Group #21462717 — subgroups

Subgroups — #21462717

Order 7808.

356 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 164 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	#16840812	C₂	1	8	yes	maximal, complemented
2	#16840783	C₂	1	4	yes	maximal
3	#16840778	C₂	1	2	yes	maximal
4	C₂×#14519742	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#92420	C₂²	1	4	yes	—
6	C₄⋊#92420	C₂²	1	8	yes	—
7	C₂²⋊#92420	C₂²	1	4	yes	—
8	#14519832	C₂²	1	8	yes	—
9	C₄×#92420	C₂²	1	4	yes	—
10	C₂²×Dic₁₂₂	C₄	1	1	yes	characteristic
11	#14519742	C₄	1	4	yes	—
12	#14519742	C₂²	1	4	yes	—
13	C₂×#11758196	C₄	1	2	yes	—
14	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₆₁	C₂²	1	2	yes	—
16	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
17	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
20	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₂₂	—	2	4	no	—
23	C₂×Dic₁₂₂	C₂×C₄	1	4	yes	—
24	C₂×#92420	C₂³	1	8	yes	—
25	C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
26	#11758196	C₂×C₄	1	8	yes	—
27	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
28	C₄×Dic₆₁	C₂×C₄	1	4	yes	—
29	C₄×Dic₆₁	C₂³	1	2	yes	—
30	C₄×Dic₆₁	C₂³	1	4	yes	—
31	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	4	2	no	—
33	C₂×C₄×C₆₁	M₁₆	1	4	yes	—
34	C₂×C₄×C₆₁	C₂²×C₄	1	4	yes	—
35	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
36	C₂×Dic₆₁	—	2	4	no	—
37	C₂×Dic₆₁	—	2	2	no	—
38	C₂×Dic₆₁	—	4	1	no	—
39	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
41	C₂×Dic₆₁	C₂²×C₄	1	4	yes	—
42	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
43	Dic₁₂₂	—	2	8	no	—
44	#92420	—	2	8	no	—
45	C₂²×C₆₁	—	2	1	no	—
46	C₂²×C₆₁	—	2	1	no	—
47	C₂²×C₆₁	C₂×M₁₆	1	2	yes	—
48	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
49	C₄×C₆₁	—	2	4	no	—
50	C₄×C₆₁	C₂×M₁₆	1	4	yes	—
51	Dic₆₁	—	2	1	no	—
52	Dic₆₁	—	2	4	no	—
53	Dic₆₁	—	2	2	no	—
54	Dic₆₁	2₋¹⁺⁴	1	2	yes	—
55	#2983	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	—	2	2	no	—
57	C₂×C₆₁	#519	1	1	yes	characteristic
58	C₂×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
59	C₂×C₆₁	#568	1	1	yes	characteristic
60	C₂×C₄×Q₈	—	61	1	no	—
61	#446	—	61	8	no	—
62	#432	—	61	4	no	—
63	#431	—	61	2	no	—
64	C₆₁	#2983	1	1	yes	characteristic, complemented, Sylow
65	C₂²×Q₈	—	61	1	no	—
66	C₄×Q₈	—	61	4	no	—
67	C₄×Q₈	—	61	4	no	—
68	C₂×C₄⋊C₄	—	61	2	no	—
69	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
70	C₂×C₄²	—	61	1	no	—
71	C₂×C₄²	—	61	2	no	—
72	C₄⋊C₈	—	61	4	no	—
73	C₄⋊C₈	—	61	8	no	—
74	C₂²⋊C₈	—	61	4	no	—
75	#97	—	61	8	no	—
76	C₄×C₈	—	61	4	no	—
77	C₂×Q₈	—	61	4	no	—
78	C₂×Q₈	—	122	4	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	—	61	2	no	—
81	C₂²×C₄	—	61	1	no	—
82	C₂²×C₄	C₂×#6923	1	2	yes	—
83	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
84	C₂×C₈	—	61	8	no	—
85	C₄⋊C₄	—	61	8	no	—
86	C₄⋊C₄	C₂×#6923	1	4	yes	—
87	C₄²	—	61	2	no	—
88	C₄²	—	61	4	no	—
89	C₄²	—	61	2	no	—
90	C₄²	—	61	4	no	—
91	C₂³	C₂²×#6923	1	1	yes	characteristic
92	Q₈	—	122	8	no	—
93	C₂×C₄	—	4	2	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	2	no	—
97	C₂×C₄	—	61	4	no	—
98	C₂×C₄	—	122	2	no	—
99	C₂×C₄	—	122	4	no	—
100	C₂×C₄	—	244	1	no	—
101	C₂×C₄	#11758213	1	4	yes	—
102	C₂×C₄	C₂²×#6923	1	4	yes	—
103	C₂×C₄	C₂²×#6923	1	2	yes	—
104	C₈	—	122	8	no	—
105	C₂²	—	2	1	no	—
106	C₂²	—	2	1	no	—
107	C₂²	C₂×#11758213	1	2	yes	—
108	C₂²	C₂³×#6923	1	1	yes	characteristic
109	C₄	—	2	4	no	—
110	C₄	—	61	2	no	—
111	C₄	—	122	1	no	—
112	C₄	—	122	4	no	—
113	C₄	—	122	2	no	—
114	C₄	C₂×#11758213	1	4	yes	—
115	C₂	—	2	2	no	—
116	C₂	#16840830	1	1	yes	characteristic
117	C₂	C₂²×#11758213	1	1	yes	characteristic
118	C₂	#16840840	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840812

C₂

yes

maximal, complemented

#16840783

C₂

yes

maximal

#16840778

C₂

yes

maximal

C₂×#14519742

C₂

yes

maximal, characteristic

C₄⋊#92420

C₂²

yes

—

C₄⋊#92420

C₂²

yes

—

C₂²⋊#92420

C₂²

yes

—

#14519832

C₂²

yes

—

C₄×#92420

C₂²

yes

—

C₂²×Dic₁₂₂

C₄

yes

characteristic

#14519742

C₄

yes

—

#14519742

C₂²

yes

—

C₂×#11758196

C₄

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

—

C₂×C₄⋊C₄×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂³

yes

characteristic

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

C₂×C₄

yes

—

C₂×#92420

C₂³

yes

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

#11758196

C₂×C₄

yes

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂³

yes

—

C₄×Dic₆₁

C₂³

yes

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

—

C₂×Dic₆₁

C₂²×C₄

yes

—

C₂×Dic₆₁

C₂⁴

yes

characteristic

Dic₁₂₂

—

#92420

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×M₁₆

yes

—

C₂²×C₆₁

C₂³×C₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

2₋¹⁺⁴

yes

—

#2983

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#519

yes

characteristic

C₂×C₆₁

C₂²×M₁₆

yes

characteristic

C₂×C₆₁

#568

yes

characteristic

C₂×C₄×Q₈

—

#446

—

#432

—

#431

—

C₆₁

#2983

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

#6923

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²×#6923

yes

characteristic

Q₈

—

122

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

100

C₂×C₄

—

244

—

101

C₂×C₄

#11758213

yes

—

102

C₂×C₄

C₂²×#6923

yes

—

103

C₂×C₄

C₂²×#6923

yes

—

104

C₈

—

122

—

105

C₂²

—

106

C₂²

—

107

C₂²

C₂×#11758213

yes

—

108

C₂²

C₂³×#6923

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

122

—

112

C₄

—

122

—

113

C₄

—

122

—

114

C₄

C₂×#11758213

yes

—

115

C₂

—

116

C₂

#16840830

yes

characteristic

117

C₂

C₂²×#11758213

yes

characteristic

118

C₂

#16840840

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂³×C₄
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#2983
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂²

C₂³×#6923

commutator, socle

C₂²×C₆₁

C₂³×C₄

Fitting

C₂×C₄⋊C₄×C₆₁

C₄

C₂×C₄⋊C₄

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂² ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
1. #16840812	C₂	semidirect
64. C₆₁	#2983	semidirect

H ≅ G/N

type

1. #16840812

C₂

semidirect

64. C₆₁

#2983

semidirect

Subgroups — #21462717

Conjugacy classes of subgroups

Complements