Group #24987049 — subgroups

Subgroups — #24987049

Order 11008.

330 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 131 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	#19134283	C₂	1	1	yes	maximal, characteristic
2	#19132888	C₂	1	2	yes	maximal
3	#19132426	C₂	1	1	yes	maximal, characteristic
4	#19132423	C₂	1	2	yes	maximal
5	C₄₃×#1275	C₂	1	1	yes	maximal, characteristic
6	#14582952	C₂²	1	2	yes	—
7	C₂×#13063235	C₄	1	2	yes	—
8	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₄₃	C₄	1	2	yes	—
10	#14582745	C₂²	1	1	yes	characteristic
11	#14582621	C₄	1	4	yes	complemented
12	#14582620	C₄	1	4	yes	complemented
13	C₄₃×#431	C₂²	1	2	yes	—
14	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
18	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
19	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
20	#13063235	—	2	4	no	—
21	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
22	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
23	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
24	C₈×Dic₄₃	—	2	4	no	—
25	C₄₃⋊#95	—	2	1	no	—
26	C₄₃⋊#95	—	2	1	no	—
27	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
29	C₄⋊C₈×C₄₃	—	2	2	no	—
30	C₂²⋊C₈×C₄₃	—	2	2	no	—
31	#97×C₄₃	—	2	2	no	—
32	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
33	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
35	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
36	C₂²×Dic₄₃	—	2	2	no	—
37	C₂×C₈×C₄₃	—	2	2	no	—
38	C₂×C₈×C₄₃	—	2	2	no	—
39	C₂×C₈×C₄₃	—	2	4	no	—
40	C₂×C₈×C₄₃	M₁₆	1	4	yes	—
41	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
42	C₄²×C₄₃	#41	1	2	yes	—
43	C₄×Dic₄₃	—	2	2	no	—
44	C₄×Dic₄₃	M₁₆	1	4	yes	—
45	C₂×C₄₃⋊C₈	—	2	2	no	—
46	C₂×C₄₃⋊C₈	—	2	2	no	—
47	C₂×C₄₃⋊C₈	—	2	4	no	—
48	C₂×C₄₃⋊C₈	C₄²	1	1	yes	characteristic
49	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
50	C₂×C₄₃⋊C₈	C₄²	1	1	yes	characteristic
51	C₂³×C₄₃	#117	1	1	yes	characteristic
52	C₂×C₄×C₄₃	—	4	1	no	—
53	C₂×C₄×C₄₃	—	4	1	no	—
54	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₄₃	#117	1	2	yes	—
56	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
57	C₂×C₄×C₄₃	#117	1	2	yes	—
58	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
59	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
60	C₂×Dic₄₃	—	2	4	no	—
61	C₂×Dic₄₃	—	4	2	no	—
62	C₂×Dic₄₃	—	4	2	no	—
63	C₈×C₄₃	—	2	4	no	—
64	C₈×C₄₃	—	4	4	no	—
65	C₄₃⋊C₈	—	2	1	no	—
66	C₄₃⋊C₈	—	2	1	no	—
67	C₄₃⋊C₈	—	2	2	no	—
68	C₄₃⋊C₈	—	4	4	no	—
69	#8140	—	43	1	no	maximal, Sylow
70	C₂²×C₄₃	—	2	1	no	—
71	C₂²×C₄₃	—	2	1	no	—
72	C₂²×C₄₃	#376	1	1	yes	characteristic
73	C₂²×C₄₃	#432	1	2	yes	—
74	C₄×C₄₃	—	2	2	no	—
75	C₄×C₄₃	—	2	2	no	—
76	C₄×C₄₃	C₄×M₁₆	1	1	yes	characteristic
77	C₄×C₄₃	C₄×M₁₆	1	1	yes	characteristic
78	C₄×C₄₃	#432	1	2	yes	—
79	Dic₄₃	—	4	4	no	—
80	#1726	—	43	1	no	—
81	#1452	—	43	2	no	—
82	#1275	—	43	1	no	—
83	#1275	D₄₃	1	1	yes	characteristic
84	#1274	—	43	2	no	—
85	C₂×C₄₃	—	2	2	no	—
86	C₂×C₄₃	#1745	1	1	yes	characteristic
87	C₂×C₄₃	#1747	1	1	yes	characteristic
88	C₂×C₄₃	#1747	1	1	yes	characteristic
89	#431	—	43	2	no	—
90	#431	C₂×D₄₃	1	2	yes	—
91	C₂×#97	—	43	2	no	—
92	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
93	C₂×C₄×C₈	—	43	1	no	—
94	C₂×C₄×C₈	—	43	2	no	—
95	#376	—	43	1	no	—
96	#322	—	43	4	no	—
97	#322	—	43	4	no	—
98	C₄₃	#8140	1	1	yes	characteristic, complemented, Sylow
99	C₂²×C₈	—	43	1	no	—
100	C₂²×C₈	—	43	1	no	—
101	C₂²×C₈	C₄×D₄₃	1	2	yes	—
102	C₂×C₄²	—	43	2	no	—
103	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
104	C₄⋊C₈	—	2	2	no	—
105	C₄⋊C₈	—	86	2	no	—
106	C₂²⋊C₈	—	2	2	no	—
107	C₂²⋊C₈	—	86	2	no	—
108	#97	—	2	2	no	—
109	#97	—	86	4	no	—
110	C₄×C₈	—	43	2	no	—
111	C₄×C₈	—	43	2	no	—
112	C₄×C₈	—	43	4	no	—
113	C₄×C₈	—	86	4	no	—
114	C₄×C₈	C₄×D₄₃	1	4	yes	—
115	#95	—	86	1	no	—
116	#95	—	86	1	no	—
117	C₂²×C₄	—	86	2	no	—
118	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
119	C₂²×C₄	#10621900	1	1	yes	characteristic
120	C₂²×C₄	#10621902	1	1	yes	characteristic
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	2	4	no	—
124	C₂×C₈	—	43	1	no	—
125	C₂×C₈	—	43	1	no	—
126	C₂×C₈	—	43	2	no	—
127	C₂×C₈	—	86	2	no	—
128	C₂×C₈	—	86	2	no	—
129	C₂×C₈	—	86	4	no	—
130	C₂×C₈	#10621872	1	4	yes	—
131	C₄²	—	43	4	no	—
132	C₄²	—	86	2	no	—
133	C₄²	C₂×C₄×D₄₃	1	2	yes	—
134	C₄²	#10621900	1	2	yes	—
135	C₂³	#13063283	1	1	yes	characteristic
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	4	1	no	—
138	C₂×C₄	—	86	4	no	—
139	C₂×C₄	—	172	2	no	—
140	C₂×C₄	—	172	2	no	—
141	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
142	C₂×C₄	#13063281	1	2	yes	—
143	C₂×C₄	#13063281	1	1	yes	characteristic
144	C₂×C₄	#13063283	1	2	yes	—
145	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
146	C₂×C₄	C₂×#10621872	1	2	yes	—
147	C₈	—	2	4	no	—
148	C₈	—	4	4	no	—
149	C₈	—	86	1	no	—
150	C₈	—	86	1	no	—
151	C₈	—	86	2	no	—
152	C₈	—	172	4	no	—
153	C₂²	—	2	1	no	—
154	C₂²	—	2	1	no	—
155	C₂²	#14582744	1	1	yes	characteristic
156	C₂²	#14582955	1	2	yes	—
157	C₄	—	2	2	no	—
158	C₄	—	2	2	no	—
159	C₄	—	172	4	no	—
160	C₄	C₄×#10621872	1	1	yes	characteristic
161	C₄	#14582851	1	1	yes	characteristic
162	C₄	#14582953	1	2	yes	—
163	C₂	—	2	2	no	—
164	C₂	#19134342	1	1	yes	characteristic
165	C₂	#19134349	1	1	yes	characteristic
166	C₂	#19134351	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134283

C₂

yes

maximal, characteristic

#19132888

C₂

yes

maximal

#19132426

C₂

yes

maximal, characteristic

#19132423

C₂

yes

maximal

C₄₃×#1275

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

—

C₂×#13063235

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₄₃

C₄

yes

—

#14582745

C₂²

yes

characteristic

#14582621

C₄

yes

complemented

#14582620

C₄

yes

complemented

C₄₃×#431

C₂²

yes

—

C₂×#97×C₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₃

C₂×C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

#13063235

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₈×Dic₄₃

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

#97×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

C₂²×C₄×C₄₃

yes

C₂²×C₄×C₄₃

yes

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

M₁₆

yes

—

C₄²×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

#41

yes

—

C₄×Dic₄₃

—

C₄×Dic₄₃

M₁₆

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₄²

yes

characteristic

C₂×C₄₃⋊C₈

C₄²

yes

—

C₂×C₄₃⋊C₈

C₄²

yes

characteristic

C₂³×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#8140

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#376

yes

characteristic

C₂²×C₄₃

#432

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×M₁₆

yes

characteristic

C₄×C₄₃

C₄×M₁₆

yes

characteristic

C₄×C₄₃

#432

yes

—

Dic₄₃

—

—

—

—

D₄₃

yes

characteristic

#1274

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×D₄₃

yes

—

C₂×#97

—

C₂×#97

C₂×D₄₃

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

#322

—

#322

—

C₄₃

#8140

yes

characteristic, complemented, Sylow

C₂²×C₈

—

100

C₂²×C₈

—

101

C₂²×C₈

C₄×D₄₃

yes

—

102

C₂×C₄²

—

103

C₂×C₄²

C₂²×D₄₃

yes

characteristic

104

C₄⋊C₈

—

105

C₄⋊C₈

—

106

C₂²⋊C₈

—

107

C₂²⋊C₈

—

108

#97

—

109

#97

—

110

C₄×C₈

—

111

C₄×C₈

—

112

C₄×C₈

—

113

C₄×C₈

—

114

C₄×C₈

C₄×D₄₃

yes

—

115

#95

—

116

#95

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

119

C₂²×C₄

#10621900

yes

characteristic

120

C₂²×C₄

#10621902

yes

characteristic

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

#10621872

yes

—

131

C₄²

—

132

C₄²

—

133

C₄²

C₂×C₄×D₄₃

yes

—

134

C₄²

#10621900

yes

—

135

C₂³

#13063283

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

172

—

140

C₂×C₄

—

172

—

141

C₂×C₄

C₄²×D₄₃

yes

characteristic

142

C₂×C₄

#13063281

yes

—

143

C₂×C₄

#13063281

yes

characteristic

144

C₂×C₄

#13063283

yes

—

145

C₂×C₄

M₁₆×D₄₃

yes

—

146

C₂×C₄

C₂×#10621872

yes

—

147

C₈

—

148

C₈

—

149

C₈

—

150

C₈

—

151

C₈

—

152

C₈

—

172

—

153

C₂²

—

154

C₂²

—

155

C₂²

#14582744

yes

characteristic

156

C₂²

#14582955

yes

—

157

C₄

—

158

C₄

—

159

C₄

—

172

—

160

C₄

C₄×#10621872

yes

characteristic

161

C₄

#14582851

yes

characteristic

162

C₄

#14582953

yes

—

163

C₂

—

164

C₂

#19134342

yes

characteristic

165

C₂

#19134349

yes

characteristic

166

C₂

#19134351

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄²×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1275	C₂
socle	C₂²×C₄₃	#376
prime radical	C₂³×C₄₃	#117
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1275	D₄₃
hypocenter	C₄₃	#8140
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #1275

subgroup

G/H

center

C₂×C₄

C₄²×D₄₃

commutator

C₂×C₄×C₄₃

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1275

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ #1275

N	H ≅ G/N	type
11. #14582621	C₄	semidirect
12. #14582620	C₄	semidirect
98. C₄₃	#8140	semidirect

H ≅ G/N

type

11. #14582621

C₄

semidirect

12. #14582620

C₄

semidirect

98. C₄₃

#8140

semidirect

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

subgroup	index
#19134283	2
#19132888	2
#19132426	2
#19132423	2
C₄₃×#1275	2
#8140	43

subgroup

index

C₄₃×#1275

Subgroups — #24987049

Conjugacy classes of subgroups

Complements

Maximal subgroups