Group #19135996 — subgroups

Subgroups — #19135996

Order 5504.

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

normal subgroups only

This group has 196 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	#14582948	C₂	1	1	yes	maximal, characteristic
2	#14582947	C₂	1	1	yes	maximal, characteristic
3	#14582947	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063244	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063244	C₂	1	1	yes	maximal, characteristic
6	C₄₃⋊#338	C₂	1	1	yes	maximal, characteristic
7	C₂×#101×C₄₃	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	C₂×#10621877	C₂²	1	1	yes	characteristic
12	#13063261	—	2	2	no	—
13	#13063260	—	2	2	no	—
14	#13063260	—	2	2	no	—
15	#13063244	—	2	2	no	—
16	#13063244	—	2	2	no	—
17	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	#101×C₄₃	—	2	2	no	—
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×Q₈×C₄₃	—	2	1	no	—
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×Q₈×C₄₃	—	2	1	no	—
25	C₂×Q₈×C₄₃	—	2	1	no	—
26	C₂×Q₈×C₄₃	—	2	1	no	—
27	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
28	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
29	M₁₆×C₄₃	—	2	1	no	—
30	M₁₆×C₄₃	—	2	1	no	—
31	M₁₆×C₄₃	—	2	1	no	—
32	M₁₆×C₄₃	D₄	1	2	yes	—
33	C₂×C₈×C₄₃	—	2	1	no	—
34	C₂×C₈×C₄₃	—	2	1	no	—
35	#10621877	—	2	1	no	—
36	#10621877	—	2	1	no	—
37	#10621877	—	2	1	no	—
38	#10621877	—	2	1	no	—
39	#10621877	—	2	1	no	—
40	#10621877	—	2	1	no	—
41	#10621877	D₄	1	2	yes	—
42	#10621877	D₄	1	2	yes	—
43	C₂×C₄₃⋊C₈	—	2	1	no	—
44	C₂×C₄₃⋊C₈	—	2	1	no	—
45	C₂×C₄₃⋊C₈	—	2	1	no	—
46	C₂×C₄₃⋊C₈	—	2	1	no	—
47	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
48	Q₈×C₄₃	—	4	1	no	—
49	Q₈×C₄₃	—	4	1	no	—
50	Q₈×C₄₃	—	4	1	no	—
51	Q₈×C₄₃	—	4	1	no	—
52	C₂×C₄×C₄₃	—	2	2	no	—
53	C₂×C₄×C₄₃	—	2	2	no	—
54	C₂×C₄×C₄₃	—	2	2	no	—
55	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
59	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
60	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
61	C₈×C₄₃	—	2	2	no	—
62	C₈×C₄₃	—	4	1	no	—
63	C₄₃⋊C₈	—	2	2	no	—
64	C₄₃⋊C₈	—	2	2	no	—
65	C₄₃⋊C₈	—	4	1	no	—
66	C₄₃⋊C₈	—	4	1	no	—
67	C₂²×C₄₃	—	4	1	no	—
68	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
69	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
70	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
71	C₄×C₄₃	—	4	2	no	—
72	C₄×C₄₃	#121	1	1	yes	characteristic
73	C₄×C₄₃	#121	1	1	yes	characteristic
74	C₄×C₄₃	#121	1	1	yes	characteristic
75	C₄×C₄₃	#126	1	1	yes	characteristic
76	#2070	—	43	1	no	maximal, Sylow
77	C₂×C₄₃	—	2	1	no	—
78	C₂×C₄₃	—	2	1	no	—
79	C₂×C₄₃	—	2	1	no	—
80	C₂×C₄₃	#396	1	1	yes	characteristic
81	#430	—	43	1	no	—
82	#430	—	43	1	no	—
83	#430	—	43	1	no	—
84	C₂×#101	—	43	1	no	—
85	C₂×#101	—	43	1	no	—
86	C₂×#101	D₄₃	1	1	yes	characteristic
87	#338	—	43	1	no	—
88	C₄₃	#2070	1	1	yes	characteristic, complemented, Sylow
89	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
90	C₂×M₁₆	—	43	1	no	—
91	C₂×M₁₆	—	43	1	no	—
92	C₂×M₁₆	—	43	1	no	—
93	C₂×M₁₆	—	43	1	no	—
94	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
95	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
96	#108	—	86	2	no	—
97	#108	—	86	2	no	—
98	#108	—	86	2	no	—
99	#101	—	2	2	no	—
100	#101	—	86	2	no	—
101	#101	—	86	2	no	—
102	C₂×Q₈	—	2	1	no	—
103	C₂×Q₈	—	2	1	no	—
104	C₂×Q₈	—	2	1	no	—
105	C₂×Q₈	—	2	1	no	—
106	C₂×Q₈	—	2	1	no	—
107	C₂×Q₈	—	2	1	no	—
108	C₂²×C₄	Dic₈₆	1	2	yes	—
109	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
110	M₁₆	—	2	1	no	—
111	M₁₆	—	2	1	no	—
112	M₁₆	—	2	1	no	—
113	M₁₆	—	43	2	no	—
114	M₁₆	—	43	2	no	—
115	M₁₆	—	86	1	no	—
116	M₁₆	—	86	1	no	—
117	M₁₆	—	86	1	no	—
118	M₁₆	—	86	1	no	—
119	M₁₆	—	86	1	no	—
120	M₁₆	—	86	1	no	—
121	M₁₆	C₂²⋊D₄₃	1	2	yes	—
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	2	1	no	—
124	C₂×C₈	—	86	1	no	—
125	C₂×C₈	—	86	1	no	—
126	C₂×C₈	—	86	1	no	—
127	C₂×C₈	—	86	1	no	—
128	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
129	Q₈	—	4	1	no	—
130	Q₈	—	4	1	no	—
131	Q₈	—	4	1	no	—
132	Q₈	—	4	1	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	#10621898	1	1	yes	characteristic
137	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
138	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
139	C₂×C₄	#10621900	1	1	yes	characteristic
140	C₂×C₄	#10621900	1	1	yes	characteristic
141	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	4	1	no	—
144	C₈	—	86	2	no	—
145	C₈	—	86	2	no	—
146	C₈	—	172	1	no	—
147	C₈	—	172	1	no	—
148	C₂²	—	4	1	no	—
149	C₂²	#13063302	1	1	yes	characteristic
150	C₂²	#13063302	1	1	yes	characteristic
151	C₂²	#13063304	1	1	yes	characteristic
152	C₄	—	4	2	no	—
153	C₄	#13063296	1	1	yes	characteristic
154	C₄	#13063297	1	1	yes	characteristic
155	C₄	#13063298	1	1	yes	characteristic
156	C₄	#13063318	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	#14582822	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582948

C₂

yes

maximal, characteristic

#14582947

C₂

yes

maximal, characteristic

#14582947

C₂

yes

maximal, characteristic

C₂×#13063244

C₂

yes

maximal, characteristic

C₂×#13063244

C₂

yes

maximal, characteristic

C₄₃⋊#338

C₂

yes

maximal, characteristic

C₂×#101×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

—

—

—

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

#101×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

—

—

—

—

—

—

D₄

yes

—

#10621877

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×Q₈

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

—

—

D₄₃

yes

characteristic

#338

—

C₄₃

#2070

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂×M₁₆

C₂×D₄₃

yes

—

—

—

—

100

#101

—

101

#101

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂²×C₄

Dic₈₆

yes

—

109

C₂²×C₄

C₂²×D₄₃

yes

characteristic

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

M₁₆

C₂²⋊D₄₃

yes

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂³

C₂×Dic₈₆

yes

characteristic

129

Q₈

—

130

Q₈

—

131

Q₈

—

132

Q₈

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#10621898

yes

characteristic

137

C₂×C₄

D₄×D₄₃

yes

characteristic

138

C₂×C₄

D₄×D₄₃

yes

characteristic

139

C₂×C₄

#10621900

yes

characteristic

140

C₂×C₄

#10621900

yes

characteristic

141

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

172

—

147

C₈

—

172

—

148

C₂²

—

149

C₂²

#13063302

yes

characteristic

150

C₂²

#13063302

yes

characteristic

151

C₂²

#13063304

yes

characteristic

152

C₄

—

153

C₄

#13063296

yes

characteristic

154

C₄

#13063297

yes

characteristic

155

C₄

#13063298

yes

characteristic

156

C₄

#13063318

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#14582822

yes

characteristic

	subgroup	G/H
center	C₂	#14582822
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#101×C₄₃	C₂
socle	C₂×C₄₃	#396
hypercenter	C₂×#101	D₄₃
hypocenter	C₄₃	#2070
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂

#14582822

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#101×C₄₃

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
88. C₄₃	#2070	semidirect

H ≅ G/N

type

88. C₄₃

#2070

semidirect

Subgroups — #19135996

Conjugacy classes of subgroups

Complements