Group #21462209 — subgroups

Subgroups — #21462209

Order 7808.

144 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 66 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	#16840820	C₂	1	2	yes	maximal, complemented
2	#16840684	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840660	C₂	1	2	yes	maximal, complemented
4	#16840651	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839879	C₂	1	1	yes	maximal, characteristic
6	#14519851	—	2	2	no	—
7	#14519851	C₂²	1	2	yes	—
8	C₂×#11758187	—	2	2	no	—
9	C₂×#11758187	C₂²	1	1	yes	characteristic
10	C₂×#11758187	C₂²	1	1	yes	characteristic
11	#14519784	C₂²	1	2	yes	—
12	#14519713	C₄	1	1	yes	characteristic
13	#14519704	C₄	1	2	yes	—
14	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
15	#135×C₆₁	C₄	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	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
22	#11758194	—	2	2	no	—
23	#11758194	C₂×C₄	1	2	yes	—
24	C₂×#92418	—	2	2	no	—
25	C₂×#92418	C₂³	1	1	yes	characteristic
26	#11758187	—	2	2	no	—
27	#11758187	—	2	1	no	—
28	#11758187	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	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	—	2	1	no	—
35	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
36	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
37	#92418	—	2	2	no	—
38	#92418	C₂×D₄	1	1	yes	characteristic
39	#92418	#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	C₄×D₄	1	1	yes	characteristic
44	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
45	Dic₆₁	—	4	1	no	—
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	—	61	1	no	—
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	#6923	1	1	yes	characteristic
57	#131	—	61	2	no	—
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	—	61	1	no	—
64	#104	—	61	2	no	—
65	C₄×C₈	—	61	1	no	—
66	#41	C₂×#6923	1	2	yes	—
67	Q₁₆	#92420	1	1	yes	characteristic
68	SD₁₆	#92420	1	2	yes	—
69	D₈	#92420	1	1	yes	characteristic
70	M₁₆	—	61	2	no	—
71	M₁₆	—	122	2	no	—
72	C₂×C₈	—	61	1	no	—
73	C₂×C₈	—	122	2	no	—
74	C₂×C₈	C₂×#6923	1	1	yes	characteristic
75	C₄²	—	61	1	no	—
76	C₁₆	—	61	2	no	—
77	C₁₆	—	122	1	no	—
78	C₁₆	—	122	2	no	—
79	Q₈	C₂×#92420	1	2	yes	—
80	D₄	—	2	2	no	—
81	D₄	C₂×#92420	1	2	yes	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
85	C₈	—	61	1	no	—
86	C₈	—	61	1	no	—
87	C₈	—	122	2	no	—
88	C₈	C₂×#92420	1	1	yes	characteristic
89	C₈	C₂×#92420	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#14519864	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	244	1	no	—
94	C₄	D₄×#6923	1	1	yes	characteristic
95	C₄	C₂²×#92420	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	4	2	no	—
98	C₂	D₄×#92420	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840820

C₂

yes

maximal, complemented

#16840684

C₂

yes

maximal, characteristic, complemented

#16840660

C₂

yes

maximal, complemented

#16840651

C₂

yes

maximal, characteristic, complemented

#16839879

C₂

yes

maximal, characteristic

#14519851

—

#14519851

C₂²

yes

—

C₂×#11758187

—

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

characteristic

#14519784

C₂²

yes

—

#14519713

C₄

yes

characteristic

#14519704

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

characteristic

#135×C₆₁

C₄

yes

characteristic

#41×C₆₁

C₂×C₄

yes

—

Q₁₆×C₆₁

C₈

yes

characteristic

SD₁₆×C₆₁

C₈

yes

—

D₈×C₆₁

C₈

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

#11758194

—

#11758194

C₂×C₄

yes

—

C₂×#92418

—

C₂×#92418

C₂³

yes

—

—

D₄

yes

—

Q₈×C₆₁

C₂×C₈

yes

—

D₄×C₆₁

—

D₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₈×C₆₁

C₂×C₈

yes

characteristic

C₈×C₆₁

C₂×C₈

yes

characteristic

#92418

—

#92418

C₂×D₄

yes

yes

C₂²×C₆₁

—

C₂²×C₆₁

#131

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

#2171

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₈×D₄

yes

—

—

—

—

—

C₆₁

#2171

yes

characteristic, complemented, Sylow

yes

—

M₃₂

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

#108

—

#104

—

C₄×C₈

—

#41

C₂×#6923

yes

—

Q₁₆

#92420

yes

characteristic

SD₁₆

#92420

yes

—

D₈

#92420

yes

characteristic

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

—

122

—

C₁₆

—

122

—

Q₈

C₂×#92420

yes

—

D₄

—

D₄

C₂×#92420

yes

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₈

yes

C₈

yes

C₂²

—

C₂²

#14519864

yes

characteristic

C₄

—

C₄

—

244

—

C₄

D₄×#6923

yes

characteristic

C₄

C₂²×#92420

yes

characteristic

C₂

—

C₂

—

C₂

D₄×#92420

yes

characteristic

	subgroup	G/H
center	C₄	D₄×#6923
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	#135×C₆₁	C₄
socle	C₂×C₆₁	C₈×D₄
hypercenter	#135	#6923
hypocenter	C₆₁	#2171
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

subgroup

G/H

center

C₄

D₄×#6923

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₄

C₂²×#6923

Fitting

#135×C₆₁

C₄

socle

C₂×C₆₁

C₈×D₄

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

N	H ≅ G/N	type
1. #16840820	C₂	semidirect
2. #16840684	C₂	semidirect
3. #16840660	C₂	semidirect
4. #16840651	C₂	semidirect
55. C₆₁	#2171	semidirect

H ≅ G/N

type

1. #16840820

C₂

semidirect

2. #16840684

C₂

semidirect

3. #16840660

C₂

semidirect

4. #16840651

C₂

semidirect

55. C₆₁

#2171

semidirect

Subgroups — #21462209

Conjugacy classes of subgroups

Complements