Group #19134162 — subgroups

Subgroups — #19134162

Order 5504.

162 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14583245	C₂	1	1	yes	maximal, characteristic
2	#14583110	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583096	C₂	1	1	yes	maximal, characteristic
4	#14583026	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582649	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582644	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#331	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₂	—	2	1	no	—
9	C₂×#10621883	—	2	1	no	—
10	#13063325	C₂²	1	1	yes	characteristic
11	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
12	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	Dic₄₃⋊C₈	—	2	1	no	—
14	#13063250	—	2	1	no	—
15	#13063246	—	2	1	no	—
16	#13063246	—	2	1	no	—
17	#13063246	—	2	1	no	—
18	#13063235	—	2	1	no	—
19	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	#127×C₄₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×D₄×C₄₃	—	2	1	no	—
24	C₂×D₄×C₄₃	—	2	1	no	—
25	C₂×D₄×C₄₃	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	C₂×Dic₈₆	D₄	1	1	yes	characteristic
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	—	2	1	no	—
30	C₄²×C₄₃	C₂³	1	1	yes	characteristic
31	#10621883	—	4	2	no	—
32	C₄⋊Dic₄₃	—	2	1	no	—
33	C₄⋊Dic₄₃	—	2	1	no	—
34	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
35	Dic₄₃⋊C₄	—	2	1	no	—
36	C₄×Dic₄₃	—	2	1	no	—
37	C₂×C₄₃⋊C₈	—	2	1	no	—
38	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
39	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
40	Dic₁₇₂	—	4	2	no	—
41	C₂³×C₄₃	—	4	1	no	—
42	D₄×C₄₃	—	4	1	no	—
43	D₄×C₄₃	—	4	1	no	—
44	D₄×C₄₃	—	4	1	no	—
45	D₄×C₄₃	—	4	1	no	—
46	D₄×C₄₃	—	8	1	no	—
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
50	C₂×Dic₄₃	—	2	1	no	—
51	C₂×Dic₄₃	—	2	1	no	—
52	C₂×Dic₄₃	—	4	1	no	—
53	Dic₈₆	—	2	1	no	—
54	Dic₈₆	—	2	1	no	—
55	Dic₈₆	—	4	1	no	—
56	Dic₈₆	—	4	1	no	—
57	C₈×C₄₃	—	4	1	no	—
58	C₈×C₄₃	—	4	1	no	—
59	C₄₃⋊C₈	—	2	1	no	—
60	C₄₃⋊C₈	—	2	1	no	—
61	C₄₃⋊C₈	—	4	1	no	—
62	C₂²×C₄₃	—	8	1	no	—
63	C₂²×C₄₃	—	8	1	no	—
64	C₂²×C₄₃	—	8	1	no	—
65	C₂²×C₄₃	#121	1	1	yes	characteristic
66	C₄×C₄₃	—	2	1	no	—
67	C₄×C₄₃	#135	1	1	yes	characteristic
68	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
69	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
70	C₄×C₄₃	#137	1	1	yes	characteristic
71	Dic₄₃	—	4	1	no	—
72	Dic₄₃	—	4	1	no	—
73	Dic₄₃	—	8	1	no	—
74	#1702	—	43	1	no	maximal, Sylow
75	C₂×C₄₃	—	16	1	no	—
76	C₂×C₄₃	#464	1	1	yes	characteristic
77	C₂×C₄₃	#469	1	1	yes	characteristic
78	C₂×C₄₃	#471	1	1	yes	characteristic
79	#486	—	43	1	no	—
80	#462	—	43	1	no	—
81	#460	—	43	1	no	—
82	#446	—	43	1	no	—
83	#334	—	43	1	no	—
84	#332	—	43	1	no	—
85	#331	D₄₃	1	1	yes	characteristic
86	C₄₃	#1702	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₁₆	—	86	1	no	—
88	C₂×SD₁₆	—	86	1	no	—
89	C₄⋊Q₈	—	43	1	no	—
90	#127	C₂×D₄₃	1	1	yes	characteristic
91	C₄×Q₈	—	43	1	no	—
92	C₄⋊C₈	—	43	1	no	—
93	C₄⋊C₈	—	86	1	no	—
94	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
95	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
96	#103	—	86	1	no	—
97	#102	—	86	1	no	—
98	#102	—	86	1	no	—
99	#102	—	86	1	no	—
100	#97	—	86	1	no	—
101	C₄×C₈	—	43	1	no	—
102	C₂×Q₈	—	43	1	no	—
103	C₂×Q₈	—	86	1	no	—
104	C₂×D₄	—	2	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	2	1	no	—
107	Q₁₆	—	172	2	no	—
108	SD₁₆	—	172	2	no	—
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	—	43	1	no	—
112	C₂×C₈	—	43	1	no	—
113	C₂×C₈	—	86	1	no	—
114	C₄⋊C₄	—	43	1	no	—
115	C₄⋊C₄	—	86	1	no	—
116	C₄⋊C₄	—	86	1	no	—
117	C₄⋊C₄	—	86	1	no	—
118	C₄²	—	86	1	no	—
119	C₄²	C₂²×D₄₃	1	1	yes	characteristic
120	C₂³	—	4	1	no	—
121	Q₈	—	86	1	no	—
122	Q₈	—	86	1	no	—
123	Q₈	—	172	1	no	—
124	Q₈	—	172	1	no	—
125	D₄	—	4	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	4	1	no	—
128	D₄	—	4	1	no	—
129	D₄	—	8	1	no	—
130	C₂×C₄	—	86	1	no	—
131	C₂×C₄	—	86	1	no	—
132	C₂×C₄	—	172	1	no	—
133	C₂×C₄	#10621898	1	1	yes	characteristic
134	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
135	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
136	C₈	—	4	1	no	—
137	C₈	—	4	1	no	—
138	C₈	—	86	1	no	—
139	C₈	—	86	1	no	—
140	C₈	—	172	1	no	—
141	C₂²	—	8	1	no	—
142	C₂²	—	8	1	no	—
143	C₂²	—	8	1	no	—
144	C₂²	#13063298	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	344	1	no	—
147	C₄	—	172	1	no	—
148	C₄	—	172	1	no	—
149	C₄	#13063344	1	1	yes	characteristic
150	C₄	#13063349	1	1	yes	characteristic
151	C₄	#13063352	1	1	yes	characteristic
152	C₄	#13063354	1	1	yes	characteristic
153	C₂	—	16	1	no	—
154	C₂	#14583120	1	1	yes	characteristic
155	C₂	#14583151	1	1	yes	characteristic
156	C₂	#14583161	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583245

C₂

yes

maximal, characteristic

#14583110

C₂

yes

maximal, characteristic, complemented

#14583096

C₂

yes

maximal, characteristic

#14583026

C₂

yes

maximal, characteristic, complemented

#14582649

C₂

yes

maximal, characteristic, complemented

#14582644

C₂

yes

maximal, characteristic, complemented

C₄₃×#331

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

—

C₂×#10621883

—

#13063325

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

—

—

—

—

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#127×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621883

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#1702

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#1702

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

#127

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

C₂×D₄₃

yes

—

—

—

—

100

#97

—

101

C₄×C₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

Q₁₆

—

172

—

108

SD₁₆

—

172

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄²

—

119

C₄²

C₂²×D₄₃

yes

characteristic

120

C₂³

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

172

—

124

Q₈

—

172

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

172

—

133

C₂×C₄

#10621898

yes

characteristic

134

C₂×C₄

D₄×D₄₃

yes

characteristic

135

C₂×C₄

D₄×D₄₃

yes

characteristic

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

172

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

#13063298

yes

characteristic

145

C₄

—

146

C₄

—

344

—

147

C₄

—

172

—

148

C₄

—

172

—

149

C₄

#13063344

yes

characteristic

150

C₄

#13063349

yes

characteristic

151

C₄

#13063352

yes

characteristic

152

C₄

#13063354

yes

characteristic

153

C₂

—

154

C₂

#14583120

yes

characteristic

155

C₂

#14583151

yes

characteristic

156

C₂

#14583161

yes

characteristic

	subgroup	G/H
center	C₂²	#13063298
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#331	C₂
socle	C₂²×C₄₃	#121
hypercenter	#331	D₄₃
hypocenter	C₄₃	#1702
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #331

subgroup

G/H

center

C₂²

#13063298

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#331

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #331

N	H ≅ G/N	type
2. #14583110	C₂	semidirect
4. #14583026	C₂	semidirect
5. #14582649	C₂	semidirect
6. #14582644	C₂	semidirect
86. C₄₃	#1702	semidirect

H ≅ G/N

type

2. #14583110

C₂

semidirect

4. #14583026

C₂

semidirect

5. #14582649

C₂

semidirect

6. #14582644

C₂

semidirect

86. C₄₃

#1702

semidirect

Subgroups — #19134162

Conjugacy classes of subgroups

Complements