Group #21447430 — subgroups

Subgroups — #21447430

Order 7808.

260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14519717	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11758185	C₂	1	4	yes	maximal, complemented
3	C₂³×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
4	#14519717	—	2	4	no	—
5	C₂×#11758185	C₂²	1	4	yes	complemented
6	C₂³×C₄×C₆₁	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₆₁	—	2	4	no	—
8	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
9	C₂²×C₈×C₆₁	C₄	1	2	yes	—
10	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₆₁	C₈	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	—	2	2	no	—
14	C₂²×C₄×C₆₁	—	2	2	no	—
15	C₂²×C₄×C₆₁	C₈	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₈	1	2	yes	—
17	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	—	2	2	no	—
20	C₂×C₈×C₆₁	—	2	4	no	—
21	C₂×C₈×C₆₁	—	2	4	no	—
22	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₆₁	D₄	1	4	yes	—
25	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
26	#11758185	—	2	4	no	—
27	C₂³×C₆₁	—	2	2	no	—
28	C₂³×C₆₁	—	2	4	no	—
29	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
30	C₂³×C₆₁	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₆₁	—	2	2	no	—
32	C₂×C₄×C₆₁	—	2	4	no	—
33	C₂×C₄×C₆₁	—	2	2	no	—
34	C₂×C₄×C₆₁	—	2	2	no	—
35	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
36	C₂×C₄×C₆₁	C₂×C₈	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	C₈×C₆₁	—	2	2	no	—
41	C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
42	C₈×C₆₁	C₂×D₄	1	2	yes	—
43	C₂²×C₆₁	—	2	8	no	—
44	C₂²×C₆₁	—	2	2	no	—
45	C₂²×C₆₁	—	2	2	no	—
46	C₂²×C₆₁	—	2	2	no	—
47	C₂²×C₆₁	C₂²⋊C₈	1	2	yes	—
48	C₂²×C₆₁	M₃₂	1	4	yes	complemented
49	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
50	C₄×C₆₁	—	2	2	no	—
51	C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
52	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
54	#2112	—	61	1	no	maximal, Sylow
55	C₂×C₆₁	—	2	2	no	—
56	C₂×C₆₁	—	2	4	no	—
57	C₂×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
58	C₂×C₆₁	C₂×M₃₂	1	2	yes	—
59	C₂³×C₈	D₆₁	1	1	yes	characteristic
60	C₂×M₃₂	—	61	2	no	—
61	C₂²⋊C₁₆	—	61	4	no	—
62	C₆₁	#2112	1	1	yes	characteristic, complemented, Sylow
63	C₂³×C₄	Dic₆₁	1	1	yes	characteristic
64	C₂²×C₈	—	2	4	no	—
65	C₂²×C₈	Dic₆₁	1	1	yes	characteristic
66	C₂²×C₈	Dic₆₁	1	2	yes	—
67	C₂²×C₈	C₂×D₆₁	1	2	yes	—
68	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
69	M₃₂	—	122	4	no	—
70	C₂×C₁₆	—	61	4	no	—
71	C₂⁴	#92418	1	1	yes	characteristic
72	C₂²×C₄	—	2	2	no	—
73	C₂²×C₄	—	2	2	no	—
74	C₂²×C₄	#92418	1	1	yes	characteristic
75	C₂²×C₄	#92418	1	2	yes	—
76	C₂²×C₄	C₂×Dic₆₁	1	2	yes	—
77	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	—	2	4	no	—
81	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
82	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₆₁	1	4	yes	—
84	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
85	C₁₆	—	122	4	no	—
86	C₂³	—	2	2	no	—
87	C₂³	—	2	4	no	—
88	C₂³	C₂×#92418	1	1	yes	characteristic
89	C₂³	C₂×#92418	1	2	yes	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	C₂×#92418	1	2	yes	—
95	C₂×C₄	C₂×#92418	1	1	yes	characteristic
96	C₂×C₄	#11758194	1	2	yes	—
97	C₂×C₄	C₂²⋊Dic₆₁	1	2	yes	—
98	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	C₂²⋊Dic₆₁	1	2	yes	—
101	C₈	C₂×C₂²⋊D₆₁	1	2	yes	—
102	C₂²	—	2	8	no	—
103	C₂²	—	2	2	no	—
104	C₂²	—	2	2	no	—
105	C₂²	—	2	2	no	—
106	C₂²	C₂²⋊#92418	1	2	yes	—
107	C₂²	#14519717	1	4	yes	complemented
108	C₂²	C₂²×#92418	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	C₂²⋊#92418	1	2	yes	—
111	C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
112	C₄	C₂×#11758194	1	1	yes	characteristic
113	C₂	—	2	2	no	—
114	C₂	—	2	4	no	—
115	C₂	C₂×C₂²⋊#92418	1	1	yes	characteristic
116	C₂	C₂×#14519717	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, complemented

C₂²⋊#11758185

C₂

yes

maximal, complemented

C₂³×C₈×C₆₁

C₂

yes

maximal, characteristic

#14519717

—

C₂×#11758185

C₂²

yes

complemented

C₂³×C₄×C₆₁

C₄

yes

characteristic

C₂²×C₈×C₆₁

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₈×C₆₁

C₄

yes

—

C₂²×C₈×C₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂⁴×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₈

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

#11758185

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂³×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

—

C₂×C₄×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

C₈×C₆₁

—

C₈×C₆₁

C₂²⋊C₄

yes

—

C₈×C₆₁

C₂×D₄

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊C₈

yes

—

C₂²×C₆₁

M₃₂

yes

complemented

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

#2112

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

—

C₂³×C₈

D₆₁

yes

characteristic

C₂×M₃₂

—

C₂²⋊C₁₆

—

C₆₁

#2112

yes

characteristic, complemented, Sylow

C₂³×C₄

Dic₆₁

yes

characteristic

C₂²×C₈

—

C₂²×C₈

Dic₆₁

yes

characteristic

C₂²×C₈

Dic₆₁

yes

—

C₂²×C₈

C₂×D₆₁

yes

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

M₃₂

—

122

—

C₂×C₁₆

—

C₂⁴

#92418

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#92418

yes

characteristic

C₂²×C₄

#92418

yes

—

C₂²×C₄

C₂×Dic₆₁

yes

—

C₂²×C₄

C₂×Dic₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₁₆

—

122

—

C₂³

—

C₂³

—

C₂³

C₂×#92418

yes

characteristic

C₂³

C₂×#92418

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#92418

yes

—

C₂×C₄

C₂×#92418

yes

characteristic

C₂×C₄

#11758194

yes

—

C₂×C₄

C₂²⋊Dic₆₁

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₈

—

100

C₈

C₂²⋊Dic₆₁

yes

—

101

C₈

C₂×C₂²⋊D₆₁

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂²⋊#92418

yes

—

107

C₂²

#14519717

yes

complemented

108

C₂²

C₂²×#92418

yes

characteristic

109

C₄

—

110

C₄

C₂²⋊#92418

yes

—

111

C₄

C₂×C₂²⋊Dic₆₁

yes

characteristic

112

C₄

C₂×#11758194

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

C₂×C₂²⋊#92418

yes

characteristic

116

C₂

C₂×#14519717

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂³×C₈×C₆₁	C₂
hypercenter	C₂³×C₈	D₆₁
hypocenter	C₆₁	#2112
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₆₁

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₂³×C₈×C₆₁

C₂

hypercenter

C₂³×C₈

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₂³×C₈

N	H ≅ G/N	type
1. C₂×#14519717	C₂	semidirect
2. C₂²⋊#11758185	C₂	semidirect
5. C₂×#11758185	C₂²	semidirect
48. C₂²×C₆₁	M₃₂	semidirect
62. C₆₁	#2112	semidirect
107. C₂²	#14519717	semidirect

H ≅ G/N

type

1. C₂×#14519717

C₂

semidirect

2. C₂²⋊#11758185

C₂

semidirect

5. C₂×#11758185

C₂²

semidirect

48. C₂²×C₆₁

M₃₂

semidirect

62. C₆₁

#2112

semidirect

107. C₂²

#14519717

semidirect

Subgroups — #21447430

Conjugacy classes of subgroups

Complements