Group #21462158 — subgroups

Subgroups — D₆₁⋊#364 #21462158

Order 7808.

168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 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	D₆₁⋊M₃₂	C₂	1	2	yes	maximal
2	#16840685	C₂	1	2	yes	maximal, complemented
3	#16840684	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
5	#14519852	—	2	2	no	—
6	#14519851	C₂²	1	4	yes	—
7	D₆₁⋊C₁₆	—	2	2	no	—
8	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
9	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
10	C₄²×D₆₁	C₄	1	1	yes	characteristic
11	C₄×#92418	C₂²	1	1	yes	characteristic
12	C₈×Dic₆₁	C₄	1	1	yes	characteristic
13	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂×C₄×D₆₁	—	2	1	no	—
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₆₁	—	2	1	no	—
21	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×#92418	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	C₂³	1	1	yes	characteristic
24	C₈×D₆₁	C₈	1	2	yes	—
25	C₈×D₆₁	C₈	1	2	yes	—
26	C₈×D₆₁	D₄	1	1	yes	characteristic
27	C₈×D₆₁	D₄	1	1	yes	characteristic
28	C₈×D₆₁	Q₈	1	1	yes	characteristic
29	C₈×D₆₁	Q₈	1	1	yes	characteristic
30	#11758187	—	2	4	no	—
31	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	2	1	no	—
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	—	2	1	no	—
35	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
36	C₄×D₆₁	—	2	4	no	—
37	C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
40	C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
41	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
43	C₈×C₆₁	C₂×C₈	1	2	yes	—
44	#92418	C₂×C₈	1	2	yes	—
45	#92418	C₂×D₄	1	1	yes	characteristic
46	#92418	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
48	C₂×D₆₁	—	2	2	no	—
49	C₂×D₆₁	C₄⋊C₈	1	1	yes	characteristic
50	C₂×D₆₁	C₄⋊C₈	1	1	yes	characteristic
51	C₄×C₆₁	—	2	2	no	—
52	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
54	Dic₆₁	—	2	2	no	—
55	Dic₆₁	C₄⋊C₈	1	1	yes	characteristic
56	Dic₆₁	C₄⋊C₈	1	1	yes	characteristic
57	C₂×#364	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	—	2	1	no	—
59	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
60	D₆₁	—	2	1	no	—
61	D₆₁	#364	1	2	yes	complemented
62	C₂×M₃₂	—	61	2	no	—
63	C₂×C₄×C₈	—	61	1	no	—
64	#364	—	61	2	no	—
65	#364	—	61	2	no	—
66	C₆₁	C₂×#364	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	4	no	—
71	M₃₂	—	122	2	no	—
72	C₂×C₁₆	—	122	2	no	—
73	C₄×C₈	—	61	1	no	—
74	C₄×C₈	—	61	1	no	—
75	C₄×C₈	—	61	1	no	—
76	C₄×C₈	#6923	1	1	yes	characteristic
77	C₂²×C₄	—	61	1	no	—
78	C₂²×C₄	—	122	1	no	—
79	C₂×C₈	—	61	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	—	61	1	no	—
85	C₂×C₈	—	61	1	no	—
86	C₂×C₈	—	61	1	no	—
87	C₂×C₈	C₂×#6923	1	1	yes	characteristic
88	C₂×C₈	C₂×#6923	1	1	yes	characteristic
89	C₄²	—	61	1	no	—
90	C₄²	—	122	1	no	—
91	C₄²	C₂×#6923	1	1	yes	characteristic
92	C₁₆	—	122	4	no	—
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	4	no	—
101	C₂×C₄	—	122	1	no	—
102	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
103	C₈	—	61	1	no	—
104	C₈	—	61	1	no	—
105	C₈	—	61	2	no	—
106	C₈	D₆₁⋊C₈	1	2	yes	—
107	C₈	C₄⋊#6923	1	1	yes	characteristic
108	C₈	C₄⋊#6923	1	1	yes	characteristic
109	C₂²	—	61	1	no	—
110	C₂²	—	61	1	no	—
111	C₂²	—	122	2	no	—
112	C₂²	D₆₁⋊M₁₆	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	61	1	no	—
115	C₄	—	61	1	no	—
116	C₄	—	122	2	no	—
117	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
118	C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	61	2	no	—
121	C₂	—	122	1	no	—
122	C₂	D₆₁⋊(C₄⋊C₈)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊M₃₂

C₂

yes

maximal

#16840685

C₂

yes

maximal, complemented

#16840684

C₂

yes

maximal, complemented

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

#14519852

—

#14519851

C₂²

yes

—

D₆₁⋊C₁₆

—

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₄²×D₆₁

C₄

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

C₈×D₆₁

C₈

yes

—

C₈×D₆₁

C₈

yes

—

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

#11758187

—

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

C₄⋊C₄

yes

characteristic

C₄×D₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

C₂×C₈

yes

characteristic

C₄×D₆₁

C₂×C₈

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₂×C₈

yes

—

#92418

C₂×C₈

yes

—

#92418

C₂×D₄

yes

characteristic

#92418

C₂×Q₈

yes

characteristic

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₄⋊C₈

yes

characteristic

C₂×D₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

Dic₆₁

C₄⋊C₈

yes

characteristic

Dic₆₁

C₄⋊C₈

yes

characteristic

C₂×#364

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₄⋊C₈

yes

characteristic

D₆₁

—

D₆₁

#364

yes

complemented

C₂×M₃₂

—

C₂×C₄×C₈

—

#364

—

#364

—

C₆₁

C₂×#364

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

122

—

C₂×C₁₆

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

122

—

C₄²

C₂×#6923

yes

characteristic

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

122

—

101

C₂×C₄

—

122

—

102

C₂×C₄

C₂²×#6923

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

D₆₁⋊C₈

yes

—

107

C₈

C₄⋊#6923

yes

characteristic

108

C₈

C₄⋊#6923

yes

characteristic

109

C₂²

—

110

C₂²

—

111

C₂²

—

122

—

112

C₂²

D₆₁⋊M₁₆

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

122

—

117

C₄

C₂×C₄⋊#6923

yes

characteristic

118

C₄

C₂×D₆₁⋊C₈

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

—

122

—

122

C₂

D₆₁⋊(C₄⋊C₈)

yes

characteristic

	subgroup	G/H
center	C₈	C₄⋊#6923
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂×C₆₁	C₂×C₄⋊C₈
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	C₂×#364
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₈

C₄⋊#6923

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₄×C₈×C₆₁

C₄

socle

C₂×C₆₁

C₂×C₄⋊C₈

C₄×C₈

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #16840685	C₂	semidirect
3. #16840684	C₂	semidirect
61. D₆₁	#364	semidirect
66. C₆₁	C₂×#364	semidirect

H ≅ G/N

type

2. #16840685

C₂

semidirect

3. #16840684

C₂

semidirect

61. D₆₁

#364

semidirect

66. C₆₁

C₂×#364

semidirect

Subgroups — D₆₁⋊#364 #21462158

Conjugacy classes of subgroups

Complements

Subgroups — D61⋊#364 #21462158

Conjugacy classes of subgroups

Complements

Subgroups — D₆₁⋊#364 #21462158