Group #19142299 — subgroups

Subgroups — #19142299

Order 5504.

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

normal subgroups only

This group has 428 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	#14582818	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582814	C₂	1	3	yes	maximal
3	#14582810	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582793	C₂	1	3	yes	maximal, complemented
5	#14582788	C₂	1	3	yes	maximal, complemented
6	#14582763	C₂	1	3	yes	maximal, complemented
7	C₄₃×#393	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	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
20	#95×C₄₃	C₂²	1	3	yes	—
21	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
22	C₂³×D₄₃	C₂³	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	4	3	no	—
24	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
26	C₂×C₂²⋊D₄₃	—	4	3	no	—
27	C₂²×Dic₄₃	C₂³	1	3	yes	—
28	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
29	C₂²×Dic₄₃	C₂³	1	3	yes	—
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	—	4	3	no	—
35	Dic₄₃⋊C₄	—	4	3	no	—
36	C₄×Dic₄₃	—	2	6	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	Q₈×C₄₃	—	4	4	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	C₂×C₄×C₄₃	—	2	3	no	—
51	C₂²⋊D₄₃	—	4	4	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	—	2	3	no	—
58	C₂×Dic₄₃	#41	1	6	yes	—
59	C₂²×C₄₃	—	4	3	no	—
60	C₂²×C₄₃	—	4	3	no	—
61	C₂²×C₄₃	—	4	1	no	—
62	C₂²×C₄₃	C₂×#41	1	3	yes	—
63	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
64	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
65	C₂×D₄₃	—	4	3	no	—
66	C₂×D₄₃	—	4	3	no	—
67	C₂×D₄₃	—	4	1	no	—
68	C₄×C₄₃	—	4	3	no	—
69	C₄×C₄₃	—	4	3	no	—
70	Dic₄₃	—	2	6	no	—
71	Dic₄₃	—	4	3	no	—
72	Dic₄₃	—	4	1	no	—
73	#2785	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	—	8	1	no	—
75	C₂×C₄₃	#539	1	3	yes	—
76	C₂×C₄₃	#555	1	3	yes	—
77	C₂×C₄₃	H(3,𝔽₄)	1	1	yes	characteristic
78	D₄₃	—	8	1	no	—
79	#395	—	43	1	no	—
80	#394	—	43	3	no	—
81	#393	—	43	1	no	—
82	#393	D₄₃	1	1	yes	characteristic, complemented
83	#388	—	43	3	no	—
84	#388	—	43	3	no	—
85	#382	—	43	3	no	—
86	C₄₃	#2785	1	1	yes	characteristic, complemented, Sylow
87	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
88	C₂²×D₄	—	43	1	no	—
89	C₂×C₄⋊C₄	—	43	3	no	—
90	C₂×C₄⋊C₄	—	43	3	no	—
91	C₂×C₂²⋊C₄	—	43	3	no	—
92	C₂×C₂²⋊C₄	—	43	3	no	—
93	C₂×C₂²⋊C₄	—	43	3	no	—
94	C₂×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
95	C₂×C₄²	—	43	3	no	—
96	#95	—	43	3	no	—
97	#95	—	43	3	no	—
98	#95	—	43	3	no	—
99	#95	C₂×D₄₃	1	3	yes	—
100	C₂⁴	—	43	1	no	—
101	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
102	C₂×Q₈	—	4	3	no	—
103	C₂×D₄	—	172	3	no	—
104	C₂²×C₄	—	43	3	no	—
105	C₂²×C₄	—	43	3	no	—
106	C₂²×C₄	—	43	1	no	—
107	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
108	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
109	C₄⋊C₄	—	172	3	no	—
110	C₄⋊C₄	—	172	3	no	—
111	C₂²⋊C₄	—	4	3	no	—
112	C₂²⋊C₄	—	86	6	no	—
113	C₂²⋊C₄	—	86	6	no	—
114	C₂²⋊C₄	—	172	3	no	—
115	C₄²	—	86	6	no	—
116	C₂³	—	2	3	no	—
117	C₂³	—	2	3	no	—
118	C₂³	—	2	1	no	—
119	C₂³	—	86	3	no	—
120	C₂³	—	86	3	no	—
121	C₂³	—	86	1	no	—
122	C₂³	C₂³×D₄₃	1	1	yes	characteristic
123	Q₈	—	4	4	no	—
124	D₄	—	172	4	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	—	2	3	no	—
130	C₂×C₄	—	2	3	no	—
131	C₂×C₄	—	43	6	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	C₂×C₄	—	86	3	no	—
137	C₂×C₄	—	86	3	no	—
138	C₂²	—	4	3	no	—
139	C₂²	—	4	1	no	—
140	C₂²	—	4	3	no	—
141	C₂²	—	172	3	no	—
142	C₂²	—	172	1	no	—
143	C₂²	—	172	3	no	—
144	C₂²	#41×D₄₃	1	3	yes	—
145	C₂²	#13063370	1	3	yes	—
146	C₂²	#13063373	1	1	yes	characteristic
147	C₄	—	4	3	no	—
148	C₄	—	4	3	no	—
149	C₄	—	86	6	no	—
150	C₄	—	172	3	no	—
151	C₄	—	172	1	no	—
152	C₂	—	8	1	no	—
153	C₂	—	344	1	no	—
154	C₂	#14583495	1	3	yes	—
155	C₂	#14583611	1	3	yes	—
156	C₂	#14583642	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582818

C₂

yes

maximal, characteristic, complemented

#14582814

C₂

yes

maximal

#14582810

C₂

yes

maximal, characteristic, complemented

#14582793

C₂

yes

maximal, complemented

#14582788

C₂

yes

maximal, complemented

#14582763

C₂

yes

maximal, complemented

C₄₃×#393

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

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂³×D₄₃

C₂³

yes

characteristic

C₂×Q₈×C₄₃

—

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

—

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

—

Q₈×C₄₃

—

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

—

#2785

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#539

yes

—

C₂×C₄₃

#555

yes

—

C₂×C₄₃

H(3,𝔽₄)

yes

characteristic

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#388

—

#388

—

#382

—

C₄₃

#2785

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

—

—

—

C₂×D₄₃

yes

—

100

C₂⁴

—

101

C₂⁴

C₂²×D₄₃

yes

characteristic

102

C₂×Q₈

—

103

C₂×D₄

—

172

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

C₂²×D₄₃

yes

—

108

C₂²×C₄

C₂²×D₄₃

yes

—

109

C₄⋊C₄

—

172

—

110

C₄⋊C₄

—

172

—

111

C₂²⋊C₄

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

172

—

115

C₄²

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

C₂³×D₄₃

yes

characteristic

123

Q₈

—

124

D₄

—

172

—

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

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

172

—

142

C₂²

—

172

—

143

C₂²

—

172

—

144

C₂²

#41×D₄₃

yes

—

145

C₂²

#13063370

yes

—

146

C₂²

#13063373

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

172

—

151

C₄

—

172

—

152

C₂

—

153

C₂

—

344

—

154

C₂

#14583495

yes

—

155

C₂

#14583611

yes

—

156

C₂

#14583642

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#393	C₂
hypercenter	#393	D₄₃
hypocenter	C₄₃	#2785
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #393

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#393

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #393

N	H ≅ G/N	type
1. #14582818	C₂	semidirect
3. #14582810	C₂	semidirect
4. #14582793	C₂	semidirect
5. #14582788	C₂	semidirect
6. #14582763	C₂	semidirect
7. C₄₃×#393	C₂	semidirect
82. #393	D₄₃	semidirect
86. C₄₃	#2785	semidirect

H ≅ G/N

type

1. #14582818

C₂

semidirect

3. #14582810

C₂

semidirect

4. #14582793

C₂

semidirect

5. #14582788

C₂

semidirect

6. #14582763

C₂

semidirect

7. C₄₃×#393

C₂

semidirect

82. #393

D₄₃

semidirect

86. C₄₃

#2785

semidirect

Subgroups — #19142299

Conjugacy classes of subgroups

Complements