Group #19132740 — subgroups

Subgroups — #19132740

Order 5504.

122 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 25 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	#14582692	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582643	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#453	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
5	#13063240	—	2	1	no	—
6	H(5,𝔽₂)×C₄₃	C₄	1	1	yes	characteristic, complemented
7	AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
8	#127×C₄₃	C₂²	1	1	yes	characteristic
9	#104×C₄₃	—	2	1	no	—
10	#100×C₄₃	C₄	1	1	yes	characteristic, complemented
11	#41×C₄₃	—	2	1	no	—
12	#41×C₄₃	—	4	1	no	—
13	C₂×D₄×C₄₃	—	4	1	no	—
14	C₂×D₄×C₄₃	—	4	1	no	—
15	C₂×D₄×C₄₃	—	4	1	no	—
16	C₂×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
18	SD₁₆×C₄₃	—	4	1	no	—
19	D₈×C₄₃	—	4	1	no	—
20	M₁₆×C₄₃	—	2	1	no	—
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₂²⋊Dic₄₃	—	4	1	no	—
23	C₂×C₄₃⋊C₈	—	4	1	no	—
24	C₂³×C₄₃	—	2	1	no	—
25	C₂³×C₄₃	—	2	1	no	—
26	C₂³×C₄₃	—	4	1	no	—
27	Q₈×C₄₃	—	2	1	no	—
28	D₄×C₄₃	—	2	1	no	—
29	D₄×C₄₃	—	4	1	no	—
30	D₄×C₄₃	—	4	1	no	—
31	D₄×C₄₃	—	4	2	no	—
32	D₄×C₄₃	—	4	1	no	—
33	D₄×C₄₃	—	8	1	no	—
34	D₄×C₄₃	—	8	1	no	—
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	—	4	1	no	—
38	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₄₃	—	8	1	no	—
40	C₈×C₄₃	—	4	1	no	—
41	C₄₃⋊C₈	—	8	1	no	—
42	C₂²×C₄₃	—	4	1	no	—
43	C₂²×C₄₃	—	4	1	no	—
44	C₂²×C₄₃	—	4	1	no	—
45	C₂²×C₄₃	—	8	1	no	—
46	C₂²×C₄₃	—	8	1	no	—
47	C₂²×C₄₃	—	16	1	no	—
48	C₂²×C₄₃	#99	1	1	yes	characteristic
49	C₄×C₄₃	—	2	1	no	—
50	C₄×C₄₃	—	2	1	no	—
51	C₄×C₄₃	—	2	1	no	—
52	C₄×C₄₃	—	4	1	no	—
53	Dic₄₃	—	16	1	no	—
54	#1402	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	—	2	1	no	—
56	C₂×C₄₃	—	8	1	no	—
57	C₂×C₄₃	—	8	1	no	—
58	C₂×C₄₃	—	8	1	no	—
59	C₂×C₄₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
60	#453	D₄₃	1	1	yes	characteristic
61	#353	—	43	1	no	—
62	#331	—	43	1	no	—
63	C₄₃	#1402	1	1	yes	characteristic, complemented, Sylow
64	H(5,𝔽₂)	Dic₄₃	1	1	yes	characteristic, complemented
65	AGL(1,ℤ/8)	—	2	1	no	—
66	#127	C₂×D₄₃	1	1	yes	characteristic
67	C₄⋊C₈	—	86	1	no	—
68	#104	—	2	1	no	—
69	#100	Dic₄₃	1	1	yes	characteristic, complemented
70	#99	—	86	1	no	—
71	#41	—	2	1	no	—
72	#41	—	4	1	no	—
73	C₂×D₄	—	4	1	no	—
74	C₂×D₄	—	4	1	no	—
75	C₂×D₄	—	4	1	no	—
76	C₂×D₄	C₂×Dic₄₃	1	1	yes	characteristic
77	C₂×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
78	SD₁₆	—	4	1	no	—
79	D₈	—	4	1	no	—
80	M₁₆	—	2	1	no	—
81	C₂×C₈	—	172	1	no	—
82	C₂²⋊C₄	—	172	1	no	—
83	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
84	C₂³	—	2	1	no	—
85	C₂³	—	2	1	no	—
86	C₂³	—	4	1	no	—
87	Q₈	—	2	1	no	—
88	D₄	—	2	1	no	—
89	D₄	—	4	1	no	—
90	D₄	—	4	1	no	—
91	D₄	—	4	2	no	—
92	D₄	—	4	1	no	—
93	D₄	—	8	1	no	—
94	D₄	—	8	1	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	344	1	no	—
99	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
100	C₈	—	4	1	no	—
101	C₈	—	344	1	no	—
102	C₂²	—	4	1	no	—
103	C₂²	—	4	1	no	—
104	C₂²	—	4	1	no	—
105	C₂²	—	8	1	no	—
106	C₂²	—	8	1	no	—
107	C₂²	—	16	1	no	—
108	C₂²	#13063240	1	1	yes	characteristic
109	C₄	—	2	1	no	—
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	—	4	1	no	—
113	C₄	—	688	1	no	—
114	C₂	—	2	1	no	—
115	C₂	—	8	1	no	—
116	C₂	—	8	1	no	—
117	C₂	—	8	1	no	—
118	C₂	#14582686	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582692

C₂

yes

maximal, characteristic, complemented

#14582643

C₂

yes

maximal, characteristic, complemented

C₄₃×#453

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₈)

—

#13063240

—

H(5,𝔽₂)×C₄₃

C₄

yes

characteristic, complemented

AGL(1,ℤ/8)×C₄₃

—

#127×C₄₃

C₂²

yes

characteristic

#104×C₄₃

—

#100×C₄₃

C₄

yes

characteristic, complemented

#41×C₄₃

—

#41×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

D₄

yes

characteristic

SD₁₆×C₄₃

—

D₈×C₄₃

—

M₁₆×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₂²⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#99

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#1402

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

AΣL(1,𝔽₁₆)

yes

characteristic

#453

D₄₃

yes

characteristic

#353

—

#331

—

C₄₃

#1402

yes

characteristic, complemented, Sylow

H(5,𝔽₂)

Dic₄₃

yes

characteristic, complemented

AGL(1,ℤ/8)

—

#127

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

#104

—

#100

Dic₄₃

yes

characteristic, complemented

#99

—

#41

—

#41

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₄₃

yes

characteristic

C₂×D₄

C₂²⋊D₄₃

yes

characteristic

SD₁₆

—

D₈

—

M₁₆

—

C₂×C₈

—

172

—

C₂²⋊C₄

—

172

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₂³

—

C₂³

—

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

100

C₈

—

101

C₈

—

344

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

#13063240

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

688

—

114

C₂

—

115

C₂

—

116

C₂

—

117

C₂

—

118

C₂

#14582686

yes

characteristic

	subgroup	G/H
center	C₂	#14582686
commutator	C₂×D₄×C₄₃	C₂×C₄
Frattini	#127	C₂×D₄₃
Fitting	C₄₃×#453	C₂
socle	C₂×C₄₃	AΣL(1,𝔽₁₆)
hypercenter	#453	D₄₃
hypocenter	C₄₃	#1402
LCS	G ▷ C₂×D₄×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #453

subgroup

G/H

center

C₂

#14582686

commutator

C₂×D₄×C₄₃

C₂×C₄

Frattini

#127

C₂×D₄₃

Fitting

C₄₃×#453

C₂

socle

C₂×C₄₃

AΣL(1,𝔽₁₆)

D₄₃

C₄₃

G ▷ C₂×D₄×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #453

N	H ≅ G/N	type
1. #14582692	C₂	semidirect
2. #14582643	C₂	semidirect
6. H(5,𝔽₂)×C₄₃	C₄	semidirect
10. #100×C₄₃	C₄	semidirect
63. C₄₃	#1402	semidirect
64. H(5,𝔽₂)	Dic₄₃	semidirect
69. #100	Dic₄₃	semidirect

H ≅ G/N

type

1. #14582692

C₂

semidirect

2. #14582643

C₂

semidirect

6. H(5,𝔽₂)×C₄₃

C₄

semidirect

10. #100×C₄₃

C₄

semidirect

63. C₄₃

#1402

semidirect

64. H(5,𝔽₂)

Dic₄₃

semidirect

69. #100

Dic₄₃

semidirect

Subgroups — #19132740

Conjugacy classes of subgroups

Complements