Group #21462038 — subgroups

Subgroups — #21462038

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	D₆₁⋊M₃₂	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	C₂×#14519716	C₂	1	1	yes	maximal, characteristic
6	D₆₁⋊M₁₆	C₄	1	1	yes	characteristic
7	#14519856	C₄	1	1	yes	characteristic
8	#14519852	C₂²	1	2	yes	—
9	#14519851	C₄	1	2	yes	complemented
10	D₆₁⋊C₁₆	C₄	1	2	yes	complemented
11	#14519831	C₂²	1	2	yes	—
12	C₈×#6923	C₄	1	2	yes	—
13	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
14	#14519716	C₄	1	1	yes	characteristic, complemented
15	#14519716	C₄	1	1	yes	characteristic, complemented
16	#14519716	C₂²	1	1	yes	characteristic
17	#14519716	C₂²	1	1	yes	characteristic
18	C₂×#11758185	C₄	1	1	yes	characteristic, complemented
19	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
20	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂²⋊#6923	—	2	1	no	—
22	#11758217	—	2	1	no	—
23	C₄⋊#6923	—	2	1	no	—
24	C₄×#6923	C₂×C₄	1	2	yes	—
25	#11758213	—	2	1	no	—
26	D₆₁⋊C₈	C₂×C₄	1	2	yes	—
27	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂×#92418	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	C₂×C₄	1	1	yes	characteristic
32	C₈×D₆₁	C₂³	1	1	yes	characteristic
33	#11758187	C₂×C₄	1	4	yes	—
34	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
35	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
36	#11758185	C₂×C₄	1	1	yes	characteristic
37	#11758185	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
39	C₂×#6923	—	2	2	no	—
40	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
41	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
42	C₄×D₆₁	C₄²	1	1	yes	characteristic
43	C₄×D₆₁	M₁₆	1	1	yes	characteristic
44	C₄×D₆₁	M₁₆	1	1	yes	characteristic
45	C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
46	#92420	—	2	2	no	—
47	C₈×C₆₁	C₄²	1	1	yes	characteristic
48	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
49	#92418	C₄²	1	1	yes	characteristic
50	#92418	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₆₁	#97	1	1	yes	characteristic
52	C₂×D₆₁	—	4	1	no	—
53	C₂×D₆₁	#97	1	1	yes	characteristic
54	C₂×D₆₁	C₂×M₁₆	1	1	yes	characteristic
55	#6923	—	4	2	no	—
56	C₄×C₆₁	#97	1	1	yes	characteristic
57	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
58	Dic₆₁	#97	1	1	yes	characteristic
59	Dic₆₁	C₂×M₁₆	1	1	yes	characteristic
60	#2110	—	61	1	no	maximal, Sylow
61	C₂×C₆₁	—	2	1	no	—
62	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
63	D₆₁	—	2	1	no	—
64	D₆₁	—	2	1	no	—
65	C₂×M₃₂	—	61	1	no	—
66	C₂×M₃₂	—	61	1	no	—
67	#405	—	61	1	no	—
68	#347	—	61	2	no	—
69	#347	—	61	2	no	—
70	C₆₁	#2110	1	1	yes	characteristic, complemented, Sylow
71	C₂×M₁₆	—	61	1	no	—
72	C₂²×C₈	—	61	1	no	—
73	#117	—	61	1	no	—
74	M₃₂	—	61	2	no	—
75	M₃₂	—	61	2	no	—
76	M₃₂	—	61	1	no	—
77	M₃₂	—	61	1	no	—
78	M₃₂	—	61	1	no	—
79	M₃₂	—	61	1	no	—
80	C₂×C₁₆	—	61	2	no	—
81	C₂×C₁₆	—	61	1	no	—
82	C₂×C₁₆	#6923	1	1	yes	characteristic, complemented
83	#97	—	61	2	no	—
84	C₄×C₈	—	61	2	no	—
85	C₂²×C₄	—	61	1	no	—
86	M₁₆	—	122	1	no	—
87	M₁₆	—	122	1	no	—
88	C₂×C₈	—	61	1	no	—
89	C₂×C₈	—	61	1	no	—
90	C₂×C₈	—	61	1	no	—
91	C₂×C₈	—	61	1	no	—
92	C₂×C₈	—	61	1	no	—
93	C₂×C₈	—	61	2	no	—
94	C₂×C₈	C₂×#6923	1	1	yes	characteristic
95	C₄⋊C₄	—	122	1	no	—
96	C₂²⋊C₄	—	122	1	no	—
97	C₄²	—	61	2	no	—
98	C₁₆	—	61	4	no	—
99	C₁₆	—	61	1	no	—
100	C₁₆	—	61	1	no	—
101	C₁₆	C₂×#6923	1	1	yes	characteristic
102	C₁₆	C₂×#6923	1	1	yes	characteristic
103	C₂³	—	61	1	no	—
104	C₂×C₄	—	61	1	no	—
105	C₂×C₄	—	61	1	no	—
106	C₂×C₄	—	61	1	no	—
107	C₂×C₄	—	61	1	no	—
108	C₂×C₄	—	61	1	no	—
109	C₂×C₄	—	122	2	no	—
110	C₂×C₄	C₄×#6923	1	1	yes	characteristic
111	C₈	—	61	1	no	—
112	C₈	—	61	1	no	—
113	C₈	—	122	2	no	—
114	C₈	C₄×#6923	1	1	yes	characteristic
115	C₈	C₂²×#6923	1	1	yes	characteristic
116	C₂²	—	61	1	no	—
117	C₂²	—	61	1	no	—
118	C₂²	—	244	1	no	—
119	C₂²	#14519831	1	1	yes	characteristic
120	C₄	—	61	1	no	—
121	C₄	—	61	1	no	—
122	C₄	—	244	2	no	—
123	C₄	#14519831	1	1	yes	characteristic
124	C₄	C₂×C₄×#6923	1	1	yes	characteristic
125	C₂	—	2	1	no	—
126	C₂	—	122	1	no	—
127	C₂	—	122	1	no	—
128	C₂	C₂×#14519831	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊M₃₂

C₂

yes

maximal, characteristic

#16840725

C₂

yes

maximal, characteristic

#16840653

C₂

yes

maximal, complemented

#16840652

C₂

yes

maximal, complemented

C₂×#14519716

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

C₄

yes

characteristic

#14519856

C₄

yes

characteristic

#14519852

C₂²

yes

—

#14519851

C₄

yes

complemented

D₆₁⋊C₁₆

C₄

yes

complemented

#14519831

C₂²

yes

—

C₈×#6923

C₄

yes

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519716

C₄

yes

characteristic, complemented

#14519716

C₄

yes

characteristic, complemented

#14519716

C₂²

yes

characteristic

#14519716

C₂²

yes

characteristic

C₂×#11758185

C₄

yes

characteristic, complemented

C₂×C₁₆×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

—

C₁₆×C₆₁

C₂×C₄

yes

characteristic

C₁₆×C₆₁

C₂×C₄

yes

characteristic

#11758185

C₂×C₄

yes

characteristic

#11758185

C₂×C₄

yes

characteristic

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

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

#6923

yes

characteristic, complemented

#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

—

100

C₁₆

—

101

C₁₆

C₂×#6923

yes

characteristic

102

C₁₆

C₂×#6923

yes

characteristic

103

C₂³

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

122

—

110

C₂×C₄

C₄×#6923

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

122

—

114

C₈

C₄×#6923

yes

characteristic

115

C₈

C₂²×#6923

yes

characteristic

116

C₂²

—

117

C₂²

—

118

C₂²

—

244

—

119

C₂²

#14519831

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

244

—

123

C₄

#14519831

yes

characteristic

124

C₄

C₂×C₄×#6923

yes

characteristic

125

C₂

—

126

C₂

—

122

—

127

C₂

—

122

—

128

C₂

C₂×#14519831

yes

characteristic

	subgroup	G/H
center	C₈	C₄×#6923
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₈	C₂²×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂×C₆₁	C₂×#97
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#2110
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆

subgroup

G/H

center

C₈

C₄×#6923

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₈

C₂²×#6923

Fitting

C₂×C₁₆×C₆₁

C₄

socle

C₂×C₆₁

C₂×#97

C₂×C₁₆

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
3. #16840653	C₂	semidirect
4. #16840652	C₂	semidirect
9. #14519851	C₄	semidirect
10. D₆₁⋊C₁₆	C₄	semidirect
14. #14519716	C₄	semidirect
15. #14519716	C₄	semidirect
18. C₂×#11758185	C₄	semidirect
19. C₂×C₁₆×C₆₁	C₄	semidirect
70. C₆₁	#2110	semidirect
82. C₂×C₁₆	#6923	semidirect

H ≅ G/N

type

3. #16840653

C₂

semidirect

4. #16840652

C₂

semidirect

9. #14519851

C₄

semidirect

10. D₆₁⋊C₁₆

C₄

semidirect

14. #14519716

C₄

semidirect

15. #14519716

C₄

semidirect

18. C₂×#11758185

C₄

semidirect

19. C₂×C₁₆×C₆₁

C₄

semidirect

70. C₆₁

#2110

semidirect

82. C₂×C₁₆

#6923

semidirect

Subgroups — #21462038

Conjugacy classes of subgroups

Complements