Group #21460653 — subgroups

Subgroups — #21460653

Order 7808.

208 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 74 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	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊#6923	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×D₆₁⋊C₈	—	2	1	no	—
5	C₂×C₄⋊#6923	C₄	1	2	yes	—
6	C₂×C₄×#6923	—	2	1	no	—
7	C₄×#92420	—	2	1	no	—
8	C₄×#92420	C₄	1	2	yes	complemented
9	(C₂×#6923)⋊C₄	—	2	1	no	—
10	C₂×C₈×D₆₁	—	2	1	no	—
11	C₄²×D₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊#92418	C₄	1	1	yes	characteristic, complemented
13	#14519706	—	2	1	no	—
14	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
15	C₂²×#6923	—	2	2	no	—
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
19	C₂×#92420	—	2	2	no	—
20	C₄⋊#6923	—	2	2	no	—
21	C₄⋊#6923	C₈	1	4	yes	complemented
22	C₄×#6923	—	4	1	no	—
23	C₄×#6923	—	4	1	no	—
24	D₆₁⋊C₈	—	2	4	no	—
25	C₂×C₈×C₆₁	—	2	1	no	—
26	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₆₁	D₄	1	1	yes	characteristic
29	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
30	C₂×#92418	—	2	1	no	—
31	C₈×D₆₁	—	4	1	no	—
32	C₈×D₆₁	—	4	1	no	—
33	C₂²×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×#6923	—	2	4	no	—
35	C₂×#6923	—	4	2	no	—
36	C₂×#6923	—	4	2	no	—
37	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
42	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
43	C₄×D₆₁	—	2	2	no	—
44	C₄×D₆₁	C₂×C₈	1	2	yes	—
45	C₄×D₆₁	M₁₆	1	2	yes	—
46	C₄×D₆₁	D₈	1	1	yes	characteristic
47	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
48	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
49	C₄×D₆₁	Q₁₆	1	1	yes	characteristic
50	#92420	—	2	4	no	—
51	C₈×C₆₁	—	4	1	no	—
52	#92418	—	4	1	no	—
53	C₂²×C₆₁	#95	1	1	yes	characteristic
54	C₂×D₆₁	C₂²⋊C₈	1	2	yes	—
55	C₂×D₆₁	#102	1	1	yes	characteristic
56	C₂×D₆₁	#103	1	1	yes	characteristic
57	C₂×D₆₁	#104	1	2	yes	—
58	#6923	—	4	4	no	—
59	C₄×C₆₁	—	2	1	no	—
60	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
61	C₄×C₆₁	#97	1	1	yes	characteristic
62	C₄×C₆₁	#102	1	1	yes	characteristic
63	C₄×C₆₁	#103	1	1	yes	characteristic
64	Dic₆₁	—	2	1	no	—
65	Dic₆₁	C₄⋊C₈	1	2	yes	—
66	Dic₆₁	#106	1	1	yes	characteristic
67	Dic₆₁	#107	1	1	yes	characteristic
68	#1279	—	61	1	no	maximal, Sylow
69	C₂×C₆₁	#336	1	1	yes	characteristic
70	C₂×C₆₁	#339	1	1	yes	characteristic
71	C₂×C₆₁	#340	1	1	yes	characteristic
72	D₆₁	D₄⋊C₈	1	2	yes	—
73	D₆₁	Q₈⋊C₈	1	2	yes	—
74	C₂×C₄⋊C₈	—	61	1	no	—
75	C₂×C₄×C₈	—	61	1	no	—
76	C₄×C₄⋊C₄	—	61	1	no	—
77	C₆₁	#1279	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₈	—	122	1	no	—
79	C₂²×C₈	—	122	1	no	—
80	C₂×C₄⋊C₄	—	61	2	no	—
81	C₂×C₄²	—	61	1	no	—
82	C₂×C₄²	—	122	1	no	—
83	C₄⋊C₈	—	61	1	no	—
84	C₄⋊C₈	—	122	1	no	—
85	C₄⋊C₈	#6923	1	1	yes	characteristic, complemented
86	C₄×C₈	—	61	2	no	—
87	C₄×C₈	—	122	1	no	—
88	#95	—	122	1	no	—
89	C₂²×C₄	—	61	1	no	—
90	C₂²×C₄	—	61	1	no	—
91	C₂²×C₄	—	61	1	no	—
92	C₂²×C₄	—	122	2	no	—
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	—	122	2	no	—
95	C₂×C₈	—	122	4	no	—
96	C₂×C₈	—	122	1	no	—
97	C₂×C₈	—	244	1	no	—
98	C₂×C₈	—	244	1	no	—
99	C₄⋊C₄	—	61	4	no	—
100	C₄⋊C₄	—	122	2	no	—
101	C₄²	—	61	1	no	—
102	C₄²	—	61	1	no	—
103	C₄²	—	61	1	no	—
104	C₄²	—	244	1	no	—
105	C₄²	—	244	1	no	—
106	C₄²	C₂×#6923	1	1	yes	characteristic
107	C₂³	—	61	1	no	—
108	C₂×C₄	—	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	—	61	1	no	—
115	C₂×C₄	—	61	1	no	—
116	C₂×C₄	—	61	1	no	—
117	C₂×C₄	—	122	2	no	—
118	C₂×C₄	—	122	4	no	—
119	C₂×C₄	—	244	2	no	—
120	C₂×C₄	—	244	2	no	—
121	C₂×C₄	C₄×#6923	1	1	yes	characteristic
122	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
123	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
124	C₈	—	4	1	no	—
125	C₈	—	122	4	no	—
126	C₈	—	244	1	no	—
127	C₂²	—	61	2	no	—
128	C₂²	—	61	2	no	—
129	C₂²	—	61	1	no	—
130	C₂²	—	61	1	no	—
131	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
132	C₄	—	2	1	no	—
133	C₄	—	61	2	no	—
134	C₄	—	61	1	no	—
135	C₄	—	61	1	no	—
136	C₄	—	122	1	no	—
137	C₄	—	244	4	no	—
138	C₄	C₈×#6923	1	1	yes	characteristic
139	C₄	#14519831	1	1	yes	characteristic
140	C₄	#14519839	1	1	yes	characteristic
141	C₄	#14519840	1	1	yes	characteristic
142	C₂	—	61	2	no	—
143	C₂	—	61	2	no	—
144	C₂	(C₂×#6923)⋊C₈	1	1	yes	characteristic
145	C₂	#16840634	1	1	yes	characteristic
146	C₂	#16840635	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₆₁⋊C₈

C₂

yes

maximal, characteristic

C₄×C₄⋊#6923

C₂

yes

maximal, characteristic

C₄⋊C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

—

C₂×C₄⋊#6923

C₄

yes

—

C₂×C₄×#6923

—

C₄×#92420

—

C₄×#92420

C₄

yes

complemented

(C₂×#6923)⋊C₄

—

C₂×C₈×D₆₁

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄⋊#92418

C₄

yes

characteristic, complemented

#14519706

—

C₄⋊C₈×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

—

—

C₈

yes

complemented

C₄×#6923

—

C₄×#6923

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂×#92418

—

C₈×D₆₁

—

C₈×D₆₁

—

C₂²×D₆₁

C₂²⋊C₄

yes

—

—

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

C₂×C₈

yes

—

C₄×D₆₁

M₁₆

yes

—

C₄×D₆₁

D₈

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

Q₁₆

yes

characteristic

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#95

yes

characteristic

C₂×D₆₁

C₂²⋊C₈

yes

—

C₂×D₆₁

yes

C₂×D₆₁

yes

C₂×D₆₁

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

C₄×C₈

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

C₄⋊C₈

yes

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

D₄⋊C₈

yes

—

D₆₁

Q₈⋊C₈

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₄×C₄⋊C₄

—

C₆₁

#1279

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

C₂²×C₈

—

122

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

122

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

#6923

yes

characteristic, complemented

C₄×C₈

—

C₄×C₈

—

122

—

#95

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₄⋊C₄

—

100

C₄⋊C₄

—

122

—

101

C₄²

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

244

—

105

C₄²

—

244

—

106

C₄²

C₂×#6923

yes

characteristic

107

C₂³

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

122

—

118

C₂×C₄

—

122

—

119

C₂×C₄

—

244

—

120

C₂×C₄

—

244

—

121

C₂×C₄

C₄×#6923

yes

characteristic

122

C₂×C₄

C₄⋊#6923

yes

characteristic

123

C₂×C₄

C₂²⋊#6923

yes

characteristic

124

C₈

—

125

C₈

—

122

—

126

C₈

—

244

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

122

—

137

C₄

—

244

—

138

C₄

C₈×#6923

yes

characteristic

139

C₄

#14519831

yes

characteristic

140

C₄

#14519839

yes

characteristic

141

C₄

#14519840

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

(C₂×#6923)⋊C₈

yes

characteristic

145

C₂

#16840634

yes

characteristic

146

C₂

#16840635

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₄×C₆₁	C₄×C₈
Frattini	C₄²	C₂×#6923
Fitting	C₄⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	#1279
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊#6923

commutator

C₄×C₆₁

C₄×C₈

Frattini

C₄²

C₂×#6923

Fitting

C₄⋊C₈×C₆₁

C₄

C₂²×C₆₁

C₄⋊C₈

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
8. C₄×#92420	C₄	semidirect
12. C₄⋊#92418	C₄	semidirect
14. C₄⋊C₈×C₆₁	C₄	semidirect
21. C₄⋊#6923	C₈	semidirect
77. C₆₁	#1279	semidirect
85. C₄⋊C₈	#6923	semidirect

H ≅ G/N

type

8. C₄×#92420

C₄

semidirect

12. C₄⋊#92418

C₄

semidirect

14. C₄⋊C₈×C₆₁

C₄

semidirect

21. C₄⋊#6923

C₈

semidirect

77. C₆₁

#1279

semidirect

85. C₄⋊C₈

#6923

semidirect

Subgroups — #21460653

Conjugacy classes of subgroups

Complements