Group #19140557 — subgroups

Subgroups — #19140557

Order 5504.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14582827	C₂	1	3	yes	maximal, complemented
2	#14582825	C₂	1	3	yes	maximal, complemented
3	#14582823	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582799	C₂	1	3	yes	maximal
5	#14582794	C₂	1	3	yes	maximal, complemented
6	#14582744	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#396	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	6	yes	—
16	C₄₃⋊#95	C₂²	1	3	yes	—
17	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
18	C₂×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
19	#95×C₄₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
21	C₂³×D₄₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
24	C₂×C₂²⋊D₄₃	—	2	6	no	—
25	C₂²×Dic₄₃	C₂³	1	3	yes	—
26	C₂²×Dic₄₃	C₂³	1	3	yes	—
27	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
28	C₄⋊C₄×C₄₃	—	4	3	no	—
29	C₂²⋊C₄×C₄₃	—	4	3	no	—
30	C₂²⋊Dic₄₃	—	4	3	no	—
31	(C₂×D₄₃)⋊C₄	—	4	3	no	—
32	(C₂×D₄₃)⋊C₄	—	4	3	no	—
33	Dic₄₃⋊C₄	—	2	6	no	—
34	Dic₄₃⋊C₄	—	4	3	no	—
35	C₄×Dic₄₃	—	2	6	no	—
36	C₂³×C₄₃	—	2	3	no	—
37	C₂³×C₄₃	—	2	3	no	—
38	C₂³×C₄₃	—	2	1	no	—
39	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
40	C₂²×D₄₃	—	2	3	no	—
41	C₂²×D₄₃	—	2	3	no	—
42	C₂²×D₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	—	2	3	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	C₂²⋊D₄₃	—	4	4	no	—
50	C₂×Dic₄₃	—	2	3	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	#41	1	6	yes	—
57	C₂²×C₄₃	—	4	1	no	—
58	C₂²×C₄₃	—	4	3	no	—
59	C₂²×C₄₃	—	4	3	no	—
60	C₂²×C₄₃	C₂×#41	1	3	yes	—
61	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
62	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
63	C₂×D₄₃	—	4	1	no	—
64	C₂×D₄₃	—	4	3	no	—
65	C₂×D₄₃	—	4	3	no	—
66	C₄×C₄₃	—	4	3	no	—
67	C₄×C₄₃	—	4	3	no	—
68	Dic₄₃	—	4	3	no	—
69	Dic₄₃	—	4	3	no	—
70	Dic₄₃	#126	1	4	yes	—
71	#2644	—	43	1	no	maximal, Sylow
72	C₂×C₄₃	—	8	1	no	—
73	C₂×C₄₃	C₂×#126	1	1	yes	characteristic
74	C₂×C₄₃	#540	1	3	yes	—
75	C₂×C₄₃	#542	1	3	yes	—
76	D₄₃	—	8	1	no	—
77	#397	—	43	3	no	—
78	#397	—	43	3	no	—
79	#396	—	43	1	no	—
80	#396	D₄₃	1	1	yes	characteristic, complemented
81	#390	—	43	3	no	—
82	#389	—	43	3	no	—
83	#376	—	43	1	no	—
84	C₄₃	#2644	1	1	yes	characteristic, complemented, Sylow
85	C₂²×D₄	—	43	1	no	—
86	C₂×C₄⋊C₄	—	43	3	no	—
87	C₂×C₄⋊C₄	—	43	3	no	—
88	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
89	C₂×C₂²⋊C₄	—	43	3	no	—
90	C₂×C₂²⋊C₄	—	43	3	no	—
91	C₂×C₂²⋊C₄	—	43	3	no	—
92	C₂×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
93	C₂×C₄²	—	43	3	no	—
94	#95	—	43	3	no	—
95	#95	—	43	6	no	—
96	#95	C₂×D₄₃	1	1	yes	characteristic
97	C₂⁴	—	43	1	no	—
98	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
99	C₂×D₄	—	86	6	no	—
100	C₂²×C₄	—	43	1	no	—
101	C₂²×C₄	—	43	3	no	—
102	C₂²×C₄	—	43	3	no	—
103	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
104	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
105	C₄⋊C₄	—	4	3	no	—
106	C₄⋊C₄	—	86	6	no	—
107	C₄⋊C₄	—	172	3	no	—
108	C₂²⋊C₄	—	4	3	no	—
109	C₂²⋊C₄	—	172	3	no	—
110	C₂²⋊C₄	—	172	3	no	—
111	C₂²⋊C₄	—	172	3	no	—
112	C₄²	—	86	6	no	—
113	C₂³	—	2	3	no	—
114	C₂³	—	2	3	no	—
115	C₂³	—	2	1	no	—
116	C₂³	—	86	3	no	—
117	C₂³	—	86	3	no	—
118	C₂³	—	86	1	no	—
119	C₂³	C₂³×D₄₃	1	1	yes	characteristic
120	D₄	—	172	4	no	—
121	C₂×C₄	—	2	3	no	—
122	C₂×C₄	—	2	3	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	—	43	6	no	—
128	C₂×C₄	—	86	3	no	—
129	C₂×C₄	—	86	3	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	C₂²	—	4	1	no	—
135	C₂²	—	4	3	no	—
136	C₂²	—	4	3	no	—
137	C₂²	—	172	1	no	—
138	C₂²	—	172	3	no	—
139	C₂²	—	172	3	no	—
140	C₂²	#41×D₄₃	1	3	yes	—
141	C₂²	#13063370	1	3	yes	—
142	C₂²	#13063373	1	1	yes	characteristic
143	C₄	—	4	3	no	—
144	C₄	—	4	3	no	—
145	C₄	—	43	4	no	—
146	C₄	—	172	3	no	—
147	C₄	—	172	3	no	—
148	C₂	—	8	1	no	—
149	C₂	—	344	1	no	—
150	C₂	#126×D₄₃	1	1	yes	characteristic
151	C₂	#14583499	1	3	yes	—
152	C₂	#14583519	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582827

C₂

yes

maximal, complemented

#14582825

C₂

yes

maximal, complemented

#14582823

C₂

yes

maximal, characteristic, complemented

#14582799

C₂

yes

maximal

#14582794

C₂

yes

maximal, complemented

#14582744

C₂

yes

maximal, characteristic, complemented

C₄₃×#396

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

—

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

—

C₂²×Dic₄₃

C₂³

yes

characteristic

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

#126

yes

—

#2644

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#126

yes

characteristic

C₂×C₄₃

#540

yes

—

C₂×C₄₃

#542

yes

—

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#390

—

#389

—

#376

—

C₄₃

#2644

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

—

#95

—

#95

—

#95

C₂×D₄₃

yes

characteristic

C₂⁴

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂×D₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₂²×D₄₃

yes

—

104

C₂²×C₄

C₂²×D₄₃

yes

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

172

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

172

—

110

C₂²⋊C₄

—

172

—

111

C₂²⋊C₄

—

172

—

112

C₄²

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₂³×D₄₃

yes

characteristic

120

D₄

—

172

—

121

C₂×C₄

—

122

C₂×C₄

—

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

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

172

—

138

C₂²

—

172

—

139

C₂²

—

172

—

140

C₂²

#41×D₄₃

yes

—

141

C₂²

#13063370

yes

—

142

C₂²

#13063373

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

172

—

147

C₄

—

172

—

148

C₂

—

149

C₂

—

344

—

150

C₂

#126×D₄₃

yes

characteristic

151

C₂

#14583499

yes

—

152

C₂

#14583519

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#396	C₂
hypercenter	#396	D₄₃
hypocenter	C₄₃	#2644
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #396

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#396

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #396

N	H ≅ G/N	type
1. #14582827	C₂	semidirect
2. #14582825	C₂	semidirect
3. #14582823	C₂	semidirect
5. #14582794	C₂	semidirect
6. #14582744	C₂	semidirect
7. C₄₃×#396	C₂	semidirect
80. #396	D₄₃	semidirect
84. C₄₃	#2644	semidirect

H ≅ G/N

type

1. #14582827

C₂

semidirect

2. #14582825

C₂

semidirect

3. #14582823

C₂

semidirect

5. #14582794

C₂

semidirect

6. #14582744

C₂

semidirect

7. C₄₃×#396

C₂

semidirect

80. #396

D₄₃

semidirect

84. C₄₃

#2644

semidirect

Subgroups — #19140557

Conjugacy classes of subgroups

Complements