Finite Group Databasebeta

← C11×AGL(1,𝔽7)×D39 #49114721

Subgroups — C11×AGL(1,𝔽7)×D39 #49114721

Order 36036.

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C11×ΓL(1,𝔽8)×D39C211yesmaximal, characteristic, complemented
2C11×C3⋊(ΓL(1,𝔽8)⋊D13)C211yesmaximal, characteristic, complemented
3C3×C11×C13×AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
4C11×D7×D39C311yesmaximal, characteristic, complemented
5C11×D13×AGL(1,𝔽7)—31nomaximal
6C3×C11×C13×ΓL(1,𝔽8)C2211yescharacteristic, complemented, Hall
7C11×ΓL(1,𝔽8)⋊D13—31no—
8C11×C13×AGL(1,𝔽7)—21no—
9C11×C13×AGL(1,𝔽7)D311yescharacteristic, complemented
10C11×ΓL(1,𝔽8)×D13—31no—
11C11×D273C2×C311yescharacteristic, complemented
12C7×C11×D39C2×C311yescharacteristic, complemented
13C3×C11×C13×D7C2×C311yescharacteristic, complemented
14C2×C3×C11×D39—71nomaximal, Hall
15C11×D7×D13—31noHall
16AGL(1,𝔽7)×D39C1111yesmaximal, characteristic, direct product factor, Hall
17C11×C13×ΓL(1,𝔽8)—21no—
18C11×C13×ΓL(1,𝔽8)C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20D3×C11×AGL(1,𝔽7)—131nomaximal, Hall
21C3×C11×D39—71no—
22C3×C11×D39—71no—
23C2×C32×C11×C13—71no—
24C11×D91—31no—
25C11×C13×D7C3×D311yescharacteristic, complemented
26C7×C11×D13—31no—
27C2×C11×D39—71no—
28C2×C3×C11×D13—211no—
29C3⋊(ΓL(1,𝔽8)⋊D13)C2×C1111yescharacteristic, complemented
30ΓL(1,𝔽8)×D39C2×C1111yescharacteristic, complemented
31C3×C13×AGL(1,𝔽7)C2×C1111yescharacteristic, complemented
32C11×C3⋊AGL(1,𝔽7)—131no—
33D3×C11×ΓL(1,𝔽8)—131no—
34C3×C11×AGL(1,𝔽7)D1311yescharacteristic, complemented
35C32×C11×C13—71noHall
36D7×D39C3×C1111yescharacteristic, complemented
37D13×AGL(1,𝔽7)—31no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D3×C11×D7—131no—
40C2×C11×AGL(1,𝔽7)—391no—
41C2×C3×C11×C13—71no—
42C2×C3×C11×C13—71no—
43C2×C3×C11×C13—141no—
44C11×D39—71no—
45C11×D39AGL(1,𝔽7)11yescharacteristic, direct product factor
46C3×C11×D13—211no—
47C3×C11×D13—211no—
48C3×C13×ΓL(1,𝔽8)C22×C1111yescharacteristic, complemented, Hall
49C3×C11×ΓL(1,𝔽8)C2×D1311yescharacteristic, complemented, Hall
50C2×C11×D13—211noHall
51D273C2×C3×C1111yescharacteristic, complemented
52C7×D39C2×C3×C1111yescharacteristic, complemented
53C3×C13×D7C2×C3×C1111yescharacteristic, complemented
54ΓL(1,𝔽8)⋊D13—31no—
55C13×AGL(1,𝔽7)—21no—
56C13×AGL(1,𝔽7)D3×C1111yescharacteristic, complemented
57ΓL(1,𝔽8)×D13—31no—
58C2×C3×D39—71noHall
59C11×D21—131no—
60D3×C7×C11—131no—
61C3×C11×D7C3×D1311yescharacteristic, complemented
62C2×C11×ΓL(1,𝔽8)—391no—
63C11×AGL(1,𝔽7)—21no—
64C11×AGL(1,𝔽7)—391no—
65C11×AGL(1,𝔽7)D3911yescharacteristic, direct product factor
66C3×C11×C13—71no—
67C3×C11×C13—141no—
68C3×C11×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
69C2×C3×D3×C11—911noHall
70D7×D13—31noHall
71C2×C11×D7—391noHall
72C2×C11×C13—71no—
73C11×D13—31no—
74C11×D13—211no—
75C3×C7×C13C22×C3×C1111yescharacteristic, complemented
76C13×ΓL(1,𝔽8)—21no—
77C13×ΓL(1,𝔽8)C2×D3×C1111yescharacteristic, complemented
78D3×AGL(1,𝔽7)—131noHall
79C2×C32×C13—71no—
80C3×D39—71no—
81C3×D39—71no—
82C3×C7×C11C2×C3×D1311yescharacteristic, complemented
83C11×ΓL(1,𝔽8)—21no—
84C11×ΓL(1,𝔽8)C2×D3911yescharacteristic, complemented
85C2×C32×C11—71no—
86C3×D3×C11—911no—
87C3×D3×C11—911no—
88D91—31no—
89C7×D13—31no—
90C13×D7C3×D3×C1111yescharacteristic, complemented
91C2×D39—71no—
92C2×C3×D13—211no—
93C2×C7×C11—391no—
94C11×D7—391no—
95C11×D7C3×D3911yescharacteristic, complemented
96C11×C13D3×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
97C22×C3×C11—2731no—
98C2×D3×C11—911no—
99C3⋊AGL(1,𝔽7)—131no—
100D3×ΓL(1,𝔽8)—131no—
101C3×AGL(1,𝔽7)C11×D1311yescharacteristic, complemented
102C32×C13—71noHall
103C32×C11—71noHall
104C7×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
105D3×D7—131no—
106C2×AGL(1,𝔽7)—391no—
107C2×C3×C13—71no—
108C2×C3×C13—71no—
109C2×C3×C13—141no—
110D39—71no—
111D39C11×AGL(1,𝔽7)11yescharacteristic, direct product factor
112C3×D13—211no—
113C3×D13—211no—
114C7×C11C2×C3×D3911yescharacteristic, complemented, Hall
115C2×C3×C11—71no—
116C2×C3×C11—71no—
117C2×C3×C11—141no—
118C2×C3×C11—2731no—
119C2×C3×C11—2731no—
120D3×C11—131no—
121D3×C11—911no—
122C3×ΓL(1,𝔽8)C2×C11×D1311yescharacteristic, complemented, Hall
123C2×D13—211noHall
124C22×C11—2731noHall
125D21—131no—
126C3×D7C3×C11×D1311yescharacteristic, complemented
127D3×C7—131no—
128C2×ΓL(1,𝔽8)—391no—
129AGL(1,𝔽7)—21no—
130AGL(1,𝔽7)—391no—
131AGL(1,𝔽7)C11×D3911yescharacteristic, direct product factor
132C3×C13—71no—
133C3×C13—141no—
134C3×C13C2×C11×AGL(1,𝔽7)11yescharacteristic, complemented
135C2×C3×D3—911noHall
136C3×C11—71no—
137C3×C11—141no—
138C3×C11D13×AGL(1,𝔽7)11yescharacteristic, complemented
139C2×D7—391noHall
140C2×C13—71no—
141D13—31no—
142D13—211no—
143C2×C11—71no—
144C2×C11—2731no—
145C2×C11—391no—
146C3×C7C2×C3×C11×D1311yescharacteristic, complemented
147ΓL(1,𝔽8)—21no—
148ΓL(1,𝔽8)C2×C11×D3911yescharacteristic, complemented
149C2×C32—71no—
150C3×D3—911no—
151C3×D3—911no—
152C2×C7—391no—
153D7—391no—
154D7C3×C11×D3911yescharacteristic, complemented
155C13D3×C11×AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
156C22×C3—2731no—
157C2×D3—911no—
158C11AGL(1,𝔽7)×D3911yescharacteristic, direct product factor, Sylow
159C32—71noSylow
160C7C2×C3×C11×D3911yescharacteristic, complemented, Sylow
161C2×C3—71no—
162C2×C3—71no—
163C2×C3—141no—
164C2×C3—2731no—
165C2×C3—2731no—
166D3—131no—
167D3—911no—
168C22—2731noSylow
169C3—71no—
170C3—141no—
171C3C11×D13×AGL(1,𝔽7)11yescharacteristic, complemented
172C2—71no—
173C2—2731no—
174C2—391no—
subgroupG/H
center, hypercenterC11AGL(1,𝔽7)×D39
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×ΓL(1,𝔽8)×D39C2semidirect
2. C11×C3⋊(ΓL(1,𝔽8)⋊D13)C2semidirect
3. C3×C11×C13×AGL(1,𝔽7)C2semidirect
4. C11×D7×D39C3semidirect
6. C3×C11×C13×ΓL(1,𝔽8)C22semidirect
9. C11×C13×AGL(1,𝔽7)D3semidirect
11. C11×D273C2×C3semidirect
12. C7×C11×D39C2×C3semidirect
13. C3×C11×C13×D7C2×C3semidirect
16. AGL(1,𝔽7)×D39C11direct (N × H)
18. C11×C13×ΓL(1,𝔽8)C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
25. C11×C13×D7C3×D3semidirect
29. C3⋊(ΓL(1,𝔽8)⋊D13)C2×C11semidirect
30. ΓL(1,𝔽8)×D39C2×C11semidirect
31. C3×C13×AGL(1,𝔽7)C2×C11semidirect
34. C3×C11×AGL(1,𝔽7)D13semidirect
36. D7×D39C3×C11semidirect
38. C7×C11×C13C2×C3×D3semidirect
45. C11×D39AGL(1,𝔽7)direct (N × H)
48. C3×C13×ΓL(1,𝔽8)C22×C11semidirect
49. C3×C11×ΓL(1,𝔽8)C2×D13semidirect
51. D273C2×C3×C11semidirect
52. C7×D39C2×C3×C11semidirect
53. C3×C13×D7C2×C3×C11semidirect
56. C13×AGL(1,𝔽7)D3×C11semidirect
61. C3×C11×D7C3×D13semidirect
65. C11×AGL(1,𝔽7)D39direct (N × H)
68. C3×C11×C13C2×AGL(1,𝔽7)semidirect
75. C3×C7×C13C22×C3×C11semidirect
77. C13×ΓL(1,𝔽8)C2×D3×C11semidirect
82. C3×C7×C11C2×C3×D13semidirect
84. C11×ΓL(1,𝔽8)C2×D39semidirect
90. C13×D7C3×D3×C11semidirect
95. C11×D7C3×D39semidirect
96. C11×C13D3×AGL(1,𝔽7)semidirect
101. C3×AGL(1,𝔽7)C11×D13semidirect
104. C7×C13C2×C3×D3×C11semidirect
111. D39C11×AGL(1,𝔽7)direct (N × H)
114. C7×C11C2×C3×D39semidirect
122. C3×ΓL(1,𝔽8)C2×C11×D13semidirect
126. C3×D7C3×C11×D13semidirect
131. AGL(1,𝔽7)C11×D39direct (N × H)
134. C3×C13C2×C11×AGL(1,𝔽7)semidirect
138. C3×C11D13×AGL(1,𝔽7)semidirect
146. C3×C7C2×C3×C11×D13semidirect
148. ΓL(1,𝔽8)C2×C11×D39semidirect
154. D7C3×C11×D39semidirect
155. C13D3×C11×AGL(1,𝔽7)semidirect
158. C11AGL(1,𝔽7)×D39direct (N × H)
160. C7C2×C3×C11×D39semidirect
171. C3C11×D13×AGL(1,𝔽7)semidirect

Maximal subgroups

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

subgroupindex
C11×ΓL(1,𝔽8)×D392
C11×C3⋊(ΓL(1,𝔽8)⋊D13)2
C3×C11×C13×AGL(1,𝔽7)2
C11×D7×D393
C11×D13×AGL(1,𝔽7)3
C2×C3×C11×D397
AGL(1,𝔽7)×D3911
D3×C11×AGL(1,𝔽7)13