Group #21462029 — subgroups

Subgroups — #21462029

Order 7808.

184 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 102 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×#14519852	C₂	1	1	yes	maximal, characteristic
2	C₂×D₆₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#16840651	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840650	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840648	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#11758187	C₂	1	1	yes	maximal, characteristic, complemented
7	#16839719	C₂	1	1	yes	maximal, characteristic
8	#14519852	C₄	1	4	yes	complemented
9	D₆₁⋊C₁₆	C₄	1	4	yes	complemented
10	C₂×#11758187	C₂²	1	1	yes	characteristic
11	C₂×#11758187	C₂²	1	1	yes	characteristic
12	C₂×#11758187	C₂²	1	1	yes	characteristic
13	C₂×#11758187	C₂²	1	1	yes	characteristic
14	C₂×#11758189	C₄	1	1	yes	characteristic
15	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
16	#14519734	C₄	1	1	yes	characteristic
17	#14519687	C₄	1	1	yes	characteristic
18	C₄×#92418	C₂²	1	1	yes	characteristic
19	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
20	#97×C₆₁	C₄	1	1	yes	characteristic
21	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
25	#11758198	C₈	1	2	yes	—
26	#11758196	C₈	1	2	yes	—
27	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂×#92418	C₂×C₄	1	1	yes	characteristic
29	C₂×#92418	C₂³	1	1	yes	characteristic
30	#11758189	C₈	1	4	yes	—
31	C₈×D₆₁	C₂×C₄	1	2	yes	—
32	C₈×D₆₁	C₂×C₄	1	2	yes	—
33	#11758187	C₂×C₄	1	2	yes	—
34	#11758187	C₂×C₄	1	2	yes	—
35	#11758187	C₂×C₄	1	2	yes	—
36	#11758187	C₂×C₄	1	2	yes	—
37	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
39	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
41	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
42	C₄×D₆₁	C₄²	1	2	yes	—
43	C₄×D₆₁	C₂×C₈	1	2	yes	—
44	C₈×C₆₁	C₄²	1	2	yes	—
45	C₈×C₆₁	C₂×C₈	1	2	yes	—
46	#92418	C₂×C₈	1	2	yes	—
47	#92418	C₂²×C₄	1	1	yes	characteristic
48	#92418	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
50	C₂×D₆₁	—	2	2	no	—
51	C₂×D₆₁	C₄×C₈	1	2	yes	—
52	C₄×C₆₁	—	2	2	no	—
53	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
54	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
55	Dic₆₁	—	2	2	no	—
56	Dic₆₁	C₄×C₈	1	2	yes	—
57	#2108	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
59	C₂×C₆₁	#504	1	2	yes	—
60	D₆₁	—	2	2	no	—
61	C₂×M₃₂	—	61	1	no	—
62	C₂²×C₁₆	—	61	1	no	—
63	#405	—	61	1	no	—
64	#346	—	61	1	no	—
65	#346	—	61	1	no	—
66	C₄×C₁₆	—	61	1	no	—
67	C₄×C₁₆	—	61	1	no	—
68	C₆₁	#2108	1	1	yes	characteristic, complemented, Sylow
69	C₂×M₁₆	—	61	1	no	—
70	C₂²×C₈	—	61	1	no	—
71	#117	—	61	1	no	—
72	M₃₂	—	61	4	no	—
73	C₂×C₁₆	—	61	1	no	—
74	C₂×C₁₆	—	61	1	no	—
75	C₂×C₁₆	—	61	1	no	—
76	C₂×C₁₆	—	61	1	no	—
77	C₂×C₁₆	—	61	4	no	—
78	#97	—	61	1	no	—
79	#97	#6923	1	1	yes	characteristic
80	C₄×C₈	—	61	1	no	—
81	C₄×C₈	—	61	1	no	—
82	C₂²×C₄	—	61	1	no	—
83	M₁₆	—	61	4	no	—
84	C₂×C₈	—	61	1	no	—
85	C₂×C₈	—	61	1	no	—
86	C₂×C₈	—	61	2	no	—
87	C₂×C₈	—	61	2	no	—
88	C₂×C₈	C₂×#6923	1	1	yes	characteristic
89	C₂×C₈	C₂×#6923	1	1	yes	characteristic
90	C₄⋊C₄	—	61	2	no	—
91	C₂²⋊C₄	—	61	2	no	—
92	C₄²	—	61	1	no	—
93	C₄²	C₂×#6923	1	1	yes	characteristic
94	C₁₆	—	61	2	no	—
95	C₁₆	—	61	2	no	—
96	C₁₆	—	61	2	no	—
97	C₁₆	—	61	2	no	—
98	C₂³	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	61	2	no	—
101	C₂×C₄	—	61	2	no	—
102	C₂×C₄	—	61	2	no	—
103	C₂×C₄	D₆₁⋊C₈	1	2	yes	—
104	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
105	C₈	—	61	1	no	—
106	C₈	—	61	1	no	—
107	C₈	—	61	2	no	—
108	C₈	D₆₁⋊C₈	1	2	yes	—
109	C₈	C₄×#6923	1	2	yes	—
110	C₂²	—	61	2	no	—
111	C₂²	—	122	2	no	—
112	C₂²	C₂×D₆₁⋊C₈	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	61	2	no	—
115	C₄	—	122	2	no	—
116	C₄	C₂×C₄×#6923	1	1	yes	characteristic
117	C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
118	C₂	—	122	2	no	—
119	C₂	C₄×D₆₁⋊C₈	1	1	yes	characteristic
120	C₂	#16840821	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519852

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₁₆

C₂

yes

maximal, characteristic

#16840651

C₂

yes

maximal, characteristic, complemented

#16840650

C₂

yes

maximal, characteristic, complemented

#16840648

C₂

yes

maximal, characteristic, complemented

C₄×#11758187

C₂

yes

maximal, characteristic, complemented

#16839719

C₂

yes

maximal, characteristic

#14519852

C₄

yes

complemented

D₆₁⋊C₁₆

C₄

yes

complemented

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758189

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519734

C₄

yes

characteristic

#14519687

C₄

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

#97×C₆₁

C₄

yes

characteristic

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

#11758198

C₈

yes

—

#11758196

C₈

yes

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

#11758189

C₈

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

#11758187

C₂×C₄

yes

—

#11758187

C₂×C₄

yes

—

#11758187

C₂×C₄

yes

—

#11758187

C₂×C₄

yes

—

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₄×D₆₁

C₄²

yes

—

C₄×D₆₁

C₂×C₈

yes

—

C₈×C₆₁

C₄²

yes

—

C₈×C₆₁

C₂×C₈

yes

—

#92418

C₂×C₈

yes

—

#92418

C₂²×C₄

yes

characteristic

#92418

C₂²×C₄

yes

characteristic

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₄×C₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

Dic₆₁

C₄×C₈

yes

—

#2108

—

maximal, Sylow

C₂×C₆₁

C₂×C₄×C₈

yes

characteristic

C₂×C₆₁

#504

yes

—

D₆₁

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₆₁

#2108

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

D₆₁⋊C₈

yes

—

104

C₂×C₄

C₂²×#6923

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

D₆₁⋊C₈

yes

—

109

C₈

C₄×#6923

yes

—

110

C₂²

—

111

C₂²

—

122

—

112

C₂²

C₂×D₆₁⋊C₈

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

122

—

116

C₄

C₂×C₄×#6923

yes

characteristic

117

C₄

C₂×D₆₁⋊C₈

yes

characteristic

118

C₂

—

122

—

119

C₂

C₄×D₆₁⋊C₈

yes

characteristic

120

C₂

#16840821

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator	C₂×C₆₁	C₂×C₄×C₈
Fitting	#97×C₆₁	C₄
socle	C₂²×C₆₁	C₂²×C₈
hypercenter	#97	#6923
hypocenter	C₆₁	#2108
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator

C₂×C₆₁

C₂×C₄×C₈

Fitting

#97×C₆₁

C₄

socle

C₂²×C₆₁

C₂²×C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #16840651	C₂	semidirect
4. #16840650	C₂	semidirect
5. #16840648	C₂	semidirect
6. C₄×#11758187	C₂	semidirect
8. #14519852	C₄	semidirect
9. D₆₁⋊C₁₆	C₄	semidirect
68. C₆₁	#2108	semidirect

H ≅ G/N

type

3. #16840651

C₂

semidirect

4. #16840650

C₂

semidirect

5. #16840648

C₂

semidirect

6. C₄×#11758187

C₂

semidirect

8. #14519852

C₄

semidirect

9. D₆₁⋊C₁₆

C₄

semidirect

68. C₆₁

#2108

semidirect

Subgroups — #21462029

Conjugacy classes of subgroups

Complements