Group #19136709 — subgroups

Subgroups — #19136709

Order 5504.

160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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×#13063270	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063264	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583141	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583136	C₂	1	1	yes	maximal, characteristic
5	#14582702	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
11	#13063305	—	2	1	no	—
12	#13063300	—	2	1	no	—
13	#13063270	—	2	2	no	—
14	#13063264	—	2	2	no	—
15	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
16	#13063248	—	2	1	no	—
17	#13063245	—	2	1	no	—
18	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	#107×C₄₃	C₂²	1	1	yes	characteristic
20	#107×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×D₁₇₂	—	2	1	no	—
22	C₂×D₁₇₂	—	4	1	no	—
23	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
24	C₂×Dic₈₆	—	2	1	no	—
25	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₄₃	—	2	1	no	—
27	C₄⋊C₄×C₄₃	—	2	1	no	—
28	(C₂×D₄₃)⋊C₄	—	4	1	no	—
29	(C₂×D₄₃)⋊C₄	—	4	1	no	—
30	C₄⋊Dic₄₃	—	4	1	no	—
31	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
32	Dic₁₇₂	—	2	1	no	—
33	Dic₁₇₂	—	2	1	no	—
34	D₃₄₄	—	2	1	no	—
35	D₃₄₄	—	2	1	no	—
36	C₈×D₄₃	—	2	1	no	—
37	C₈×D₄₃	—	2	1	no	—
38	C₁₆×C₄₃	D₄	1	2	yes	complemented
39	C₄₃⋊C₁₆	—	2	1	no	—
40	C₂²×D₄₃	—	4	1	no	—
41	C₂²×D₄₃	D₈	1	1	yes	characteristic
42	C₂×C₄×C₄₃	—	4	1	no	—
43	C₂×C₄×C₄₃	—	4	1	no	—
44	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₄₃	—	4	1	no	—
46	C₂×Dic₄₃	D₈	1	1	yes	characteristic
47	D₁₇₂	—	4	1	no	—
48	D₁₇₂	—	4	1	no	—
49	D₁₇₂	—	8	2	no	—
50	C₄×D₄₃	—	2	1	no	—
51	C₄×D₄₃	—	2	1	no	—
52	Dic₈₆	—	4	1	no	—
53	Dic₈₆	—	4	1	no	—
54	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₈×C₄₃	#41	1	1	yes	characteristic
56	C₄₃⋊C₈	—	2	1	no	—
57	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
58	C₂×D₄₃	—	2	1	no	—
59	C₂×D₄₃	—	2	1	no	—
60	C₂×D₄₃	—	2	1	no	—
61	C₂×D₄₃	—	8	1	no	—
62	C₂×D₄₃	—	8	1	no	—
63	C₂×D₄₃	—	8	1	no	—
64	C₄×C₄₃	—	8	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	—	2	1	no	—
69	Dic₄₃	—	8	1	no	—
70	#2220	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	#466	1	1	yes	characteristic
72	C₂×C₄₃	#509	1	1	yes	characteristic
73	C₂×C₄₃	#510	1	1	yes	characteristic
74	D₄₃	—	4	1	no	—
75	D₄₃	—	16	1	no	—
76	C₂×SD₃₂	—	43	1	no	—
77	C₂×M₃₂	—	43	1	no	—
78	#467	—	43	1	no	—
79	#466	—	43	1	no	—
80	#366	D₄₃	1	1	yes	characteristic, complemented
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	—	43	1	no	—
86	C₂²×C₈	—	43	1	no	—
87	C₂²⋊Q₈	—	86	1	no	—
88	#121	—	86	1	no	—
89	SD₃₂	—	86	2	no	—
90	M₃₂	—	86	2	no	—
91	C₂×C₁₆	—	43	1	no	—
92	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
93	#107	C₂×D₄₃	1	1	yes	characteristic
94	#107	C₂×D₄₃	1	1	yes	characteristic
95	#103	—	86	1	no	—
96	#102	—	86	1	no	—
97	C₂×Q₈	—	86	1	no	—
98	C₂×D₄	—	86	1	no	—
99	C₂×D₄	—	172	1	no	—
100	C₂²×C₄	—	43	1	no	—
101	Q₁₆	—	86	1	no	—
102	Q₁₆	—	86	1	no	—
103	D₈	—	86	1	no	—
104	D₈	—	86	1	no	—
105	C₂×C₈	—	43	1	no	—
106	C₂×C₈	—	86	1	no	—
107	C₂×C₈	—	86	1	no	—
108	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	2	1	no	—
111	C₄⋊C₄	—	172	1	no	—
112	C₂²⋊C₄	—	172	1	no	—
113	C₂²⋊C₄	—	172	1	no	—
114	C₁₆	—	86	1	no	—
115	C₁₆	D₁₇₂	1	2	yes	complemented
116	C₂³	—	43	1	no	—
117	C₂³	—	172	1	no	—
118	Q₈	—	172	1	no	—
119	Q₈	—	172	1	no	—
120	D₄	—	344	2	no	—
121	D₄	—	172	1	no	—
122	D₄	—	172	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	43	1	no	—
126	C₂×C₄	—	86	1	no	—
127	C₂×C₄	—	86	1	no	—
128	C₂×C₄	—	172	1	no	—
129	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
130	C₈	—	86	1	no	—
131	C₈	C₂×D₁₇₂	1	1	yes	characteristic
132	C₈	#10621902	1	1	yes	characteristic
133	C₂²	—	86	1	no	—
134	C₂²	—	86	1	no	—
135	C₂²	—	86	1	no	—
136	C₂²	—	344	1	no	—
137	C₂²	—	344	1	no	—
138	C₂²	—	344	1	no	—
139	C₂²	D₈×D₄₃	1	1	yes	characteristic
140	C₄	—	8	1	no	—
141	C₄	—	8	1	no	—
142	C₄	—	86	1	no	—
143	C₄	—	344	1	no	—
144	C₄	#13063300	1	1	yes	characteristic
145	C₄	#13063348	1	1	yes	characteristic
146	C₂	—	172	1	no	—
147	C₂	—	688	1	no	—
148	C₂	#14583136	1	1	yes	characteristic
149	C₂	#14583333	1	1	yes	characteristic
150	C₂	#14583341	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063270

C₂

yes

maximal, characteristic, complemented

C₂×#13063264

C₂

yes

maximal, characteristic, complemented

#14583141

C₂

yes

maximal, characteristic, complemented

#14583136

C₂

yes

maximal, characteristic

#14582702

C₂

yes

maximal, characteristic, complemented

#14582699

C₂

yes

maximal, characteristic, complemented

C₄₃×#366

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×D₃₄₄

C₂²

yes

characteristic

C₂×C₈×D₄₃

C₂²

yes

—

—

—

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063248

—

#13063245

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

—

D₃₄₄

—

D₃₄₄

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

D₄

yes

complemented

C₄₃⋊C₁₆

—

C₂²×D₄₃

—

C₂²×D₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

D₄₃

—

C₂×SD₃₂

—

C₂×M₃₂

—

#467

—

#466

—

#366

D₄₃

yes

characteristic, complemented

#358

—

#357

—

C₄₃

#2220

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×D₈

—

C₂²×C₈

—

C₂²⋊Q₈

—

#121

—

SD₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

C₂×D₄₃

yes

characteristic

#107

C₂×D₄₃

yes

characteristic

#103

—

#102

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

172

—

100

C₂²×C₄

—

101

Q₁₆

—

102

Q₁₆

—

103

D₈

—

104

D₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²×D₄₃

yes

characteristic

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

172

—

112

C₂²⋊C₄

—

172

—

113

C₂²⋊C₄

—

172

—

114

C₁₆

—

115

C₁₆

D₁₇₂

yes

complemented

116

C₂³

—

117

C₂³

—

172

—

118

Q₈

—

172

—

119

Q₈

—

172

—

120

D₄

—

344

—

121

D₄

—

172

—

122

D₄

—

172

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

172

—

129

C₂×C₄

D₄×D₄₃

yes

characteristic

130

C₈

—

131

C₈

C₂×D₁₇₂

yes

characteristic

132

C₈

#10621902

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

344

—

137

C₂²

—

344

—

138

C₂²

—

344

—

139

C₂²

D₈×D₄₃

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

344

—

144

C₄

#13063300

yes

characteristic

145

C₄

#13063348

yes

characteristic

146

C₂

—

172

—

147

C₂

—

688

—

148

C₂

#14583136

yes

characteristic

149

C₂

#14583333

yes

characteristic

150

C₂

#14583341

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#366	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#366	D₄₃
hypocenter	C₄₃	#2220
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#366

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

N	H ≅ G/N	type
1. C₂×#13063270	C₂	semidirect
2. C₂×#13063264	C₂	semidirect
3. #14583141	C₂	semidirect
5. #14582702	C₂	semidirect
6. #14582699	C₂	semidirect
7. C₄₃×#366	C₂	semidirect
38. C₁₆×C₄₃	D₄	semidirect
80. #366	D₄₃	semidirect
83. C₄₃	#2220	semidirect
115. C₁₆	D₁₇₂	semidirect

H ≅ G/N

type

1. C₂×#13063270

C₂

semidirect

2. C₂×#13063264

C₂

semidirect

3. #14583141

C₂

semidirect

5. #14582702

C₂

semidirect

6. #14582699

C₂

semidirect

7. C₄₃×#366

C₂

semidirect

38. C₁₆×C₄₃

D₄

semidirect

80. #366

D₄₃

semidirect

83. C₄₃

#2220

semidirect

115. C₁₆

D₁₇₂

semidirect

Subgroups — #19136709

Conjugacy classes of subgroups

Complements