Group #19136706 — subgroups

Subgroups — #19136706

Order 5504.

160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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×#13063269	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063265	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583140	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582724	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582702	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#466	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	#13063304	—	2	1	no	—
10	#13063269	—	2	2	no	—
11	#13063265	—	2	2	no	—
12	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
14	#13063259	C₂²	1	1	yes	characteristic
15	#13063250	—	2	1	no	—
16	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	#121×C₄₃	—	2	1	no	—
19	#107×C₄₃	C₂²	1	1	yes	characteristic
20	#102×C₄₃	—	2	1	no	—
21	C₂×D₄×C₄₃	—	2	1	no	—
22	C₂×D₄×C₄₃	—	4	1	no	—
23	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
24	C₂×Dic₈₆	—	2	1	no	—
25	D₈×C₄₃	—	2	1	no	—
26	D₈×C₄₃	—	2	1	no	—
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
30	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
31	C₄⋊C₄×C₄₃	—	2	1	no	—
32	C₂²⋊C₄×C₄₃	—	4	1	no	—
33	C₂²⋊Dic₄₃	—	4	1	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	Dic₄₃⋊C₄	—	4	1	no	—
36	Dic₁₇₂	—	2	1	no	—
37	Dic₁₇₂	—	2	1	no	—
38	C₄₃⋊C₁₆	—	2	1	no	—
39	C₄₃⋊C₁₆	D₄	1	2	yes	complemented
40	C₂³×C₄₃	—	4	1	no	—
41	C₂³×C₄₃	D₈	1	1	yes	characteristic
42	D₄×C₄₃	—	4	1	no	—
43	D₄×C₄₃	—	4	1	no	—
44	D₄×C₄₃	—	8	2	no	—
45	C₂×C₄×C₄₃	—	2	1	no	—
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	—	4	1	no	—
48	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
49	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₄₃	—	4	1	no	—
51	C₂×Dic₄₃	—	4	1	no	—
52	Dic₈₆	—	4	1	no	—
53	Dic₈₆	—	4	1	no	—
54	C₈×C₄₃	—	2	1	no	—
55	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₈×C₄₃	#41	1	1	yes	characteristic
57	C₂²×C₄₃	—	2	1	no	—
58	C₂²×C₄₃	—	2	1	no	—
59	C₂²×C₄₃	—	2	1	no	—
60	C₂²×C₄₃	—	8	1	no	—
61	C₂²×C₄₃	—	8	1	no	—
62	C₂²×C₄₃	—	8	1	no	—
63	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
64	C₄×C₄₃	—	2	1	no	—
65	C₄×C₄₃	—	8	1	no	—
66	C₄×C₄₃	#121	1	1	yes	characteristic
67	C₄×C₄₃	#135	1	1	yes	characteristic
68	Dic₄₃	—	8	1	no	—
69	Dic₄₃	—	8	1	no	—
70	#2220	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	—	4	1	no	—
72	C₂×C₄₃	—	16	1	no	—
73	C₂×C₄₃	#466	1	1	yes	characteristic
74	C₂×C₄₃	#509	1	1	yes	characteristic
75	C₂×C₄₃	#510	1	1	yes	characteristic
76	C₂×SD₃₂	—	43	1	no	—
77	C₂×M₃₂	—	43	1	no	—
78	#467	—	43	1	no	—
79	#466	D₄₃	1	1	yes	characteristic
80	#366	—	43	1	no	—
81	#358	—	43	1	no	—
82	#357	—	43	1	no	—
83	C₄₃	#2220	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₁₆	—	43	1	no	—
85	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
86	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
87	C₂²⋊Q₈	—	86	1	no	—
88	#121	—	2	1	no	—
89	SD₃₂	—	86	2	no	—
90	M₃₂	—	86	2	no	—
91	C₂×C₁₆	—	43	1	no	—
92	C₂×C₁₆	—	43	1	no	—
93	#107	—	43	1	no	—
94	#107	C₂×D₄₃	1	1	yes	characteristic
95	#103	—	86	1	no	—
96	#102	—	2	1	no	—
97	C₂×Q₈	—	86	1	no	—
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	4	1	no	—
100	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
101	Q₁₆	—	86	1	no	—
102	Q₁₆	—	86	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	2	1	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
108	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	86	1	no	—
111	C₄⋊C₄	—	172	1	no	—
112	C₂²⋊C₄	—	4	1	no	—
113	C₂²⋊C₄	—	172	1	no	—
114	C₁₆	—	43	2	no	—
115	C₁₆	—	86	1	no	—
116	C₂³	—	4	1	no	—
117	C₂³	#10621882	1	1	yes	characteristic
118	Q₈	—	172	1	no	—
119	Q₈	—	172	1	no	—
120	D₄	—	4	1	no	—
121	D₄	—	4	1	no	—
122	D₄	—	8	2	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	172	1	no	—
127	C₂×C₄	—	172	1	no	—
128	C₂×C₄	#10621882	1	1	yes	characteristic
129	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
130	C₈	—	2	1	no	—
131	C₈	D₄×D₄₃	1	1	yes	characteristic
132	C₈	#10621900	1	1	yes	characteristic
133	C₂²	—	2	1	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	—	8	1	no	—
137	C₂²	—	8	1	no	—
138	C₂²	—	8	1	no	—
139	C₂²	C₂×#10621882	1	1	yes	characteristic
140	C₄	—	2	1	no	—
141	C₄	—	8	1	no	—
142	C₄	—	344	1	no	—
143	C₄	—	344	1	no	—
144	C₄	#13063297	1	1	yes	characteristic
145	C₄	#13063345	1	1	yes	characteristic
146	C₂	—	4	1	no	—
147	C₂	—	16	1	no	—
148	C₂	#14583133	1	1	yes	characteristic
149	C₂	#14583335	1	1	yes	characteristic
150	C₂	#14583339	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063269

C₂

yes

maximal, characteristic, complemented

C₂×#13063265

C₂

yes

maximal, characteristic, complemented

#14583140

C₂

yes

maximal, characteristic, complemented

#14582724

C₂

yes

maximal, characteristic, complemented

#14582702

C₂

yes

maximal, characteristic, complemented

#14582700

C₂

yes

maximal, characteristic, complemented

C₄₃×#466

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

—

—

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063250

—

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#121×C₄₃

—

#107×C₄₃

C₂²

yes

characteristic

#102×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₁₇₂

—

Dic₁₇₂

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

D₄

yes

complemented

C₂³×C₄₃

—

C₂³×C₄₃

D₈

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2220

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×SD₃₂

—

C₂×M₃₂

—

#467

—

#466

D₄₃

yes

—

—

—

C₄₃

#2220

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×D₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

#121

—

SD₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₄₃

yes

characteristic

#103

—

#102

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

100

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

101

Q₁₆

—

102

Q₁₆

—

103

D₈

—

104

D₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

108

C₂×C₈

C₂²×D₄₃

yes

characteristic

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

172

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

172

—

114

C₁₆

—

115

C₁₆

—

116

C₂³

—

117

C₂³

#10621882

yes

characteristic

118

Q₈

—

172

—

119

Q₈

—

172

—

120

D₄

—

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

172

—

127

C₂×C₄

—

172

—

128

C₂×C₄

#10621882

yes

characteristic

129

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

130

C₈

—

131

C₈

D₄×D₄₃

yes

characteristic

132

C₈

#10621900

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

C₂×#10621882

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

344

—

143

C₄

—

344

—

144

C₄

#13063297

yes

characteristic

145

C₄

#13063345

yes

characteristic

146

C₂

—

147

C₂

—

148

C₂

#14583133

yes

characteristic

149

C₂

#14583335

yes

characteristic

150

C₂

#14583339

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#466	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#466	D₄₃
hypocenter	C₄₃	#2220
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #466

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#466

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #466

N	H ≅ G/N	type
1. C₂×#13063269	C₂	semidirect
2. C₂×#13063265	C₂	semidirect
3. #14583140	C₂	semidirect
4. #14582724	C₂	semidirect
5. #14582702	C₂	semidirect
6. #14582700	C₂	semidirect
39. C₄₃⋊C₁₆	D₄	semidirect
83. C₄₃	#2220	semidirect

H ≅ G/N

type

1. C₂×#13063269

C₂

semidirect

2. C₂×#13063265

C₂

semidirect

3. #14583140

C₂

semidirect

4. #14582724

C₂

semidirect

5. #14582702

C₂

semidirect

6. #14582700

C₂

semidirect

39. C₄₃⋊C₁₆

D₄

semidirect

83. C₄₃

#2220

semidirect

Subgroups — #19136706

Conjugacy classes of subgroups

Complements