Group #19134107 — subgroups

Subgroups — #19134107

Order 5504.

166 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14583302	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583105	C₂	1	1	yes	maximal, characteristic
3	#14583101	C₂	1	1	yes	maximal, characteristic
4	#14582976	C₂	1	1	yes	maximal, characteristic
5	#14582649	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582644	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621873	—	2	1	no	—
9	C₂×#10621884	—	2	1	no	—
10	C₂×#10621872	—	2	1	no	—
11	#13063325	C₂²	1	1	yes	characteristic
12	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
13	#13063258	—	2	1	no	—
14	#13063258	—	2	1	no	—
15	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	#13063250	—	2	1	no	—
17	#13063249	—	2	1	no	—
18	(C₂×D₄₃)⋊C₈	—	2	1	no	—
19	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×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×Q₈×C₄₃	—	2	1	no	—
24	C₂×D₁₇₂	D₄	1	1	yes	characteristic
25	C₂×C₄×D₄₃	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄⋊C₄×C₄₃	—	2	1	no	—
31	C₄²×C₄₃	C₂³	1	1	yes	characteristic
32	#10621884	—	4	2	no	—
33	(C₂×D₄₃)⋊C₄	—	2	1	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₄⋊Dic₄₃	—	2	1	no	—
36	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
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	#10621873	—	4	2	no	—
41	#10621872	—	4	2	no	—
42	C₂²×D₄₃	—	2	1	no	—
43	Q₈×C₄₃	—	4	1	no	—
44	Q₈×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
49	C₂×Dic₄₃	—	2	1	no	—
50	C₂×Dic₄₃	—	4	1	no	—
51	D₁₇₂	—	2	1	no	—
52	D₁₇₂	—	2	1	no	—
53	C₄×D₄₃	—	4	1	no	—
54	C₄×D₄₃	—	4	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	—	4	1	no	—
61	C₄₃⋊C₈	SD₁₆	1	2	yes	complemented
62	C₂²×C₄₃	#121	1	1	yes	characteristic
63	C₂×D₄₃	—	4	1	no	—
64	C₂×D₄₃	—	4	1	no	—
65	C₂×D₄₃	—	4	1	no	—
66	C₄×C₄₃	—	2	1	no	—
67	C₄×C₄₃	—	8	1	no	—
68	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
69	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
70	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
71	C₄×C₄₃	#137	1	1	yes	characteristic
72	Dic₄₃	—	4	1	no	—
73	Dic₄₃	—	8	1	no	—
74	#1693	—	43	1	no	maximal, Sylow
75	C₂×C₄₃	#461	1	1	yes	characteristic
76	C₂×C₄₃	#469	1	1	yes	characteristic
77	C₂×C₄₃	#473	1	1	yes	characteristic
78	D₄₃	—	8	1	no	—
79	#500	—	43	1	no	—
80	#461	—	43	1	no	—
81	#461	—	43	1	no	—
82	#436	—	43	1	no	—
83	#334	—	43	1	no	—
84	#332	—	43	1	no	—
85	#332	D₄₃	1	1	yes	characteristic, complemented
86	C₄₃	#1693	1	1	yes	characteristic, complemented, Sylow
87	C₂×SD₁₆	—	86	1	no	—
88	C₂×SD₁₆	—	86	1	no	—
89	C₂×M₁₆	—	86	1	no	—
90	C₄⋊Q₈	—	43	1	no	—
91	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
92	C₄×D₄	—	43	1	no	—
93	#107	—	86	1	no	—
94	#107	—	86	1	no	—
95	C₄⋊C₈	—	43	1	no	—
96	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
97	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
98	#103	—	86	1	no	—
99	#103	—	86	1	no	—
100	C₂²⋊C₈	—	86	1	no	—
101	C₄×C₈	—	43	1	no	—
102	C₂×Q₈	—	2	1	no	—
103	C₂×Q₈	—	86	1	no	—
104	C₂×D₄	—	43	1	no	—
105	C₂²×C₄	—	86	1	no	—
106	SD₁₆	—	172	2	no	—
107	SD₁₆	—	172	2	no	—
108	M₁₆	—	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	—	2	1	no	—
115	C₄⋊C₄	—	2	1	no	—
116	C₄⋊C₄	—	43	1	no	—
117	C₄⋊C₄	—	86	1	no	—
118	C₄⋊C₄	—	86	1	no	—
119	C₂²⋊C₄	—	86	1	no	—
120	C₄²	C₂²×D₄₃	1	1	yes	characteristic
121	C₂³	—	86	1	no	—
122	Q₈	—	4	1	no	—
123	Q₈	—	4	1	no	—
124	Q₈	—	172	1	no	—
125	Q₈	—	172	1	no	—
126	D₄	—	86	1	no	—
127	D₄	—	86	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	86	1	no	—
130	C₂×C₄	—	172	1	no	—
131	C₂×C₄	—	172	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	—	43	2	no	—
139	C₈	—	86	1	no	—
140	C₈	—	172	1	no	—
141	C₂²	—	172	1	no	—
142	C₂²	—	172	1	no	—
143	C₂²	—	172	1	no	—
144	C₂²	#13063298	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	8	1	no	—
147	C₄	—	344	1	no	—
148	C₄	—	172	1	no	—
149	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
150	C₄	#13063349	1	1	yes	characteristic
151	C₄	#13063352	1	1	yes	characteristic
152	C₄	#13063357	1	1	yes	characteristic
153	C₂	—	344	1	no	—
154	C₂	#14583103	1	1	yes	characteristic
155	C₂	#14583151	1	1	yes	characteristic
156	C₂	#14583173	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583302

C₂

yes

maximal, characteristic, complemented

#14583105

C₂

yes

maximal, characteristic

#14583101

C₂

yes

maximal, characteristic

#14582976

C₂

yes

maximal, characteristic

#14582649

C₂

yes

maximal, characteristic, complemented

#14582644

C₂

yes

maximal, characteristic, complemented

C₄₃×#332

C₂

yes

maximal, characteristic, complemented

—

—

—

C₂²

yes

characteristic

C₄×D₁₇₂

C₂²

yes

characteristic

#13063258

—

#13063258

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

#13063250

—

#13063249

—

(C₂×D₄₃)⋊C₈

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₁₇₂

D₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621884

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

#10621873

—

#10621872

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×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

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

SD₁₆

yes

complemented

C₂²×C₄₃

#121

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#1693

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄×D₄

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

C₂×D₄₃

yes

characteristic

#103

—

#103

—

100

C₂²⋊C₈

—

101

C₄×C₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂²×C₄

—

106

SD₁₆

—

172

—

107

SD₁₆

—

172

—

108

M₁₆

—

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

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

C₂²×D₄₃

yes

characteristic

121

C₂³

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

172

—

125

Q₈

—

172

—

126

D₄

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

172

—

131

C₂×C₄

—

172

—

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

—

172

—

142

C₂²

—

172

—

143

C₂²

—

172

—

144

C₂²

#13063298

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

344

—

148

C₄

—

172

—

149

C₄

SD₁₆×D₄₃

yes

characteristic

150

C₄

#13063349

yes

characteristic

151

C₄

#13063352

yes

characteristic

152

C₄

#13063357

yes

characteristic

153

C₂

—

344

—

154

C₂

#14583103

yes

characteristic

155

C₂

#14583151

yes

characteristic

156

C₂

#14583173

yes

characteristic

	subgroup	G/H
center	C₂²	#13063298
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#332	C₂
socle	C₂²×C₄₃	#121
hypercenter	#332	D₄₃
hypocenter	C₄₃	#1693
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #332

subgroup

G/H

center

C₂²

#13063298

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#332

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #332

N	H ≅ G/N	type
1. #14583302	C₂	semidirect
5. #14582649	C₂	semidirect
6. #14582644	C₂	semidirect
7. C₄₃×#332	C₂	semidirect
61. C₄₃⋊C₈	SD₁₆	semidirect
85. #332	D₄₃	semidirect
86. C₄₃	#1693	semidirect

H ≅ G/N

type

1. #14583302

C₂

semidirect

5. #14582649

C₂

semidirect

6. #14582644

C₂

semidirect

7. C₄₃×#332

C₂

semidirect

61. C₄₃⋊C₈

SD₁₆

semidirect

85. #332

D₄₃

semidirect

86. C₄₃

#1693

semidirect

Subgroups — #19134107

Conjugacy classes of subgroups

Complements