Group #14647526 — subgroups

Subgroups — #14647526

Order 2816.

402 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 211 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	#13068768	C₂	1	2	yes	maximal
2	C₂×#10622095	C₂	1	4	yes	maximal
3	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
5	C₄³×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
7	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
8	C₁₁×#336	C₄	1	4	yes	—
9	#10622095	—	2	8	no	—
10	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₁	D₄	1	2	yes	—
13	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
14	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
15	C₂²×C₁₁⋊C₈	—	2	4	no	—
16	C₄×C₈×C₁₁	D₄	1	4	yes	—
17	C₄×C₈×C₁₁	Q₈	1	4	yes	—
18	C₄⋊(C₁₁⋊C₈)	—	2	8	no	—
19	C₄⋊(C₁₁⋊C₈)	—	4	8	no	—
20	#8809	—	11	1	no	maximal, Sylow
21	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
22	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₈×C₁₁	—	2	8	no	—
26	C₂×C₈×C₁₁	C₄⋊C₄	1	8	yes	—
27	C₄²×C₁₁	—	2	4	no	—
28	C₄²×C₁₁	—	4	2	no	—
29	C₄²×C₁₁	SD₁₆	1	8	yes	—
30	C₄²×C₁₁	C₂×D₄	1	2	yes	—
31	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
32	C₂×C₁₁⋊C₈	—	4	4	no	—
33	C₂×C₁₁⋊C₈	—	4	8	no	—
34	#1842	—	11	2	no	—
35	#1744	D₁₁	1	1	yes	characteristic
36	C₂×#334	—	11	4	no	—
37	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₁	—	2	4	no	—
39	C₂×C₄×C₁₁	—	2	4	no	—
40	C₂×C₄×C₁₁	—	2	2	no	—
41	C₂×C₄×C₁₁	#106	1	8	yes	—
42	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
43	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
44	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
45	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₄×C₁₁	#131	1	4	yes	—
47	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
48	C₈×C₁₁	—	2	8	no	—
49	C₁₁⋊C₈	—	8	4	no	—
50	C₂×C₄⋊C₈	—	11	4	no	—
51	C₂×C₄⋊C₈	—	22	4	no	—
52	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
53	C₄³	C₂×D₁₁	1	1	yes	characteristic
54	#336	Dic₁₁	1	4	yes	—
55	#334	—	22	8	no	—
56	C₂²×C₁₁	#384	1	1	yes	characteristic
57	C₂²×C₁₁	#424	1	2	yes	—
58	C₂²×C₁₁	C₂×#106	1	2	yes	—
59	C₂²×C₁₁	#430	1	2	yes	—
60	C₄×C₁₁	—	2	8	no	—
61	C₄×C₁₁	—	2	2	no	—
62	C₄×C₁₁	#424	1	4	yes	—
63	C₄×C₁₁	#492	1	2	yes	—
64	C₄×C₁₁	#498	1	2	yes	—
65	C₂²×C₈	—	22	4	no	—
66	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
67	C₂×C₄²	Dic₂₂	1	2	yes	—
68	C₂×C₄²	D₄₄	1	2	yes	—
69	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
70	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
71	C₄⋊C₈	—	22	8	no	—
72	C₄⋊C₈	—	44	8	no	—
73	C₄×C₈	Dic₂₂	1	4	yes	—
74	C₄×C₈	D₄₄	1	4	yes	—
75	C₂×C₁₁	#1570	1	4	yes	—
76	C₂×C₁₁	#1843	1	1	yes	characteristic
77	C₂×C₁₁	#1844	1	1	yes	characteristic
78	C₂×C₁₁	#1849	1	1	yes	characteristic
79	C₂²×C₄	C₄⋊Dic₁₁	1	4	yes	—
80	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
81	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
82	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
83	C₂×C₈	—	2	8	no	—
84	C₂×C₈	—	44	4	no	—
85	C₂×C₈	—	44	8	no	—
86	C₂×C₈	C₄⋊Dic₁₁	1	8	yes	—
87	C₄²	—	2	4	no	—
88	C₄²	—	4	2	no	—
89	C₄²	#4314	1	8	yes	—
90	C₄²	C₂×Dic₂₂	1	2	yes	—
91	C₄²	C₂×D₄₄	1	2	yes	—
92	C₁₁	#8809	1	1	yes	characteristic, complemented, Sylow
93	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	#66881	1	8	yes	—
98	C₂×C₄	#66922	1	2	yes	—
99	C₂×C₄	#66922	1	1	yes	characteristic
100	C₂×C₄	#66927	1	1	yes	characteristic
101	C₂×C₄	C₂×#4314	1	4	yes	—
102	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
103	C₂×C₄	#67001	1	4	yes	—
104	C₈	—	2	8	no	—
105	C₈	—	88	4	no	—
106	C₂²	#10622548	1	1	yes	characteristic
107	C₂²	#10622612	1	2	yes	—
108	C₂²	C₂×#66881	1	2	yes	—
109	C₂²	#10622738	1	2	yes	—
110	C₄	—	2	8	no	—
111	C₄	—	2	2	no	—
112	C₄	#10622293	1	2	yes	—
113	C₄	#10622306	1	2	yes	—
114	C₄	#10622612	1	4	yes	—
115	C₂	#13067387	1	4	yes	—
116	C₂	#13068770	1	1	yes	characteristic
117	C₂	#13068773	1	1	yes	characteristic
118	C₂	#13068791	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068768

C₂

yes

maximal

C₂×#10622095

C₂

yes

maximal

C₁₁×#1744

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₄³×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊(C₁₁⋊C₈)

—

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

C₁₁×#336

C₄

yes

—

#10622095

—

C₂²×C₈×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂²×C₁₁⋊C₈

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#8809

—

maximal, Sylow

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

SD₁₆

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#1842

—

#1744

D₁₁

yes

characteristic

C₂×#334

—

C₂³×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#106

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

#131

yes

—

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

C₄³

C₂×D₁₁

yes

characteristic

#336

Dic₁₁

yes

—

#334

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#424

yes

—

C₂²×C₁₁

C₂×#106

yes

—

C₂²×C₁₁

#430

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#424

yes

—

C₄×C₁₁

#492

yes

—

C₄×C₁₁

#498

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₁

yes

—

C₂×C₄²

Dic₂₂

yes

—

C₂×C₄²

D₄₄

yes

—

C₂×C₄²

C₂×Dic₁₁

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

D₄₄

yes

—

C₂×C₁₁

#1570

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂²×C₄

C₄⋊Dic₁₁

yes

—

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

C₂²×C₄

C₂×D₄₄

yes

characteristic

C₂²×C₄

C₂²×Dic₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₄²

—

C₄²

—

C₄²

#4314

yes

—

C₄²

C₂×Dic₂₂

yes

—

C₄²

C₂×D₄₄

yes

—

C₁₁

#8809

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄⋊Dic₁₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#66881

yes

—

C₂×C₄

#66922

yes

—

C₂×C₄

#66922

yes

characteristic

100

C₂×C₄

#66927

yes

characteristic

101

C₂×C₄

C₂×#4314

yes

—

102

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

—

103

C₂×C₄

#67001

yes

—

104

C₈

—

105

C₈

—

106

C₂²

#10622548

yes

characteristic

107

C₂²

#10622612

yes

—

108

C₂²

C₂×#66881

yes

—

109

C₂²

#10622738

yes

—

110

C₄

—

111

C₄

—

112

C₄

#10622293

yes

—

113

C₄

#10622306

yes

—

114

C₄

#10622612

yes

—

115

C₂

#13067387

yes

—

116

C₂

#13068770

yes

characteristic

117

C₂

#13068773

yes

characteristic

118

C₂

#13068791

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₄
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1744	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1744	D₁₁
hypocenter	C₁₁	#8809
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₂×D₄₄

commutator

C₂²×C₄×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1744

C₂

socle, prime radical

C₂³×C₁₁

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
92. C₁₁	#8809	semidirect

H ≅ G/N

type

92. C₁₁

#8809

semidirect

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

subgroup	index
#13068768	2
C₂×#10622095	2
C₁₁×#1744	2
#8809	11

subgroup

index

#13068768

C₂×#10622095

C₁₁×#1744

#8809

Subgroups — #14647526

Conjugacy classes of subgroups

Complements

Maximal subgroups