Group #19144984 — subgroups

Subgroups — #19144984

Order 5504.

400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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	#14583261	C₂	1	4	yes	maximal, complemented
3	#14583256	C₂	1	4	yes	maximal, complemented
4	#14582907	C₂	1	2	yes	maximal, complemented
5	#14582903	C₂	1	2	yes	maximal
6	C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
9	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
10	C₂×#10621877	C₂²	1	2	yes	—
11	#13063313	—	2	2	no	—
12	#13063313	C₂²	1	2	yes	—
13	#13063313	C₂²	1	2	yes	—
14	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
15	#13063248	C₂²	1	8	yes	complemented
16	#13063245	C₂²	1	8	yes	—
17	#13063236	C₂²	1	2	yes	complemented
18	C₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
19	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
20	#125×C₄₃	C₂²	1	2	yes	complemented
21	C₂²⋊Q₈×C₄₃	—	2	2	no	—
22	C₄×Q₈×C₄₃	—	2	2	no	—
23	#117×C₄₃	C₂²	1	2	yes	—
24	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
25	C₂³×D₄₃	—	2	1	no	—
26	C₂×Q₈×C₄₃	—	2	2	no	—
27	C₂²×C₄×C₄₃	D₄	1	2	yes	—
28	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
29	C₂²×Dic₄₃	—	2	1	no	—
30	C₂×D₁₇₂	—	2	1	no	—
31	C₂×D₁₇₂	—	2	4	no	—
32	C₂×D₁₇₂	C₂³	1	2	yes	—
33	C₂×Dic₈₆	—	2	4	no	—
34	C₂×Dic₈₆	—	2	1	no	—
35	C₂×Dic₈₆	C₂³	1	2	yes	—
36	C₄⋊C₄×C₄₃	—	2	4	no	—
37	C₄⋊C₄×C₄₃	—	2	2	no	—
38	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
39	C₂²⋊C₄×C₄₃	—	2	2	no	—
40	C₄²×C₄₃	—	2	2	no	—
41	C₄²×C₄₃	D₄	1	2	yes	—
42	C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	C₄²×C₄₃	C₂³	1	1	yes	characteristic
44	(C₂×D₄₃)⋊C₄	—	2	4	no	—
45	(C₂×D₄₃)⋊C₄	—	2	4	no	—
46	#10621877	—	2	4	no	—
47	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
48	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×D₄₃	—	2	2	no	—
50	C₂²×D₄₃	—	4	4	no	—
51	C₂²×D₄₃	—	4	2	no	—
52	Q₈×C₄₃	—	4	4	no	—
53	C₂×C₄×C₄₃	—	2	4	no	—
54	C₂×C₄×C₄₃	—	4	2	no	—
55	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₄₃	#41	1	4	yes	—
59	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
60	C₂×Dic₄₃	—	2	2	no	—
61	C₂×Dic₄₃	—	4	2	no	—
62	D₁₇₂	—	2	4	no	—
63	D₁₇₂	—	4	2	no	—
64	Dic₈₆	—	2	4	no	—
65	Dic₈₆	—	4	2	no	—
66	C₄₃⋊C₈	—	2	4	no	—
67	C₂²×C₄₃	—	2	2	no	—
68	C₂²×C₄₃	#124	1	2	yes	—
69	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
70	C₂×D₄₃	—	4	2	no	—
71	C₂×D₄₃	—	4	4	no	—
72	C₂×D₄₃	—	8	4	no	—
73	C₄×C₄₃	—	2	2	no	—
74	C₄×C₄₃	—	2	2	no	—
75	C₄×C₄₃	—	4	4	no	—
76	C₄×C₄₃	#124	1	2	yes	—
77	C₄×C₄₃	C₂×#41	1	2	yes	—
78	Dic₄₃	—	4	2	no	—
79	#3140	—	43	1	no	maximal, Sylow
80	C₂×C₄₃	—	2	2	no	—
81	C₂×C₄₃	C₂×#124	1	1	yes	characteristic
82	C₂×C₄₃	#575	1	2	yes	—
83	D₄₃	—	8	2	no	—
84	#533	D₄₃	1	1	yes	characteristic, complemented
85	C₂×#124	—	43	1	no	—
86	#489	—	43	4	no	—
87	#488	—	43	4	no	—
88	#419	—	43	2	no	—
89	#418	—	43	2	no	—
90	C₄×M₁₆	—	43	1	no	—
91	C₄₃	#3140	1	1	yes	characteristic, complemented, Sylow
92	C₂²×Q₈	—	43	1	no	—
93	C₂²×D₄	—	43	1	no	—
94	C₂×M₁₆	—	43	2	no	—
95	C₄⋊Q₈	C₂×D₄₃	1	2	yes	complemented
96	#125	C₂×D₄₃	1	2	yes	complemented
97	#124	—	43	2	no	—
98	#124	—	43	2	no	—
99	#124	—	86	2	no	—
100	C₂²⋊Q₈	—	2	2	no	—
101	C₄×Q₈	—	2	2	no	—
102	#117	C₂×D₄₃	1	2	yes	—
103	C₂×C₂²⋊C₄	—	86	2	no	—
104	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
105	#103	—	43	8	no	—
106	#102	—	43	8	no	—
107	#97	—	43	2	no	—
108	C₄×C₈	—	43	2	no	—
109	C₂⁴	—	86	1	no	—
110	C₂×Q₈	—	2	2	no	—
111	C₂×Q₈	—	43	2	no	—
112	C₂×Q₈	—	86	1	no	—
113	C₂×Q₈	—	86	4	no	—
114	C₂×D₄	—	43	2	no	—
115	C₂×D₄	—	86	4	no	—
116	C₂×D₄	—	86	1	no	—
117	C₂²×C₄	—	86	1	no	—
118	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
119	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
120	M₁₆	—	86	4	no	—
121	C₂×C₈	—	43	4	no	—
122	C₄⋊C₄	—	2	4	no	—
123	C₄⋊C₄	—	2	2	no	—
124	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
125	C₂²⋊C₄	—	2	2	no	—
126	C₂²⋊C₄	—	86	4	no	—
127	C₂²⋊C₄	—	86	4	no	—
128	C₄²	—	2	2	no	—
129	C₄²	C₂²⋊D₄₃	1	2	yes	—
130	C₄²	C₂²×D₄₃	1	1	yes	characteristic
131	C₄²	C₂²×D₄₃	1	1	yes	characteristic
132	C₂³	—	86	2	no	—
133	C₂³	—	172	4	no	—
134	C₂³	—	172	2	no	—
135	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
136	Q₈	—	4	4	no	—
137	Q₈	—	86	4	no	—
138	Q₈	—	172	2	no	—
139	D₄	—	86	4	no	—
140	D₄	—	172	2	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	86	2	no	—
144	C₂×C₄	—	172	2	no	—
145	C₂×C₄	#10621902	1	4	yes	—
146	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
147	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
148	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
149	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
150	C₈	—	86	4	no	—
151	C₂²	—	2	2	no	—
152	C₂²	—	344	4	no	—
153	C₂²	—	172	2	no	—
154	C₂²	—	172	4	no	—
155	C₂²	#13063314	1	2	yes	—
156	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
157	C₄	—	2	2	no	—
158	C₄	—	2	2	no	—
159	C₄	—	4	4	no	—
160	C₄	—	172	2	no	—
161	C₄	#13063314	1	2	yes	—
162	C₄	C₂×#10621902	1	2	yes	—
163	C₂	—	2	2	no	—
164	C₂	—	344	2	no	—
165	C₂	C₂×#13063314	1	1	yes	characteristic
166	C₂	#14583697	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063313

C₂

yes

maximal, characteristic

#14583261

C₂

yes

maximal, complemented

#14583256

C₂

yes

maximal, complemented

#14582907

C₂

yes

maximal, complemented

#14582903

C₂

yes

maximal

C₄×#10621877

C₂

yes

maximal, characteristic, complemented

C₄₃×#533

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×D₁₇₂

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

#13063313

—

#13063313

C₂²

yes

—

#13063313

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

—

#13063248

C₂²

yes

complemented

#13063245

C₂²

yes

—

#13063236

C₂²

yes

complemented

C₄×C₄₃⋊C₈

C₂²

yes

complemented

C₄⋊Q₈×C₄₃

C₂²

yes

complemented

#125×C₄₃

C₂²

yes

complemented

C₂²⋊Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

#10621877

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

#124

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#124

yes

—

C₄×C₄₃

C₂×#41

yes

—

Dic₄₃

—

#3140

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#124

yes

characteristic

C₂×C₄₃

#575

yes

—

D₄₃

—

#533

D₄₃

yes

characteristic, complemented

—

—

—

—

—

C₄×M₁₆

—

C₄₃

#3140

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₄₃

yes

complemented

#125

C₂×D₄₃

yes

—

—

—

100

C₂²⋊Q₈

—

101

C₄×Q₈

—

102

#117

C₂×D₄₃

yes

—

103

C₂×C₂²⋊C₄

—

104

C₂×C₄²

C₂×D₄₃

yes

characteristic

105

#103

—

106

#102

—

107

#97

—

108

C₄×C₈

—

109

C₂⁴

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂²⋊D₄₃

yes

—

119

C₂²×C₄

C₂²×D₄₃

yes

characteristic

120

M₁₆

—

121

C₂×C₈

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

C₂²×D₄₃

yes

—

125

C₂²⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₄²

C₂²⋊D₄₃

yes

—

130

C₄²

C₂²×D₄₃

yes

characteristic

131

C₄²

C₂²×D₄₃

yes

characteristic

132

C₂³

—

133

C₂³

—

172

—

134

C₂³

—

172

—

135

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

136

Q₈

—

137

Q₈

—

138

Q₈

—

172

—

139

D₄

—

140

D₄

—

172

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

172

—

145

C₂×C₄

#10621902

yes

—

146

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

147

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

148

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

149

C₂×C₄

C₂³×D₄₃

yes

characteristic

150

C₈

—

151

C₂²

—

152

C₂²

—

344

—

153

C₂²

—

172

—

154

C₂²

—

172

—

155

C₂²

#13063314

yes

—

156

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

172

—

161

C₄

#13063314

yes

—

162

C₄

C₂×#10621902

yes

—

163

C₂

—

164

C₂

—

344

—

165

C₂

C₂×#13063314

yes

characteristic

166

C₂

#14583697

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#533	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#533	D₄₃
hypocenter	C₄₃	#3140
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#533

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
2. #14583261	C₂	semidirect
3. #14583256	C₂	semidirect
4. #14582907	C₂	semidirect
6. C₄×#10621877	C₂	semidirect
7. C₄₃×#533	C₂	semidirect
15. #13063248	C₂²	semidirect
17. #13063236	C₂²	semidirect
18. C₄×C₄₃⋊C₈	C₂²	semidirect
19. C₄⋊Q₈×C₄₃	C₂²	semidirect
20. #125×C₄₃	C₂²	semidirect
84. #533	D₄₃	semidirect
91. C₄₃	#3140	semidirect
95. C₄⋊Q₈	C₂×D₄₃	semidirect
96. #125	C₂×D₄₃	semidirect

H ≅ G/N

type

2. #14583261

C₂

semidirect

3. #14583256

C₂

semidirect

4. #14582907

C₂

semidirect

6. C₄×#10621877

C₂

semidirect

7. C₄₃×#533

C₂

semidirect

15. #13063248

C₂²

semidirect

17. #13063236

C₂²

semidirect

18. C₄×C₄₃⋊C₈

C₂²

semidirect

19. C₄⋊Q₈×C₄₃

C₂²

semidirect

20. #125×C₄₃

C₂²

semidirect

84. #533

D₄₃

semidirect

91. C₄₃

#3140

semidirect

95. C₄⋊Q₈

C₂×D₄₃

semidirect

96. #125

C₂×D₄₃

semidirect

Subgroups — #19144984

Conjugacy classes of subgroups

Complements