Group #19142588 — subgroups

Subgroups — #19142588

Order 5504.

432 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 157 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	#14582820	C₂	1	4	yes	maximal
2	#14582819	C₂	1	2	yes	maximal
3	#14582806	C₂	1	2	yes	maximal
4	#14582805	C₂	1	2	yes	maximal
5	#14582803	C₂	1	4	yes	maximal
6	C₄₃×#391	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₈₆	C₂²	1	2	yes	—
8	C₂²×Dic₈₆	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
11	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
12	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
13	C₄₃⋊#95	C₂²	1	2	yes	—
14	C₄₃⋊#95	C₂²	1	4	yes	—
15	C₄₃⋊#95	C₂²	1	4	yes	—
16	C₄₃⋊#95	C₂²	1	4	yes	—
17	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	#95×C₄₃	C₂²	1	4	yes	—
21	C₂×Q₈×C₄₃	—	4	1	no	—
22	C₂×Q₈×C₄₃	—	4	1	no	—
23	C₂×Q₈×C₄₃	Q₈	1	4	yes	complemented
24	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
27	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²×Dic₄₃	C₂³	1	4	yes	—
29	C₂²×Dic₄₃	C₂³	1	4	yes	—
30	C₂×Dic₈₆	—	4	2	no	—
31	C₂×Dic₈₆	—	4	2	no	—
32	C₂×Dic₈₆	—	4	4	no	—
33	C₂×Dic₈₆	—	4	2	no	—
34	C₂×Dic₈₆	Q₈	1	8	yes	complemented
35	C₄⋊C₄×C₄₃	—	4	1	no	—
36	C₄²×C₄₃	—	4	1	no	—
37	C₄⋊Dic₄₃	—	4	2	no	—
38	C₄⋊Dic₄₃	—	4	2	no	—
39	Dic₄₃⋊C₄	—	4	4	no	—
40	C₄×Dic₄₃	—	4	2	no	—
41	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
42	Q₈×C₄₃	—	4	4	no	—
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	—	2	2	no	—
46	C₂×C₄×C₄₃	—	2	2	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	—	2	1	no	—
49	C₂×C₄×C₄₃	—	2	4	no	—
50	C₂×C₄×C₄₃	—	2	2	no	—
51	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
52	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
53	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
54	C₂×Dic₄₃	—	2	4	no	—
55	C₂×Dic₄₃	—	2	4	no	—
56	C₂×Dic₄₃	—	2	4	no	—
57	C₂×Dic₄₃	—	2	4	no	—
58	C₂×Dic₄₃	—	2	4	no	—
59	C₂×Dic₄₃	C₂×Q₈	1	8	yes	—
60	Dic₈₆	—	4	8	no	—
61	Dic₈₆	—	4	8	no	—
62	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
63	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
64	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
65	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
66	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
67	C₄×C₄₃	—	2	4	no	—
68	C₄×C₄₃	—	2	4	no	—
69	C₄×C₄₃	—	2	2	no	—
70	C₄×C₄₃	—	4	2	no	—
71	Dic₄₃	—	2	8	no	—
72	Dic₄₃	—	4	4	no	—
73	#2811	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	#543	1	2	yes	—
75	C₂×C₄₃	#543	1	1	yes	characteristic
76	C₂×C₄₃	Q₈²	1	1	yes	characteristic
77	C₂×C₄₃	Q₈²	1	2	yes	—
78	C₂×C₄₃	H(3,𝔽₄)	1	1	yes	characteristic
79	#395	—	43	2	no	—
80	#395	—	43	4	no	—
81	#391	—	43	2	no	—
82	#391	—	43	2	no	—
83	#391	—	43	4	no	—
84	#391	D₄₃	1	1	yes	characteristic
85	C₄₃	#2811	1	1	yes	characteristic, complemented, Sylow
86	C₂²×Q₈	—	43	2	no	—
87	C₂²×Q₈	—	43	2	no	—
88	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
89	C₂×C₄⋊C₄	—	43	4	no	—
90	C₂×C₄⋊C₄	—	43	2	no	—
91	C₂×C₄⋊C₄	—	43	2	no	—
92	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
93	C₂×C₄²	—	43	2	no	—
94	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
95	#95	—	43	2	no	—
96	#95	—	43	4	no	—
97	#95	—	43	4	no	—
98	#95	—	43	4	no	—
99	#95	C₂×D₄₃	1	4	yes	—
100	C₂×Q₈	—	4	1	no	—
101	C₂×Q₈	—	4	1	no	—
102	C₂×Q₈	—	43	8	no	—
103	C₂×Q₈	—	172	2	no	—
104	C₂×Q₈	—	172	2	no	—
105	C₂×Q₈	—	172	2	no	—
106	C₂×Q₈	—	172	4	no	—
107	C₂×Q₈	Dic₈₆	1	4	yes	complemented
108	C₂²×C₄	—	43	4	no	—
109	C₂²×C₄	—	43	4	no	—
110	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
111	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
112	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
113	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
114	C₄⋊C₄	—	4	1	no	—
115	C₄⋊C₄	—	172	4	no	—
116	C₄⋊C₄	—	172	2	no	—
117	C₄⋊C₄	—	172	2	no	—
118	C₄²	—	4	1	no	—
119	C₄²	—	172	2	no	—
120	C₂³	C₂³×D₄₃	1	1	yes	characteristic
121	Q₈	—	4	4	no	—
122	Q₈	—	172	8	no	—
123	Q₈	—	172	8	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	43	8	no	—
133	C₂×C₄	—	86	4	no	—
134	C₂×C₄	—	86	4	no	—
135	C₂×C₄	—	86	4	no	—
136	C₂×C₄	—	86	4	no	—
137	C₂×C₄	—	86	4	no	—
138	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
139	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
140	C₂×C₄	Q₈×D₄₃	1	4	yes	—
141	C₂²	C₂×Q₈×D₄₃	1	2	yes	—
142	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
143	C₂²	#13063370	1	1	yes	characteristic
144	C₂²	#13063370	1	1	yes	characteristic
145	C₂²	#13063371	1	2	yes	—
146	C₄	—	2	4	no	—
147	C₄	—	2	2	no	—
148	C₄	—	2	4	no	—
149	C₄	—	4	2	no	—
150	C₄	—	86	8	no	—
151	C₄	—	172	4	no	—
152	C₂	#14583524	1	2	yes	—
153	C₂	#14583525	1	1	yes	characteristic
154	C₂	#14583629	1	1	yes	characteristic
155	C₂	Q₈×Dic₈₆	1	2	yes	—
156	C₂	#14583641	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582820

C₂

yes

maximal

#14582819

C₂

yes

maximal

#14582806

C₂

yes

maximal

#14582805

C₂

yes

maximal

#14582803

C₂

yes

maximal

C₄₃×#391

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

C₂²×Dic₈₆

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

Q₈

yes

complemented

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

Q₈

yes

complemented

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×Q₈

yes

—

Dic₈₆

—

Dic₈₆

—

C₂²×C₄₃

C₂²×Q₈

yes

—

C₂²×C₄₃

C₂²×Q₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2811

—

maximal, Sylow

C₂×C₄₃

#543

yes

—

C₂×C₄₃

#543

yes

characteristic

C₂×C₄₃

Q₈²

yes

characteristic

C₂×C₄₃

Q₈²

yes

—

C₂×C₄₃

yes

—

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#2811

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

C₂×D₄₃

yes

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

172

—

104

C₂×Q₈

—

172

—

105

C₂×Q₈

—

172

—

106

C₂×Q₈

—

172

—

107

C₂×Q₈

Dic₈₆

yes

complemented

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²×D₄₃

yes

—

111

C₂²×C₄

C₂²×D₄₃

yes

characteristic

112

C₂²×C₄

C₂²×D₄₃

yes

—

113

C₂²×C₄

C₂²×D₄₃

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

172

—

116

C₄⋊C₄

—

172

—

117

C₄⋊C₄

—

172

—

118

C₄²

—

119

C₄²

—

172

—

120

C₂³

C₂³×D₄₃

yes

characteristic

121

Q₈

—

122

Q₈

—

172

—

123

Q₈

—

172

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

C₂×Dic₈₆

yes

—

139

C₂×C₄

C₂×Dic₈₆

yes

—

140

C₂×C₄

Q₈×D₄₃

yes

—

141

C₂²

C₂×Q₈×D₄₃

yes

—

142

C₂²

C₂²×Dic₈₆

yes

characteristic

143

C₂²

#13063370

yes

characteristic

144

C₂²

#13063370

yes

characteristic

145

C₂²

#13063371

yes

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

172

—

152

C₂

#14583524

yes

—

153

C₂

#14583525

yes

characteristic

154

C₂

#14583629

yes

characteristic

155

C₂

Q₈×Dic₈₆

yes

—

156

C₂

#14583641

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#391	C₂
hypercenter	#391	D₄₃
hypocenter	C₄₃	#2811
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #391

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#391

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #391

N	H ≅ G/N	type
23. C₂×Q₈×C₄₃	Q₈	semidirect
34. C₂×Dic₈₆	Q₈	semidirect
85. C₄₃	#2811	semidirect
107. C₂×Q₈	Dic₈₆	semidirect

H ≅ G/N

type

23. C₂×Q₈×C₄₃

Q₈

semidirect

34. C₂×Dic₈₆

Q₈

semidirect

85. C₄₃

#2811

semidirect

107. C₂×Q₈

Dic₈₆

semidirect

Subgroups — #19142588

Conjugacy classes of subgroups

Complements