Group #19134263 — subgroups

Subgroups — #19134263

Order 5504.

242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14583276	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583275	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583275	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583273	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583247	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582621	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621884	—	2	2	no	—
9	C₂×D₃₄₄	—	2	2	no	—
10	C₂×#10621882	—	2	2	no	—
11	C₂×#10621882	—	2	2	no	—
12	#13063322	C₂²	1	1	yes	characteristic
13	#13063322	C₂²	1	1	yes	characteristic
14	#13063245	—	2	2	no	—
15	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	#127×C₄₃	C₂²	1	1	yes	characteristic
19	#102×C₄₃	—	2	2	no	—
20	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×D₄×C₄₃	—	2	1	no	—
23	C₂×D₄×C₄₃	—	2	1	no	—
24	C₂×D₄×C₄₃	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	—	2	1	no	—
28	C₂×D₁₇₂	—	2	1	no	—
29	C₂×D₁₇₂	—	2	1	no	—
30	C₂×D₁₇₂	—	2	1	no	—
31	C₂×C₈×C₄₃	D₄	1	2	yes	—
32	C₄⋊C₄×C₄₃	—	2	1	no	—
33	C₄⋊C₄×C₄₃	—	2	1	no	—
34	C₄²×C₄₃	C₂³	1	1	yes	characteristic
35	#10621884	—	4	4	no	—
36	#10621882	—	4	4	no	—
37	#10621882	—	4	4	no	—
38	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
39	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
40	D₃₄₄	—	4	4	no	—
41	C₂³×C₄₃	—	4	1	no	—
42	C₂²×D₄₃	—	4	1	no	—
43	C₂²×D₄₃	—	4	1	no	—
44	Q₈×C₄₃	—	4	2	no	—
45	D₄×C₄₃	—	4	2	no	—
46	D₄×C₄₃	—	4	2	no	—
47	D₄×C₄₃	—	4	2	no	—
48	C₂×C₄×C₄₃	—	4	1	no	—
49	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	D₁₇₂	—	4	2	no	—
53	D₁₇₂	—	4	2	no	—
54	D₁₇₂	—	4	2	no	—
55	D₁₇₂	—	4	2	no	—
56	D₁₇₂	—	4	2	no	—
57	D₁₇₂	—	4	2	no	—
58	C₈×C₄₃	—	2	2	no	—
59	C₄₃⋊C₈	—	2	2	no	—
60	C₄₃⋊C₈	D₈	1	4	yes	complemented
61	C₂²×C₄₃	—	8	1	no	—
62	C₂²×C₄₃	—	8	1	no	—
63	C₂²×C₄₃	—	8	1	no	—
64	C₂²×C₄₃	#127	1	1	yes	characteristic
65	C₂×D₄₃	—	8	1	no	—
66	C₂×D₄₃	—	8	1	no	—
67	C₂×D₄₃	—	8	1	no	—
68	C₂×D₄₃	—	8	1	no	—
69	C₂×D₄₃	—	8	1	no	—
70	C₂×D₄₃	—	8	1	no	—
71	C₄×C₄₃	—	8	1	no	—
72	C₄×C₄₃	C₂×D₈	1	2	yes	—
73	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
74	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
75	#1721	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	16	1	no	—
77	C₂×C₄₃	#493	1	1	yes	characteristic
78	C₂×C₄₃	#496	1	1	yes	characteristic
79	C₂×C₄₃	#496	1	1	yes	characteristic
80	D₄₃	—	16	1	no	—
81	D₄₃	—	16	1	no	—
82	#493	—	43	1	no	—
83	#493	—	43	1	no	—
84	#493	—	43	1	no	—
85	#492	—	43	1	no	—
86	#486	—	43	1	no	—
87	#486	D₄₃	1	1	yes	characteristic, complemented
88	#322	—	43	1	no	—
89	C₄₃	#1721	1	1	yes	characteristic, complemented, Sylow
90	C₂×SD₁₆	—	86	2	no	—
91	C₂×D₈	—	86	2	no	—
92	C₂×D₈	—	86	2	no	—
93	C₂×D₈	—	86	2	no	—
94	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
95	#127	—	43	1	no	—
96	#127	—	43	1	no	—
97	#127	C₂×D₄₃	1	1	yes	characteristic
98	#102	—	2	2	no	—
99	#102	—	86	2	no	—
100	C₄×C₈	—	43	1	no	—
101	C₄×C₈	—	43	1	no	—
102	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
103	C₂×Q₈	—	2	1	no	—
104	C₂×D₄	—	2	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	2	1	no	—
107	C₂×D₄	—	86	1	no	—
108	C₂×D₄	—	86	1	no	—
109	C₂×D₄	—	86	1	no	—
110	C₂×D₄	—	86	1	no	—
111	C₂×D₄	—	86	1	no	—
112	C₂×D₄	—	86	1	no	—
113	SD₁₆	—	172	4	no	—
114	D₈	—	172	4	no	—
115	D₈	—	172	4	no	—
116	D₈	—	172	4	no	—
117	C₂×C₈	—	43	2	no	—
118	C₂×C₈	—	43	2	no	—
119	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
120	C₄⋊C₄	—	2	1	no	—
121	C₄⋊C₄	—	2	1	no	—
122	C₄²	C₂²×D₄₃	1	1	yes	characteristic
123	C₂³	—	4	1	no	—
124	C₂³	—	172	1	no	—
125	C₂³	—	172	1	no	—
126	Q₈	—	4	2	no	—
127	D₄	—	4	2	no	—
128	D₄	—	4	2	no	—
129	D₄	—	4	2	no	—
130	D₄	—	172	2	no	—
131	D₄	—	172	2	no	—
132	D₄	—	172	2	no	—
133	D₄	—	172	2	no	—
134	D₄	—	172	2	no	—
135	D₄	—	172	2	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
138	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
139	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
140	C₈	—	2	2	no	—
141	C₈	—	43	4	no	—
142	C₈	—	86	2	no	—
143	C₂²	—	8	1	no	—
144	C₂²	—	8	1	no	—
145	C₂²	—	8	1	no	—
146	C₂²	—	344	1	no	—
147	C₂²	—	344	1	no	—
148	C₂²	—	344	1	no	—
149	C₂²	—	344	1	no	—
150	C₂²	—	344	1	no	—
151	C₂²	—	344	1	no	—
152	C₂²	#13063321	1	1	yes	characteristic
153	C₄	—	8	1	no	—
154	C₄	D₈×D₄₃	1	2	yes	—
155	C₄	#13063350	1	2	yes	—
156	C₄	#13063352	1	2	yes	—
157	C₂	—	16	1	no	—
158	C₂	—	688	1	no	—
159	C₂	—	688	1	no	—
160	C₂	#14583274	1	1	yes	characteristic
161	C₂	#14583285	1	1	yes	characteristic
162	C₂	#14583289	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583276

C₂

yes

maximal, characteristic, complemented

#14583275

C₂

yes

maximal, characteristic, complemented

#14583275

C₂

yes

maximal, characteristic, complemented

#14583273

C₂

yes

maximal, characteristic, complemented

#14583247

C₂

yes

maximal, characteristic, complemented

#14582621

C₂

yes

maximal, characteristic, complemented

C₄₃×#486

C₂

yes

maximal, characteristic, complemented

C₂×#10621884

—

C₂×D₃₄₄

—

C₂×#10621882

—

C₂×#10621882

—

#13063322

C₂²

yes

characteristic

#13063322

C₂²

yes

characteristic

#13063245

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#127×C₄₃

C₂²

yes

characteristic

#102×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

—

—

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

—

D₃₄₄

—

C₂³×C₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

D₈

yes

complemented

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#127

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

#1721

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

D₄₃

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

#322

—

C₄₃

#1721

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

characteristic

#102

—

#102

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₄×C₈

C₂×D₄₃

yes

characteristic

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

SD₁₆

—

172

—

114

D₈

—

172

—

115

D₈

—

172

—

116

D₈

—

172

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

C₂²⋊D₄₃

yes

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄²

C₂²×D₄₃

yes

characteristic

123

C₂³

—

124

C₂³

—

172

—

125

C₂³

—

172

—

126

Q₈

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

—

172

—

131

D₄

—

172

—

132

D₄

—

172

—

133

D₄

—

172

—

134

D₄

—

172

—

135

D₄

—

172

—

136

C₂×C₄

—

137

C₂×C₄

D₄×D₄₃

yes

characteristic

138

C₂×C₄

D₄×D₄₃

yes

characteristic

139

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

344

—

147

C₂²

—

344

—

148

C₂²

—

344

—

149

C₂²

—

344

—

150

C₂²

—

344

—

151

C₂²

—

344

—

152

C₂²

#13063321

yes

characteristic

153

C₄

—

154

C₄

D₈×D₄₃

yes

—

155

C₄

#13063350

yes

—

156

C₄

#13063352

yes

—

157

C₂

—

158

C₂

—

688

—

159

C₂

—

688

—

160

C₂

#14583274

yes

characteristic

161

C₂

#14583285

yes

characteristic

162

C₂

#14583289

yes

characteristic

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#486	C₂
socle	C₂²×C₄₃	#127
hypercenter	#486	D₄₃
hypocenter	C₄₃	#1721
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

#13063321

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#486

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. #14583276	C₂	semidirect
2. #14583275	C₂	semidirect
3. #14583275	C₂	semidirect
4. #14583273	C₂	semidirect
5. #14583247	C₂	semidirect
6. #14582621	C₂	semidirect
7. C₄₃×#486	C₂	semidirect
60. C₄₃⋊C₈	D₈	semidirect
87. #486	D₄₃	semidirect
89. C₄₃	#1721	semidirect

H ≅ G/N

type

1. #14583276

C₂

semidirect

2. #14583275

C₂

semidirect

3. #14583275

C₂

semidirect

4. #14583273

C₂

semidirect

5. #14583247

C₂

semidirect

6. #14582621

C₂

semidirect

7. C₄₃×#486

C₂

semidirect

60. C₄₃⋊C₈

D₈

semidirect

87. #486

D₄₃

semidirect

89. C₄₃

#1721

semidirect

Subgroups — #19134263

Conjugacy classes of subgroups

Complements