Group #19136697 — subgroups

Subgroups — #19136697

Order 5504.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#13063266	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063264	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583136	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583132	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582726	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582701	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
10	#13063300	—	2	1	no	—
11	#13063296	—	2	1	no	—
12	#13063266	—	2	2	no	—
13	#13063264	—	2	2	no	—
14	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	#13063259	C₂²	1	1	yes	characteristic
16	#13063246	—	2	1	no	—
17	#13063245	—	2	1	no	—
18	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	#107×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×D₄×C₄₃	—	2	1	no	—
22	C₂×C₂²⋊D₄₃	—	4	1	no	—
23	C₂×D₁₇₂	—	2	1	no	—
24	C₂×D₁₇₂	—	4	1	no	—
25	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
26	D₈×C₄₃	—	2	1	no	—
27	D₈×C₄₃	—	2	1	no	—
28	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₂²⋊Dic₄₃	—	4	1	no	—
31	(C₂×D₄₃)⋊C₄	—	4	1	no	—
32	C₄⋊Dic₄₃	—	2	1	no	—
33	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
34	D₃₄₄	—	2	1	no	—
35	D₃₄₄	—	2	1	no	—
36	C₈×D₄₃	—	2	1	no	—
37	C₈×D₄₃	—	2	1	no	—
38	C₁₆×C₄₃	—	2	1	no	—
39	C₄₃⋊C₁₆	D₄	1	2	yes	complemented
40	C₂³×C₄₃	—	4	1	no	—
41	C₂²×D₄₃	—	4	1	no	—
42	C₂²×D₄₃	D₈	1	1	yes	characteristic
43	D₄×C₄₃	—	4	1	no	—
44	D₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂²⋊D₄₃	—	8	2	no	—
48	C₂×Dic₄₃	—	4	1	no	—
49	C₂×Dic₄₃	D₈	1	1	yes	characteristic
50	D₁₇₂	—	4	1	no	—
51	D₁₇₂	—	4	1	no	—
52	D₁₇₂	—	8	2	no	—
53	C₄×D₄₃	—	2	1	no	—
54	C₄×D₄₃	—	2	1	no	—
55	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₈×C₄₃	#41	1	1	yes	characteristic
57	C₄₃⋊C₈	—	2	1	no	—
58	C₂²×C₄₃	—	8	1	no	—
59	C₂²×C₄₃	—	8	1	no	—
60	C₂²×C₄₃	—	8	1	no	—
61	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
62	C₂×D₄₃	—	2	1	no	—
63	C₂×D₄₃	—	2	1	no	—
64	C₂×D₄₃	—	2	1	no	—
65	C₂×D₄₃	—	8	1	no	—
66	C₂×D₄₃	—	8	1	no	—
67	C₂×D₄₃	—	8	1	no	—
68	C₄×C₄₃	—	8	1	no	—
69	C₄×C₄₃	#121	1	1	yes	characteristic
70	C₄×C₄₃	#135	1	1	yes	characteristic
71	Dic₄₃	—	2	1	no	—
72	Dic₄₃	—	8	1	no	—
73	#2218	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	—	16	1	no	—
75	C₂×C₄₃	#466	1	1	yes	characteristic
76	C₂×C₄₃	#509	1	1	yes	characteristic
77	C₂×C₄₃	#509	1	1	yes	characteristic
78	D₄₃	—	4	1	no	—
79	D₄₃	—	16	1	no	—
80	C₂×D₁₆	—	43	1	no	—
81	C₂×M₃₂	—	43	1	no	—
82	#466	—	43	1	no	—
83	#466	—	43	1	no	—
84	#367	—	43	1	no	—
85	#357	—	43	1	no	—
86	#357	D₄₃	1	1	yes	characteristic, complemented
87	C₄₃	#2218	1	1	yes	characteristic, complemented, Sylow
88	C₂×D₈	—	43	1	no	—
89	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
90	C₂²×C₈	—	43	1	no	—
91	#121	—	86	1	no	—
92	#121	—	86	1	no	—
93	D₁₆	—	86	2	no	—
94	M₃₂	—	86	2	no	—
95	C₂×C₁₆	—	43	1	no	—
96	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
97	#107	—	43	1	no	—
98	#107	C₂×D₄₃	1	1	yes	characteristic
99	#102	—	86	1	no	—
100	#102	—	86	1	no	—
101	C₂×D₄	—	2	1	no	—
102	C₂×D₄	—	86	1	no	—
103	C₂×D₄	—	172	1	no	—
104	C₂×D₄	—	172	1	no	—
105	C₂²×C₄	—	43	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	86	1	no	—
109	D₈	—	86	1	no	—
110	C₂×C₈	—	43	1	no	—
111	C₂×C₈	—	86	1	no	—
112	C₂×C₈	—	86	1	no	—
113	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
114	C₄⋊C₄	—	2	1	no	—
115	C₄⋊C₄	—	86	1	no	—
116	C₂²⋊C₄	—	172	1	no	—
117	C₂²⋊C₄	—	172	1	no	—
118	C₁₆	—	2	1	no	—
119	C₁₆	—	43	2	no	—
120	C₂³	—	4	1	no	—
121	C₂³	—	43	1	no	—
122	C₂³	—	172	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	1	no	—
125	D₄	—	344	2	no	—
126	D₄	—	344	2	no	—
127	D₄	—	172	1	no	—
128	D₄	—	172	1	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	43	1	no	—
131	C₂×C₄	—	86	1	no	—
132	C₂×C₄	—	86	1	no	—
133	C₂×C₄	—	172	1	no	—
134	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
135	C₈	—	86	1	no	—
136	C₈	#10621898	1	1	yes	characteristic
137	C₈	D₄×D₄₃	1	1	yes	characteristic
138	C₂²	—	8	1	no	—
139	C₂²	—	8	1	no	—
140	C₂²	—	8	1	no	—
141	C₂²	—	86	1	no	—
142	C₂²	—	86	1	no	—
143	C₂²	—	86	1	no	—
144	C₂²	—	344	1	no	—
145	C₂²	—	344	1	no	—
146	C₂²	—	344	1	no	—
147	C₂²	D₈×D₄₃	1	1	yes	characteristic
148	C₄	—	8	1	no	—
149	C₄	—	86	1	no	—
150	C₄	—	344	1	no	—
151	C₄	#13063298	1	1	yes	characteristic
152	C₄	#13063346	1	1	yes	characteristic
153	C₂	—	16	1	no	—
154	C₂	—	172	1	no	—
155	C₂	—	688	1	no	—
156	C₂	#14583134	1	1	yes	characteristic
157	C₂	#14583333	1	1	yes	characteristic
158	C₂	#14583336	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063266

C₂

yes

maximal, characteristic, complemented

C₂×#13063264

C₂

yes

maximal, characteristic, complemented

#14583136

C₂

yes

maximal, characteristic, complemented

#14583132

C₂

yes

maximal, characteristic, complemented

#14582726

C₂

yes

maximal, characteristic, complemented

#14582701

C₂

yes

maximal, characteristic, complemented

C₄₃×#357

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

C₂²

yes

characteristic

C₂×C₈×D₄₃

C₂²

yes

—

—

—

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063246

—

#13063245

—

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×C₂²⋊D₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

D₄

yes

characteristic

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

D₄

yes

complemented

C₂³×C₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

D₈

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2218

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

D₄₃

—

C₂×D₁₆

—

C₂×M₃₂

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2218

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

#121

—

#121

—

D₁₆

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

—

#107

C₂×D₄₃

yes

characteristic

#102

—

100

#102

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

172

—

104

C₂×D₄

—

172

—

105

C₂²×C₄

—

106

D₈

—

107

D₈

—

108

D₈

—

109

D₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₄₃

yes

characteristic

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

172

—

117

C₂²⋊C₄

—

172

—

118

C₁₆

—

119

C₁₆

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

172

—

123

D₄

—

124

D₄

—

125

D₄

—

344

—

126

D₄

—

344

—

127

D₄

—

172

—

128

D₄

—

172

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

172

—

134

C₂×C₄

D₄×D₄₃

yes

characteristic

135

C₈

—

136

C₈

#10621898

yes

characteristic

137

C₈

D₄×D₄₃

yes

characteristic

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

344

—

145

C₂²

—

344

—

146

C₂²

—

344

—

147

C₂²

D₈×D₄₃

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

344

—

151

C₄

#13063298

yes

characteristic

152

C₄

#13063346

yes

characteristic

153

C₂

—

154

C₂

—

172

—

155

C₂

—

688

—

156

C₂

#14583134

yes

characteristic

157

C₂

#14583333

yes

characteristic

158

C₂

#14583336

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#357	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#357	D₄₃
hypocenter	C₄₃	#2218
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#357

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×#13063266	C₂	semidirect
2. C₂×#13063264	C₂	semidirect
3. #14583136	C₂	semidirect
4. #14583132	C₂	semidirect
5. #14582726	C₂	semidirect
6. #14582701	C₂	semidirect
7. C₄₃×#357	C₂	semidirect
39. C₄₃⋊C₁₆	D₄	semidirect
86. #357	D₄₃	semidirect
87. C₄₃	#2218	semidirect

H ≅ G/N

type

1. C₂×#13063266

C₂

semidirect

2. C₂×#13063264

C₂

semidirect

3. #14583136

C₂

semidirect

4. #14583132

C₂

semidirect

5. #14582726

C₂

semidirect

6. #14582701

C₂

semidirect

7. C₄₃×#357

C₂

semidirect

39. C₄₃⋊C₁₆

D₄

semidirect

86. #357

D₄₃

semidirect

87. C₄₃

#2218

semidirect

Subgroups — #19136697

Conjugacy classes of subgroups

Complements