Group #19136173 — subgroups

Subgroups — #19136173

Order 5504.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#14582947	C₂	1	1	yes	maximal, characteristic
2	#14582923	C₂	1	1	yes	maximal, characteristic
3	#14582670	C₂	1	1	yes	maximal, characteristic
4	#14582669	C₂	1	1	yes	maximal, characteristic
5	#14582659	C₂	1	1	yes	maximal, characteristic
6	#14582655	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#339	C₂	1	1	yes	maximal, characteristic
8	C₂×#10621877	C₂²	1	1	yes	characteristic
9	C₂×#10621877	C₂²	1	1	yes	characteristic
10	C₂×#10621877	C₂²	1	1	yes	characteristic
11	#13063284	C₂²	1	1	yes	characteristic
12	#13063260	—	2	2	no	—
13	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
14	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	#117×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	—	2	1	no	—
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	M₁₆×C₄₃	—	2	1	no	—
20	M₁₆×C₄₃	—	2	1	no	—
21	C₂×C₈×C₄₃	—	2	1	no	—
22	C₄⋊C₄×C₄₃	—	2	1	no	—
23	C₂²⋊C₄×C₄₃	—	2	1	no	—
24	C₄²×C₄₃	—	2	1	no	—
25	C₄²×C₄₃	—	2	1	no	—
26	C₄²×C₄₃	Q₈	1	1	yes	characteristic
27	C₄²×C₄₃	Q₈	1	1	yes	characteristic
28	C₂²⋊Dic₄₃	—	2	1	no	—
29	C₄⋊Dic₄₃	—	2	1	no	—
30	C₄×Dic₄₃	—	2	1	no	—
31	#10621877	—	2	1	no	—
32	#10621877	—	2	1	no	—
33	#10621877	—	2	1	no	—
34	#10621877	—	2	1	no	—
35	#10621877	—	2	1	no	—
36	#10621877	—	2	1	no	—
37	C₂×C₄₃⋊C₈	—	2	1	no	—
38	C₂×C₄₃⋊C₈	—	2	1	no	—
39	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
40	C₂³×C₄₃	#41	1	1	yes	characteristic
41	C₂×C₄×C₄₃	—	2	1	no	—
42	C₂×C₄×C₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	—	4	2	no	—
44	C₂×C₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
48	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
49	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
50	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
51	C₂×Dic₄₃	—	4	1	no	—
52	C₈×C₄₃	—	4	1	no	—
53	C₄₃⋊C₈	—	2	2	no	—
54	C₄₃⋊C₈	—	4	1	no	—
55	C₄₃⋊C₈	—	4	1	no	—
56	C₂²×C₄₃	—	4	1	no	—
57	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
58	C₂²×C₄₃	#126	1	1	yes	characteristic
59	C₂²×C₄₃	#126	1	1	yes	characteristic
60	C₄×C₄₃	—	2	2	no	—
61	C₄×C₄₃	—	4	1	no	—
62	C₄×C₄₃	—	8	1	no	—
63	C₄×C₄₃	#123	1	1	yes	characteristic
64	C₄×C₄₃	#124	1	1	yes	characteristic
65	C₄×C₄₃	#125	1	1	yes	characteristic
66	C₄×C₄₃	#125	1	1	yes	characteristic
67	Dic₄₃	—	8	1	no	—
68	#2102	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	—	2	1	no	—
70	C₂×C₄₃	—	2	1	no	—
71	C₂×C₄₃	—	2	1	no	—
72	C₂×C₄₃	#400	1	1	yes	characteristic
73	#430	—	43	1	no	—
74	#423	—	43	1	no	—
75	#344	—	43	1	no	—
76	#344	—	43	1	no	—
77	#339	—	43	1	no	—
78	#339	D₄₃	1	1	yes	characteristic
79	H(3,ℤ/4)	—	43	1	no	—
80	C₄₃	#2102	1	1	yes	characteristic, complemented, Sylow
81	C₂×M₁₆	—	43	1	no	—
82	C₂×M₁₆	—	43	1	no	—
83	C₂×M₁₆	—	43	1	no	—
84	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
85	#117	—	43	1	no	—
86	#117	C₂×D₄₃	1	1	yes	characteristic
87	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
88	#108	—	86	2	no	—
89	C₄⋊C₈	—	86	2	no	—
90	C₂²×C₄	—	2	1	no	—
91	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
92	M₁₆	—	2	1	no	—
93	M₁₆	—	2	1	no	—
94	M₁₆	—	86	1	no	—
95	M₁₆	—	86	1	no	—
96	M₁₆	—	86	1	no	—
97	M₁₆	—	86	1	no	—
98	M₁₆	—	86	1	no	—
99	M₁₆	—	86	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	43	2	no	—
102	C₂×C₈	—	86	1	no	—
103	C₂×C₈	—	86	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	86	1	no	—
106	C₂²⋊C₄	—	2	1	no	—
107	C₂²⋊C₄	—	86	1	no	—
108	C₄²	—	2	1	no	—
109	C₄²	—	2	1	no	—
110	C₄²	—	86	1	no	—
111	C₄²	Dic₈₆	1	1	yes	characteristic
112	C₄²	Dic₈₆	1	1	yes	characteristic
113	C₂³	#10621900	1	1	yes	characteristic
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	172	1	no	—
119	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
120	C₂×C₄	#10621898	1	1	yes	characteristic
121	C₂×C₄	#10621898	1	1	yes	characteristic
122	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
123	C₂×C₄	#10621900	1	1	yes	characteristic
124	C₂×C₄	#10621902	1	1	yes	characteristic
125	C₈	—	4	1	no	—
126	C₈	—	86	2	no	—
127	C₈	—	172	1	no	—
128	C₈	—	172	1	no	—
129	C₂²	—	4	1	no	—
130	C₂²	#13063302	1	1	yes	characteristic
131	C₂²	#13063318	1	1	yes	characteristic
132	C₂²	#13063320	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	4	1	no	—
135	C₄	—	8	1	no	—
136	C₄	—	344	1	no	—
137	C₄	#13063310	1	1	yes	characteristic
138	C₄	#13063311	1	1	yes	characteristic
139	C₄	#13063316	1	1	yes	characteristic
140	C₄	#13063317	1	1	yes	characteristic
141	C₂	—	2	1	no	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#14582841	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582947

C₂

yes

maximal, characteristic

#14582923

C₂

yes

maximal, characteristic

#14582670

C₂

yes

maximal, characteristic

#14582669

C₂

yes

maximal, characteristic

#14582659

C₂

yes

maximal, characteristic

#14582655

C₂

yes

maximal, characteristic

C₄₃×#339

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

#13063284

C₂²

yes

characteristic

#13063260

—

C₄⋊(C₄₃⋊C₈)

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

Q₈

yes

characteristic

C₄²×C₄₃

Q₈

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

—

—

—

—

—

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂³×C₄₃

#41

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊Q₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#2102

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

—

—

D₄₃

yes

characteristic

H(3,ℤ/4)

—

C₄₃

#2102

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

#117

—

#117

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

#108

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

Dic₈₆

yes

characteristic

112

C₄²

Dic₈₆

yes

characteristic

113

C₂³

#10621900

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

172

—

119

C₂×C₄

C₂×Dic₈₆

yes

characteristic

120

C₂×C₄

#10621898

yes

characteristic

121

C₂×C₄

#10621898

yes

characteristic

122

C₂×C₄

D₄×D₄₃

yes

characteristic

123

C₂×C₄

#10621900

yes

characteristic

124

C₂×C₄

#10621902

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

172

—

128

C₈

—

172

—

129

C₂²

—

130

C₂²

#13063302

yes

characteristic

131

C₂²

#13063318

yes

characteristic

132

C₂²

#13063320

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

344

—

137

C₄

#13063310

yes

characteristic

138

C₄

#13063311

yes

characteristic

139

C₄

#13063316

yes

characteristic

140

C₄

#13063317

yes

characteristic

141

C₂

—

142

C₂

—

143

C₂

—

144

C₂

#14582841

yes

characteristic

	subgroup	G/H
center	C₄	#13063311
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#339	C₂
socle	C₂×C₄₃	#400
hypercenter	#339	D₄₃
hypocenter	C₄₃	#2102
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #339

subgroup

G/H

center

C₄

#13063311

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#339

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #339

N	H ≅ G/N	type
80. C₄₃	#2102	semidirect

H ≅ G/N

type

80. C₄₃

#2102

semidirect

Subgroups — #19136173

Conjugacy classes of subgroups

Complements