Group #19143237 — subgroups

Subgroups — #19143237

Order 5504.

400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 181 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	C₄×#10621898	C₂	1	1	yes	maximal, characteristic
2	#14582958	C₂	1	4	yes	maximal, complemented
3	#14582950	C₂	1	4	yes	maximal, complemented
4	#14582925	C₂	1	2	yes	maximal, complemented
5	#14582865	C₂	1	2	yes	maximal
6	C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621898	C₂²	1	1	yes	characteristic
9	C₂×#10621877	C₂²	1	2	yes	—
10	C₄×Dic₈₆	C₄	1	2	yes	—
11	C₄×D₁₇₂	C₄	1	2	yes	—
12	C₄×C₂²⋊D₄₃	C₄	1	4	yes	—
13	#13063284	C₂²	1	1	yes	characteristic
14	#13063282	C₂²	1	2	yes	—
15	C₄²×D₄₃	C₂²	1	2	yes	—
16	Dic₄₃⋊C₈	C₂²	1	8	yes	—
17	(C₂×D₄₃)⋊C₈	C₂²	1	8	yes	—
18	#13063236	C₂²	1	2	yes	—
19	C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
20	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×C₈×C₄₃	C₂²	1	2	yes	—
23	C₄×C₈×C₄₃	C₂²	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
27	#10621898	—	2	4	no	—
28	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×D₄₃	C₂×C₄	1	4	yes	—
30	C₂×C₄×D₄₃	C₂³	1	2	yes	—
31	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×C₄₃	—	2	4	no	—
33	C₂×C₈×C₄₃	C₂³	1	4	yes	—
34	C₄²×C₄₃	C₂×C₄	1	2	yes	—
35	C₄²×C₄₃	C₂³	1	1	yes	characteristic
36	C₄²×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
38	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	—
39	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
40	Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
41	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
42	C₄×Dic₄₃	C₂³	1	2	yes	—
43	#10621877	—	2	4	no	—
44	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
45	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
46	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₄₃	—	2	4	no	—
48	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
49	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
51	C₂×C₄×C₄₃	#41	1	4	yes	—
52	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
53	C₂²⋊D₄₃	—	2	4	no	—
54	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
55	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
56	D₁₇₂	—	2	2	no	—
57	C₄×D₄₃	—	2	8	no	—
58	C₄×D₄₃	—	2	4	no	—
59	Dic₈₆	—	2	2	no	—
60	C₈×C₄₃	—	2	4	no	—
61	C₄₃⋊C₈	—	2	4	no	—
62	C₂²×C₄₃	—	2	2	no	—
63	C₂²×C₄₃	#117	1	2	yes	—
64	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
65	C₂×D₄₃	—	2	2	no	—
66	C₂×D₄₃	—	2	4	no	—
67	C₄×C₄₃	—	2	2	no	—
68	C₄×C₄₃	#117	1	2	yes	—
69	C₄×C₄₃	#131	1	4	yes	—
70	C₄×C₄₃	C₂×#41	1	2	yes	—
71	Dic₄₃	—	2	2	no	—
72	Dic₄₃	—	2	4	no	—
73	#2922	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	—	2	2	no	—
75	C₂×C₄₃	C₂×#117	1	1	yes	characteristic
76	C₂×C₄₃	C₂×#131	1	2	yes	—
77	D₄₃	—	4	2	no	—
78	C₄×#41	—	43	1	no	—
79	#433	—	43	4	no	—
80	#431	—	43	4	no	—
81	#424	—	43	2	no	—
82	#408	—	43	2	no	—
83	C₄×M₁₆	—	43	1	no	—
84	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic, complemented
85	C₄₃	#2922	1	1	yes	characteristic, complemented, Sylow
86	C₂×#41	—	43	1	no	—
87	C₂×M₁₆	—	43	2	no	—
88	C₂²×C₈	C₂×D₄₃	1	2	yes	—
89	C₄×Q₈	—	43	2	no	—
90	C₄×D₄	—	43	4	no	—
91	C₄×D₄	—	43	2	no	—
92	#117	—	43	1	no	—
93	#117	—	43	2	no	—
94	C₂×C₄²	—	43	2	no	—
95	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
96	C₄⋊C₈	—	43	8	no	—
97	C₂²⋊C₈	—	43	8	no	—
98	#97	—	43	2	no	—
99	C₄×C₈	—	43	2	no	—
100	C₄×C₈	C₂×D₄₃	1	2	yes	—
101	C₄×C₈	C₂×D₄₃	1	2	yes	—
102	#41	—	86	4	no	—
103	C₂×Q₈	—	43	1	no	—
104	C₂×D₄	—	43	2	no	—
105	C₂×D₄	—	43	1	no	—
106	C₂²×C₄	—	43	4	no	—
107	C₂²×C₄	—	43	2	no	—
108	C₂²×C₄	C₄×D₄₃	1	2	yes	—
109	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
110	M₁₆	—	86	4	no	—
111	C₂×C₈	—	2	4	no	—
112	C₂×C₈	—	43	4	no	—
113	C₂×C₈	C₂²×D₄₃	1	4	yes	—
114	C₄⋊C₄	—	43	4	no	—
115	C₄⋊C₄	—	43	2	no	—
116	C₂²⋊C₄	—	43	2	no	—
117	C₂²⋊C₄	—	43	4	no	—
118	C₄²	—	43	4	no	—
119	C₄²	—	43	2	no	—
120	C₄²	C₄×D₄₃	1	2	yes	—
121	C₄²	C₂²×D₄₃	1	1	yes	characteristic
122	C₄²	C₂²×D₄₃	1	1	yes	characteristic
123	C₂³	—	43	2	no	—
124	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
125	Q₈	—	86	2	no	—
126	D₄	—	86	4	no	—
127	D₄	—	86	2	no	—
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	43	4	no	—
130	C₂×C₄	—	43	2	no	—
131	C₂×C₄	—	86	8	no	—
132	C₂×C₄	—	86	4	no	—
133	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
134	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
135	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
136	C₂×C₄	#10621898	1	4	yes	—
137	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
138	C₈	—	2	4	no	—
139	C₈	—	86	4	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	86	2	no	—
142	C₂²	—	86	4	no	—
143	C₂²	#13063282	1	2	yes	—
144	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	86	2	no	—
147	C₄	—	86	4	no	—
148	C₄	#13063282	1	2	yes	—
149	C₄	#13063331	1	4	yes	—
150	C₄	C₂×#10621898	1	2	yes	—
151	C₂	—	2	2	no	—
152	C₂	—	172	2	no	—
153	C₂	C₂×#13063282	1	1	yes	characteristic
154	C₂	C₂×#13063331	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10621898

C₂

yes

maximal, characteristic

#14582958

C₂

yes

maximal, complemented

#14582950

C₂

yes

maximal, complemented

#14582925

C₂

yes

maximal, complemented

#14582865

C₂

yes

maximal

C₄×#10621877

C₂

yes

maximal, characteristic, complemented

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

C₄×Dic₈₆

C₄

yes

—

C₄×D₁₇₂

C₄

yes

—

C₄×C₂²⋊D₄₃

C₄

yes

—

#13063284

C₂²

yes

characteristic

#13063282

C₂²

yes

—

C₄²×D₄₃

C₂²

yes

—

Dic₄₃⋊C₈

C₂²

yes

—

(C₂×D₄₃)⋊C₈

C₂²

yes

—

#13063236

C₂²

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₂²⋊D₄₃

C₂×C₄

yes

—

#10621898

—

C₂×D₁₇₂

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂³

yes

—

C₂×Dic₈₆

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

C₂×C₄

yes

—

(C₂×D₄₃)⋊C₄

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂³

yes

—

#10621877

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂²×D₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#117

yes

—

C₄×C₄₃

#131

yes

—

C₄×C₄₃

C₂×#41

yes

—

Dic₄₃

—

Dic₄₃

—

#2922

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#117

yes

characteristic

C₂×C₄₃

C₂×#131

yes

—

D₄₃

—

C₄×#41

—

—

—

—

—

C₄×M₁₆

—

C₂×C₄×C₈

D₄₃

yes

characteristic, complemented

C₄₃

#2922

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₃

yes

—

C₄×Q₈

—

C₄×D₄

—

C₄×D₄

—

#117

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

100

C₄×C₈

C₂×D₄₃

yes

—

101

C₄×C₈

C₂×D₄₃

yes

—

102

#41

—

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₄×D₄₃

yes

—

109

C₂²×C₄

C₂²×D₄₃

yes

characteristic

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₄₃

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₄×D₄₃

yes

—

121

C₄²

C₂²×D₄₃

yes

characteristic

122

C₄²

C₂²×D₄₃

yes

characteristic

123

C₂³

—

124

C₂³

C₂×C₄×D₄₃

yes

characteristic

125

Q₈

—

126

D₄

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂×C₄×D₄₃

yes

—

134

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

135

C₂×C₄

C₂×C₄×D₄₃

yes

—

136

C₂×C₄

#10621898

yes

—

137

C₂×C₄

C₂³×D₄₃

yes

characteristic

138

C₈

—

139

C₈

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#13063282

yes

—

144

C₂²

C₂²×C₄×D₄₃

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

#13063282

yes

—

149

C₄

#13063331

yes

—

150

C₄

C₂×#10621898

yes

—

151

C₂

—

152

C₂

—

172

—

153

C₂

C₂×#13063282

yes

characteristic

154

C₂

C₂×#13063331

yes

—

	subgroup	G/H
center	C₄²	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#2922
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₄²

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

hypercenter

C₂×C₄×C₈

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #14582958	C₂	semidirect
3. #14582950	C₂	semidirect
4. #14582925	C₂	semidirect
6. C₄×#10621877	C₂	semidirect
7. C₂×C₄×C₈×C₄₃	C₂	semidirect
84. C₂×C₄×C₈	D₄₃	semidirect
85. C₄₃	#2922	semidirect

H ≅ G/N

type

2. #14582958

C₂

semidirect

3. #14582950

C₂

semidirect

4. #14582925

C₂

semidirect

6. C₄×#10621877

C₂

semidirect

7. C₂×C₄×C₈×C₄₃

C₂

semidirect

84. C₂×C₄×C₈

D₄₃

semidirect

85. C₄₃

#2922

semidirect

Subgroups — #19143237

Conjugacy classes of subgroups

Complements