Group #21462787 — subgroups

Subgroups — #21462787

Order 7808.

360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 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	#16840821	C₂	1	6	yes	maximal, complemented
2	#16840820	C₂	1	2	yes	maximal, complemented
3	C₂×#14519852	C₂	1	3	yes	maximal, complemented
4	D₆₁⋊M₃₂	C₂	1	3	yes	maximal, complemented
5	#131×D₆₁	C₂	1	1	yes	maximal, characteristic
6	#14519852	C₂²	1	3	yes	—
7	#14519852	C₂²	1	1	yes	characteristic
8	#14519852	C₂²	1	6	yes	complemented
9	#14519851	C₂²	1	6	yes	complemented
10	D₆₁⋊C₁₆	C₂²	1	6	yes	complemented
11	C₂×#11758187	C₂²	1	6	yes	complemented
12	#41×D₆₁	C₄	1	1	yes	characteristic
13	#14519785	C₂²	1	3	yes	—
14	#14519784	C₂²	1	1	yes	characteristic
15	#14519783	C₄	1	3	yes	—
16	M₁₆×D₆₁	C₄	1	3	yes	—
17	C₂×C₈×D₆₁	C₂²	1	3	yes	—
18	#131×C₆₁	C₄	1	1	yes	characteristic
19	#41×C₆₁	C₂×C₄	1	1	yes	characteristic
20	#11758226	C₈	1	1	yes	characteristic
21	Q₈×D₆₁	C₈	1	1	yes	characteristic
22	#11758224	C₈	1	3	yes	—
23	D₄×D₆₁	C₈	1	3	yes	—
24	#11758222	C₂×C₄	1	3	yes	—
25	C₂×C₄×D₆₁	C₂×C₄	1	3	yes	—
26	M₁₆×C₆₁	C₂×C₄	1	3	yes	—
27	C₂×C₈×C₆₁	C₂×C₄	1	3	yes	—
28	#11758194	C₂×C₄	1	3	yes	—
29	C₂×#92418	C₂³	1	3	yes	—
30	#11758189	C₂×C₄	1	6	yes	—
31	C₈×D₆₁	C₂×C₄	1	3	yes	—
32	C₈×D₆₁	C₂×C₄	1	3	yes	—
33	C₈×D₆₁	C₂³	1	3	yes	—
34	C₈×D₆₁	C₂³	1	1	yes	characteristic
35	#11758187	C₂³	1	2	yes	—
36	#11758187	C₂³	1	6	yes	—
37	C₂²×D₆₁	C₂×C₈	1	3	yes	—
38	Q₈×C₆₁	C₂×C₈	1	1	yes	characteristic
39	D₄×C₆₁	C₂×C₈	1	3	yes	—
40	C₂×C₄×C₆₁	C₂²×C₄	1	3	yes	—
41	C₂²⋊D₆₁	C₂×C₈	1	6	yes	—
42	C₂×Dic₆₁	C₂×C₈	1	3	yes	—
43	D₂₄₄	C₂×C₈	1	3	yes	—
44	C₄×D₆₁	C₂×C₈	1	3	yes	—
45	C₄×D₆₁	C₂×C₈	1	3	yes	—
46	C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
47	C₄×D₆₁	C₂²×C₄	1	3	yes	—
48	Dic₁₂₂	C₂×C₈	1	3	yes	—
49	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
50	C₈×C₆₁	C₂²×C₄	1	3	yes	—
51	#92418	C₂²×C₄	1	3	yes	—
52	#92418	C₂⁴	1	1	yes	characteristic
53	C₂²×C₆₁	C₂²×C₈	1	3	yes	—
54	C₂×D₆₁	—	4	3	no	—
55	C₂×D₆₁	C₂²×C₈	1	1	yes	characteristic
56	C₂×D₆₁	C₂²×C₈	1	3	yes	—
57	C₄×C₆₁	C₂²×C₈	1	3	yes	—
58	C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
59	Dic₆₁	C₂²×C₈	1	3	yes	—
60	Dic₆₁	C₂²×C₈	1	1	yes	characteristic
61	#3407	—	61	1	no	maximal, Sylow
62	C₂×C₆₁	—	2	3	no	—
63	C₂×C₆₁	C₂³×C₈	1	1	yes	characteristic
64	D₆₁	—	2	1	no	—
65	D₆₁	—	2	3	no	—
66	C₂×#131	—	61	1	no	—
67	#504	—	61	2	no	—
68	#504	—	61	6	no	—
69	C₂×M₃₂	—	61	3	no	—
70	C₂×M₃₂	—	61	3	no	—
71	C₆₁	#3407	1	1	yes	characteristic, complemented, Sylow
72	C₂×#41	—	61	1	no	—
73	#131	—	61	1	no	—
74	#131	—	61	3	no	—
75	#131	—	61	3	no	—
76	#131	#6923	1	1	yes	characteristic
77	C₂×M₁₆	—	61	3	no	—
78	C₂²×C₈	—	61	3	no	—
79	M₃₂	—	61	6	no	—
80	M₃₂	—	61	3	no	—
81	M₃₂	—	61	1	no	—
82	M₃₂	—	61	6	no	—
83	C₂×C₁₆	—	61	6	no	—
84	C₂×C₁₆	—	61	6	no	—
85	#41	—	61	1	no	—
86	#41	—	61	3	no	—
87	#41	—	61	3	no	—
88	#41	C₂×#6923	1	1	yes	characteristic
89	C₂×Q₈	—	61	1	no	—
90	C₂×D₄	—	61	3	no	—
91	C₂²×C₄	—	61	3	no	—
92	M₁₆	—	61	3	no	—
93	M₁₆	—	61	6	no	—
94	M₁₆	C₂×#6923	1	3	yes	—
95	C₂×C₈	—	61	3	no	—
96	C₂×C₈	—	61	3	no	—
97	C₂×C₈	—	61	3	no	—
98	C₂×C₈	—	61	3	no	—
99	C₂×C₈	—	61	1	no	—
100	C₂×C₈	C₂×#6923	1	3	yes	—
101	C₁₆	—	61	2	no	—
102	C₁₆	—	61	6	no	—
103	C₂³	—	61	3	no	—
104	Q₈	—	61	3	no	—
105	Q₈	D₆₁⋊C₈	1	1	yes	characteristic
106	D₄	—	61	6	no	—
107	D₄	—	61	3	no	—
108	D₄	D₆₁⋊C₈	1	3	yes	—
109	C₂×C₄	—	61	3	no	—
110	C₂×C₄	—	61	3	no	—
111	C₂×C₄	—	61	3	no	—
112	C₂×C₄	—	61	1	no	—
113	C₂×C₄	—	61	3	no	—
114	C₂×C₄	C₂²×#6923	1	3	yes	—
115	C₈	—	61	3	no	—
116	C₈	—	61	1	no	—
117	C₈	C₂²×#6923	1	1	yes	characteristic
118	C₈	C₂²×#6923	1	3	yes	—
119	C₂²	—	61	1	no	—
120	C₂²	—	61	3	no	—
121	C₂²	—	244	3	no	—
122	C₂²	C₂×D₆₁⋊C₈	1	3	yes	—
123	C₄	—	61	1	no	—
124	C₄	—	61	3	no	—
125	C₄	C₂×D₆₁⋊C₈	1	3	yes	—
126	C₄	C₂³×#6923	1	1	yes	characteristic
127	C₂	—	2	3	no	—
128	C₂	—	122	1	no	—
129	C₂	—	122	3	no	—
130	C₂	C₂²×D₆₁⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840821

C₂

yes

maximal, complemented

#16840820

C₂

yes

maximal, complemented

C₂×#14519852

C₂

yes

maximal, complemented

D₆₁⋊M₃₂

C₂

yes

maximal, complemented

#131×D₆₁

C₂

yes

maximal, characteristic

#14519852

C₂²

yes

—

#14519852

C₂²

yes

characteristic

#14519852

C₂²

yes

complemented

#14519851

C₂²

yes

complemented

D₆₁⋊C₁₆

C₂²

yes

complemented

C₂×#11758187

C₂²

yes

complemented

#41×D₆₁

C₄

yes

characteristic

#14519785

C₂²

yes

—

#14519784

C₂²

yes

characteristic

#14519783

C₄

yes

—

M₁₆×D₆₁

C₄

yes

—

C₂×C₈×D₆₁

C₂²

yes

—

#131×C₆₁

C₄

yes

characteristic

#41×C₆₁

C₂×C₄

yes

characteristic

#11758226

C₈

yes

characteristic

Q₈×D₆₁

C₈

yes

characteristic

#11758224

C₈

yes

—

D₄×D₆₁

C₈

yes

—

#11758222

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂×C₄

yes

—

M₁₆×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

#11758194

C₂×C₄

yes

—

C₂×#92418

C₂³

yes

—

#11758189

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂³

yes

—

C₈×D₆₁

C₂³

yes

characteristic

#11758187

C₂³

yes

—

#11758187

C₂³

yes

—

C₂²×D₆₁

C₂×C₈

yes

—

Q₈×C₆₁

C₂×C₈

yes

characteristic

D₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂²⋊D₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂×C₈

yes

—

D₂₄₄

C₂×C₈

yes

—

C₄×D₆₁

C₂×C₈

yes

—

C₄×D₆₁

C₂×C₈

yes

—

C₄×D₆₁

C₂²×C₄

yes

characteristic

C₄×D₆₁

C₂²×C₄

yes

—

Dic₁₂₂

C₂×C₈

yes

—

C₈×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

C₂²×C₄

yes

—

#92418

C₂²×C₄

yes

—

#92418

C₂⁴

yes

characteristic

C₂²×C₆₁

C₂²×C₈

yes

—

C₂×D₆₁

—

C₂×D₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

C₂²×C₈

yes

—

C₄×C₆₁

C₂²×C₈

yes

—

C₄×C₆₁

C₂³×C₄

yes

characteristic

Dic₆₁

C₂²×C₈

yes

—

Dic₆₁

C₂²×C₈

yes

characteristic

#3407

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂³×C₈

yes

characteristic

D₆₁

—

D₆₁

—

C₂×#131

—

#504

—

#504

—

C₂×M₃₂

—

C₂×M₃₂

—

C₆₁

#3407

yes

characteristic, complemented, Sylow

C₂×#41

—

—

—

—

yes

C₂×M₁₆

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

—

—

—

yes

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

C₂×#6923

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

C₂×#6923

yes

—

101

C₁₆

—

102

C₁₆

—

103

C₂³

—

104

Q₈

—

105

Q₈

D₆₁⋊C₈

yes

characteristic

106

D₄

—

107

D₄

—

108

D₄

D₆₁⋊C₈

yes

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂²×#6923

yes

—

115

C₈

—

116

C₈

—

117

C₈

C₂²×#6923

yes

characteristic

118

C₈

C₂²×#6923

yes

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

244

—

122

C₂²

C₂×D₆₁⋊C₈

yes

—

123

C₄

—

124

C₄

—

125

C₄

C₂×D₆₁⋊C₈

yes

—

126

C₄

C₂³×#6923

yes

characteristic

127

C₂

—

128

C₂

—

122

—

129

C₂

—

122

—

130

C₂

C₂²×D₆₁⋊C₈

yes

characteristic

	subgroup	G/H
center, Frattini	C₄	C₂³×#6923
commutator, socle	C₂×C₆₁	C₂³×C₈
Fitting	#131×C₆₁	C₄
hypercenter	#131	#6923
hypocenter	C₆₁	#3407
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ #131

subgroup

G/H

center, Frattini

C₄

C₂³×#6923

commutator, socle

C₂×C₆₁

C₂³×C₈

Fitting

#131×C₆₁

C₄

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₄ ◁ #131

N	H ≅ G/N	type
1. #16840821	C₂	semidirect
2. #16840820	C₂	semidirect
3. C₂×#14519852	C₂	semidirect
4. D₆₁⋊M₃₂	C₂	semidirect
8. #14519852	C₂²	semidirect
9. #14519851	C₂²	semidirect
10. D₆₁⋊C₁₆	C₂²	semidirect
11. C₂×#11758187	C₂²	semidirect
71. C₆₁	#3407	semidirect

H ≅ G/N

type

1. #16840821

C₂

semidirect

2. #16840820

C₂

semidirect

3. C₂×#14519852

C₂

semidirect

4. D₆₁⋊M₃₂

C₂

semidirect

8. #14519852

C₂²

semidirect

9. #14519851

C₂²

semidirect

10. D₆₁⋊C₁₆

C₂²

semidirect

11. C₂×#11758187

C₂²

semidirect

71. C₆₁

#3407

semidirect

Subgroups — #21462787

Conjugacy classes of subgroups

Complements