Group #19132597 — subgroups

Subgroups — #19132597

Order 5504.

168 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 35 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	#14582816	C₂	1	1	yes	maximal, characteristic
2	#14582625	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#343	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₇₂	C₄	1	1	yes	characteristic
5	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
6	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
7	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
8	C₄₃⋊#95	C₄	1	1	yes	characteristic
9	C₂×M₁₆×C₄₃	—	2	1	no	—
10	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄₃	—	2	1	no	—
12	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
15	C₂²×Dic₄₃	—	2	1	no	—
16	C₂×D₁₇₂	—	4	2	no	—
17	C₂×D₁₇₂	—	4	1	no	—
18	M₁₆×C₄₃	—	2	2	no	—
19	M₁₆×C₄₃	—	4	1	no	—
20	C₂×C₈×C₄₃	—	4	1	no	—
21	C₄⋊C₄×C₄₃	—	4	1	no	—
22	(C₂×D₄₃)⋊C₄	—	4	2	no	—
23	(C₂×D₄₃)⋊C₄	—	4	1	no	—
24	(C₂×D₄₃)⋊C₄	—	4	1	no	—
25	C₂×C₄₃⋊C₈	—	4	1	no	—
26	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×D₄₃	—	2	2	no	—
28	C₂²×D₄₃	—	4	1	no	—
29	C₂²×D₄₃	—	4	1	no	—
30	C₂²×D₄₃	—	4	1	no	—
31	C₂²×D₄₃	—	4	1	no	—
32	C₂²×D₄₃	—	4	1	no	—
33	C₂²×D₄₃	—	4	1	no	—
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	2	1	no	—
37	C₂×C₄×C₄₃	—	2	1	no	—
38	C₂×C₄×C₄₃	—	4	1	no	—
39	C₂×C₄×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
41	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
42	C₂×Dic₄₃	—	4	1	no	—
43	C₂×Dic₄₃	—	4	1	no	—
44	C₂×Dic₄₃	—	4	1	no	—
45	D₁₇₂	—	4	2	no	—
46	D₁₇₂	—	4	2	no	—
47	C₈×C₄₃	—	4	2	no	—
48	C₄₃⋊C₈	—	8	1	no	—
49	C₂²×C₄₃	—	2	1	no	—
50	C₂²×C₄₃	—	2	1	no	—
51	C₂²×C₄₃	#99	1	1	yes	characteristic
52	C₂²×C₄₃	#102	1	1	yes	characteristic
53	C₂²×C₄₃	#104	1	1	yes	characteristic
54	C₂×D₄₃	—	4	2	no	—
55	C₂×D₄₃	—	4	2	no	—
56	C₂×D₄₃	—	4	2	no	—
57	C₂×D₄₃	—	8	1	no	—
58	C₂×D₄₃	—	8	1	no	—
59	C₂×D₄₃	—	8	1	no	—
60	C₂×D₄₃	—	8	1	no	—
61	C₄×C₄₃	—	2	1	no	—
62	C₄×C₄₃	—	2	1	no	—
63	C₄×C₄₃	—	4	1	no	—
64	C₄×C₄₃	—	4	1	no	—
65	Dic₄₃	—	8	1	no	—
66	#1345	—	43	1	no	maximal, Sylow
67	C₂×C₄₃	—	2	1	no	—
68	C₂×C₄₃	—	2	1	no	—
69	C₂×C₄₃	#327	1	1	yes	characteristic
70	C₂×C₄₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
71	C₂×C₄₃	#355	1	1	yes	characteristic
72	D₄₃	—	8	2	no	—
73	#394	—	43	1	no	—
74	#343	D₄₃	1	1	yes	characteristic, complemented
75	#324	—	43	1	no	—
76	C₄₃	#1345	1	1	yes	characteristic, complemented, Sylow
77	C₂²×D₄	—	43	1	no	—
78	C₂×M₁₆	—	2	1	no	—
79	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
80	C₂×C₂²⋊C₄	—	86	1	no	—
81	C₂×C₂²⋊C₄	—	86	1	no	—
82	C₂²⋊C₈	—	86	1	no	—
83	#95	—	43	1	no	—
84	C₂⁴	—	86	1	no	—
85	C₂×D₄	—	172	1	no	—
86	C₂×D₄	—	172	2	no	—
87	C₂²×C₄	—	86	1	no	—
88	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
89	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
90	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
91	M₁₆	—	2	2	no	—
92	M₁₆	—	4	1	no	—
93	C₂×C₈	—	4	1	no	—
94	C₂×C₈	—	172	1	no	—
95	C₄⋊C₄	—	4	1	no	—
96	C₂²⋊C₄	—	172	2	no	—
97	C₂²⋊C₄	—	172	1	no	—
98	C₂²⋊C₄	—	172	1	no	—
99	C₂³	—	86	2	no	—
100	C₂³	—	172	1	no	—
101	C₂³	—	172	1	no	—
102	C₂³	—	172	1	no	—
103	C₂³	—	172	1	no	—
104	C₂³	—	172	1	no	—
105	C₂³	—	172	1	no	—
106	C₂³	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
107	D₄	—	172	2	no	—
108	D₄	—	172	2	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	172	1	no	—
116	C₂×C₄	—	172	1	no	—
117	C₂×C₄	—	172	1	no	—
118	C₂×C₄	#10621882	1	1	yes	characteristic
119	C₂×C₄	#10621884	1	1	yes	characteristic
120	C₈	—	4	2	no	—
121	C₈	—	344	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	2	1	no	—
124	C₂²	—	344	1	no	—
125	C₂²	—	344	1	no	—
126	C₂²	—	344	1	no	—
127	C₂²	—	344	1	no	—
128	C₂²	—	172	2	no	—
129	C₂²	—	172	2	no	—
130	C₂²	—	172	2	no	—
131	C₂²	#13063239	1	1	yes	characteristic
132	C₂²	#13063245	1	1	yes	characteristic
133	C₂²	#13063253	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	2	1	no	—
136	C₄	—	4	1	no	—
137	C₄	—	4	1	no	—
138	C₄	—	344	1	no	—
139	C₂	—	2	1	no	—
140	C₂	—	2	1	no	—
141	C₂	—	344	2	no	—
142	C₂	#14582632	1	1	yes	characteristic
143	C₂	#14582687	1	1	yes	characteristic
144	C₂	#14582695	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582816

C₂

yes

maximal, characteristic

#14582625

C₂

yes

maximal, characteristic, complemented

C₄₃×#343

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₄

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂²⋊(C₄₃⋊C₈)

—

C₄₃⋊#95

C₄

yes

characteristic

C₂×M₁₆×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#1345

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#327

yes

characteristic

C₂×C₄₃

AΣL(1,𝔽₁₆)

yes

characteristic

C₂×C₄₃

#355

yes

characteristic

D₄₃

—

#394

—

#343

D₄₃

yes

characteristic, complemented

#324

—

C₄₃

#1345

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×M₁₆

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂²⋊C₈

—

#95

—

C₂⁴

—

C₂×D₄

—

172

—

C₂×D₄

—

172

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₂³

—

100

C₂³

—

172

—

101

C₂³

—

172

—

102

C₂³

—

172

—

103

C₂³

—

172

—

104

C₂³

—

172

—

105

C₂³

—

172

—

106

C₂³

(C₂×D₄₃)⋊C₄

yes

characteristic

107

D₄

—

172

—

108

D₄

—

172

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

172

—

116

C₂×C₄

—

172

—

117

C₂×C₄

—

172

—

118

C₂×C₄

#10621882

yes

characteristic

119

C₂×C₄

#10621884

yes

characteristic

120

C₈

—

121

C₈

—

344

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

344

—

125

C₂²

—

344

—

126

C₂²

—

344

—

127

C₂²

—

344

—

128

C₂²

—

172

—

129

C₂²

—

172

—

130

C₂²

—

172

—

131

C₂²

#13063239

yes

characteristic

132

C₂²

#13063245

yes

characteristic

133

C₂²

#13063253

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

344

—

139

C₂

—

140

C₂

—

141

C₂

—

344

—

142

C₂

#14582632

yes

characteristic

143

C₂

#14582687

yes

characteristic

144

C₂

#14582695

yes

characteristic

	subgroup	G/H
center	C₂²	#13063239
commutator	C₂²×C₄×C₄₃	C₂×C₄
Frattini	C₂×C₄⋊C₄	C₂×D₄₃
Fitting	C₄₃×#343	C₂
socle	C₂²×C₄₃	#99
hypercenter	#343	D₄₃
hypocenter	C₄₃	#1345
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #343

subgroup

G/H

center

C₂²

#13063239

commutator

C₂²×C₄×C₄₃

C₂×C₄

Frattini

C₂×C₄⋊C₄

C₂×D₄₃

Fitting

C₄₃×#343

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #343

N	H ≅ G/N	type
2. #14582625	C₂	semidirect
3. C₄₃×#343	C₂	semidirect
74. #343	D₄₃	semidirect
76. C₄₃	#1345	semidirect

H ≅ G/N

type

2. #14582625

C₂

semidirect

3. C₄₃×#343

C₂

semidirect

74. #343

D₄₃

semidirect

76. C₄₃

#1345

semidirect

Subgroups — #19132597

Conjugacy classes of subgroups

Complements