Group #21461477 — subgroups

Subgroups — #21461477

Order 7808.

328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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×#14519831	C₂	1	2	yes	maximal
2	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×#6923	C₂	1	2	yes	maximal
4	#16840698	C₂	1	1	yes	maximal, characteristic
5	#97×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×#6923	C₂²	1	2	yes	—
9	#14519831	C₄	1	8	yes	complemented
10	C₄×#92420	C₄	1	4	yes	complemented
11	C₈×#6923	C₄	1	8	yes	complemented
12	(C₂×#6923)⋊C₄	C₄	1	4	yes	—
13	C₂×C₈×D₆₁	C₂²	1	2	yes	—
14	C₄²×D₆₁	C₂²	1	1	yes	characteristic
15	#14519688	C₄	1	1	yes	characteristic, complemented
16	#14519687	C₄	1	2	yes	complemented
17	#97×C₆₁	C₄	1	1	yes	characteristic, complemented
18	C₂²×#6923	C₂×C₄	1	4	yes	—
19	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
20	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
21	C₂×#92420	C₂×C₄	1	2	yes	—
22	C₂×#92420	C₂×C₄	1	2	yes	—
23	C₄×#6923	C₂×C₄	1	4	yes	—
24	C₄×#6923	C₂×C₄	1	4	yes	—
25	D₆₁⋊C₈	C₂×C₄	1	4	yes	—
26	D₆₁⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
28	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
31	C₂×#92418	C₂×C₄	1	2	yes	—
32	C₈×D₆₁	C₂×C₄	1	4	yes	—
33	C₈×D₆₁	C₂×C₄	1	4	yes	—
34	C₂²×D₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×#6923	—	2	8	no	—
36	C₂×#6923	C₄²	1	8	yes	—
37	C₂×C₄×C₆₁	C₄²	1	2	yes	—
38	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	C₄²	1	2	yes	—
40	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
41	C₄×D₆₁	—	2	4	no	—
42	C₄×D₆₁	C₂²×C₄	1	2	yes	—
43	C₄×D₆₁	C₂²×C₄	1	2	yes	—
44	#92420	C₄²	1	4	yes	—
45	#92420	C₄²	1	4	yes	—
46	C₈×C₆₁	C₄²	1	4	yes	—
47	#92418	C₄²	1	4	yes	—
48	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
49	C₂×D₆₁	C₂×C₄²	1	2	yes	—
50	C₂×D₆₁	#131	1	4	yes	—
51	#6923	—	2	8	no	—
52	C₄×C₆₁	—	2	2	no	—
53	C₄×C₆₁	C₂×C₄²	1	2	yes	—
54	Dic₆₁	—	2	2	no	—
55	Dic₆₁	C₂×C₄²	1	1	yes	characteristic
56	Dic₆₁	C₂×C₄²	1	1	yes	characteristic
57	#1726	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	C₄³	1	1	yes	characteristic
59	C₂×C₆₁	#405	1	2	yes	—
60	D₆₁	#405	1	4	yes	—
61	C₂×#97	—	61	2	no	—
62	C₂×#97	—	61	1	no	—
63	C₂×C₄×C₈	—	61	2	no	—
64	C₂×C₄×C₈	—	61	1	no	—
65	#376	—	61	1	no	—
66	C₆₁	#1726	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	61	1	no	—
68	C₂²×C₈	—	61	1	no	—
69	C₂²×C₈	—	61	2	no	—
70	C₂×C₄²	—	61	2	no	—
71	C₂×C₄²	—	61	1	no	—
72	#97	—	61	8	no	—
73	#97	—	61	2	no	—
74	#97	—	61	1	no	—
75	#97	#6923	1	1	yes	characteristic, complemented
76	C₄×C₈	—	61	8	no	—
77	C₄×C₈	—	61	4	no	—
78	#95	—	61	4	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	—	61	4	no	—
81	C₂²×C₄	—	61	2	no	—
82	C₂×C₈	—	61	4	no	—
83	C₂×C₈	—	61	2	no	—
84	C₂×C₈	—	61	2	no	—
85	C₂×C₈	—	61	4	no	—
86	C₂×C₈	—	61	2	no	—
87	C₂×C₈	—	61	4	no	—
88	C₂×C₈	—	61	4	no	—
89	C₂×C₈	C₂×#6923	1	2	yes	—
90	C₄²	—	61	4	no	—
91	C₄²	—	61	4	no	—
92	C₄²	—	61	2	no	—
93	C₄²	—	61	1	no	—
94	C₄²	C₂×#6923	1	1	yes	characteristic
95	C₂³	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	2	no	—
98	C₂×C₄	—	61	2	no	—
99	C₂×C₄	—	61	8	no	—
100	C₂×C₄	—	61	2	no	—
101	C₂×C₄	—	122	4	no	—
102	C₂×C₄	—	122	8	no	—
103	C₂×C₄	C₄×#6923	1	2	yes	—
104	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
105	C₈	—	61	4	no	—
106	C₈	—	61	4	no	—
107	C₈	—	61	4	no	—
108	C₈	C₄×#6923	1	4	yes	—
109	C₂²	—	61	4	no	—
110	C₂²	—	61	2	no	—
111	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	61	1	no	—
114	C₄	—	61	1	no	—
115	C₄	—	122	8	no	—
116	C₄	—	122	2	no	—
117	C₄	C₂×C₄×#6923	1	2	yes	—
118	C₂	—	61	4	no	—
119	C₂	C₄²×#6923	1	1	yes	characteristic
120	C₂	#16840728	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519831

C₂

yes

maximal

C₄×D₆₁⋊C₈

C₂

yes

maximal, characteristic

C₂×C₈×#6923

C₂

yes

maximal

#16840698

C₂

yes

maximal, characteristic

#97×D₆₁

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

C₂²

yes

characteristic

C₂×D₆₁⋊C₈

C₂²

yes

characteristic

C₂×C₄×#6923

C₂²

yes

—

#14519831

C₄

yes

complemented

C₄×#92420

C₄

yes

complemented

C₈×#6923

C₄

yes

complemented

(C₂×#6923)⋊C₄

C₄

yes

—

C₂×C₈×D₆₁

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic, complemented

#14519687

C₄

yes

complemented

#97×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂×#92420

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

C₄×#6923

C₂×C₄

yes

—

C₄×#6923

C₂×C₄

yes

—

D₆₁⋊C₈

C₂×C₄

yes

—

D₆₁⋊C₈

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₂²×D₆₁

C₂²×C₄

yes

characteristic

C₂×#6923

—

C₂×#6923

C₄²

yes

—

C₂×C₄×C₆₁

C₄²

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

—

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

C₂²×C₄

yes

—

C₄×D₆₁

C₂²×C₄

yes

—

#92420

C₄²

yes

—

#92420

C₄²

yes

—

C₈×C₆₁

C₄²

yes

—

#92418

C₄²

yes

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

C₂×C₄²

yes

—

C₂×D₆₁

#131

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

—

Dic₆₁

—

Dic₆₁

C₂×C₄²

yes

characteristic

Dic₆₁

C₂×C₄²

yes

characteristic

#1726

—

maximal, Sylow

C₂×C₆₁

C₄³

yes

characteristic

C₂×C₆₁

#405

yes

—

D₆₁

#405

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₆₁

#1726

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₄×C₈

—

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

122

—

102

C₂×C₄

—

122

—

103

C₂×C₄

C₄×#6923

yes

—

104

C₂×C₄

C₂²×#6923

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

C₄×#6923

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂×C₄×#6923

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

122

—

116

C₄

—

122

—

117

C₄

C₂×C₄×#6923

yes

—

118

C₂

—

119

C₂

C₄²×#6923

yes

characteristic

120

C₂

#16840728

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator	C₂×C₆₁	C₄³
Fitting	#97×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄²
hypercenter	#97	#6923
hypocenter	C₆₁	#1726
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator

C₂×C₆₁

C₄³

Fitting

#97×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄²

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
9. #14519831	C₄	semidirect
10. C₄×#92420	C₄	semidirect
11. C₈×#6923	C₄	semidirect
15. #14519688	C₄	semidirect
16. #14519687	C₄	semidirect
17. #97×C₆₁	C₄	semidirect
66. C₆₁	#1726	semidirect
75. #97	#6923	semidirect

H ≅ G/N

type

9. #14519831

C₄

semidirect

10. C₄×#92420

C₄

semidirect

11. C₈×#6923

C₄

semidirect

15. #14519688

C₄

semidirect

16. #14519687

C₄

semidirect

17. #97×C₆₁

C₄

semidirect

66. C₆₁

#1726

semidirect

75. #97

#6923

semidirect

Subgroups — #21461477

Conjugacy classes of subgroups

Complements