Group #21461362 — subgroups

Subgroups — C₂×#16840624 #21461362

Order 7808.

200 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 106 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×C₄⋊#92420	C₂	1	2	yes	maximal
2	#16840624	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#92420	—	2	2	no	—
5	C₄⋊#92420	—	2	2	no	—
6	C₄⋊#92420	C₂²	1	4	yes	—
7	C₂²×#92418	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	C₈×Dic₆₁	C₄	1	2	yes	—
10	C₈×Dic₆₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
14	C₂²×Dic₆₁	Q₈	1	1	yes	characteristic
15	C₂×#92420	—	2	4	no	—
16	C₂×#92420	—	4	4	no	—
17	C₂×C₈×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
19	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₆₁	D₄	1	1	yes	characteristic
21	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
22	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
23	C₂×#92418	C₈	1	4	yes	complemented
24	C₂×#92418	C₂×C₄	1	2	yes	—
25	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
28	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
29	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₆₁	—	2	2	no	—
31	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	SD₁₆	1	4	yes	—
34	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
36	#92420	—	4	4	no	—
37	C₈×C₆₁	—	2	2	no	—
38	#92418	C₂×C₈	1	4	yes	complemented
39	C₂²×C₆₁	C₄⋊C₈	1	2	yes	—
40	C₂²×C₆₁	#106	1	2	yes	—
41	C₂²×C₆₁	#108	1	2	yes	—
42	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₆₁	C₄⋊C₈	1	2	yes	—
44	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
45	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
46	Dic₆₁	—	2	1	no	—
47	Dic₆₁	—	2	1	no	—
48	Dic₆₁	#106	1	2	yes	—
49	Dic₆₁	C₂×SD₁₆	1	2	yes	—
50	C₂×#334	—	61	1	no	maximal, Sylow
51	C₂×C₆₁	#334	1	4	yes	complemented
52	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₆₁	C₂×#106	1	1	yes	characteristic
54	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
55	C₂×C₄⋊C₈	—	61	2	no	—
56	C₂×C₄×C₈	—	61	1	no	—
57	#334	—	61	4	no	—
58	C₆₁	C₂×#334	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	—	61	1	no	—
60	C₂²×C₈	—	122	2	no	—
61	C₂²×C₈	#6923	1	1	yes	characteristic
62	C₂×C₄²	—	61	1	no	—
63	C₄⋊C₈	—	61	4	no	—
64	C₄⋊C₈	—	122	2	no	—
65	C₄×C₈	—	61	2	no	—
66	C₄×C₈	—	61	2	no	—
67	C₂²×C₄	—	61	1	no	—
68	C₂²×C₄	—	61	1	no	—
69	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	—	61	4	no	—
72	C₂×C₈	—	61	2	no	—
73	C₂×C₈	—	122	4	no	—
74	C₂×C₈	—	244	4	no	—
75	C₂×C₈	C₂×#6923	1	2	yes	—
76	C₄²	—	61	1	no	—
77	C₄²	—	61	1	no	—
78	C₄²	—	61	1	no	—
79	C₄²	—	61	1	no	—
80	C₂³	C₄⋊#6923	1	1	yes	characteristic
81	C₂×C₄	—	61	4	no	—
82	C₂×C₄	—	61	1	no	—
83	C₂×C₄	—	61	1	no	—
84	C₂×C₄	—	61	1	no	—
85	C₂×C₄	—	61	1	no	—
86	C₂×C₄	—	122	2	no	—
87	C₂×C₄	D₆₁⋊C₈	1	2	yes	—
88	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
89	C₂×C₄	#11758217	1	2	yes	—
90	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
91	C₈	—	2	2	no	—
92	C₈	—	61	4	no	—
93	C₈	—	244	4	no	—
94	C₂²	#14519844	1	2	yes	—
95	C₂²	#14519845	1	2	yes	—
96	C₂²	#14519848	1	2	yes	—
97	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
98	C₄	—	61	2	no	—
99	C₄	—	61	2	no	—
100	C₄	—	122	1	no	—
101	C₄	—	122	1	no	—
102	C₄	#14519844	1	2	yes	—
103	C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
104	C₄	C₂×#11758217	1	1	yes	characteristic
105	C₂	#16840624	1	4	yes	direct product factor
106	C₂	C₂×#14519844	1	1	yes	characteristic
107	C₂	C₂×#14519845	1	1	yes	characteristic
108	C₂	C₂×#14519848	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#92420

C₂

yes

maximal

#16840624

C₂

yes

maximal, direct product factor

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

C₂²×#92420

—

C₄⋊#92420

—

C₄⋊#92420

C₂²

yes

—

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

Q₈

yes

characteristic

C₂×#92420

—

C₂×#92420

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₈

yes

complemented

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

C₂×Q₈

yes

characteristic

#92420

—

C₈×C₆₁

—

#92418

C₂×C₈

yes

complemented

C₂²×C₆₁

C₄⋊C₈

yes

—

C₂²×C₆₁

#106

yes

—

C₂²×C₆₁

#108

yes

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

—

C₄×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

#106

yes

—

Dic₆₁

C₂×SD₁₆

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₂×C₄⋊C₈

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

#334

—

C₆₁

C₂×#334

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

122

—

C₂²×C₈

#6923

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

D₆₁⋊C₈

yes

—

C₂×C₄

C₄⋊#6923

yes

characteristic

C₂×C₄

#11758217

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

244

—

C₂²

#14519844

yes

—

C₂²

#14519845

yes

—

C₂²

#14519848

yes

—

C₂²

C₂×C₄⋊#6923

yes

characteristic

C₄

—

C₄

—

100

C₄

—

122

—

101

C₄

—

122

—

102

C₄

#14519844

yes

—

103

C₄

C₂×D₆₁⋊C₈

yes

characteristic

104

C₄

C₂×#11758217

yes

characteristic

105

C₂

#16840624

yes

direct product factor

106

C₂

C₂×#14519844

yes

characteristic

107

C₂

C₂×#14519845

yes

characteristic

108

C₂

C₂×#14519848

yes

characteristic

	subgroup	G/H
center	C₂³	C₄⋊#6923
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂³×C₆₁	C₄⋊C₄
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	C₂×#334
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂³

C₄⋊#6923

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂²×C₈×C₆₁

C₄

socle

C₂³×C₆₁

C₄⋊C₄

C₂²×C₈

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. #16840624	C₂	direct (N × H)
23. C₂×#92418	C₈	semidirect
38. #92418	C₂×C₈	semidirect
51. C₂×C₆₁	#334	semidirect
58. C₆₁	C₂×#334	semidirect
105. C₂	#16840624	direct (N × H)

H ≅ G/N

type

2. #16840624

C₂

direct (N × H)

23. C₂×#92418

C₈

semidirect

38. #92418

C₂×C₈

semidirect

51. C₂×C₆₁

#334

semidirect

58. C₆₁

C₂×#334

semidirect

105. C₂

#16840624

direct (N × H)

Subgroups — C₂×#16840624 #21461362

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16840624 #21461362

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16840624 #21461362