Group #21447419 — subgroups

Subgroups — #347×D₆₁ #21447419

Order 7808.

168 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 87 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	M₃₂×D₆₁	C₂	1	2	yes	maximal
2	#97×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839540	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839539	C₂	1	2	yes	maximal, complemented
5	C₆₁×#347	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
7	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
8	C₄²×D₆₁	C₄	1	1	yes	characteristic
9	#14519717	C₂²	1	2	yes	—
10	#14519716	C₄	1	4	yes	complemented
11	C₁₆×D₆₁	C₄	1	4	yes	complemented
12	#14519688	C₄	1	1	yes	characteristic
13	#14519687	C₄	1	1	yes	characteristic
14	#14519687	C₂²	1	1	yes	characteristic
15	M₃₂×C₆₁	C₂²	1	2	yes	—
16	#97×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₆₁	—	2	1	no	—
18	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
21	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₆₁	—	2	1	no	—
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	C₂×C₄	1	1	yes	characteristic
25	C₂×#92418	C₂×C₄	1	1	yes	characteristic
26	C₈×D₆₁	—	2	1	no	—
27	C₈×D₆₁	—	2	1	no	—
28	C₈×D₆₁	C₂×C₄	1	2	yes	—
29	C₈×D₆₁	C₂×C₄	1	2	yes	—
30	C₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
31	#11758185	C₂×C₄	1	4	yes	complemented
32	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
33	C₂×C₄×C₆₁	—	2	1	no	—
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	—	2	1	no	—
36	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
37	C₄×D₆₁	—	4	2	no	—
38	C₄×D₆₁	C₄²	1	1	yes	characteristic
39	C₄×D₆₁	C₄²	1	1	yes	characteristic
40	C₄×D₆₁	M₁₆	1	1	yes	characteristic
41	C₄×D₆₁	M₁₆	1	1	yes	characteristic
42	C₈×C₆₁	—	2	1	no	—
43	C₈×C₆₁	C₂²×C₄	1	2	yes	—
44	#92418	—	2	1	no	—
45	#92418	C₄²	1	2	yes	—
46	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
47	C₂×D₆₁	—	2	2	no	—
48	C₂×D₆₁	#97	1	1	yes	characteristic
49	C₂×D₆₁	#97	1	1	yes	characteristic
50	C₄×C₆₁	—	4	1	no	—
51	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
52	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
53	Dic₆₁	—	4	1	no	—
54	Dic₆₁	#97	1	1	yes	characteristic
55	Dic₆₁	#97	1	1	yes	characteristic
56	C₂×#347	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	—	2	1	no	—
58	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
59	D₆₁	—	2	1	no	—
60	D₆₁	#347	1	2	yes	direct product factor
61	C₂×M₃₂	—	61	2	no	—
62	C₂×#97	—	61	1	no	—
63	#347	—	61	2	no	—
64	#347	—	61	1	no	—
65	#347	D₆₁	1	1	yes	characteristic, direct product factor
66	C₆₁	C₂×#347	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	61	1	no	—
68	C₂²×C₈	—	61	1	no	—
69	C₂×C₄²	—	61	1	no	—
70	M₃₂	—	61	2	no	—
71	M₃₂	—	61	4	no	—
72	M₃₂	C₂×D₆₁	1	2	yes	—
73	C₂×C₁₆	—	61	4	no	—
74	#97	—	61	1	no	—
75	#97	—	61	1	no	—
76	#97	—	61	1	no	—
77	#97	C₂×D₆₁	1	1	yes	characteristic
78	C₂²×C₄	—	61	1	no	—
79	C₂²×C₄	—	122	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	61	2	no	—
82	C₂×C₈	—	61	2	no	—
83	C₂×C₈	—	61	1	no	—
84	C₂×C₈	—	122	1	no	—
85	C₂×C₈	—	122	1	no	—
86	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
87	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
88	C₄²	—	61	1	no	—
89	C₄²	—	122	1	no	—
90	C₄²	C₄×D₆₁	1	1	yes	characteristic
91	C₁₆	—	61	4	no	—
92	C₁₆	C₄×D₆₁	1	4	yes	complemented
93	C₂³	—	61	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	122	1	no	—
101	C₂×C₄	—	244	2	no	—
102	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	61	2	no	—
105	C₈	—	122	1	no	—
106	C₈	C₂×C₄×D₆₁	1	2	yes	—
107	C₂²	—	61	1	no	—
108	C₂²	—	61	1	no	—
109	C₂²	—	122	2	no	—
110	C₂²	M₁₆×D₆₁	1	1	yes	characteristic
111	C₄	—	4	1	no	—
112	C₄	—	61	1	no	—
113	C₄	—	61	1	no	—
114	C₄	—	244	1	no	—
115	C₄	C₄²×D₆₁	1	1	yes	characteristic
116	C₄	M₁₆×D₆₁	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	61	2	no	—
119	C₂	—	122	1	no	—
120	C₂	#97×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₃₂×D₆₁

C₂

yes

maximal

#97×D₆₁

C₂

yes

maximal, characteristic

#16839540

C₂

yes

maximal, characteristic, complemented

#16839539

C₂

yes

maximal, complemented

C₆₁×#347

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₄²×D₆₁

C₄

yes

characteristic

#14519717

C₂²

yes

—

#14519716

C₄

yes

complemented

C₁₆×D₆₁

C₄

yes

complemented

#14519688

C₄

yes

characteristic

#14519687

C₄

yes

characteristic

#14519687

C₂²

yes

characteristic

M₃₂×C₆₁

C₂²

yes

—

#97×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

—

C₈×D₆₁

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₁₆×C₆₁

C₂×C₄

yes

complemented

#11758185

C₂×C₄

yes

complemented

C₂²×D₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

M₁₆

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

C₄²

yes

characteristic

C₄×D₆₁

C₄²

yes

characteristic

C₄×D₆₁

M₁₆

yes

characteristic

C₄×D₆₁

M₁₆

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

C₂²×C₄

yes

—

#92418

—

#92418

C₄²

yes

—

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

C₂×#97

yes

characteristic

D₆₁

—

D₆₁

#347

yes

direct product factor

C₂×M₃₂

—

C₂×#97

—

#347

—

#347

—

#347

D₆₁

yes

characteristic, direct product factor

C₆₁

C₂×#347

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

C₂×D₆₁

yes

—

C₂×C₁₆

—

—

—

—

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

—

C₄²

—

122

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

C₄×D₆₁

yes

complemented

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

122

—

101

C₂×C₄

—

244

—

102

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

122

—

106

C₈

C₂×C₄×D₆₁

yes

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

122

—

110

C₂²

M₁₆×D₆₁

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

244

—

115

C₄

C₄²×D₆₁

yes

characteristic

116

C₄

M₁₆×D₆₁

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

122

—

120

C₂

#97×D₆₁

yes

characteristic

	subgroup	G/H
center	C₄	C₄²×D₆₁
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#347	C₂
socle	C₂×C₆₁	C₂×#97
hypercenter	#347	D₆₁
hypocenter	C₆₁	C₂×#347
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ #347

subgroup

G/H

center

C₄

C₄²×D₆₁

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#347

C₂

socle

C₂×C₆₁

C₂×#97

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₄ ◁ #347

N	H ≅ G/N	type
3. #16839540	C₂	semidirect
4. #16839539	C₂	semidirect
5. C₆₁×#347	C₂	semidirect
10. #14519716	C₄	semidirect
11. C₁₆×D₆₁	C₄	semidirect
30. C₁₆×C₆₁	C₂×C₄	semidirect
31. #11758185	C₂×C₄	semidirect
60. D₆₁	#347	direct (N × H)
65. #347	D₆₁	direct (N × H)
66. C₆₁	C₂×#347	semidirect
92. C₁₆	C₄×D₆₁	semidirect

H ≅ G/N

type

3. #16839540

C₂

semidirect

4. #16839539

C₂

semidirect

5. C₆₁×#347

C₂

semidirect

10. #14519716

C₄

semidirect

11. C₁₆×D₆₁

C₄

semidirect

30. C₁₆×C₆₁

C₂×C₄

semidirect

31. #11758185

C₂×C₄

semidirect

60. D₆₁

#347

direct (N × H)

65. #347

D₆₁

direct (N × H)

66. C₆₁

C₂×#347

semidirect

92. C₁₆

C₄×D₆₁

semidirect

Subgroups — #347×D₆₁ #21447419

Conjugacy classes of subgroups

Complements

Subgroups — #347×D61 #21447419

Conjugacy classes of subgroups

Complements

Subgroups — #347×D₆₁ #21447419