Group #19135442 — subgroups

Subgroups — #19135442

Order 5504.

312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13063313	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063243	C₂	1	2	yes	maximal, complemented
3	C₂×#13063241	C₂	1	2	yes	maximal
4	C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
8	C₂×#10621877	C₂²	1	2	yes	—
9	#13063313	—	2	1	no	—
10	#13063313	—	2	1	no	—
11	#13063313	—	2	2	no	—
12	C₂×(C₂×D₄₃)⋊C₄	C₄	1	4	yes	—
13	#13063243	—	2	4	no	—
14	#13063241	—	2	4	no	—
15	#13063236	—	2	1	no	—
16	C₄×C₄₃⋊C₈	—	2	1	no	—
17	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄⋊C₈×C₄₃	—	2	2	no	—
20	C₂³×D₄₃	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
23	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
24	C₂×D₁₇₂	—	2	2	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	—	2	2	no	—
28	C₂×Dic₈₆	—	2	2	no	—
29	C₂×Dic₈₆	—	2	1	no	—
30	C₂×Dic₈₆	—	2	1	no	—
31	C₂×Dic₈₆	—	2	2	no	—
32	M₁₆×C₄₃	—	2	2	no	—
33	M₁₆×C₄₃	—	2	2	no	—
34	C₂×C₈×C₄₃	—	2	2	no	—
35	C₄²×C₄₃	D₄	1	1	yes	characteristic
36	C₄²×C₄₃	D₄	1	1	yes	characteristic
37	C₄²×C₄₃	D₄	1	2	yes	—
38	(C₂×D₄₃)⋊C₄	—	2	4	no	—
39	(C₂×D₄₃)⋊C₄	—	2	4	no	—
40	#10621877	—	2	2	no	—
41	#10621877	D₄	1	4	yes	—
42	C₂×C₄₃⋊C₈	—	2	2	no	—
43	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
44	C₂²×D₄₃	—	2	2	no	—
45	C₂²×D₄₃	—	2	4	no	—
46	C₂²×D₄₃	—	4	4	no	—
47	C₂×C₄×C₄₃	—	4	2	no	—
48	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
49	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
50	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	#41	1	2	yes	—
54	C₂×Dic₄₃	—	2	2	no	—
55	C₂×Dic₄₃	—	2	4	no	—
56	D₁₇₂	—	4	2	no	—
57	D₁₇₂	—	4	1	no	—
58	D₁₇₂	—	4	1	no	—
59	Dic₈₆	—	4	2	no	—
60	Dic₈₆	—	4	1	no	—
61	Dic₈₆	—	4	1	no	—
62	C₈×C₄₃	—	4	2	no	—
63	C₄₃⋊C₈	—	2	4	no	—
64	C₂²×C₄₃	—	2	2	no	—
65	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄₃	C₄×D₄	1	2	yes	—
67	C₂×D₄₃	—	4	2	no	—
68	C₂×D₄₃	—	4	4	no	—
69	C₂×D₄₃	—	8	4	no	—
70	C₄×C₄₃	—	2	2	no	—
71	C₄×C₄₃	—	2	2	no	—
72	C₄×C₄₃	#121	1	2	yes	—
73	C₄×C₄₃	#124	1	1	yes	characteristic
74	C₄×C₄₃	#127	1	1	yes	characteristic
75	Dic₄₃	—	4	2	no	—
76	#1967	—	43	1	no	maximal, Sylow
77	C₂×C₄₃	—	2	2	no	—
78	C₂×C₄₃	#390	1	1	yes	characteristic
79	C₂×C₄₃	#413	1	2	yes	—
80	D₄₃	—	8	2	no	—
81	C₂×#124	—	43	1	no	—
82	#423	D₄₃	1	1	yes	characteristic, complemented
83	C₂×#101	—	43	2	no	—
84	C₂×#100	—	43	2	no	—
85	C₄×M₁₆	—	43	1	no	—
86	C₄₃	#1967	1	1	yes	characteristic, complemented, Sylow
87	C₂²×Q₈	—	43	1	no	—
88	C₂²×D₄	—	43	1	no	—
89	C₂×M₁₆	—	43	2	no	—
90	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
91	#124	—	86	1	no	—
92	#124	—	86	1	no	—
93	#124	—	86	2	no	—
94	C₂×C₂²⋊C₄	—	43	4	no	—
95	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
96	C₄⋊C₈	—	2	2	no	—
97	#101	—	86	4	no	—
98	#100	—	86	4	no	—
99	#97	—	86	1	no	—
100	C₄×C₈	—	86	1	no	—
101	C₂⁴	—	43	2	no	—
102	C₂×Q₈	—	86	1	no	—
103	C₂×Q₈	—	86	2	no	—
104	C₂×Q₈	—	86	2	no	—
105	C₂×Q₈	—	86	1	no	—
106	C₂×D₄	—	86	1	no	—
107	C₂×D₄	—	86	2	no	—
108	C₂×D₄	—	86	2	no	—
109	C₂×D₄	—	86	1	no	—
110	C₂²×C₄	—	43	2	no	—
111	C₂²×C₄	C₄×D₄₃	1	2	yes	—
112	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
113	M₁₆	—	2	2	no	—
114	M₁₆	—	2	2	no	—
115	M₁₆	—	43	4	no	—
116	M₁₆	—	86	2	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	86	2	no	—
119	C₂²⋊C₄	—	86	4	no	—
120	C₂²⋊C₄	—	86	4	no	—
121	C₄²	D₁₇₂	1	1	yes	characteristic
122	C₄²	D₁₇₂	1	1	yes	characteristic
123	C₄²	C₂²⋊D₄₃	1	2	yes	—
124	C₂³	—	86	4	no	—
125	C₂³	—	86	2	no	—
126	C₂³	—	172	4	no	—
127	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
128	Q₈	—	172	2	no	—
129	Q₈	—	172	1	no	—
130	Q₈	—	172	1	no	—
131	D₄	—	172	2	no	—
132	D₄	—	172	1	no	—
133	D₄	—	172	1	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	86	2	no	—
136	C₂×C₄	—	86	4	no	—
137	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
138	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
139	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
140	C₂×C₄	D₄×D₄₃	1	2	yes	—
141	C₂×C₄	#10621902	1	2	yes	—
142	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
143	C₈	—	4	2	no	—
144	C₈	—	86	4	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	344	4	no	—
147	C₂²	—	172	2	no	—
148	C₂²	—	172	4	no	—
149	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
150	C₂²	#13063287	1	2	yes	—
151	C₄	—	2	2	no	—
152	C₄	—	2	2	no	—
153	C₄	—	172	2	no	—
154	C₄	#13063300	1	2	yes	—
155	C₄	#13063314	1	1	yes	characteristic
156	C₄	#13063321	1	1	yes	characteristic
157	C₂	—	2	2	no	—
158	C₂	—	344	2	no	—
159	C₂	#14582800	1	1	yes	characteristic
160	C₂	#14582881	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063313

C₂

yes

maximal, characteristic

C₂×#13063243

C₂

yes

maximal, complemented

C₂×#13063241

C₂

yes

maximal

C₄×#10621877

C₂

yes

maximal, characteristic, complemented

C₄₃×#423

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×D₁₇₂

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

#13063313

—

#13063313

—

#13063313

—

C₂×(C₂×D₄₃)⋊C₄

C₄

yes

—

#13063243

—

#13063241

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂³×D₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

#10621877

—

#10621877

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

C₄×D₄

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1967

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#390

yes

characteristic

C₂×C₄₃

#413

yes

—

D₄₃

—

C₂×#124

—

#423

D₄₃

yes

characteristic, complemented

C₂×#101

—

C₂×#100

—

C₄×M₁₆

—

C₄₃

#1967

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

#124

—

#124

—

#124

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

#101

—

#100

—

#97

—

100

C₄×C₈

—

101

C₂⁴

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₄×D₄₃

yes

—

112

C₂²×C₄

C₂²×D₄₃

yes

characteristic

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

M₁₆

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

D₁₇₂

yes

characteristic

122

C₄²

D₁₇₂

yes

characteristic

123

C₄²

C₂²⋊D₄₃

yes

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

172

—

127

C₂³

C₂×C₄×D₄₃

yes

characteristic

128

Q₈

—

172

—

129

Q₈

—

172

—

130

Q₈

—

172

—

131

D₄

—

172

—

132

D₄

—

172

—

133

D₄

—

172

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

138

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

139

C₂×C₄

C₂×D₁₇₂

yes

characteristic

140

C₂×C₄

D₄×D₄₃

yes

—

141

C₂×C₄

#10621902

yes

—

142

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

143

C₈

—

144

C₈

—

145

C₂²

—

146

C₂²

—

344

—

147

C₂²

—

172

—

148

C₂²

—

172

—

149

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

150

C₂²

#13063287

yes

—

151

C₄

—

152

C₄

—

153

C₄

—

172

—

154

C₄

#13063300

yes

—

155

C₄

#13063314

yes

characteristic

156

C₄

#13063321

yes

characteristic

157

C₂

—

158

C₂

—

344

—

159

C₂

#14582800

yes

characteristic

160

C₂

#14582881

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#423	D₄₃
hypocenter	C₄₃	#1967
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂×(C₂×D₄₃)⋊C₄

commutator

C₂³×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#423

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
2. C₂×#13063243	C₂	semidirect
4. C₄×#10621877	C₂	semidirect
5. C₄₃×#423	C₂	semidirect
82. #423	D₄₃	semidirect
86. C₄₃	#1967	semidirect

H ≅ G/N

type

2. C₂×#13063243

C₂

semidirect

4. C₄×#10621877

C₂

semidirect

5. C₄₃×#423

C₂

semidirect

82. #423

D₄₃

semidirect

86. C₄₃

#1967

semidirect

Subgroups — #19135442

Conjugacy classes of subgroups

Complements