Group #21445944 — subgroups

Subgroups — #21445944

Order 7808.

172 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 81 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	#16839800	C₂	1	1	yes	maximal, characteristic
2	#16839717	C₂	1	1	yes	maximal, characteristic
3	#16839534	C₂	1	2	yes	maximal
4	#16839519	C₂	1	2	yes	maximal
5	C₂×#108×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	1	yes	characteristic
7	#14519736	C₂²	1	2	yes	—
8	#14519736	C₂²	1	1	yes	characteristic
9	#14519711	—	2	1	no	—
10	#14519709	—	2	1	no	—
11	#14519687	C₄	1	2	yes	complemented
12	C₈×Dic₆₁	C₄	1	2	yes	complemented
13	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	#108×C₆₁	—	2	1	no	—
16	#108×C₆₁	—	2	1	no	—
17	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
18	M₁₆×C₆₁	—	2	2	no	—
19	M₁₆×C₆₁	—	2	2	no	—
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
24	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
25	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
26	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
27	C₂²⋊Dic₆₁	—	2	1	no	—
28	C₂²⋊Dic₆₁	—	2	2	no	—
29	C₄⋊Dic₆₁	—	2	1	no	—
30	C₄⋊Dic₆₁	—	2	2	no	—
31	C₄×Dic₆₁	—	2	2	no	—
32	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
33	#11758194	—	2	1	no	—
34	#11758194	—	2	1	no	—
35	C₂×#92418	C₂×C₄	1	2	yes	—
36	C₂³×C₆₁	#41	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
41	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
42	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
43	C₂×Dic₆₁	—	2	2	no	—
44	C₂×Dic₆₁	—	4	2	no	—
45	C₈×C₆₁	—	4	2	no	—
46	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
47	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
48	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
49	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
50	#92418	—	2	2	no	—
51	C₂²×C₆₁	—	4	1	no	—
52	C₂²×C₆₁	#117	1	1	yes	characteristic
53	C₂²×C₆₁	#124	1	1	yes	characteristic
54	C₂²×C₆₁	#125	1	1	yes	characteristic
55	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₄×C₆₁	#117	1	1	yes	characteristic
57	C₄×C₆₁	#124	1	1	yes	characteristic
58	C₄×C₆₁	#125	1	1	yes	characteristic
59	Dic₆₁	—	4	2	no	—
60	Dic₆₁	—	8	2	no	—
61	#1833	—	61	1	no	maximal, Sylow
62	C₂×C₆₁	—	2	1	no	—
63	C₂×C₆₁	—	2	1	no	—
64	C₂×C₆₁	—	2	1	no	—
65	C₂×C₆₁	#382	1	1	yes	characteristic
66	C₂×#108	D₆₁	1	1	yes	characteristic
67	#427	—	61	1	no	—
68	#405	—	61	1	no	—
69	#344	—	61	2	no	—
70	H(3,ℤ/4)	—	61	2	no	—
71	C₆₁	#1833	1	1	yes	characteristic, complemented, Sylow
72	C₂×M₁₆	—	61	1	no	—
73	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
74	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
75	#117	—	61	1	no	—
76	#117	—	61	2	no	—
77	#108	—	2	1	no	—
78	#108	—	2	1	no	—
79	#107	—	122	1	no	—
80	#106	—	122	1	no	—
81	#97	—	61	2	no	—
82	C₄×C₈	—	61	2	no	—
83	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	—	2	2	no	—
86	M₁₆	—	122	1	no	—
87	M₁₆	—	122	1	no	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	61	2	no	—
90	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
91	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
92	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
93	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
94	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
95	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
96	C₄⋊C₄	—	122	1	no	—
97	C₄⋊C₄	—	122	2	no	—
98	C₂²⋊C₄	—	122	1	no	—
99	C₂²⋊C₄	—	122	2	no	—
100	C₄²	—	61	2	no	—
101	C₄²	—	122	2	no	—
102	C₂³	#11758226	1	1	yes	characteristic
103	C₂×C₄	—	122	2	no	—
104	C₂×C₄	—	244	2	no	—
105	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
106	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
107	C₂×C₄	#11758224	1	1	yes	characteristic
108	C₂×C₄	#11758224	1	1	yes	characteristic
109	C₂×C₄	#11758226	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
111	C₈	—	4	2	no	—
112	C₈	—	122	2	no	—
113	C₈	#11758196	1	1	yes	characteristic
114	C₈	#11758196	1	1	yes	characteristic
115	C₈	#11758196	1	1	yes	characteristic
116	C₈	#11758196	1	1	yes	characteristic
117	C₂²	—	4	1	no	—
118	C₂²	#14519735	1	1	yes	characteristic
119	C₂²	#14519766	1	1	yes	characteristic
120	C₂²	#14519768	1	1	yes	characteristic
121	C₄	—	488	2	no	—
122	C₄	—	244	2	no	—
123	C₄	C₂×#11758196	1	1	yes	characteristic
124	C₄	#14519735	1	1	yes	characteristic
125	C₄	#14519764	1	1	yes	characteristic
126	C₄	#14519768	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	2	1	no	—
129	C₂	—	2	1	no	—
130	C₂	#16839627	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839800

C₂

yes

maximal, characteristic

#16839717

C₂

yes

maximal, characteristic

#16839534

C₂

yes

maximal

#16839519

C₂

yes

maximal

C₂×#108×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

characteristic

#14519736

C₂²

yes

—

#14519736

C₂²

yes

—

—

C₄

yes

complemented

C₈×Dic₆₁

C₄

yes

complemented

C₂×M₁₆×C₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#108×C₆₁

—

#108×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₂²⋊Dic₆₁

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

—

#11758194

—

#11758194

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

C₂×C₄⋊C₄

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

—

#1833

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#382

yes

characteristic

C₂×#108

D₆₁

yes

—

—

—

—

C₆₁

#1833

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

—

C₂²×C₈

C₂×D₆₁

yes

—

—

—

—

—

122

—

#106

—

122

—

#97

—

C₄×C₈

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

100

C₄²

—

101

C₄²

—

122

—

102

C₂³

#11758226

yes

characteristic

103

C₂×C₄

—

122

—

104

C₂×C₄

—

244

—

105

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

106

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

107

C₂×C₄

#11758224

yes

characteristic

108

C₂×C₄

#11758224

yes

characteristic

109

C₂×C₄

#11758226

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

111

C₈

—

112

C₈

—

122

—

113

C₈

#11758196

yes

characteristic

114

C₈

#11758196

yes

characteristic

115

C₈

#11758196

yes

characteristic

116

C₈

#11758196

yes

characteristic

117

C₂²

—

118

C₂²

#14519735

yes

characteristic

119

C₂²

#14519766

yes

characteristic

120

C₂²

#14519768

yes

characteristic

121

C₄

—

488

—

122

C₄

—

244

—

123

C₄

C₂×#11758196

yes

characteristic

124

C₄

#14519735

yes

characteristic

125

C₄

#14519764

yes

characteristic

126

C₄

#14519768

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#16839627

yes

characteristic

	subgroup	G/H
center	C₄	#14519735
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#108×C₆₁	C₂
socle	C₂×C₆₁	#382
hypercenter	C₂×#108	D₆₁
hypocenter	C₆₁	#1833
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#14519735

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#108×C₆₁

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
11. #14519687	C₄	semidirect
12. C₈×Dic₆₁	C₄	semidirect
71. C₆₁	#1833	semidirect

H ≅ G/N

type

11. #14519687

C₄

semidirect

12. C₈×Dic₆₁

C₄

semidirect

71. C₆₁

#1833

semidirect

Subgroups — #21445944

Conjugacy classes of subgroups

Complements