Group #21462051 — subgroups

Subgroups — #21462051

Order 7808.

228 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 82 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×#14519851	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11758187	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840657	C₂	1	4	yes	maximal, complemented
4	C₂×#14519785	C₂	1	1	yes	maximal, characteristic
5	#14519851	—	2	2	no	—
6	C₂×#11758187	—	2	2	no	—
7	C₂×#11758187	C₂²	1	2	yes	—
8	C₂×#11758187	C₂²	1	2	yes	—
9	C₂×#11758222	C₄	1	1	yes	characteristic
10	#14519785	—	2	2	no	—
11	#14519785	—	2	2	no	—
12	C₂×#11758189	C₄	1	2	yes	—
13	C₂²×#92418	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₆₁	C₂²	1	2	yes	—
15	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₂²⋊D₆₁	C₈	1	2	yes	—
18	#11758222	—	2	2	no	—
19	#11758222	—	2	2	no	—
20	C₂×D₂₄₄	C₈	1	1	yes	characteristic
21	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
22	C₂×Dic₁₂₂	C₈	1	1	yes	characteristic
23	M₁₆×C₆₁	—	2	2	no	—
24	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
25	C₂×#92418	C₂×C₄	1	1	yes	characteristic
26	C₂×#92418	D₄	1	2	yes	—
27	C₂×#92418	D₄	1	2	yes	—
28	C₂×#92418	C₂³	1	1	yes	characteristic
29	#11758189	—	2	4	no	—
30	C₈×D₆₁	—	2	2	no	—
31	C₈×D₆₁	—	2	2	no	—
32	#11758187	—	2	2	no	—
33	#11758187	—	2	2	no	—
34	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₆₁	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
39	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
40	C₂²⋊D₆₁	—	2	4	no	—
41	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
42	D₂₄₄	—	2	2	no	—
43	C₄×D₆₁	—	2	2	no	—
44	C₄×D₆₁	—	2	2	no	—
45	Dic₁₂₂	—	2	2	no	—
46	C₈×C₆₁	—	2	2	no	—
47	#92418	C₂²⋊C₄	1	2	yes	—
48	#92418	C₂×D₄	1	1	yes	characteristic
49	#92418	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₆₁	—	2	2	no	—
51	C₂²×C₆₁	C₂²⋊C₈	1	2	yes	—
52	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
53	C₂×D₆₁	—	2	2	no	—
54	C₂×D₆₁	—	2	4	no	—
55	C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
56	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
58	Dic₆₁	—	2	2	no	—
59	#2113	—	61	1	no	maximal, Sylow
60	C₂×C₆₁	—	2	2	no	—
61	C₂×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
62	C₂×C₆₁	#504	1	2	yes	—
63	D₆₁	—	4	2	no	—
64	C₂×#131	—	61	1	no	—
65	C₂×M₃₂	—	61	1	no	—
66	C₂²×C₁₆	—	61	1	no	—
67	C₂²⋊C₁₆	—	61	4	no	—
68	C₆₁	#2113	1	1	yes	characteristic, complemented, Sylow
69	C₂×#41	—	61	1	no	—
70	#131	—	122	2	no	—
71	#131	—	122	2	no	—
72	C₂×M₁₆	—	61	2	no	—
73	C₂×M₁₆	#6923	1	1	yes	characteristic
74	C₂²×C₈	—	61	1	no	—
75	C₂²×C₈	—	61	2	no	—
76	M₃₂	—	122	2	no	—
77	C₂×C₁₆	—	61	2	no	—
78	C₂×C₁₆	—	61	2	no	—
79	C₂×C₁₆	—	122	2	no	—
80	#41	—	122	2	no	—
81	#41	—	122	2	no	—
82	C₂×Q₈	—	61	1	no	—
83	C₂×D₄	—	61	2	no	—
84	C₂×D₄	—	61	1	no	—
85	C₂²×C₄	—	61	2	no	—
86	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
87	M₁₆	—	2	2	no	—
88	M₁₆	—	122	4	no	—
89	C₂×C₈	—	61	2	no	—
90	C₂×C₈	—	61	2	no	—
91	C₂×C₈	—	61	1	no	—
92	C₂×C₈	—	61	1	no	—
93	C₂×C₈	—	122	2	no	—
94	C₂×C₈	—	122	2	no	—
95	C₂×C₈	C₂×#6923	1	2	yes	—
96	C₁₆	—	122	2	no	—
97	C₁₆	—	122	2	no	—
98	C₂³	—	61	2	no	—
99	C₂³	D₆₁⋊C₈	1	1	yes	characteristic
100	Q₈	—	122	2	no	—
101	D₄	—	122	4	no	—
102	D₄	—	122	2	no	—
103	C₂×C₄	—	61	2	no	—
104	C₂×C₄	—	122	2	no	—
105	C₂×C₄	—	122	2	no	—
106	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
107	C₂×C₄	#11758213	1	2	yes	—
108	C₂×C₄	C₂²⋊#6923	1	2	yes	—
109	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	—	61	2	no	—
112	C₈	—	61	1	no	—
113	C₈	—	61	1	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	122	2	no	—
116	C₂²	—	122	4	no	—
117	C₂²	#14519834	1	2	yes	—
118	C₂²	C₂×D₆₁⋊C₈	1	1	yes	characteristic
119	C₄	—	122	2	no	—
120	C₄	#14519834	1	2	yes	—
121	C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
122	C₄	C₂×#11758213	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	244	2	no	—
125	C₂	C₂×#14519834	1	1	yes	characteristic
126	C₂	#16840821	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519851

C₂

yes

maximal, characteristic, complemented

C₂²×#11758187

C₂

yes

maximal, characteristic, complemented

#16840657

C₂

yes

maximal, complemented

C₂×#14519785

C₂

yes

maximal, characteristic

#14519851

—

C₂×#11758187

—

C₂×#11758187

C₂²

yes

—

C₂×#11758187

C₂²

yes

—

C₂×#11758222

C₄

yes

—

—

C₄

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

—

C₂×M₁₆×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₆₁

C₈

yes

—

#11758222

—

#11758222

—

C₂×D₂₄₄

C₈

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×Dic₁₂₂

C₈

yes

characteristic

M₁₆×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

D₄

yes

—

C₂×#92418

D₄

yes

—

C₂×#92418

C₂³

yes

characteristic

#11758189

—

C₈×D₆₁

—

C₈×D₆₁

—

#11758187

—

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂²×D₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂²⋊D₆₁

—

C₂×Dic₆₁

C₂×C₈

yes

—

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

—

Dic₁₂₂

—

C₈×C₆₁

—

#92418

C₂²⋊C₄

yes

—

#92418

C₂×D₄

yes

characteristic

#92418

C₂×D₄

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊C₈

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

C₂²⋊C₈

yes

—

C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

#2113

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₆₁

#504

yes

—

D₆₁

—

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₆₁

#2113

yes

characteristic, complemented, Sylow

C₂×#41

—

#131

—

122

—

#131

—

122

—

C₂×M₁₆

—

C₂×M₁₆

#6923

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

#41

—

122

—

#41

—

122

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

—

C₂³

D₆₁⋊C₈

yes

characteristic

100

Q₈

—

122

—

101

D₄

—

122

—

102

D₄

—

122

—

103

C₂×C₄

—

104

C₂×C₄

—

122

—

105

C₂×C₄

—

122

—

106

C₂×C₄

D₆₁⋊C₈

yes

characteristic

107

C₂×C₄

#11758213

yes

—

108

C₂×C₄

C₂²⋊#6923

yes

—

109

C₂×C₄

C₂²×#6923

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

—

122

—

116

C₂²

—

122

—

117

C₂²

#14519834

yes

—

118

C₂²

C₂×D₆₁⋊C₈

yes

characteristic

119

C₄

—

122

—

120

C₄

#14519834

yes

—

121

C₄

C₂×C₂²⋊#6923

yes

characteristic

122

C₄

C₂×#11758213

yes

characteristic

123

C₂

—

124

C₂

—

244

—

125

C₂

C₂×#14519834

yes

characteristic

126

C₂

#16840821

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×M₁₆×C₆₁	C₄
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#2113
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₂×M₁₆×C₆₁

C₄

C₂×M₁₆

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. C₂×#14519851	C₂	semidirect
2. C₂²×#11758187	C₂	semidirect
3. #16840657	C₂	semidirect
68. C₆₁	#2113	semidirect

H ≅ G/N

type

1. C₂×#14519851

C₂

semidirect

2. C₂²×#11758187

C₂

semidirect

3. #16840657

C₂

semidirect

68. C₆₁

#2113

semidirect

Subgroups — #21462051

Conjugacy classes of subgroups

Complements