Group #19133217 — subgroups

Subgroups — #19133217

Order 5504.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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	#124×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#14582954	C₂	1	2	yes	maximal, complemented
3	#14582639	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582638	C₂	1	2	yes	maximal, complemented
5	C₄₃×#329	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×D₄₃	C₄	1	1	yes	characteristic
7	C₂×D₄×D₄₃	C₄	1	1	yes	characteristic
8	#13063314	C₄	1	1	yes	characteristic
9	#13063313	C₂²	1	1	yes	characteristic
10	#13063312	C₄	1	1	yes	characteristic
11	#13063311	—	2	2	no	—
12	C₂²⋊C₄×D₄₃	—	2	2	no	—
13	C₄²×D₄₃	C₂²	1	1	yes	characteristic
14	Dic₄₃⋊C₈	—	2	2	no	—
15	(C₂×D₄₃)⋊C₈	—	2	2	no	—
16	#13063236	C₂²	1	2	yes	complemented
17	#124×C₄₃	C₂²	1	1	yes	characteristic
18	#97×C₄₃	C₂²	1	2	yes	complemented
19	C₂³×D₄₃	—	2	1	no	—
20	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₂²⋊D₄₃	—	2	1	no	—
23	Q₈×D₄₃	—	4	2	no	—
24	D₄×D₄₃	—	4	2	no	—
25	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×D₄₃	—	2	1	no	—
27	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×D₄₃	D₄	1	2	yes	—
29	C₂×Dic₈₆	—	2	1	no	—
30	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
31	C₂×C₈×C₄₃	—	2	2	no	—
32	C₂²⋊C₄×C₄₃	—	2	2	no	—
33	C₄²×C₄₃	C₂³	1	1	yes	characteristic
34	C₂²⋊Dic₄₃	—	2	2	no	—
35	(C₂×D₄₃)⋊C₄	—	2	2	no	—
36	(C₂×D₄₃)⋊C₄	—	2	2	no	—
37	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
38	C₄×Dic₄₃	D₄	1	2	yes	—
39	C₂×C₄₃⋊C₈	—	2	2	no	—
40	C₂³×C₄₃	—	2	1	no	—
41	C₂²×D₄₃	—	2	1	no	—
42	C₂²×D₄₃	—	4	4	no	—
43	C₂²×D₄₃	—	4	2	no	—
44	C₂²×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
45	Q₈×C₄₃	—	4	1	no	—
46	D₄×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
50	C₂²⋊D₄₃	—	4	2	no	—
51	C₂×Dic₄₃	—	2	1	no	—
52	C₂×Dic₄₃	C₂²⋊C₄	1	2	yes	—
53	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
54	D₁₇₂	—	4	1	no	—
55	C₄×D₄₃	—	2	2	no	—
56	C₄×D₄₃	—	4	2	no	—
57	C₄×D₄₃	—	4	2	no	—
58	Dic₈₆	—	4	2	no	—
59	Dic₈₆	—	4	1	no	—
60	C₈×C₄₃	—	4	2	no	—
61	C₄₃⋊C₈	—	4	2	no	—
62	C₂²×C₄₃	—	4	1	no	—
63	C₂²×C₄₃	—	4	2	no	—
64	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×D₄₃	—	2	2	no	—
66	C₂×D₄₃	—	4	1	no	—
67	C₂×D₄₃	—	4	2	no	—
68	C₂×D₄₃	—	8	4	no	—
69	C₂×D₄₃	#100	1	2	yes	—
70	C₄×C₄₃	—	2	1	no	—
71	C₄×C₄₃	—	2	2	no	—
72	C₄×C₄₃	—	4	1	no	—
73	Dic₄₃	—	2	1	no	—
74	Dic₄₃	—	2	2	no	—
75	Dic₄₃	—	4	1	no	—
76	#1533	—	43	1	no	maximal, Sylow
77	C₂×C₄₃	—	8	1	no	—
78	C₂×C₄₃	C₂×#100	1	1	yes	characteristic
79	C₂×C₄₃	#421	1	2	yes	—
80	D₄₃	—	2	2	no	—
81	D₄₃	—	8	1	no	—
82	C₂×#124	—	43	1	no	—
83	#432	—	43	2	no	—
84	#329	—	43	1	no	—
85	#329	—	43	2	no	—
86	#329	D₄₃	1	1	yes	characteristic, complemented
87	C₄₃	#1533	1	1	yes	characteristic, complemented, Sylow
88	C₂²×Q₈	—	43	1	no	—
89	C₂²×D₄	—	43	1	no	—
90	#124	—	43	1	no	—
91	#124	—	43	1	no	—
92	#124	—	43	1	no	—
93	#124	—	86	2	no	—
94	#124	C₂×D₄₃	1	1	yes	characteristic
95	C₂×C₂²⋊C₄	—	86	2	no	—
96	C₂×C₄²	—	43	1	no	—
97	C₄⋊C₈	—	86	2	no	—
98	C₂²⋊C₈	—	86	2	no	—
99	#97	—	43	2	no	—
100	#97	C₂×D₄₃	1	2	yes	complemented
101	C₂⁴	—	86	1	no	—
102	C₂×Q₈	—	43	1	no	—
103	C₂×Q₈	—	86	1	no	—
104	C₂×Q₈	—	172	2	no	—
105	C₂×Q₈	C₄×D₄₃	1	1	yes	characteristic
106	C₂×D₄	—	43	1	no	—
107	C₂×D₄	—	86	1	no	—
108	C₂×D₄	—	172	2	no	—
109	C₂×D₄	C₄×D₄₃	1	1	yes	characteristic
110	C₂²×C₄	—	43	1	no	—
111	C₂²×C₄	—	43	2	no	—
112	C₂²×C₄	—	86	1	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	86	2	no	—
115	C₂²⋊C₄	—	2	2	no	—
116	C₂²⋊C₄	—	86	2	no	—
117	C₂²⋊C₄	—	86	2	no	—
118	C₂²⋊C₄	—	86	2	no	—
119	C₄²	—	43	1	no	—
120	C₄²	—	43	2	no	—
121	C₄²	C₂²×D₄₃	1	1	yes	characteristic
122	C₂³	—	2	1	no	—
123	C₂³	—	43	1	no	—
124	C₂³	—	86	1	no	—
125	C₂³	—	172	2	no	—
126	C₂³	—	172	4	no	—
127	Q₈	—	4	1	no	—
128	Q₈	—	172	1	no	—
129	Q₈	—	172	2	no	—
130	D₄	—	4	1	no	—
131	D₄	—	172	1	no	—
132	D₄	—	172	2	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	43	2	no	—
135	C₂×C₄	—	43	1	no	—
136	C₂×C₄	—	86	2	no	—
137	C₂×C₄	—	86	1	no	—
138	C₂×C₄	—	172	2	no	—
139	C₂×C₄	—	172	2	no	—
140	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
141	C₂×C₄	D₄×D₄₃	1	2	yes	—
142	C₈	—	4	2	no	—
143	C₈	—	172	2	no	—
144	C₂²	—	4	1	no	—
145	C₂²	—	4	2	no	—
146	C₂²	—	43	2	no	—
147	C₂²	—	86	2	no	—
148	C₂²	—	344	4	no	—
149	C₂²	—	172	1	no	—
150	C₂²	—	172	2	no	—
151	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
152	C₄	—	2	1	no	—
153	C₄	—	2	2	no	—
154	C₄	—	4	1	no	—
155	C₄	—	86	1	no	—
156	C₄	—	86	2	no	—
157	C₄	—	172	1	no	—
158	C₂	—	8	1	no	—
159	C₂	—	86	2	no	—
160	C₂	—	344	1	no	—
161	C₂	#100×D₄₃	1	1	yes	characteristic
162	C₂	#14582914	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#124×D₄₃

C₂

yes

maximal, characteristic

#14582954

C₂

yes

maximal, complemented

#14582639

C₂

yes

maximal, characteristic, complemented

#14582638

C₂

yes

maximal, complemented

C₄₃×#329

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₃

C₄

yes

characteristic

C₂×D₄×D₄₃

C₄

yes

characteristic

#13063314

C₄

yes

characteristic

#13063313

C₂²

yes

characteristic

#13063312

C₄

yes

characteristic

#13063311

—

C₂²⋊C₄×D₄₃

—

C₄²×D₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

(C₂×D₄₃)⋊C₈

—

#13063236

C₂²

yes

complemented

#124×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

complemented

C₂³×D₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

Q₈×D₄₃

—

D₄×D₄₃

—

C₂×D₁₇₂

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

#100

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#1533

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#100

yes

characteristic

C₂×C₄₃

#421

yes

—

D₄₃

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#1533

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

—

—

—

—

C₂×D₄₃

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

100

#97

C₂×D₄₃

yes

complemented

101

C₂⁴

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

172

—

105

C₂×Q₈

C₄×D₄₃

yes

characteristic

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

172

—

109

C₂×D₄

C₄×D₄₃

yes

characteristic

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₂²⋊C₄

—

119

C₄²

—

120

C₄²

—

121

C₄²

C₂²×D₄₃

yes

characteristic

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

—

172

—

126

C₂³

—

172

—

127

Q₈

—

128

Q₈

—

172

—

129

Q₈

—

172

—

130

D₄

—

131

D₄

—

172

—

132

D₄

—

172

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

172

—

139

C₂×C₄

—

172

—

140

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

141

C₂×C₄

D₄×D₄₃

yes

—

142

C₈

—

143

C₈

—

172

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

344

—

149

C₂²

—

172

—

150

C₂²

—

172

—

151

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

172

—

158

C₂

—

159

C₂

—

160

C₂

—

344

—

161

C₂

#100×D₄₃

yes

characteristic

162

C₂

#14582914

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#329	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#329	D₄₃
hypocenter	C₄₃	#1533
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #329

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#329

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #329

N	H ≅ G/N	type
2. #14582954	C₂	semidirect
3. #14582639	C₂	semidirect
4. #14582638	C₂	semidirect
5. C₄₃×#329	C₂	semidirect
16. #13063236	C₂²	semidirect
18. #97×C₄₃	C₂²	semidirect
86. #329	D₄₃	semidirect
87. C₄₃	#1533	semidirect
100. #97	C₂×D₄₃	semidirect

H ≅ G/N

type

2. #14582954

C₂

semidirect

3. #14582639

C₂

semidirect

4. #14582638

C₂

semidirect

5. C₄₃×#329

C₂

semidirect

16. #13063236

C₂²

semidirect

18. #97×C₄₃

C₂²

semidirect

86. #329

D₄₃

semidirect

87. C₄₃

#1533

semidirect

100. #97

C₂×D₄₃

semidirect

Subgroups — #19133217

Conjugacy classes of subgroups

Complements