Group #19136545 — subgroups

Subgroups — #19136545

Order 5504.

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

normal subgroups only

This group has 216 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
2	#14583340	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×#470	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	#13063271	—	2	2	no	—
12	#13063268	—	2	2	no	—
13	#13063265	C₂²	1	2	yes	complemented
14	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²⋊Q₈×C₄₃	—	2	1	no	—
17	#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
18	#103×C₄₃	—	2	1	no	—
19	C₂×Q₈×C₄₃	—	2	1	no	—
20	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₂²⋊D₄₃	—	4	1	no	—
22	#10621898	—	2	2	no	—
23	#10621898	—	2	2	no	—
24	#10621898	—	4	1	no	—
25	#10621898	—	4	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×C₄×D₄₃	—	4	1	no	—
28	C₂×Dic₈₆	—	2	1	no	—
29	Q₁₆×C₄₃	—	2	2	no	—
30	M₁₆×C₄₃	—	2	2	no	—
31	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
32	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₄₃	—	2	1	no	—
34	C₄⋊C₄×C₄₃	—	4	1	no	—
35	C₂²⋊C₄×C₄₃	—	4	1	no	—
36	Dic₁₇₂	—	2	1	no	—
37	Dic₁₇₂	D₄	1	2	yes	—
38	D₃₄₄	—	2	1	no	—
39	D₃₄₄	D₄	1	2	yes	—
40	#10621873	—	2	2	no	—
41	#10621873	—	2	2	no	—
42	C₄₃⋊C₁₆	—	2	2	no	—
43	C₂³×C₄₃	D₈	1	1	yes	characteristic
44	C₂²×D₄₃	—	4	1	no	—
45	Q₈×C₄₃	—	4	1	no	—
46	Q₈×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	—	2	1	no	—
49	C₂×C₄×C₄₃	—	4	1	no	—
50	C₂×C₄×C₄₃	—	4	1	no	—
51	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂²⋊D₄₃	—	4	2	no	—
54	C₂²⋊D₄₃	—	4	2	no	—
55	C₂×Dic₄₃	—	4	1	no	—
56	D₁₇₂	—	2	2	no	—
57	D₁₇₂	—	4	1	no	—
58	C₄×D₄₃	—	4	2	no	—
59	C₄×D₄₃	—	4	2	no	—
60	Dic₈₆	—	2	2	no	—
61	Dic₈₆	—	4	1	no	—
62	C₈×C₄₃	—	2	1	no	—
63	C₈×C₄₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄₃	—	2	1	no	—
65	C₂²×C₄₃	—	4	1	no	—
66	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
67	C₂×D₄₃	—	4	2	no	—
68	C₂×D₄₃	—	8	2	no	—
69	C₄×C₄₃	—	2	1	no	—
70	C₄×C₄₃	—	8	1	no	—
71	C₄×C₄₃	—	8	1	no	—
72	C₄×C₄₃	#120	1	1	yes	characteristic
73	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
74	Dic₄₃	—	4	2	no	—
75	#2191	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	—	4	1	no	—
78	C₂×C₄₃	#447	1	1	yes	characteristic
79	D₄₃	—	8	2	no	—
80	#575	—	43	1	no	—
81	#510	—	43	2	no	—
82	#470	D₄₃	1	1	yes	characteristic, complemented
83	#360	—	43	2	no	—
84	#349	—	43	1	no	—
85	C₄₃	#2191	1	1	yes	characteristic, complemented, Sylow
86	C₂×#41	—	86	1	no	—
87	#137	—	86	2	no	—
88	AGL(1,ℤ/8)	—	86	2	no	—
89	#135	—	43	2	no	—
90	#135	—	86	1	no	—
91	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
92	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
93	C₂²⋊Q₈	—	2	1	no	—
94	Q₃₂	—	86	2	no	—
95	SD₃₂	—	86	2	no	—
96	M₃₂	—	43	2	no	—
97	#106	C₂×D₄₃	1	1	yes	characteristic, complemented
98	#103	—	2	1	no	—
99	#41	—	86	2	no	—
100	#41	—	86	2	no	—
101	#41	—	172	1	no	—
102	#41	—	172	1	no	—
103	C₂×Q₈	—	2	1	no	—
104	C₂×Q₈	—	86	1	no	—
105	C₂×D₄	—	86	1	no	—
106	C₂×D₄	—	172	1	no	—
107	C₂²×C₄	—	172	1	no	—
108	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
109	Q₁₆	—	2	2	no	—
110	Q₁₆	—	43	2	no	—
111	Q₁₆	—	86	1	no	—
112	SD₁₆	—	86	2	no	—
113	SD₁₆	—	86	2	no	—
114	D₈	—	43	2	no	—
115	D₈	—	86	1	no	—
116	M₁₆	—	2	2	no	—
117	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
118	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
119	C₄⋊C₄	—	2	1	no	—
120	C₄⋊C₄	—	4	1	no	—
121	C₂²⋊C₄	—	4	1	no	—
122	C₁₆	—	86	2	no	—
123	C₂³	—	172	1	no	—
124	C₂³	#10621882	1	1	yes	characteristic
125	Q₈	—	4	1	no	—
126	Q₈	—	4	1	no	—
127	Q₈	—	86	2	no	—
128	Q₈	—	172	1	no	—
129	D₄	—	86	2	no	—
130	D₄	—	172	1	no	—
131	D₄	—	172	2	no	—
132	D₄	—	172	2	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	172	2	no	—
138	C₂×C₄	—	172	1	no	—
139	C₂×C₄	—	172	2	no	—
140	C₂×C₄	#10621882	1	1	yes	characteristic
141	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
142	C₈	—	2	1	no	—
143	C₈	D₄×D₄₃	1	2	yes	—
144	C₂²	—	2	1	no	—
145	C₂²	—	4	1	no	—
146	C₂²	—	344	2	no	—
147	C₂²	—	172	2	no	—
148	C₂²	C₂×#10621882	1	1	yes	characteristic
149	C₄	—	2	1	no	—
150	C₄	—	8	1	no	—
151	C₄	—	8	1	no	—
152	C₄	—	172	2	no	—
153	C₄	#13063293	1	1	yes	characteristic
154	C₄	#13063350	1	1	yes	characteristic
155	C₂	—	2	1	no	—
156	C₂	—	4	1	no	—
157	C₂	—	344	2	no	—
158	C₂	#14583032	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583699

C₂

yes

maximal, characteristic

#14583340

C₂

yes

maximal, complemented

#14582708

C₂

yes

maximal, complemented

#14582681

C₂

yes

maximal, characteristic, complemented

C₄₃×#470

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

—

#13063271

—

#13063268

—

#13063265

C₂²

yes

complemented

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic, complemented

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂²⋊Q₈×C₄₃

—

#106×C₄₃

C₂²

yes

characteristic, complemented

#103×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

—

—

—

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

Dic₁₇₂

—

Dic₁₇₂

D₄

yes

—

D₃₄₄

—

D₃₄₄

D₄

yes

—

#10621873

—

#10621873

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

D₈

yes

characteristic

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×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

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#2191

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#447

yes

characteristic

D₄₃

—

#575

—

#510

—

#470

D₄₃

yes

characteristic, complemented

#360

—

#349

—

C₄₃

#2191

yes

characteristic, complemented, Sylow

C₂×#41

—

—

—

—

—

C₂×Q₁₆

C₂×D₄₃

yes

characteristic, complemented

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

—

#106

C₂×D₄₃

yes

characteristic, complemented

#103

—

#41

—

100

#41

—

101

#41

—

172

—

102

#41

—

172

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂×D₄

—

172

—

107

C₂²×C₄

—

172

—

108

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

109

Q₁₆

—

110

Q₁₆

—

111

Q₁₆

—

112

SD₁₆

—

113

SD₁₆

—

114

D₈

—

115

D₈

—

116

M₁₆

—

117

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

118

C₂×C₈

C₂²×D₄₃

yes

characteristic

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₂²⋊C₄

—

122

C₁₆

—

123

C₂³

—

172

—

124

C₂³

#10621882

yes

characteristic

125

Q₈

—

126

Q₈

—

127

Q₈

—

128

Q₈

—

172

—

129

D₄

—

130

D₄

—

172

—

131

D₄

—

172

—

132

D₄

—

172

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

172

—

138

C₂×C₄

—

172

—

139

C₂×C₄

—

172

—

140

C₂×C₄

#10621882

yes

characteristic

141

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

142

C₈

—

143

C₈

D₄×D₄₃

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

344

—

147

C₂²

—

172

—

148

C₂²

C₂×#10621882

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

172

—

153

C₄

#13063293

yes

characteristic

154

C₄

#13063350

yes

characteristic

155

C₂

—

156

C₂

—

157

C₂

—

344

—

158

C₂

#14583032

yes

characteristic

	subgroup	G/H
center	C₂	#14583032
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#470	C₂
socle	C₂×C₄₃	#447
hypercenter	#470	D₄₃
hypocenter	C₄₃	#2191
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

subgroup

G/H

center

C₂

#14583032

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#470

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

N	H ≅ G/N	type
2. #14583340	C₂	semidirect
3. #14582708	C₂	semidirect
4. #14582681	C₂	semidirect
5. C₄₃×#470	C₂	semidirect
13. #13063265	C₂²	semidirect
14. C₂×Q₁₆×C₄₃	C₂²	semidirect
17. #106×C₄₃	C₂²	semidirect
82. #470	D₄₃	semidirect
85. C₄₃	#2191	semidirect
91. C₂×Q₁₆	C₂×D₄₃	semidirect
97. #106	C₂×D₄₃	semidirect

H ≅ G/N

type

2. #14583340

C₂

semidirect

3. #14582708

C₂

semidirect

4. #14582681

C₂

semidirect

5. C₄₃×#470

C₂

semidirect

13. #13063265

C₂²

semidirect

14. C₂×Q₁₆×C₄₃

C₂²

semidirect

17. #106×C₄₃

C₂²

semidirect

82. #470

D₄₃

semidirect

85. C₄₃

#2191

semidirect

91. C₂×Q₁₆

C₂×D₄₃

semidirect

97. #106

C₂×D₄₃

semidirect

Subgroups — #19136545

Conjugacy classes of subgroups

Complements