Group #21461423 — subgroups

Subgroups — #21461423

Order 7808.

168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 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	#16840812	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840790	C₂	1	1	yes	maximal, characteristic
3	#16840624	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840612	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840610	C₂	1	1	yes	maximal, characteristic
6	#92420⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#16839849	C₂	1	1	yes	maximal, characteristic
8	C₂×D₆₁⋊C₈	—	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	#14519834	—	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×#11758190	C₄	1	1	yes	characteristic
17	#14519742	C₂²	1	1	yes	characteristic
18	#14519739	C₂²	1	1	yes	characteristic
19	#14519700	C₄	1	1	yes	characteristic
20	#14519697	C₄	1	1	yes	characteristic
21	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
22	#106×C₆₁	C₄	1	1	yes	characteristic
23	C₂×D₂₄₄	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×D₆₁	—	2	1	no	—
25	C₂×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
26	C₂×#92420	—	2	1	no	—
27	C₂×#92420	—	2	1	no	—
28	C₂×#92420	—	2	1	no	—
29	C₂×#92420	D₄	1	1	yes	characteristic
30	C₂×#92420	D₄	1	1	yes	characteristic
31	D₆₁⋊C₈	—	4	2	no	—
32	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
33	C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
34	C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
35	#11758198	—	2	1	no	—
36	#11758196	—	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	#11758190	—	2	2	no	—
41	C₂²×D₆₁	—	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	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₆₁	#41	1	1	yes	characteristic
48	D₂₄₄	—	2	1	no	—
49	D₂₄₄	M₁₆	1	2	yes	—
50	C₄×D₆₁	—	4	1	no	—
51	C₄×D₆₁	—	4	1	no	—
52	Dic₁₂₂	—	2	1	no	—
53	Dic₁₂₂	—	2	1	no	—
54	#92420	—	2	1	no	—
55	#92420	—	4	1	no	—
56	#92420	—	4	1	no	—
57	#92420	—	4	1	no	—
58	#92420	SD₁₆	1	2	yes	complemented
59	C₈×C₆₁	—	2	1	no	—
60	#92418	—	2	1	no	—
61	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
62	C₂×D₆₁	—	2	2	no	—
63	C₂×D₆₁	—	4	1	no	—
64	C₂×D₆₁	—	4	1	no	—
65	C₄×C₆₁	—	4	1	no	—
66	C₄×C₆₁	—	4	1	no	—
67	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
68	C₄×C₆₁	#131	1	1	yes	characteristic
69	Dic₆₁	—	2	1	no	—
70	Dic₆₁	—	4	1	no	—
71	Dic₆₁	C₂×SD₁₆	1	1	yes	characteristic
72	Dic₆₁	#135	1	1	yes	characteristic
73	#1582	—	61	1	no	maximal, Sylow
74	C₂×C₆₁	#435	1	1	yes	characteristic
75	C₂×C₆₁	C₄×SD₁₆	1	1	yes	characteristic
76	C₂×C₆₁	#444	1	1	yes	characteristic
77	D₆₁	—	4	2	no	—
78	#446	—	61	1	no	—
79	C₄×SD₁₆	—	61	1	no	—
80	C₈×D₄	—	61	1	no	—
81	#334	—	61	1	no	—
82	Q₈⋊C₈	—	61	1	no	—
83	D₄⋊C₈	—	61	1	no	—
84	#322	—	61	1	no	—
85	C₆₁	#1582	1	1	yes	characteristic, complemented, Sylow
86	C₂×SD₁₆	—	61	1	no	—
87	C₂²×C₈	—	122	1	no	—
88	C₄×Q₈	—	61	1	no	—
89	C₄×D₄	—	61	1	no	—
90	#106	#6923	1	1	yes	characteristic
91	C₄⋊C₈	—	61	1	no	—
92	C₄⋊C₈	—	61	1	no	—
93	C₄⋊C₈	—	122	1	no	—
94	#103	—	61	1	no	—
95	#102	—	61	1	no	—
96	C₂²⋊C₈	—	122	1	no	—
97	#97	—	122	1	no	—
98	C₄×C₈	—	61	1	no	—
99	C₄×C₈	—	61	1	no	—
100	C₄×C₈	—	61	1	no	—
101	C₂×Q₈	—	61	1	no	—
102	C₂×D₄	—	61	1	no	—
103	C₂²×C₄	—	122	1	no	—
104	SD₁₆	—	122	2	no	—
105	C₂×C₈	—	61	1	no	—
106	C₂×C₈	—	61	1	no	—
107	C₂×C₈	—	61	1	no	—
108	C₂×C₈	—	122	1	no	—
109	C₂×C₈	—	122	1	no	—
110	C₂×C₈	—	122	1	no	—
111	C₂×C₈	—	244	2	no	—
112	C₂×C₈	C₂×#6923	1	1	yes	characteristic
113	C₄⋊C₄	—	122	1	no	—
114	C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
115	C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
116	C₂²⋊C₄	—	122	1	no	—
117	C₄²	—	61	1	no	—
118	C₄²	—	122	1	no	—
119	C₂³	—	122	1	no	—
120	Q₈	—	122	1	no	—
121	Q₈	—	122	1	no	—
122	D₄	—	61	2	no	—
123	D₄	—	122	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	61	1	no	—
127	C₂×C₄	—	61	1	no	—
128	C₂×C₄	—	122	1	no	—
129	C₂×C₄	—	244	1	no	—
130	C₂×C₄	—	244	1	no	—
131	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
132	C₈	—	2	1	no	—
133	C₈	—	61	2	no	—
134	C₈	—	122	1	no	—
135	C₈	—	122	1	no	—
136	C₈	—	244	1	no	—
137	C₈	—	244	1	no	—
138	C₈	—	244	1	no	—
139	C₂²	—	122	2	no	—
140	C₂²	—	244	1	no	—
141	C₂²	—	244	1	no	—
142	C₂²	D₄×#6923	1	1	yes	characteristic
143	C₄	—	4	1	no	—
144	C₄	—	4	1	no	—
145	C₄	—	61	1	no	—
146	C₄	—	61	1	no	—
147	C₄	—	122	1	no	—
148	C₄	—	244	1	no	—
149	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
150	C₄	#14519865	1	1	yes	characteristic
151	C₂	—	244	2	no	—
152	C₂	#16840792	1	1	yes	characteristic
153	C₂	SD₁₆×#6923	1	1	yes	characteristic
154	C₂	#16840807	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840812

C₂

yes

maximal, characteristic, complemented

#16840790

C₂

yes

maximal, characteristic

#16840624

C₂

yes

maximal, characteristic, complemented

#16840612

C₂

yes

maximal, characteristic, complemented

#16840610

C₂

yes

maximal, characteristic

#92420⋊C₈

C₂

yes

maximal, characteristic, complemented

#16839849

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

—

C₄⋊#92420

—

C₄⋊#92420

C₂²

yes

characteristic

C₄⋊#92420

C₂²

yes

—

—

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

characteristic

C₂×#11758190

C₄

yes

characteristic

#14519742

C₂²

yes

characteristic

#14519739

C₂²

yes

characteristic

#14519700

C₄

yes

characteristic

#14519697

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

#106×C₆₁

C₄

yes

characteristic

C₂×D₂₄₄

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

—

C₂×Dic₁₂₂

C₂×C₄

yes

—

—

—

D₄

yes

characteristic

C₂×#92420

D₄

yes

characteristic

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

C₂×C₄

yes

characteristic

#11758198

—

#11758196

—

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758190

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

#41

yes

characteristic

D₂₄₄

—

D₂₄₄

M₁₆

yes

—

C₄×D₆₁

—

C₄×D₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

—

—

—

—

SD₁₆

yes

complemented

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

C₂×SD₁₆

yes

Dic₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

C₄×SD₁₆

yes

characteristic

C₂×C₆₁

#444

yes

characteristic

D₆₁

—

#446

—

C₄×SD₁₆

—

C₈×D₄

—

#334

—

Q₈⋊C₈

—

D₄⋊C₈

—

#322

—

C₆₁

#1582

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂²×C₈

—

122

—

C₄×Q₈

—

C₄×D₄

—

#106

#6923

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

#103

—

#102

—

C₂²⋊C₈

—

122

—

#97

—

122

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

—

101

C₂×Q₈

—

102

C₂×D₄

—

103

C₂²×C₄

—

122

—

104

SD₁₆

—

122

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

122

—

109

C₂×C₈

—

122

—

110

C₂×C₈

—

122

—

111

C₂×C₈

—

244

—

112

C₂×C₈

C₂×#6923

yes

characteristic

113

C₄⋊C₄

—

122

—

114

C₄⋊C₄

C₂×#6923

yes

characteristic

115

C₄⋊C₄

C₂×#6923

yes

characteristic

116

C₂²⋊C₄

—

122

—

117

C₄²

—

118

C₄²

—

122

—

119

C₂³

—

122

—

120

Q₈

—

122

—

121

Q₈

—

122

—

122

D₄

—

123

D₄

—

122

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

122

—

129

C₂×C₄

—

244

—

130

C₂×C₄

—

244

—

131

C₂×C₄

C₂²×#6923

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

122

—

135

C₈

—

122

—

136

C₈

—

244

—

137

C₈

—

244

—

138

C₈

—

244

—

139

C₂²

—

122

—

140

C₂²

—

244

—

141

C₂²

—

244

—

142

C₂²

D₄×#6923

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

122

—

148

C₄

—

244

—

149

C₄

D₆₁⋊M₁₆

yes

characteristic

150

C₄

#14519865

yes

characteristic

151

C₂

—

244

—

152

C₂

#16840792

yes

characteristic

153

C₂

SD₁₆×#6923

yes

characteristic

154

C₂

#16840807

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#106×C₆₁	C₄
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#106	#6923
hypocenter	C₆₁	#1582
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#106×C₆₁

C₄

socle

C₂²×C₆₁

C₄×D₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
1. #16840812	C₂	semidirect
3. #16840624	C₂	semidirect
4. #16840612	C₂	semidirect
6. #92420⋊C₈	C₂	semidirect
58. #92420	SD₁₆	semidirect
85. C₆₁	#1582	semidirect

H ≅ G/N

type

1. #16840812

C₂

semidirect

3. #16840624

C₂

semidirect

4. #16840612

C₂

semidirect

6. #92420⋊C₈

C₂

semidirect

58. #92420

SD₁₆

semidirect

85. C₆₁

#1582

semidirect

Subgroups — #21461423

Conjugacy classes of subgroups

Complements