Group #25008160 — subgroups

Subgroups — #25008160

Order 11008.

220 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 99 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	#364×D₄₃	C₂	1	2	yes	maximal
2	#19136188	C₂	1	1	yes	maximal, characteristic
3	#19132663	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132662	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063264	C₄	1	1	yes	characteristic
7	C₂×#13063264	C₄	1	1	yes	characteristic
8	M₃₂×D₄₃	—	2	2	no	—
9	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
10	#14582720	C₂²	1	2	yes	—
11	#14582719	—	2	2	no	—
12	#14582675	C₂²	1	1	yes	characteristic
13	C₁₆×Dic₄₃	C₄	1	1	yes	characteristic
14	C₁₆×Dic₄₃	C₄	1	1	yes	characteristic
15	C₄₃×#364	C₂²	1	2	yes	—
16	C₄₃×#346	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
19	C₄²×D₄₃	Q₈	1	1	yes	characteristic
20	#13063265	—	2	2	no	—
21	#13063264	—	2	2	no	—
22	#13063264	—	4	2	no	—
23	#13063264	C₈	1	4	yes	—
24	C₂×C₄₃⋊C₁₆	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄₃⋊C₁₆	C₂×C₄	1	1	yes	characteristic
26	C₁₆×D₄₃	—	4	2	no	—
27	C₄×C₄₃⋊C₈	Q₈	1	1	yes	characteristic
28	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₄₃	D₄	1	1	yes	characteristic
30	M₃₂×C₄₃	—	2	2	no	—
31	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
33	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
34	C₂×C₄×D₄₃	—	2	1	no	—
35	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
39	C₄×Dic₄₃	—	2	1	no	—
40	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₄₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
43	C₈×D₄₃	C₂×C₈	1	2	yes	—
44	C₈×D₄₃	M₁₆	1	2	yes	—
45	C₈×D₄₃	SD₁₆	1	2	yes	—
46	C₈×D₄₃	SD₁₆	1	2	yes	—
47	C₁₆×C₄₃	—	2	1	no	—
48	C₁₆×C₄₃	—	4	2	no	—
49	C₁₆×C₄₃	C₂×C₈	1	2	yes	—
50	C₄₃⋊C₁₆	—	2	1	no	—
51	C₄₃⋊C₁₆	—	4	2	no	—
52	C₄₃⋊C₁₆	C₂×C₈	1	2	yes	—
53	C₂²×D₄₃	#108	1	1	yes	characteristic
54	C₂×C₄×C₄₃	—	2	1	no	—
55	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×Dic₄₃	—	2	1	no	—
57	C₂×Dic₄₃	#108	1	1	yes	characteristic
58	C₄×D₄₃	—	4	2	no	—
59	C₄×D₄₃	C₄⋊C₈	1	2	yes	—
60	C₄×D₄₃	#106	1	2	yes	—
61	C₈×C₄₃	C₂²×C₈	1	1	yes	characteristic
62	C₈×C₄₃	C₂×M₁₆	1	1	yes	characteristic
63	C₈×C₄₃	C₂×SD₁₆	1	2	yes	—
64	C₄₃⋊C₈	C₄⋊C₈	1	2	yes	—
65	C₄₃⋊C₈	#106	1	1	yes	characteristic
66	C₄₃⋊C₈	#106	1	1	yes	characteristic
67	#12002	—	43	1	no	maximal, Sylow
68	C₂²×C₄₃	C₂×#108	1	1	yes	characteristic
69	C₂×D₄₃	—	4	1	no	—
70	C₂×D₄₃	#334	1	2	yes	—
71	C₄×C₄₃	—	4	1	no	—
72	C₄×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
73	C₄×C₄₃	C₂×#106	1	1	yes	characteristic
74	Dic₄₃	—	2	2	no	—
75	Dic₄₃	#334	1	2	yes	—
76	C₂×#364	—	43	2	no	—
77	C₄×M₃₂	—	43	1	no	—
78	#1369	—	43	2	no	—
79	#1369	—	43	1	no	—
80	#1369	D₄₃	1	1	yes	characteristic, complemented
81	C₂×C₄₃	—	2	1	no	—
82	C₂×C₄₃	C₂×#334	1	1	yes	characteristic
83	D₄₃	—	2	2	no	—
84	C₂×M₃₂	—	43	1	no	—
85	C₂×M₃₂	—	43	1	no	—
86	C₂×M₃₂	—	86	2	no	—
87	C₂×C₄×C₈	—	43	1	no	—
88	#364	—	43	2	no	—
89	#364	—	86	2	no	—
90	#364	C₂×D₄₃	1	2	yes	—
91	#346	—	43	1	no	—
92	#346	C₂×D₄₃	1	1	yes	characteristic
93	C₄×C₁₆	—	43	1	no	—
94	C₄×C₁₆	—	43	1	no	—
95	C₄₃	#12002	1	1	yes	characteristic, complemented, Sylow
96	C₂²×C₈	—	43	1	no	—
97	C₂²×C₈	—	43	1	no	—
98	C₂×C₄²	—	43	1	no	—
99	M₃₂	—	2	2	no	—
100	M₃₂	—	43	4	no	—
101	M₃₂	—	86	2	no	—
102	M₃₂	—	86	2	no	—
103	M₃₂	—	172	2	no	—
104	C₂×C₁₆	—	43	1	no	—
105	C₂×C₁₆	—	43	1	no	—
106	C₂×C₁₆	—	172	2	no	—
107	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
108	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
109	C₄×C₈	—	43	1	no	—
110	C₄×C₈	—	43	1	no	—
111	C₄×C₈	—	43	1	no	—
112	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
113	C₂²×C₄	—	43	1	no	—
114	C₂²×C₄	—	86	1	no	—
115	C₂×C₈	—	43	1	no	—
116	C₂×C₈	—	43	1	no	—
117	C₂×C₈	—	43	2	no	—
118	C₂×C₈	—	43	2	no	—
119	C₂×C₈	—	43	2	no	—
120	C₂×C₈	—	43	2	no	—
121	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
122	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
123	C₄²	—	43	1	no	—
124	C₄²	—	86	1	no	—
125	C₄²	Q₈×D₄₃	1	1	yes	characteristic
126	C₁₆	—	2	1	no	—
127	C₁₆	—	4	2	no	—
128	C₁₆	—	43	2	no	—
129	C₁₆	—	86	1	no	—
130	C₁₆	—	172	2	no	—
131	C₁₆	C₈×D₄₃	1	2	yes	—
132	C₂³	—	43	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	43	1	no	—
135	C₂×C₄	—	43	2	no	—
136	C₂×C₄	—	43	2	no	—
137	C₂×C₄	—	86	1	no	—
138	C₂×C₄	—	172	2	no	—
139	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
140	C₈	—	43	2	no	—
141	C₈	—	43	1	no	—
142	C₈	—	43	1	no	—
143	C₈	C₂×C₈×D₄₃	1	1	yes	characteristic
144	C₈	M₁₆×D₄₃	1	1	yes	characteristic
145	C₈	SD₁₆×D₄₃	1	2	yes	—
146	C₂²	—	43	2	no	—
147	C₂²	—	172	1	no	—
148	C₂²	#108×D₄₃	1	1	yes	characteristic
149	C₄	—	4	1	no	—
150	C₄	—	43	2	no	—
151	C₄	—	86	2	no	—
152	C₄	C₄⋊C₈×D₄₃	1	1	yes	characteristic
153	C₄	#106×D₄₃	1	1	yes	characteristic
154	C₂	—	2	1	no	—
155	C₂	—	86	2	no	—
156	C₂	#334×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#364×D₄₃

C₂

yes

maximal

#19136188

C₂

yes

maximal, characteristic

#19132663

C₂

yes

maximal, characteristic, complemented

#19132662

C₂

yes

maximal, complemented

C₄₃×#1369

C₂

yes

maximal, characteristic, complemented

C₂×#13063264

C₄

yes

characteristic

C₂×#13063264

C₄

yes

characteristic

M₃₂×D₄₃

—

C₄×C₈×D₄₃

C₂²

yes

characteristic

#14582720

C₂²

yes

—

#14582719

—

#14582675

C₂²

yes

characteristic

C₁₆×Dic₄₃

C₄

yes

characteristic

C₁₆×Dic₄₃

C₄

yes

characteristic

C₄₃×#364

C₂²

yes

—

C₄₃×#346

C₂²

yes

characteristic

C₂×C₈×D₄₃

C₂×C₄

yes

characteristic

C₂×C₈×D₄₃

D₄

yes

characteristic

C₄²×D₄₃

Q₈

yes

—

—

—

C₈

yes

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

characteristic

C₁₆×D₄₃

—

C₄×C₄₃⋊C₈

Q₈

yes

characteristic

C₈×Dic₄₃

C₂×C₄

yes

characteristic

C₈×Dic₄₃

D₄

yes

characteristic

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄×Dic₄₃

—

C₄×Dic₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

characteristic

C₈×D₄₃

C₂×C₈

yes

—

C₈×D₄₃

M₁₆

yes

—

C₈×D₄₃

SD₁₆

yes

—

C₈×D₄₃

SD₁₆

yes

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

C₂×C₈

yes

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

C₂×C₈

yes

—

C₂²×D₄₃

#108

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

#108

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

C₄⋊C₈

yes

—

C₄×D₄₃

#106

yes

—

C₈×C₄₃

C₂²×C₈

yes

characteristic

C₈×C₄₃

C₂×M₁₆

yes

characteristic

C₈×C₄₃

C₂×SD₁₆

yes

—

C₄₃⋊C₈

C₄⋊C₈

yes

—

C₄₃⋊C₈

yes

C₄₃⋊C₈

yes

—

C₂²×C₄₃

yes

C₂×D₄₃

—

C₂×D₄₃

#334

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₈

yes

characteristic

C₄×C₄₃

C₂×#106

yes

characteristic

Dic₄₃

—

Dic₄₃

#334

yes

—

C₂×#364

—

C₄×M₃₂

—

#1369

—

#1369

—

#1369

D₄₃

yes

characteristic, complemented

C₂×C₄₃

—

C₂×C₄₃

C₂×#334

yes

characteristic

D₄₃

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×C₄×C₈

—

#364

—

#364

—

#364

C₂×D₄₃

yes

—

#346

—

#346

C₂×D₄₃

yes

characteristic

C₄×C₁₆

—

C₄×C₁₆

—

C₄₃

#12002

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

100

M₃₂

—

101

M₃₂

—

102

M₃₂

—

103

M₃₂

—

172

—

104

C₂×C₁₆

—

105

C₂×C₁₆

—

106

C₂×C₁₆

—

172

—

107

C₂×C₁₆

C₄×D₄₃

yes

characteristic

108

C₂×C₁₆

C₄×D₄₃

yes

characteristic

109

C₄×C₈

—

110

C₄×C₈

—

111

C₄×C₈

—

112

C₄×C₈

C₂²×D₄₃

yes

characteristic

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

122

C₂×C₈

D₄×D₄₃

yes

characteristic

123

C₄²

—

124

C₄²

—

125

C₄²

Q₈×D₄₃

yes

characteristic

126

C₁₆

—

127

C₁₆

—

128

C₁₆

—

129

C₁₆

—

130

C₁₆

—

172

—

131

C₁₆

C₈×D₄₃

yes

—

132

C₂³

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

172

—

139

C₂×C₄

C₄⋊C₄×D₄₃

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

—

143

C₈

C₂×C₈×D₄₃

yes

characteristic

144

C₈

M₁₆×D₄₃

yes

characteristic

145

C₈

SD₁₆×D₄₃

yes

—

146

C₂²

—

147

C₂²

—

172

—

148

C₂²

#108×D₄₃

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

C₄⋊C₈×D₄₃

yes

characteristic

153

C₄

#106×D₄₃

yes

characteristic

154

C₂

—

155

C₂

—

156

C₂

#334×D₄₃

yes

characteristic

	subgroup	G/H
center	C₄	#106×D₄₃
commutator	C₈×C₄₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×#1369	C₂
socle	C₂×C₄₃	C₂×#334
prime radical	C₂²×D₄₃	#108
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#1369	D₄₃
hypocenter	C₄₃	#12002
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1369

subgroup

G/H

center

C₄

#106×D₄₃

commutator

C₈×C₄₃

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₄₃×#1369

C₂

C₂×C₄₃

C₂²×D₄₃

C₄×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1369

N	H ≅ G/N	type
3. #19132663	C₂	semidirect
4. #19132662	C₂	semidirect
5. C₄₃×#1369	C₂	semidirect
80. #1369	D₄₃	semidirect
95. C₄₃	#12002	semidirect

H ≅ G/N

type

3. #19132663

C₂

semidirect

4. #19132662

C₂

semidirect

5. C₄₃×#1369

C₂

semidirect

80. #1369

D₄₃

semidirect

95. C₄₃

#12002

semidirect

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

subgroup	index
#364×D₄₃	2
#19136188	2
#19132663	2
#19132662	2
C₄₃×#1369	2
#12002	43

subgroup

index

#364×D₄₃

C₄₃×#1369

Subgroups — #25008160

Conjugacy classes of subgroups

Complements

Maximal subgroups