Group #19143077 — subgroups

Subgroups — #19143077

Order 5504.

704 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 249 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	C₂×#13063372	C₂	1	1	yes	maximal, characteristic
2	#14583666	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582881	C₂	1	6	yes	maximal, complemented
4	C₂×#13063243	C₂	1	6	yes	maximal, complemented
5	C₄₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063372	—	2	4	no	—
7	#13063372	—	2	4	no	—
8	C₂×#10621898	C₂²	1	3	yes	—
9	C₂×#10621900	C₄	1	6	yes	—
10	C₂²×Dic₈₆	C₂²	1	3	yes	—
11	C₂×Q₈×D₄₃	C₄	1	2	yes	—
12	#13063332	—	2	4	no	—
13	C₂×#10621877	C₂²	1	6	yes	—
14	#13063243	C₂²	1	12	yes	—
15	#13063241	C₂²	1	4	yes	—
16	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
17	#131×C₄₃	—	2	4	no	—
18	C₂×M₁₆×C₄₃	C₂²	1	6	yes	—
19	#41×C₄₃	D₄	1	4	yes	—
20	#41×C₄₃	D₄	1	4	yes	—
21	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×D₄×C₄₃	C₂×C₄	1	3	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
24	C₂×C₂²⋊D₄₃	C₂×C₄	1	6	yes	—
25	C₂²×Dic₄₃	C₂×C₄	1	6	yes	—
26	Q₈×D₄₃	—	2	8	no	—
27	#10621900	—	2	24	no	—
28	#10621898	—	2	6	no	—
29	#10621898	—	2	6	no	—
30	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
31	C₂×C₄×D₄₃	C₂×C₄	1	6	yes	—
32	C₂×Dic₈₆	—	2	6	no	—
33	C₂×Dic₈₆	—	2	6	no	—
34	C₂×Dic₈₆	C₂×C₄	1	6	yes	—
35	C₂×Dic₈₆	C₂³	1	3	yes	—
36	M₁₆×C₄₃	—	2	6	no	—
37	M₁₆×C₄₃	C₂³	1	4	yes	—
38	C₂×C₈×C₄₃	—	2	6	no	—
39	#10621877	—	2	6	no	—
40	#10621877	C₂³	1	4	yes	—
41	C₂×C₄₃⋊C₈	—	2	6	no	—
42	C₂³×C₄₃	C₂²×C₄	1	3	yes	—
43	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
44	Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
45	D₄×C₄₃	C₂²⋊C₄	1	12	yes	—
46	C₂×C₄×C₄₃	C₂²×C₄	1	3	yes	—
47	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
48	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
49	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
50	C₂²⋊D₄₃	—	2	12	no	—
51	C₂×Dic₄₃	—	2	12	no	—
52	C₂×Dic₄₃	C₂²×C₄	1	6	yes	—
53	D₁₇₂	—	2	1	no	—
54	D₁₇₂	—	2	1	no	—
55	C₄×D₄₃	—	2	12	no	—
56	Dic₈₆	—	2	12	no	—
57	Dic₈₆	—	2	3	no	—
58	Dic₈₆	—	2	3	no	—
59	C₈×C₄₃	—	2	4	no	—
60	C₄₃⋊C₈	—	2	4	no	—
61	C₂²×C₄₃	—	4	3	no	—
62	C₂²×C₄₃	C₂×C₂²⋊C₄	1	6	yes	—
63	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
64	C₂×D₄₃	—	2	2	no	—
65	C₂×D₄₃	—	4	2	no	—
66	C₄×C₄₃	C₂×C₂²⋊C₄	1	6	yes	—
67	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
68	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
69	Dic₄₃	—	2	6	no	—
70	#2889	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	—	2	1	no	—
72	C₂×C₄₃	—	2	6	no	—
73	C₂×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
74	D₄₃	—	4	2	no	—
75	C₂×2₋¹⁺⁴	—	43	1	no	—
76	#568	—	43	1	no	—
77	#568	D₄₃	1	1	yes	characteristic, complemented
78	#413	—	43	6	no	—
79	C₂×#101	—	43	6	no	—
80	C₄₃	#2889	1	1	yes	characteristic, complemented, Sylow
81	2₋¹⁺⁴	—	86	4	no	—
82	2₋¹⁺⁴	—	86	4	no	—
83	C₂×#41	—	43	6	no	—
84	C₂×#41	—	43	3	no	—
85	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
86	C₂²×Q₈	—	43	2	no	—
87	C₂²×Q₈	—	43	3	no	—
88	#131	—	2	4	no	—
89	#131	—	86	4	no	—
90	C₂×M₁₆	—	43	6	no	—
91	C₂×M₁₆	C₂×D₄₃	1	6	yes	—
92	#101	—	43	12	no	—
93	#100	—	43	4	no	—
94	#41	—	86	24	no	—
95	#41	—	86	6	no	—
96	#41	—	86	6	no	—
97	#41	D₁₇₂	1	4	yes	—
98	#41	C₂²⋊D₄₃	1	4	yes	—
99	C₂×Q₈	—	43	6	no	—
100	C₂×Q₈	—	43	3	no	—
101	C₂×Q₈	—	86	8	no	—
102	C₂×Q₈	—	86	6	no	—
103	C₂×Q₈	—	86	6	no	—
104	C₂×Q₈	C₄×D₄₃	1	1	yes	characteristic
105	C₂×D₄	—	43	6	no	—
106	C₂×D₄	—	43	1	no	—
107	C₂×D₄	C₄×D₄₃	1	3	yes	—
108	C₂²×C₄	—	43	6	no	—
109	C₂²×C₄	—	43	6	no	—
110	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
111	M₁₆	—	2	6	no	—
112	M₁₆	—	43	4	no	—
113	M₁₆	—	86	6	no	—
114	M₁₆	C₂²×D₄₃	1	4	yes	—
115	C₂×C₈	—	2	6	no	—
116	C₂×C₈	—	86	6	no	—
117	C₂³	—	43	2	no	—
118	C₂³	C₂×C₄×D₄₃	1	3	yes	—
119	Q₈	—	86	12	no	—
120	Q₈	—	86	3	no	—
121	Q₈	—	86	3	no	—
122	Q₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
123	D₄	—	86	12	no	—
124	D₄	—	86	1	no	—
125	D₄	—	86	1	no	—
126	D₄	(C₂×D₄₃)⋊C₄	1	12	yes	—
127	C₂×C₄	—	43	6	no	—
128	C₂×C₄	—	86	12	no	—
129	C₂×C₄	—	86	12	no	—
130	C₂×C₄	C₂×C₄×D₄₃	1	3	yes	—
131	C₂×C₄	C₂×D₁₇₂	1	6	yes	—
132	C₂×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
133	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
134	C₈	—	2	4	no	—
135	C₈	—	86	4	no	—
136	C₂²	—	4	3	no	—
137	C₂²	—	86	2	no	—
138	C₂²	—	172	2	no	—
139	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	6	yes	—
140	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
141	C₄	—	86	6	no	—
142	C₄	C₂×(C₂×D₄₃)⋊C₄	1	6	yes	—
143	C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
144	C₄	C₂²×D₁₇₂	1	1	yes	characteristic
145	C₂	—	2	1	no	—
146	C₂	—	2	6	no	—
147	C₂	—	172	2	no	—
148	C₂	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063372

C₂

yes

maximal, characteristic

#14583666

C₂

yes

maximal, characteristic, complemented

#14582881

C₂

yes

maximal, complemented

C₂×#13063243

C₂

yes

maximal, complemented

C₄₃×#568

C₂

yes

maximal, characteristic, complemented

#13063372

—

#13063372

—

C₂×#10621898

C₂²

yes

—

C₂×#10621900

C₄

yes

—

C₂²×Dic₈₆

C₂²

yes

—

C₂×Q₈×D₄₃

C₄

yes

—

#13063332

—

C₂×#10621877

C₂²

yes

—

#13063243

C₂²

yes

—

#13063241

C₂²

yes

—

C₂×#41×C₄₃

C₂²

yes

characteristic

#131×C₄₃

—

C₂×M₁₆×C₄₃

C₂²

yes

—

#41×C₄₃

D₄

yes

—

#41×C₄₃

D₄

yes

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊D₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂×C₄

yes

—

Q₈×D₄₃

—

#10621900

—

#10621898

—

#10621898

—

C₂×D₁₇₂

C₂³

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×Dic₈₆

C₂³

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

—

#10621877

—

#10621877

C₂³

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂²×D₄₃

C₂²×C₄

yes

—

Q₈×C₄₃

C₂²⋊C₄

yes

—

D₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

—

C₄×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

C₂²×D₄

yes

characteristic

Dic₄₃

—

#2889

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₂²×C₂²⋊C₄

yes

characteristic

D₄₃

—

C₂×2₋¹⁺⁴

—

#568

—

#568

D₄₃

yes

characteristic, complemented

#413

—

C₂×#101

—

C₄₃

#2889

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

2₋¹⁺⁴

—

C₂×#41

—

C₂×#41

—

C₂×#41

C₂×D₄₃

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

—

—

—

—

—

D₁₇₂

yes

—

#41

C₂²⋊D₄₃

yes

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

C₄×D₄₃

yes

characteristic

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

C₄×D₄₃

yes

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²×D₄₃

yes

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

C₂²×D₄₃

yes

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂³

—

118

C₂³

C₂×C₄×D₄₃

yes

—

119

Q₈

—

120

Q₈

—

121

Q₈

—

122

Q₈

(C₂×D₄₃)⋊C₄

yes

—

123

D₄

—

124

D₄

—

125

D₄

—

126

D₄

(C₂×D₄₃)⋊C₄

yes

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

C₂×C₄×D₄₃

yes

—

131

C₂×C₄

C₂×D₁₇₂

yes

—

132

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

133

C₂×C₄

C₂³×D₄₃

yes

characteristic

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

172

—

139

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

—

140

C₂²

C₂²×C₄×D₄₃

yes

characteristic

141

C₄

—

142

C₄

C₂×(C₂×D₄₃)⋊C₄

yes

—

143

C₄

C₂²×C₂²⋊D₄₃

yes

characteristic

144

C₄

C₂²×D₁₇₂

yes

characteristic

145

C₂

—

146

C₂

—

147

C₂

—

172

—

148

C₂

C₂²×(C₂×D₄₃)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#568	C₂
socle	C₂×C₄₃	C₂²×C₂²⋊C₄
hypercenter	#568	D₄₃
hypocenter	C₄₃	#2889
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #568

subgroup

G/H

center

C₂

C₂²×(C₂×D₄₃)⋊C₄

commutator

C₂²×C₄₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#568

C₂

socle

C₂×C₄₃

C₂²×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×#41 ◁ #568

N	H ≅ G/N	type
2. #14583666	C₂	semidirect
3. #14582881	C₂	semidirect
4. C₂×#13063243	C₂	semidirect
5. C₄₃×#568	C₂	semidirect
77. #568	D₄₃	semidirect
80. C₄₃	#2889	semidirect

H ≅ G/N

type

2. #14583666

C₂

semidirect

3. #14582881

C₂

semidirect

4. C₂×#13063243

C₂

semidirect

5. C₄₃×#568

C₂

semidirect

77. #568

D₄₃

semidirect

80. C₄₃

#2889

semidirect

Subgroups — #19143077

Conjugacy classes of subgroups

Complements