Group #25012985 — subgroups

Subgroups — #25012985

Order 11008.

282 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 119 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	C₂×C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	#19134765	C₂	1	2	yes	maximal
3	#19132689	C₂	1	1	yes	maximal, characteristic
4	#19132688	C₂	1	2	yes	maximal
5	C₄₃×#1381	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×#13063261	C₂²	1	2	yes	—
8	C₂×#13063260	—	2	2	no	—
9	#14582922	—	2	2	no	—
10	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
11	C₁₆×Dic₄₃	C₄	1	2	yes	—
12	C₁₆×Dic₄₃	C₄	1	2	yes	—
13	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#108×C₄₃	C₂²	1	2	yes	—
15	C₂×#10621877	—	2	2	no	—
16	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
17	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
18	C₂×C₄₃⋊C₁₆	—	2	2	no	—
19	C₂×C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
20	#13063261	—	2	2	no	—
21	#13063261	—	2	2	no	—
22	#13063260	—	4	4	no	—
23	Dic₄₃⋊C₈	—	4	4	no	—
24	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
25	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
26	C₈×Dic₄₃	Q₈	1	1	yes	characteristic
27	C₈×Dic₄₃	Q₈	1	1	yes	characteristic
28	C₂×M₁₆×C₄₃	—	2	2	no	—
29	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	C₂×C₁₆×C₄₃	—	2	2	no	—
31	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
32	#108×C₄₃	—	2	2	no	—
33	#108×C₄₃	—	2	2	no	—
34	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂²×Dic₄₃	Q₁₆	1	2	yes	—
36	M₁₆×C₄₃	—	4	2	no	—
37	M₁₆×C₄₃	—	4	2	no	—
38	C₂×C₈×C₄₃	—	4	2	no	—
39	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₈×C₄₃	#41	1	2	yes	—
42	C₂×C₈×C₄₃	#41	1	2	yes	—
43	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
44	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
45	C₄×Dic₄₃	D₈	1	2	yes	—
46	#10621877	—	4	2	no	—
47	#10621877	—	4	2	no	—
48	C₂×C₄₃⋊C₈	—	4	2	no	—
49	C₂×C₄₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄₃⋊C₈	SD₁₆	1	4	yes	—
52	C₁₆×C₄₃	—	2	2	no	—
53	C₄₃⋊C₁₆	—	2	2	no	—
54	C₂³×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
55	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#124	1	2	yes	—
57	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
58	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
59	C₂×Dic₄₃	—	2	4	no	—
60	C₂×Dic₄₃	#107	1	2	yes	—
61	C₂×Dic₄₃	#107	1	2	yes	—
62	C₈×C₄₃	—	8	2	no	—
63	C₈×C₄₃	#117	1	1	yes	characteristic
64	C₈×C₄₃	#117	1	1	yes	characteristic
65	C₈×C₄₃	#125	1	2	yes	—
66	C₄₃⋊C₈	—	8	2	no	—
67	C₄₃⋊C₈	#106	1	2	yes	—
68	C₄₃⋊C₈	#106	1	2	yes	—
69	#12891	—	43	1	no	maximal, Sylow
70	C₂²×C₄₃	—	2	2	no	—
71	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
72	C₂²×C₄₃	#487	1	2	yes	—
73	C₄×C₄₃	#382	1	1	yes	characteristic
74	C₄×C₄₃	C₂×#106	1	1	yes	characteristic
75	C₄×C₄₃	#486	1	2	yes	—
76	Dic₄₃	—	2	2	no	—
77	Dic₄₃	#368	1	4	yes	—
78	C₂×C₄×C₁₆	—	43	1	no	—
79	#1848	—	43	2	no	—
80	#1381	—	43	1	no	—
81	#1381	—	43	2	no	—
82	#1381	D₄₃	1	1	yes	characteristic
83	C₂×C₄₃	—	2	2	no	—
84	C₂×C₄₃	#1834	1	1	yes	characteristic
85	C₂×C₄₃	C₂×#368	1	2	yes	—
86	C₂²×C₁₆	—	43	1	no	—
87	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
88	C₂×#108	—	43	2	no	—
89	C₂×#108	—	86	2	no	—
90	C₂×#108	C₂×D₄₃	1	2	yes	—
91	#423	—	86	2	no	—
92	C₂×C₄×C₈	—	43	1	no	—
93	C₄×C₁₆	—	43	2	no	—
94	C₄×C₁₆	—	43	2	no	—
95	C₄₃	#12891	1	1	yes	characteristic, complemented, Sylow
96	C₂×M₁₆	—	2	2	no	—
97	C₂×M₁₆	—	86	2	no	—
98	C₂²×C₈	—	43	1	no	—
99	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
100	C₂×C₄²	—	43	1	no	—
101	C₂×C₁₆	—	2	2	no	—
102	C₂×C₁₆	—	43	2	no	—
103	C₂×C₁₆	—	86	2	no	—
104	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
105	#108	—	2	2	no	—
106	#108	—	2	2	no	—
107	#108	—	86	2	no	—
108	#108	—	86	2	no	—
109	#108	—	172	4	no	—
110	C₄⋊C₈	—	172	4	no	—
111	C₄×C₈	—	43	1	no	—
112	C₄×C₈	—	43	1	no	—
113	C₄×C₈	—	43	1	no	—
114	C₄×C₈	—	43	1	no	—
115	C₂²×C₄	—	43	2	no	—
116	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
117	M₁₆	—	4	2	no	—
118	M₁₆	—	4	2	no	—
119	M₁₆	—	172	2	no	—
120	M₁₆	—	172	2	no	—
121	C₂×C₈	—	4	2	no	—
122	C₂×C₈	—	43	1	no	—
123	C₂×C₈	—	43	1	no	—
124	C₂×C₈	—	43	4	no	—
125	C₂×C₈	—	172	2	no	—
126	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
127	C₂×C₈	#10621898	1	2	yes	—
128	C₂×C₈	#10621900	1	2	yes	—
129	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
130	C₄²	—	43	1	no	—
131	C₄²	—	43	1	no	—
132	C₄²	—	43	2	no	—
133	C₁₆	—	2	2	no	—
134	C₁₆	—	86	2	no	—
135	C₂³	Q₁₆×D₄₃	1	1	yes	characteristic
136	C₂×C₄	—	43	2	no	—
137	C₂×C₄	—	43	2	no	—
138	C₂×C₄	—	86	4	no	—
139	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
140	C₂×C₄	#13063311	1	2	yes	—
141	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
142	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
143	C₈	—	8	2	no	—
144	C₈	—	43	2	no	—
145	C₈	—	43	2	no	—
146	C₈	—	344	2	no	—
147	C₈	#13063281	1	1	yes	characteristic
148	C₈	#13063282	1	1	yes	characteristic
149	C₈	#13063315	1	2	yes	—
150	C₂²	—	2	2	no	—
151	C₂²	#107×D₄₃	1	1	yes	characteristic
152	C₂²	#14583248	1	2	yes	—
153	C₄	—	43	4	no	—
154	C₄	—	86	2	no	—
155	C₄	#14582763	1	1	yes	characteristic
156	C₄	#106×D₄₃	1	1	yes	characteristic
157	C₄	#14583244	1	2	yes	—
158	C₂	—	2	2	no	—
159	C₂	#19134721	1	1	yes	characteristic
160	C₂	#368×D₄₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×Dic₄₃

C₂

yes

maximal, characteristic

#19134765

C₂

yes

maximal

#19132689

C₂

yes

maximal, characteristic

#19132688

C₂

yes

maximal

C₄₃×#1381

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×#13063261

C₂²

yes

—

C₂×#13063260

—

#14582922

—

C₂×C₈×Dic₄₃

C₂²

yes

characteristic

C₁₆×Dic₄₃

C₄

yes

—

C₁₆×Dic₄₃

C₄

yes

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×#108×C₄₃

C₂²

yes

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

#13063261

—

#13063261

—

#13063260

—

Dic₄₃⋊C₈

—

C₈×Dic₄₃

C₂×C₄

yes

characteristic

C₈×Dic₄₃

C₂×C₄

yes

characteristic

C₈×Dic₄₃

Q₈

yes

characteristic

C₈×Dic₄₃

Q₈

yes

characteristic

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

#108×C₄₃

—

#108×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

Q₁₆

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₂×C₈×C₄₃

#41

yes

—

C₄×Dic₄₃

C₄⋊C₄

yes

characteristic

C₄×Dic₄₃

C₄⋊C₄

yes

characteristic

C₄×Dic₄₃

D₈

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

SD₁₆

yes

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#107

yes

—

C₂×Dic₄₃

#107

yes

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

#106

yes

—

C₄₃⋊C₈

#106

yes

—

#12891

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

C₂×#107

yes

characteristic

C₂²×C₄₃

#487

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

Dic₄₃

#368

yes

—

C₂×C₄×C₁₆

—

—

—

—

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

#1834

yes

characteristic

C₂×C₄₃

C₂×#368

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

—

#423

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄₃

#12891

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₄₃

yes

characteristic

100

C₂×C₄²

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₂×C₁₆

—

104

C₂×C₁₆

C₄×D₄₃

yes

—

105

#108

—

106

#108

—

107

#108

—

108

#108

—

109

#108

—

172

—

110

C₄⋊C₈

—

172

—

111

C₄×C₈

—

112

C₄×C₈

—

113

C₄×C₈

—

114

C₄×C₈

—

115

C₂²×C₄

—

116

C₂²×C₄

D₄×D₄₃

yes

characteristic

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

172

—

120

M₁₆

—

172

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

172

—

126

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

127

C₂×C₈

#10621898

yes

—

128

C₂×C₈

#10621900

yes

—

129

C₂×C₈

Q₈×D₄₃

yes

characteristic

130

C₄²

—

131

C₄²

—

132

C₄²

—

133

C₁₆

—

134

C₁₆

—

135

C₂³

Q₁₆×D₄₃

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

C₄⋊C₄×D₄₃

yes

characteristic

140

C₂×C₄

#13063311

yes

—

141

C₂×C₄

D₈×D₄₃

yes

characteristic

142

C₂×C₄

SD₁₆×D₄₃

yes

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

344

—

147

C₈

#13063281

yes

characteristic

148

C₈

#13063282

yes

characteristic

149

C₈

#13063315

yes

—

150

C₂²

—

151

C₂²

#107×D₄₃

yes

characteristic

152

C₂²

#14583248

yes

—

153

C₄

—

154

C₄

—

155

C₄

#14582763

yes

characteristic

156

C₄

#106×D₄₃

yes

characteristic

157

C₄

#14583244

yes

—

158

C₂

—

159

C₂

#19134721

yes

characteristic

160

C₂

#368×D₄₃

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1381	C₂
socle	C₂²×C₄₃	C₂×#107
prime radical	C₂³×C₄₃	C₂×Q₁₆
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1381	D₄₃
hypocenter	C₄₃	#12891
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

subgroup

G/H

center

C₂×C₄

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#1381

C₂

socle

C₂²×C₄₃

C₂×#107

prime radical

C₂³×C₄₃

C₂×Q₁₆

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

N	H ≅ G/N	type
95. C₄₃	#12891	semidirect

H ≅ G/N

type

95. C₄₃

#12891

semidirect

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

subgroup	index
C₂×C₁₆×Dic₄₃	2
#19134765	2
#19132689	2
#19132688	2
C₄₃×#1381	2
#12891	43

subgroup

index

C₂×C₁₆×Dic₄₃

C₄₃×#1381

Subgroups — #25012985

Conjugacy classes of subgroups

Complements

Maximal subgroups