Group #20245230 — subgroups

Subgroups — #20245230

Order 6016.

144 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 79 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	#15689540	C₂	1	2	yes	maximal, complemented
2	#15688944	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688907	C₂	1	2	yes	maximal, complemented
4	#15688899	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#443	C₂	1	1	yes	maximal, characteristic
6	#13093964	—	2	2	no	—
7	#13093964	C₂²	1	2	yes	—
8	C₂×C₄₇⋊C₁₆	—	2	2	no	—
9	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	#135×C₄₇	C₄	1	1	yes	characteristic
12	#131×C₄₇	C₂²	1	2	yes	—
13	#108×C₄₇	C₄	1	1	yes	characteristic
14	#104×C₄₇	C₄	1	2	yes	—
15	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	#41×C₄₇	C₂×C₄	1	2	yes	—
17	Q₁₆×C₄₇	C₈	1	1	yes	characteristic
18	SD₁₆×C₄₇	C₈	1	2	yes	—
19	D₈×C₄₇	C₈	1	1	yes	characteristic
20	M₁₆×C₄₇	—	2	2	no	—
21	M₁₆×C₄₇	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₄₇	—	2	2	no	—
23	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
25	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₄₇⋊C₁₆	—	2	2	no	—
27	C₄₇⋊C₁₆	—	2	1	no	—
28	C₄₇⋊C₁₆	D₄	1	2	yes	—
29	Q₈×C₄₇	C₂×C₈	1	2	yes	—
30	D₄×C₄₇	—	2	2	no	—
31	D₄×C₄₇	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₄₇	—	2	2	no	—
33	C₂×C₄×C₄₇	—	2	1	no	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₄₇	—	2	2	no	—
36	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
37	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
38	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₈×C₄₇	#41	1	1	yes	characteristic
40	C₂²×C₄₇	—	2	2	no	—
41	C₂²×C₄₇	#131	1	1	yes	characteristic
42	C₄×C₄₇	—	2	2	no	—
43	C₄×C₄₇	—	4	1	no	—
44	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
45	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
46	#2171	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	—	2	1	no	—
48	C₂×C₄₇	—	4	2	no	—
49	C₂×C₄₇	C₈×D₄	1	1	yes	characteristic
50	#504	—	47	2	no	—
51	#443	D₄₇	1	1	yes	characteristic
52	#364	—	47	1	no	—
53	#350	—	47	2	no	—
54	#346	—	47	1	no	—
55	C₄₇	#2171	1	1	yes	characteristic, complemented, Sylow
56	#135	Dic₄₇	1	1	yes	characteristic
57	#131	C₂×D₄₇	1	2	yes	—
58	M₃₂	—	47	2	no	—
59	M₃₂	—	94	2	no	—
60	C₂×C₁₆	—	47	1	no	—
61	C₂×C₁₆	—	47	1	no	—
62	C₂×C₁₆	—	94	2	no	—
63	#108	Dic₄₇	1	1	yes	characteristic
64	#104	Dic₄₇	1	2	yes	—
65	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
66	#41	C₂×Dic₄₇	1	2	yes	—
67	Q₁₆	C₄₇⋊C₈	1	1	yes	characteristic
68	SD₁₆	C₄₇⋊C₈	1	2	yes	—
69	D₈	C₄₇⋊C₈	1	1	yes	characteristic
70	M₁₆	—	2	2	no	—
71	M₁₆	C₂×Dic₄₇	1	2	yes	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
75	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
76	C₁₆	—	47	2	no	—
77	C₁₆	—	94	2	no	—
78	C₁₆	—	94	1	no	—
79	Q₈	C₂×C₄₇⋊C₈	1	2	yes	—
80	D₄	—	2	2	no	—
81	D₄	C₂×C₄₇⋊C₈	1	2	yes	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	C₂×C₄₇⋊C₈	1	1	yes	characteristic
87	C₈	C₂×C₄₇⋊C₈	1	1	yes	characteristic
88	C₈	D₄×D₄₇	1	1	yes	characteristic
89	C₈	#10625352	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#13094031	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	4	1	no	—
94	C₄	D₄×Dic₄₇	1	1	yes	characteristic
95	C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	4	2	no	—
98	C₂	D₄×C₄₇⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689540

C₂

yes

maximal, complemented

#15688944

C₂

yes

maximal, characteristic, complemented

#15688907

C₂

yes

maximal, complemented

#15688899

C₂

yes

maximal, characteristic, complemented

C₄₇×#443

C₂

yes

maximal, characteristic

#13093964

—

#13093964

C₂²

yes

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#135×C₄₇

C₄

yes

characteristic

#131×C₄₇

C₂²

yes

—

#108×C₄₇

C₄

yes

characteristic

#104×C₄₇

C₄

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

#41×C₄₇

C₂×C₄

yes

—

Q₁₆×C₄₇

C₈

yes

characteristic

SD₁₆×C₄₇

C₈

yes

—

D₈×C₄₇

C₈

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

D₄

yes

—

Q₈×C₄₇

C₂×C₈

yes

—

D₄×C₄₇

—

D₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

C₂×C₈

yes

characteristic

C₈×C₄₇

C₂×C₈

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

#131

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

C₂²×C₈

yes

characteristic

#2171

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

C₈×D₄

yes

characteristic

#504

—

#443

D₄₇

yes

—

—

—

C₄₇

#2171

yes

characteristic, complemented, Sylow

#135

Dic₄₇

yes

characteristic

#131

C₂×D₄₇

yes

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

Dic₄₇

yes

characteristic

#104

Dic₄₇

yes

—

C₄×C₈

C₂×D₄₇

yes

characteristic

#41

C₂×Dic₄₇

yes

—

Q₁₆

C₄₇⋊C₈

yes

characteristic

SD₁₆

C₄₇⋊C₈

yes

—

D₈

C₄₇⋊C₈

yes

characteristic

M₁₆

—

M₁₆

C₂×Dic₄₇

yes

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

C₂×Dic₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

C₂×C₄₇⋊C₈

yes

—

D₄

—

D₄

C₂×C₄₇⋊C₈

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₈

C₂×C₄₇⋊C₈

yes

characteristic

C₈

C₂×C₄₇⋊C₈

yes

characteristic

C₈

D₄×D₄₇

yes

characteristic

C₈

#10625352

yes

characteristic

C₂²

—

C₂²

#13094031

yes

characteristic

C₄

—

C₄

—

C₄

D₄×Dic₄₇

yes

characteristic

C₄

C₂²×C₄₇⋊C₈

yes

characteristic

C₂

—

C₂

—

C₂

D₄×C₄₇⋊C₈

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#443	C₂
socle	C₂×C₄₇	C₈×D₄
hypercenter	#443	D₄₇
hypocenter	C₄₇	#2171
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #443

subgroup

G/H

center

C₈

D₄×D₄₇

commutator

C₄×C₄₇

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#443

C₂

socle

C₂×C₄₇

C₈×D₄

D₄₇

C₄₇

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #443

N	H ≅ G/N	type
1. #15689540	C₂	semidirect
2. #15688944	C₂	semidirect
3. #15688907	C₂	semidirect
4. #15688899	C₂	semidirect
55. C₄₇	#2171	semidirect

H ≅ G/N

type

1. #15689540

C₂

semidirect

2. #15688944

C₂

semidirect

3. #15688907

C₂

semidirect

4. #15688899

C₂

semidirect

55. C₄₇

#2171

semidirect

Subgroups — #20245230

Conjugacy classes of subgroups

Complements