Group #19136430 — subgroups

Subgroups — #19136430

Order 5504.

146 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14583315	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583014	C₂	1	1	yes	maximal, characteristic
3	#14582719	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582684	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582683	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063345	C₄	1	1	yes	characteristic
9	#13063331	C₂²	1	1	yes	characteristic
10	#13063265	C₂²	1	1	yes	characteristic
11	#13063264	—	2	1	no	—
12	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₁₆×D₄₃	—	2	1	no	—
14	#13063260	C₄	1	1	yes	characteristic
15	#13063252	C₄	1	1	yes	characteristic
16	#13063251	C₄	1	1	yes	characteristic
17	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
18	#131×C₄₃	C₂²	1	1	yes	characteristic
19	M₃₂×C₄₃	—	2	1	no	—
20	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×C₄₃	—	2	1	no	—
22	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	#41×C₄₃	C₂×C₄	1	1	yes	characteristic
24	#10621898	C₂×C₄	1	1	yes	characteristic
25	M₁₆×C₄₃	—	2	1	no	—
26	M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
29	#10621885	C₈	1	1	yes	characteristic
30	#10621884	C₈	1	1	yes	characteristic
31	#10621883	C₈	1	1	yes	characteristic
32	#10621882	C₈	1	1	yes	characteristic
33	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
34	#10621877	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
36	#10621872	—	2	1	no	—
37	C₈×D₄₃	—	2	1	no	—
38	C₁₆×C₄₃	—	2	1	no	—
39	C₁₆×C₄₃	D₄	1	1	yes	characteristic
40	C₁₆×C₄₃	D₄	1	1	yes	characteristic
41	C₄₃⋊C₁₆	—	2	1	no	—
42	C₄₃⋊C₁₆	—	2	1	no	—
43	Q₈×C₄₃	C₂×C₈	1	1	yes	characteristic
44	D₄×C₄₃	—	2	1	no	—
45	D₄×C₄₃	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²⋊D₄₃	—	2	1	no	—
49	C₂×Dic₄₃	—	2	1	no	—
50	D₁₇₂	C₂×C₈	1	1	yes	characteristic
51	C₄×D₄₃	—	2	1	no	—
52	Dic₈₆	C₂×C₈	1	1	yes	characteristic
53	C₈×C₄₃	—	2	1	no	—
54	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₈×C₄₃	#41	1	1	yes	characteristic
56	C₄₃⋊C₈	—	2	1	no	—
57	C₄₃⋊C₈	C₂×C₈	1	1	yes	characteristic
58	C₄₃⋊C₈	C₂×C₈	1	1	yes	characteristic
59	C₂²×C₄₃	—	2	1	no	—
60	C₂²×C₄₃	#131	1	1	yes	characteristic
61	C₂×D₄₃	—	2	1	no	—
62	C₄×C₄₃	—	2	1	no	—
63	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
64	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
65	Dic₄₃	—	2	2	no	—
66	Dic₄₃	—	2	1	no	—
67	#2170	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	—	2	1	no	—
69	C₂×C₄₃	—	4	1	no	—
70	C₂×C₄₃	C₈×D₄	1	1	yes	characteristic
71	D₄₃	—	4	1	no	—
72	#504	—	43	1	no	—
73	#504	D₄₃	1	1	yes	characteristic, complemented
74	#443	—	43	1	no	—
75	#364	—	43	1	no	—
76	#350	—	43	1	no	—
77	#350	—	43	1	no	—
78	C₄×C₁₆	—	43	1	no	—
79	C₄₃	#2170	1	1	yes	characteristic, complemented, Sylow
80	#135	—	43	1	no	—
81	#131	—	43	1	no	—
82	#131	C₂×D₄₃	1	1	yes	characteristic
83	M₃₂	—	2	1	no	—
84	M₃₂	—	43	1	no	—
85	M₃₂	—	86	1	no	—
86	M₃₂	C₂×D₄₃	1	1	yes	characteristic
87	C₂×C₁₆	—	2	1	no	—
88	C₂×C₁₆	—	43	1	no	—
89	C₂×C₁₆	—	86	1	no	—
90	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
91	#108	—	43	1	no	—
92	#104	—	43	1	no	—
93	#104	—	43	1	no	—
94	C₄×C₈	—	43	1	no	—
95	#41	—	43	1	no	—
96	#41	C₄×D₄₃	1	1	yes	characteristic
97	Q₁₆	—	43	1	no	—
98	SD₁₆	—	43	1	no	—
99	SD₁₆	—	43	1	no	—
100	D₈	—	43	1	no	—
101	M₁₆	—	2	1	no	—
102	M₁₆	—	43	1	no	—
103	M₁₆	—	86	1	no	—
104	M₁₆	C₄×D₄₃	1	1	yes	characteristic
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	43	1	no	—
107	C₂×C₈	—	86	1	no	—
108	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
109	C₄²	—	43	1	no	—
110	C₁₆	—	2	1	no	—
111	C₁₆	—	86	1	no	—
112	C₁₆	—	86	1	no	—
113	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
114	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
115	Q₈	—	43	1	no	—
116	Q₈	C₈×D₄₃	1	1	yes	characteristic
117	D₄	—	2	1	no	—
118	D₄	—	43	1	no	—
119	D₄	—	86	1	no	—
120	D₄	C₈×D₄₃	1	1	yes	characteristic
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	86	1	no	—
123	C₂×C₄	—	86	1	no	—
124	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	43	1	no	—
127	C₈	—	43	1	no	—
128	C₈	—	86	1	no	—
129	C₈	#10621898	1	1	yes	characteristic
130	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
131	C₂²	—	2	1	no	—
132	C₂²	—	86	1	no	—
133	C₂²	#13063331	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	86	2	no	—
136	C₄	—	86	1	no	—
137	C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
138	C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	172	1	no	—
142	C₂	C₈×C₂²⋊D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583315

C₂

yes

maximal, characteristic, complemented

#14583014

C₂

yes

maximal, characteristic

#14582719

C₂

yes

maximal, characteristic, complemented

#14582684

C₂

yes

maximal, characteristic, complemented

#14582683

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₄₃

C₂

yes

maximal, characteristic, complemented

C₄₃×#504

C₂

yes

maximal, characteristic, complemented

#13063345

C₄

yes

characteristic

#13063331

C₂²

yes

characteristic

#13063265

C₂²

yes

characteristic

#13063264

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₄₃

—

#13063260

C₄

yes

characteristic

#13063252

C₄

yes

characteristic

#13063251

C₄

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

#131×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#41×C₄₃

C₂×C₄

yes

characteristic

#10621898

C₂×C₄

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

#10621885

C₈

yes

characteristic

#10621884

C₈

yes

characteristic

#10621883

C₈

yes

characteristic

#10621882

C₈

yes

characteristic

C₄×Dic₄₃

C₂×C₄

yes

characteristic

#10621877

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

D₄

yes

characteristic

C₁₆×C₄₃

D₄

yes

characteristic

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

—

Q₈×C₄₃

C₂×C₈

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

C₂×C₈

yes

characteristic

C₄×D₄₃

—

Dic₈₆

C₂×C₈

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

C₂×C₈

yes

characteristic

C₄₃⋊C₈

C₂×C₈

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

#131

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

C₂²×C₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2170

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₈×D₄

yes

characteristic

D₄₃

—

#504

—

#504

D₄₃

yes

characteristic, complemented

—

—

—

—

C₄×C₁₆

—

C₄₃

#2170

yes

characteristic, complemented, Sylow

#135

—

#131

—

#131

C₂×D₄₃

yes

characteristic

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

—

C₄×C₈

—

#41

—

#41

C₄×D₄₃

yes

characteristic

Q₁₆

—

SD₁₆

—

SD₁₆

—

100

D₈

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

C₄×D₄₃

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²×D₄₃

yes

characteristic

109

C₄²

—

110

C₁₆

—

111

C₁₆

—

112

C₁₆

—

113

C₁₆

C₂²⋊D₄₃

yes

characteristic

114

C₁₆

C₂²⋊D₄₃

yes

characteristic

115

Q₈

—

116

Q₈

C₈×D₄₃

yes

characteristic

117

D₄

—

118

D₄

—

119

D₄

—

120

D₄

C₈×D₄₃

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

#10621898

yes

characteristic

130

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

131

C₂²

—

132

C₂²

—

133

C₂²

#13063331

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

C₄×C₂²⋊D₄₃

yes

characteristic

138

C₄

C₂×C₈×D₄₃

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

172

—

142

C₂

C₈×C₂²⋊D₄₃

yes

characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#504	C₂
socle	C₂×C₄₃	C₈×D₄
hypercenter	#504	D₄₃
hypocenter	C₄₃	#2170
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #504

subgroup

G/H

center

C₁₆

C₂²⋊D₄₃

commutator

C₄×C₄₃

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#504

C₂

socle

C₂×C₄₃

C₈×D₄

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #504

N	H ≅ G/N	type
1. #14583315	C₂	semidirect
3. #14582719	C₂	semidirect
4. #14582684	C₂	semidirect
5. #14582683	C₂	semidirect
6. C₁₆×Dic₄₃	C₂	semidirect
7. C₄₃×#504	C₂	semidirect
73. #504	D₄₃	semidirect
79. C₄₃	#2170	semidirect

H ≅ G/N

type

1. #14583315

C₂

semidirect

3. #14582719

C₂

semidirect

4. #14582684

C₂

semidirect

5. #14582683

C₂

semidirect

6. C₁₆×Dic₄₃

C₂

semidirect

7. C₄₃×#504

C₂

semidirect

73. #504

D₄₃

semidirect

79. C₄₃

#2170

semidirect

Subgroups — #19136430

Conjugacy classes of subgroups

Complements