Group #24983843 — subgroups

Subgroups — #24983843

Order 11008.

188 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 87 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	#19136398	C₂	1	1	yes	maximal, characteristic
2	#19133351	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1564	C₂	1	1	yes	maximal, characteristic
4	#14582923	—	2	1	no	—
5	C₄⋊(C₄₃⋊C₁₆)	—	2	1	no	—
6	C₂²⋊(C₄₃⋊C₁₆)	C₄	1	2	yes	—
7	#14582675	—	2	1	no	—
8	#14582650	—	2	1	no	—
9	#14582650	C₄	1	2	yes	—
10	C₄₃×#431	—	2	1	no	—
11	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#335	C₄	1	2	yes	—
13	C₄₃×#334	—	2	1	no	—
14	C₂×#10621877	—	4	1	no	—
15	C₂×C₄₃⋊C₁₆	—	2	2	no	—
16	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
17	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
18	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₄₃	Q₈	1	1	yes	characteristic
20	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
21	C₄⋊C₈×C₄₃	—	2	2	no	—
22	C₂²⋊C₈×C₄₃	—	4	1	no	—
23	C₄×C₈×C₄₃	—	4	1	no	—
24	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
27	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
30	C₂²×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
31	C₂×C₈×C₄₃	—	2	2	no	—
32	C₂×C₈×C₄₃	—	4	1	no	—
33	C₂×C₈×C₄₃	—	4	2	no	—
34	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
38	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
41	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
42	#10621877	—	8	2	no	—
43	C₂×C₄₃⋊C₈	—	4	2	no	—
44	C₄₃⋊C₁₆	—	4	2	no	—
45	C₂³×C₄₃	#107	1	1	yes	characteristic
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	—	2	2	no	—
49	C₂×C₄×C₄₃	—	4	1	no	—
50	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
51	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
52	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
53	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
55	C₂×C₄×C₄₃	#106	1	1	yes	characteristic
56	C₈×C₄₃	—	2	1	no	—
57	C₈×C₄₃	—	2	1	no	—
58	C₈×C₄₃	—	2	1	no	—
59	C₈×C₄₃	—	8	2	no	—
60	C₈×C₄₃	#108	1	2	yes	—
61	C₄₃⋊C₈	—	8	2	no	—
62	#7295	—	43	1	no	maximal, Sylow
63	C₂²×C₄₃	—	2	1	no	—
64	C₂²×C₄₃	—	2	1	no	—
65	C₂²×C₄₃	—	2	1	no	—
66	C₂²×C₄₃	#340	1	1	yes	characteristic
67	C₄×C₄₃	—	2	1	no	—
68	C₄×C₄₃	—	2	1	no	—
69	C₄×C₄₃	—	2	1	no	—
70	C₄×C₄₃	—	2	1	no	—
71	C₄×C₄₃	#341	1	1	yes	characteristic
72	C₄×C₄₃	#344	1	1	yes	characteristic
73	C₄×C₄₃	#360	1	2	yes	—
74	#2163	—	43	1	no	—
75	#1566	—	43	1	no	—
76	#1564	D₄₃	1	1	yes	characteristic
77	C₂×C₄₃	—	4	1	no	—
78	C₂×C₄₃	#1301	1	1	yes	characteristic
79	C₂×C₄₃	#1385	1	1	yes	characteristic
80	C₂×C₄₃	#1386	1	1	yes	characteristic
81	#431	—	2	1	no	—
82	#423	—	86	1	no	—
83	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
84	C₄⋊C₁₆	—	86	1	no	—
85	C₂²⋊C₁₆	—	43	2	no	—
86	#346	—	86	1	no	—
87	#335	Dic₄₃	1	2	yes	—
88	#334	—	2	1	no	—
89	#334	—	43	2	no	—
90	#334	—	86	1	no	—
91	C₄₃	#7295	1	1	yes	characteristic, complemented, Sylow
92	C₂×M₁₆	—	172	1	no	—
93	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
94	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
95	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
96	C₂×C₁₆	—	86	2	no	—
97	C₄⋊C₈	—	2	2	no	—
98	C₄⋊C₈	—	86	2	no	—
99	C₄⋊C₈	—	172	1	no	—
100	C₂²⋊C₈	—	4	1	no	—
101	C₄×C₈	—	4	1	no	—
102	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
103	C₄×C₈	D₁₇₂	1	1	yes	characteristic
104	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
105	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
106	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
107	C₂²×C₄	#10621882	1	1	yes	characteristic
108	C₂²×C₄	#10621885	1	1	yes	characteristic
109	M₁₆	—	344	2	no	—
110	C₂×C₈	—	2	2	no	—
111	C₂×C₈	—	4	1	no	—
112	C₂×C₈	—	4	2	no	—
113	C₂×C₈	—	172	2	no	—
114	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
115	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
116	C₂×C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
117	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
118	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
119	C₄²	#10621883	1	1	yes	characteristic
120	C₄²	#10621884	1	1	yes	characteristic
121	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
122	C₁₆	—	172	2	no	—
123	C₂³	#13063258	1	1	yes	characteristic
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
129	C₂×C₄	#13063245	1	1	yes	characteristic
130	C₂×C₄	#13063246	1	1	yes	characteristic
131	C₂×C₄	#13063248	1	1	yes	characteristic
132	C₂×C₄	#13063249	1	1	yes	characteristic
133	C₂×C₄	#13063256	1	1	yes	characteristic
134	C₈	—	2	1	no	—
135	C₈	—	2	1	no	—
136	C₈	—	2	1	no	—
137	C₈	—	8	2	no	—
138	C₈	—	344	2	no	—
139	C₈	#13063261	1	2	yes	—
140	C₂²	—	2	1	no	—
141	C₂²	—	2	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	#14582661	1	1	yes	characteristic
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	2	1	no	—
148	C₄	#14582664	1	1	yes	characteristic
149	C₄	#14582671	1	1	yes	characteristic
150	C₄	#14582709	1	2	yes	—
151	C₂	—	4	1	no	—
152	C₂	#19132492	1	1	yes	characteristic
153	C₂	#19132698	1	1	yes	characteristic
154	C₂	#19132700	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136398

C₂

yes

maximal, characteristic

#19133351

C₂

yes

maximal, characteristic

C₄₃×#1564

C₂

yes

maximal, characteristic

#14582923

—

C₄⋊(C₄₃⋊C₁₆)

—

C₂²⋊(C₄₃⋊C₁₆)

C₄

yes

—

#14582675

—

#14582650

—

#14582650

C₄

yes

—

C₄₃×#431

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#335

C₄

yes

—

C₄₃×#334

—

C₂×#10621877

—

C₂×C₄₃⋊C₁₆

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

Q₈

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

Q₁₆

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

SD₁₆

yes

characteristic

C₄²×C₄₃

SD₁₆

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

#107

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#108

yes

—

C₄₃⋊C₈

—

#7295

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#340

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

#2163

—

#1566

—

#1564

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#335

Dic₄₃

yes

—

#334

—

#334

—

#334

—

C₄₃

#7295

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

172

—

C₂²×C₈

Dic₈₆

yes

characteristic

C₂²×C₈

C₄×D₄₃

yes

characteristic

C₂×C₄²

C₂²⋊D₄₃

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

172

—

100

C₂²⋊C₈

—

101

C₄×C₈

—

102

C₄×C₈

C₄×D₄₃

yes

characteristic

103

C₄×C₈

D₁₇₂

yes

characteristic

104

C₄×C₈

C₂×Dic₄₃

yes

characteristic

105

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

106

C₂²×C₄

Dic₄₃⋊C₄

yes

characteristic

107

C₂²×C₄

#10621882

yes

characteristic

108

C₂²×C₄

#10621885

yes

characteristic

109

M₁₆

—

344

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

172

—

114

C₂×C₈

C₄×Dic₄₃

yes

characteristic

115

C₂×C₈

Dic₄₃⋊C₄

yes

characteristic

116

C₂×C₈

C₄⋊Dic₄₃

yes

characteristic

117

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

118

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

119

C₄²

#10621883

yes

characteristic

120

C₄²

#10621884

yes

characteristic

121

C₄²

C₂²⋊Dic₄₃

yes

characteristic

122

C₁₆

—

172

—

123

C₂³

#13063258

yes

characteristic

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₄₃⋊#95

yes

characteristic

129

C₂×C₄

#13063245

yes

characteristic

130

C₂×C₄

#13063246

yes

characteristic

131

C₂×C₄

#13063248

yes

characteristic

132

C₂×C₄

#13063249

yes

characteristic

133

C₂×C₄

#13063256

yes

characteristic

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

344

—

139

C₈

#13063261

yes

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#14582661

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

#14582664

yes

characteristic

149

C₄

#14582671

yes

characteristic

150

C₄

#14582709

yes

—

151

C₂

—

152

C₂

#19132492

yes

characteristic

153

C₂

#19132698

yes

characteristic

154

C₂

#19132700

yes

characteristic

	subgroup	G/H
center	C₂²	#14582661
commutator	C₂×C₈×C₄₃	C₄²
Frattini	C₂×C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#1564	C₂
socle	C₂²×C₄₃	#340
prime radical	C₂³×C₄₃	#107
cosocle	C₂×C₄×C₈×C₄₃	C₂²
hypercenter	#1564	D₄₃
hypocenter	C₄₃	#7295
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1564

subgroup

G/H

center

C₂²

#14582661

commutator

C₂×C₈×C₄₃

C₄²

Frattini

C₂×C₄×C₈

C₂×D₄₃

Fitting

C₄₃×#1564

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄×C₈×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1564

N	H ≅ G/N	type
91. C₄₃	#7295	semidirect

H ≅ G/N

type

91. C₄₃

#7295

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19136398	2
#19133351	2
C₄₃×#1564	2
#7295	43

subgroup

index

#19136398

#19133351

C₄₃×#1564

#7295

Subgroups — #24983843

Conjugacy classes of subgroups

Complements

Maximal subgroups