Group #19134019 — subgroups

Subgroups — #19134019

Order 5504.

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

normal subgroups only

This group has 166 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	#14583250	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583180	C₂	1	1	yes	maximal, characteristic
3	#14583105	C₂	1	1	yes	maximal, characteristic
4	C₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic
5	#14582646	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582644	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621873	—	2	1	no	—
9	C₂×C₈×D₄₃	—	2	1	no	—
10	#13063325	C₂²	1	1	yes	characteristic
11	#13063325	C₂²	1	1	yes	characteristic
12	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
13	#13063259	—	2	1	no	—
14	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	#13063250	—	2	1	no	—
16	#13063250	—	2	1	no	—
17	#13063250	—	2	1	no	—
18	#13063247	—	2	1	no	—
19	(C₂×D₄₃)⋊C₈	—	2	1	no	—
20	C₄⋊C₈×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×D₁₇₂	D₄	1	1	yes	characteristic
24	C₂×C₄×D₄₃	—	2	1	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
30	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
31	C₄²×C₄₃	C₂³	1	1	yes	characteristic
32	(C₂×D₄₃)⋊C₄	—	2	1	no	—
33	C₄⋊Dic₄₃	—	2	1	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₄⋊Dic₄₃	—	2	1	no	—
36	C₄⋊Dic₄₃	—	2	1	no	—
37	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
38	C₂×C₄₃⋊C₈	—	2	1	no	—
39	#10621873	—	4	2	no	—
40	C₈×D₄₃	—	4	2	no	—
41	C₂²×D₄₃	—	2	1	no	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
45	C₂×Dic₄₃	—	2	1	no	—
46	C₂×Dic₄₃	—	4	1	no	—
47	C₂×Dic₄₃	—	4	1	no	—
48	D₁₇₂	—	2	1	no	—
49	D₁₇₂	SD₁₆	1	2	yes	—
50	C₄×D₄₃	—	4	1	no	—
51	C₄×D₄₃	—	4	1	no	—
52	Dic₈₆	—	4	1	no	—
53	Dic₈₆	—	4	1	no	—
54	Dic₈₆	—	4	1	no	—
55	Dic₈₆	—	4	1	no	—
56	C₈×C₄₃	—	2	1	no	—
57	C₈×C₄₃	—	2	1	no	—
58	C₈×C₄₃	—	4	1	no	—
59	C₈×C₄₃	—	4	1	no	—
60	C₄₃⋊C₈	—	4	1	no	—
61	C₂²×C₄₃	#121	1	1	yes	characteristic
62	C₂×D₄₃	—	2	2	no	—
63	C₂×D₄₃	—	4	1	no	—
64	C₂×D₄₃	—	4	1	no	—
65	C₄×C₄₃	—	2	1	no	—
66	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
67	C₄×C₄₃	#135	1	1	yes	characteristic
68	C₄×C₄₃	#135	1	1	yes	characteristic
69	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
70	Dic₄₃	—	4	1	no	—
71	Dic₄₃	—	8	1	no	—
72	Dic₄₃	—	8	1	no	—
73	#1679	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	#463	1	1	yes	characteristic
75	C₂×C₄₃	#465	1	1	yes	characteristic
76	C₂×C₄₃	#473	1	1	yes	characteristic
77	D₄₃	—	4	2	no	—
78	#487	—	43	1	no	—
79	#474	—	43	1	no	—
80	#461	—	43	1	no	—
81	C₈×D₄	—	43	1	no	—
82	#334	D₄₃	1	1	yes	characteristic, complemented
83	#332	—	43	1	no	—
84	#332	—	43	1	no	—
85	C₄₃	#1679	1	1	yes	characteristic, complemented, Sylow
86	C₂×SD₁₆	—	86	1	no	—
87	C₂²×C₈	—	86	1	no	—
88	C₄⋊Q₈	—	43	1	no	—
89	C₄⋊Q₈	—	43	1	no	—
90	C₄×D₄	—	43	1	no	—
91	#107	—	86	1	no	—
92	C₄⋊C₈	—	43	1	no	—
93	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
94	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
95	#103	—	86	1	no	—
96	#103	—	86	1	no	—
97	#103	—	86	1	no	—
98	#102	—	86	1	no	—
99	C₂²⋊C₈	—	86	1	no	—
100	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
101	C₂×Q₈	—	86	1	no	—
102	C₂×Q₈	—	86	1	no	—
103	C₂×D₄	—	43	1	no	—
104	C₂²×C₄	—	86	1	no	—
105	SD₁₆	—	172	2	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	86	1	no	—
109	C₂×C₈	—	172	2	no	—
110	C₂×C₈	D₁₇₂	1	1	yes	characteristic
111	C₂×C₈	D₁₇₂	1	1	yes	characteristic
112	C₄⋊C₄	—	43	1	no	—
113	C₄⋊C₄	—	86	1	no	—
114	C₄⋊C₄	—	86	1	no	—
115	C₄⋊C₄	—	86	1	no	—
116	C₄⋊C₄	—	86	1	no	—
117	C₂²⋊C₄	—	86	1	no	—
118	C₄²	C₂²×D₄₃	1	1	yes	characteristic
119	C₂³	—	86	1	no	—
120	Q₈	—	172	1	no	—
121	Q₈	—	172	1	no	—
122	Q₈	—	172	1	no	—
123	Q₈	—	172	1	no	—
124	D₄	—	43	2	no	—
125	D₄	—	86	1	no	—
126	C₂×C₄	—	86	1	no	—
127	C₂×C₄	—	172	1	no	—
128	C₂×C₄	—	172	1	no	—
129	C₂×C₄	—	172	1	no	—
130	C₂×C₄	—	172	1	no	—
131	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
132	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
133	C₂×C₄	#10621902	1	1	yes	characteristic
134	C₈	—	2	1	no	—
135	C₈	—	2	1	no	—
136	C₈	—	4	1	no	—
137	C₈	—	4	1	no	—
138	C₈	—	172	1	no	—
139	C₂²	—	86	2	no	—
140	C₂²	—	172	1	no	—
141	C₂²	—	172	1	no	—
142	C₂²	#13063300	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	344	1	no	—
145	C₄	—	344	1	no	—
146	C₄	—	172	1	no	—
147	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
148	C₄	#13063346	1	1	yes	characteristic
149	C₄	#13063347	1	1	yes	characteristic
150	C₄	#13063353	1	1	yes	characteristic
151	C₂	—	172	2	no	—
152	C₂	#14583115	1	1	yes	characteristic
153	C₂	#14583129	1	1	yes	characteristic
154	C₂	#14583175	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583250

C₂

yes

maximal, characteristic, complemented

#14583180

C₂

yes

maximal, characteristic

#14583105

C₂

yes

maximal, characteristic

C₈×D₁₇₂

C₂

yes

maximal, characteristic

#14582646

C₂

yes

maximal, characteristic, complemented

#14582644

C₂

yes

maximal, characteristic, complemented

C₄₃×#334

C₂

yes

maximal, characteristic, complemented

C₂×#10621873

—

C₂×C₈×D₄₃

—

#13063325

C₂²

yes

characteristic

#13063325

C₂²

yes

characteristic

C₄×D₁₇₂

C₂²

yes

characteristic

#13063259

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

—

—

—

(C₂×D₄₃)⋊C₈

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

D₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

#10621873

—

C₈×D₄₃

—

C₂²×D₄₃

—

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

—

D₁₇₂

—

D₁₇₂

SD₁₆

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#487

—

#474

—

#461

—

C₈×D₄

—

#334

D₄₃

yes

characteristic, complemented

#332

—

#332

—

C₄₃

#1679

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

C₂×D₄₃

yes

—

—

—

—

C₂²⋊C₈

—

100

C₄×C₈

C₂×D₄₃

yes

characteristic

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×D₄

—

104

C₂²×C₄

—

105

SD₁₆

—

172

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

172

—

110

C₂×C₈

D₁₇₂

yes

characteristic

111

C₂×C₈

D₁₇₂

yes

characteristic

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

C₂²×D₄₃

yes

characteristic

119

C₂³

—

120

Q₈

—

172

—

121

Q₈

—

172

—

122

Q₈

—

172

—

123

Q₈

—

172

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

172

—

128

C₂×C₄

—

172

—

129

C₂×C₄

—

172

—

130

C₂×C₄

—

172

—

131

C₂×C₄

C₂×D₁₇₂

yes

characteristic

132

C₂×C₄

D₄×D₄₃

yes

characteristic

133

C₂×C₄

#10621902

yes

characteristic

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

172

—

139

C₂²

—

140

C₂²

—

172

—

141

C₂²

—

172

—

142

C₂²

#13063300

yes

characteristic

143

C₄

—

144

C₄

—

344

—

145

C₄

—

344

—

146

C₄

—

172

—

147

C₄

SD₁₆×D₄₃

yes

characteristic

148

C₄

#13063346

yes

characteristic

149

C₄

#13063347

yes

characteristic

150

C₄

#13063353

yes

characteristic

151

C₂

—

172

—

152

C₂

#14583115

yes

characteristic

153

C₂

#14583129

yes

characteristic

154

C₂

#14583175

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	#121
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1679
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#13063300

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#334

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #14583250	C₂	semidirect
5. #14582646	C₂	semidirect
6. #14582644	C₂	semidirect
7. C₄₃×#334	C₂	semidirect
82. #334	D₄₃	semidirect
85. C₄₃	#1679	semidirect

H ≅ G/N

type

1. #14583250

C₂

semidirect

5. #14582646

C₂

semidirect

6. #14582644

C₂

semidirect

7. C₄₃×#334

C₂

semidirect

82. #334

D₄₃

semidirect

85. C₄₃

#1679

semidirect

Subgroups — #19134019

Conjugacy classes of subgroups

Complements