Group #20245558 — subgroups

Subgroups — #20245558

Order 6016.

126 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 43 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	#15689239	C₂	1	1	yes	maximal, characteristic
3	#15688947	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688943	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688934	C₂	1	1	yes	maximal, characteristic
6	#15688932	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#365	C₂	1	1	yes	maximal, characteristic, complemented
8	#13094046	C₂²	1	1	yes	characteristic
9	#13094032	—	2	1	no	—
10	#13094023	—	2	1	no	—
11	#13093964	C₂²	1	1	yes	characteristic
12	#13093956	C₂²	1	1	yes	characteristic
13	#13093955	—	2	1	no	—
14	#13093950	—	2	1	no	—
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	M₃₂×C₄₇	C₂²	1	1	yes	characteristic
17	#108×C₄₇	C₂²	1	1	yes	characteristic
18	#106×C₄₇	C₂²	1	1	yes	characteristic
19	#10625350	—	2	1	no	—
20	C₂×Dic₉₄	—	4	1	no	—
21	M₁₆×C₄₇	—	2	1	no	—
22	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₄₇	—	2	1	no	—
24	C₄⋊Dic₄₇	—	2	1	no	—
25	Dic₄₇⋊C₄	—	4	1	no	—
26	C₄×Dic₄₇	D₄	1	1	yes	characteristic
27	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
28	Dic₁₈₈	Q₈	1	1	yes	characteristic, complemented
29	D₃₇₆	Q₈	1	1	yes	characteristic, complemented
30	#10625325	—	2	1	no	—
31	#10625324	—	4	1	no	—
32	C₈×D₄₇	—	4	1	no	—
33	C₁₆×C₄₇	—	2	1	no	—
34	C₄₇⋊C₁₆	—	2	1	no	—
35	C₂×C₄×C₄₇	—	4	1	no	—
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂²⋊D₄₇	—	4	1	no	—
38	C₂×Dic₄₇	—	2	1	no	—
39	C₂×Dic₄₇	—	4	1	no	—
40	D₁₈₈	—	2	1	no	—
41	C₄×D₄₇	—	4	1	no	—
42	Dic₉₄	—	2	1	no	—
43	Dic₉₄	—	8	2	no	—
44	C₈×C₄₇	—	4	1	no	—
45	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
46	C₈×C₄₇	#41	1	1	yes	characteristic
47	C₄₇⋊C₈	SD₁₆	1	1	yes	characteristic
48	C₄₇⋊C₈	SD₁₆	1	1	yes	characteristic
49	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
50	C₂×D₄₇	—	4	1	no	—
51	C₄×C₄₇	—	8	1	no	—
52	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
53	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
54	Dic₄₇	—	2	2	no	—
55	Dic₄₇	—	4	1	no	—
56	Dic₄₇	—	8	1	no	—
57	#2230	—	47	1	no	maximal, Sylow
58	C₂×C₄₇	—	2	1	no	—
59	C₂×C₄₇	#476	1	1	yes	characteristic
60	D₄₇	—	8	1	no	—
61	#498	—	47	1	no	—
62	#443	—	47	1	no	—
63	#365	—	47	1	no	—
64	#365	D₄₇	1	1	yes	characteristic, complemented
65	#364	—	47	1	no	—
66	#360	—	47	1	no	—
67	#360	—	47	1	no	—
68	C₄₇	#2230	1	1	yes	characteristic, complemented, Sylow
69	#135	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
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	—	94	1	no	—
81	C₂×Q₈	—	188	1	no	—
82	Q₁₆	—	47	1	no	—
83	SD₁₆	—	94	1	no	—
84	D₈	—	47	1	no	—
85	M₁₆	—	2	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	—	94	1	no	—
97	Q₈	—	376	2	no	—
98	D₄	—	94	1	no	—
99	D₄	—	188	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	94	1	no	—
102	C₂×C₄	—	188	1	no	—
103	C₂×C₄	—	188	1	no	—
104	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
105	C₈	—	4	1	no	—
106	C₈	—	47	1	no	—
107	C₈	—	47	1	no	—
108	C₈	#10625350	1	1	yes	characteristic
109	C₈	Q₈×D₄₇	1	1	yes	characteristic
110	C₂²	—	188	1	no	—
111	C₂²	#13094051	1	1	yes	characteristic
112	C₄	—	8	1	no	—
113	C₄	—	94	2	no	—
114	C₄	—	376	1	no	—
115	C₄	—	188	1	no	—
116	C₄	#13094002	1	1	yes	characteristic
117	C₄	SD₁₆×D₄₇	1	1	yes	characteristic
118	C₂	—	2	1	no	—
119	C₂	—	376	1	no	—
120	C₂	#15689412	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689520

C₂

yes

maximal, characteristic, complemented

#15689239

C₂

yes

maximal, characteristic

#15688947

C₂

yes

maximal, characteristic, complemented

#15688943

C₂

yes

maximal, characteristic, complemented

#15688934

C₂

yes

maximal, characteristic

#15688932

C₂

yes

maximal, characteristic

C₄₇×#365

C₂

yes

maximal, characteristic, complemented

#13094046

C₂²

yes

—

—

C₂²

yes

characteristic

#13093956

C₂²

yes

characteristic

#13093955

—

#13093950

—

C₈×Dic₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₂²

yes

characteristic

#108×C₄₇

C₂²

yes

characteristic

#106×C₄₇

C₂²

yes

characteristic

#10625350

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

Q₈

yes

characteristic, complemented

D₃₇₆

Q₈

yes

characteristic, complemented

#10625325

—

#10625324

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

SD₁₆

yes

characteristic

C₄₇⋊C₈

SD₁₆

yes

characteristic

C₂²×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2230

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#476

yes

characteristic

D₄₇

—

—

—

—

D₄₇

yes

characteristic, complemented

#364

—

#360

—

#360

—

C₄₇

#2230

yes

characteristic, complemented, Sylow

#135

—

#131

—

C₄⋊Q₈

—

M₃₂

—

M₃₂

C₂×D₄₇

yes

characteristic

#108

C₂×D₄₇

yes

—

—

C₂×D₄₇

yes

characteristic

#104

—

C₄×C₈

—

#41

—

C₂×Q₈

—

188

—

Q₁₆

—

SD₁₆

—

D₈

—

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

—

188

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

188

—

103

C₂×C₄

—

188

—

104

C₂×C₄

D₄×D₄₇

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#10625350

yes

characteristic

109

C₈

Q₈×D₄₇

yes

characteristic

110

C₂²

—

188

—

111

C₂²

#13094051

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

376

—

115

C₄

—

188

—

116

C₄

#13094002

yes

characteristic

117

C₄

SD₁₆×D₄₇

yes

characteristic

118

C₂

—

119

C₂

—

376

—

120

C₂

#15689412

yes

characteristic

	subgroup	G/H
center	C₂	#15689412
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#365	C₂
socle	C₂×C₄₇	#476
hypercenter	#365	D₄₇
hypocenter	C₄₇	#2230
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

subgroup

G/H

center

C₂

#15689412

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#365

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

N	H ≅ G/N	type
1. #15689520	C₂	semidirect
3. #15688947	C₂	semidirect
4. #15688943	C₂	semidirect
7. C₄₇×#365	C₂	semidirect
28. Dic₁₈₈	Q₈	semidirect
29. D₃₇₆	Q₈	semidirect
64. #365	D₄₇	semidirect
68. C₄₇	#2230	semidirect

H ≅ G/N

type

1. #15689520

C₂

semidirect

3. #15688947

C₂

semidirect

4. #15688943

C₂

semidirect

7. C₄₇×#365

C₂

semidirect

28. Dic₁₈₈

Q₈

semidirect

29. D₃₇₆

Q₈

semidirect

64. #365

D₄₇

semidirect

68. C₄₇

#2230

semidirect

Subgroups — #20245558

Conjugacy classes of subgroups

Complements