Group #21462039 — subgroups

Subgroups — #21462039

Order 7808.

160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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	#16840725	C₂	1	1	yes	maximal, characteristic
3	#16840653	C₂	1	2	yes	maximal, complemented
4	#16840652	C₂	1	2	yes	maximal, complemented
5	M₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
6	D₆₁⋊M₁₆	C₄	1	1	yes	characteristic
7	#14519856	C₄	1	1	yes	characteristic
8	#14519852	C₄	1	2	yes	complemented
9	#14519852	C₂²	1	1	yes	characteristic
10	#14519852	C₂²	1	1	yes	characteristic
11	C₂×#11758187	C₄	1	2	yes	complemented
12	#14519831	C₂²	1	2	yes	—
13	C₈×#6923	C₄	1	2	yes	—
14	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
15	#14519717	C₄	1	1	yes	characteristic, complemented
16	#14519716	C₂²	1	2	yes	—
17	C₁₆×D₆₁	C₄	1	2	yes	complemented
18	M₃₂×C₆₁	C₄	1	1	yes	characteristic, complemented
19	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂²⋊#6923	—	2	1	no	—
21	#11758217	—	2	1	no	—
22	C₄⋊#6923	—	2	1	no	—
23	C₄×#6923	C₂×C₄	1	2	yes	—
24	#11758213	—	2	1	no	—
25	D₆₁⋊C₈	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂×#92418	C₂×C₄	1	1	yes	characteristic
28	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
29	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
30	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
31	C₈×D₆₁	C₂³	1	1	yes	characteristic
32	#11758187	C₂×C₄	1	2	yes	—
33	#11758187	C₂×C₄	1	2	yes	—
34	C₁₆×C₆₁	C₂×C₄	1	2	yes	—
35	#11758185	C₂×C₄	1	2	yes	—
36	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
37	C₂×#6923	—	2	2	no	—
38	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
39	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
40	C₄×D₆₁	C₄²	1	1	yes	characteristic
41	C₄×D₆₁	M₁₆	1	1	yes	characteristic
42	C₄×D₆₁	M₁₆	1	1	yes	characteristic
43	C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
44	#92420	—	2	2	no	—
45	C₈×C₆₁	C₄²	1	1	yes	characteristic
46	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
47	#92418	C₄²	1	1	yes	characteristic
48	#92418	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₆₁	#97	1	1	yes	characteristic
50	C₂×D₆₁	—	4	1	no	—
51	C₂×D₆₁	#97	1	1	yes	characteristic
52	C₂×D₆₁	C₂×M₁₆	1	1	yes	characteristic
53	#6923	—	4	2	no	—
54	C₄×C₆₁	#97	1	1	yes	characteristic
55	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
56	Dic₆₁	#97	1	1	yes	characteristic
57	Dic₆₁	C₂×M₁₆	1	1	yes	characteristic
58	#2110	—	61	1	no	maximal, Sylow
59	C₂×C₆₁	—	2	1	no	—
60	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
61	D₆₁	—	2	1	no	—
62	D₆₁	—	2	1	no	—
63	C₂×M₃₂	—	61	1	no	—
64	C₂×M₃₂	—	61	1	no	—
65	#405	—	61	1	no	—
66	#347	—	61	2	no	—
67	#347	—	61	2	no	—
68	C₆₁	#2110	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	2	no	—
73	M₃₂	—	61	1	no	—
74	M₃₂	—	61	1	no	—
75	M₃₂	—	61	1	no	—
76	M₃₂	—	61	2	no	—
77	M₃₂	#6923	1	1	yes	characteristic, complemented
78	C₂×C₁₆	—	61	2	no	—
79	C₂×C₁₆	—	61	2	no	—
80	#97	—	61	2	no	—
81	C₄×C₈	—	61	2	no	—
82	C₂²×C₄	—	61	1	no	—
83	M₁₆	—	122	1	no	—
84	M₁₆	—	122	1	no	—
85	C₂×C₈	—	61	1	no	—
86	C₂×C₈	—	61	1	no	—
87	C₂×C₈	—	61	1	no	—
88	C₂×C₈	—	61	1	no	—
89	C₂×C₈	—	61	1	no	—
90	C₂×C₈	—	61	2	no	—
91	C₂×C₈	C₂×#6923	1	1	yes	characteristic
92	C₄⋊C₄	—	122	1	no	—
93	C₂²⋊C₄	—	122	1	no	—
94	C₄²	—	61	2	no	—
95	C₁₆	—	61	2	no	—
96	C₁₆	—	61	2	no	—
97	C₁₆	—	61	2	no	—
98	C₁₆	C₂×#6923	1	2	yes	—
99	C₂³	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	61	1	no	—
102	C₂×C₄	—	61	1	no	—
103	C₂×C₄	—	61	1	no	—
104	C₂×C₄	—	61	1	no	—
105	C₂×C₄	—	122	2	no	—
106	C₂×C₄	C₄×#6923	1	1	yes	characteristic
107	C₈	—	61	1	no	—
108	C₈	—	61	1	no	—
109	C₈	—	122	2	no	—
110	C₈	C₄×#6923	1	1	yes	characteristic
111	C₈	C₂²×#6923	1	1	yes	characteristic
112	C₂²	—	61	1	no	—
113	C₂²	—	61	1	no	—
114	C₂²	—	244	1	no	—
115	C₂²	#14519831	1	1	yes	characteristic
116	C₄	—	61	1	no	—
117	C₄	—	61	1	no	—
118	C₄	—	244	2	no	—
119	C₄	#14519831	1	1	yes	characteristic
120	C₄	C₂×C₄×#6923	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	122	1	no	—
123	C₂	—	122	1	no	—
124	C₂	C₂×#14519831	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519852

C₂

yes

maximal, characteristic

#16840725

C₂

yes

maximal, characteristic

#16840653

C₂

yes

maximal, complemented

#16840652

C₂

yes

maximal, complemented

M₃₂×D₆₁

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

C₄

yes

characteristic

#14519856

C₄

yes

characteristic

#14519852

C₄

yes

complemented

#14519852

C₂²

yes

characteristic

#14519852

C₂²

yes

characteristic

C₂×#11758187

C₄

yes

complemented

#14519831

C₂²

yes

—

C₈×#6923

C₄

yes

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519717

C₄

yes

characteristic, complemented

#14519716

C₂²

yes

—

C₁₆×D₆₁

C₄

yes

complemented

M₃₂×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂²⋊#6923

—

#11758217

—

C₄⋊#6923

—

C₄×#6923

C₂×C₄

yes

—

#11758213

—

D₆₁⋊C₈

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂³

yes

characteristic

#11758187

C₂×C₄

yes

—

#11758187

C₂×C₄

yes

—

C₁₆×C₆₁

C₂×C₄

yes

—

#11758185

C₂×C₄

yes

—

C₂²×D₆₁

M₁₆

yes

characteristic

C₂×#6923

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

M₁₆

yes

characteristic

C₄×D₆₁

C₄²

yes

characteristic

C₄×D₆₁

M₁₆

yes

characteristic

C₄×D₆₁

M₁₆

yes

characteristic

C₄×D₆₁

C₂²×C₄

yes

characteristic

#92420

—

C₈×C₆₁

C₄²

yes

characteristic

C₈×C₆₁

C₂²×C₄

yes

characteristic

#92418

C₄²

yes

characteristic

#92418

C₂²×C₄

yes

characteristic

C₂²×C₆₁

#97

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#97

yes

characteristic

C₂×D₆₁

C₂×M₁₆

yes

characteristic

#6923

—

C₄×C₆₁

#97

yes

characteristic

C₄×C₆₁

C₂×C₄²

yes

characteristic

Dic₆₁

#97

yes

characteristic

Dic₆₁

C₂×M₁₆

yes

characteristic

#2110

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×#97

yes

characteristic

D₆₁

—

D₆₁

—

C₂×M₃₂

—

C₂×M₃₂

—

#405

—

#347

—

#347

—

C₆₁

#2110

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

#6923

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

C₂×#6923

yes

—

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

122

—

106

C₂×C₄

C₄×#6923

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

122

—

110

C₈

C₄×#6923

yes

characteristic

111

C₈

C₂²×#6923

yes

characteristic

112

C₂²

—

113

C₂²

—

114

C₂²

—

244

—

115

C₂²

#14519831

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

244

—

119

C₄

#14519831

yes

characteristic

120

C₄

C₂×C₄×#6923

yes

characteristic

121

C₂

—

122

C₂

—

122

—

123

C₂

—

122

—

124

C₂

C₂×#14519831

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#6923
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₈	C₂²×#6923
Fitting	M₃₂×C₆₁	C₄
socle	C₂×C₆₁	C₂×#97
hypercenter	M₃₂	#6923
hypocenter	C₆₁	#2110
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ M₃₂

subgroup

G/H

center

C₄

C₂×C₄×#6923

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₈

C₂²×#6923

Fitting

M₃₂×C₆₁

C₄

socle

C₂×C₆₁

C₂×#97

M₃₂

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₄ ◁ M₃₂

N	H ≅ G/N	type
3. #16840653	C₂	semidirect
4. #16840652	C₂	semidirect
8. #14519852	C₄	semidirect
11. C₂×#11758187	C₄	semidirect
15. #14519717	C₄	semidirect
17. C₁₆×D₆₁	C₄	semidirect
18. M₃₂×C₆₁	C₄	semidirect
68. C₆₁	#2110	semidirect
77. M₃₂	#6923	semidirect

H ≅ G/N

type

3. #16840653

C₂

semidirect

4. #16840652

C₂

semidirect

8. #14519852

C₄

semidirect

11. C₂×#11758187

C₄

semidirect

15. #14519717

C₄

semidirect

17. C₁₆×D₆₁

C₄

semidirect

18. M₃₂×C₆₁

C₄

semidirect

68. C₆₁

#2110

semidirect

77. M₃₂

#6923

semidirect

Subgroups — #21462039

Conjugacy classes of subgroups

Complements