Group #21447661 — subgroups

Subgroups — #21447661

Order 7808.

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	#16840179	C₂	1	2	yes	maximal, complemented
2	#16839583	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839546	C₂	1	2	yes	maximal, complemented
4	#16839538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#443	C₂	1	1	yes	maximal, characteristic
6	#14519717	—	2	2	no	—
7	#14519717	C₂²	1	2	yes	—
8	C₂×#11758185	—	2	2	no	—
9	C₂×#11758185	C₂²	1	1	yes	characteristic
10	C₂×#11758185	C₂²	1	1	yes	characteristic
11	#135×C₆₁	C₄	1	1	yes	characteristic
12	#131×C₆₁	C₂²	1	2	yes	—
13	#108×C₆₁	C₄	1	1	yes	characteristic
14	#104×C₆₁	C₄	1	2	yes	—
15	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	#41×C₆₁	C₂×C₄	1	2	yes	—
17	Q₁₆×C₆₁	C₈	1	1	yes	characteristic
18	SD₁₆×C₆₁	C₈	1	2	yes	—
19	D₈×C₆₁	C₈	1	1	yes	characteristic
20	M₁₆×C₆₁	—	2	2	no	—
21	M₁₆×C₆₁	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₆₁	—	2	2	no	—
23	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
25	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
26	#11758185	—	2	2	no	—
27	#11758185	—	2	1	no	—
28	#11758185	D₄	1	2	yes	—
29	Q₈×C₆₁	C₂×C₈	1	2	yes	—
30	D₄×C₆₁	—	2	2	no	—
31	D₄×C₆₁	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₆₁	—	2	2	no	—
33	C₂×C₄×C₆₁	—	2	1	no	—
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₆₁	—	2	2	no	—
36	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
37	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
38	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₈×C₆₁	#41	1	1	yes	characteristic
40	C₂²×C₆₁	—	2	2	no	—
41	C₂²×C₆₁	#131	1	1	yes	characteristic
42	C₄×C₆₁	—	2	2	no	—
43	C₄×C₆₁	—	4	1	no	—
44	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
45	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
46	#2171	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	—	2	1	no	—
48	C₂×C₆₁	—	4	2	no	—
49	C₂×C₆₁	C₈×D₄	1	1	yes	characteristic
50	#504	—	61	2	no	—
51	#443	D₆₁	1	1	yes	characteristic
52	#364	—	61	1	no	—
53	#350	—	61	2	no	—
54	#346	—	61	1	no	—
55	C₆₁	#2171	1	1	yes	characteristic, complemented, Sylow
56	#135	Dic₆₁	1	1	yes	characteristic
57	#131	C₂×D₆₁	1	2	yes	—
58	M₃₂	—	61	2	no	—
59	M₃₂	—	122	2	no	—
60	C₂×C₁₆	—	61	1	no	—
61	C₂×C₁₆	—	61	1	no	—
62	C₂×C₁₆	—	122	2	no	—
63	#108	Dic₆₁	1	1	yes	characteristic
64	#104	Dic₆₁	1	2	yes	—
65	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
66	#41	C₂×Dic₆₁	1	2	yes	—
67	Q₁₆	#92418	1	1	yes	characteristic
68	SD₁₆	#92418	1	2	yes	—
69	D₈	#92418	1	1	yes	characteristic
70	M₁₆	—	2	2	no	—
71	M₁₆	C₂×Dic₆₁	1	2	yes	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
75	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
76	C₁₆	—	61	2	no	—
77	C₁₆	—	122	2	no	—
78	C₁₆	—	122	1	no	—
79	Q₈	C₂×#92418	1	2	yes	—
80	D₄	—	2	2	no	—
81	D₄	C₂×#92418	1	2	yes	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	C₂×#92418	1	1	yes	characteristic
87	C₈	C₂×#92418	1	1	yes	characteristic
88	C₈	D₄×D₆₁	1	1	yes	characteristic
89	C₈	#11758224	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#14519784	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	4	1	no	—
94	C₄	D₄×Dic₆₁	1	1	yes	characteristic
95	C₄	C₂²×#92418	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	4	2	no	—
98	C₂	D₄×#92418	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840179

C₂

yes

maximal, complemented

#16839583

C₂

yes

maximal, characteristic, complemented

#16839546

C₂

yes

maximal, complemented

#16839538

C₂

yes

maximal, characteristic, complemented

C₆₁×#443

C₂

yes

maximal, characteristic

#14519717

—

#14519717

C₂²

yes

—

C₂×#11758185

—

C₂×#11758185

C₂²

yes

characteristic

C₂×#11758185

C₂²

yes

characteristic

#135×C₆₁

C₄

yes

characteristic

#131×C₆₁

C₂²

yes

—

#108×C₆₁

C₄

yes

characteristic

#104×C₆₁

C₄

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

#41×C₆₁

C₂×C₄

yes

—

Q₁₆×C₆₁

C₈

yes

characteristic

SD₁₆×C₆₁

C₈

yes

—

D₈×C₆₁

C₈

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

—

—

D₄

yes

—

Q₈×C₆₁

C₂×C₈

yes

—

D₄×C₆₁

—

D₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

C₂×C₈

yes

characteristic

C₈×C₆₁

C₂×C₈

yes

characteristic

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

#41

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

#131

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

#2171

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₈×D₄

yes

characteristic

#504

—

#443

D₆₁

yes

—

—

—

C₆₁

#2171

yes

characteristic, complemented, Sylow

#135

Dic₆₁

yes

characteristic

#131

C₂×D₆₁

yes

—

M₃₂

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

#108

Dic₆₁

yes

characteristic

#104

Dic₆₁

yes

—

C₄×C₈

C₂×D₆₁

yes

characteristic

#41

C₂×Dic₆₁

yes

—

Q₁₆

#92418

yes

characteristic

SD₁₆

#92418

yes

—

D₈

#92418

yes

characteristic

M₁₆

—

M₁₆

C₂×Dic₆₁

yes

—

C₂×C₈

—

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

C₂×Dic₆₁

yes

characteristic

C₁₆

—

C₁₆

—

122

—

C₁₆

—

122

—

Q₈

C₂×#92418

yes

—

D₄

—

D₄

C₂×#92418

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₈

—

C₈

yes

C₈

yes

C₈

D₄×D₆₁

yes

characteristic

C₈

#11758224

yes

characteristic

C₂²

—

C₂²

#14519784

yes

characteristic

C₄

—

C₄

—

C₄

D₄×Dic₆₁

yes

characteristic

C₄

C₂²×#92418

yes

characteristic

C₂

—

C₂

—

C₂

D₄×#92418

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₆₁
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#443	C₂
socle	C₂×C₆₁	C₈×D₄
hypercenter	#443	D₆₁
hypocenter	C₆₁	#2171
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #443

subgroup

G/H

center

C₈

D₄×D₆₁

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#443

C₂

socle

C₂×C₆₁

C₈×D₄

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #443

N	H ≅ G/N	type
1. #16840179	C₂	semidirect
2. #16839583	C₂	semidirect
3. #16839546	C₂	semidirect
4. #16839538	C₂	semidirect
55. C₆₁	#2171	semidirect

H ≅ G/N

type

1. #16840179

C₂

semidirect

2. #16839583

C₂

semidirect

3. #16839546

C₂

semidirect

4. #16839538

C₂

semidirect

55. C₆₁

#2171

semidirect

Subgroups — #21447661

Conjugacy classes of subgroups

Complements