Group #21461464 — subgroups

Subgroups — #21461464

Order 7808.

148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 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	#16840813	C₂	1	1	yes	maximal, characteristic
2	#16840812	C₂	1	1	yes	maximal, characteristic
3	#16840624	C₂	1	1	yes	maximal, characteristic
4	#16840612	C₂	1	1	yes	maximal, characteristic
5	Q₈⋊#92420	C₂	1	1	yes	maximal, characteristic
6	#16840603	C₂	1	1	yes	maximal, characteristic
7	#16839854	C₂	1	1	yes	maximal, characteristic
8	#14519844	—	2	1	no	—
9	C₄⋊#92420	—	2	1	no	—
10	C₄⋊#92420	C₂²	1	1	yes	characteristic
11	C₄⋊#92420	C₂²	1	1	yes	characteristic
12	#14519832	—	2	1	no	—
13	#14519832	—	2	1	no	—
14	C₄×#92420	C₂²	1	1	yes	characteristic
15	C₄×#92420	C₂²	1	1	yes	characteristic
16	C₂×#11758202	C₄	1	1	yes	characteristic
17	Q₈×Dic₆₁	C₂²	1	1	yes	characteristic
18	#14519742	C₂²	1	1	yes	characteristic
19	#14519710	C₄	1	1	yes	characteristic
20	#14519702	C₄	1	1	yes	characteristic
21	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
22	#103×C₆₁	C₄	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×#92420	—	2	1	no	—
26	C₂×#92420	—	2	1	no	—
27	C₂×#92420	—	2	1	no	—
28	C₂×#92420	D₄	1	1	yes	characteristic
29	C₂×#92420	D₄	1	1	yes	characteristic
30	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
31	C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
32	#11758202	—	2	2	no	—
33	C₄⋊Dic₆₁	—	2	1	no	—
34	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
35	#11758196	—	2	1	no	—
36	C₄×Dic₆₁	—	2	1	no	—
37	C₄×Dic₆₁	—	2	1	no	—
38	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
39	C₂×#92418	C₂×C₄	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×Dic₆₁	—	2	1	no	—
46	C₂×Dic₆₁	—	2	1	no	—
47	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₆₁	#41	1	1	yes	characteristic
49	Dic₁₂₂	—	2	1	no	—
50	Dic₁₂₂	—	2	1	no	—
51	#92420	—	2	1	no	—
52	#92420	—	2	1	no	—
53	#92420	—	4	1	no	—
54	#92420	—	4	1	no	—
55	#92420	—	4	1	no	—
56	C₈×C₆₁	—	2	1	no	—
57	#92418	M₁₆	1	2	yes	—
58	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
59	C₄×C₆₁	—	4	1	no	—
60	C₄×C₆₁	—	4	1	no	—
61	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
62	C₄×C₆₁	#131	1	1	yes	characteristic
63	Dic₆₁	—	2	1	no	—
64	Dic₆₁	—	4	1	no	—
65	Dic₆₁	—	4	1	no	—
66	Dic₆₁	#137	1	1	yes	characteristic
67	Dic₆₁	#137	1	1	yes	characteristic
68	#1593	—	61	1	no	maximal, Sylow
69	C₂×C₆₁	#436	1	1	yes	characteristic
70	C₂×C₆₁	#441	1	1	yes	characteristic
71	C₂×C₆₁	#444	1	1	yes	characteristic
72	#446	—	61	1	no	—
73	#446	—	61	1	no	—
74	C₄×Q₁₆	—	61	1	no	—
75	#334	—	61	1	no	—
76	Q₈⋊C₈	—	61	1	no	—
77	Q₈⋊C₈	—	61	1	no	—
78	#322	—	61	1	no	—
79	C₆₁	#1593	1	1	yes	characteristic, complemented, Sylow
80	C₂×Q₁₆	—	61	1	no	—
81	C₄×Q₈	—	61	1	no	—
82	C₄×Q₈	—	61	1	no	—
83	#107	—	61	1	no	—
84	C₄⋊C₈	—	61	1	no	—
85	C₄⋊C₈	—	61	1	no	—
86	C₄⋊C₈	—	122	1	no	—
87	C₄⋊C₈	—	122	1	no	—
88	#103	—	61	1	no	—
89	#103	#6923	1	1	yes	characteristic
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	—	61	1	no	—
95	C₂×Q₈	—	61	1	no	—
96	C₂×Q₈	C₂×#6923	1	1	yes	characteristic
97	Q₁₆	—	122	2	no	—
98	C₂×C₈	—	61	1	no	—
99	C₂×C₈	—	61	1	no	—
100	C₂×C₈	—	61	1	no	—
101	C₂×C₈	—	122	1	no	—
102	C₂×C₈	—	122	1	no	—
103	C₂×C₈	—	122	1	no	—
104	C₂×C₈	C₂×#6923	1	1	yes	characteristic
105	C₄⋊C₄	—	61	1	no	—
106	C₄⋊C₄	—	122	1	no	—
107	C₄⋊C₄	—	122	1	no	—
108	C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
109	C₄²	—	61	1	no	—
110	C₄²	—	122	1	no	—
111	C₄²	—	122	1	no	—
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	—	61	1	no	—
119	C₂×C₄	—	61	1	no	—
120	C₂×C₄	—	122	1	no	—
121	C₂×C₄	—	122	1	no	—
122	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	61	2	no	—
125	C₈	—	122	1	no	—
126	C₈	—	122	1	no	—
127	C₈	—	244	1	no	—
128	C₈	—	244	1	no	—
129	C₈	—	244	1	no	—
130	C₂²	D₄×#6923	1	1	yes	characteristic
131	C₄	—	4	1	no	—
132	C₄	—	4	1	no	—
133	C₄	—	61	1	no	—
134	C₄	—	61	1	no	—
135	C₄	—	122	1	no	—
136	C₄	—	244	1	no	—
137	C₄	—	244	1	no	—
138	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
139	C₄	#14519864	1	1	yes	characteristic
140	C₂	#16840795	1	1	yes	characteristic
141	C₂	#16840802	1	1	yes	characteristic
142	C₂	#16840807	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840813

C₂

yes

maximal, characteristic

#16840812

C₂

yes

maximal, characteristic

#16840624

C₂

yes

maximal, characteristic

#16840612

C₂

yes

maximal, characteristic

Q₈⋊#92420

C₂

yes

maximal, characteristic

#16840603

C₂

yes

maximal, characteristic

#16839854

C₂

yes

maximal, characteristic

#14519844

—

C₄⋊#92420

—

C₄⋊#92420

C₂²

yes

characteristic

C₄⋊#92420

C₂²

yes

—

—

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

characteristic

C₂×#11758202

C₄

yes

characteristic

Q₈×Dic₆₁

C₂²

yes

characteristic

#14519742

C₂²

yes

characteristic

#14519710

C₄

yes

characteristic

#14519702

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

#103×C₆₁

C₄

yes

characteristic

C₂×Q₈×C₆₁

C₂×C₄

yes

characteristic

C₂×Dic₁₂₂

C₂×C₄

yes

—

—

—

D₄

yes

characteristic

C₂×#92420

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

C₂×C₄

yes

characteristic

#11758202

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

characteristic

#11758196

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

#41

yes

characteristic

Dic₁₂₂

—

Dic₁₂₂

—

—

—

—

—

—

C₈×C₆₁

—

#92418

M₁₆

yes

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

Q₈⋊C₈

—

#322

—

C₆₁

#1593

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

—

yes

—

122

—

#97

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

C₂×#6923

yes

characteristic

Q₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

122

—

102

C₂×C₈

—

122

—

103

C₂×C₈

—

122

—

104

C₂×C₈

C₂×#6923

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

122

—

107

C₄⋊C₄

—

122

—

108

C₄⋊C₄

C₂×#6923

yes

characteristic

109

C₄²

—

110

C₄²

—

122

—

111

C₄²

—

122

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

122

—

115

Q₈

—

122

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

122

—

121

C₂×C₄

—

122

—

122

C₂×C₄

C₂²×#6923

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

122

—

126

C₈

—

122

—

127

C₈

—

244

—

128

C₈

—

244

—

129

C₈

—

244

—

130

C₂²

D₄×#6923

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

122

—

136

C₄

—

244

—

137

C₄

—

244

—

138

C₄

D₆₁⋊M₁₆

yes

characteristic

139

C₄

#14519864

yes

characteristic

140

C₂

#16840795

yes

characteristic

141

C₂

#16840802

yes

characteristic

142

C₂

#16840807

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#103×C₆₁	C₄
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#103	#6923
hypocenter	C₆₁	#1593
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

subgroup

G/H

center

C₂²

D₄×#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#103×C₆₁

C₄

socle

C₂²×C₆₁

C₄×D₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

N	H ≅ G/N	type
79. C₆₁	#1593	semidirect

H ≅ G/N

type

79. C₆₁

#1593

semidirect

Subgroups — #21461464

Conjugacy classes of subgroups

Complements