Group #21446626 — subgroups

Subgroups — #21446626

Order 7808.

436 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14519698	C₂	1	4	yes	maximal, complemented
2	C₂×C₄×#92418	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839632	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#127×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₆₁	—	2	2	no	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	#14519698	—	2	8	no	—
9	C₄×#92418	—	2	2	no	—
10	C₂²×D₄×C₆₁	—	2	2	no	—
11	C₂²×D₄×C₆₁	C₂²	1	2	yes	—
12	#127×C₆₁	—	2	2	no	—
13	#127×C₆₁	C₄	1	4	yes	complemented
14	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₆₁	—	2	2	no	—
16	C₂×D₄×C₆₁	—	2	8	no	—
17	C₂×D₄×C₆₁	—	2	4	no	—
18	C₂×D₄×C₆₁	—	2	2	no	—
19	C₂×D₄×C₆₁	—	2	4	no	—
20	C₂×D₄×C₆₁	—	4	4	no	—
21	C₂×D₄×C₆₁	—	4	4	no	—
22	C₂×D₄×C₆₁	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₆₁	D₄	1	2	yes	—
24	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
25	C₂²×Dic₆₁	—	2	2	no	—
26	C₄²×C₆₁	C₂×C₄	1	2	yes	—
27	C₄²×C₆₁	D₄	1	2	yes	—
28	C₄⋊Dic₆₁	—	2	4	no	—
29	C₄⋊Dic₆₁	—	4	4	no	—
30	C₂×#92418	—	2	2	no	—
31	C₂×#92418	—	2	2	no	—
32	C₂×#92418	D₄	1	4	yes	complemented
33	C₂³×C₆₁	—	2	4	no	—
34	C₂³×C₆₁	—	4	2	no	—
35	C₂³×C₆₁	—	4	2	no	—
36	C₂³×C₆₁	—	4	4	no	—
37	C₂³×C₆₁	—	4	4	no	—
38	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
39	D₄×C₆₁	—	2	8	no	—
40	D₄×C₆₁	—	4	16	no	—
41	D₄×C₆₁	—	4	4	no	—
42	C₂×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
43	C₂×C₄×C₆₁	D₈	1	4	yes	—
44	C₂×C₄×C₆₁	SD₁₆	1	4	yes	—
45	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₆₁	#41	1	2	yes	—
49	C₂×Dic₆₁	—	4	2	no	—
50	C₂×Dic₆₁	—	4	4	no	—
51	#92418	—	2	4	no	—
52	C₂²×C₆₁	—	4	4	no	—
53	C₂²×C₆₁	—	4	8	no	—
54	C₂²×C₆₁	—	8	4	no	—
55	C₂²×C₆₁	—	8	2	no	—
56	C₂²×C₆₁	—	8	2	no	—
57	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₆₁	#124	1	1	yes	characteristic
59	C₂²×C₆₁	#127	1	1	yes	characteristic
60	C₂²×C₆₁	C₂×D₈	1	2	yes	—
61	C₂²×C₆₁	C₂×SD₁₆	1	2	yes	—
62	C₄×C₆₁	#102	1	8	yes	complemented
63	C₄×C₆₁	C₄×D₄	1	2	yes	—
64	C₄×C₆₁	#121	1	2	yes	—
65	Dic₆₁	—	8	2	no	—
66	#1957	—	61	1	no	maximal, Sylow
67	C₂×C₆₁	—	8	4	no	—
68	C₂×C₆₁	#390	1	1	yes	characteristic
69	C₂×C₆₁	C₂×#102	1	2	yes	—
70	C₂×C₆₁	#486	1	2	yes	—
71	C₂×C₆₁	#492	1	1	yes	characteristic
72	C₂×C₆₁	#493	1	1	yes	characteristic
73	C₂×#127	D₆₁	1	1	yes	characteristic
74	C₂×#102	—	61	4	no	—
75	C₂×C₄×C₈	—	61	1	no	—
76	#384	—	61	1	no	—
77	C₆₁	#1957	1	1	yes	characteristic, complemented, Sylow
78	C₂²×D₄	—	2	2	no	—
79	C₂²×D₄	C₂×D₆₁	1	2	yes	—
80	C₂²×C₈	—	61	2	no	—
81	#127	—	2	2	no	—
82	#127	Dic₆₁	1	4	yes	complemented
83	C₂×C₄⋊C₄	—	61	2	no	—
84	C₂×C₄⋊C₄	—	122	2	no	—
85	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
86	#102	—	122	8	no	—
87	C₄×C₈	—	122	2	no	—
88	C₂⁴	—	2	2	no	—
89	C₂×D₄	—	2	8	no	—
90	C₂×D₄	—	2	4	no	—
91	C₂×D₄	—	2	4	no	—
92	C₂×D₄	—	2	2	no	—
93	C₂×D₄	—	4	4	no	—
94	C₂×D₄	—	4	4	no	—
95	C₂×D₄	C₂×Dic₆₁	1	4	yes	—
96	C₂²×C₄	—	122	2	no	—
97	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
98	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
99	C₂×C₈	—	61	4	no	—
100	C₂×C₈	—	122	2	no	—
101	C₂×C₈	—	122	2	no	—
102	C₄⋊C₄	—	122	4	no	—
103	C₄⋊C₄	—	244	4	no	—
104	C₄²	C₂×Dic₆₁	1	2	yes	—
105	C₄²	C₂²⋊D₆₁	1	2	yes	—
106	C₂³	—	2	4	no	—
107	C₂³	—	4	2	no	—
108	C₂³	—	4	2	no	—
109	C₂³	—	4	4	no	—
110	C₂³	—	4	4	no	—
111	C₂³	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
112	D₄	—	2	8	no	—
113	D₄	—	4	16	no	—
114	D₄	—	4	4	no	—
115	C₂×C₄	—	244	2	no	—
116	C₂×C₄	—	244	4	no	—
117	C₂×C₄	#11758199	1	4	yes	—
118	C₂×C₄	#11758200	1	4	yes	—
119	C₂×C₄	C₂²⋊Dic₆₁	1	4	yes	—
120	C₂×C₄	D₄×D₆₁	1	2	yes	—
121	C₂×C₄	#11758224	1	2	yes	—
122	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
123	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
124	C₈	—	122	4	no	—
125	C₂²	—	4	8	no	—
126	C₂²	—	4	4	no	—
127	C₂²	—	8	4	no	—
128	C₂²	—	8	2	no	—
129	C₂²	—	8	2	no	—
130	C₂²	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
131	C₂²	#14519764	1	1	yes	characteristic
132	C₂²	#14519773	1	1	yes	characteristic
133	C₂²	C₂×#11758199	1	2	yes	—
134	C₂²	C₂×#11758200	1	2	yes	—
135	C₄	—	488	2	no	—
136	C₄	#14519698	1	8	yes	complemented
137	C₄	D₄×Dic₆₁	1	2	yes	—
138	C₄	#14519748	1	2	yes	—
139	C₂	—	8	4	no	—
140	C₂	#16839665	1	1	yes	characteristic
141	C₂	C₂×#14519698	1	2	yes	—
142	C₂	#16840108	1	2	yes	—
143	C₂	#16840134	1	1	yes	characteristic
144	C₂	#16840138	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519698

C₂

yes

maximal, complemented

C₂×C₄×#92418

C₂

yes

maximal, characteristic, complemented

#16839632

C₂

yes

maximal, characteristic, complemented

C₂×#127×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₂²

yes

—

C₂×C₄⋊Dic₆₁

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519698

—

C₄×#92418

—

C₂²×D₄×C₆₁

—

C₂²×D₄×C₆₁

C₂²

yes

—

#127×C₆₁

—

#127×C₆₁

C₄

yes

complemented

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂⁴×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

D₄

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

D₄

yes

complemented

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

D₄×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

D₈

yes

—

C₂×C₄×C₆₁

SD₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

C₂×D₈

yes

—

C₂²×C₆₁

C₂×SD₁₆

yes

—

C₄×C₆₁

#102

yes

complemented

C₄×C₆₁

C₄×D₄

yes

—

C₄×C₆₁

#121

yes

—

Dic₆₁

—

#1957

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#390

yes

characteristic

C₂×C₆₁

C₂×#102

yes

—

C₂×C₆₁

#486

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

yes

characteristic

C₂×#102

—

C₂×C₄×C₈

—

#384

—

C₆₁

#1957

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

C₂×D₆₁

yes

—

C₂²×C₈

—

#127

—

#127

Dic₆₁

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

#102

—

122

—

C₄×C₈

—

122

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₆₁

yes

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²⋊D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

122

—

101

C₂×C₈

—

122

—

102

C₄⋊C₄

—

122

—

103

C₄⋊C₄

—

244

—

104

C₄²

C₂×Dic₆₁

yes

—

105

C₄²

C₂²⋊D₆₁

yes

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

C₂×C₂²⋊D₆₁

yes

characteristic

112

D₄

—

113

D₄

—

114

D₄

—

115

C₂×C₄

—

244

—

116

C₂×C₄

—

244

—

117

C₂×C₄

#11758199

yes

—

118

C₂×C₄

#11758200

yes

—

119

C₂×C₄

C₂²⋊Dic₆₁

yes

—

120

C₂×C₄

D₄×D₆₁

yes

—

121

C₂×C₄

#11758224

yes

—

122

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

123

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

124

C₈

—

122

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

C₂×C₂²⋊Dic₆₁

yes

characteristic

131

C₂²

#14519764

yes

characteristic

132

C₂²

#14519773

yes

characteristic

133

C₂²

C₂×#11758199

yes

—

134

C₂²

C₂×#11758200

yes

—

135

C₄

—

488

—

136

C₄

#14519698

yes

complemented

137

C₄

D₄×Dic₆₁

yes

—

138

C₄

#14519748

yes

—

139

C₂

—

140

C₂

#16839665

yes

characteristic

141

C₂

C₂×#14519698

yes

—

142

C₂

#16840108

yes

—

143

C₂

#16840134

yes

characteristic

144

C₂

#16840138

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#127×C₆₁	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	C₂×#127	D₆₁
hypocenter	C₆₁	#1957
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#127×C₆₁

C₂

socle

C₂³×C₆₁

C₂×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×#14519698	C₂	semidirect
2. C₂×C₄×#92418	C₂	semidirect
3. #16839632	C₂	semidirect
13. #127×C₆₁	C₄	semidirect
32. C₂×#92418	D₄	semidirect
62. C₄×C₆₁	#102	semidirect
77. C₆₁	#1957	semidirect
82. #127	Dic₆₁	semidirect
136. C₄	#14519698	semidirect

H ≅ G/N

type

1. C₂×#14519698

C₂

semidirect

2. C₂×C₄×#92418

C₂

semidirect

3. #16839632

C₂

semidirect

13. #127×C₆₁

C₄

semidirect

32. C₂×#92418

D₄

semidirect

62. C₄×C₆₁

#102

semidirect

77. C₆₁

#1957

semidirect

82. #127

Dic₆₁

semidirect

136. C₄

#14519698

semidirect

Subgroups — #21446626

Conjugacy classes of subgroups

Complements