Group #21444579 — subgroups

Subgroups — #21444579

Order 7808.

168 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 73 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	#16839818	C₂	1	2	yes	maximal
2	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839514	C₂	1	2	yes	maximal, complemented
4	#16839513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
7	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
8	C₄²×D₆₁	C₂²	1	1	yes	characteristic
9	C₄⋊#92418	C₂²	1	2	yes	—
10	#14519689	—	2	2	no	—
11	#14519687	—	2	2	no	—
12	C₄×#92418	C₂²	1	1	yes	characteristic
13	C₈×Dic₆₁	C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₄	1	1	yes	characteristic
15	C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
19	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
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	C₄²×C₆₁	C₂³	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	2	no	—
28	C₂×#92418	C₂×C₄	1	1	yes	characteristic
29	C₂×#92418	C₂×C₄	1	1	yes	characteristic
30	C₈×D₆₁	—	2	2	no	—
31	C₈×D₆₁	—	2	2	no	—
32	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
36	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₆₁	—	2	2	no	—
40	C₄×D₆₁	—	2	1	no	—
41	C₄×D₆₁	—	2	1	no	—
42	C₄×D₆₁	—	2	2	no	—
43	C₈×C₆₁	—	2	1	no	—
44	C₈×C₆₁	—	4	2	no	—
45	C₈×C₆₁	M₁₆	1	2	yes	—
46	#92418	—	2	1	no	—
47	#92418	—	4	2	no	—
48	#92418	M₁₆	1	2	yes	—
49	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×D₆₁	—	2	1	no	—
51	C₂×D₆₁	—	2	1	no	—
52	C₂×D₆₁	#108	1	2	yes	—
53	C₄×C₆₁	—	2	1	no	—
54	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
55	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
56	C₄×C₆₁	#135	1	2	yes	—
57	Dic₆₁	—	2	1	no	—
58	Dic₆₁	—	2	1	no	—
59	Dic₆₁	—	2	1	no	—
60	#1568	—	61	1	no	maximal, Sylow
61	C₂×C₆₁	#423	1	1	yes	characteristic
62	C₂×C₆₁	#427	1	1	yes	characteristic
63	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
64	D₆₁	—	2	2	no	—
65	#432	—	61	2	no	—
66	C₂×C₄×C₈	—	61	1	no	—
67	#335	—	61	2	no	—
68	#334	—	61	1	no	—
69	#334	D₆₁	1	1	yes	characteristic, complemented
70	C₆₁	#1568	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₈	—	61	1	no	—
72	C₂²×C₈	—	61	1	no	—
73	C₂×C₄²	—	61	1	no	—
74	C₄⋊C₈	—	61	2	no	—
75	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
76	C₂²⋊C₈	—	122	2	no	—
77	#97	—	122	2	no	—
78	C₄×C₈	—	61	1	no	—
79	C₄×C₈	—	61	1	no	—
80	C₄×C₈	—	61	1	no	—
81	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
82	C₂²×C₄	—	61	1	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	61	1	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	61	1	no	—
87	C₂×C₈	—	61	1	no	—
88	C₂×C₈	—	122	2	no	—
89	C₂×C₈	—	122	2	no	—
90	C₂×C₈	—	122	2	no	—
91	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
92	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
93	C₄²	—	61	1	no	—
94	C₄²	—	61	1	no	—
95	C₄²	—	61	1	no	—
96	C₄²	C₂²×D₆₁	1	1	yes	characteristic
97	C₂³	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	122	2	no	—
102	C₂×C₄	—	122	1	no	—
103	C₂×C₄	—	122	1	no	—
104	C₂×C₄	—	122	2	no	—
105	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
106	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
107	C₂×C₄	Q₈×D₆₁	1	1	yes	characteristic
108	C₈	—	2	1	no	—
109	C₈	—	4	2	no	—
110	C₈	—	61	2	no	—
111	C₈	—	122	1	no	—
112	C₈	—	244	2	no	—
113	C₈	#11758189	1	2	yes	—
114	C₂²	—	61	2	no	—
115	C₂²	—	122	1	no	—
116	C₂²	—	122	1	no	—
117	C₂²	C₄⋊C₄×D₆₁	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	122	1	no	—
120	C₄	—	122	1	no	—
121	C₄	—	122	1	no	—
122	C₄	M₁₆×D₆₁	1	1	yes	characteristic
123	C₄	C₂×#11758189	1	1	yes	characteristic
124	C₄	#14519798	1	2	yes	—
125	C₂	—	122	2	no	—
126	C₂	#16839784	1	1	yes	characteristic
127	C₂	#16839797	1	1	yes	characteristic
128	C₂	#108×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839818

C₂

yes

maximal

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

#16839514

C₂

yes

maximal, complemented

#16839513

C₂

yes

maximal, characteristic, complemented

C₆₁×#334

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₄

yes

characteristic

C₄²×D₆₁

C₂²

yes

characteristic

C₄⋊#92418

C₂²

yes

—

#14519689

—

#14519687

—

C₄×#92418

C₂²

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₄⋊C₈×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂³

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

—

C₈×D₆₁

—

C₂²×D₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

—

#92418

—

#92418

—

#92418

M₁₆

yes

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

#108

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

#135

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#432

—

C₂×C₄×C₈

—

#335

—

#334

—

#334

D₆₁

yes

characteristic, complemented

C₆₁

#1568

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₆₁

yes

—

C₂²⋊C₈

—

122

—

#97

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

122

—

102

C₂×C₄

—

122

—

103

C₂×C₄

—

122

—

104

C₂×C₄

—

122

—

105

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

106

C₂×C₄

D₄×D₆₁

yes

characteristic

107

C₂×C₄

Q₈×D₆₁

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

122

—

112

C₈

—

244

—

113

C₈

#11758189

yes

—

114

C₂²

—

115

C₂²

—

122

—

116

C₂²

—

122

—

117

C₂²

C₄⋊C₄×D₆₁

yes

characteristic

118

C₄

—

119

C₄

—

122

—

120

C₄

—

122

—

121

C₄

—

122

—

122

C₄

M₁₆×D₆₁

yes

characteristic

123

C₄

C₂×#11758189

yes

characteristic

124

C₄

#14519798

yes

—

125

C₂

—

122

—

126

C₂

#16839784

yes

characteristic

127

C₂

#16839797

yes

characteristic

128

C₂

#108×D₆₁

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#334	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#334	D₆₁
hypocenter	C₆₁	#1568
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#334

C₂

socle

C₂²×C₆₁

C₂×C₄⋊C₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

N	H ≅ G/N	type
3. #16839514	C₂	semidirect
4. #16839513	C₂	semidirect
5. C₆₁×#334	C₂	semidirect
69. #334	D₆₁	semidirect
70. C₆₁	#1568	semidirect

H ≅ G/N

type

3. #16839514

C₂

semidirect

4. #16839513

C₂

semidirect

5. C₆₁×#334

C₂

semidirect

69. #334

D₆₁

semidirect

70. C₆₁

#1568

semidirect

Subgroups — #21444579

Conjugacy classes of subgroups

Complements