Group #19133228 — subgroups

Subgroups — #19133228

Order 5504.

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

normal subgroups only

This group has 238 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	#14583448	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×#10621902	C₄	1	1	yes	characteristic
7	C₂×#10621900	C₄	1	1	yes	characteristic
8	#13063323	C₄	1	1	yes	characteristic
9	#13063321	C₄	1	1	yes	characteristic
10	#13063313	C₂²	1	1	yes	characteristic
11	#13063298	—	2	2	no	—
12	(C₂²⋊D₄₃)⋊C₄	—	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	—
17	#124×C₄₃	C₂²	1	1	yes	characteristic
18	#97×C₄₃	C₂²	1	2	yes	—
19	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₂²⋊D₄₃	—	2	2	no	—
22	C₂×C₂²⋊D₄₃	—	2	1	no	—
23	C₂²×Dic₄₃	—	2	1	no	—
24	#10621902	—	4	2	no	—
25	#10621900	—	4	2	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×D₄₃	—	2	1	no	—
29	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₄₃	D₄	1	2	yes	—
31	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×C₄₃	—	2	2	no	—
33	C₂²⋊C₄×C₄₃	—	2	2	no	—
34	C₄²×C₄₃	C₂³	1	1	yes	characteristic
35	(C₂×D₄₃)⋊C₄	—	2	2	no	—
36	Dic₄₃⋊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	C₂²⋊C₄	1	1	yes	characteristic
43	Q₈×C₄₃	—	4	1	no	—
44	D₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	2	1	no	—
46	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
48	C₂²⋊D₄₃	—	4	4	no	—
49	C₂²⋊D₄₃	—	4	2	no	—
50	C₂×Dic₄₃	—	2	1	no	—
51	C₂×Dic₄₃	—	4	2	no	—
52	C₂×Dic₄₃	C₂²⋊C₄	1	2	yes	—
53	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
54	D₁₇₂	—	4	1	no	—
55	D₁₇₂	—	4	2	no	—
56	C₄×D₄₃	—	2	2	no	—
57	C₄×D₄₃	—	4	2	no	—
58	C₄×D₄₃	—	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	1	no	—
66	C₂×D₄₃	—	2	2	no	—
67	C₂×D₄₃	—	4	1	no	—
68	C₂×D₄₃	—	4	2	no	—
69	C₄×C₄₃	—	2	1	no	—
70	C₄×C₄₃	—	2	2	no	—
71	C₄×C₄₃	—	4	1	no	—
72	Dic₄₃	—	2	2	no	—
73	Dic₄₃	—	4	1	no	—
74	Dic₄₃	#100	1	2	yes	—
75	#1536	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	8	1	no	—
77	C₂×C₄₃	C₂×#100	1	1	yes	characteristic
78	C₂×C₄₃	#421	1	2	yes	—
79	D₄₃	—	4	1	no	—
80	D₄₃	—	8	1	no	—
81	#532	—	43	1	no	—
82	#432	—	43	2	no	—
83	#329	—	43	1	no	—
84	#329	—	43	2	no	—
85	#329	D₄₃	1	1	yes	characteristic, complemented
86	C₄₃	#1536	1	1	yes	characteristic, complemented, Sylow
87	C₂×#41	—	43	1	no	—
88	C₂×#41	—	43	1	no	—
89	C₄⋊Q₈	—	43	1	no	—
90	#127	—	43	1	no	—
91	#124	—	43	1	no	—
92	#124	C₂×D₄₃	1	1	yes	characteristic
93	#121	—	86	2	no	—
94	C₄×D₄	—	86	2	no	—
95	C₂×C₄²	—	43	1	no	—
96	C₄⋊C₈	—	86	2	no	—
97	C₂²⋊C₈	—	86	2	no	—
98	#97	—	43	2	no	—
99	#97	C₂×D₄₃	1	2	yes	—
100	#41	—	172	2	no	—
101	#41	—	172	2	no	—
102	C₂×Q₈	—	43	1	no	—
103	C₂×Q₈	C₄×D₄₃	1	1	yes	characteristic
104	C₂×D₄	—	43	1	no	—
105	C₂×D₄	—	86	1	no	—
106	C₂×D₄	—	86	2	no	—
107	C₂×D₄	—	86	1	no	—
108	C₂×D₄	C₄×D₄₃	1	1	yes	characteristic
109	C₂²×C₄	—	43	1	no	—
110	C₂²×C₄	—	43	2	no	—
111	C₂²×C₄	—	86	1	no	—
112	C₂²×C₄	—	86	1	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	86	2	no	—
115	C₄⋊C₄	—	86	2	no	—
116	C₂²⋊C₄	—	2	2	no	—
117	C₂²⋊C₄	—	86	2	no	—
118	C₄²	—	43	1	no	—
119	C₄²	—	43	2	no	—
120	C₄²	C₂²×D₄₃	1	1	yes	characteristic
121	C₂³	—	2	1	no	—
122	C₂³	—	43	1	no	—
123	C₂³	—	86	1	no	—
124	Q₈	—	4	1	no	—
125	Q₈	—	172	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	172	1	no	—
128	D₄	—	172	2	no	—
129	D₄	—	172	4	no	—
130	D₄	—	172	2	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	43	1	no	—
133	C₂×C₄	—	43	2	no	—
134	C₂×C₄	—	86	2	no	—
135	C₂×C₄	—	86	1	no	—
136	C₂×C₄	—	172	2	no	—
137	C₂×C₄	—	172	2	no	—
138	C₂×C₄	—	172	2	no	—
139	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
140	C₂×C₄	D₄×D₄₃	1	2	yes	—
141	C₈	—	4	2	no	—
142	C₈	—	172	2	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	4	2	no	—
145	C₂²	—	86	1	no	—
146	C₂²	—	86	2	no	—
147	C₂²	—	172	1	no	—
148	C₂²	—	172	2	no	—
149	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
150	C₄	—	2	1	no	—
151	C₄	—	2	2	no	—
152	C₄	—	4	1	no	—
153	C₄	—	43	2	no	—
154	C₄	—	86	2	no	—
155	C₄	—	172	1	no	—
156	C₂	—	8	1	no	—
157	C₂	—	344	1	no	—
158	C₂	—	172	1	no	—
159	C₂	#100×D₄₃	1	1	yes	characteristic
160	C₂	#14582914	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583448

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×#10621902

C₄

yes

characteristic

C₂×#10621900

C₄

yes

characteristic

#13063323

C₄

yes

characteristic

#13063321

C₄

yes

characteristic

#13063313

C₂²

yes

characteristic

#13063298

—

(C₂²⋊D₄₃)⋊C₄

—

C₄²×D₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

(C₂×D₄₃)⋊C₈

—

#13063236

C₂²

yes

—

#124×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

—

#10621902

—

#10621900

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

—

C₂×Dic₈₆

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

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

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#100

yes

—

#1536

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#100

yes

characteristic

C₂×C₄₃

#421

yes

—

D₄₃

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#1536

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×#41

—

C₄⋊Q₈

—

#127

—

#124

—

#124

C₂×D₄₃

yes

characteristic

#121

—

C₄×D₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₂×D₄₃

yes

—

100

#41

—

172

—

101

#41

—

172

—

102

C₂×Q₈

—

103

C₂×Q₈

C₄×D₄₃

yes

characteristic

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

C₄×D₄₃

yes

characteristic

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₂²×D₄₃

yes

characteristic

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

Q₈

—

125

Q₈

—

172

—

126

D₄

—

127

D₄

—

172

—

128

D₄

—

172

—

129

D₄

—

172

—

130

D₄

—

172

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

172

—

137

C₂×C₄

—

172

—

138

C₂×C₄

—

172

—

139

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

140

C₂×C₄

D₄×D₄₃

yes

—

141

C₈

—

142

C₈

—

172

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

172

—

148

C₂²

—

172

—

149

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

172

—

156

C₂

—

157

C₂

—

344

—

158

C₂

—

172

—

159

C₂

#100×D₄₃

yes

characteristic

160

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	#1536
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
85. #329	D₄₃	semidirect
86. C₄₃	#1536	semidirect

H ≅ G/N

type

2. #14582954

C₂

semidirect

3. #14582639

C₂

semidirect

4. #14582638

C₂

semidirect

5. C₄₃×#329

C₂

semidirect

85. #329

D₄₃

semidirect

86. C₄₃

#1536

semidirect

Subgroups — #19133228

Conjugacy classes of subgroups

Complements