Group #21462477 — subgroups

Subgroups — C₂²×#14519848 #21462477

Order 7808.

480 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 218 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	C₂²×#11758213	C₂	1	2	yes	maximal
2	C₂×#14519848	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758213	—	2	6	no	—
5	C₂×#11758213	C₂²	1	12	yes	—
6	C₂²×#92420	—	2	2	no	—
7	#14519848	C₂²	1	16	yes	direct product factor
8	C₂²×C₄×D₆₁	C₂²	1	1	yes	characteristic
9	C₂²×#92418	C₄	1	1	yes	characteristic
10	C₂×C₈×D₆₁	C₄	1	6	yes	—
11	C₂×C₈×D₆₁	C₂²	1	6	yes	—
12	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
13	C₂³×D₆₁	Q₈	1	1	yes	characteristic
14	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
16	C₂×C₄×D₆₁	C₂×C₄	1	3	yes	—
17	C₂×C₄×D₆₁	D₄	1	3	yes	—
18	C₂×C₄×D₆₁	Q₈	1	3	yes	—
19	C₂×C₄×D₆₁	C₂³	1	3	yes	—
20	C₂×#92420	—	2	12	no	—
21	#11758213	—	2	12	no	—
22	#11758213	C₂³	1	8	yes	—
23	C₂×C₈×C₆₁	C₂×C₄	1	6	yes	—
24	C₂×#92418	C₂×C₄	1	6	yes	—
25	C₈×D₆₁	C₂×C₄	1	12	yes	—
26	C₈×D₆₁	C₂³	1	4	yes	—
27	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×D₆₁	—	2	4	no	—
29	C₂²×D₆₁	C₄⋊C₄	1	3	yes	—
30	C₂²×D₆₁	C₂×Q₈	1	3	yes	—
31	C₂×C₄×C₆₁	C₄⋊C₄	1	3	yes	—
32	C₂×C₄×C₆₁	C₂²×C₄	1	3	yes	—
33	C₂×Dic₆₁	C₄⋊C₄	1	3	yes	—
34	C₂×Dic₆₁	C₂×D₄	1	3	yes	—
35	C₄×D₆₁	C₄⋊C₄	1	6	yes	—
36	C₄×D₆₁	C₂²×C₄	1	3	yes	—
37	C₄×D₆₁	C₂×D₄	1	3	yes	—
38	C₄×D₆₁	C₂×Q₈	1	3	yes	—
39	C₄×D₆₁	C₂⁴	1	1	yes	characteristic
40	#92420	—	2	8	no	—
41	C₈×C₆₁	C₂²×C₄	1	4	yes	—
42	#92418	C₂²×C₄	1	4	yes	—
43	C₂²×C₆₁	#108	1	4	yes	complemented
44	C₂²×C₆₁	C₂×C₄⋊C₄	1	3	yes	—
45	C₂×D₆₁	—	2	6	no	—
46	C₂×D₆₁	—	2	6	no	—
47	C₂×D₆₁	C₂×C₄⋊C₄	1	3	yes	—
48	C₂×D₆₁	C₂²×Q₈	1	1	yes	characteristic
49	C₄×C₆₁	C₂×C₄⋊C₄	1	3	yes	—
50	C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
51	Dic₆₁	C₂×C₄⋊C₄	1	3	yes	—
52	Dic₆₁	C₂²×D₄	1	1	yes	characteristic
53	C₂²×#108	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	C₂×#108	1	6	yes	complemented
55	C₂×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
56	D₆₁	—	2	3	no	—
57	D₆₁	—	2	1	no	—
58	C₂²×M₁₆	—	61	2	no	—
59	C₂³×C₈	—	61	1	no	—
60	C₂×#108	—	61	12	no	—
61	C₆₁	C₂²×#108	1	1	yes	characteristic, complemented, Sylow
62	C₂³×C₄	—	61	1	no	—
63	C₂×M₁₆	—	61	12	no	—
64	C₂×M₁₆	—	122	6	no	—
65	C₂²×C₈	—	61	1	no	—
66	C₂²×C₈	—	61	6	no	—
67	C₂²×C₈	—	61	6	no	—
68	C₂²×C₈	—	122	2	no	—
69	C₂²×C₈	#6923	1	1	yes	characteristic
70	#108	—	61	16	no	—
71	C₂⁴	—	61	1	no	—
72	C₂²×C₄	—	61	1	no	—
73	C₂²×C₄	—	61	3	no	—
74	C₂²×C₄	—	61	3	no	—
75	C₂²×C₄	—	61	3	no	—
76	C₂²×C₄	—	61	3	no	—
77	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
78	M₁₆	—	61	8	no	—
79	M₁₆	—	122	12	no	—
80	C₂×C₈	—	61	6	no	—
81	C₂×C₈	—	61	4	no	—
82	C₂×C₈	—	61	12	no	—
83	C₂×C₈	—	122	12	no	—
84	C₂×C₈	C₂×#6923	1	6	yes	—
85	C₂³	—	61	3	no	—
86	C₂³	—	61	3	no	—
87	C₂³	—	122	4	no	—
88	C₂³	C₄⋊#6923	1	1	yes	characteristic
89	C₂×C₄	—	61	3	no	—
90	C₂×C₄	—	61	3	no	—
91	C₂×C₄	—	61	6	no	—
92	C₂×C₄	—	61	3	no	—
93	C₂×C₄	—	61	3	no	—
94	C₂×C₄	—	61	3	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	C₄⋊#6923	1	3	yes	—
97	C₂×C₄	C₂²×#6923	1	3	yes	—
98	C₈	—	61	4	no	—
99	C₈	—	122	8	no	—
100	C₈	C₂²×#6923	1	4	yes	—
101	C₂²	—	61	3	no	—
102	C₂²	—	61	1	no	—
103	C₂²	—	122	6	no	—
104	C₂²	—	122	6	no	—
105	C₂²	#14519848	1	4	yes	direct product factor
106	C₂²	C₂×C₄⋊#6923	1	3	yes	—
107	C₄	—	61	3	no	—
108	C₄	—	61	1	no	—
109	C₄	C₂×C₄⋊#6923	1	3	yes	—
110	C₄	C₂³×#6923	1	1	yes	characteristic
111	C₂	—	122	3	no	—
112	C₂	—	122	1	no	—
113	C₂	C₂×#14519848	1	6	yes	direct product factor
114	C₂	C₂²×C₄⋊#6923	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11758213

C₂

yes

maximal

C₂×#14519848

C₂

yes

maximal, direct product factor

C₂²×C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×#11758213

—

C₂×#11758213

C₂²

yes

—

C₂²×#92420

—

#14519848

C₂²

yes

direct product factor

C₂²×C₄×D₆₁

C₂²

yes

characteristic

C₂²×#92418

C₄

yes

characteristic

C₂×C₈×D₆₁

C₄

yes

—

C₂×C₈×D₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂³×D₆₁

Q₈

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×C₄×D₆₁

D₄

yes

—

C₂×C₄×D₆₁

Q₈

yes

—

C₂×C₄×D₆₁

C₂³

yes

—

C₂×#92420

—

#11758213

—

#11758213

C₂³

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂³

yes

—

C₂³×C₆₁

C₄⋊C₄

yes

characteristic

C₂²×D₆₁

—

C₂²×D₆₁

C₄⋊C₄

yes

—

C₂²×D₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

C₂×D₄

yes

—

C₄×D₆₁

C₄⋊C₄

yes

—

C₄×D₆₁

C₂²×C₄

yes

—

C₄×D₆₁

C₂×D₄

yes

—

C₄×D₆₁

C₂×Q₈

yes

—

C₄×D₆₁

C₂⁴

yes

characteristic

#92420

—

C₈×C₆₁

C₂²×C₄

yes

—

#92418

C₂²×C₄

yes

—

C₂²×C₆₁

#108

yes

complemented

C₂²×C₆₁

C₂×C₄⋊C₄

yes

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₂×C₄⋊C₄

yes

—

C₂×D₆₁

C₂²×Q₈

yes

characteristic

C₄×C₆₁

C₂×C₄⋊C₄

yes

—

C₄×C₆₁

C₂³×C₄

yes

characteristic

Dic₆₁

C₂×C₄⋊C₄

yes

—

Dic₆₁

C₂²×D₄

yes

characteristic

C₂²×#108

—

maximal, Sylow

C₂×C₆₁

C₂×#108

yes

complemented

C₂×C₆₁

C₂²×C₄⋊C₄

yes

characteristic

D₆₁

—

D₆₁

—

C₂²×M₁₆

—

C₂³×C₈

—

C₂×#108

—

C₆₁

C₂²×#108

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

122

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

122

—

C₂²×C₈

#6923

yes

characteristic

#108

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₂³

—

C₂³

—

C₂³

—

122

—

C₂³

C₄⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊#6923

yes

—

C₂×C₄

C₂²×#6923

yes

—

C₈

—

C₈

—

122

—

100

C₈

C₂²×#6923

yes

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

122

—

104

C₂²

—

122

—

105

C₂²

#14519848

yes

direct product factor

106

C₂²

C₂×C₄⋊#6923

yes

—

107

C₄

—

108

C₄

—

109

C₄

C₂×C₄⋊#6923

yes

—

110

C₄

C₂³×#6923

yes

characteristic

111

C₂

—

122

—

112

C₂

—

122

—

113

C₂

C₂×#14519848

yes

direct product factor

114

C₂

C₂²×C₄⋊#6923

yes

characteristic

	subgroup	G/H
center	C₂³	C₄⋊#6923
commutator	C₄×C₆₁	C₂³×C₄
Frattini	C₄	C₂³×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂³×C₆₁	C₄⋊C₄
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	C₂²×#108
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂³

C₄⋊#6923

commutator

C₄×C₆₁

C₂³×C₄

Frattini

C₄

C₂³×#6923

Fitting

C₂²×C₈×C₆₁

C₄

socle

C₂³×C₆₁

C₄⋊C₄

hypercenter

C₂²×C₈

#6923

hypocenter

C₆₁

C₂²×#108

LCS

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. C₂×#14519848	C₂	direct (N × H)
7. #14519848	C₂²	direct (N × H)
43. C₂²×C₆₁	#108	semidirect
54. C₂×C₆₁	C₂×#108	semidirect
61. C₆₁	C₂²×#108	semidirect
105. C₂²	#14519848	direct (N × H)
113. C₂	C₂×#14519848	direct (N × H)

H ≅ G/N

type

2. C₂×#14519848

C₂

direct (N × H)

7. #14519848

C₂²

direct (N × H)

43. C₂²×C₆₁

#108

semidirect

54. C₂×C₆₁

C₂×#108

semidirect

61. C₆₁

C₂²×#108

semidirect

105. C₂²

#14519848

direct (N × H)

113. C₂

C₂×#14519848

direct (N × H)

Subgroups — C₂²×#14519848 #21462477

Conjugacy classes of subgroups

Complements

Subgroups — C22×#14519848 #21462477

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14519848 #21462477