Group #19142503 — subgroups

Subgroups — #19142503

Order 5504.

420 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 119 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	C₄₃⋊#401	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582823	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582814	C₂	1	3	yes	maximal
4	#14582794	C₂	1	3	yes	maximal, complemented
5	#14582789	C₂	1	3	yes	maximal, complemented
6	#14582787	C₂	1	3	yes	maximal, complemented
7	C₄₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
10	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
11	C₂×C₂²⋊Dic₄₃	C₂²	1	3	yes	—
12	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
13	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
15	C₄₃⋊#95	C₂²	1	3	yes	—
16	C₄₃⋊#95	C₂²	1	3	yes	—
17	C₄₃⋊#95	C₂²	1	3	yes	—
18	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
19	C₂×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
20	#95×C₄₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
22	C₂³×D₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
25	C₂×C₂²⋊D₄₃	—	4	3	no	—
26	C₂²×Dic₄₃	C₂³	1	3	yes	—
27	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
28	C₂²×Dic₄₃	C₂³	1	3	yes	—
29	C₄⋊C₄×C₄₃	—	4	3	no	—
30	C₂²⋊C₄×C₄₃	—	4	3	no	—
31	C₂²⋊Dic₄₃	—	2	6	no	—
32	(C₂×D₄₃)⋊C₄	—	2	6	no	—
33	(C₂×D₄₃)⋊C₄	—	4	3	no	—
34	Dic₄₃⋊C₄	—	2	6	no	—
35	Dic₄₃⋊C₄	—	4	3	no	—
36	C₄×Dic₄₃	—	4	3	no	—
37	C₂³×C₄₃	—	2	3	no	—
38	C₂³×C₄₃	—	2	3	no	—
39	C₂³×C₄₃	—	2	1	no	—
40	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
41	C₂²×D₄₃	—	2	3	no	—
42	C₂²×D₄₃	—	2	3	no	—
43	C₂²×D₄₃	—	2	1	no	—
44	C₂×C₄×C₄₃	—	2	3	no	—
45	C₂×C₄×C₄₃	—	2	3	no	—
46	C₂×C₄×C₄₃	—	2	3	no	—
47	C₂×C₄×C₄₃	—	2	3	no	—
48	C₂×C₄×C₄₃	—	2	3	no	—
49	C₂×C₄×C₄₃	—	2	3	no	—
50	C₂²⋊D₄₃	—	4	4	no	—
51	C₂×Dic₄₃	—	2	3	no	—
52	C₂×Dic₄₃	—	2	3	no	—
53	C₂×Dic₄₃	—	2	3	no	—
54	C₂×Dic₄₃	—	2	3	no	—
55	C₂×Dic₄₃	—	2	3	no	—
56	C₂×Dic₄₃	—	2	3	no	—
57	C₂×Dic₄₃	#41	1	6	yes	—
58	C₂²×C₄₃	—	4	3	no	—
59	C₂²×C₄₃	—	4	3	no	—
60	C₂²×C₄₃	—	4	1	no	—
61	C₂²×C₄₃	C₂×#41	1	3	yes	—
62	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
63	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
64	C₂×D₄₃	—	4	3	no	—
65	C₂×D₄₃	—	4	3	no	—
66	C₂×D₄₃	—	4	1	no	—
67	C₄×C₄₃	—	4	3	no	—
68	C₄×C₄₃	—	4	3	no	—
69	Dic₄₃	—	2	6	no	—
70	Dic₄₃	—	4	3	no	—
71	Dic₄₃	—	4	1	no	—
72	#2801	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	—	8	1	no	—
74	C₂×C₄₃	#542	1	3	yes	—
75	C₂×C₄₃	#553	1	3	yes	—
76	C₂×C₄₃	#560	1	1	yes	characteristic
77	D₄₃	—	8	1	no	—
78	#401	—	43	1	no	—
79	#399	D₄₃	1	1	yes	characteristic, complemented
80	#396	—	43	1	no	—
81	#394	—	43	3	no	—
82	#389	—	43	3	no	—
83	#388	—	43	3	no	—
84	#388	—	43	3	no	—
85	C₄₃	#2801	1	1	yes	characteristic, complemented, Sylow
86	C₂²×D₄	—	43	1	no	—
87	C₂×C₄⋊C₄	—	43	3	no	—
88	C₂×C₄⋊C₄	—	43	3	no	—
89	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
90	C₂×C₂²⋊C₄	—	43	3	no	—
91	C₂×C₂²⋊C₄	—	43	3	no	—
92	C₂×C₂²⋊C₄	—	43	3	no	—
93	C₂×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
94	C₂×C₄²	—	43	3	no	—
95	#95	—	43	3	no	—
96	#95	—	43	3	no	—
97	#95	—	43	3	no	—
98	#95	C₂×D₄₃	1	1	yes	characteristic
99	C₂⁴	—	43	1	no	—
100	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
101	C₂×D₄	—	172	3	no	—
102	C₂²×C₄	—	43	3	no	—
103	C₂²×C₄	—	43	3	no	—
104	C₂²×C₄	—	43	1	no	—
105	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
106	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
107	C₄⋊C₄	—	4	3	no	—
108	C₄⋊C₄	—	86	6	no	—
109	C₄⋊C₄	—	172	3	no	—
110	C₂²⋊C₄	—	4	3	no	—
111	C₂²⋊C₄	—	86	6	no	—
112	C₂²⋊C₄	—	86	6	no	—
113	C₂²⋊C₄	—	172	3	no	—
114	C₄²	—	172	3	no	—
115	C₂³	—	2	3	no	—
116	C₂³	—	2	3	no	—
117	C₂³	—	2	1	no	—
118	C₂³	—	86	3	no	—
119	C₂³	—	86	3	no	—
120	C₂³	—	86	1	no	—
121	C₂³	C₂³×D₄₃	1	1	yes	characteristic
122	D₄	—	172	4	no	—
123	C₂×C₄	—	2	3	no	—
124	C₂×C₄	—	2	3	no	—
125	C₂×C₄	—	2	3	no	—
126	C₂×C₄	—	2	3	no	—
127	C₂×C₄	—	2	3	no	—
128	C₂×C₄	—	2	3	no	—
129	C₂×C₄	—	43	6	no	—
130	C₂×C₄	—	86	3	no	—
131	C₂×C₄	—	86	3	no	—
132	C₂×C₄	—	86	3	no	—
133	C₂×C₄	—	86	3	no	—
134	C₂×C₄	—	86	3	no	—
135	C₂×C₄	—	86	3	no	—
136	C₂²	—	4	3	no	—
137	C₂²	—	4	1	no	—
138	C₂²	—	4	3	no	—
139	C₂²	—	172	3	no	—
140	C₂²	—	172	1	no	—
141	C₂²	—	172	3	no	—
142	C₂²	#41×D₄₃	1	3	yes	—
143	C₂²	#13063370	1	3	yes	—
144	C₂²	#13063373	1	1	yes	characteristic
145	C₄	—	4	3	no	—
146	C₄	—	4	3	no	—
147	C₄	—	86	6	no	—
148	C₄	—	172	1	no	—
149	C₄	—	172	3	no	—
150	C₂	—	8	1	no	—
151	C₂	—	344	1	no	—
152	C₂	#14583519	1	3	yes	—
153	C₂	#14583594	1	3	yes	—
154	C₂	#14583636	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₃⋊#401

C₂

yes

maximal, characteristic, complemented

#14582823

C₂

yes

maximal, characteristic, complemented

#14582814

C₂

yes

maximal

#14582794

C₂

yes

maximal, complemented

#14582789

C₂

yes

maximal, complemented

#14582787

C₂

yes

maximal, complemented

C₄₃×#399

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂³×D₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#41

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2801

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#542

yes

—

C₂×C₄₃

#553

yes

—

C₂×C₄₃

#560

yes

characteristic

D₄₃

—

#401

—

#399

D₄₃

yes

characteristic, complemented

—

—

—

—

—

C₄₃

#2801

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

—

—

—

C₂×D₄₃

yes

characteristic

C₂⁴

—

100

C₂⁴

C₂²×D₄₃

yes

characteristic

101

C₂×D₄

—

172

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

C₂²×D₄₃

yes

—

106

C₂²×C₄

C₂²×D₄₃

yes

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

172

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

172

—

114

C₄²

—

172

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

C₂³×D₄₃

yes

characteristic

122

D₄

—

172

—

123

C₂×C₄

—

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

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

172

—

140

C₂²

—

172

—

141

C₂²

—

172

—

142

C₂²

#41×D₄₃

yes

—

143

C₂²

#13063370

yes

—

144

C₂²

#13063373

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

172

—

149

C₄

—

172

—

150

C₂

—

151

C₂

—

344

—

152

C₂

#14583519

yes

—

153

C₂

#14583594

yes

—

154

C₂

#14583636

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#399	C₂
hypercenter	#399	D₄₃
hypocenter	C₄₃	#2801
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #399

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#399

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #399

N	H ≅ G/N	type
1. C₄₃⋊#401	C₂	semidirect
2. #14582823	C₂	semidirect
4. #14582794	C₂	semidirect
5. #14582789	C₂	semidirect
6. #14582787	C₂	semidirect
7. C₄₃×#399	C₂	semidirect
79. #399	D₄₃	semidirect
85. C₄₃	#2801	semidirect

H ≅ G/N

type

1. C₄₃⋊#401

C₂

semidirect

2. #14582823

C₂

semidirect

4. #14582794

C₂

semidirect

5. #14582789

C₂

semidirect

6. #14582787

C₂

semidirect

7. C₄₃×#399

C₂

semidirect

79. #399

D₄₃

semidirect

85. C₄₃

#2801

semidirect

Subgroups — #19142503

Conjugacy classes of subgroups

Complements