Group #21447576 — subgroups

Subgroups — #21447576

Order 7808.

160 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 79 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	C₂×#14519716	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839716	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#11758185	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839580	C₂	1	1	yes	maximal, characteristic, complemented
6	#16839580	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11758189	C₄	1	1	yes	characteristic
9	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
10	#14519734	C₄	1	1	yes	characteristic
11	#14519716	—	2	2	no	—
12	C₂×#11758185	C₂²	1	1	yes	characteristic
13	C₂×#11758185	C₂²	1	1	yes	characteristic
14	C₁₆×D₆₁	—	2	2	no	—
15	#14519688	C₄	1	1	yes	characteristic
16	#14519687	C₄	1	1	yes	characteristic
17	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
24	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
25	#11758198	C₈	1	1	yes	characteristic
26	#11758198	C₈	1	1	yes	characteristic
27	#11758196	C₈	1	1	yes	characteristic
28	#11758196	C₈	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
30	C₂×#92418	C₂×C₄	1	1	yes	characteristic
31	C₂×#92418	C₂×C₄	1	1	yes	characteristic
32	#11758189	—	2	2	no	—
33	C₈×D₆₁	D₄	1	2	yes	—
34	C₈×D₆₁	Q₈	1	2	yes	—
35	C₁₆×C₆₁	—	2	1	no	—
36	C₁₆×C₆₁	—	2	1	no	—
37	#11758185	—	2	1	no	—
38	#11758185	—	2	1	no	—
39	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
40	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
42	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
44	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
45	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
46	C₄×D₆₁	C₄⋊C₄	1	2	yes	—
47	C₄×D₆₁	M₁₆	1	2	yes	—
48	C₈×C₆₁	—	2	1	no	—
49	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
50	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
51	#92418	—	2	1	no	—
52	#92418	C₄⋊C₄	1	2	yes	—
53	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
54	C₂×D₆₁	—	2	1	no	—
55	C₂×D₆₁	—	2	1	no	—
56	C₂×D₆₁	C₄⋊C₈	1	2	yes	—
57	C₄×C₆₁	—	2	1	no	—
58	C₄×C₆₁	—	2	1	no	—
59	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
61	Dic₆₁	—	2	1	no	—
62	Dic₆₁	—	2	1	no	—
63	Dic₆₁	C₄⋊C₈	1	2	yes	—
64	#2151	—	61	1	no	maximal, Sylow
65	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₆₁	#504	1	1	yes	characteristic
67	C₂×C₆₁	#504	1	1	yes	characteristic
68	D₆₁	—	2	2	no	—
69	C₂×M₃₂	—	61	1	no	—
70	C₂²×C₁₆	—	61	1	no	—
71	#405	—	61	1	no	—
72	C₄⋊C₁₆	—	61	1	no	—
73	C₄⋊C₁₆	—	61	1	no	—
74	C₄⋊C₁₆	—	61	1	no	—
75	C₄⋊C₁₆	D₆₁	1	1	yes	characteristic, complemented
76	C₆₁	#2151	1	1	yes	characteristic, complemented, Sylow
77	C₂×M₁₆	—	61	1	no	—
78	C₂²×C₈	—	61	1	no	—
79	#117	—	61	1	no	—
80	M₃₂	—	122	2	no	—
81	C₂×C₁₆	—	61	1	no	—
82	C₂×C₁₆	—	61	1	no	—
83	C₂×C₁₆	—	122	2	no	—
84	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
85	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
86	#97	—	61	1	no	—
87	#97	—	61	1	no	—
88	C₄×C₈	—	61	1	no	—
89	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
90	C₂²×C₄	—	61	1	no	—
91	M₁₆	—	122	2	no	—
92	C₂×C₈	—	61	1	no	—
93	C₂×C₈	—	61	2	no	—
94	C₂×C₈	—	61	2	no	—
95	C₂×C₈	—	61	1	no	—
96	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
97	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
98	C₄⋊C₄	—	61	1	no	—
99	C₄⋊C₄	—	61	1	no	—
100	C₂²⋊C₄	—	61	1	no	—
101	C₂²⋊C₄	—	61	1	no	—
102	C₄²	—	61	1	no	—
103	C₄²	C₄×D₆₁	1	1	yes	characteristic
104	C₁₆	—	2	1	no	—
105	C₁₆	—	2	1	no	—
106	C₁₆	—	122	1	no	—
107	C₁₆	—	122	1	no	—
108	C₂³	—	61	1	no	—
109	C₂×C₄	—	61	1	no	—
110	C₂×C₄	—	61	2	no	—
111	C₂×C₄	—	61	2	no	—
112	C₂×C₄	—	61	1	no	—
113	C₂×C₄	—	61	1	no	—
114	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
115	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
116	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
117	C₈	—	2	1	no	—
118	C₈	—	61	2	no	—
119	C₈	—	122	1	no	—
120	C₈	D₄×D₆₁	1	1	yes	characteristic
121	C₈	Q₈×D₆₁	1	1	yes	characteristic
122	C₂²	—	61	2	no	—
123	C₂²	—	122	1	no	—
124	C₂²	—	122	1	no	—
125	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
126	C₄	—	2	1	no	—
127	C₄	—	2	1	no	—
128	C₄	—	61	2	no	—
129	C₄	—	122	1	no	—
130	C₄	—	122	1	no	—
131	C₄	C₄⋊C₄×D₆₁	1	1	yes	characteristic
132	C₄	M₁₆×D₆₁	1	1	yes	characteristic
133	C₂	—	122	2	no	—
134	C₂	C₄⋊C₈×D₆₁	1	1	yes	characteristic
135	C₂	#16840178	1	1	yes	characteristic
136	C₂	#16840180	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519716

C₂

yes

maximal, characteristic

C₂×C₁₆×D₆₁

C₂

yes

maximal, characteristic

#16839716

C₂

yes

maximal, characteristic

C₄⋊#11758185

C₂

yes

maximal, characteristic, complemented

#16839580

C₂

yes

maximal, characteristic, complemented

#16839580

C₂

yes

maximal, characteristic, complemented

C₆₁×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×#11758189

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519734

C₄

yes

characteristic

#14519716

—

C₂×#11758185

C₂²

yes

characteristic

C₂×#11758185

C₂²

yes

characteristic

C₁₆×D₆₁

—

#14519688

C₄

yes

characteristic

#14519687

C₄

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×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

C₈

yes

characteristic

#11758198

C₈

yes

characteristic

#11758196

C₈

yes

characteristic

#11758196

C₈

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

Q₈

yes

—

C₁₆×C₆₁

—

C₁₆×C₆₁

—

#11758185

—

#11758185

—

C₂²×D₆₁

C₂×C₈

yes

characteristic

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

C₄×D₆₁

C₄⋊C₄

yes

—

C₄×D₆₁

M₁₆

yes

—

C₈×C₆₁

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

#92418

—

#92418

C₄⋊C₄

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₄⋊C₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

C₄⋊C₈

yes

—

#2151

—

maximal, Sylow

C₂×C₆₁

C₂×C₄⋊C₈

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

D₆₁

yes

characteristic, complemented

C₆₁

#2151

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₂×C₁₆

C₂×D₆₁

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₄²

C₄×D₆₁

yes

characteristic

104

C₁₆

—

105

C₁₆

—

106

C₁₆

—

122

—

107

C₁₆

—

122

—

108

C₂³

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₈×D₆₁

yes

characteristic

115

C₂×C₄

C₈×D₆₁

yes

characteristic

116

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

122

—

120

C₈

D₄×D₆₁

yes

characteristic

121

C₈

Q₈×D₆₁

yes

characteristic

122

C₂²

—

123

C₂²

—

122

—

124

C₂²

—

122

—

125

C₂²

C₂×C₈×D₆₁

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

122

—

130

C₄

—

122

—

131

C₄

C₄⋊C₄×D₆₁

yes

characteristic

132

C₄

M₁₆×D₆₁

yes

characteristic

133

C₂

—

122

—

134

C₂

C₄⋊C₈×D₆₁

yes

characteristic

135

C₂

#16840178

yes

characteristic

136

C₂

#16840180

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	#2151
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
4. C₄⋊#11758185	C₂	semidirect
5. #16839580	C₂	semidirect
6. #16839580	C₂	semidirect
7. C₆₁×C₄⋊C₁₆	C₂	semidirect
75. C₄⋊C₁₆	D₆₁	semidirect
76. C₆₁	#2151	semidirect

H ≅ G/N

type

4. C₄⋊#11758185

C₂

semidirect

5. #16839580

C₂

semidirect

6. #16839580

C₂

semidirect

7. C₆₁×C₄⋊C₁₆

C₂

semidirect

75. C₄⋊C₁₆

D₆₁

semidirect

76. C₆₁

#2151

semidirect

Subgroups — #21447576

Conjugacy classes of subgroups

Complements