Group #21447726 — subgroups

Subgroups — #21447726

Order 7808.

126 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 69 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	C₈×Dic₁₂₂	C₂	1	1	yes	maximal, characteristic
2	#16839580	C₂	1	1	yes	maximal, characteristic
3	#16839580	C₂	1	1	yes	maximal, characteristic
4	#16839538	C₂	1	1	yes	maximal, characteristic
5	#16839537	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
7	C₆₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₁₂₂	C₄	1	1	yes	characteristic
9	C₂×#11758185	C₂²	1	1	yes	characteristic
10	C₂×#11758185	C₂²	1	1	yes	characteristic
11	C₄⋊#92418	C₄	1	1	yes	characteristic
12	#14519706	C₄	1	1	yes	characteristic
13	#14519706	C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
15	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₂₂	C₈	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
22	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄⋊Dic₆₁	C₈	1	1	yes	characteristic
24	#11758196	C₈	1	1	yes	characteristic
25	#11758196	C₈	1	1	yes	characteristic
26	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂×#92418	C₂×C₄	1	1	yes	characteristic
29	C₂×#92418	C₂×C₄	1	1	yes	characteristic
30	C₁₆×C₆₁	—	2	1	no	—
31	C₁₆×C₆₁	—	2	1	no	—
32	#11758185	—	2	1	no	—
33	#11758185	Q₈	1	2	yes	complemented
34	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
41	Dic₁₂₂	—	2	2	no	—
42	C₈×C₆₁	—	2	1	no	—
43	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
44	C₈×C₆₁	#41	1	1	yes	characteristic
45	#92418	—	2	1	no	—
46	#92418	—	2	1	no	—
47	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
48	C₄×C₆₁	—	2	1	no	—
49	C₄×C₆₁	—	2	1	no	—
50	C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
51	C₄×C₆₁	#131	1	1	yes	characteristic
52	Dic₆₁	—	2	1	no	—
53	Dic₆₁	—	2	1	no	—
54	Dic₆₁	—	2	1	no	—
55	Dic₆₁	M₃₂	1	2	yes	—
56	#2183	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	C₈×Q₈	1	1	yes	characteristic
58	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
59	C₂×C₆₁	#504	1	1	yes	characteristic
60	C₈×Q₈	—	61	1	no	—
61	C₄⋊C₁₆	—	61	1	no	—
62	C₄⋊C₁₆	—	61	1	no	—
63	C₄⋊C₁₆	D₆₁	1	1	yes	characteristic
64	#346	—	61	1	no	—
65	#346	—	61	1	no	—
66	C₄×C₁₆	—	61	1	no	—
67	C₆₁	#2183	1	1	yes	characteristic, complemented, Sylow
68	C₄×Q₈	—	61	1	no	—
69	C₂×C₁₆	—	61	1	no	—
70	C₂×C₁₆	—	61	1	no	—
71	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
72	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
73	C₄⋊C₈	—	61	1	no	—
74	C₄⋊C₈	—	61	1	no	—
75	C₄⋊C₈	—	61	1	no	—
76	C₄×C₈	—	61	1	no	—
77	C₄×C₈	—	61	1	no	—
78	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
79	C₂×Q₈	—	61	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
83	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
84	C₄⋊C₄	—	61	1	no	—
85	C₄⋊C₄	—	61	1	no	—
86	C₄⋊C₄	—	61	1	no	—
87	C₄²	—	61	1	no	—
88	C₄²	—	61	1	no	—
89	C₄²	C₄×D₆₁	1	1	yes	characteristic
90	C₁₆	—	2	1	no	—
91	C₁₆	—	2	1	no	—
92	C₁₆	—	61	2	no	—
93	C₁₆	—	122	1	no	—
94	Q₈	—	122	2	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
100	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	122	1	no	—
104	C₈	—	122	1	no	—
105	C₈	#11758224	1	1	yes	characteristic
106	C₈	Q₈×D₆₁	1	1	yes	characteristic
107	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	61	2	no	—
111	C₄	—	122	1	no	—
112	C₄	—	122	1	no	—
113	C₄	—	122	1	no	—
114	C₄	#14519742	1	1	yes	characteristic
115	C₄	#14519785	1	1	yes	characteristic
116	C₂	#16839886	1	1	yes	characteristic
117	C₂	M₃₂×D₆₁	1	1	yes	characteristic
118	C₂	#16840178	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₁₂₂

C₂

yes

maximal, characteristic

#16839580

C₂

yes

maximal, characteristic

#16839580

C₂

yes

maximal, characteristic

#16839538

C₂

yes

maximal, characteristic

#16839537

C₂

yes

maximal, characteristic

C₁₆×Dic₆₁

C₂

yes

maximal, characteristic

C₆₁×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₄×Dic₁₂₂

C₄

yes

characteristic

C₂×#11758185

C₂²

yes

characteristic

C₂×#11758185

C₂²

yes

characteristic

C₄⋊#92418

C₄

yes

characteristic

#14519706

C₄

yes

characteristic

#14519706

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Dic₁₂₂

C₈

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄⋊Dic₆₁

C₈

yes

characteristic

#11758196

C₈

yes

characteristic

#11758196

C₈

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₁₆×C₆₁

—

C₁₆×C₆₁

—

#11758185

—

#11758185

Q₈

yes

complemented

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

C₂×Q₈

yes

C₈×C₆₁

yes

—

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₄×Q₈

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

M₃₂

yes

—

#2183

—

maximal, Sylow

C₂×C₆₁

C₈×Q₈

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

C₂×C₆₁

#504

yes

characteristic

C₈×Q₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

D₆₁

yes

characteristic

#346

—

#346

—

C₄×C₁₆

—

C₆₁

#2183

yes

characteristic, complemented, Sylow

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

122

—

Q₈

—

122

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₆₁

yes

characteristic

100

C₂×C₄

C₈×D₆₁

yes

characteristic

101

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

102

C₈

—

103

C₈

—

122

—

104

C₈

—

122

—

105

C₈

#11758224

yes

characteristic

106

C₈

Q₈×D₆₁

yes

characteristic

107

C₂²

C₂×C₈×D₆₁

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

122

—

112

C₄

—

122

—

113

C₄

—

122

—

114

C₄

#14519742

yes

characteristic

115

C₄

#14519785

yes

characteristic

116

C₂

#16839886

yes

characteristic

117

C₂

M₃₂×D₆₁

yes

characteristic

118

C₂

#16840178

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₆₁×C₄⋊C₁₆	C₂
hypercenter	C₄⋊C₁₆	D₆₁
hypocenter	C₆₁	#2183
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₆₁

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₆₁×C₄⋊C₁₆

C₂

hypercenter

C₄⋊C₁₆

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
33. #11758185	Q₈	semidirect
67. C₆₁	#2183	semidirect

H ≅ G/N

type

33. #11758185

Q₈

semidirect

67. C₆₁

#2183

semidirect

Subgroups — #21447726

Conjugacy classes of subgroups

Complements