Group #19133102 — subgroups

Subgroups — #19133102

Order 5504.

272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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	#14583449	C₂	1	1	yes	maximal, characteristic
2	#14582956	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582632	C₂	1	4	yes	maximal, complemented
4	C₄₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10621898	—	2	1	no	—
6	#13063325	C₄	1	1	yes	characteristic, complemented
7	#13063322	C₄	1	1	yes	characteristic, complemented
8	#13063313	—	2	1	no	—
9	#13063299	—	2	1	no	—
10	#13063299	C₂²	1	2	yes	—
11	C₄×D₁₇₂	—	2	1	no	—
12	C₄×D₁₇₂	C₄	1	2	yes	complemented
13	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
14	C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
15	#13063236	—	2	1	no	—
16	C₂×C₄²×C₄₃	—	2	1	no	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	#95×C₄₃	—	2	1	no	—
19	#95×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₄×C₄₃	—	2	2	no	—
21	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂×C₂²⋊D₄₃	—	2	2	no	—
25	#10621898	—	4	4	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	—	2	1	no	—
28	C₂×D₁₇₂	C₂×C₄	1	2	yes	—
29	C₂×C₄×D₄₃	—	2	2	no	—
30	C₂×Dic₈₆	—	2	1	no	—
31	C₄²×C₄₃	—	2	4	no	—
32	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
33	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
34	C₄²×C₄₃	D₄	1	1	yes	characteristic
35	C₄²×C₄₃	D₄	1	1	yes	characteristic
36	(C₂×D₄₃)⋊C₄	—	2	2	no	—
37	(C₂×D₄₃)⋊C₄	—	2	2	no	—
38	C₄⋊Dic₄₃	—	2	1	no	—
39	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
40	C₂×C₄₃⋊C₈	—	2	2	no	—
41	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×D₄₃	—	2	2	no	—
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	—	2	4	no	—
46	C₂×C₄×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	—	4	2	no	—
48	C₂×C₄×C₄₃	—	4	2	no	—
49	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂²⋊D₄₃	—	4	4	no	—
56	C₂×Dic₄₃	—	2	2	no	—
57	D₁₇₂	—	4	2	no	—
58	D₁₇₂	—	4	2	no	—
59	D₁₇₂	—	4	2	no	—
60	C₄×D₄₃	—	4	4	no	—
61	Dic₈₆	—	4	2	no	—
62	C₄₃⋊C₈	—	4	2	no	—
63	C₂²×C₄₃	—	2	1	no	—
64	C₂²×C₄₃	—	2	1	no	—
65	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
67	C₂×D₄₃	—	4	2	no	—
68	C₂×D₄₃	—	4	2	no	—
69	C₂×D₄₃	—	4	2	no	—
70	C₄×C₄₃	—	2	1	no	—
71	C₄×C₄₃	—	2	1	no	—
72	C₄×C₄₃	—	2	1	no	—
73	C₄×C₄₃	—	2	1	no	—
74	C₄×C₄₃	—	2	1	no	—
75	C₄×C₄₃	—	4	4	no	—
76	C₄×C₄₃	#104	1	2	yes	—
77	Dic₄₃	—	4	2	no	—
78	#1505	—	43	1	no	maximal, Sylow
79	C₂×C₄₃	—	2	2	no	—
80	C₂×C₄₃	#410	1	1	yes	characteristic
81	C₂×C₄₃	#418	1	1	yes	characteristic
82	C₂×C₄₃	C₂×#104	1	1	yes	characteristic
83	D₄₃	—	8	2	no	—
84	#532	—	43	1	no	—
85	#432	—	43	1	no	—
86	#376	D₄₃	1	1	yes	characteristic, complemented
87	#327	—	43	4	no	—
88	C₄₃	#1505	1	1	yes	characteristic, complemented, Sylow
89	C₂×#41	—	86	1	no	—
90	C₄⋊Q₈	—	43	1	no	—
91	#127	—	43	1	no	—
92	#124	—	86	1	no	—
93	#121	—	43	2	no	—
94	#121	—	86	1	no	—
95	C₄×D₄	—	43	2	no	—
96	C₄×D₄	—	86	1	no	—
97	C₂×C₄²	—	2	1	no	—
98	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
99	C₄⋊C₈	—	86	1	no	—
100	C₂²⋊C₈	—	43	2	no	—
101	#97	—	86	1	no	—
102	#95	—	2	1	no	—
103	#95	C₂×D₄₃	1	2	yes	—
104	#41	—	172	4	no	—
105	C₂×Q₈	—	86	1	no	—
106	C₂×D₄	—	43	2	no	—
107	C₂×D₄	—	86	2	no	—
108	C₂×D₄	—	86	1	no	—
109	C₂×D₄	—	86	1	no	—
110	C₂²×C₄	—	2	2	no	—
111	C₂²×C₄	—	86	2	no	—
112	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
113	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
114	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
115	C₂×C₈	—	86	2	no	—
116	C₄⋊C₄	—	43	2	no	—
117	C₄⋊C₄	—	86	1	no	—
118	C₂²⋊C₄	—	86	2	no	—
119	C₂²⋊C₄	—	86	2	no	—
120	C₄²	—	2	4	no	—
121	C₄²	C₄×D₄₃	1	1	yes	characteristic
122	C₄²	C₄×D₄₃	1	1	yes	characteristic
123	C₄²	D₁₇₂	1	1	yes	characteristic
124	C₄²	D₁₇₂	1	1	yes	characteristic
125	C₂³	—	86	2	no	—
126	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
127	Q₈	—	172	2	no	—
128	D₄	—	172	2	no	—
129	D₄	—	172	2	no	—
130	D₄	—	172	4	no	—
131	D₄	—	172	2	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	4	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	—	4	2	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	86	2	no	—
139	C₂×C₄	—	172	4	no	—
140	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
141	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
142	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
143	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
144	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
145	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
146	C₈	—	172	2	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	172	2	no	—
150	C₂²	—	172	2	no	—
151	C₂²	—	172	2	no	—
152	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
153	C₂²	#13063350	1	2	yes	—
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	—	2	1	no	—
159	C₄	—	4	4	no	—
160	C₄	—	172	2	no	—
161	C₄	#13063253	1	2	yes	—
162	C₂	—	2	2	no	—
163	C₂	—	344	2	no	—
164	C₂	#14582872	1	1	yes	characteristic
165	C₂	#14582903	1	1	yes	characteristic
166	C₂	C₂×#13063253	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583449

C₂

yes

maximal, characteristic

#14582956

C₂

yes

maximal, characteristic, complemented

#14582632

C₂

yes

maximal, complemented

C₄₃×#376

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

—

#13063325

C₄

yes

characteristic, complemented

#13063322

C₄

yes

characteristic, complemented

#13063313

—

#13063299

—

#13063299

C₂²

yes

—

C₄×D₁₇₂

—

C₄×D₁₇₂

C₄

yes

complemented

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063236

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

#95×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₂²⋊D₄₃

—

#10621898

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂×C₄

yes

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#104

yes

—

Dic₄₃

—

#1505

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#532

—

#432

—

#376

D₄₃

yes

characteristic, complemented

#327

—

C₄₃

#1505

yes

characteristic, complemented, Sylow

C₂×#41

—

C₄⋊Q₈

—

—

—

—

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

100

C₂²⋊C₈

—

101

#97

—

102

#95

—

103

#95

C₂×D₄₃

yes

—

104

#41

—

172

—

105

C₂×Q₈

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

113

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

114

C₂²×C₄

C₂²×D₄₃

yes

characteristic

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

—

121

C₄²

C₄×D₄₃

yes

characteristic

122

C₄²

C₄×D₄₃

yes

characteristic

123

C₄²

D₁₇₂

yes

characteristic

124

C₄²

D₁₇₂

yes

characteristic

125

C₂³

—

126

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

127

Q₈

—

172

—

128

D₄

—

172

—

129

D₄

—

172

—

130

D₄

—

172

—

131

D₄

—

172

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

172

—

140

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

141

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

142

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

143

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

144

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

145

C₂×C₄

C₂×D₁₇₂

yes

characteristic

146

C₈

—

172

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

172

—

150

C₂²

—

172

—

151

C₂²

—

172

—

152

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

153

C₂²

#13063350

yes

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

172

—

161

C₄

#13063253

yes

—

162

C₂

—

163

C₂

—

344

—

164

C₂

#14582872

yes

characteristic

165

C₂

#14582903

yes

characteristic

166

C₂

C₂×#13063253

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#376	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#376	D₄₃
hypocenter	C₄₃	#1505
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #376

subgroup

G/H

center

C₂²

C₂×(C₂×D₄₃)⋊C₄

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#376

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #376

N	H ≅ G/N	type
2. #14582956	C₂	semidirect
3. #14582632	C₂	semidirect
4. C₄₃×#376	C₂	semidirect
6. #13063325	C₄	semidirect
7. #13063322	C₄	semidirect
12. C₄×D₁₇₂	C₄	semidirect
86. #376	D₄₃	semidirect
88. C₄₃	#1505	semidirect

H ≅ G/N

type

2. #14582956

C₂

semidirect

3. #14582632

C₂

semidirect

4. C₄₃×#376

C₂

semidirect

6. #13063325

C₄

semidirect

7. #13063322

C₄

semidirect

12. C₄×D₁₇₂

C₄

semidirect

86. #376

D₄₃

semidirect

88. C₄₃

#1505

semidirect

Subgroups — #19133102

Conjugacy classes of subgroups

Complements