Group #21444566 — subgroups

Subgroups — #21444566

Order 7808.

180 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 85 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	#16839814	C₂	1	2	yes	maximal
2	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839515	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839512	C₂	1	2	yes	maximal, complemented
5	C₆₁×#335	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	C₄×#92418	C₂²	1	1	yes	characteristic
12	C₈×Dic₆₁	—	2	2	no	—
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	C₈	1	4	yes	complemented
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	1	no	—
40	C₄×D₆₁	—	2	1	no	—
41	C₄×D₆₁	—	2	2	no	—
42	C₄×D₆₁	C₂×C₈	1	2	yes	—
43	C₄×D₆₁	M₁₆	1	2	yes	—
44	C₈×C₆₁	—	2	1	no	—
45	C₈×C₆₁	—	4	2	no	—
46	C₈×C₆₁	C₂×C₈	1	2	yes	—
47	#92418	—	2	1	no	—
48	#92418	—	4	2	no	—
49	#92418	C₂×C₈	1	2	yes	—
50	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×D₆₁	—	2	1	no	—
52	C₂×D₆₁	—	2	1	no	—
53	C₂×D₆₁	C₄⋊C₈	1	2	yes	—
54	C₄×C₆₁	—	2	1	no	—
55	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
56	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
57	C₄×C₆₁	#135	1	1	yes	characteristic
58	C₄×C₆₁	#135	1	1	yes	characteristic
59	Dic₆₁	—	2	1	no	—
60	Dic₆₁	C₄⋊C₈	1	2	yes	—
61	Dic₆₁	#108	1	2	yes	—
62	#1564	—	61	1	no	maximal, Sylow
63	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
64	C₂×C₆₁	#427	1	1	yes	characteristic
65	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
66	D₆₁	—	2	2	no	—
67	#431	—	61	2	no	—
68	C₂×C₄×C₈	—	61	1	no	—
69	#335	—	61	1	no	—
70	#335	D₆₁	1	1	yes	characteristic, complemented
71	#334	—	61	2	no	—
72	C₆₁	#1564	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₈	—	61	1	no	—
74	C₂²×C₈	—	61	1	no	—
75	C₂×C₄²	—	61	1	no	—
76	C₄⋊C₈	—	61	2	no	—
77	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
78	C₂²⋊C₈	—	122	2	no	—
79	C₄×C₈	—	61	1	no	—
80	C₄×C₈	—	61	1	no	—
81	C₄×C₈	—	61	1	no	—
82	C₄×C₈	—	122	2	no	—
83	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
84	C₂²×C₄	—	61	1	no	—
85	C₂²×C₄	—	61	1	no	—
86	C₂²×C₄	—	61	1	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	61	1	no	—
89	C₂×C₈	—	61	4	no	—
90	C₂×C₈	—	61	1	no	—
91	C₂×C₈	—	122	2	no	—
92	C₂×C₈	—	122	2	no	—
93	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
94	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
95	C₄²	—	61	1	no	—
96	C₄²	—	61	1	no	—
97	C₄²	—	61	1	no	—
98	C₄²	C₂²×D₆₁	1	1	yes	characteristic
99	C₂³	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	61	1	no	—
102	C₂×C₄	—	61	2	no	—
103	C₂×C₄	—	61	2	no	—
104	C₂×C₄	—	61	1	no	—
105	C₂×C₄	—	122	2	no	—
106	C₂×C₄	—	122	1	no	—
107	C₂×C₄	—	122	1	no	—
108	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
109	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
110	C₂×C₄	Q₈×D₆₁	1	1	yes	characteristic
111	C₈	—	2	1	no	—
112	C₈	—	4	2	no	—
113	C₈	—	61	2	no	—
114	C₈	—	122	1	no	—
115	C₈	—	244	2	no	—
116	C₈	C₈×D₆₁	1	2	yes	—
117	C₂²	—	61	2	no	—
118	C₂²	—	122	1	no	—
119	C₂²	—	122	1	no	—
120	C₂²	C₄⋊C₄×D₆₁	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	61	2	no	—
123	C₄	—	61	2	no	—
124	C₄	—	122	1	no	—
125	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
126	C₄	M₁₆×D₆₁	1	1	yes	characteristic
127	C₄	#14519796	1	1	yes	characteristic
128	C₄	#14519800	1	1	yes	characteristic
129	C₂	—	122	2	no	—
130	C₂	C₄⋊C₈×D₆₁	1	1	yes	characteristic
131	C₂	#16839799	1	1	yes	characteristic
132	C₂	#108×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839814

C₂

yes

maximal

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

#16839515

C₂

yes

maximal, characteristic, complemented

#16839512

C₂

yes

maximal, complemented

C₆₁×#335

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

—

C₄×#92418

C₂²

yes

characteristic

C₈×Dic₆₁

—

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

C₈

yes

complemented

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

C₂×C₈

yes

—

C₄×D₆₁

M₁₆

yes

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

C₂×C₈

yes

—

#92418

—

#92418

—

#92418

C₂×C₈

yes

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₄⋊C₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

C₄⋊C₈

yes

—

Dic₆₁

#108

yes

—

#1564

—

maximal, Sylow

C₂×C₆₁

C₂×C₄⋊C₈

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#431

—

C₂×C₄×C₈

—

#335

—

#335

D₆₁

yes

characteristic, complemented

#334

—

C₆₁

#1564

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₆₁

yes

—

C₂²⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

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

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

122

—

106

C₂×C₄

—

122

—

107

C₂×C₄

—

122

—

108

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

109

C₂×C₄

D₄×D₆₁

yes

characteristic

110

C₂×C₄

Q₈×D₆₁

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

122

—

115

C₈

—

244

—

116

C₈

C₈×D₆₁

yes

—

117

C₂²

—

118

C₂²

—

122

—

119

C₂²

—

122

—

120

C₂²

C₄⋊C₄×D₆₁

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

122

—

125

C₄

C₂×C₈×D₆₁

yes

characteristic

126

C₄

M₁₆×D₆₁

yes

characteristic

127

C₄

#14519796

yes

characteristic

128

C₄

#14519800

yes

characteristic

129

C₂

—

122

—

130

C₂

C₄⋊C₈×D₆₁

yes

characteristic

131

C₂

#16839799

yes

characteristic

132

C₂

#108×D₆₁

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#335	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#335	D₆₁
hypocenter	C₆₁	#1564
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#335

C₂

socle

C₂²×C₆₁

C₂×C₄⋊C₄

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

N	H ≅ G/N	type
3. #16839515	C₂	semidirect
4. #16839512	C₂	semidirect
5. C₆₁×#335	C₂	semidirect
31. C₈×D₆₁	C₈	semidirect
70. #335	D₆₁	semidirect
72. C₆₁	#1564	semidirect

H ≅ G/N

type

3. #16839515

C₂

semidirect

4. #16839512

C₂

semidirect

5. C₆₁×#335

C₂

semidirect

31. C₈×D₆₁

C₈

semidirect

70. #335

D₆₁

semidirect

72. C₆₁

#1564

semidirect

Subgroups — #21444566

Conjugacy classes of subgroups

Complements