Group #21462055 — subgroups

Subgroups — #21462055

Order 7808.

220 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 86 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	2	yes	maximal, complemented
2	#16840658	C₂	1	4	yes	maximal, complemented
3	C₂×#14519784	C₂	1	1	yes	maximal, characteristic
4	#14519851	—	2	2	no	—
5	#14519851	C₂²	1	4	yes	—
6	C₂×#11758187	—	2	2	no	—
7	#14519784	—	2	2	no	—
8	#14519784	—	2	2	no	—
9	C₂×#11758194	C₄	1	1	yes	characteristic
10	C₂×#11758194	C₂²	1	2	yes	—
11	C₂²×#92418	C₄	1	2	yes	—
12	C₂²×#92418	C₂²	1	1	yes	characteristic
13	C₂×#41×C₆₁	C₄	1	1	yes	characteristic
14	#41×C₆₁	—	2	2	no	—
15	#41×C₆₁	—	2	2	no	—
16	C₂×Q₈×C₆₁	C₈	1	1	yes	characteristic
17	C₂×D₄×C₆₁	C₈	1	2	yes	—
18	C₂×D₄×C₆₁	C₈	1	1	yes	characteristic
19	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
21	#11758194	—	2	2	no	—
22	#11758194	—	2	4	no	—
23	C₂×#92418	—	2	2	no	—
24	C₂×#92418	—	2	2	no	—
25	C₂×#92418	C₂×C₄	1	2	yes	—
26	C₂×#92418	C₂×C₄	1	1	yes	characteristic
27	C₂×#92418	D₄	1	2	yes	—
28	C₂×#92418	D₄	1	2	yes	—
29	C₂×#92418	C₂³	1	1	yes	characteristic
30	#11758187	—	2	4	no	—
31	C₂³×C₆₁	C₂×C₈	1	2	yes	—
32	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
33	Q₈×C₆₁	—	2	2	no	—
34	D₄×C₆₁	—	2	4	no	—
35	D₄×C₆₁	—	2	2	no	—
36	C₂×C₄×C₆₁	—	2	2	no	—
37	C₂×C₄×C₆₁	—	2	2	no	—
38	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
40	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
42	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
43	#92418	—	2	2	no	—
44	#92418	C₂²⋊C₄	1	1	yes	characteristic
45	#92418	C₂²⋊C₄	1	1	yes	characteristic
46	#92418	C₂×D₄	1	2	yes	—
47	C₂²×C₆₁	—	2	2	no	—
48	C₂²×C₆₁	—	4	1	no	—
49	C₂²×C₆₁	—	4	2	no	—
50	C₂²×C₆₁	C₂²⋊C₈	1	2	yes	—
51	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
52	C₄×C₆₁	—	2	2	no	—
53	C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
54	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
56	#2115	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	—	2	1	no	—
58	C₂×C₆₁	—	2	2	no	—
59	C₂×C₆₁	—	4	2	no	—
60	C₂×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
61	C₂×#131	—	61	1	no	—
62	C₂×M₃₂	—	61	2	no	—
63	#349	—	61	4	no	—
64	C₆₁	#2115	1	1	yes	characteristic, complemented, Sylow
65	C₂×#41	#6923	1	1	yes	characteristic
66	#131	—	122	2	no	—
67	#131	—	122	2	no	—
68	C₂×M₁₆	—	61	2	no	—
69	C₂×M₁₆	—	61	1	no	—
70	C₂²×C₈	—	61	1	no	—
71	C₂²×C₈	—	61	2	no	—
72	M₃₂	—	61	4	no	—
73	M₃₂	—	122	2	no	—
74	C₂×C₁₆	—	122	2	no	—
75	#41	—	2	2	no	—
76	#41	—	2	2	no	—
77	C₂×Q₈	#92420	1	1	yes	characteristic
78	C₂×D₄	#92420	1	2	yes	—
79	C₂×D₄	#92420	1	1	yes	characteristic
80	C₂²×C₄	C₂×#6923	1	2	yes	—
81	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
82	M₁₆	—	122	4	no	—
83	M₁₆	—	122	2	no	—
84	C₂×C₈	—	61	2	no	—
85	C₂×C₈	—	61	2	no	—
86	C₂×C₈	—	61	1	no	—
87	C₂×C₈	—	61	1	no	—
88	C₂×C₈	—	61	2	no	—
89	C₂×C₈	—	122	2	no	—
90	C₂×C₈	—	122	2	no	—
91	C₁₆	—	122	4	no	—
92	C₂³	C₂×#92420	1	2	yes	—
93	C₂³	C₂×#92420	1	1	yes	characteristic
94	Q₈	—	2	2	no	—
95	D₄	—	2	4	no	—
96	D₄	—	2	2	no	—
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	C₂×#92420	1	2	yes	—
100	C₂×C₄	C₂×#92420	1	1	yes	characteristic
101	C₂×C₄	#11758217	1	2	yes	—
102	C₂×C₄	C₂²⋊#6923	1	2	yes	—
103	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
104	C₈	—	61	1	no	—
105	C₈	—	61	1	no	—
106	C₈	—	61	2	no	—
107	C₈	—	122	2	no	—
108	C₂²	—	2	2	no	—
109	C₂²	—	4	1	no	—
110	C₂²	—	4	2	no	—
111	C₂²	C₂²⋊#92420	1	2	yes	—
112	C₂²	C₂²×#92420	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	C₂²⋊#92420	1	2	yes	—
115	C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
116	C₄	C₂×#11758217	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	2	no	—
119	C₂	—	4	2	no	—
120	C₂	C₂×C₂²⋊#92420	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519851

C₂

yes

maximal, complemented

#16840658

C₂

yes

maximal, complemented

C₂×#14519784

C₂

yes

maximal, characteristic

#14519851

—

#14519851

C₂²

yes

—

—

—

—

C₄

yes

characteristic

C₂×#11758194

C₂²

yes

—

C₂²×#92418

C₄

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂×#41×C₆₁

C₄

yes

characteristic

#41×C₆₁

—

#41×C₆₁

—

C₂×Q₈×C₆₁

C₈

yes

characteristic

C₂×D₄×C₆₁

C₈

yes

—

C₂×D₄×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

D₄

yes

—

C₂×#92418

D₄

yes

—

C₂×#92418

C₂³

yes

characteristic

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

#92418

—

#92418

C₂²⋊C₄

yes

characteristic

#92418

C₂²⋊C₄

yes

characteristic

#92418

C₂×D₄

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊C₈

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂²⋊C₈

yes

—

C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

#2115

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₂×C₂²⋊C₈

yes

characteristic

C₂×#131

—

C₂×M₃₂

—

#349

—

C₆₁

#2115

yes

characteristic, complemented, Sylow

C₂×#41

#6923

yes

characteristic

#131

—

122

—

#131

—

122

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

122

—

C₂×C₁₆

—

122

—

#41

—

#41

—

C₂×Q₈

#92420

yes

characteristic

C₂×D₄

#92420

yes

—

C₂×D₄

#92420

yes

characteristic

C₂²×C₄

C₂×#6923

yes

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₁₆

—

122

—

C₂³

C₂×#92420

yes

—

C₂³

C₂×#92420

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#92420

yes

—

100

C₂×C₄

C₂×#92420

yes

characteristic

101

C₂×C₄

#11758217

yes

—

102

C₂×C₄

C₂²⋊#6923

yes

—

103

C₂×C₄

C₂²×#6923

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

—

122

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂²⋊#92420

yes

—

112

C₂²

C₂²×#92420

yes

characteristic

113

C₄

—

114

C₄

C₂²⋊#92420

yes

—

115

C₄

C₂×C₂²⋊#6923

yes

characteristic

116

C₄

C₂×#11758217

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

C₂×C₂²⋊#92420

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊#6923
commutator	C₂²×C₆₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂×#41×C₆₁	C₄
socle	C₂×C₆₁	C₂×C₂²⋊C₈
hypercenter	C₂×#41	#6923
hypocenter	C₆₁	#2115
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

subgroup

G/H

center

C₄

C₂×C₂²⋊#6923

commutator

C₂²×C₆₁

C₂²×C₈

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂×#41×C₆₁

C₄

socle

C₂×C₆₁

C₂×C₂²⋊C₈

C₂×#41

C₆₁

G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

N	H ≅ G/N	type
1. C₂×#14519851	C₂	semidirect
2. #16840658	C₂	semidirect
64. C₆₁	#2115	semidirect

H ≅ G/N

type

1. C₂×#14519851

C₂

semidirect

2. #16840658

C₂

semidirect

64. C₆₁

#2115

semidirect

Subgroups — #21462055

Conjugacy classes of subgroups

Complements