Group #25005653 — subgroups

Subgroups — #25005653

Order 11008.

228 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 123 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	#19136398	C₂	1	1	yes	maximal, characteristic
2	#19132878	C₂	1	1	yes	maximal, characteristic
3	#19132517	C₂	1	2	yes	maximal, complemented
4	#19132515	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2163	C₂	1	1	yes	maximal, characteristic
6	#14582952	C₄	1	2	yes	—
7	C₄⋊(C₄₃⋊C₁₆)	C₄	1	2	yes	—
8	C₂²⋊(C₄₃⋊C₁₆)	C₄	1	2	yes	—
9	#14582675	C₂²	1	2	yes	—
10	#14582620	C₂²	1	1	yes	characteristic
11	#14582620	C₂²	1	1	yes	characteristic
12	C₈×C₄₃⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×C₄⋊C₁₆	C₄	1	2	yes	—
15	C₄₃×C₂²⋊C₁₆	C₄	1	2	yes	—
16	C₄₃×#346	C₂²	1	2	yes	—
17	C₂×C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
18	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
19	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
20	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
21	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	—
26	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₄₃	M₁₆	1	2	yes	—
32	C₂×C₈×C₄₃	—	2	2	no	—
33	C₂×C₈×C₄₃	—	2	2	no	—
34	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₄²×C₄₃	C₄²	1	1	yes	characteristic
39	C₄²×C₄₃	M₁₆	1	2	yes	—
40	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄₃⋊C₈	—	2	2	no	—
42	C₂×C₄₃⋊C₈	—	2	2	no	—
43	C₁₆×C₄₃	—	2	4	no	—
44	C₄₃⋊C₁₆	—	2	4	no	—
45	C₂³×C₄₃	#97	1	1	yes	characteristic
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	—	4	2	no	—
49	C₂×C₄×C₄₃	#97	1	2	yes	—
50	C₂×C₄×C₄₃	#97	1	1	yes	characteristic
51	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
53	C₈×C₄₃	—	2	1	no	—
54	C₈×C₄₃	—	2	1	no	—
55	C₈×C₄₃	#131	1	2	yes	—
56	C₈×C₄₃	#131	1	2	yes	—
57	C₄₃⋊C₈	—	4	2	no	—
58	C₄₃⋊C₈	—	4	2	no	—
59	#11416	—	43	1	no	maximal, Sylow
60	C₂²×C₄₃	—	2	2	no	—
61	C₂²×C₄₃	—	2	1	no	—
62	C₂²×C₄₃	C₂×#97	1	1	yes	characteristic
63	C₄×C₄₃	—	2	2	no	—
64	C₄×C₄₃	—	2	2	no	—
65	C₄×C₄₃	—	2	1	no	—
66	C₄×C₄₃	#405	1	1	yes	characteristic
67	C₄×C₄₃	#405	1	1	yes	characteristic
68	#2163	—	43	1	no	—
69	#2163	D₄₃	1	1	yes	characteristic
70	#1450	—	43	1	no	—
71	#1313	—	43	2	no	—
72	#1313	—	43	2	no	—
73	C₂×C₄₃	—	4	1	no	—
74	C₂×C₄₃	#1452	1	1	yes	characteristic
75	C₂×C₄₃	#2110	1	2	yes	—
76	#431	—	43	2	no	—
77	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
78	C₄⋊C₁₆	—	43	2	no	—
79	C₄⋊C₁₆	Dic₄₃	1	2	yes	—
80	C₂²⋊C₁₆	—	43	2	no	—
81	C₂²⋊C₁₆	Dic₄₃	1	2	yes	—
82	#346	—	43	2	no	—
83	#346	C₂×D₄₃	1	2	yes	—
84	#322	—	43	1	no	—
85	#322	—	43	1	no	—
86	C₈²	—	43	2	no	—
87	C₄₃	#11416	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
89	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
90	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
91	C₂×C₁₆	—	43	4	no	—
92	C₂×C₁₆	C₂×Dic₄₃	1	4	yes	—
93	C₄⋊C₈	—	86	2	no	—
94	C₂²⋊C₈	—	86	2	no	—
95	C₄×C₈	—	43	2	no	—
96	C₄×C₈	—	43	2	no	—
97	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
98	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
99	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
100	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
101	C₂²×C₄	#10621872	1	2	yes	—
102	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	—	2	2	no	—
105	C₂×C₈	—	86	2	no	—
106	C₂×C₈	—	86	2	no	—
107	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
108	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
109	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
110	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
111	C₄²	#10621872	1	2	yes	—
112	C₄²	C₄×Dic₄₃	1	1	yes	characteristic
113	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
114	C₁₆	—	2	4	no	—
115	C₁₆	—	86	4	no	—
116	C₂³	#13063235	1	1	yes	characteristic
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	#13063235	1	1	yes	characteristic
121	C₂×C₄	#13063235	1	2	yes	—
122	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
123	C₂×C₄	C₂×#10621872	1	2	yes	—
124	C₈	—	2	1	no	—
125	C₈	—	2	1	no	—
126	C₈	—	172	2	no	—
127	C₈	—	172	2	no	—
128	C₈	#13063332	1	2	yes	—
129	C₈	#13063333	1	2	yes	—
130	C₂²	—	2	2	no	—
131	C₂²	—	2	1	no	—
132	C₂²	C₂×#13063235	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	2	2	no	—
135	C₄	—	2	1	no	—
136	C₄	#14582855	1	1	yes	characteristic
137	C₄	#14582857	1	1	yes	characteristic
138	C₂	—	4	1	no	—
139	C₂	#19132888	1	1	yes	characteristic
140	C₂	#19136199	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19136398

C₂

yes

maximal, characteristic

#19132878

C₂

yes

maximal, characteristic

#19132517

C₂

yes

maximal, complemented

#19132515

C₂

yes

maximal, complemented

C₄₃×#2163

C₂

yes

maximal, characteristic

#14582952

C₄

yes

—

C₄⋊(C₄₃⋊C₁₆)

C₄

yes

—

C₂²⋊(C₄₃⋊C₁₆)

C₄

yes

—

#14582675

C₂²

yes

—

#14582620

C₂²

yes

characteristic

#14582620

C₂²

yes

characteristic

C₈×C₄₃⋊C₈

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

C₄

yes

—

C₄₃×C₂²⋊C₁₆

C₄

yes

—

C₄₃×#346

C₂²

yes

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

M₁₆

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

characteristic

C₂×C₈×C₄₃

C₄²

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₄²

yes

characteristic

C₄²×C₄₃

M₁₆

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

#97

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#97

yes

—

C₂×C₄×C₄₃

#97

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#131

yes

—

C₈×C₄₃

#131

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#11416

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×#97

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

D₄₃

yes

—

—

—

C₂×C₄₃

—

C₂×C₄₃

#1452

yes

characteristic

C₂×C₄₃

#2110

yes

—

#431

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

C₄⋊C₁₆

Dic₄₃

yes

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

Dic₄₃

yes

—

#346

—

#346

C₂×D₄₃

yes

—

#322

—

#322

—

C₈²

—

C₄₃

#11416

yes

characteristic, complemented, Sylow

C₂²×C₈

C₄×D₄₃

yes

characteristic

C₂²×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₄²

C₄×D₄₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₄₃

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₄₃

yes

characteristic

C₄×C₈

C₄×D₄₃

yes

characteristic

C₄×C₈

C₂×Dic₄₃

yes

characteristic

100

C₄×C₈

C₂²×D₄₃

yes

characteristic

101

C₂²×C₄

#10621872

yes

—

102

C₂²×C₄

C₄×Dic₄₃

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

C₄×Dic₄₃

yes

characteristic

108

C₂×C₈

C₄×Dic₄₃

yes

characteristic

109

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

110

C₂×C₈

C₂²×Dic₄₃

yes

characteristic

111

C₄²

#10621872

yes

—

112

C₄²

C₄×Dic₄₃

yes

characteristic

113

C₄²

C₂×C₄×D₄₃

yes

characteristic

114

C₁₆

—

115

C₁₆

—

116

C₂³

#13063235

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

#13063235

yes

characteristic

121

C₂×C₄

#13063235

yes

—

122

C₂×C₄

C₂×C₄×Dic₄₃

yes

characteristic

123

C₂×C₄

C₂×#10621872

yes

—

124

C₈

—

125

C₈

—

126

C₈

—

172

—

127

C₈

—

172

—

128

C₈

#13063332

yes

—

129

C₈

#13063333

yes

—

130

C₂²

—

131

C₂²

—

132

C₂²

C₂×#13063235

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#14582855

yes

characteristic

137

C₄

#14582857

yes

characteristic

138

C₂

—

139

C₂

#19132888

yes

characteristic

140

C₂

#19136199

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×#2163	C₂
socle	C₂²×C₄₃	C₂×#97
prime radical	C₂³×C₄₃	#97
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#2163	D₄₃
hypocenter	C₄₃	#11416
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #2163

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₄₃

commutator

C₂×C₄×C₄₃

C₂×C₄²

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₄₃×#2163

C₂

socle

C₂²×C₄₃

C₂×#97

prime radical

C₂³×C₄₃

#97

cosocle

C₄×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ #2163

N	H ≅ G/N	type
3. #19132517	C₂	semidirect
4. #19132515	C₂	semidirect
87. C₄₃	#11416	semidirect

H ≅ G/N

type

3. #19132517

C₂

semidirect

4. #19132515

C₂

semidirect

87. C₄₃

#11416

semidirect

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

subgroup	index
#19136398	2
#19132878	2
#19132517	2
#19132515	2
C₄₃×#2163	2
#11416	43

subgroup

index

C₄₃×#2163

Subgroups — #25005653

Conjugacy classes of subgroups

Complements

Maximal subgroups