327111yescharacteristic, complemented
114C22×C7—31noHall
115C2×C13—32no—
116C2×C13D3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
117C2×C11—32no—
118C2×C11D3×#6327111yescharacteristic, direct product factor
119C3×C7C22×C11×C13⋊C311yescharacteristic, complemented
120ΓL(1,𝔽8)—131no—
121ΓL(1,𝔽8)—261no—
122C2×C32—911no—
123C3×D3—912no—
124C2×C7—32no—
125C2×C7D3×C11×C13⋊C311yescharacteristic, complemented
126C13C2×D3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
127C22×C3—2731no—
128C2×D3C11×#6327111yescharacteristic, direct product factor
129C11C2×D3×#6327111yescharacteristic, direct product factor, Sylow
130C32—911noSylow
131C7C2×D3×C11×C13⋊C311yescharacteristic, complemented, Sylow
132C2×C3—2732no—
133C2×C3—911no—
134C2×C3—1821no—
135C2×C3C2×C11×#6327111yescharacteristic, complemented
136D3C2×C11×#6327112yesdirect product factor
137C22—31noSylow
138C3—911no—
139C3—1821no—
140C3C22×C11×#6327111yescharacteristic, complemented
141C2—32no—
142C2D3×C11×#6327111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11D3×#63271
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C2×C3×C11×#63271C2semidirect
2. D3×C11×#63271C2direct (N × H)
3. C2×D3×C7×C11×C13C3semidirect
5. C3×C11×#63271C22semidirect
6. D3×C7×C11×C13C2×C3semidirect
9. C2×C11×#63271D3direct (N × H)
10. C2×C3×C7×C11×C13C2×C3semidirect
13. C2×D3×#63271C11direct (N × H)
15. C11×#63271C2×D3direct (N × H)
16. C3×C7×C11×C13C22×C3semidirect
21. C2×C7×C11×C13C3×D3semidirect
22. C2×D3×C11×C13ΓL(1,𝔽8)semidirect
24. C2×C3×#63271C2×C11semidirect
25. D3×#63271C2×C11direct (N × H)
29. C2×D3×C7×C13C3×C11semidirect
31. C7×C11×C13C2×C3×D3semidirect
32. C2×D3×C7×C11C13⋊C3semidirect
34. C2×C3×C11×C13C2×ΓL(1,𝔽8)semidirect
35. D3×C11×C13C2×ΓL(1,𝔽8)semidirect
39. C3×#63271C22×C11semidirect
42. C2×C3×C7×C13C2×C3×C11semidirect
43. D3×C7×C13C2×C3×C11semidirect
46. C2×#63271D3×C11direct (N × H)
48. C2×C3×C7×C11C2×C13⋊C3semidirect
49. D3×C7×C11C2×C13⋊C3semidirect
53. C3×C11×C13C22×ΓL(1,𝔽8)semidirect
60. C2×C11×C13D3×ΓL(1,𝔽8)semidirect
61. C3×C7×C13C22×C3×C11semidirect
63. #63271C2×D3×C11direct (N × H)
67. C3×C7×C11C22×C13⋊C3semidirect
73. C2×C7×C13C3×D3×C11semidirect
74. C2×D3×C13C11×ΓL(1,𝔽8)semidirect
77. C2×C7×C11D3×C13⋊C3semidirect
78. C11×C13C2×D3×ΓL(1,𝔽8)semidirect
80. C2×D3×C11#63271direct (N × H)
85. C7×C13C2×C3×D3×C11semidirect
86. C2×D3×C7C11×C13⋊C3semidirect
88. C2×C3×C13C2×C11×ΓL(1,𝔽8)semidirect
89. D3×C13C2×C11×ΓL(1,𝔽8)semidirect
93. C7×C11C2×D3×C13⋊C3semidirect
97. C2×C3×C11C2×#63271semidirect
98. D3×C11C2×#63271direct (N × H)
102. C2×C3×C7C2×C11×C13⋊C3semidirect
103. D3×C7C2×C11×C13⋊C3semidirect
107. C3×C13C22×C11×ΓL(1,𝔽8)semidirect
113. C3×C11C22×#63271semidirect
116. C2×C13D3×C11×ΓL(1,𝔽8)semidirect
118. C2×C11D3×#63271direct (N × H)
119. C3×C7C22×C11×C13⋊C3semidirect
125. C2×C7D3×C11×C13⋊C3semidirect
126. C13C2×D3×C11×ΓL(1,𝔽8)semidirect
128. C2×D3C11×#63271direct (N × H)
129. C11C2×D3×#63271direct (N × H)
131. C7C2×D3×C11×C13⋊C3semidirect
135. C2×C3C2×C11×#63271semidirect
136. D3C2×C11×#63271direct (N × H)
140. C3C22×C11×#63271semidirect
142. C2D3×C11×#63271direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C11×#632712
D3×C11×#632712
C2×D3×C7×C11×C133
C22×C11×#632713
C2×D3×C11×C13⋊C37
C2×D3×#6327111
C2×D3×C11×ΓL(1,𝔽8)13