Group #21461283 — subgroups

Subgroups — #21461283

Order 7808.

212 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 62 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	#16840783	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758217	C₂	1	1	yes	maximal, characteristic
3	#16840619	C₂	1	4	yes	maximal, complemented
4	C₂×#14519768	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758217	—	2	1	no	—
6	C₄⋊#92420	—	2	1	no	—
7	C₂²⋊#92420	—	2	1	no	—
8	#14519832	C₂²	1	2	yes	—
9	#14519832	C₂²	1	2	yes	—
10	C₄×#92420	—	2	1	no	—
11	#14519768	—	2	1	no	—
12	#14519768	—	2	1	no	—
13	#14519768	C₄	1	2	yes	—
14	#14519768	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₆₁	—	2	1	no	—
16	C₂×C₄⋊Dic₆₁	C₄	1	1	yes	characteristic
17	C₂×#11758196	—	2	1	no	—
18	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
20	C₂²×C₄×C₆₁	—	2	1	no	—
21	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×Dic₆₁	—	2	1	no	—
23	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
24	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
25	#11758217	—	2	4	no	—
26	C₂×#92420	—	2	2	no	—
27	C₂×#92420	—	2	2	no	—
28	C₄⋊C₄×C₆₁	—	2	1	no	—
29	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
30	C₄⋊Dic₆₁	—	2	1	no	—
31	C₄⋊Dic₆₁	—	2	2	no	—
32	C₄⋊Dic₆₁	—	2	2	no	—
33	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
34	#11758196	—	2	2	no	—
35	#11758196	—	2	2	no	—
36	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
37	C₄×Dic₆₁	D₄	1	1	yes	characteristic
38	C₄×Dic₆₁	D₄	1	1	yes	characteristic
39	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
40	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₆₁	—	2	2	no	—
42	C₂×C₄×C₆₁	—	2	2	no	—
43	C₂×C₄×C₆₁	—	4	2	no	—
44	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
46	C₂×Dic₆₁	—	2	2	no	—
47	C₂×Dic₆₁	—	2	2	no	—
48	C₂×Dic₆₁	—	4	1	no	—
49	C₂×Dic₆₁	—	4	2	no	—
50	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
53	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
54	#92420	—	2	4	no	—
55	#92420	—	4	2	no	—
56	C₂²×C₆₁	—	2	1	no	—
57	C₂²×C₆₁	—	2	1	no	—
58	C₂²×C₆₁	#104	1	2	yes	—
59	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₄×C₆₁	—	2	1	no	—
61	C₄×C₆₁	—	4	2	no	—
62	C₄×C₆₁	#101	1	2	yes	—
63	Dic₆₁	—	2	1	no	—
64	Dic₆₁	—	2	1	no	—
65	Dic₆₁	—	2	1	no	—
66	Dic₆₁	—	2	1	no	—
67	Dic₆₁	—	4	2	no	—
68	#1528	—	61	1	no	maximal, Sylow
69	C₂×C₆₁	—	2	2	no	—
70	C₂×C₆₁	C₂×#101	1	1	yes	characteristic
71	C₂×C₆₁	C₂×#104	1	1	yes	characteristic
72	C₂×C₆₁	#421	1	1	yes	characteristic
73	C₂×#125	—	61	1	no	—
74	#432	—	61	1	no	—
75	C₄×M₁₆	—	61	1	no	—
76	#330	—	61	4	no	—
77	C₆₁	#1528	1	1	yes	characteristic, complemented, Sylow
78	C₂×M₁₆	—	122	1	no	—
79	#125	—	61	2	no	—
80	#125	—	61	2	no	—
81	#125	—	122	1	no	—
82	#125	—	122	1	no	—
83	C₂×C₄⋊C₄	—	61	1	no	—
84	C₂×C₄⋊C₄	—	122	1	no	—
85	C₂×C₄⋊C₄	—	122	1	no	—
86	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
87	C₂×C₄²	—	61	1	no	—
88	C₄⋊C₈	—	122	1	no	—
89	C₂²⋊C₈	—	122	1	no	—
90	#97	—	61	2	no	—
91	#97	—	61	2	no	—
92	C₄×C₈	—	122	1	no	—
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	61	1	no	—
95	C₂²×C₄	—	61	1	no	—
96	C₂²×C₄	—	122	1	no	—
97	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
98	M₁₆	—	122	4	no	—
99	C₂×C₈	—	122	2	no	—
100	C₂×C₈	—	122	2	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	61	2	no	—
103	C₄⋊C₄	—	122	2	no	—
104	C₄⋊C₄	—	122	2	no	—
105	C₄⋊C₄	—	122	2	no	—
106	C₄⋊C₄	—	122	2	no	—
107	C₄⋊C₄	—	122	1	no	—
108	C₄⋊C₄	C₂×#6923	1	2	yes	—
109	C₄²	—	61	1	no	—
110	C₄²	—	61	1	no	—
111	C₄²	—	61	1	no	—
112	C₄²	—	61	1	no	—
113	C₂³	C₂²⋊#6923	1	1	yes	characteristic
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	61	1	no	—
118	C₂×C₄	—	61	1	no	—
119	C₂×C₄	—	61	1	no	—
120	C₂×C₄	—	61	1	no	—
121	C₂×C₄	—	122	2	no	—
122	C₂×C₄	—	122	2	no	—
123	C₂×C₄	—	244	1	no	—
124	C₂×C₄	—	244	2	no	—
125	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
126	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
127	C₈	—	122	4	no	—
128	C₈	—	244	2	no	—
129	C₂²	—	2	1	no	—
130	C₂²	—	2	1	no	—
131	C₂²	#14519842	1	2	yes	—
132	C₂²	C₂×C₂²⋊#6923	1	1	yes	characteristic
133	C₄	—	2	1	no	—
134	C₄	—	4	2	no	—
135	C₄	—	122	1	no	—
136	C₄	—	122	1	no	—
137	C₄	—	122	1	no	—
138	C₄	—	122	1	no	—
139	C₄	—	244	2	no	—
140	C₄	#14519838	1	2	yes	—
141	C₂	—	2	2	no	—
142	C₂	C₂×#14519838	1	1	yes	characteristic
143	C₂	C₂×#14519842	1	1	yes	characteristic
144	C₂	#16840760	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840783

C₂

yes

maximal, characteristic

C₄×#11758217

C₂

yes

maximal, characteristic

#16840619

C₂

yes

maximal, complemented

C₂×#14519768

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#14519832

C₂²

yes

—

—

—

—

C₄

yes

—

#14519768

C₂²

yes

—

C₂×C₄⋊Dic₆₁

—

C₂×C₄⋊Dic₆₁

C₄

yes

characteristic

C₂×#11758196

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

—

—

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

#11758196

—

#11758196

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

C₂×D₄

yes

characteristic

#92420

—

#92420

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#104

yes

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#101

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

#1528

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₄×M₁₆

—

#330

—

C₆₁

#1528

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

#125

—

#125

—

#125

—

122

—

#125

—

122

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄⋊C₄

#6923

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

#97

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

122

—

C₂×C₈

—

122

—

100

C₂×C₈

—

122

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

122

—

104

C₄⋊C₄

—

122

—

105

C₄⋊C₄

—

122

—

106

C₄⋊C₄

—

122

—

107

C₄⋊C₄

—

122

—

108

C₄⋊C₄

C₂×#6923

yes

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₂³

C₂²⋊#6923

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

—

122

C₂×C₄

—

122

—

123

C₂×C₄

—

244

—

124

C₂×C₄

—

244

—

125

C₂×C₄

C₂²⋊#6923

yes

characteristic

126

C₂×C₄

C₂²×#6923

yes

characteristic

127

C₈

—

122

—

128

C₈

—

244

—

129

C₂²

—

130

C₂²

—

131

C₂²

#14519842

yes

—

132

C₂²

C₂×C₂²⋊#6923

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

122

—

136

C₄

—

122

—

137

C₄

—

122

—

138

C₄

—

122

—

139

C₄

—

244

—

140

C₄

#14519838

yes

—

141

C₂

—

142

C₂

C₂×#14519838

yes

characteristic

143

C₂

C₂×#14519842

yes

characteristic

144

C₂

#16840760

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#1528
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂²

C₂×C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂×C₄⋊C₄×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₂²⋊C₄

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
3. #16840619	C₂	semidirect
77. C₆₁	#1528	semidirect

H ≅ G/N

type

3. #16840619

C₂

semidirect

77. C₆₁

#1528

semidirect

Subgroups — #21461283

Conjugacy classes of subgroups

Complements