Finite Group Databasebeta

← D11×C3⋊#10587720 #49114708

Subgroups — D11×C3⋊#10587720 #49114708

Order 36036.

176 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 42 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⋊#10587720C211yesmaximal, characteristic, complemented
3C3×D11×#63270C211yesmaximal, characteristic, complemented
4C13×D11×D21C311yesmaximal, characteristic, complemented
5D11×#10587720—31nomaximal
6C3×C11×#63270C2211yescharacteristic, complemented, Hall
7C11⋊#10587720—31no—
8C11×#10587720—31no—
9D11×#63270—21no—
10D11×#63270D311yescharacteristic, complemented
11C13×D231C2×C311yescharacteristic, complemented
12C11×C13×D21C2×C311yescharacteristic, complemented
13C3×C7×C13×D11C2×C311yescharacteristic, complemented
14D3×D11×C13⋊C3—71nomaximal, Hall
15C13×D7×D11—31noHall
16C2×C3⋊#10587720—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—
22D3×C11×C13⋊C3—71no—
23C3×D11×C13⋊C3—71no—
24C13×D77—31no—
25C11×C13×D7—31no—
26C7×C13×D11C3×D311yescharacteristic, complemented
27D3×C13×D11—71no—
28C2×D11×C13⋊C3—211no—
29C2×C3×#63270—111no—
30C3⋊#10587720—111no—
31C3⋊#10587720D1111yescharacteristic, direct product factor
32C3⋊(C11⋊AGL(1,𝔽7))—131no—
33C11×C3⋊AGL(1,𝔽7)—131no—
34C3×ΓL(1,𝔽8)×D11—131no—
35C3×C11×C13⋊C3—71noHall
36C2×C13×D21—111no—
37C2×#10587720—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D11×D21C13⋊C311yescharacteristic, complemented
40D11×AGL(1,𝔽7)—391no—
41C13×D33—71no—
42D3×C11×C13—71no—
43C3×C13×D11AGL(1,𝔽7)11yescharacteristic, complemented
44C2×C11×C13⋊C3—211no—
45D11×C13⋊C3—71no—
46D11×C13⋊C3—141no—
47D11×C13⋊C3—211no—
48C3×#63270C2×D1111yescharacteristic, complemented, Hall
49C3×C11×ΓL(1,𝔽8)—131noHall
50C2×C13×D11—211noHall
51C2×C3×C7×C13—111no—
52C13×D21—111no—
53C13×D21C3×D1111yescharacteristic, complemented
54C2×#63270—111no—
55C2×#63270—221no—
56#10587720—31no—
57#10587720—331no—
58C2×D3×C13⋊C3—771noHall
59D231C2×C13⋊C311yescharacteristic, complemented
60C11×D21C2×C13⋊C311yescharacteristic, complemented
61C3×C7×D11C2×C13⋊C311yescharacteristic, complemented
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
70C2×C13×D7—331noHall
71D7×D11—31noHall
72C2×C11×C13—211no—
73C13×D11—211no—
74C13×D11C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76#63270—21no—
77#63270D3×D1111yescharacteristic, complemented
78C2×C3⋊AGL(1,𝔽7)—1431noHall
79C2×C3×C13⋊C3—771no—
80D3×C13⋊C3—71no—
81D3×C13⋊C3—771no—
82C3×C7×C11C22×C13⋊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—111no—
89C13×D7—31no—
90C13×D7—331no—
91C2×D3×C13—771no—
92C22×C13⋊C3—2311no—
93D77—31no—
94C7×D11D3×C13⋊C311yescharacteristic, complemented
95C11×D7—31no—
96C11×C13C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11—71no—
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—111no—
106C2×AGL(1,𝔽7)—4291no—
107C2×C3×C13—111no—
108D3×C13—71no—
109D3×C13—771no—
110C2×C13⋊C3—211no—
111C2×C13⋊C3—771no—
112C2×C13⋊C3—1541no—
113C2×C13⋊C3—2311no—
114C7×C11C2×D3×C13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33—71no—
117C3×D11—2731no—
118C3×D11—911no—
119C3×D11—1821no—
120C3×D11#1058772011yescharacteristic, complemented
121D3×C11—71no—
122C3×ΓL(1,𝔽8)—131noHall
123C22×C13—2311noHall
124C2×D11—211noHall
125C2×C3×C7—111no—
126D21—111no—
127D21D11×C13⋊C311yescharacteristic, complemented
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×C11C2×#1058772011yescharacteristic, complemented
139C2×D7—331noHall
140C2×C13—111no—
141C2×C13—211no—
142C2×C13—2311no—
143C2×C11—211no—
144D11—211no—
145D11C3⋊#1058772011yescharacteristic, direct product factor
146C3×C7C2×D11×C13⋊C311yescharacteristic, complemented
147ΓL(1,𝔽8)—131no—
148ΓL(1,𝔽8)—261no—
149C2×C32—10011no—
150C3×D3—911no—
151C3×D3—10011no—
152C2×C7—111no—
153D7—31no—
154D7—331no—
155C13D11×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—771no—
158C11C2×C3⋊#1058772011yescharacteristic, complemented, Sylow
159C32—911noSylow
160C7D3×D11×C13⋊C311yescharacteristic, complemented, Sylow
161C2×C3—111no—
162C2×C3—2731no—
163C2×C3—30031no—
164C2×C3—20021no—
165C2×C3—10011no—
166D3—71no—
167D3—771no—
168C22—2311noSylow
169C3—911no—
170C3—1821no—
171C3D11×#1058772011yescharacteristic, complemented
172C2—111no—
173C2—211no—
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⋊#10587720C2semidirect
3. C3×D11×#63270C2semidirect
4. C13×D11×D21C3semidirect
6. C3×C11×#63270C22semidirect
10. D11×#63270D3semidirect
11. C13×D231C2×C3semidirect
12. C11×C13×D21C2×C3semidirect
13. C3×C7×C13×D11C2×C3semidirect
18. C11×#63270C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
26. C7×C13×D11C3×D3semidirect
31. C3⋊#10587720D11direct (N × H)
38. C7×C11×C13C2×C3×D3semidirect
39. D11×D21C13⋊C3semidirect
43. C3×C13×D11AGL(1,𝔽7)semidirect
48. C3×#63270C2×D11semidirect
53. C13×D21C3×D11semidirect
59. D231C2×C13⋊C3semidirect
60. C11×D21C2×C13⋊C3semidirect
61. C3×C7×D11C2×C13⋊C3semidirect
66. C3×C11×C13C2×AGL(1,𝔽7)semidirect
74. C13×D11C3⋊AGL(1,𝔽7)semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. #63270D3×D11semidirect
82. C3×C7×C11C22×C13⋊C3semidirect
94. C7×D11D3×C13⋊C3semidirect
96. C11×C13C2×C3⋊AGL(1,𝔽7)semidirect
104. C7×C13C3×D3×D11semidirect
114. C7×C11C2×D3×C13⋊C3semidirect
120. C3×D11#10587720semidirect
127. D21D11×C13⋊C3semidirect
132. C3×C13D11×AGL(1,𝔽7)semidirect
138. C3×C11C2×#10587720semidirect
145. D11C3⋊#10587720direct (N × H)
146. C3×C7C2×D11×C13⋊C3semidirect
155. C13D11×C3⋊AGL(1,𝔽7)semidirect
158. C11C2×C3⋊#10587720semidirect
160. C7D3×D11×C13⋊C3semidirect
171. C3D11×#10587720semidirect

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⋊#105877202
C3×D11×#632702
C13×D11×D213
D11×#105877203
D3×D11×C13⋊C37
C2×C3⋊#1058772011
D11×C3⋊AGL(1,𝔽7)13