Group #19132418 — subgroups

Subgroups — #19132418

Order 5504.

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

normal subgroups only

This group has 158 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	#14582654	C₂	1	1	yes	maximal, characteristic
2	#14582654	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#389	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₈	—	2	1	no	—
5	C₂²×C₄₃⋊C₈	—	2	1	no	—
6	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
7	C₂×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
9	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	#95×C₄₃	—	2	1	no	—
11	C₂²×C₄×C₄₃	—	2	1	no	—
12	C₂²×C₄×C₄₃	—	2	1	no	—
13	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₄⋊C₄×C₄₃	—	2	1	no	—
17	C₄⋊C₄×C₄₃	—	4	1	no	—
18	C₄⋊C₄×C₄₃	—	4	1	no	—
19	C₄⋊C₄×C₄₃	—	4	1	no	—
20	C₄⋊C₄×C₄₃	C₈	1	2	yes	complemented
21	C₄²×C₄₃	—	4	1	no	—
22	C₂×C₄₃⋊C₈	—	2	2	no	—
23	C₂×C₄₃⋊C₈	—	2	2	no	—
24	C₂×C₄₃⋊C₈	—	4	1	no	—
25	C₂×C₄₃⋊C₈	—	4	1	no	—
26	C₂×C₄₃⋊C₈	—	4	1	no	—
27	C₂×C₄₃⋊C₈	—	4	1	no	—
28	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	—	2	1	no	—
32	C₂×C₄×C₄₃	—	2	1	no	—
33	C₂×C₄×C₄₃	—	2	1	no	—
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	—	4	1	no	—
38	C₂×C₄×C₄₃	—	4	1	no	—
39	C₂×C₄×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
42	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
43	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
44	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
45	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
46	C₂×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
47	C₄₃⋊C₈	—	4	2	no	—
48	C₄₃⋊C₈	—	4	2	no	—
49	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
50	C₂²×C₄₃	#99	1	1	yes	characteristic
51	C₂²×C₄₃	#101	1	1	yes	characteristic
52	C₂²×C₄₃	#102	1	1	yes	characteristic
53	C₂²×C₄₃	#103	1	1	yes	characteristic
54	C₂²×C₄₃	#104	1	1	yes	characteristic
55	C₂²×C₄₃	#104	1	1	yes	characteristic
56	C₄×C₄₃	—	2	1	no	—
57	C₄×C₄₃	—	2	1	no	—
58	C₄×C₄₃	—	2	1	no	—
59	C₄×C₄₃	—	2	1	no	—
60	C₄×C₄₃	—	2	1	no	—
61	C₄×C₄₃	—	2	1	no	—
62	C₄×C₄₃	—	4	2	no	—
63	C₄×C₄₃	—	8	1	no	—
64	#1271	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	#324	1	1	yes	characteristic
66	C₂×C₄₃	D₄⋊C₈	1	1	yes	characteristic
67	C₂×C₄₃	Q₈⋊C₈	1	1	yes	characteristic
68	C₂×C₄₃	#327	1	1	yes	characteristic
69	C₂×C₄₃	#328	1	1	yes	characteristic
70	C₂×C₄₃	#330	1	1	yes	characteristic
71	C₂×C₄₃	#332	1	1	yes	characteristic
72	#389	D₄₃	1	1	yes	characteristic
73	#336	—	43	1	no	—
74	#336	—	43	1	no	—
75	C₄₃	#1271	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₈	—	86	1	no	—
77	C₂²×C₈	—	86	1	no	—
78	C₂×C₄⋊C₄	—	2	1	no	—
79	C₂×C₄⋊C₄	Dic₄₃	1	1	yes	characteristic
80	C₂×C₄⋊C₄	Dic₄₃	1	1	yes	characteristic
81	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
82	#95	—	2	1	no	—
83	C₂²×C₄	—	2	1	no	—
84	C₂²×C₄	—	2	1	no	—
85	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
86	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
87	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
88	C₂×C₈	—	86	2	no	—
89	C₂×C₈	—	86	2	no	—
90	C₂×C₈	—	172	1	no	—
91	C₂×C₈	—	172	1	no	—
92	C₂×C₈	—	172	1	no	—
93	C₂×C₈	—	172	1	no	—
94	C₄⋊C₄	—	2	1	no	—
95	C₄⋊C₄	—	4	1	no	—
96	C₄⋊C₄	—	4	1	no	—
97	C₄⋊C₄	—	4	1	no	—
98	C₄⋊C₄	C₄₃⋊C₈	1	2	yes	complemented
99	C₄²	—	4	1	no	—
100	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	4	1	no	—
109	C₂×C₄	—	4	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
114	C₂×C₄	#10621877	1	1	yes	characteristic
115	C₂×C₄	#10621882	1	1	yes	characteristic
116	C₂×C₄	#10621883	1	1	yes	characteristic
117	C₂×C₄	#10621884	1	1	yes	characteristic
118	C₂×C₄	#10621885	1	1	yes	characteristic
119	C₈	—	172	2	no	—
120	C₈	—	172	2	no	—
121	C₂²	C₂²⋊(C₄₃⋊C₈)	1	1	yes	characteristic
122	C₂²	#13063240	1	1	yes	characteristic
123	C₂²	#13063244	1	1	yes	characteristic
124	C₂²	#13063246	1	1	yes	characteristic
125	C₂²	#13063249	1	1	yes	characteristic
126	C₂²	#13063252	1	1	yes	characteristic
127	C₂²	#13063252	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	—	2	1	no	—
130	C₄	—	2	1	no	—
131	C₄	—	2	1	no	—
132	C₄	—	2	1	no	—
133	C₄	—	2	1	no	—
134	C₄	—	4	2	no	—
135	C₄	—	8	1	no	—
136	C₂	#14582625	1	1	yes	characteristic
137	C₂	D₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
138	C₂	Q₈⋊(C₄₃⋊C₈)	1	1	yes	characteristic
139	C₂	#14582633	1	1	yes	characteristic
140	C₂	#14582636	1	1	yes	characteristic
141	C₂	#14582641	1	1	yes	characteristic
142	C₂	#14582645	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582654

C₂

yes

maximal, characteristic

#14582654

C₂

yes

maximal, characteristic

C₄₃×#389

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₄

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₈

yes

complemented

C₄²×C₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

Q₁₆

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂²⋊C₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

D₄⋊C₈

yes

characteristic

C₂×C₄₃

Q₈⋊C₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

characteristic

#336

—

#336

—

C₄₃

#1271

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

Dic₄₃

yes

characteristic

C₂×C₄⋊C₄

Dic₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

—

172

—

C₂×C₈

—

172

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄₃⋊C₈

yes

complemented

C₄²

—

100

C₂³

C₂²⋊Dic₄₃

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×C₄₃⋊C₈

yes

characteristic

114

C₂×C₄

#10621877

yes

characteristic

115

C₂×C₄

#10621882

yes

characteristic

116

C₂×C₄

#10621883

yes

characteristic

117

C₂×C₄

#10621884

yes

characteristic

118

C₂×C₄

#10621885

yes

characteristic

119

C₈

—

172

—

120

C₈

—

172

—

121

C₂²

C₂²⋊(C₄₃⋊C₈)

yes

characteristic

122

C₂²

#13063240

yes

characteristic

123

C₂²

#13063244

yes

characteristic

124

C₂²

#13063246

yes

characteristic

125

C₂²

#13063249

yes

characteristic

126

C₂²

#13063252

yes

characteristic

127

C₂²

#13063252

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₂

#14582625

yes

characteristic

137

C₂

D₄⋊(C₄₃⋊C₈)

yes

characteristic

138

C₂

Q₈⋊(C₄₃⋊C₈)

yes

characteristic

139

C₂

#14582633

yes

characteristic

140

C₂

#14582636

yes

characteristic

141

C₂

#14582641

yes

characteristic

142

C₂

#14582645

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂×C₈
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₄₃×#389	C₂
socle	C₂³×C₄₃	C₂²⋊C₄
hypercenter	#389	D₄₃
hypocenter	C₄₃	#1271
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

subgroup

G/H

center

C₂³

C₂²⋊Dic₄₃

commutator

C₂×C₄×C₄₃

C₂×C₈

Frattini

C₂×C₄²

C₂×D₄₃

Fitting

C₄₃×#389

C₂

socle

C₂³×C₄₃

C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

N	H ≅ G/N	type
20. C₄⋊C₄×C₄₃	C₈	semidirect
75. C₄₃	#1271	semidirect
98. C₄⋊C₄	C₄₃⋊C₈	semidirect

H ≅ G/N

type

20. C₄⋊C₄×C₄₃

C₈

semidirect

75. C₄₃

#1271

semidirect

98. C₄⋊C₄

C₄₃⋊C₈

semidirect

Subgroups — #19132418

Conjugacy classes of subgroups

Complements