Group #20245509 — subgroups

Subgroups — #20245509

Order 6016.

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

normal subgroups only

This group has 148 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	C₂×D₇₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689539	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689394	C₂	1	2	yes	maximal, complemented
4	#15688935	C₂	1	2	yes	maximal, complemented
5	C₄₇×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094052	—	2	2	no	—
7	C₂×D₃₇₆	C₂²	1	2	yes	—
8	#13094030	C₂²	1	1	yes	characteristic
9	D₇₅₂	—	2	1	no	—
10	D₇₅₂	—	2	1	no	—
11	#13093964	C₂²	1	1	yes	characteristic
12	#13093963	—	2	1	no	—
13	C₁₆×D₄₇	—	2	1	no	—
14	#13093940	—	2	2	no	—
15	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
16	#108×C₄₇	C₂²	1	2	yes	—
17	#10625350	D₄	1	1	yes	characteristic
18	C₂×D₁₈₈	—	2	2	no	—
19	M₁₆×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
21	#10625329	D₄	1	1	yes	characteristic
22	D₃₇₆	—	2	2	no	—
23	D₃₇₆	—	2	2	no	—
24	D₃₇₆	—	4	2	no	—
25	#10625325	—	4	2	no	—
26	#10625324	—	2	1	no	—
27	C₈×D₄₇	—	2	1	no	—
28	C₁₆×C₄₇	D₄	1	1	yes	characteristic
29	C₁₆×C₄₇	D₄	1	1	yes	characteristic
30	C₄₇⋊C₁₆	—	2	1	no	—
31	C₂²×D₄₇	—	4	2	no	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂²⋊D₄₇	—	2	1	no	—
34	D₁₈₈	—	4	2	no	—
35	D₁₈₈	—	4	2	no	—
36	D₁₈₈	D₈	1	1	yes	characteristic
37	C₄×D₄₇	—	2	1	no	—
38	Dic₉₄	D₈	1	1	yes	characteristic
39	C₈×C₄₇	—	4	2	no	—
40	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
41	C₈×C₄₇	#41	1	1	yes	characteristic
42	C₄₇⋊C₈	—	2	1	no	—
43	C₂²×C₄₇	#135	1	1	yes	characteristic
44	C₂×D₄₇	—	2	1	no	—
45	C₂×D₄₇	—	8	2	no	—
46	C₂×D₄₇	—	16	2	no	—
47	C₄×C₄₇	#121	1	1	yes	characteristic
48	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
49	Dic₄₇	—	2	1	no	—
50	#2221	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	—	2	1	no	—
52	C₂×C₄₇	#466	1	1	yes	characteristic
53	D₄₇	—	4	1	no	—
54	D₄₇	—	16	2	no	—
55	C₂×D₁₆	—	47	1	no	—
56	#504	—	47	1	no	—
57	#472	—	47	2	no	—
58	#368	D₄₇	1	1	yes	characteristic, complemented
59	#361	—	47	2	no	—
60	C₄₇	#2221	1	1	yes	characteristic, complemented, Sylow
61	AGL(1,ℤ/8)	—	94	2	no	—
62	C₂×D₈	—	47	2	no	—
63	#131	—	47	1	no	—
64	D₁₆	—	94	1	no	—
65	D₁₆	—	94	1	no	—
66	M₃₂	—	47	1	no	—
67	M₃₂	—	94	1	no	—
68	C₂×C₁₆	—	94	1	no	—
69	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
70	#108	C₂×D₄₇	1	2	yes	—
71	#100	—	94	2	no	—
72	#41	—	47	1	no	—
73	C₂×D₄	—	94	2	no	—
74	SD₁₆	—	188	2	no	—
75	D₈	—	94	2	no	—
76	D₈	—	94	2	no	—
77	D₈	—	188	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	47	1	no	—
80	M₁₆	—	94	1	no	—
81	C₂×C₈	—	94	1	no	—
82	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
83	C₁₆	—	94	1	no	—
84	C₁₆	D₁₈₈	1	1	yes	characteristic
85	C₁₆	D₁₈₈	1	1	yes	characteristic
86	C₂³	—	188	2	no	—
87	Q₈	—	47	1	no	—
88	D₄	—	47	1	no	—
89	D₄	—	94	1	no	—
90	D₄	—	188	2	no	—
91	D₄	—	188	2	no	—
92	C₂×C₄	—	94	1	no	—
93	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
94	C₈	—	4	2	no	—
95	C₈	—	94	1	no	—
96	C₈	C₂×D₁₈₈	1	1	yes	characteristic
97	C₈	#10625354	1	1	yes	characteristic
98	C₂²	—	94	1	no	—
99	C₂²	—	376	2	no	—
100	C₂²	—	752	2	no	—
101	C₂²	#13094047	1	1	yes	characteristic
102	C₄	—	94	1	no	—
103	C₄	#13093999	1	1	yes	characteristic
104	C₄	D₈×D₄₇	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	188	1	no	—
107	C₂	—	752	2	no	—
108	C₂	#15689360	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₇₅₂

C₂

yes

maximal, characteristic, complemented

#15689539

C₂

yes

maximal, characteristic, complemented

#15689394

C₂

yes

maximal, complemented

#15688935

C₂

yes

maximal, complemented

C₄₇×#368

C₂

yes

maximal, characteristic, complemented

#13094052

—

C₂×D₃₇₆

C₂²

yes

—

#13094030

C₂²

yes

characteristic

D₇₅₂

—

D₇₅₂

—

#13093964

C₂²

yes

characteristic

#13093963

—

C₁₆×D₄₇

—

#13093940

—

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#108×C₄₇

C₂²

yes

—

#10625350

D₄

yes

characteristic

C₂×D₁₈₈

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

#10625329

D₄

yes

characteristic

D₃₇₆

—

D₃₇₆

—

D₃₇₆

—

#10625325

—

#10625324

—

C₈×D₄₇

—

C₁₆×C₄₇

D₄

yes

characteristic

C₁₆×C₄₇

D₄

yes

characteristic

C₄₇⋊C₁₆

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

D₈

yes

characteristic

C₄×D₄₇

—

Dic₉₄

D₈

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

#135

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

#121

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

#2221

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#466

yes

characteristic

D₄₇

—

D₄₇

—

C₂×D₁₆

—

#504

—

#472

—

#368

D₄₇

yes

characteristic, complemented

#361

—

C₄₇

#2221

yes

characteristic, complemented, Sylow

AGL(1,ℤ/8)

—

C₂×D₈

—

#131

—

D₁₆

—

D₁₆

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#108

C₂×D₄₇

yes

—

#100

—

#41

—

C₂×D₄

—

SD₁₆

—

188

—

D₈

—

D₈

—

D₈

—

188

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₁₆

—

C₁₆

D₁₈₈

yes

characteristic

C₁₆

D₁₈₈

yes

characteristic

C₂³

—

188

—

Q₈

—

D₄

—

D₄

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₈

—

C₈

—

C₈

C₂×D₁₈₈

yes

characteristic

C₈

#10625354

yes

characteristic

C₂²

—

C₂²

—

376

—

100

C₂²

—

752

—

101

C₂²

#13094047

yes

characteristic

102

C₄

—

103

C₄

#13093999

yes

characteristic

104

C₄

D₈×D₄₇

yes

characteristic

105

C₂

—

106

C₂

—

188

—

107

C₂

—

752

—

108

C₂

#15689360

yes

characteristic

	subgroup	G/H
center	C₂	#15689360
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#368	C₂
socle	C₂×C₄₇	#466
hypercenter	#368	D₄₇
hypocenter	C₄₇	#2221
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

subgroup

G/H

center

C₂

#15689360

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#368

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

N	H ≅ G/N	type
1. C₂×D₇₅₂	C₂	semidirect
2. #15689539	C₂	semidirect
3. #15689394	C₂	semidirect
4. #15688935	C₂	semidirect
5. C₄₇×#368	C₂	semidirect
58. #368	D₄₇	semidirect
60. C₄₇	#2221	semidirect

H ≅ G/N

type

1. C₂×D₇₅₂

C₂

semidirect

2. #15689539

C₂

semidirect

3. #15689394

C₂

semidirect

4. #15688935

C₂

semidirect

5. C₄₇×#368

C₂

semidirect

58. #368

D₄₇

semidirect

60. C₄₇

#2221

semidirect

Subgroups — #20245509

Conjugacy classes of subgroups

Complements