Group #21447616 — subgroups

Subgroups — #21447616

Order 7808.

160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
2	#16839580	C₂	1	2	yes	maximal, complemented
3	#16839541	C₂	1	2	yes	maximal
4	C₄×#11758185	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₆×C₆₁	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	C₂×#11758185	C₂²	1	2	yes	—
10	C₄×#92418	C₄	1	1	yes	characteristic
11	C₈×Dic₆₁	C₄	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
16	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
20	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₆₁	C₈	1	1	yes	characteristic
22	C₄×Dic₆₁	C₈	1	1	yes	characteristic
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	2	no	—
27	C₈×D₆₁	—	2	2	no	—
28	C₁₆×C₆₁	—	2	2	no	—
29	#11758185	—	2	2	no	—
30	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
37	C₄×D₆₁	—	2	2	no	—
38	C₄×D₆₁	—	2	1	no	—
39	C₄×D₆₁	—	2	1	no	—
40	C₄×D₆₁	C₁₆	1	4	yes	complemented
41	C₈×C₆₁	M₁₆	1	2	yes	—
42	C₈×C₆₁	#41	1	2	yes	—
43	#92418	—	2	1	no	—
44	#92418	—	2	1	no	—
45	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
46	C₂×D₆₁	—	2	1	no	—
47	C₂×D₆₁	—	2	1	no	—
48	C₂×D₆₁	C₂×C₁₆	1	2	yes	—
49	C₄×C₆₁	C₂×C₁₆	1	2	yes	—
50	C₄×C₆₁	M₃₂	1	2	yes	—
51	C₄×C₆₁	#117	1	1	yes	characteristic
52	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
53	Dic₆₁	—	2	1	no	—
54	Dic₆₁	—	2	1	no	—
55	Dic₆₁	C₂×C₁₆	1	2	yes	—
56	#2162	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	#431	1	1	yes	characteristic
58	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
59	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
60	D₆₁	—	2	2	no	—
61	C₂×C₄×C₈	—	61	1	no	—
62	C₄⋊C₁₆	—	61	2	no	—
63	C₂²⋊C₁₆	—	61	2	no	—
64	C₄×C₁₆	—	61	1	no	—
65	C₄×C₁₆	D₆₁	1	1	yes	characteristic, complemented
66	C₆₁	#2162	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	C₂×C₁₆	—	61	2	no	—
71	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
72	C₄×C₈	—	61	1	no	—
73	C₄×C₈	—	61	1	no	—
74	C₄×C₈	—	61	1	no	—
75	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
76	C₂²×C₄	—	61	1	no	—
77	C₂²×C₄	—	61	1	no	—
78	C₂²×C₄	—	61	1	no	—
79	C₂×C₈	—	61	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	122	2	no	—
82	C₂×C₈	—	122	2	no	—
83	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
85	C₄²	—	61	1	no	—
86	C₄²	—	61	1	no	—
87	C₄²	—	61	1	no	—
88	C₄²	C₄×D₆₁	1	1	yes	characteristic
89	C₁₆	—	2	2	no	—
90	C₁₆	—	122	2	no	—
91	C₂³	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	4	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	122	2	no	—
97	C₂×C₄	—	122	1	no	—
98	C₂×C₄	—	122	1	no	—
99	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
100	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
102	C₈	—	122	1	no	—
103	C₈	—	122	1	no	—
104	C₈	#11758189	1	2	yes	—
105	C₈	#11758222	1	2	yes	—
106	C₂²	—	61	2	no	—
107	C₂²	—	122	1	no	—
108	C₂²	—	122	1	no	—
109	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
110	C₄	—	61	2	no	—
111	C₄	—	122	1	no	—
112	C₄	—	122	1	no	—
113	C₄	C₁₆×D₆₁	1	2	yes	—
114	C₄	#14519716	1	2	yes	—
115	C₄	#14519734	1	1	yes	characteristic
116	C₄	C₂×#11758189	1	1	yes	characteristic
117	C₂	—	122	2	no	—
118	C₂	#16839813	1	1	yes	characteristic
119	C₂	C₂×C₁₆×D₆₁	1	1	yes	characteristic
120	C₂	C₂×#14519716	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

#16839580

C₂

yes

maximal, complemented

#16839541

C₂

yes

maximal

C₄×#11758185

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₆₁

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₄²×D₆₁

C₄

yes

characteristic

C₂×#11758185

C₂²

yes

—

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₈

yes

characteristic

C₂×C₄×D₆₁

C₈

yes

characteristic

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

C₈

yes

characteristic

C₄×Dic₆₁

C₈

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

—

C₈×D₆₁

—

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

C₁₆

yes

complemented

C₈×C₆₁

M₁₆

yes

—

C₈×C₆₁

#41

yes

—

#92418

—

#92418

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₂×C₁₆

yes

—

C₄×C₆₁

C₂×C₁₆

yes

—

C₄×C₆₁

M₃₂

yes

—

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

C₂×C₁₆

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₂²×C₁₆

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

D₆₁

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

D₆₁

yes

characteristic, complemented

C₆₁

#2162

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₈×D₆₁

yes

characteristic

100

C₂×C₄

C₈×D₆₁

yes

characteristic

101

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

102

C₈

—

122

—

103

C₈

—

122

—

104

C₈

#11758189

yes

—

105

C₈

#11758222

yes

—

106

C₂²

—

107

C₂²

—

122

—

108

C₂²

—

122

—

109

C₂²

C₂×C₈×D₆₁

yes

characteristic

110

C₄

—

111

C₄

—

122

—

112

C₄

—

122

—

113

C₄

C₁₆×D₆₁

yes

—

114

C₄

#14519716

yes

—

115

C₄

#14519734

yes

characteristic

116

C₄

C₂×#11758189

yes

characteristic

117

C₂

—

122

—

118

C₂

#16839813

yes

characteristic

119

C₂

C₂×C₁₆×D₆₁

yes

characteristic

120

C₂

C₂×#14519716

yes

characteristic

	subgroup	G/H
center	C₄×C₈	C₂×D₆₁
commutator	C₂×C₆₁	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₄×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂²×C₈
hypercenter	C₄×C₁₆	D₆₁
hypocenter	C₆₁	#2162
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₄×C₈

C₂×D₆₁

commutator

C₂×C₆₁

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₄×C₁₆×C₆₁

C₂

socle

C₂²×C₆₁

C₂²×C₈

hypercenter

C₄×C₁₆

D₆₁

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. #16839580	C₂	semidirect
4. C₄×#11758185	C₂	semidirect
5. C₄×C₁₆×C₆₁	C₂	semidirect
40. C₄×D₆₁	C₁₆	semidirect
65. C₄×C₁₆	D₆₁	semidirect
66. C₆₁	#2162	semidirect

H ≅ G/N

type

2. #16839580

C₂

semidirect

4. C₄×#11758185

C₂

semidirect

5. C₄×C₁₆×C₆₁

C₂

semidirect

40. C₄×D₆₁

C₁₆

semidirect

65. C₄×C₁₆

D₆₁

semidirect

66. C₆₁

#2162

semidirect

Subgroups — #21447616

Conjugacy classes of subgroups

Complements