Group #20245557 — subgroups

Subgroups — #20245557

Order 6016.

126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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	#15689520	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689240	C₂	1	1	yes	maximal, characteristic
3	#15688946	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688945	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688943	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688933	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#360	C₂	1	1	yes	maximal, characteristic
8	#13094031	—	2	1	no	—
9	#13094023	—	2	1	no	—
10	#13093964	C₂²	1	1	yes	characteristic
11	#13093960	C₂²	1	1	yes	characteristic
12	#13093956	C₂²	1	1	yes	characteristic
13	#13093955	—	2	1	no	—
14	#13093951	—	2	1	no	—
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	#135×C₄₇	C₂²	1	1	yes	characteristic
17	M₃₂×C₄₇	C₂²	1	1	yes	characteristic
18	#106×C₄₇	C₂²	1	1	yes	characteristic
19	#41×C₄₇	—	2	1	no	—
20	C₂×Dic₉₄	—	4	1	no	—
21	Q₁₆×C₄₇	Q₈	1	1	yes	characteristic, complemented
22	SD₁₆×C₄₇	—	2	1	no	—
23	D₈×C₄₇	Q₈	1	1	yes	characteristic, complemented
24	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₄₇	—	2	1	no	—
26	C₄⋊Dic₄₇	—	2	1	no	—
27	Dic₄₇⋊C₄	—	4	1	no	—
28	C₄×Dic₄₇	D₄	1	1	yes	characteristic
29	#10625329	—	2	1	no	—
30	#10625329	—	4	1	no	—
31	C₂×C₄₇⋊C₈	—	4	1	no	—
32	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
33	C₁₆×C₄₇	—	2	1	no	—
34	C₄₇⋊C₁₆	—	2	1	no	—
35	Q₈×C₄₇	—	2	1	no	—
36	D₄×C₄₇	—	2	1	no	—
37	D₄×C₄₇	—	4	1	no	—
38	C₂×C₄×C₄₇	—	4	1	no	—
39	C₂×C₄×C₄₇	—	4	1	no	—
40	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₄₇	—	2	1	no	—
42	C₂×Dic₄₇	—	4	1	no	—
43	Dic₉₄	—	8	2	no	—
44	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₄₇	#41	1	1	yes	characteristic
46	C₄₇⋊C₈	—	4	1	no	—
47	C₄₇⋊C₈	SD₁₆	1	1	yes	characteristic
48	C₄₇⋊C₈	SD₁₆	1	1	yes	characteristic
49	C₂²×C₄₇	—	4	1	no	—
50	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
51	C₄×C₄₇	—	4	1	no	—
52	C₄×C₄₇	—	8	1	no	—
53	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
54	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
55	Dic₄₇	—	2	2	no	—
56	Dic₄₇	—	8	1	no	—
57	#2230	—	47	1	no	maximal, Sylow
58	C₂×C₄₇	—	2	1	no	—
59	C₂×C₄₇	—	8	1	no	—
60	C₂×C₄₇	#476	1	1	yes	characteristic
61	#498	—	47	1	no	—
62	#443	—	47	1	no	—
63	#365	—	47	1	no	—
64	#365	—	47	1	no	—
65	#364	—	47	1	no	—
66	#360	—	47	1	no	—
67	#360	D₄₇	1	1	yes	characteristic
68	C₄₇	#2230	1	1	yes	characteristic, complemented, Sylow
69	#135	C₂×D₄₇	1	1	yes	characteristic
70	#131	—	94	1	no	—
71	C₄⋊Q₈	—	94	1	no	—
72	M₃₂	—	47	1	no	—
73	M₃₂	C₂×D₄₇	1	1	yes	characteristic
74	#108	—	47	1	no	—
75	#106	—	47	1	no	—
76	#106	—	94	1	no	—
77	#106	C₂×D₄₇	1	1	yes	characteristic
78	#104	—	94	1	no	—
79	C₄×C₈	—	47	1	no	—
80	#41	—	2	1	no	—
81	C₂×Q₈	—	188	1	no	—
82	Q₁₆	Dic₉₄	1	1	yes	characteristic, complemented
83	SD₁₆	—	2	1	no	—
84	D₈	Dic₉₄	1	1	yes	characteristic, complemented
85	M₁₆	—	94	1	no	—
86	M₁₆	—	188	1	no	—
87	C₂×C₈	—	47	1	no	—
88	C₂×C₈	—	188	1	no	—
89	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
90	C₄⋊C₄	—	2	1	no	—
91	C₄⋊C₄	—	94	1	no	—
92	C₄⋊C₄	—	188	1	no	—
93	C₄²	—	47	1	no	—
94	C₁₆	—	2	1	no	—
95	C₁₆	—	94	1	no	—
96	Q₈	—	2	1	no	—
97	Q₈	—	376	2	no	—
98	D₄	—	2	1	no	—
99	D₄	—	4	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	94	1	no	—
103	C₂×C₄	—	188	1	no	—
104	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
105	C₈	—	47	1	no	—
106	C₈	—	47	1	no	—
107	C₈	—	188	1	no	—
108	C₈	C₂×Dic₉₄	1	1	yes	characteristic
109	C₈	#10625352	1	1	yes	characteristic
110	C₂²	—	4	1	no	—
111	C₂²	#13094048	1	1	yes	characteristic
112	C₄	—	4	1	no	—
113	C₄	—	8	1	no	—
114	C₄	—	94	2	no	—
115	C₄	—	376	1	no	—
116	C₄	#13094001	1	1	yes	characteristic
117	C₄	SD₁₆×D₄₇	1	1	yes	characteristic
118	C₂	—	2	1	no	—
119	C₂	—	8	1	no	—
120	C₂	#15689411	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689520

C₂

yes

maximal, characteristic, complemented

#15689240

C₂

yes

maximal, characteristic

#15688946

C₂

yes

maximal, characteristic, complemented

#15688945

C₂

yes

maximal, characteristic, complemented

#15688943

C₂

yes

maximal, characteristic, complemented

#15688933

C₂

yes

maximal, characteristic

C₄₇×#360

C₂

yes

maximal, characteristic

#13094031

—

#13094023

—

#13093964

C₂²

yes

characteristic

#13093960

C₂²

yes

characteristic

#13093956

C₂²

yes

characteristic

#13093955

—

#13093951

—

C₈×Dic₄₇

C₂²

yes

characteristic

#135×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₂²

yes

characteristic

#106×C₄₇

C₂²

yes

characteristic

#41×C₄₇

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

Q₈

yes

characteristic, complemented

SD₁₆×C₄₇

—

D₈×C₄₇

Q₈

yes

characteristic, complemented

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₄₇⋊C₈

SD₁₆

yes

characteristic

C₄₇⋊C₈

SD₁₆

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2230

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2230

yes

characteristic, complemented, Sylow

#135

C₂×D₄₇

yes

characteristic

#131

—

C₄⋊Q₈

—

M₃₂

—

M₃₂

C₂×D₄₇

yes

—

—

—

C₂×D₄₇

yes

characteristic

#104

—

C₄×C₈

—

#41

—

C₂×Q₈

—

188

—

Q₁₆

Dic₉₄

yes

characteristic, complemented

SD₁₆

—

D₈

Dic₉₄

yes

characteristic, complemented

M₁₆

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

188

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄²

—

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

376

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

188

—

104

C₂×C₄

D₄×D₄₇

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

188

—

108

C₈

C₂×Dic₉₄

yes

characteristic

109

C₈

#10625352

yes

characteristic

110

C₂²

—

111

C₂²

#13094048

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

376

—

116

C₄

#13094001

yes

characteristic

117

C₄

SD₁₆×D₄₇

yes

characteristic

118

C₂

—

119

C₂

—

120

C₂

#15689411

yes

characteristic

	subgroup	G/H
center	C₂	#15689411
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#360	C₂
socle	C₂×C₄₇	#476
hypercenter	#360	D₄₇
hypocenter	C₄₇	#2230
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

subgroup

G/H

center

C₂

#15689411

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#360

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

N	H ≅ G/N	type
1. #15689520	C₂	semidirect
3. #15688946	C₂	semidirect
4. #15688945	C₂	semidirect
5. #15688943	C₂	semidirect
21. Q₁₆×C₄₇	Q₈	semidirect
23. D₈×C₄₇	Q₈	semidirect
68. C₄₇	#2230	semidirect
82. Q₁₆	Dic₉₄	semidirect
84. D₈	Dic₉₄	semidirect

H ≅ G/N

type

1. #15689520

C₂

semidirect

3. #15688946

C₂

semidirect

4. #15688945

C₂

semidirect

5. #15688943

C₂

semidirect

21. Q₁₆×C₄₇

Q₈

semidirect

23. D₈×C₄₇

Q₈

semidirect

68. C₄₇

#2230

semidirect

82. Q₁₆

Dic₉₄

semidirect

84. D₈

Dic₉₄

semidirect

Subgroups — #20245557

Conjugacy classes of subgroups

Complements