Group #21462211 — subgroups

Subgroups — #21462211

Order 7808.

144 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 58 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	#16840821	C₂	1	2	yes	maximal, complemented
2	#16840684	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840661	C₂	1	2	yes	maximal, complemented
4	#16840651	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839878	C₂	1	1	yes	maximal, characteristic
6	#14519852	—	2	2	no	—
7	#14519851	C₂²	1	2	yes	—
8	D₆₁⋊C₁₆	—	2	2	no	—
9	C₂×#11758187	C₂²	1	1	yes	characteristic
10	C₂×#11758187	C₂²	1	1	yes	characteristic
11	#14519799	C₄	1	1	yes	characteristic
12	#14519785	C₂²	1	2	yes	—
13	#14519703	C₄	1	2	yes	—
14	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
15	#108×C₆₁	C₄	1	1	yes	characteristic
16	#11758222	C₂×C₄	1	2	yes	—
17	M₁₆×C₆₁	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×#92418	C₂³	1	1	yes	characteristic
21	Dic₂₄₄	C₈	1	1	yes	characteristic
22	D₄₈₈	C₈	1	1	yes	characteristic
23	#11758190	C₈	1	2	yes	—
24	#11758189	—	2	2	no	—
25	C₈×D₆₁	—	2	2	no	—
26	#11758187	—	2	2	no	—
27	#11758187	—	2	1	no	—
28	#11758187	D₄	1	2	yes	—
29	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂²⋊D₆₁	—	2	2	no	—
31	C₂×Dic₆₁	—	2	1	no	—
32	D₂₄₄	C₂×C₈	1	2	yes	—
33	C₄×D₆₁	—	2	2	no	—
34	Dic₁₂₂	C₂×C₈	1	2	yes	—
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	#92418	C₂×D₄	1	1	yes	characteristic
39	#92418	#41	1	1	yes	characteristic
40	C₂²×C₆₁	#131	1	1	yes	characteristic
41	C₂×D₆₁	—	2	2	no	—
42	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
43	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
44	Dic₆₁	—	2	2	no	—
45	Dic₆₁	—	4	1	no	—
46	#2171	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	—	2	1	no	—
48	C₂×C₆₁	C₈×D₄	1	1	yes	characteristic
49	D₆₁	—	4	2	no	—
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	—	61	1	no	—
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	#6923	1	1	yes	characteristic
64	#104	—	61	2	no	—
65	C₄×C₈	—	61	1	no	—
66	#41	—	61	2	no	—
67	Q₁₆	—	61	1	no	—
68	SD₁₆	—	61	2	no	—
69	D₈	—	61	1	no	—
70	M₁₆	—	122	2	no	—
71	M₁₆	C₂×#6923	1	2	yes	—
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	—	61	2	no	—
80	D₄	—	61	2	no	—
81	D₄	—	122	2	no	—
82	C₂×C₄	—	122	2	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	—	61	1	no	—
87	C₈	—	61	1	no	—
88	C₈	D₆₁⋊C₈	1	1	yes	characteristic
89	C₈	D₆₁⋊C₈	1	1	yes	characteristic
90	C₂²	—	122	2	no	—
91	C₂²	#14519865	1	1	yes	characteristic
92	C₄	—	122	2	no	—
93	C₄	—	244	1	no	—
94	C₄	D₄×#6923	1	1	yes	characteristic
95	C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	244	2	no	—
98	C₂	#16840790	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840821

C₂

yes

maximal, complemented

#16840684

C₂

yes

maximal, characteristic, complemented

#16840661

C₂

yes

maximal, complemented

#16840651

C₂

yes

maximal, characteristic, complemented

#16839878

C₂

yes

maximal, characteristic

#14519852

—

#14519851

C₂²

yes

—

D₆₁⋊C₁₆

—

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

characteristic

#14519799

C₄

yes

characteristic

#14519785

C₂²

yes

—

#14519703

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

characteristic

#108×C₆₁

C₄

yes

characteristic

#11758222

C₂×C₄

yes

—

M₁₆×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

Dic₂₄₄

C₈

yes

characteristic

D₄₈₈

C₈

yes

characteristic

#11758190

C₈

yes

—

#11758189

—

C₈×D₆₁

—

#11758187

—

#11758187

—

#11758187

D₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂²⋊D₆₁

—

C₂×Dic₆₁

—

D₂₄₄

C₂×C₈

yes

—

C₄×D₆₁

—

Dic₁₂₂

C₂×C₈

yes

—

C₈×C₆₁

—

C₈×C₆₁

C₂×C₈

yes

characteristic

C₈×C₆₁

C₂×C₈

yes

characteristic

#92418

C₂×D₄

yes

yes

C₂²×C₆₁

yes

C₂×D₆₁

—

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

Dic₆₁

—

#2171

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₈×D₄

yes

characteristic

D₆₁

—

—

—

—

—

—

C₆₁

#2171

yes

characteristic, complemented, Sylow

#135

—

#131

—

M₃₂

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

yes

—

C₄×C₈

—

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

122

—

M₁₆

C₂×#6923

yes

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

—

122

—

C₁₆

—

122

—

Q₈

—

D₄

—

D₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

D₆₁⋊C₈

yes

characteristic

C₈

D₆₁⋊C₈

yes

characteristic

C₂²

—

122

—

C₂²

#14519865

yes

characteristic

C₄

—

122

—

C₄

—

244

—

C₄

D₄×#6923

yes

characteristic

C₄

C₂×D₆₁⋊C₈

yes

characteristic

C₂

—

C₂

—

244

—

C₂

#16840790

yes

characteristic

	subgroup	G/H
center	C₄	D₄×#6923
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	#108×C₆₁	C₄
socle	C₂×C₆₁	C₈×D₄
hypercenter	#108	#6923
hypocenter	C₆₁	#2171
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

subgroup

G/H

center

C₄

D₄×#6923

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₄

C₂²×#6923

Fitting

#108×C₆₁

C₄

socle

C₂×C₆₁

C₈×D₄

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

N	H ≅ G/N	type
1. #16840821	C₂	semidirect
2. #16840684	C₂	semidirect
3. #16840661	C₂	semidirect
4. #16840651	C₂	semidirect
55. C₆₁	#2171	semidirect

H ≅ G/N

type

1. #16840821

C₂

semidirect

2. #16840684

C₂

semidirect

3. #16840661

C₂

semidirect

4. #16840651

C₂

semidirect

55. C₆₁

#2171

semidirect

Subgroups — #21462211

Conjugacy classes of subgroups

Complements