Group #20241533 — subgroups

Subgroups — #20241533

Order 6016.

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	#15688916	C₂	1	1	yes	maximal, characteristic, complemented
2	#15688867	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#453	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
5	#13093939	—	2	1	no	—
6	H(5,𝔽₂)×C₄₇	C₄	1	1	yes	characteristic, complemented
7	AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
8	#127×C₄₇	C₂²	1	1	yes	characteristic
9	#104×C₄₇	—	2	1	no	—
10	#100×C₄₇	C₄	1	1	yes	characteristic, complemented
11	#41×C₄₇	—	2	1	no	—
12	#41×C₄₇	—	4	1	no	—
13	C₂×D₄×C₄₇	—	4	1	no	—
14	C₂×D₄×C₄₇	—	4	1	no	—
15	C₂×D₄×C₄₇	—	4	1	no	—
16	C₂×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
18	SD₁₆×C₄₇	—	4	1	no	—
19	D₈×C₄₇	—	4	1	no	—
20	M₁₆×C₄₇	—	2	1	no	—
21	C₄²×C₄₇	D₄	1	1	yes	characteristic
22	C₂²⋊Dic₄₇	—	4	1	no	—
23	C₂×C₄₇⋊C₈	—	4	1	no	—
24	C₂³×C₄₇	—	2	1	no	—
25	C₂³×C₄₇	—	2	1	no	—
26	C₂³×C₄₇	—	4	1	no	—
27	Q₈×C₄₇	—	2	1	no	—
28	D₄×C₄₇	—	2	1	no	—
29	D₄×C₄₇	—	4	1	no	—
30	D₄×C₄₇	—	4	1	no	—
31	D₄×C₄₇	—	4	2	no	—
32	D₄×C₄₇	—	4	1	no	—
33	D₄×C₄₇	—	8	1	no	—
34	D₄×C₄₇	—	8	1	no	—
35	C₂×C₄×C₄₇	—	2	1	no	—
36	C₂×C₄×C₄₇	—	4	1	no	—
37	C₂×C₄×C₄₇	—	4	1	no	—
38	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₄₇	—	8	1	no	—
40	C₈×C₄₇	—	4	1	no	—
41	C₄₇⋊C₈	—	8	1	no	—
42	C₂²×C₄₇	—	4	1	no	—
43	C₂²×C₄₇	—	4	1	no	—
44	C₂²×C₄₇	—	4	1	no	—
45	C₂²×C₄₇	—	8	1	no	—
46	C₂²×C₄₇	—	8	1	no	—
47	C₂²×C₄₇	—	16	1	no	—
48	C₂²×C₄₇	#99	1	1	yes	characteristic
49	C₄×C₄₇	—	2	1	no	—
50	C₄×C₄₇	—	2	1	no	—
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	—	4	1	no	—
53	Dic₄₇	—	16	1	no	—
54	#1402	—	47	1	no	maximal, Sylow
55	C₂×C₄₇	—	2	1	no	—
56	C₂×C₄₇	—	8	1	no	—
57	C₂×C₄₇	—	8	1	no	—
58	C₂×C₄₇	—	8	1	no	—
59	C₂×C₄₇	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
60	#453	D₄₇	1	1	yes	characteristic
61	#353	—	47	1	no	—
62	#331	—	47	1	no	—
63	C₄₇	#1402	1	1	yes	characteristic, complemented, Sylow
64	H(5,𝔽₂)	Dic₄₇	1	1	yes	characteristic, complemented
65	AGL(1,ℤ/8)	—	2	1	no	—
66	#127	C₂×D₄₇	1	1	yes	characteristic
67	C₄⋊C₈	—	94	1	no	—
68	#104	—	2	1	no	—
69	#100	Dic₄₇	1	1	yes	characteristic, complemented
70	#99	—	94	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×Dic₄₇	1	1	yes	characteristic
77	C₂×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
78	SD₁₆	—	4	1	no	—
79	D₈	—	4	1	no	—
80	M₁₆	—	2	1	no	—
81	C₂×C₈	—	188	1	no	—
82	C₂²⋊C₄	—	188	1	no	—
83	C₄²	C₂²⋊D₄₇	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	—	376	1	no	—
99	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
100	C₈	—	4	1	no	—
101	C₈	—	376	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	#13093939	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	—	752	1	no	—
114	C₂	—	2	1	no	—
115	C₂	—	8	1	no	—
116	C₂	—	8	1	no	—
117	C₂	—	8	1	no	—
118	C₂	#15688910	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15688916

C₂

yes

maximal, characteristic, complemented

#15688867

C₂

yes

maximal, characteristic, complemented

C₄₇×#453

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₈)

—

#13093939

—

H(5,𝔽₂)×C₄₇

C₄

yes

characteristic, complemented

AGL(1,ℤ/8)×C₄₇

—

#127×C₄₇

C₂²

yes

characteristic

#104×C₄₇

—

#100×C₄₇

C₄

yes

characteristic, complemented

#41×C₄₇

—

#41×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂×C₄

yes

characteristic

C₂×D₄×C₄₇

D₄

yes

characteristic

SD₁₆×C₄₇

—

D₈×C₄₇

—

M₁₆×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

C₂²⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#99

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

#1402

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

AΣL(1,𝔽₁₆)

yes

characteristic

#453

D₄₇

yes

characteristic

#353

—

#331

—

C₄₇

#1402

yes

characteristic, complemented, Sylow

H(5,𝔽₂)

Dic₄₇

yes

characteristic, complemented

AGL(1,ℤ/8)

—

#127

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

#104

—

#100

Dic₄₇

yes

characteristic, complemented

#99

—

#41

—

#41

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₄₇

yes

characteristic

C₂×D₄

C₂²⋊D₄₇

yes

characteristic

SD₁₆

—

D₈

—

M₁₆

—

C₂×C₈

—

188

—

C₂²⋊C₄

—

188

—

C₄²

C₂²⋊D₄₇

yes

characteristic

C₂³

—

C₂³

—

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

376

—

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

100

C₈

—

101

C₈

—

376

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

#13093939

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

752

—

114

C₂

—

115

C₂

—

116

C₂

—

117

C₂

—

118

C₂

#15688910

yes

characteristic

	subgroup	G/H
center	C₂	#15688910
commutator	C₂×D₄×C₄₇	C₂×C₄
Frattini	#127	C₂×D₄₇
Fitting	C₄₇×#453	C₂
socle	C₂×C₄₇	AΣL(1,𝔽₁₆)
hypercenter	#453	D₄₇
hypocenter	C₄₇	#1402
LCS	G ▷ C₂×D₄×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #453

subgroup

G/H

center

C₂

#15688910

commutator

C₂×D₄×C₄₇

C₂×C₄

Frattini

#127

C₂×D₄₇

Fitting

C₄₇×#453

C₂

socle

C₂×C₄₇

AΣL(1,𝔽₁₆)

D₄₇

C₄₇

G ▷ C₂×D₄×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #453

N	H ≅ G/N	type
1. #15688916	C₂	semidirect
2. #15688867	C₂	semidirect
6. H(5,𝔽₂)×C₄₇	C₄	semidirect
10. #100×C₄₇	C₄	semidirect
63. C₄₇	#1402	semidirect
64. H(5,𝔽₂)	Dic₄₇	semidirect
69. #100	Dic₄₇	semidirect

H ≅ G/N

type

1. #15688916

C₂

semidirect

2. #15688867

C₂

semidirect

6. H(5,𝔽₂)×C₄₇

C₄

semidirect

10. #100×C₄₇

C₄

semidirect

63. C₄₇

#1402

semidirect

64. H(5,𝔽₂)

Dic₄₇

semidirect

69. #100

Dic₄₇

semidirect

Subgroups — #20241533

Conjugacy classes of subgroups

Complements