Group #19136854 — subgroups

Subgroups — #19136854

Order 5504.

184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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×#13063271	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063269	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13063268	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13063266	C₂	1	1	yes	maximal, characteristic
5	#14583283	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#10621873	—	2	1	no	—
10	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
11	#13063313	—	2	1	no	—
12	#13063271	—	2	2	no	—
13	#13063269	—	2	2	no	—
14	#13063268	—	2	2	no	—
15	#13063266	—	2	2	no	—
16	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×SD₁₆×C₄₃	—	2	1	no	—
20	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
21	#124×C₄₃	—	2	1	no	—
22	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×D₄×C₄₃	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	Q₁₆×C₄₃	—	2	1	no	—
28	Q₁₆×C₄₃	—	2	1	no	—
29	SD₁₆×C₄₃	—	4	2	no	—
30	D₈×C₄₃	—	2	1	no	—
31	D₈×C₄₃	—	2	1	no	—
32	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
33	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
34	C₂²⋊C₄×C₄₃	—	4	2	no	—
35	C₄²×C₄₃	D₄	1	1	yes	characteristic
36	(C₂×D₄₃)⋊C₄	—	4	2	no	—
37	Dic₁₇₂	—	2	1	no	—
38	Dic₁₇₂	—	2	1	no	—
39	D₃₄₄	—	2	1	no	—
40	D₃₄₄	—	2	1	no	—
41	#10621873	—	4	2	no	—
42	C₄₃⋊C₁₆	D₄	1	2	yes	—
43	C₄₃⋊C₁₆	D₄	1	2	yes	—
44	C₂³×C₄₃	—	4	1	no	—
45	C₂²×D₄₃	—	4	1	no	—
46	Q₈×C₄₃	—	4	1	no	—
47	Q₈×C₄₃	—	4	1	no	—
48	D₄×C₄₃	—	4	1	no	—
49	D₄×C₄₃	—	4	1	no	—
50	C₂×C₄×C₄₃	—	4	1	no	—
51	C₂×C₄×C₄₃	D₈	1	2	yes	—
52	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂×Dic₄₃	—	4	1	no	—
54	D₁₇₂	—	4	1	no	—
55	D₁₇₂	—	4	1	no	—
56	Dic₈₆	—	4	1	no	—
57	Dic₈₆	—	4	1	no	—
58	C₈×C₄₃	D₈	1	2	yes	—
59	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
60	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄₃	—	8	1	no	—
62	C₂²×C₄₃	—	8	2	no	—
63	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
64	C₂×D₄₃	—	8	1	no	—
65	C₂×D₄₃	—	8	2	no	—
66	C₄×C₄₃	—	2	2	no	—
67	C₄×C₄₃	—	8	1	no	—
68	C₄×C₄₃	#127	1	1	yes	characteristic
69	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
70	Dic₄₃	—	8	1	no	—
71	#2249	—	43	1	no	maximal, Sylow
72	C₂×C₄₃	—	16	1	no	—
73	C₂×C₄₃	#493	1	1	yes	characteristic
74	C₂×C₄₃	#508	1	2	yes	—
75	D₄₃	—	16	1	no	—
76	C₂×Q₃₂	—	43	1	no	—
77	C₂×SD₃₂	—	43	1	no	—
78	C₂×SD₃₂	—	43	1	no	—
79	C₂×D₁₆	—	43	1	no	—
80	#495	—	43	1	no	—
81	#495	D₄₃	1	1	yes	characteristic, complemented
82	C₄×C₁₆	—	43	1	no	—
83	C₄₃	#2249	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₁₆	—	43	1	no	—
85	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
86	C₂×SD₁₆	—	2	1	no	—
87	C₂×SD₁₆	—	86	1	no	—
88	C₂×D₈	—	43	1	no	—
89	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
90	#124	—	2	1	no	—
91	#124	—	86	1	no	—
92	Q₃₂	—	86	2	no	—
93	SD₃₂	—	86	2	no	—
94	SD₃₂	—	86	2	no	—
95	D₁₆	—	86	2	no	—
96	C₂×C₁₆	—	43	1	no	—
97	C₂×C₁₆	—	43	1	no	—
98	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
99	C₂×Q₈	—	2	1	no	—
100	C₂×Q₈	—	86	1	no	—
101	C₂×D₄	—	2	1	no	—
102	C₂×D₄	—	86	1	no	—
103	Q₁₆	—	2	1	no	—
104	Q₁₆	—	2	1	no	—
105	Q₁₆	—	86	1	no	—
106	Q₁₆	—	86	1	no	—
107	SD₁₆	—	4	2	no	—
108	SD₁₆	—	172	2	no	—
109	D₈	—	2	1	no	—
110	D₈	—	2	1	no	—
111	D₈	—	86	1	no	—
112	D₈	—	86	1	no	—
113	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
114	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
115	C₂²⋊C₄	—	4	2	no	—
116	C₂²⋊C₄	—	172	2	no	—
117	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
118	C₁₆	—	43	2	no	—
119	C₁₆	—	43	2	no	—
120	C₂³	—	4	1	no	—
121	C₂³	—	172	1	no	—
122	Q₈	—	4	1	no	—
123	Q₈	—	4	1	no	—
124	Q₈	—	172	1	no	—
125	Q₈	—	172	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	4	1	no	—
128	D₄	—	172	1	no	—
129	D₄	—	172	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	172	1	no	—
132	C₂×C₄	#10621882	1	2	yes	—
133	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
134	C₈	#10621882	1	2	yes	—
135	C₈	D₄×D₄₃	1	1	yes	characteristic
136	C₈	D₄×D₄₃	1	1	yes	characteristic
137	C₂²	—	8	2	no	—
138	C₂²	—	8	1	no	—
139	C₂²	—	344	2	no	—
140	C₂²	—	344	1	no	—
141	C₂²	C₂×#10621882	1	1	yes	characteristic
142	C₄	—	2	2	no	—
143	C₄	—	8	1	no	—
144	C₄	—	344	1	no	—
145	C₄	#13063321	1	1	yes	characteristic
146	C₄	C₂×#10621882	1	1	yes	characteristic
147	C₂	—	16	1	no	—
148	C₂	—	688	1	no	—
149	C₂	#14583275	1	1	yes	characteristic
150	C₂	#14583329	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063271

C₂

yes

maximal, characteristic, complemented

C₂×#13063269

C₂

yes

maximal, characteristic, complemented

C₂×#13063268

C₂

yes

maximal, characteristic, complemented

C₂×#13063266

C₂

yes

maximal, characteristic

#14583283

C₂

yes

maximal, characteristic, complemented

C₄×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₃×#495

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×#10621873

—

C₂×D₃₄₄

C₂²

yes

—

—

—

—

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×SD₁₆×C₄₃

—

C₂×D₈×C₄₃

C₂²

yes

characteristic

#124×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

SD₁₆×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

Dic₁₇₂

—

Dic₁₇₂

—

D₃₄₄

—

D₃₄₄

—

#10621873

—

C₄₃⋊C₁₆

D₄

yes

—

C₄₃⋊C₁₆

D₄

yes

—

C₂³×C₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

D₈

yes

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#127

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

#2249

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#493

yes

characteristic

C₂×C₄₃

#508

yes

—

D₄₃

—

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

#495

D₄₃

yes

characteristic, complemented

C₄×C₁₆

—

C₄₃

#2249

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

characteristic

#124

—

#124

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×D₄

—

102

C₂×D₄

—

103

Q₁₆

—

104

Q₁₆

—

105

Q₁₆

—

106

Q₁₆

—

107

SD₁₆

—

108

SD₁₆

—

172

—

109

D₈

—

110

D₈

—

111

D₈

—

112

D₈

—

113

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

114

C₂×C₈

C₂²×D₄₃

yes

characteristic

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

172

—

117

C₄²

C₂²⋊D₄₃

yes

characteristic

118

C₁₆

—

119

C₁₆

—

120

C₂³

—

121

C₂³

—

172

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

172

—

125

Q₈

—

172

—

126

D₄

—

127

D₄

—

128

D₄

—

172

—

129

D₄

—

172

—

130

C₂×C₄

—

131

C₂×C₄

—

172

—

132

C₂×C₄

#10621882

yes

—

133

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

134

C₈

#10621882

yes

—

135

C₈

D₄×D₄₃

yes

characteristic

136

C₈

D₄×D₄₃

yes

characteristic

137

C₂²

—

138

C₂²

—

139

C₂²

—

344

—

140

C₂²

—

344

—

141

C₂²

C₂×#10621882

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

344

—

145

C₄

#13063321

yes

characteristic

146

C₄

C₂×#10621882

yes

characteristic

147

C₂

—

148

C₂

—

688

—

149

C₂

#14583275

yes

characteristic

150

C₂

#14583329

yes

—

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#495	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#495	D₄₃
hypocenter	C₄₃	#2249
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#495

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. C₂×#13063271	C₂	semidirect
2. C₂×#13063269	C₂	semidirect
3. C₂×#13063268	C₂	semidirect
5. #14583283	C₂	semidirect
6. C₄×C₄₃⋊C₁₆	C₂	semidirect
7. C₄₃×#495	C₂	semidirect
81. #495	D₄₃	semidirect
83. C₄₃	#2249	semidirect

H ≅ G/N

type

1. C₂×#13063271

C₂

semidirect

2. C₂×#13063269

C₂

semidirect

3. C₂×#13063268

C₂

semidirect

5. #14583283

C₂

semidirect

6. C₄×C₄₃⋊C₁₆

C₂

semidirect

7. C₄₃×#495

C₂

semidirect

81. #495

D₄₃

semidirect

83. C₄₃

#2249

semidirect

Subgroups — #19136854

Conjugacy classes of subgroups

Complements