Group #19133964 — subgroups

Subgroups — #19133964

Order 5504.

156 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14583278	C₂	1	1	yes	maximal, characteristic
2	#14583185	C₂	1	1	yes	maximal, characteristic
3	#14583181	C₂	1	1	yes	maximal, characteristic
4	#14583023	C₂	1	1	yes	maximal, characteristic
5	#14582651	C₂	1	1	yes	maximal, characteristic
6	#14582646	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#332	C₂	1	1	yes	maximal, characteristic
8	C₂×#10621885	—	2	1	no	—
9	C₂×#10621885	—	2	1	no	—
10	#13063325	C₂²	1	1	yes	characteristic
11	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
12	#13063257	—	2	1	no	—
13	#13063256	—	2	1	no	—
14	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	Dic₄₃⋊C₈	—	2	1	no	—
16	#13063250	—	2	1	no	—
17	#13063248	—	2	1	no	—
18	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₈×Dic₄₃	—	2	1	no	—
20	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×Dic₈₆	—	2	1	no	—
25	C₂×Dic₈₆	D₄	1	1	yes	characteristic
26	C₂×C₈×C₄₃	—	2	1	no	—
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₄⋊C₄×C₄₃	—	2	1	no	—
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄²×C₄₃	C₂³	1	1	yes	characteristic
31	#10621885	—	4	2	no	—
32	#10621885	—	4	2	no	—
33	C₄⋊Dic₄₃	—	2	1	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
36	Dic₄₃⋊C₄	—	2	1	no	—
37	C₄×Dic₄₃	—	2	1	no	—
38	C₂×C₄₃⋊C₈	—	2	1	no	—
39	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
40	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
41	Q₈×C₄₃	—	4	1	no	—
42	Q₈×C₄₃	—	4	1	no	—
43	C₂×C₄×C₄₃	—	4	1	no	—
44	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
47	C₂×Dic₄₃	—	2	1	no	—
48	C₂×Dic₄₃	—	2	1	no	—
49	C₂×Dic₄₃	—	4	1	no	—
50	Dic₈₆	—	2	1	no	—
51	Dic₈₆	—	4	1	no	—
52	Dic₈₆	—	4	1	no	—
53	Dic₈₆	Q₁₆	1	2	yes	complemented
54	C₈×C₄₃	—	4	1	no	—
55	C₈×C₄₃	—	4	1	no	—
56	C₄₃⋊C₈	—	2	1	no	—
57	C₄₃⋊C₈	—	4	1	no	—
58	C₄₃⋊C₈	SD₁₆	1	2	yes	—
59	C₂²×C₄₃	#121	1	1	yes	characteristic
60	C₄×C₄₃	—	2	1	no	—
61	C₄×C₄₃	—	8	1	no	—
62	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
63	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
64	C₄×C₄₃	#135	1	1	yes	characteristic
65	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
66	Dic₄₃	—	2	2	no	—
67	Dic₄₃	—	4	1	no	—
68	Dic₄₃	—	8	1	no	—
69	#1670	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	#460	1	1	yes	characteristic
71	C₂×C₄₃	#467	1	1	yes	characteristic
72	C₂×C₄₃	#473	1	1	yes	characteristic
73	#494	—	43	1	no	—
74	#475	—	43	1	no	—
75	#475	—	43	1	no	—
76	C₈×Q₈	—	43	1	no	—
77	#335	—	43	1	no	—
78	#332	—	43	1	no	—
79	#332	D₄₃	1	1	yes	characteristic
80	C₄₃	#1670	1	1	yes	characteristic, complemented, Sylow
81	C₂×Q₁₆	—	86	1	no	—
82	C₂×Q₁₆	—	86	1	no	—
83	C₄⋊Q₈	—	43	1	no	—
84	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
85	C₄×Q₈	—	43	1	no	—
86	#106	—	86	1	no	—
87	#106	—	86	1	no	—
88	C₄⋊C₈	—	43	1	no	—
89	C₄⋊C₈	—	86	1	no	—
90	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
91	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
92	#103	—	86	1	no	—
93	#103	—	86	1	no	—
94	C₄×C₈	—	43	1	no	—
95	C₄×C₈	—	86	1	no	—
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	43	1	no	—
98	C₂×Q₈	—	86	1	no	—
99	Q₁₆	—	172	2	no	—
100	Q₁₆	—	172	2	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	2	1	no	—
103	C₂×C₈	—	43	1	no	—
104	C₂×C₈	—	43	1	no	—
105	C₂×C₈	—	86	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	2	1	no	—
108	C₄⋊C₄	—	43	1	no	—
109	C₄⋊C₄	—	86	1	no	—
110	C₄⋊C₄	—	86	1	no	—
111	C₄⋊C₄	—	86	1	no	—
112	C₄²	—	86	1	no	—
113	C₄²	C₂²×D₄₃	1	1	yes	characteristic
114	Q₈	—	4	1	no	—
115	Q₈	—	4	1	no	—
116	Q₈	—	43	2	no	—
117	Q₈	—	86	1	no	—
118	Q₈	—	172	1	no	—
119	Q₈	—	172	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	86	1	no	—
122	C₂×C₄	—	86	1	no	—
123	C₂×C₄	—	172	1	no	—
124	C₂×C₄	#10621898	1	1	yes	characteristic
125	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
126	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
127	C₈	—	4	1	no	—
128	C₈	—	4	1	no	—
129	C₈	—	43	2	no	—
130	C₈	—	86	1	no	—
131	C₈	—	172	1	no	—
132	C₂²	#13063298	1	1	yes	characteristic
133	C₄	—	2	1	no	—
134	C₄	—	8	1	no	—
135	C₄	—	86	2	no	—
136	C₄	—	344	1	no	—
137	C₄	—	172	1	no	—
138	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
139	C₄	Q₁₆×D₄₃	1	1	yes	characteristic
140	C₄	#13063346	1	1	yes	characteristic
141	C₄	#13063349	1	1	yes	characteristic
142	C₂	#14583098	1	1	yes	characteristic
143	C₂	#14583139	1	1	yes	characteristic
144	C₂	#14583173	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583278

C₂

yes

maximal, characteristic

#14583185

C₂

yes

maximal, characteristic

#14583181

C₂

yes

maximal, characteristic

#14583023

C₂

yes

maximal, characteristic

#14582651

C₂

yes

maximal, characteristic

#14582646

C₂

yes

maximal, characteristic

C₄₃×#332

C₂

yes

maximal, characteristic

C₂×#10621885

—

C₂×#10621885

—

#13063325

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

characteristic

#13063257

—

#13063256

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063250

—

#13063248

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621885

—

#10621885

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

Q₁₆

yes

complemented

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

SD₁₆

yes

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

C₈×Q₈

—

#335

—

#332

—

#332

D₄₃

yes

characteristic

C₄₃

#1670

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

#106

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

C₂×D₄₃

yes

characteristic

#103

—

#103

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

172

—

100

Q₁₆

—

172

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

—

113

C₄²

C₂²×D₄₃

yes

characteristic

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

172

—

119

Q₈

—

172

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

172

—

124

C₂×C₄

#10621898

yes

characteristic

125

C₂×C₄

D₄×D₄₃

yes

characteristic

126

C₂×C₄

D₄×D₄₃

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

—

172

—

132

C₂²

#13063298

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

344

—

137

C₄

—

172

—

138

C₄

SD₁₆×D₄₃

yes

characteristic

139

C₄

Q₁₆×D₄₃

yes

characteristic

140

C₄

#13063346

yes

characteristic

141

C₄

#13063349

yes

characteristic

142

C₂

#14583098

yes

characteristic

143

C₂

#14583139

yes

characteristic

144

C₂

#14583173

yes

characteristic

	subgroup	G/H
center	C₂²	#13063298
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#332	C₂
socle	C₂²×C₄₃	#121
hypercenter	#332	D₄₃
hypocenter	C₄₃	#1670
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #332

subgroup

G/H

center

C₂²

#13063298

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#332

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #332

N	H ≅ G/N	type
53. Dic₈₆	Q₁₆	semidirect
80. C₄₃	#1670	semidirect

H ≅ G/N

type

53. Dic₈₆

Q₁₆

semidirect

80. C₄₃

#1670

semidirect

Subgroups — #19133964

Conjugacy classes of subgroups

Complements