Group #19136540 — subgroups

Subgroups — #19136540

Order 5504.

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

normal subgroups only

This group has 226 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	#14583699	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583335	C₂	1	2	yes	maximal, complemented
3	#14582708	C₂	1	2	yes	maximal, complemented
4	#14582681	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621898	—	2	1	no	—
7	#13063358	—	2	2	no	—
8	#13063353	—	2	2	no	—
9	#13063347	—	2	1	no	—
10	#13063347	C₂²	1	2	yes	—
11	#13063269	—	2	2	no	—
12	#13063266	—	2	2	no	—
13	#13063265	C₂²	1	2	yes	complemented
14	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	#121×C₄₃	—	2	1	no	—
17	#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
18	#102×C₄₃	—	2	1	no	—
19	C₂×D₄×C₄₃	—	2	1	no	—
20	C₂×D₄×C₄₃	—	4	1	no	—
21	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₂²⋊D₄₃	—	4	1	no	—
23	#10621898	—	2	2	no	—
24	#10621898	—	2	2	no	—
25	#10621898	—	4	1	no	—
26	#10621898	—	4	1	no	—
27	C₂×D₁₇₂	—	2	1	no	—
28	C₂×C₄×D₄₃	—	4	1	no	—
29	C₂×Dic₈₆	—	2	1	no	—
30	D₈×C₄₃	—	2	2	no	—
31	M₁₆×C₄₃	—	2	2	no	—
32	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
33	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₄₃	—	2	1	no	—
35	C₂²⋊C₄×C₄₃	—	4	1	no	—
36	Dic₁₇₂	—	2	1	no	—
37	Dic₁₇₂	D₄	1	2	yes	complemented
38	D₃₄₄	—	2	1	no	—
39	D₃₄₄	D₄	1	2	yes	complemented
40	#10621873	—	2	2	no	—
41	#10621873	—	2	2	no	—
42	C₄₃⋊C₁₆	—	2	2	no	—
43	C₂³×C₄₃	—	4	1	no	—
44	C₂³×C₄₃	D₈	1	1	yes	characteristic
45	C₂²×D₄₃	—	4	1	no	—
46	D₄×C₄₃	—	4	1	no	—
47	D₄×C₄₃	—	4	1	no	—
48	D₄×C₄₃	—	8	2	no	—
49	C₂×C₄×C₄₃	—	2	1	no	—
50	C₂×C₄×C₄₃	—	2	1	no	—
51	C₂×C₄×C₄₃	—	4	1	no	—
52	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂²⋊D₄₃	—	4	2	no	—
55	C₂²⋊D₄₃	—	4	2	no	—
56	C₂×Dic₄₃	—	4	1	no	—
57	D₁₇₂	—	2	2	no	—
58	D₁₇₂	—	4	1	no	—
59	C₄×D₄₃	—	4	2	no	—
60	C₄×D₄₃	—	4	2	no	—
61	Dic₈₆	—	2	2	no	—
62	Dic₈₆	—	4	1	no	—
63	C₈×C₄₃	—	2	1	no	—
64	C₈×C₄₃	C₂×D₄	1	2	yes	—
65	C₂²×C₄₃	—	2	1	no	—
66	C₂²×C₄₃	—	4	1	no	—
67	C₂²×C₄₃	—	8	1	no	—
68	C₂²×C₄₃	—	8	1	no	—
69	C₂²×C₄₃	—	8	1	no	—
70	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
71	C₂×D₄₃	—	4	2	no	—
72	C₂×D₄₃	—	8	2	no	—
73	C₄×C₄₃	—	2	1	no	—
74	C₄×C₄₃	—	8	1	no	—
75	C₄×C₄₃	#120	1	1	yes	characteristic
76	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
77	Dic₄₃	—	4	2	no	—
78	#2190	—	43	1	no	maximal, Sylow
79	C₂×C₄₃	—	2	1	no	—
80	C₂×C₄₃	—	4	1	no	—
81	C₂×C₄₃	—	16	1	no	—
82	C₂×C₄₃	#447	1	1	yes	characteristic
83	D₄₃	—	8	2	no	—
84	#575	—	43	1	no	—
85	#509	—	43	2	no	—
86	#469	D₄₃	1	1	yes	characteristic, complemented
87	#360	—	43	2	no	—
88	#349	—	43	1	no	—
89	C₄₃	#2190	1	1	yes	characteristic, complemented, Sylow
90	C₂×#41	—	86	1	no	—
91	#137	—	86	2	no	—
92	AGL(1,ℤ/8)	—	86	2	no	—
93	#135	—	43	2	no	—
94	#135	—	86	1	no	—
95	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
96	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
97	#121	—	2	1	no	—
98	SD₃₂	—	86	2	no	—
99	D₁₆	—	86	2	no	—
100	M₃₂	—	43	2	no	—
101	#106	C₂×D₄₃	1	1	yes	characteristic, complemented
102	#102	—	2	1	no	—
103	#41	—	86	2	no	—
104	#41	—	86	2	no	—
105	#41	—	172	1	no	—
106	#41	—	172	1	no	—
107	C₂×Q₈	—	86	1	no	—
108	C₂×D₄	—	2	1	no	—
109	C₂×D₄	—	4	1	no	—
110	C₂×D₄	—	86	1	no	—
111	C₂×D₄	—	172	1	no	—
112	C₂²×C₄	—	172	1	no	—
113	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
114	Q₁₆	—	43	2	no	—
115	Q₁₆	—	86	1	no	—
116	SD₁₆	—	86	2	no	—
117	SD₁₆	—	86	2	no	—
118	D₈	—	2	2	no	—
119	D₈	—	43	2	no	—
120	D₈	—	86	1	no	—
121	M₁₆	—	2	2	no	—
122	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
123	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
124	C₄⋊C₄	—	2	1	no	—
125	C₂²⋊C₄	—	4	1	no	—
126	C₁₆	—	86	2	no	—
127	C₂³	—	4	1	no	—
128	C₂³	—	172	1	no	—
129	C₂³	#10621882	1	1	yes	characteristic
130	Q₈	—	86	2	no	—
131	Q₈	—	172	1	no	—
132	D₄	—	4	1	no	—
133	D₄	—	4	1	no	—
134	D₄	—	8	2	no	—
135	D₄	—	86	2	no	—
136	D₄	—	172	1	no	—
137	D₄	—	172	2	no	—
138	D₄	—	172	2	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	4	1	no	—
142	C₂×C₄	—	172	2	no	—
143	C₂×C₄	—	172	1	no	—
144	C₂×C₄	—	172	2	no	—
145	C₂×C₄	#10621882	1	1	yes	characteristic
146	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
147	C₈	—	2	1	no	—
148	C₈	D₄×D₄₃	1	2	yes	—
149	C₂²	—	2	1	no	—
150	C₂²	—	4	1	no	—
151	C₂²	—	8	1	no	—
152	C₂²	—	8	1	no	—
153	C₂²	—	8	1	no	—
154	C₂²	—	344	2	no	—
155	C₂²	—	172	2	no	—
156	C₂²	C₂×#10621882	1	1	yes	characteristic
157	C₄	—	2	1	no	—
158	C₄	—	8	1	no	—
159	C₄	—	172	2	no	—
160	C₄	#13063293	1	1	yes	characteristic
161	C₄	#13063350	1	1	yes	characteristic
162	C₂	—	2	1	no	—
163	C₂	—	4	1	no	—
164	C₂	—	16	1	no	—
165	C₂	—	344	2	no	—
166	C₂	#14583032	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583699

C₂

yes

maximal, characteristic, complemented

#14583335

C₂

yes

maximal, complemented

#14582708

C₂

yes

maximal, complemented

#14582681

C₂

yes

maximal, characteristic, complemented

C₄₃×#469

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

—

#13063269

—

#13063266

—

#13063265

C₂²

yes

complemented

C₂×D₈×C₄₃

C₂²

yes

characteristic, complemented

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

#121×C₄₃

—

#106×C₄₃

C₂²

yes

characteristic, complemented

#102×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

—

—

—

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

D₈×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

Dic₁₇₂

—

Dic₁₇₂

D₄

yes

complemented

D₃₄₄

—

D₃₄₄

D₄

yes

complemented

#10621873

—

#10621873

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂³×C₄₃

D₈

yes

characteristic

C₂²×D₄₃

—

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

C₂²⋊D₄₃

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#2190

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#447

yes

characteristic

D₄₃

—

#575

—

#509

—

#469

D₄₃

yes

characteristic, complemented

#360

—

#349

—

C₄₃

#2190

yes

characteristic, complemented, Sylow

C₂×#41

—

—

—

—

—

C₂×D₈

C₂×D₄₃

yes

characteristic, complemented

C₂×M₁₆

C₂×D₄₃

yes

characteristic

#121

—

SD₃₂

—

D₁₆

—

100

M₃₂

—

101

#106

C₂×D₄₃

yes

characteristic, complemented

102

#102

—

103

#41

—

104

#41

—

105

#41

—

172

—

106

#41

—

172

—

107

C₂×Q₈

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

172

—

112

C₂²×C₄

—

172

—

113

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

114

Q₁₆

—

115

Q₁₆

—

116

SD₁₆

—

117

SD₁₆

—

118

D₈

—

119

D₈

—

120

D₈

—

121

M₁₆

—

122

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

123

C₂×C₈

C₂²×D₄₃

yes

characteristic

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₁₆

—

127

C₂³

—

128

C₂³

—

172

—

129

C₂³

#10621882

yes

characteristic

130

Q₈

—

131

Q₈

—

172

—

132

D₄

—

133

D₄

—

134

D₄

—

135

D₄

—

136

D₄

—

172

—

137

D₄

—

172

—

138

D₄

—

172

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

172

—

143

C₂×C₄

—

172

—

144

C₂×C₄

—

172

—

145

C₂×C₄

#10621882

yes

characteristic

146

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

147

C₈

—

148

C₈

D₄×D₄₃

yes

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

344

—

155

C₂²

—

172

—

156

C₂²

C₂×#10621882

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

—

172

—

160

C₄

#13063293

yes

characteristic

161

C₄

#13063350

yes

characteristic

162

C₂

—

163

C₂

—

164

C₂

—

165

C₂

—

344

—

166

C₂

#14583032

yes

characteristic

	subgroup	G/H
center	C₂	#14583032
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#469	C₂
socle	C₂×C₄₃	#447
hypercenter	#469	D₄₃
hypocenter	C₄₃	#2190
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

subgroup

G/H

center

C₂

#14583032

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#469

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

N	H ≅ G/N	type
1. #14583699	C₂	semidirect
2. #14583335	C₂	semidirect
3. #14582708	C₂	semidirect
4. #14582681	C₂	semidirect
5. C₄₃×#469	C₂	semidirect
13. #13063265	C₂²	semidirect
14. C₂×D₈×C₄₃	C₂²	semidirect
17. #106×C₄₃	C₂²	semidirect
37. Dic₁₇₂	D₄	semidirect
39. D₃₄₄	D₄	semidirect
86. #469	D₄₃	semidirect
89. C₄₃	#2190	semidirect
95. C₂×D₈	C₂×D₄₃	semidirect
101. #106	C₂×D₄₃	semidirect

H ≅ G/N

type

1. #14583699

C₂

semidirect

2. #14583335

C₂

semidirect

3. #14582708

C₂

semidirect

4. #14582681

C₂

semidirect

5. C₄₃×#469

C₂

semidirect

13. #13063265

C₂²

semidirect

14. C₂×D₈×C₄₃

C₂²

semidirect

17. #106×C₄₃

C₂²

semidirect

37. Dic₁₇₂

D₄

semidirect

39. D₃₄₄

D₄

semidirect

86. #469

D₄₃

semidirect

89. C₄₃

#2190

semidirect

95. C₂×D₈

C₂×D₄₃

semidirect

101. #106

C₂×D₄₃

semidirect

Subgroups — #19136540

Conjugacy classes of subgroups

Complements