Group #25012966 — subgroups

Subgroups — #25012966

Order 11008.

234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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	#19136354	C₂	1	1	yes	maximal, characteristic
2	#19134350	C₂	1	1	yes	maximal, characteristic
3	#19132685	C₂	1	2	yes	maximal
4	#19132680	C₂	1	2	yes	maximal
5	C₄₃×#2153	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063265	C₂²	1	1	yes	characteristic
7	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
8	#14582854	C₂²	1	2	yes	—
9	C₄⋊(C₄₃⋊C₁₆)	—	2	2	no	—
10	C₄₃⋊#338	C₄	1	1	yes	characteristic
11	#14582656	C₄	1	1	yes	characteristic
12	#14582655	C₄	1	2	yes	—
13	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
14	C₄₃×#405	C₂²	1	1	yes	characteristic
15	C₄₃×#364	—	2	2	no	—
16	C₂×#10621877	C₂×C₄	1	2	yes	—
17	#13063284	C₂×C₄	1	2	yes	—
18	#13063265	—	2	2	no	—
19	C₂×C₄₃⋊C₁₆	—	2	1	no	—
20	C₂×C₄₃⋊C₁₆	—	2	1	no	—
21	C₂×C₄₃⋊C₁₆	—	2	2	no	—
22	#13063235	—	2	2	no	—
23	C₈×Dic₄₃	—	2	2	no	—
24	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
27	M₃₂×C₄₃	—	2	2	no	—
28	M₃₂×C₄₃	—	2	2	no	—
29	C₂×C₁₆×C₄₃	—	2	2	no	—
30	#97×C₄₃	Q₈	1	2	yes	—
31	C₄×C₈×C₄₃	D₄	1	2	yes	—
32	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	M₁₆×C₄₃	—	2	2	no	—
34	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₈×C₄₃	#41	1	2	yes	—
38	C₂×C₈×C₄₃	#41	1	2	yes	—
39	C₄⋊C₄×C₄₃	—	2	1	no	—
40	C₂²⋊C₄×C₄₃	—	2	1	no	—
41	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
42	C₂²⋊Dic₄₃	—	2	2	no	—
43	C₄⋊Dic₄₃	—	2	2	no	—
44	C₄×Dic₄₃	—	2	2	no	—
45	#10621877	—	2	2	no	—
46	#10621877	—	2	2	no	—
47	C₂×C₄₃⋊C₈	—	2	2	no	—
48	C₁₆×C₄₃	—	4	2	no	—
49	C₄₃⋊C₁₆	—	4	1	no	—
50	C₄₃⋊C₁₆	—	4	1	no	—
51	C₂³×C₄₃	#131	1	1	yes	characteristic
52	C₂×C₄×C₄₃	—	2	2	no	—
53	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#117	1	2	yes	—
55	C₂×C₄×C₄₃	#131	1	2	yes	—
56	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
57	C₂×Dic₄₃	—	4	2	no	—
58	C₈×C₄₃	—	2	2	no	—
59	C₈×C₄₃	#124	1	1	yes	characteristic
60	C₈×C₄₃	#124	1	1	yes	characteristic
61	C₈×C₄₃	#125	1	2	yes	—
62	C₄₃⋊C₈	—	4	2	no	—
63	#12885	—	43	1	no	maximal, Sylow
64	C₂²×C₄₃	—	4	1	no	—
65	C₂²×C₄₃	#424	1	1	yes	characteristic
66	C₂²×C₄₃	#433	1	2	yes	—
67	C₄×C₄₃	—	4	2	no	—
68	C₄×C₄₃	#382	1	1	yes	characteristic
69	C₄×C₄₃	#424	1	1	yes	characteristic
70	C₄×C₄₃	#433	1	2	yes	—
71	Dic₄₃	—	8	2	no	—
72	#2153	D₄₃	1	1	yes	characteristic
73	#2151	—	43	1	no	—
74	#1747	—	43	1	no	—
75	#1379	—	43	2	no	—
76	#1378	—	43	2	no	—
77	C₂×C₄₃	—	2	2	no	—
78	C₂×C₄₃	—	2	1	no	—
79	C₂×C₄₃	#1832	1	1	yes	characteristic
80	C₂×M₃₂	—	43	1	no	—
81	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
82	C₂²×C₁₆	—	43	1	no	—
83	#405	—	43	2	no	—
84	#405	C₂×D₄₃	1	1	yes	characteristic
85	#364	—	2	2	no	—
86	C₄⋊C₁₆	—	86	2	no	—
87	#338	—	43	1	no	—
88	H(3,ℤ/4)	—	43	1	no	—
89	H(3,ℤ/4)	—	43	2	no	—
90	C₄₃	#12885	1	1	yes	characteristic, complemented, Sylow
91	C₂×M₁₆	—	43	2	no	—
92	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
93	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
94	#117	—	43	2	no	—
95	#117	C₄×D₄₃	1	1	yes	characteristic
96	M₃₂	—	2	2	no	—
97	M₃₂	—	2	2	no	—
98	M₃₂	—	86	2	no	—
99	C₂×C₁₆	—	2	2	no	—
100	C₂×C₁₆	—	86	2	no	—
101	C₂×C₁₆	—	86	1	no	—
102	C₂×C₁₆	—	86	1	no	—
103	#97	—	86	2	no	—
104	#97	Dic₈₆	1	2	yes	—
105	C₄×C₈	—	86	2	no	—
106	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
107	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
108	M₁₆	—	2	2	no	—
109	M₁₆	—	86	2	no	—
110	M₁₆	—	86	2	no	—
111	C₂×C₈	—	86	2	no	—
112	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
113	C₂×C₈	C₂×Dic₈₆	1	1	yes	characteristic
114	C₂×C₈	#10621900	1	2	yes	—
115	C₂×C₈	#10621902	1	2	yes	—
116	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
117	C₄⋊C₄	—	2	1	no	—
118	C₄⋊C₄	—	86	2	no	—
119	C₂²⋊C₄	—	2	1	no	—
120	C₂²⋊C₄	—	86	2	no	—
121	C₄²	—	86	2	no	—
122	C₄²	Dic₄₃⋊C₄	1	2	yes	—
123	C₁₆	—	4	2	no	—
124	C₁₆	—	172	1	no	—
125	C₁₆	—	172	1	no	—
126	C₂³	#13063333	1	1	yes	characteristic
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	172	2	no	—
129	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
130	C₂×C₄	#13063283	1	2	yes	—
131	C₂×C₄	#13063331	1	2	yes	—
132	C₂×C₄	#13063333	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	172	2	no	—
135	C₈	#13063312	1	1	yes	characteristic
136	C₈	#13063314	1	1	yes	characteristic
137	C₈	#13063316	1	2	yes	—
138	C₂²	—	4	1	no	—
139	C₂²	#14582927	1	1	yes	characteristic
140	C₂²	#14582959	1	2	yes	—
141	C₄	—	4	2	no	—
142	C₄	—	344	2	no	—
143	C₄	#14582764	1	1	yes	characteristic
144	C₄	#14582925	1	1	yes	characteristic
145	C₄	#14582959	1	2	yes	—
146	C₂	—	2	1	no	—
147	C₂	—	2	2	no	—
148	C₂	#19134714	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136354

C₂

yes

maximal, characteristic

#19134350

C₂

yes

maximal, characteristic

#19132685

C₂

yes

maximal

#19132680

C₂

yes

maximal

C₄₃×#2153

C₂

yes

maximal, characteristic

C₂×#13063265

C₂²

yes

characteristic

C₂²×C₄₃⋊C₁₆

C₂²

yes

characteristic

#14582854

C₂²

yes

—

C₄⋊(C₄₃⋊C₁₆)

—

C₄₃⋊#338

C₄

yes

characteristic

#14582656

C₄

yes

characteristic

#14582655

C₄

yes

—

C₂×M₃₂×C₄₃

C₂²

yes

—

C₄₃×#405

C₂²

yes

characteristic

C₄₃×#364

—

C₂×#10621877

C₂×C₄

yes

—

#13063284

C₂×C₄

yes

—

#13063265

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

—

#13063235

—

C₈×Dic₄₃

—

C₂×M₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

#117×C₄₃

C₂×C₄

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

#97×C₄₃

Q₈

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₂×C₈×C₄₃

#41

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₄⋊C₄

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

#131

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#131

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₄₃⋊C₈

—

#12885

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#424

yes

characteristic

C₂²×C₄₃

#433

yes

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

#2153

D₄₃

yes

—

—

—

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#1832

yes

characteristic

C₂×M₃₂

—

C₂×M₃₂

C₂×D₄₃

yes

—

C₂²×C₁₆

—

#405

—

#405

C₂×D₄₃

yes

characteristic

#364

—

C₄⋊C₁₆

—

#338

—

H(3,ℤ/4)

—

H(3,ℤ/4)

—

C₄₃

#12885

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₄×D₄₃

yes

characteristic

C₂²×C₈

C₂²×D₄₃

yes

characteristic

#117

—

#117

C₄×D₄₃

yes

characteristic

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

#97

—

104

#97

Dic₈₆

yes

—

105

C₄×C₈

—

106

C₄×C₈

C₂²⋊D₄₃

yes

—

107

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

Dic₄₃⋊C₄

yes

—

113

C₂×C₈

C₂×Dic₈₆

yes

characteristic

114

C₂×C₈

#10621900

yes

—

115

C₂×C₈

#10621902

yes

—

116

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

Dic₄₃⋊C₄

yes

—

123

C₁₆

—

124

C₁₆

—

172

—

125

C₁₆

—

172

—

126

C₂³

#13063333

yes

characteristic

127

C₂×C₄

—

128

C₂×C₄

—

172

—

129

C₂×C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

130

C₂×C₄

#13063283

yes

—

131

C₂×C₄

#13063331

yes

—

132

C₂×C₄

#13063333

yes

characteristic

133

C₈

—

134

C₈

—

172

—

135

C₈

#13063312

yes

characteristic

136

C₈

#13063314

yes

characteristic

137

C₈

#13063316

yes

—

138

C₂²

—

139

C₂²

#14582927

yes

characteristic

140

C₂²

#14582959

yes

—

141

C₄

—

142

C₄

—

344

—

143

C₄

#14582764

yes

characteristic

144

C₄

#14582925

yes

characteristic

145

C₄

#14582959

yes

—

146

C₂

—

147

C₂

—

148

C₂

#19134714

yes

characteristic

	subgroup	G/H
center	C₈	#13063312
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#2153	C₂
socle	C₂×C₄₃	#1832
prime radical	C₂³×C₄₃	#131
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#2153	D₄₃
hypocenter	C₄₃	#12885
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2153

subgroup

G/H

center

C₈

#13063312

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#2153

C₂

C₂×C₄₃

C₂³×C₄₃

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2153

N	H ≅ G/N	type
90. C₄₃	#12885	semidirect

H ≅ G/N

type

90. C₄₃

#12885

semidirect

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

subgroup	index
#19136354	2
#19134350	2
#19132685	2
#19132680	2
C₄₃×#2153	2
#12885	43

subgroup

index

C₄₃×#2153

Subgroups — #25012966

Conjugacy classes of subgroups

Complements

Maximal subgroups