Group #19136068 — subgroups

Subgroups — #19136068

Order 5504.

230 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 95 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×#13063259	C₂	1	2	yes	maximal
2	#14582797	C₂	1	1	yes	maximal, characteristic
3	#14582769	C₂	1	1	yes	maximal, characteristic
4	#14582662	C₂	1	2	yes	maximal
5	C₄₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₃	—	2	1	no	—
7	C₂×C₄⋊Dic₄₃	—	2	1	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₃⋊C₄	—	2	1	no	—
12	#13063259	—	2	4	no	—
13	C₄₃⋊#95	—	2	1	no	—
14	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₃	—	2	1	no	—
20	C₂²×Dic₄₃	—	2	1	no	—
21	C₂²×Dic₄₃	—	2	2	no	—
22	C₂×C₈×C₄₃	—	2	2	no	—
23	C₂×C₈×C₄₃	—	2	2	no	—
24	C₂×C₈×C₄₃	Q₈	1	4	yes	—
25	C₄²×C₄₃	—	2	2	no	—
26	C₄⋊Dic₄₃	—	2	1	no	—
27	C₄⋊Dic₄₃	—	2	2	no	—
28	C₄⋊Dic₄₃	—	2	2	no	—
29	C₄⋊Dic₄₃	—	2	2	no	—
30	C₄⋊Dic₄₃	—	4	2	no	—
31	C₄⋊Dic₄₃	—	4	2	no	—
32	C₄⋊Dic₄₃	D₄	1	2	yes	—
33	Dic₄₃⋊C₄	—	4	2	no	—
34	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	2	1	no	—
37	C₂×C₄×C₄₃	—	2	1	no	—
38	C₂×C₄×C₄₃	—	2	1	no	—
39	C₂×C₄×C₄₃	D₈	1	2	yes	—
40	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
43	C₂×C₄×C₄₃	#41	1	2	yes	—
44	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
45	C₂×Dic₄₃	—	2	2	no	—
46	C₂×Dic₄₃	—	4	1	no	—
47	C₂×Dic₄₃	—	4	1	no	—
48	C₂×Dic₄₃	—	4	2	no	—
49	C₂×Dic₄₃	—	4	1	no	—
50	C₂×Dic₄₃	—	4	1	no	—
51	C₂×Dic₄₃	—	4	2	no	—
52	C₂×Dic₄₃	—	4	2	no	—
53	C₂×Dic₄₃	—	4	1	no	—
54	C₈×C₄₃	—	2	4	no	—
55	C₂²×C₄₃	#121	1	1	yes	characteristic
56	C₂²×C₄₃	#123	1	1	yes	characteristic
57	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
58	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
59	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
60	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
61	C₂²×C₄₃	#137	1	1	yes	characteristic
62	C₄×C₄₃	—	2	2	no	—
63	C₄×C₄₃	—	2	2	no	—
64	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
65	C₄×C₄₃	#125	1	2	yes	—
66	Dic₄₃	—	4	2	no	—
67	Dic₄₃	—	8	2	no	—
68	Dic₄₃	—	8	1	no	—
69	#2083	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	#398	1	1	yes	characteristic
71	C₂×C₄₃	#459	1	1	yes	characteristic
72	C₂×C₄₃	#462	1	1	yes	characteristic
73	C₂×C₄₃	#480	1	1	yes	characteristic
74	C₂×C₄₃	#484	1	1	yes	characteristic
75	C₂×C₄₃	#500	1	1	yes	characteristic
76	C₂×C₄₃	#501	1	1	yes	characteristic
77	C₂×#107	—	43	2	no	—
78	#389	—	43	1	no	—
79	#384	—	43	1	no	—
80	#340	—	43	2	no	—
81	#336	D₄₃	1	1	yes	characteristic
82	C₄₃	#2083	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₈	C₂×D₄₃	1	2	yes	—
84	C₂×C₄⋊C₄	—	43	1	no	—
85	C₂×C₄⋊C₄	—	43	1	no	—
86	C₂×C₄⋊C₄	—	43	2	no	—
87	C₂×C₄⋊C₄	—	86	1	no	—
88	C₂×C₄⋊C₄	—	86	1	no	—
89	C₂×C₄⋊C₄	—	86	1	no	—
90	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
91	#107	—	86	4	no	—
92	#95	—	86	1	no	—
93	C₂²×C₄	—	86	1	no	—
94	C₂²×C₄	—	86	1	no	—
95	C₂²×C₄	—	86	2	no	—
96	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
97	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	Dic₈₆	1	4	yes	—
102	C₄⋊C₄	—	43	2	no	—
103	C₄⋊C₄	—	86	1	no	—
104	C₄⋊C₄	—	86	2	no	—
105	C₄⋊C₄	—	86	2	no	—
106	C₄⋊C₄	—	86	2	no	—
107	C₄⋊C₄	—	172	2	no	—
108	C₄⋊C₄	—	172	2	no	—
109	C₄⋊C₄	—	172	2	no	—
110	C₄²	—	2	2	no	—
111	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	86	2	no	—
117	C₂×C₄	—	172	2	no	—
118	C₂×C₄	—	172	1	no	—
119	C₂×C₄	—	172	2	no	—
120	C₂×C₄	—	172	1	no	—
121	C₂×C₄	—	172	2	no	—
122	C₂×C₄	—	172	1	no	—
123	C₂×C₄	—	172	1	no	—
124	C₂×C₄	—	172	1	no	—
125	C₂×C₄	D₃₄₄	1	2	yes	—
126	C₂×C₄	Dic₁₇₂	1	2	yes	—
127	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
128	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
129	C₂×C₄	#10621900	1	2	yes	—
130	C₂×C₄	#10621902	1	1	yes	characteristic
131	C₈	—	2	4	no	—
132	C₂²	#13063300	1	1	yes	characteristic
133	C₂²	#13063309	1	1	yes	characteristic
134	C₂²	#13063325	1	1	yes	characteristic
135	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
136	C₂²	C₂×Dic₁₇₂	1	1	yes	characteristic
137	C₂²	#13063353	1	1	yes	characteristic
138	C₂²	#13063358	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	2	2	no	—
141	C₄	—	344	2	no	—
142	C₄	—	344	1	no	—
143	C₄	—	172	2	no	—
144	C₄	#13063302	1	2	yes	—
145	C₄	#13063316	1	2	yes	—
146	C₂	#14582831	1	1	yes	characteristic
147	C₂	#14583095	1	1	yes	characteristic
148	C₂	#14583110	1	1	yes	characteristic
149	C₂	#14583213	1	1	yes	characteristic
150	C₂	#14583235	1	1	yes	characteristic
151	C₂	#14583304	1	1	yes	characteristic
152	C₂	#14583308	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063259

C₂

yes

maximal

#14582797

C₂

yes

maximal, characteristic

#14582769

C₂

yes

maximal, characteristic

#14582662

C₂

yes

maximal

C₄₃×#336

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

—

#13063259

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

Q₈

yes

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂²×C₄₃

C₂×Q₁₆

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#125

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#2083

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#107

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

Dic₈₆

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

172

—

108

C₄⋊C₄

—

172

—

109

C₄⋊C₄

—

172

—

110

C₄²

—

111

C₂³

C₂×D₁₇₂

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

172

—

118

C₂×C₄

—

172

—

119

C₂×C₄

—

172

—

120

C₂×C₄

—

172

—

121

C₂×C₄

—

172

—

122

C₂×C₄

—

172

—

123

C₂×C₄

—

172

—

124

C₂×C₄

—

172

—

125

C₂×C₄

D₃₄₄

yes

—

126

C₂×C₄

Dic₁₇₂

yes

—

127

C₂×C₄

C₂×Dic₈₆

yes

—

128

C₂×C₄

D₄×D₄₃

yes

characteristic

129

C₂×C₄

#10621900

yes

—

130

C₂×C₄

#10621902

yes

characteristic

131

C₈

—

132

C₂²

#13063300

yes

characteristic

133

C₂²

#13063309

yes

characteristic

134

C₂²

#13063325

yes

characteristic

135

C₂²

C₂×D₃₄₄

yes

characteristic

136

C₂²

C₂×Dic₁₇₂

yes

characteristic

137

C₂²

#13063353

yes

characteristic

138

C₂²

#13063358

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

344

—

142

C₄

—

344

—

143

C₄

—

172

—

144

C₄

#13063302

yes

—

145

C₄

#13063316

yes

—

146

C₂

#14582831

yes

characteristic

147

C₂

#14583095

yes

characteristic

148

C₂

#14583110

yes

characteristic

149

C₂

#14583213

yes

characteristic

150

C₂

#14583235

yes

characteristic

151

C₂

#14583304

yes

characteristic

152

C₂

#14583308

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#336	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#336	D₄₃
hypocenter	C₄₃	#2083
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#336

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
82. C₄₃	#2083	semidirect

H ≅ G/N

type

82. C₄₃

#2083

semidirect

Subgroups — #19136068

Conjugacy classes of subgroups

Complements