Group #25005589 — subgroups

Subgroups — #25005589

Order 11008.

322 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 163 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	C₄×#13063264	C₂	1	2	yes	maximal
2	C₈²×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19132514	C₂	1	2	yes	maximal, complemented
4	#19132513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1312	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063264	C₄	1	4	yes	—
7	C₄×C₈×D₄₃	C₄	1	1	yes	characteristic
8	C₄×C₈×D₄₃	C₄	1	1	yes	characteristic
9	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
10	#14582674	C₄	1	4	yes	—
11	C₄×C₄₃⋊C₁₆	C₂²	1	2	yes	—
12	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₁₆×C₄₃	C₂²	1	2	yes	—
16	C₈²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₄₃	C₈	1	2	yes	—
18	C₂×C₈×D₄₃	C₈	1	2	yes	—
19	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
20	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
21	#13063264	—	2	8	no	—
22	C₂×C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
23	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₈×Dic₄₃	C₈	1	2	yes	—
27	C₈×Dic₄₃	C₈	1	2	yes	—
28	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
29	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	—
30	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
33	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
34	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
37	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
39	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
41	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
42	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
44	C₂×C₄₃⋊C₈	C₂×C₈	1	2	yes	—
45	C₂×C₄₃⋊C₈	C₂×C₈	1	2	yes	—
46	C₈×D₄₃	—	2	4	no	—
47	C₈×D₄₃	—	2	4	no	—
48	C₈×D₄₃	M₁₆	1	8	yes	—
49	C₁₆×C₄₃	—	2	4	no	—
50	C₄₃⋊C₁₆	—	2	4	no	—
51	C₂²×D₄₃	C₄×C₈	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
54	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
55	C₂×Dic₄₃	C₄×C₈	1	1	yes	characteristic
56	C₂×Dic₄₃	C₄×C₈	1	1	yes	characteristic
57	C₂×Dic₄₃	C₄×C₈	1	1	yes	characteristic
58	C₄×D₄₃	—	2	2	no	—
59	C₄×D₄₃	—	2	2	no	—
60	C₄×D₄₃	#97	1	4	yes	—
61	C₈×C₄₃	—	2	2	no	—
62	C₈×C₄₃	M₃₂	1	4	yes	complemented
63	C₈×C₄₃	C₂×M₁₆	1	4	yes	—
64	C₄₃⋊C₈	—	2	2	no	—
65	C₄₃⋊C₈	#97	1	4	yes	—
66	C₄₃⋊C₈	M₃₂	1	4	yes	complemented
67	#11402	—	43	1	no	maximal, Sylow
68	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
69	C₂×D₄₃	—	2	1	no	—
70	C₂×D₄₃	—	2	1	no	—
71	C₂×D₄₃	#322	1	2	yes	—
72	C₄×C₄₃	C₂×#97	1	2	yes	—
73	C₄×C₄₃	C₂×M₃₂	1	2	yes	—
74	C₄×C₄₃	C₂×M₃₂	1	2	yes	—
75	Dic₄₃	—	2	1	no	—
76	Dic₄₃	—	2	1	no	—
77	Dic₄₃	#322	1	2	yes	—
78	C₄×M₃₂	—	43	2	no	—
79	C₂×C₈²	—	43	1	no	—
80	#1312	—	43	2	no	—
81	#1312	—	43	1	no	—
82	#1312	D₄₃	1	1	yes	characteristic, complemented
83	C₂×C₄₃	C₂×#322	1	1	yes	characteristic
84	C₂×C₄₃	C₄×M₃₂	1	1	yes	characteristic
85	C₂×C₄₃	C₄×M₃₂	1	1	yes	characteristic
86	D₄₃	—	2	2	no	—
87	C₂×M₃₂	—	43	4	no	—
88	C₂×C₄×C₈	—	43	1	no	—
89	C₂×C₄×C₈	—	43	1	no	—
90	C₂×C₄×C₈	—	43	1	no	—
91	#346	—	43	4	no	—
92	C₄×C₁₆	—	43	2	no	—
93	C₄×C₁₆	C₂×D₄₃	1	2	yes	—
94	C₈²	—	43	1	no	—
95	C₈²	—	43	1	no	—
96	C₈²	—	43	1	no	—
97	C₈²	C₂×D₄₃	1	1	yes	characteristic
98	C₄₃	#11402	1	1	yes	characteristic, complemented, Sylow
99	C₂²×C₈	—	43	2	no	—
100	C₂²×C₈	—	43	2	no	—
101	C₂²×C₈	—	43	2	no	—
102	C₂×C₄²	—	43	1	no	—
103	M₃₂	—	86	8	no	—
104	C₂×C₁₆	—	43	4	no	—
105	C₂×C₁₆	C₄×D₄₃	1	4	yes	—
106	C₄×C₈	—	43	2	no	—
107	C₄×C₈	—	43	2	no	—
108	C₄×C₈	—	43	2	no	—
109	C₄×C₈	—	43	1	no	—
110	C₄×C₈	—	43	1	no	—
111	C₄×C₈	—	43	1	no	—
112	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
113	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
114	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
115	C₂²×C₄	—	43	1	no	—
116	C₂²×C₄	—	43	1	no	—
117	C₂²×C₄	—	43	1	no	—
118	C₂×C₈	—	43	2	no	—
119	C₂×C₈	—	43	2	no	—
120	C₂×C₈	—	43	8	no	—
121	C₂×C₈	—	43	2	no	—
122	C₂×C₈	—	86	4	no	—
123	C₂×C₈	—	86	4	no	—
124	C₂×C₈	C₈×D₄₃	1	2	yes	—
125	C₂×C₈	C₈×D₄₃	1	2	yes	—
126	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
127	C₄²	—	43	1	no	—
128	C₄²	—	43	1	no	—
129	C₄²	—	43	1	no	—
130	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
131	C₁₆	—	2	4	no	—
132	C₁₆	—	86	4	no	—
133	C₂³	—	43	1	no	—
134	C₂×C₄	—	43	1	no	—
135	C₂×C₄	—	43	4	no	—
136	C₂×C₄	—	43	1	no	—
137	C₂×C₄	—	43	1	no	—
138	C₂×C₄	—	86	2	no	—
139	C₂×C₄	—	86	2	no	—
140	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
141	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
142	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
143	C₈	—	2	2	no	—
144	C₈	—	43	4	no	—
145	C₈	—	43	4	no	—
146	C₈	—	86	2	no	—
147	C₈	#13063264	1	4	yes	complemented
148	C₈	M₁₆×D₄₃	1	4	yes	—
149	C₂²	—	43	2	no	—
150	C₂²	—	86	1	no	—
151	C₂²	—	86	1	no	—
152	C₂²	C₄×C₈×D₄₃	1	1	yes	characteristic
153	C₄	—	43	2	no	—
154	C₄	—	86	1	no	—
155	C₄	—	86	1	no	—
156	C₄	#97×D₄₃	1	2	yes	—
157	C₄	M₃₂×D₄₃	1	2	yes	—
158	C₄	C₂×#13063264	1	2	yes	—
159	C₂	—	86	2	no	—
160	C₂	#322×D₄₃	1	1	yes	characteristic
161	C₂	C₄×#13063264	1	1	yes	characteristic
162	C₂	#19136188	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063264

C₂

yes

maximal

C₈²×D₄₃

C₂

yes

maximal, characteristic

#19132514

C₂

yes

maximal, complemented

#19132513

C₂

yes

maximal, characteristic, complemented

C₄₃×#1312

C₂

yes

maximal, characteristic, complemented

C₂×#13063264

C₄

yes

—

C₄×C₈×D₄₃

C₄

yes

characteristic

C₄×C₈×D₄₃

C₄

yes

characteristic

C₄×C₈×D₄₃

C₂²

yes

characteristic

#14582674

C₄

yes

—

C₄×C₄₃⋊C₁₆

C₂²

yes

—

C₈×C₄₃⋊C₈

C₄

yes

characteristic

C₈×C₄₃⋊C₈

C₄

yes

characteristic

C₈×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₁₆×C₄₃

C₂²

yes

—

C₈²×C₄₃

C₂²

yes

characteristic

C₂×C₈×D₄₃

C₈

yes

—

C₂×C₈×D₄₃

C₈

yes

—

C₂×C₈×D₄₃

C₂×C₄

yes

—

C₄²×D₄₃

C₂×C₄

yes

characteristic

#13063264

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₈×Dic₄₃

C₈

yes

—

C₈×Dic₄₃

C₈

yes

—

C₈×Dic₄₃

C₂×C₄

yes

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄×D₄₃

C₄²

yes

characteristic

C₂×C₄×D₄₃

C₂×C₈

yes

characteristic

C₂×C₄×D₄₃

C₂×C₈

yes

characteristic

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄×Dic₄₃

C₄²

yes

characteristic

C₄×Dic₄₃

C₂×C₈

yes

characteristic

C₄×Dic₄₃

C₂×C₈

yes

characteristic

C₂×C₄₃⋊C₈

C₄²

yes

—

C₂×C₄₃⋊C₈

C₂×C₈

yes

—

C₂×C₄₃⋊C₈

C₂×C₈

yes

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

M₁₆

yes

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₈

yes

characteristic

C₂×Dic₄₃

C₄×C₈

yes

characteristic

C₂×Dic₄₃

C₄×C₈

yes

characteristic

C₂×Dic₄₃

C₄×C₈

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

#97

yes

—

C₈×C₄₃

—

C₈×C₄₃

M₃₂

yes

complemented

C₈×C₄₃

C₂×M₁₆

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

#97

yes

—

C₄₃⋊C₈

M₃₂

yes

complemented

#11402

—

maximal, Sylow

C₂²×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

#322

yes

—

C₄×C₄₃

C₂×#97

yes

—

C₄×C₄₃

C₂×M₃₂

yes

—

C₄×C₄₃

C₂×M₃₂

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#322

yes

—

C₄×M₃₂

—

C₂×C₈²

—

#1312

—

#1312

—

#1312

D₄₃

yes

characteristic, complemented

C₂×C₄₃

C₂×#322

yes

characteristic

C₂×C₄₃

C₄×M₃₂

yes

characteristic

C₂×C₄₃

C₄×M₃₂

yes

characteristic

D₄₃

—

C₂×M₃₂

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₄₃

yes

—

C₈²

—

C₈²

—

C₈²

—

C₈²

C₂×D₄₃

yes

characteristic

C₄₃

#11402

yes

characteristic, complemented, Sylow

C₂²×C₈

—

100

C₂²×C₈

—

101

C₂²×C₈

—

102

C₂×C₄²

—

103

M₃₂

—

104

C₂×C₁₆

—

105

C₂×C₁₆

C₄×D₄₃

yes

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

—

110

C₄×C₈

—

111

C₄×C₈

—

112

C₄×C₈

C₄×D₄₃

yes

characteristic

113

C₄×C₈

C₄×D₄₃

yes

characteristic

114

C₄×C₈

C₂²×D₄₃

yes

characteristic

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

C₈×D₄₃

yes

—

125

C₂×C₈

C₈×D₄₃

yes

—

126

C₂×C₈

C₂×C₄×D₄₃

yes

—

127

C₄²

—

128

C₄²

—

129

C₄²

—

130

C₄²

C₂×C₄×D₄₃

yes

characteristic

131

C₁₆

—

132

C₁₆

—

133

C₂³

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

C₄²×D₄₃

yes

characteristic

141

C₂×C₄

C₂×C₈×D₄₃

yes

characteristic

142

C₂×C₄

C₂×C₈×D₄₃

yes

characteristic

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

#13063264

yes

complemented

148

C₈

M₁₆×D₄₃

yes

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

C₄×C₈×D₄₃

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

#97×D₄₃

yes

—

157

C₄

M₃₂×D₄₃

yes

—

158

C₄

C₂×#13063264

yes

—

159

C₂

—

160

C₂

#322×D₄₃

yes

characteristic

161

C₂

C₄×#13063264

yes

characteristic

162

C₂

#19136188

yes

characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂×C₄×C₈
Fitting	C₄₃×#1312	C₂
prime radical	C₂²×D₄₃	C₄×C₈
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#1312	D₄₃
hypocenter	C₄₃	#11402
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ #1312

subgroup

G/H

center, Frattini

C₄×C₈

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂×C₄×C₈

Fitting

C₄₃×#1312

C₂

prime radical

C₂²×D₄₃

C₄×C₈

cosocle

C₄×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₄×C₈ ◁ #1312

N	H ≅ G/N	type
3. #19132514	C₂	semidirect
4. #19132513	C₂	semidirect
5. C₄₃×#1312	C₂	semidirect
62. C₈×C₄₃	M₃₂	semidirect
66. C₄₃⋊C₈	M₃₂	semidirect
82. #1312	D₄₃	semidirect
98. C₄₃	#11402	semidirect
147. C₈	#13063264	semidirect

H ≅ G/N

type

3. #19132514

C₂

semidirect

4. #19132513

C₂

semidirect

5. C₄₃×#1312

C₂

semidirect

62. C₈×C₄₃

M₃₂

semidirect

66. C₄₃⋊C₈

M₃₂

semidirect

82. #1312

D₄₃

semidirect

98. C₄₃

#11402

semidirect

147. C₈

#13063264

semidirect

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

subgroup	index
C₄×#13063264	2
C₈²×D₄₃	2
#19132514	2
#19132513	2
C₄₃×#1312	2
#11402	43

subgroup

index

C₈²×D₄₃

C₄₃×#1312

Subgroups — #25005589

Conjugacy classes of subgroups

Complements

Maximal subgroups