Group #21444713 — subgroups

Subgroups — #21444713

Order 7808.

152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 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	#16839893	C₂	1	1	yes	maximal, characteristic
2	#16839889	C₂	1	1	yes	maximal, characteristic
3	C₄×#11758202	C₂	1	1	yes	maximal, characteristic
4	#16839514	C₂	1	1	yes	maximal, characteristic
5	#16839494	C₂	1	1	yes	maximal, characteristic
6	C₈×#92418	C₂	1	1	yes	maximal, characteristic
7	C₆₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×#11758202	C₄	1	1	yes	characteristic
9	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic
10	#14519710	C₄	1	1	yes	characteristic
11	C₄⋊#92418	—	2	1	no	—
12	C₄⋊#92418	C₂²	1	1	yes	characteristic
13	#14519706	—	2	1	no	—
14	#14519701	C₄	1	1	yes	characteristic
15	#14519700	C₄	1	1	yes	characteristic
16	#14519688	—	2	1	no	—
17	#14519687	—	2	1	no	—
18	C₄×#92418	C₂²	1	1	yes	characteristic
19	C₄×#92418	C₂²	1	1	yes	characteristic
20	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₆₁	—	2	1	no	—
26	C₂×C₈×C₆₁	—	2	1	no	—
27	C₄⋊C₄×C₆₁	—	2	1	no	—
28	C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₆₁	—	2	1	no	—
30	C₄²×C₆₁	C₂³	1	1	yes	characteristic
31	#11758202	—	2	2	no	—
32	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
33	#11758196	—	2	1	no	—
34	C₄×Dic₆₁	—	2	1	no	—
35	C₂×#92418	—	2	1	no	—
36	C₂×#92418	C₂×C₄	1	1	yes	characteristic
37	C₂×#92418	C₂×C₄	1	1	yes	characteristic
38	C₂×#92418	D₄	1	1	yes	characteristic
39	C₂×#92418	D₄	1	1	yes	characteristic
40	Q₈×C₆₁	—	2	1	no	—
41	Q₈×C₆₁	—	2	1	no	—
42	C₂×C₄×C₆₁	—	2	1	no	—
43	C₂×C₄×C₆₁	—	2	1	no	—
44	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
47	C₂×Dic₆₁	—	2	1	no	—
48	C₂×Dic₆₁	—	2	1	no	—
49	Dic₁₂₂	—	2	1	no	—
50	Dic₁₂₂	—	2	1	no	—
51	C₈×C₆₁	—	2	2	no	—
52	C₈×C₆₁	—	4	1	no	—
53	#92418	—	2	1	no	—
54	#92418	—	2	1	no	—
55	#92418	—	4	1	no	—
56	#92418	M₁₆	1	2	yes	—
57	#92418	Q₁₆	1	2	yes	complemented
58	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
59	C₄×C₆₁	—	2	1	no	—
60	C₄×C₆₁	—	4	1	no	—
61	C₄×C₆₁	—	4	1	no	—
62	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
63	C₄×C₆₁	#131	1	1	yes	characteristic
64	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
65	C₄×C₆₁	#135	1	1	yes	characteristic
66	Dic₆₁	—	4	1	no	—
67	Dic₆₁	—	4	1	no	—
68	#1591	—	61	1	no	maximal, Sylow
69	C₂×C₆₁	#436	1	1	yes	characteristic
70	C₂×C₆₁	C₄×Q₁₆	1	1	yes	characteristic
71	C₂×C₆₁	#443	1	1	yes	characteristic
72	#446	—	61	1	no	—
73	#446	—	61	1	no	—
74	C₄×Q₁₆	—	61	1	no	—
75	#335	—	61	1	no	—
76	Q₈⋊C₈	—	61	1	no	—
77	Q₈⋊C₈	D₆₁	1	1	yes	characteristic
78	C₈²	—	61	1	no	—
79	C₆₁	#1591	1	1	yes	characteristic, complemented, Sylow
80	C₂×Q₁₆	—	61	1	no	—
81	C₄×Q₈	—	61	1	no	—
82	C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
83	#107	—	61	1	no	—
84	C₄⋊C₈	—	61	1	no	—
85	C₄⋊C₈	—	122	1	no	—
86	C₄⋊C₈	—	122	1	no	—
87	C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
88	#103	—	61	1	no	—
89	#103	—	61	1	no	—
90	#97	—	122	1	no	—
91	#97	—	122	1	no	—
92	C₄×C₈	—	61	1	no	—
93	C₄×C₈	—	61	1	no	—
94	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
95	C₂×Q₈	—	61	1	no	—
96	C₂×Q₈	C₄×D₆₁	1	1	yes	characteristic
97	Q₁₆	—	122	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	61	1	no	—
101	C₂×C₈	—	61	1	no	—
102	C₂×C₈	—	61	1	no	—
103	C₂×C₈	—	61	1	no	—
104	C₂×C₈	—	122	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	61	1	no	—
107	C₄⋊C₄	—	122	1	no	—
108	C₄⋊C₄	C₄×D₆₁	1	1	yes	characteristic
109	C₄²	—	2	1	no	—
110	C₄²	—	122	1	no	—
111	C₄²	C₂²×D₆₁	1	1	yes	characteristic
112	Q₈	—	2	1	no	—
113	Q₈	—	2	1	no	—
114	Q₈	—	122	1	no	—
115	Q₈	—	122	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	122	1	no	—
119	C₂×C₄	—	122	1	no	—
120	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
121	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
122	C₂×C₄	#11758224	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	—	4	1	no	—
125	C₈	—	61	2	no	—
126	C₈	—	61	2	no	—
127	C₈	—	122	1	no	—
128	C₈	—	122	1	no	—
129	C₈	—	244	1	no	—
130	C₂²	#14519737	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	4	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	244	1	no	—
135	C₄	—	244	1	no	—
136	C₄	M₁₆×D₆₁	1	1	yes	characteristic
137	C₄	#14519783	1	1	yes	characteristic
138	C₄	Q₁₆×D₆₁	1	1	yes	characteristic
139	C₄	#14519798	1	1	yes	characteristic
140	C₂	#16839837	1	1	yes	characteristic
141	C₂	#16839854	1	1	yes	characteristic
142	C₂	#16839876	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839893

C₂

yes

maximal, characteristic

#16839889

C₂

yes

maximal, characteristic

C₄×#11758202

C₂

yes

maximal, characteristic

#16839514

C₂

yes

maximal, characteristic

#16839494

C₂

yes

maximal, characteristic

C₈×#92418

C₂

yes

maximal, characteristic

C₆₁×Q₈⋊C₈

C₂

yes

maximal, characteristic

C₂×#11758202

C₄

yes

characteristic

C₄×Dic₁₂₂

C₂²

yes

characteristic

#14519710

C₄

yes

characteristic

C₄⋊#92418

—

C₄⋊#92418

C₂²

yes

characteristic

#14519706

—

#14519701

C₄

yes

characteristic

#14519700

C₄

yes

—

—

C₂²

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₄×Q₈×C₆₁

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

C₂×C₄

yes

characteristic

C₂×Dic₁₂₂

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

#11758202

—

C₄⋊Dic₆₁

C₂×C₄

yes

characteristic

#11758196

—

C₄×Dic₆₁

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

—

—

—

M₁₆

yes

—

#92418

Q₁₆

yes

complemented

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

C₄×C₆₁

C₂×Q₁₆

yes

characteristic

C₄×C₆₁

#135

yes

characteristic

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₄×Q₁₆

yes

C₂×C₆₁

yes

—

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

Q₈⋊C₈

D₆₁

yes

characteristic

C₈²

—

C₆₁

#1591

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

C₄×Q₈

C₂×D₆₁

yes

characteristic

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

C₂×D₆₁

yes

—

—

—

122

—

#97

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×Q₈

C₄×D₆₁

yes

characteristic

Q₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

122

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

122

—

108

C₄⋊C₄

C₄×D₆₁

yes

characteristic

109

C₄²

—

110

C₄²

—

122

—

111

C₄²

C₂²×D₆₁

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

122

—

115

Q₈

—

122

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

122

—

119

C₂×C₄

—

122

—

120

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

121

C₂×C₄

D₄×D₆₁

yes

characteristic

122

C₂×C₄

#11758224

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

122

—

128

C₈

—

122

—

129

C₈

—

244

—

130

C₂²

#14519737

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

244

—

135

C₄

—

244

—

136

C₄

M₁₆×D₆₁

yes

characteristic

137

C₄

#14519783

yes

characteristic

138

C₄

Q₁₆×D₆₁

yes

characteristic

139

C₄

#14519798

yes

characteristic

140

C₂

#16839837

yes

characteristic

141

C₂

#16839854

yes

characteristic

142

C₂

#16839876

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×Q₈⋊C₈	C₂
socle	C₂²×C₆₁	C₄×D₄
hypercenter	Q₈⋊C₈	D₆₁
hypocenter	C₆₁	#1591
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ Q₈⋊C₈

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×Q₈⋊C₈

C₂

socle

C₂²×C₆₁

C₄×D₄

hypercenter

Q₈⋊C₈

D₆₁

hypocenter

C₆₁

#1591

LCS

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ Q₈⋊C₈

N	H ≅ G/N	type
57. #92418	Q₁₆	semidirect
79. C₆₁	#1591	semidirect

H ≅ G/N

type

57. #92418

Q₁₆

semidirect

79. C₆₁

#1591

semidirect

Subgroups — #21444713

Conjugacy classes of subgroups

Complements