Group #14647480 — subgroups

Subgroups — #14647480

Order 2816.

228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13067379	C₂	1	2	yes	maximal
2	#13066478	C₂	1	4	yes	maximal
3	C₁₁×#1450	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#431	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	#10622539	C₂²	1	4	yes	—
7	C₁₁×#322	C₄	1	2	yes	—
8	C₈²×C₁₁	C₄	1	2	yes	—
9	#10622096	—	2	2	no	—
10	#10622095	—	2	2	no	—
11	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
13	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
14	C₁₁×C₄⋊C₈	—	2	2	no	—
15	C₁₁×C₂²⋊C₈	—	2	2	no	—
16	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
17	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
21	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
22	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
23	#66867	—	2	4	no	—
24	#8796	—	11	1	no	maximal, Sylow
25	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
26	C₂²×C₄×C₁₁	#41	1	2	yes	—
27	C₂×C₈×C₁₁	—	2	2	no	—
28	C₂×C₈×C₁₁	—	2	2	no	—
29	C₂×C₈×C₁₁	—	2	4	no	—
30	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
34	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₄²×C₁₁	#41	1	2	yes	—
37	C₂×C₁₁⋊C₈	—	4	4	no	—
38	#1568	—	11	2	no	—
39	#1450	D₁₁	1	1	yes	characteristic
40	#1287	—	11	4	no	—
41	C₂³×C₁₁	#125	1	1	yes	characteristic
42	C₂×C₄×C₁₁	—	2	1	no	—
43	C₂×C₄×C₁₁	—	2	1	no	—
44	C₂×C₄×C₁₁	—	4	2	no	—
45	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₁	#117	1	2	yes	—
47	C₂×C₄×C₁₁	#124	1	2	yes	—
48	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
49	C₈×C₁₁	—	2	1	no	—
50	C₈×C₁₁	—	2	1	no	—
51	C₈×C₁₁	—	4	4	no	—
52	C₈×C₁₁	#108	1	2	yes	—
53	C₈×C₁₁	#108	1	2	yes	—
54	C₁₁⋊C₈	—	8	4	no	—
55	#432	—	11	4	no	—
56	#431	C₂×D₁₁	1	2	yes	—
57	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
58	#335	—	22	2	no	—
59	#334	—	22	2	no	—
60	#322	Dic₁₁	1	2	yes	—
61	C₈²	Dic₁₁	1	2	yes	—
62	C₂²×C₁₁	—	2	2	no	—
63	C₂²×C₁₁	—	2	1	no	—
64	C₂²×C₁₁	#382	1	1	yes	characteristic
65	C₄×C₁₁	—	2	2	no	—
66	C₄×C₁₁	—	2	2	no	—
67	C₄×C₁₁	—	2	1	no	—
68	C₄×C₁₁	C₂×#108	1	1	yes	characteristic
69	C₄×C₁₁	C₂×#108	1	1	yes	characteristic
70	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
71	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
72	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
73	C₄⋊C₈	—	2	2	no	—
74	C₄⋊C₈	—	22	4	no	—
75	C₂²⋊C₈	—	2	2	no	—
76	C₂²⋊C₈	—	22	4	no	—
77	#97	—	22	4	no	—
78	C₄×C₈	D₄₄	1	1	yes	characteristic
79	C₄×C₈	D₄₄	1	1	yes	characteristic
80	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
81	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
82	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
83	C₂×C₁₁	—	4	1	no	—
84	C₂×C₁₁	#1833	1	2	yes	—
85	C₂×C₁₁	#1837	1	1	yes	characteristic
86	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
87	C₂²×C₄	#4339	1	2	yes	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	4	no	—
91	C₂×C₈	—	44	4	no	—
92	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
93	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
94	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
95	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
96	C₄²	C₂×D₄₄	1	1	yes	characteristic
97	C₄²	#4339	1	2	yes	—
98	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
99	C₁₁	#8796	1	1	yes	characteristic, complemented, Sylow
100	C₂³	#66923	1	1	yes	characteristic
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	#66923	1	1	yes	characteristic
105	C₂×C₄	#66928	1	2	yes	—
106	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
107	C₂×C₄	#66979	1	2	yes	—
108	C₈	—	2	1	no	—
109	C₈	—	2	1	no	—
110	C₈	—	4	4	no	—
111	C₈	—	88	4	no	—
112	C₈	#66883	1	2	yes	—
113	C₈	#66883	1	2	yes	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	1	no	—
116	C₂²	#10622549	1	1	yes	characteristic
117	C₄	—	2	2	no	—
118	C₄	—	2	2	no	—
119	C₄	—	2	1	no	—
120	C₄	C₂×#66883	1	1	yes	characteristic
121	C₄	C₂×#66883	1	1	yes	characteristic
122	C₂	—	4	1	no	—
123	C₂	#13068740	1	2	yes	—
124	C₂	#13068754	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13067379

C₂

yes

maximal

#13066478

C₂

yes

maximal

C₁₁×#1450

C₂

yes

maximal, characteristic

C₁₁×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622539

C₂²

yes

—

C₁₁×#322

C₄

yes

—

C₈²×C₁₁

C₄

yes

—

#10622096

—

#10622095

—

C₂²×C₈×C₁₁

Q₈

yes

characteristic

C₂²×C₈×C₁₁

Q₈

yes

characteristic

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₁₁×C₄⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#66867

—

#8796

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

characteristic

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

#41

yes

—

C₂×C₁₁⋊C₈

—

#1568

—

#1450

D₁₁

yes

characteristic

#1287

—

C₂³×C₁₁

#125

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#117

yes

—

C₂×C₄×C₁₁

#124

yes

—

C₂×C₄×C₁₁

#125

yes

characteristic

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#108

yes

—

C₈×C₁₁

#108

yes

—

C₁₁⋊C₈

—

#432

—

#431

C₂×D₁₁

yes

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

Dic₁₁

yes

—

C₈²

Dic₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#382

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂²×C₈

Dic₂₂

yes

characteristic

C₂²×C₈

Dic₂₂

yes

characteristic

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

D₄₄

yes

characteristic

C₄×C₈

D₄₄

yes

characteristic

C₄×C₈

C₂×Dic₁₁

yes

—

C₄×C₈

C₂×Dic₁₁

yes

characteristic

C₄×C₈

C₂×Dic₁₁

yes

characteristic

C₂×C₁₁

—

C₂×C₁₁

#1833

yes

—

C₂×C₁₁

#1837

yes

characteristic

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

C₂²×C₄

#4339

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₁

yes

characteristic

C₂×C₈

C₄⋊Dic₁₁

yes

characteristic

C₂×C₈

C₄⋊Dic₁₁

yes

characteristic

C₂×C₈

C₄⋊Dic₁₁

yes

characteristic

C₄²

C₂×D₄₄

yes

characteristic

C₄²

#4339

yes

—

C₄²

C₂²×Dic₁₁

yes

characteristic

C₁₁

#8796

yes

characteristic, complemented, Sylow

100

C₂³

#66923

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

#66923

yes

characteristic

105

C₂×C₄

#66928

yes

—

106

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

107

C₂×C₄

#66979

yes

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

112

C₈

#66883

yes

—

113

C₈

#66883

yes

—

114

C₂²

—

115

C₂²

—

116

C₂²

#10622549

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

C₂×#66883

yes

characteristic

121

C₄

C₂×#66883

yes

characteristic

122

C₂

—

123

C₂

#13068740

yes

—

124

C₂

#13068754

yes

characteristic

	subgroup	G/H
center	C₂²	#10622549
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1450	C₂
socle	C₂²×C₁₁	#382
prime radical	C₂³×C₁₁	#125
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1450	D₁₁
hypocenter	C₁₁	#8796
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

subgroup

G/H

center

C₂²

#10622549

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1450

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

N	H ≅ G/N	type
99. C₁₁	#8796	semidirect

H ≅ G/N

type

99. C₁₁

#8796

semidirect

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

subgroup	index
#13067379	2
#13066478	2
C₁₁×#1450	2
#8796	11

subgroup

index

#13067379

#13066478

C₁₁×#1450

#8796

Subgroups — #14647480

Conjugacy classes of subgroups

Complements

Maximal subgroups