Group #21460708 — subgroups

Subgroups — #21460708

Order 7808.

172 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 44 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	#16840784	C₂	1	1	yes	maximal, characteristic
2	#16840698	C₂	1	1	yes	maximal, characteristic
3	#16839714	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#6923	—	2	1	no	—
5	C₄⋊#92420	C₄	1	2	yes	complemented
6	#14519834	—	2	1	no	—
7	#14519832	—	2	1	no	—
8	(C₂×#6923)⋊C₄	—	2	1	no	—
9	(C₂×#6923)⋊C₄	C₄	1	2	yes	—
10	C₂×#11758189	—	2	1	no	—
11	C₄²×D₆₁	C₂²	1	1	yes	characteristic
12	#14519688	C₄	1	1	yes	characteristic, complemented
13	C₈×Dic₆₁	—	2	1	no	—
14	#97×C₆₁	C₄	1	1	yes	characteristic, complemented
15	C₂²×#6923	—	2	2	no	—
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
19	C₂×#92420	—	2	2	no	—
20	C₄×#6923	—	2	4	no	—
21	C₂×C₈×C₆₁	—	2	1	no	—
22	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	D₄	1	1	yes	characteristic
25	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
26	C₂×#92418	—	2	1	no	—
27	#11758189	—	2	4	no	—
28	C₂²×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×#6923	—	2	4	no	—
30	C₂×#6923	—	4	2	no	—
31	C₂×#6923	—	4	2	no	—
32	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₆₁	—	2	2	no	—
39	C₄×D₆₁	—	2	2	no	—
40	C₄×D₆₁	—	4	1	no	—
41	#92420	—	4	2	no	—
42	C₈×C₆₁	—	2	2	no	—
43	#92418	—	2	2	no	—
44	C₂²×C₆₁	#95	1	1	yes	characteristic
45	C₂×D₆₁	—	2	1	no	—
46	C₂×D₆₁	—	2	1	no	—
47	C₂×D₆₁	#104	1	2	yes	—
48	#6923	—	4	4	no	—
49	C₄×C₆₁	—	2	1	no	—
50	C₄×C₆₁	—	2	1	no	—
51	C₄×C₆₁	—	2	1	no	—
52	Dic₆₁	—	2	1	no	—
53	Dic₆₁	—	2	1	no	—
54	Dic₆₁	#104	1	2	yes	—
55	#1300	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	#339	1	1	yes	characteristic
57	C₂×C₆₁	#339	1	1	yes	characteristic
58	C₂×C₆₁	#344	1	1	yes	characteristic
59	D₆₁	—	2	2	no	—
60	#432	—	61	1	no	—
61	C₄×M₁₆	—	61	1	no	—
62	#376	—	61	1	no	—
63	C₆₁	#1300	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	—	122	1	no	—
65	C₂×C₄²	—	61	1	no	—
66	C₂×C₄²	—	122	1	no	—
67	C₄⋊C₈	—	61	2	no	—
68	C₂²⋊C₈	—	122	1	no	—
69	#97	—	61	1	no	—
70	#97	—	122	1	no	—
71	#97	#6923	1	1	yes	characteristic, complemented
72	C₄×C₈	—	122	1	no	—
73	#95	—	61	2	no	—
74	#95	—	122	1	no	—
75	C₂²×C₄	—	61	1	no	—
76	C₂²×C₄	—	61	1	no	—
77	C₂²×C₄	—	61	1	no	—
78	C₂²×C₄	—	122	2	no	—
79	M₁₆	—	122	4	no	—
80	C₂×C₈	—	2	1	no	—
81	C₂×C₈	—	122	1	no	—
82	C₂×C₈	—	122	2	no	—
83	C₄²	—	61	1	no	—
84	C₄²	—	61	1	no	—
85	C₄²	—	61	1	no	—
86	C₄²	—	122	4	no	—
87	C₄²	C₂×#6923	1	1	yes	characteristic
88	C₂³	—	61	1	no	—
89	C₂×C₄	—	61	1	no	—
90	C₂×C₄	—	61	1	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	122	2	no	—
93	C₂×C₄	—	122	2	no	—
94	C₂×C₄	—	122	4	no	—
95	C₂×C₄	—	244	1	no	—
96	C₂×C₄	—	244	2	no	—
97	C₂×C₄	—	244	2	no	—
98	C₂×C₄	C₄×#6923	1	1	yes	characteristic
99	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
100	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
101	C₈	—	2	2	no	—
102	C₈	—	122	2	no	—
103	C₈	—	244	2	no	—
104	C₂²	—	61	2	no	—
105	C₂²	—	122	1	no	—
106	C₂²	—	122	1	no	—
107	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	2	1	no	—
111	C₄	—	61	2	no	—
112	C₄	—	122	1	no	—
113	C₄	—	122	1	no	—
114	C₄	—	244	4	no	—
115	C₂	—	122	2	no	—
116	C₂	#16840633	1	1	yes	characteristic
117	C₂	#16840634	1	1	yes	characteristic
118	C₂	#16840645	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840784

C₂

yes

maximal, characteristic

#16840698

C₂

yes

maximal, characteristic

#16839714

C₂

yes

maximal, characteristic

C₂×C₄×#6923

—

C₄⋊#92420

C₄

yes

—

—

—

C₄

yes

—

C₂×#11758189

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic, complemented

C₈×Dic₆₁

—

#97×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×#92420

—

C₄×#6923

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂×#92418

—

#11758189

—

C₂²×D₆₁

C₂²⋊C₄

yes

—

—

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#95

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

#104

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

#104

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#432

—

C₄×M₁₆

—

#376

—

C₆₁

#1300

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂×C₄²

—

C₂×C₄²

—

122

—

C₄⋊C₈

—

C₂²⋊C₈

—

122

—

#97

—

#97

—

122

—

#97

#6923

yes

characteristic, complemented

C₄×C₈

—

122

—

#95

—

#95

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

100

C₂×C₄

C₂²⋊#6923

yes

characteristic

101

C₈

—

102

C₈

—

122

—

103

C₈

—

244

—

104

C₂²

—

105

C₂²

—

122

—

106

C₂²

—

122

—

107

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

122

—

113

C₄

—

122

—

114

C₄

—

244

—

115

C₂

—

122

—

116

C₂

#16840633

yes

characteristic

117

C₂

#16840634

yes

characteristic

118

C₂

#16840645

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#6923)⋊C₄
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₄²	C₂×#6923
Fitting	#97×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	#97	#6923
hypocenter	C₆₁	#1300
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

(C₂×#6923)⋊C₄

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₄²

C₂×#6923

Fitting

#97×C₆₁

C₄

C₂²×C₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
5. C₄⋊#92420	C₄	semidirect
12. #14519688	C₄	semidirect
14. #97×C₆₁	C₄	semidirect
63. C₆₁	#1300	semidirect
71. #97	#6923	semidirect

H ≅ G/N

type

5. C₄⋊#92420

C₄

semidirect

12. #14519688

C₄

semidirect

14. #97×C₆₁

C₄

semidirect

63. C₆₁

#1300

semidirect

71. #97

#6923

semidirect

Subgroups — #21460708

Conjugacy classes of subgroups

Complements