Group #19136865 — subgroups

Subgroups — #19136865

Order 5504.

178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063271	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13063269	C₂	1	1	yes	maximal, characteristic
4	#14583282	C₂	1	1	yes	maximal, characteristic
5	#14583277	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×SD₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
10	C₂×#10621885	—	2	1	no	—
11	C₂×#10621883	—	2	1	no	—
12	#13063323	—	2	1	no	—
13	#13063312	—	2	1	no	—
14	Dic₃₄₄	—	2	2	no	—
15	#13063271	—	2	2	no	—
16	#13063269	—	2	2	no	—
17	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
19	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
21	SD₃₂×C₄₃	—	2	2	no	—
22	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×D₄×C₄₃	—	2	1	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	Q₁₆×C₄₃	—	2	1	no	—
28	Q₁₆×C₄₃	—	2	1	no	—
29	D₈×C₄₃	—	2	1	no	—
30	D₈×C₄₃	—	2	1	no	—
31	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
32	C₂²⋊Dic₄₃	—	4	2	no	—
33	#10621885	—	4	2	no	—
34	#10621883	—	4	2	no	—
35	Dic₄₃⋊C₄	—	4	2	no	—
36	C₄×Dic₄₃	D₄	1	1	yes	characteristic
37	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
38	Dic₁₇₂	—	2	1	no	—
39	Dic₁₇₂	—	2	1	no	—
40	Dic₁₇₂	—	2	1	no	—
41	Dic₁₇₂	—	2	1	no	—
42	C₁₆×C₄₃	D₄	1	2	yes	—
43	C₄₃⋊C₁₆	D₄	1	2	yes	—
44	C₂³×C₄₃	—	4	1	no	—
45	Q₈×C₄₃	—	4	1	no	—
46	Q₈×C₄₃	—	4	1	no	—
47	D₄×C₄₃	—	4	1	no	—
48	D₄×C₄₃	—	4	1	no	—
49	C₂×C₄×C₄₃	—	4	1	no	—
50	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₄₃	—	4	1	no	—
52	C₂×Dic₄₃	—	4	1	no	—
53	C₂×Dic₄₃	D₈	1	2	yes	—
54	Dic₈₆	—	4	1	no	—
55	Dic₈₆	—	4	1	no	—
56	Dic₈₆	—	4	1	no	—
57	Dic₈₆	—	4	1	no	—
58	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
59	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
60	C₄₃⋊C₈	D₈	1	2	yes	—
61	C₂²×C₄₃	—	8	1	no	—
62	C₂²×C₄₃	—	8	2	no	—
63	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
64	C₄×C₄₃	—	8	1	no	—
65	C₄×C₄₃	#127	1	1	yes	characteristic
66	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
67	Dic₄₃	—	2	2	no	—
68	Dic₄₃	—	8	1	no	—
69	Dic₄₃	—	8	1	no	—
70	#2251	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	—	16	1	no	—
72	C₂×C₄₃	#493	1	1	yes	characteristic
73	C₂×C₄₃	#510	1	2	yes	—
74	C₂×Q₃₂	—	43	1	no	—
75	C₂×Q₃₂	—	43	1	no	—
76	C₂×SD₃₂	—	43	1	no	—
77	C₂×SD₃₂	D₄₃	1	1	yes	characteristic
78	#495	—	43	1	no	—
79	#494	—	43	1	no	—
80	#346	—	43	1	no	—
81	C₄₃	#2251	1	1	yes	characteristic, complemented, Sylow
82	C₂×Q₁₆	—	43	1	no	—
83	C₂×Q₁₆	—	43	1	no	—
84	C₂×Q₁₆	—	86	1	no	—
85	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
86	C₂×SD₁₆	—	86	1	no	—
87	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
88	C₄⋊Q₈	—	86	1	no	—
89	#124	—	86	1	no	—
90	Q₃₂	—	86	2	no	—
91	Q₃₂	—	86	2	no	—
92	SD₃₂	—	2	2	no	—
93	SD₃₂	—	86	2	no	—
94	C₂×C₁₆	—	43	1	no	—
95	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
96	C₄×C₈	—	43	1	no	—
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	—	86	1	no	—
99	C₂×Q₈	—	86	1	no	—
100	C₂×D₄	—	2	1	no	—
101	Q₁₆	—	2	1	no	—
102	Q₁₆	—	2	1	no	—
103	Q₁₆	—	86	1	no	—
104	Q₁₆	—	86	1	no	—
105	Q₁₆	—	86	1	no	—
106	Q₁₆	—	86	1	no	—
107	Q₁₆	—	172	2	no	—
108	SD₁₆	—	172	2	no	—
109	D₈	—	2	1	no	—
110	D₈	—	2	1	no	—
111	C₂×C₈	—	43	1	no	—
112	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
113	C₄⋊C₄	—	172	2	no	—
114	C₂²⋊C₄	—	172	2	no	—
115	C₄²	—	43	1	no	—
116	C₁₆	—	43	2	no	—
117	C₁₆	C₂²⋊D₄₃	1	2	yes	—
118	C₂³	—	4	1	no	—
119	Q₈	—	4	1	no	—
120	Q₈	—	4	1	no	—
121	Q₈	—	172	1	no	—
122	Q₈	—	172	1	no	—
123	Q₈	—	172	1	no	—
124	Q₈	—	172	1	no	—
125	D₄	—	4	1	no	—
126	D₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	43	2	no	—
129	C₂×C₄	—	172	1	no	—
130	C₂×C₄	—	172	1	no	—
131	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
132	C₈	—	43	2	no	—
133	C₈	D₄×D₄₃	1	1	yes	characteristic
134	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
135	C₂²	—	8	2	no	—
136	C₂²	—	8	1	no	—
137	C₂²	D₈×D₄₃	1	1	yes	characteristic
138	C₄	—	8	1	no	—
139	C₄	—	86	2	no	—
140	C₄	—	344	1	no	—
141	C₄	—	344	1	no	—
142	C₄	#13063321	1	1	yes	characteristic
143	C₄	D₈×D₄₃	1	1	yes	characteristic
144	C₂	—	16	1	no	—
145	C₂	#14583274	1	1	yes	characteristic
146	C₂	#14583338	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₃₄₄

C₂

yes

maximal, characteristic, complemented

C₂×#13063271

C₂

yes

maximal, characteristic, complemented

C₂×#13063269

C₂

yes

maximal, characteristic

#14583282

C₂

yes

maximal, characteristic

#14583277

C₂

yes

maximal, characteristic, complemented

#14582674

C₂

yes

maximal, characteristic, complemented

C₂×SD₃₂×C₄₃

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×Dic₁₇₂

C₂²

yes

—

—

—

—

Dic₃₄₄

—

#13063271

—

#13063269

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×D₈×C₄₃

C₂²

yes

characteristic

SD₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

#10621885

—

#10621883

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

D₄

yes

—

C₄₃⋊C₁₆

D₄

yes

—

C₂³×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₄₃⋊C₈

D₈

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#127

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2251

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#493

yes

characteristic

C₂×C₄₃

#510

yes

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×SD₃₂

D₄₃

yes

—

—

—

C₄₃

#2251

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

#124

—

Q₃₂

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×D₄

—

101

Q₁₆

—

102

Q₁₆

—

103

Q₁₆

—

104

Q₁₆

—

105

Q₁₆

—

106

Q₁₆

—

107

Q₁₆

—

172

—

108

SD₁₆

—

172

—

109

D₈

—

110

D₈

—

111

C₂×C₈

—

112

C₂×C₈

C₂²×D₄₃

yes

characteristic

113

C₄⋊C₄

—

172

—

114

C₂²⋊C₄

—

172

—

115

C₄²

—

116

C₁₆

—

117

C₁₆

C₂²⋊D₄₃

yes

—

118

C₂³

—

119

Q₈

—

120

Q₈

—

121

Q₈

—

172

—

122

Q₈

—

172

—

123

Q₈

—

172

—

124

Q₈

—

172

—

125

D₄

—

126

D₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

172

—

130

C₂×C₄

—

172

—

131

C₂×C₄

D₄×D₄₃

yes

characteristic

132

C₈

—

133

C₈

D₄×D₄₃

yes

characteristic

134

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

135

C₂²

—

136

C₂²

—

137

C₂²

D₈×D₄₃

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

344

—

141

C₄

—

344

—

142

C₄

#13063321

yes

characteristic

143

C₄

D₈×D₄₃

yes

characteristic

144

C₂

—

145

C₂

#14583274

yes

characteristic

146

C₂

#14583338

yes

—

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×SD₃₂×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₂×SD₃₂	D₄₃
hypocenter	C₄₃	#2251
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×SD₃₂×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₂×SD₃₂

D₄₃

hypocenter

C₄₃

#2251

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

N	H ≅ G/N	type
1. C₂×Dic₃₄₄	C₂	semidirect
2. C₂×#13063271	C₂	semidirect
5. #14583277	C₂	semidirect
6. #14582674	C₂	semidirect
81. C₄₃	#2251	semidirect

H ≅ G/N

type

1. C₂×Dic₃₄₄

C₂

semidirect

2. C₂×#13063271

C₂

semidirect

5. #14583277

C₂

semidirect

6. #14582674

C₂

semidirect

81. C₄₃

#2251

semidirect

Subgroups — #19136865

Conjugacy classes of subgroups

Complements