Group #21460669 — subgroups

Subgroups — #21460669

Order 7808.

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

normal subgroups only

This group has 164 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	#16840785	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊#6923	C₂	1	1	yes	maximal, characteristic
3	#16839817	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#6923	—	2	1	no	—
5	C₂×C₄×#6923	C₄	1	2	yes	—
6	#14519844	C₄	1	2	yes	complemented
7	#14519834	—	2	1	no	—
8	#14519832	—	2	1	no	—
9	(C₂×#6923)⋊C₄	—	2	1	no	—
10	C₄²×D₆₁	C₂²	1	1	yes	characteristic
11	#14519706	—	2	1	no	—
12	#14519689	—	2	1	no	—
13	#14519688	C₄	1	1	yes	characteristic, complemented
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	C₄×#6923	—	4	2	no	—
22	C₂×C₈×C₆₁	—	2	1	no	—
23	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₆₁	D₄	1	1	yes	characteristic
26	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
27	C₂×#92418	—	2	1	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	1	no	—
39	C₄×D₆₁	—	2	1	no	—
40	C₄×D₆₁	—	2	2	no	—
41	C₄×D₆₁	—	4	1	no	—
42	#92420	—	4	2	no	—
43	C₈×C₆₁	—	4	1	no	—
44	#92418	—	4	1	no	—
45	C₂²×C₆₁	#95	1	1	yes	characteristic
46	C₂×D₆₁	—	2	1	no	—
47	C₂×D₆₁	—	2	1	no	—
48	C₂×D₆₁	#100	1	1	yes	characteristic
49	C₂×D₆₁	#101	1	1	yes	characteristic
50	#6923	—	4	4	no	—
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	—	2	1	no	—
53	C₄×C₆₁	—	2	1	no	—
54	Dic₆₁	—	2	1	no	—
55	Dic₆₁	—	2	1	no	—
56	Dic₆₁	#104	1	2	yes	—
57	#1285	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	H(3,ℤ/4)	1	1	yes	characteristic
59	C₂×C₆₁	#339	1	1	yes	characteristic
60	C₂×C₆₁	#343	1	1	yes	characteristic
61	D₆₁	—	2	1	no	—
62	D₆₁	—	2	1	no	—
63	#432	—	61	1	no	—
64	#432	—	61	1	no	—
65	C₄×C₄⋊C₄	—	61	1	no	—
66	C₆₁	#1285	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₄⋊C₄	—	122	1	no	—
68	C₂×C₄²	—	61	1	no	—
69	C₂×C₄²	—	61	2	no	—
70	C₄⋊C₈	—	61	2	no	—
71	C₄⋊C₈	—	122	1	no	—
72	C₂²⋊C₈	—	122	1	no	—
73	C₂²⋊C₈	—	122	1	no	—
74	#97	—	61	1	no	—
75	#97	—	122	1	no	—
76	#97	#6923	1	1	yes	characteristic, complemented
77	#95	—	122	1	no	—
78	C₂²×C₄	—	61	1	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	—	61	1	no	—
81	C₂²×C₄	—	122	2	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	122	2	no	—
84	C₂×C₈	—	122	1	no	—
85	C₄⋊C₄	—	122	4	no	—
86	C₄²	—	61	1	no	—
87	C₄²	—	61	1	no	—
88	C₄²	—	61	1	no	—
89	C₄²	—	244	2	no	—
90	C₄²	C₂×#6923	1	1	yes	characteristic
91	C₂³	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	122	2	no	—
96	C₂×C₄	—	122	1	no	—
97	C₂×C₄	—	122	1	no	—
98	C₂×C₄	—	122	4	no	—
99	C₂×C₄	—	244	1	no	—
100	C₂×C₄	—	244	2	no	—
101	C₂×C₄	—	244	2	no	—
102	C₂×C₄	C₄×#6923	1	1	yes	characteristic
103	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
104	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
105	C₈	—	4	1	no	—
106	C₈	—	244	1	no	—
107	C₈	—	244	2	no	—
108	C₂²	—	61	1	no	—
109	C₂²	—	61	1	no	—
110	C₂²	—	122	1	no	—
111	C₂²	—	122	1	no	—
112	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	2	1	no	—
116	C₄	—	61	2	no	—
117	C₄	—	122	1	no	—
118	C₄	—	122	1	no	—
119	C₄	—	244	4	no	—
120	C₂	—	122	1	no	—
121	C₂	—	122	1	no	—
122	C₂	#16840629	1	1	yes	characteristic
123	C₂	#16840634	1	1	yes	characteristic
124	C₂	#16840641	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840785

C₂

yes

maximal, characteristic

C₄×C₄⋊#6923

C₂

yes

maximal, characteristic

#16839817

C₂

yes

maximal, characteristic

C₂×C₄⋊#6923

—

C₂×C₄×#6923

C₄

yes

—

#14519844

C₄

yes

—

—

—

C₄²×D₆₁

C₂²

yes

—

—

C₄

yes

characteristic, complemented

#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

—

—

—

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

—

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

—

C₄×D₆₁

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#95

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

#104

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

D₆₁

—

#432

—

#432

—

C₄×C₄⋊C₄

—

C₆₁

#1285

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

#97

—

122

—

#97

#6923

yes

characteristic, complemented

#95

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

122

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

244

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

100

C₂×C₄

—

244

—

101

C₂×C₄

—

244

—

102

C₂×C₄

C₄×#6923

yes

characteristic

103

C₂×C₄

C₄⋊#6923

yes

characteristic

104

C₂×C₄

C₂²⋊#6923

yes

characteristic

105

C₈

—

106

C₈

—

244

—

107

C₈

—

244

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

122

—

111

C₂²

—

122

—

112

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

122

—

118

C₄

—

122

—

119

C₄

—

244

—

120

C₂

—

122

—

121

C₂

—

122

—

122

C₂

#16840629

yes

characteristic

123

C₂

#16840634

yes

characteristic

124

C₂

#16840641

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	#1285
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×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 ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
6. #14519844	C₄	semidirect
13. #14519688	C₄	semidirect
14. #97×C₆₁	C₄	semidirect
66. C₆₁	#1285	semidirect
76. #97	#6923	semidirect

H ≅ G/N

type

6. #14519844

C₄

semidirect

13. #14519688

C₄

semidirect

14. #97×C₆₁

C₄

semidirect

66. C₆₁

#1285

semidirect

76. #97

#6923

semidirect

Subgroups — #21460669

Conjugacy classes of subgroups

Complements