Group #24983898 — subgroups

Subgroups — C₄₃⋊#7317 #24983898

Order 11008.

432 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 67 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	#19134519	C₂	1	2	yes	maximal
2	C₄₃×#1784	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063244	—	2	2	no	—
4	C₂×#13063244	—	2	2	no	—
5	#14582863	C₄	1	4	yes	—
6	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×#101×C₄₃	—	2	2	no	—
8	C₄₃×#407	C₄	1	2	yes	—
9	C₂×#10621877	—	2	4	no	—
10	#13063244	—	4	4	no	—
11	#13063244	—	4	4	no	—
12	C₂²⋊(C₄₃⋊C₈)	—	4	4	no	—
13	C₂²×Q₈×C₄₃	—	4	2	no	—
14	C₂²×Q₈×C₄₃	—	4	4	no	—
15	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
16	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
17	C₂²×Q₈×C₄₃	Q₈	1	1	yes	characteristic
18	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×M₁₆×C₄₃	—	2	2	no	—
21	#101×C₄₃	—	4	4	no	—
22	C₂²⋊C₈×C₄₃	—	4	2	no	—
23	C₂⁴×C₄₃	C₄²	1	1	yes	characteristic
24	C₂×Q₈×C₄₃	—	2	4	no	—
25	C₂×Q₈×C₄₃	—	2	4	no	—
26	C₂×Q₈×C₄₃	—	2	4	no	—
27	C₂×Q₈×C₄₃	—	4	1	no	—
28	C₂×Q₈×C₄₃	—	4	2	no	—
29	C₂×Q₈×C₄₃	—	4	2	no	—
30	C₂×Q₈×C₄₃	—	4	1	no	—
31	C₂×Q₈×C₄₃	—	4	16	no	—
32	C₂²×C₄×C₄₃	—	2	2	no	—
33	C₂²×C₄×C₄₃	—	2	4	no	—
34	C₂²×C₄×C₄₃	—	4	2	no	—
35	C₂²×C₄×C₄₃	—	4	2	no	—
36	C₂²×C₄×C₄₃	—	4	2	no	—
37	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
38	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
40	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
41	M₁₆×C₄₃	—	4	4	no	—
42	C₂×C₈×C₄₃	—	4	2	no	—
43	#10621877	—	4	4	no	—
44	#10621877	—	4	4	no	—
45	C₂×C₄₃⋊C₈	—	4	4	no	—
46	C₂³×C₄₃	—	2	2	no	—
47	C₂³×C₄₃	—	2	1	no	—
48	C₂³×C₄₃	—	4	2	no	—
49	C₂³×C₄₃	#95	1	1	yes	characteristic
50	Q₈×C₄₃	—	4	4	no	—
51	Q₈×C₄₃	—	4	8	no	—
52	Q₈×C₄₃	—	4	4	no	—
53	C₂×C₄×C₄₃	—	2	2	no	—
54	C₂×C₄×C₄₃	—	2	2	no	—
55	C₂×C₄×C₄₃	—	2	2	no	—
56	C₂×C₄×C₄₃	—	2	2	no	—
57	C₂×C₄×C₄₃	—	2	1	no	—
58	C₂×C₄×C₄₃	—	2	2	no	—
59	C₂×C₄×C₄₃	—	2	2	no	—
60	C₂×C₄×C₄₃	—	2	2	no	—
61	C₂×C₄×C₄₃	—	4	8	no	—
62	C₂×C₄×C₄₃	—	4	4	no	—
63	C₂×C₄×C₄₃	#99	1	4	yes	—
64	C₂×C₄×C₄₃	#99	1	2	yes	—
65	C₈×C₄₃	—	8	2	no	—
66	C₄₃⋊C₈	—	8	4	no	—
67	#7317	—	43	1	no	maximal, Sylow
68	C₂²×C₄₃	—	2	4	no	—
69	C₂²×C₄₃	—	2	2	no	—
70	C₂²×C₄₃	—	4	1	no	—
71	C₂²×C₄₃	—	4	2	no	—
72	C₂²×C₄₃	—	4	1	no	—
73	C₂²×C₄₃	—	4	1	no	—
74	C₂²×C₄₃	#342	1	2	yes	—
75	C₂²×C₄₃	#342	1	1	yes	characteristic
76	C₄×C₄₃	—	2	4	no	—
77	C₄×C₄₃	—	2	2	no	—
78	C₄×C₄₃	—	4	2	no	—
79	C₄×C₄₃	—	4	1	no	—
80	#1784	—	43	2	no	—
81	#1784	D₄₃	1	1	yes	characteristic
82	C₂×C₄₃	—	2	2	no	—
83	C₂×C₄₃	—	2	1	no	—
84	C₂×C₄₃	—	4	2	no	—
85	C₂×C₄₃	#1304	1	1	yes	characteristic
86	C₂³×Q₈	C₂×D₄₃	1	1	yes	characteristic
87	C₂×#101	—	2	2	no	—
88	C₂×#101	—	86	2	no	—
89	C₂×#101	—	86	2	no	—
90	#407	—	43	4	no	—
91	#407	Dic₄₃	1	2	yes	—
92	C₄₃	#7317	1	1	yes	characteristic, complemented, Sylow
93	C₂²×Q₈	—	4	4	no	—
94	C₂²×Q₈	—	4	2	no	—
95	C₂²×Q₈	Dic₈₆	1	1	yes	characteristic
96	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
97	C₂²×Q₈	C₂²⋊D₄₃	1	2	yes	—
98	C₂³×C₄	C₄×D₄₃	1	2	yes	—
99	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
100	C₂×M₁₆	—	2	2	no	—
101	C₂×M₁₆	—	86	4	no	—
102	#101	—	4	4	no	—
103	#101	—	172	4	no	—
104	#101	—	172	4	no	—
105	C₂²⋊C₈	—	4	2	no	—
106	C₂²⋊C₈	—	172	4	no	—
107	C₂⁴	C₄×Dic₄₃	1	1	yes	characteristic
108	C₂×Q₈	—	2	4	no	—
109	C₂×Q₈	—	2	4	no	—
110	C₂×Q₈	—	2	4	no	—
111	C₂×Q₈	—	4	2	no	—
112	C₂×Q₈	—	4	1	no	—
113	C₂×Q₈	—	4	1	no	—
114	C₂×Q₈	—	4	2	no	—
115	C₂×Q₈	—	4	16	no	—
116	C₂²×C₄	—	2	4	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	—	4	2	no	—
119	C₂²×C₄	—	4	2	no	—
120	C₂²×C₄	—	4	2	no	—
121	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
122	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
123	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
124	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
125	M₁₆	—	4	4	no	—
126	M₁₆	—	172	4	no	—
127	M₁₆	—	172	4	no	—
128	C₂×C₈	—	4	2	no	—
129	C₂×C₈	—	172	4	no	—
130	C₂³	—	2	2	no	—
131	C₂³	—	2	1	no	—
132	C₂³	—	4	2	no	—
133	C₂³	C₄₃⋊#95	1	1	yes	characteristic
134	Q₈	—	4	8	no	—
135	Q₈	—	4	4	no	—
136	Q₈	—	4	4	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	4	4	no	—
146	C₂×C₄	—	4	8	no	—
147	C₂×C₄	#13063239	1	4	yes	—
148	C₂×C₄	#13063240	1	2	yes	—
149	C₈	—	8	2	no	—
150	C₈	—	344	4	no	—
151	C₂²	—	2	4	no	—
152	C₂²	—	2	2	no	—
153	C₂²	—	4	1	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	4	1	no	—
156	C₂²	—	4	1	no	—
157	C₂²	#14582665	1	2	yes	—
158	C₂²	#14582666	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	2	4	no	—
161	C₄	—	4	2	no	—
162	C₄	—	4	1	no	—
163	C₂	—	2	2	no	—
164	C₂	—	2	1	no	—
165	C₂	—	4	2	no	—
166	C₂	C₄₃⋊#1304	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134519

C₂

yes

maximal

C₄₃×#1784

C₂

yes

maximal, characteristic

C₂×#13063244

—

C₂×#13063244

—

#14582863

C₄

yes

—

C₂³×Q₈×C₄₃

C₂²

yes

characteristic

C₂×#101×C₄₃

—

C₄₃×#407

C₄

yes

—

C₂×#10621877

—

#13063244

—

#13063244

—

C₂²⋊(C₄₃⋊C₈)

—

C₂²×Q₈×C₄₃

—

C₂²×Q₈×C₄₃

—

C₂²×Q₈×C₄₃

D₄

yes

characteristic

C₂²×Q₈×C₄₃

D₄

yes

—

C₂²×Q₈×C₄₃

Q₈

yes

characteristic

C₂³×C₄×C₄₃

C₂×C₄

yes

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₄₃

—

#101×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₂⁴×C₄₃

C₄²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#95

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#99

yes

—

C₂×C₄×C₄₃

#99

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#7317

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#342

yes

—

C₂²×C₄₃

#342

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#1784

—

#1784

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#1304

yes

characteristic

C₂³×Q₈

C₂×D₄₃

yes

—

—

—

—

Dic₄₃

yes

—

C₄₃

#7317

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

Dic₈₆

yes

characteristic

C₂²×Q₈

D₁₇₂

yes

characteristic

C₂²×Q₈

C₂²⋊D₄₃

yes

—

C₂³×C₄

C₄×D₄₃

yes

—

C₂³×C₄

C₂×Dic₄₃

yes

characteristic

100

C₂×M₁₆

—

101

C₂×M₁₆

—

102

#101

—

103

#101

—

172

—

104

#101

—

172

—

105

C₂²⋊C₈

—

106

C₂²⋊C₈

—

172

—

107

C₂⁴

C₄×Dic₄₃

yes

characteristic

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

Dic₄₃⋊C₄

yes

—

122

C₂²×C₄

C₄⋊Dic₄₃

yes

characteristic

123

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

124

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

125

M₁₆

—

126

M₁₆

—

172

—

127

M₁₆

—

172

—

128

C₂×C₈

—

129

C₂×C₈

—

172

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

C₄₃⋊#95

yes

characteristic

134

Q₈

—

135

Q₈

—

136

Q₈

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

#13063239

yes

—

148

C₂×C₄

#13063240

yes

—

149

C₈

—

150

C₈

—

344

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

#14582665

yes

—

158

C₂²

#14582666

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₂

—

164

C₂

—

165

C₂

—

166

C₂

C₄₃⋊#1304

yes

characteristic

	subgroup	G/H
center	C₂	C₄₃⋊#1304
commutator, prime radical	C₂⁴×C₄₃	C₄²
Frattini	C₂³×Q₈	C₂×D₄₃
Fitting	C₄₃×#1784	C₂
socle	C₂×C₄₃	#1304
cosocle	C₂³×Q₈×C₄₃	C₂²
hypercenter	#1784	D₄₃
hypocenter	C₄₃	#7317
LCS	G ▷ C₂⁴×C₄₃ ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×Q₈ ◁ #1784

subgroup

G/H

center

C₂

C₄₃⋊#1304

commutator, prime radical

C₂⁴×C₄₃

C₄²

Frattini

C₂³×Q₈

C₂×D₄₃

Fitting

C₄₃×#1784

C₂

socle

C₂×C₄₃

#1304

cosocle

C₂³×Q₈×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂⁴×C₄₃ ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×Q₈ ◁ #1784

N	H ≅ G/N	type
92. C₄₃	#7317	semidirect

H ≅ G/N

type

92. C₄₃

#7317

semidirect

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

subgroup	index
#19134519	2
C₄₃×#1784	2
#7317	43

subgroup

index

#19134519

C₄₃×#1784

#7317

Subgroups — C₄₃⋊#7317 #24983898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C43⋊#7317 #24983898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃⋊#7317 #24983898