Group #19145254 — subgroups

Subgroups — #19145254

Order 5504.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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	#14583511	C₂	1	2	yes	maximal
2	#14583301	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583279	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583268	C₂	1	2	yes	maximal, complemented
5	#14583157	C₂	1	2	yes	maximal
6	#14583140	C₂	1	2	yes	maximal
7	#14583007	C₂	1	2	yes	maximal, complemented
8	C₄×Dic₁₇₂	C₂	1	2	yes	maximal, complemented
9	C₄₃×#405	C₂	1	1	yes	maximal, characteristic
10	C₂×Dic₁₇₂	C₂²	1	2	yes	—
11	C₂×Dic₁₇₂	C₂²	1	2	yes	—
12	#13063325	C₂²	1	2	yes	—
13	#13063318	—	2	4	no	—
14	#13063317	C₂²	1	2	yes	—
15	#13063315	—	2	4	no	—
16	#13063304	C₂²	1	4	yes	—
17	C₄×Dic₈₆	C₂²	1	4	yes	—
18	#13063259	C₂²	1	2	yes	—
19	#13063257	C₂²	1	2	yes	—
20	#13063250	C₂²	1	4	yes	—
21	#13063250	C₂²	1	4	yes	—
22	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	#117×C₄₃	C₂²	1	1	yes	characteristic
25	#97×C₄₃	C₂²	1	1	yes	characteristic
26	#97×C₄₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
30	C₂×Dic₈₆	C₂³	1	4	yes	—
31	M₁₆×C₄₃	—	2	2	no	—
32	C₂×C₈×C₄₃	—	2	2	no	—
33	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
35	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
37	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
38	C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
39	C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	C₄²×C₄₃	C₂³	1	1	yes	characteristic
41	C₂²⋊Dic₄₃	—	2	4	no	—
42	C₄⋊Dic₄₃	—	2	4	no	—
43	C₄⋊Dic₄₃	C₂³	1	4	yes	—
44	Dic₄₃⋊C₄	—	2	4	no	—
45	Dic₄₃⋊C₄	—	2	4	no	—
46	Dic₄₃⋊C₄	—	2	4	no	—
47	C₄×Dic₄₃	—	2	4	no	—
48	Dic₁₇₂	—	2	4	no	—
49	Dic₁₇₂	—	2	4	no	—
50	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₃	—	2	1	no	—
52	C₂×C₄×C₄₃	—	2	1	no	—
53	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
57	C₂×Dic₄₃	—	2	4	no	—
58	C₂×Dic₄₃	—	2	4	no	—
59	Dic₈₆	—	2	4	no	—
60	Dic₈₆	—	2	4	no	—
61	C₈×C₄₃	—	2	1	no	—
62	C₈×C₄₃	—	2	1	no	—
63	C₈×C₄₃	#41	1	2	yes	—
64	C₈×C₄₃	#41	1	2	yes	—
65	C₂²×C₄₃	—	2	1	no	—
66	C₂²×C₄₃	—	2	2	no	—
67	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
68	C₄×C₄₃	—	2	1	no	—
69	C₄×C₄₃	—	2	2	no	—
70	C₄×C₄₃	—	2	2	no	—
71	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
72	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
73	Dic₄₃	—	4	4	no	—
74	Dic₄₃	—	4	4	no	—
75	#3177	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	4	1	no	—
77	C₂×C₄₃	#532	1	1	yes	characteristic
78	C₂×C₄₃	#578	1	2	yes	—
79	#541	—	43	2	no	—
80	#499	—	43	1	no	—
81	#494	—	43	1	no	—
82	#491	—	43	2	no	—
83	#470	—	43	2	no	—
84	#467	—	43	2	no	—
85	#441	—	43	2	no	—
86	C₄×Q₁₆	—	43	2	no	—
87	#405	D₄₃	1	1	yes	characteristic
88	C₄₃	#3177	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₁₆	—	43	2	no	—
90	C₂×Q₁₆	—	43	2	no	—
91	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
92	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
93	C₄⋊Q₈	—	43	2	no	—
94	#126	—	86	4	no	—
95	#125	—	43	2	no	—
96	#125	—	86	4	no	—
97	C₂²⋊Q₈	—	43	4	no	—
98	C₄×Q₈	—	43	4	no	—
99	#117	C₂×D₄₃	1	1	yes	characteristic
100	#107	—	43	2	no	—
101	#106	—	43	2	no	—
102	#103	—	43	4	no	—
103	#103	—	43	4	no	—
104	#97	C₂×D₄₃	1	1	yes	characteristic
105	#97	C₂×D₄₃	1	1	yes	characteristic
106	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
107	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
108	C₂×Q₈	—	43	4	no	—
109	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
110	Q₁₆	—	86	4	no	—
111	Q₁₆	—	86	4	no	—
112	M₁₆	—	2	2	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
115	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
116	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
117	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
118	C₄⋊C₄	—	43	4	no	—
119	C₄⋊C₄	—	86	4	no	—
120	C₄⋊C₄	—	86	4	no	—
121	C₄⋊C₄	—	86	4	no	—
122	C₄⋊C₄	—	86	4	no	—
123	C₄⋊C₄	D₁₇₂	1	2	yes	—
124	C₂²⋊C₄	—	86	4	no	—
125	C₂²⋊C₄	D₁₇₂	1	2	yes	—
126	C₄²	—	86	4	no	—
127	C₄²	C₂²×D₄₃	1	1	yes	characteristic
128	C₄²	C₂²×D₄₃	1	1	yes	characteristic
129	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
130	Q₈	—	86	4	no	—
131	Q₈	—	86	4	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	86	4	no	—
135	C₂×C₄	—	86	4	no	—
136	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
137	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
138	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
139	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
140	C₈	—	2	1	no	—
141	C₈	—	2	1	no	—
142	C₈	#10621898	1	2	yes	—
143	C₈	#10621898	1	2	yes	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	2	no	—
146	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	2	2	no	—
149	C₄	—	2	2	no	—
150	C₄	—	172	4	no	—
151	C₄	—	172	4	no	—
152	C₄	C₂×#10621898	1	1	yes	characteristic
153	C₄	C₂×#10621898	1	1	yes	characteristic
154	C₂	—	4	1	no	—
155	C₂	#14583449	1	1	yes	characteristic
156	C₂	#14583716	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583511

C₂

yes

maximal

#14583301

C₂

yes

maximal, characteristic, complemented

#14583279

C₂

yes

maximal, characteristic, complemented

#14583268

C₂

yes

maximal, complemented

#14583157

C₂

yes

maximal

#14583140

C₂

yes

maximal

#14583007

C₂

yes

maximal, complemented

C₄×Dic₁₇₂

C₂

yes

maximal, complemented

C₄₃×#405

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

—

C₂×Dic₁₇₂

C₂²

yes

—

#13063325

C₂²

yes

—

#13063318

—

#13063317

C₂²

yes

—

#13063315

—

#13063304

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

—

#13063259

C₂²

yes

—

#13063257

C₂²

yes

—

#13063250

C₂²

yes

—

#13063250

C₂²

yes

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

C₂³

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

D₄

yes

—

C₂²⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#41

yes

—

C₈×C₄₃

#41

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×#41

yes

characteristic

C₄×C₄₃

C₂×#41

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#3177

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#532

yes

characteristic

C₂×C₄₃

#578

yes

—

—

—

—

—

—

—

—

C₄×Q₁₆

—

#405

D₄₃

yes

characteristic

C₄₃

#3177

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

#126

—

#125

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×D₄₃

yes

characteristic

100

#107

—

101

#106

—

102

#103

—

103

#103

—

104

#97

C₂×D₄₃

yes

characteristic

105

#97

C₂×D₄₃

yes

characteristic

106

C₄×C₈

C₂×D₄₃

yes

characteristic

107

C₄×C₈

C₂×D₄₃

yes

characteristic

108

C₂×Q₈

—

109

C₂²×C₄

C₂²×D₄₃

yes

characteristic

110

Q₁₆

—

111

Q₁₆

—

112

M₁₆

—

113

C₂×C₈

—

114

C₂×C₈

C₂²×D₄₃

yes

characteristic

115

C₂×C₈

C₂²×D₄₃

yes

characteristic

116

C₂×C₈

C₂²×D₄₃

yes

characteristic

117

C₂×C₈

C₂²×D₄₃

yes

characteristic

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

D₁₇₂

yes

—

124

C₂²⋊C₄

—

125

C₂²⋊C₄

D₁₇₂

yes

—

126

C₄²

—

127

C₄²

C₂²×D₄₃

yes

characteristic

128

C₄²

C₂²×D₄₃

yes

characteristic

129

C₂³

C₂×D₁₇₂

yes

characteristic

130

Q₈

—

131

Q₈

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×D₁₇₂

yes

—

137

C₂×C₄

C₂×D₁₇₂

yes

—

138

C₂×C₄

C₂×D₁₇₂

yes

characteristic

139

C₂×C₄

C₂³×D₄₃

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

#10621898

yes

—

143

C₈

#10621898

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₂²×D₁₇₂

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

172

—

151

C₄

—

172

—

152

C₄

C₂×#10621898

yes

characteristic

153

C₄

C₂×#10621898

yes

characteristic

154

C₂

—

155

C₂

#14583449

yes

characteristic

156

C₂

#14583716

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#405	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#405	D₄₃
hypocenter	C₄₃	#3177
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

subgroup

G/H

center

C₂²

C₂²×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#405

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405

N	H ≅ G/N	type
2. #14583301	C₂	semidirect
3. #14583279	C₂	semidirect
4. #14583268	C₂	semidirect
7. #14583007	C₂	semidirect
8. C₄×Dic₁₇₂	C₂	semidirect
88. C₄₃	#3177	semidirect

H ≅ G/N

type

2. #14583301

C₂

semidirect

3. #14583279

C₂

semidirect

4. #14583268

C₂

semidirect

7. #14583007

C₂

semidirect

8. C₄×Dic₁₇₂

C₂

semidirect

88. C₄₃

#3177

semidirect

Subgroups — #19145254

Conjugacy classes of subgroups

Complements