Group #24983448 — subgroups

Subgroups — #24983448

Order 11008.

210 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 95 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	2	yes	maximal
2	C₂×C₄₃×#322	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₃⋊C₁₆)	—	2	2	no	—
4	C₂²⋊(C₄₃⋊C₁₆)	—	2	2	no	—
5	#14582675	C₄	1	4	yes	—
6	C₂×C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#322	—	2	2	no	—
10	C₂×C₄₃⋊C₁₆	—	2	4	no	—
11	C₂²×C₈×C₄₃	—	2	1	no	—
12	C₂²×C₈×C₄₃	C₈	1	2	yes	—
13	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
14	C₂²×C₈×C₄₃	Q₈	1	1	yes	characteristic
15	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₈×C₄₃	—	2	1	no	—
17	C₄×C₈×C₄₃	—	2	1	no	—
18	C₄×C₈×C₄₃	—	2	1	no	—
19	C₄×C₈×C₄₃	C₈	1	2	yes	—
20	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₄₃	D₄	1	2	yes	—
22	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	M₁₆	1	1	yes	characteristic
25	C₂×C₈×C₄₃	—	2	4	no	—
26	C₂×C₈×C₄₃	—	2	2	no	—
27	C₂×C₈×C₄₃	—	2	2	no	—
28	C₂×C₈×C₄₃	—	4	1	no	—
29	C₂×C₈×C₄₃	—	4	1	no	—
30	C₂×C₈×C₄₃	—	4	2	no	—
31	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
32	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
33	C₄²×C₄₃	C₄²	1	1	yes	characteristic
34	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₄²×C₄₃	C₂×C₈	1	1	yes	characteristic
36	C₄²×C₄₃	M₁₆	1	1	yes	characteristic
37	C₄₃⋊C₁₆	—	4	4	no	—
38	C₂³×C₄₃	C₄⋊C₈	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	2	2	no	—
40	C₂×C₄×C₄₃	—	2	1	no	—
41	C₂×C₄×C₄₃	—	2	1	no	—
42	C₂×C₄×C₄₃	—	2	2	no	—
43	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
44	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
45	C₂×C₄×C₄₃	#97	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
49	C₈×C₄₃	—	2	4	no	—
50	C₈×C₄₃	—	2	2	no	—
51	C₈×C₄₃	—	2	2	no	—
52	C₈×C₄₃	—	4	2	no	—
53	#7146	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	—	2	1	no	—
55	C₂²×C₄₃	—	2	1	no	—
56	C₂²×C₄₃	#336	1	1	yes	characteristic
57	C₂²×C₄₃	#364	1	2	yes	—
58	C₄×C₄₃	—	2	1	no	—
59	C₄×C₄₃	—	2	1	no	—
60	C₄×C₄₃	—	2	1	no	—
61	C₄×C₄₃	—	2	1	no	—
62	C₄×C₄₃	H(3,ℤ/4)	1	1	yes	characteristic
63	C₄×C₄₃	#338	1	1	yes	characteristic
64	C₄×C₄₃	#349	1	2	yes	—
65	#2163	—	43	2	no	—
66	C₂×#322	D₄₃	1	1	yes	characteristic
67	C₂×C₄₃	—	2	2	no	—
68	C₂×C₄₃	#1275	1	1	yes	characteristic
69	C₂×C₄₃	#1376	1	1	yes	characteristic
70	C₂×C₄₃	#1377	1	1	yes	characteristic
71	C₂×C₄×C₈	Dic₄₃	1	1	yes	characteristic
72	C₂×C₄×C₈	Dic₄₃	1	1	yes	characteristic
73	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
74	C₄⋊C₁₆	—	86	2	no	—
75	C₂²⋊C₁₆	—	86	2	no	—
76	#346	—	43	4	no	—
77	#322	—	2	2	no	—
78	C₄₃	#7146	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₈	—	2	1	no	—
80	C₂²×C₈	C₄₃⋊C₈	1	2	yes	—
81	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
82	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
83	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
84	C₂×C₁₆	—	86	4	no	—
85	C₄×C₈	—	2	1	no	—
86	C₄×C₈	—	2	1	no	—
87	C₄×C₈	—	2	1	no	—
88	C₄×C₈	C₄₃⋊C₈	1	2	yes	—
89	C₄×C₈	C₄×D₄₃	1	2	yes	—
90	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
91	C₂²×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
92	C₂²×C₄	#10621877	1	1	yes	characteristic
93	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
94	C₂×C₈	—	2	4	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	4	1	no	—
98	C₂×C₈	—	4	1	no	—
99	C₂×C₈	—	4	2	no	—
100	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
101	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
102	C₄²	C₂×C₄₃⋊C₈	1	1	yes	characteristic
103	C₄²	#10621877	1	1	yes	characteristic
104	C₄²	C₄×Dic₄₃	1	1	yes	characteristic
105	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
106	C₁₆	—	172	4	no	—
107	C₂³	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
113	C₂×C₄	C₄×C₄₃⋊C₈	1	1	yes	characteristic
114	C₂×C₄	#13063236	1	1	yes	characteristic
115	C₂×C₄	C₂²⋊(C₄₃⋊C₈)	1	1	yes	characteristic
116	C₂×C₄	C₂²⋊(C₄₃⋊C₈)	1	1	yes	characteristic
117	C₂×C₄	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
118	C₈	—	2	4	no	—
119	C₈	—	2	2	no	—
120	C₈	—	2	2	no	—
121	C₈	—	4	2	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	2	1	no	—
124	C₂²	#14582654	1	1	yes	characteristic
125	C₂²	#14582720	1	2	yes	—
126	C₄	—	2	1	no	—
127	C₄	—	2	1	no	—
128	C₄	—	2	1	no	—
129	C₄	—	2	1	no	—
130	C₄	#14582656	1	1	yes	characteristic
131	C₄	C₄₃⋊#338	1	1	yes	characteristic
132	C₄	#14582681	1	2	yes	—
133	C₂	—	2	2	no	—
134	C₂	#19132426	1	1	yes	characteristic
135	C₂	#19132677	1	1	yes	characteristic
136	C₂	#19132679	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136398

C₂

yes

maximal

C₂×C₄₃×#322

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₁₆)

—

C₂²⋊(C₄₃⋊C₁₆)

—

#14582675

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₄

yes

characteristic

C₂×C₄×C₈×C₄₃

C₄

yes

characteristic

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#322

—

C₂×C₄₃⋊C₁₆

—

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

C₈

yes

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

Q₈

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₈

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₃

M₁₆

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₄²×C₄₃

C₄²

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

C₂×C₈

yes

characteristic

C₄²×C₄₃

M₁₆

yes

characteristic

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₄⋊C₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#95

yes

characteristic

C₂×C₄×C₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

#97

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₈

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

#7146

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#336

yes

characteristic

C₂²×C₄₃

#364

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

#2163

—

C₂×#322

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄×C₈

Dic₄₃

yes

characteristic

C₂×C₄×C₈

Dic₄₃

yes

characteristic

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#322

—

C₄₃

#7146

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₄₃⋊C₈

yes

—

C₂²×C₈

Dic₈₆

yes

characteristic

C₂²×C₈

D₁₇₂

yes

characteristic

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄₃⋊C₈

yes

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂×C₄₃⋊C₈

yes

characteristic

C₂²×C₄

#10621877

yes

characteristic

C₂²×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

Dic₄₃⋊C₄

yes

—

101

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

102

C₄²

C₂×C₄₃⋊C₈

yes

characteristic

103

C₄²

#10621877

yes

characteristic

104

C₄²

C₄×Dic₄₃

yes

characteristic

105

C₄²

C₂²⋊Dic₄₃

yes

characteristic

106

C₁₆

—

172

—

107

C₂³

C₄⋊(C₄₃⋊C₈)

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₄₃⋊#95

yes

characteristic

113

C₂×C₄

C₄×C₄₃⋊C₈

yes

characteristic

114

C₂×C₄

#13063236

yes

characteristic

115

C₂×C₄

C₂²⋊(C₄₃⋊C₈)

yes

characteristic

116

C₂×C₄

C₂²⋊(C₄₃⋊C₈)

yes

characteristic

117

C₂×C₄

C₄⋊(C₄₃⋊C₈)

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

122

C₂²

—

123

C₂²

—

124

C₂²

#14582654

yes

characteristic

125

C₂²

#14582720

yes

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

#14582656

yes

characteristic

131

C₄

C₄₃⋊#338

yes

characteristic

132

C₄

#14582681

yes

—

133

C₂

—

134

C₂

#19132426

yes

characteristic

135

C₂

#19132677

yes

characteristic

136

C₂

#19132679

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄₃⋊#95
commutator	C₂×C₄×C₄₃	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₄₃
Fitting	C₂×C₄₃×#322	C₂
socle	C₂²×C₄₃	#336
prime radical	C₂³×C₄₃	C₄⋊C₈
cosocle	C₂×C₄×C₈×C₄₃	C₂²
hypercenter	C₂×#322	D₄₃
hypocenter	C₄₃	#7146
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

C₄₃⋊#95

commutator

C₂×C₄×C₄₃

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₄₃

Fitting

C₂×C₄₃×#322

C₂

socle

C₂²×C₄₃

#336

prime radical

C₂³×C₄₃

C₄⋊C₈

cosocle

C₂×C₄×C₈×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

N	H ≅ G/N	type
78. C₄₃	#7146	semidirect

H ≅ G/N

type

78. C₄₃

#7146

semidirect

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

subgroup	index
#19136398	2
C₂×C₄₃×#322	2
#7146	43

subgroup

index

#19136398

C₂×C₄₃×#322

#7146

Subgroups — #24983448

Conjugacy classes of subgroups

Complements

Maximal subgroups