Group #24987017 — subgroups

Subgroups — #24987017

Order 11008.

520 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 151 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	#19143227	C₂	1	3	yes	maximal
2	C₄₃⋊#1309	C₂	1	3	yes	maximal, complemented
3	C₄₃×#1309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
5	#14582955	—	2	6	no	—
6	#14582951	—	2	6	no	—
7	#14582923	C₂²	1	3	yes	—
8	#14582862	C₄	1	6	yes	—
9	M₁₆×Dic₄₃	C₄	1	6	yes	—
10	C₄₃×#423	C₂²	1	3	yes	—
11	C₂²×C₄×D₄₃	C₂×C₄	1	3	yes	—
12	C₂×#10621877	C₂×C₄	1	6	yes	—
13	C₂×C₄×Dic₄₃	C₂×C₄	1	3	yes	—
14	C₄²×D₄₃	D₄	1	6	yes	—
15	C₄²×D₄₃	Q₈	1	2	yes	—
16	C₄⋊(C₄₃⋊C₈)	—	2	6	no	—
17	(C₂×D₄₃)⋊C₈	—	2	12	no	—
18	#13063235	—	2	6	no	—
19	C₈×Dic₄₃	—	2	6	no	—
20	C₂×M₁₆×C₄₃	C₂×C₄	1	6	yes	—
21	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	—	2	6	no	—
23	C₂³×D₄₃	C₄²	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
25	C₂²×Dic₄₃	C₄²	1	3	yes	—
26	C₂×C₄×D₄₃	—	4	3	no	—
27	C₂×C₄×D₄₃	—	4	3	no	—
28	C₂×C₄×D₄₃	C₂²⋊C₄	1	6	yes	—
29	C₂×C₄×D₄₃	C₄⋊C₄	1	6	yes	—
30	M₁₆×C₄₃	—	4	6	no	—
31	C₂×C₈×C₄₃	—	2	6	no	—
32	C₄²×C₄₃	C₂×D₄	1	3	yes	—
33	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
34	C₄×Dic₄₃	C₂²⋊C₄	1	3	yes	—
35	C₄×Dic₄₃	C₂²⋊C₄	1	3	yes	—
36	C₄×Dic₄₃	C₄⋊C₄	1	6	yes	—
37	#10621877	—	4	6	no	—
38	C₂×C₄₃⋊C₈	—	2	6	no	—
39	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
40	C₂²×D₄₃	—	4	3	no	—
41	C₂²×D₄₃	#95	1	2	yes	—
42	C₂×C₄×C₄₃	—	2	3	no	—
43	C₂×C₄×C₄₃	—	2	3	no	—
44	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	3	yes	—
45	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	3	yes	—
46	C₂×Dic₄₃	—	4	3	no	—
47	C₂×Dic₄₃	#95	1	6	yes	—
48	C₄×D₄₃	—	2	6	no	—
49	C₄×D₄₃	—	2	6	no	—
50	C₄×D₄₃	—	4	6	no	—
51	C₈×C₄₃	—	4	6	no	—
52	C₄₃⋊C₈	—	4	6	no	—
53	#8130	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	—	2	3	no	—
55	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
56	C₂×D₄₃	—	2	6	no	—
57	C₂×D₄₃	—	4	4	no	—
58	C₄×C₄₃	—	2	3	no	—
59	C₄×C₄₃	#413	1	3	yes	—
60	C₄×C₄₃	#413	1	3	yes	—
61	Dic₄₃	—	2	6	no	—
62	#2920	—	43	3	no	—
63	#1309	—	43	3	no	—
64	#1309	D₄₃	1	1	yes	characteristic, complemented
65	C₂×C₄₃	—	4	1	no	—
66	C₂×C₄₃	#1742	1	3	yes	—
67	D₄₃	—	4	2	no	—
68	C₂²×C₄²	—	43	1	no	—
69	#432	—	86	6	no	—
70	#431	—	86	6	no	—
71	#423	—	43	3	no	—
72	#423	C₂×D₄₃	1	3	yes	—
73	#407	—	43	6	no	—
74	C₄×M₁₆	—	43	6	no	—
75	C₄₃	#8130	1	1	yes	characteristic, complemented, Sylow
76	C₂³×C₄	—	43	3	no	—
77	C₂×M₁₆	—	43	6	no	—
78	C₂×M₁₆	C₄×D₄₃	1	6	yes	—
79	C₂×C₄²	—	43	3	no	—
80	C₂×C₄²	—	43	6	no	—
81	C₂×C₄²	—	43	2	no	—
82	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
83	C₄⋊C₈	—	2	6	no	—
84	C₄⋊C₈	—	86	6	no	—
85	C₂²⋊C₈	—	86	12	no	—
86	#97	—	86	6	no	—
87	C₄×C₈	—	86	6	no	—
88	C₂⁴	—	43	1	no	—
89	C₂²×C₄	—	43	3	no	—
90	C₂²×C₄	—	43	6	no	—
91	C₂²×C₄	—	43	6	no	—
92	C₂²×C₄	—	172	3	no	—
93	C₂²×C₄	—	172	3	no	—
94	C₂²×C₄	C₂×C₄×D₄₃	1	3	yes	—
95	M₁₆	—	4	6	no	—
96	M₁₆	—	172	6	no	—
97	C₂×C₈	—	2	6	no	—
98	C₂×C₈	—	86	6	no	—
99	C₄²	—	43	3	no	—
100	C₄²	—	43	3	no	—
101	C₄²	—	43	6	no	—
102	C₄²	D₄×D₄₃	1	3	yes	—
103	C₄²	Q₈×D₄₃	1	1	yes	characteristic
104	C₂³	—	43	2	no	—
105	C₂³	—	172	3	no	—
106	C₂³	C₄²×D₄₃	1	1	yes	characteristic
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	43	6	no	—
110	C₂×C₄	—	86	6	no	—
111	C₂×C₄	—	86	6	no	—
112	C₂×C₄	—	172	6	no	—
113	C₂×C₄	—	172	3	no	—
114	C₂×C₄	C₂²⋊C₄×D₄₃	1	3	yes	—
115	C₂×C₄	C₄⋊C₄×D₄₃	1	3	yes	—
116	C₈	—	4	6	no	—
117	C₈	—	172	6	no	—
118	C₂²	—	2	3	no	—
119	C₂²	—	86	6	no	—
120	C₂²	—	172	4	no	—
121	C₂²	#95×D₄₃	1	1	yes	characteristic
122	C₄	—	2	3	no	—
123	C₄	—	86	6	no	—
124	C₄	#14582880	1	3	yes	—
125	C₄	#14582882	1	3	yes	—
126	C₂	—	4	1	no	—
127	C₂	—	172	2	no	—
128	C₂	#19134332	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19143227

C₂

yes

maximal

C₄₃⋊#1309

C₂

yes

maximal, complemented

C₄₃×#1309

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₄₃

C₂²

yes

—

—

C₂²

yes

—

#14582862

C₄

yes

—

M₁₆×Dic₄₃

C₄

yes

—

C₄₃×#423

C₂²

yes

—

C₂²×C₄×D₄₃

C₂×C₄

yes

—

C₂×#10621877

C₂×C₄

yes

—

C₂×C₄×Dic₄₃

C₂×C₄

yes

—

C₄²×D₄₃

D₄

yes

—

C₄²×D₄₃

Q₈

yes

—

C₄⋊(C₄₃⋊C₈)

—

(C₂×D₄₃)⋊C₈

—

#13063235

—

C₈×Dic₄₃

—

C₂×M₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂³×D₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

—

C₂²×Dic₄₃

C₄²

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂²⋊C₄

yes

—

C₂×C₄×D₄₃

C₄⋊C₄

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄×Dic₄₃

C₂²⋊C₄

yes

—

C₄×Dic₄₃

C₂²⋊C₄

yes

—

C₄×Dic₄₃

C₄⋊C₄

yes

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₄²

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

#95

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#95

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#8130

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

C₂×#95

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#413

yes

—

C₄×C₄₃

#413

yes

—

Dic₄₃

—

#2920

—

#1309

—

#1309

D₄₃

yes

characteristic, complemented

C₂×C₄₃

—

C₂×C₄₃

#1742

yes

—

D₄₃

—

C₂²×C₄²

—

—

—

—

C₂×D₄₃

yes

—

#407

—

C₄×M₁₆

—

C₄₃

#8130

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₄×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂×C₄×D₄₃

yes

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

D₄×D₄₃

yes

—

103

C₄²

Q₈×D₄₃

yes

characteristic

104

C₂³

—

105

C₂³

—

172

—

106

C₂³

C₄²×D₄₃

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

172

—

113

C₂×C₄

—

172

—

114

C₂×C₄

C₂²⋊C₄×D₄₃

yes

—

115

C₂×C₄

C₄⋊C₄×D₄₃

yes

—

116

C₈

—

117

C₈

—

172

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

172

—

121

C₂²

#95×D₄₃

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

#14582880

yes

—

125

C₄

#14582882

yes

—

126

C₂

—

127

C₂

—

172

—

128

C₂

#19134332

yes

—

	subgroup	G/H
center	C₂²	#95×D₄₃
commutator	C₂³×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1309	C₂
socle	C₂²×C₄₃	C₂×#95
prime radical	C₂³×D₄₃	C₄²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1309	D₄₃
hypocenter	C₄₃	#8130
LCS	G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#95×D₄₃

commutator

C₂³×C₄₃

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1309

C₂

socle

C₂²×C₄₃

C₂×#95

prime radical

C₂³×D₄₃

C₄²

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
2. C₄₃⋊#1309	C₂	semidirect
3. C₄₃×#1309	C₂	semidirect
64. #1309	D₄₃	semidirect
75. C₄₃	#8130	semidirect

H ≅ G/N

type

2. C₄₃⋊#1309

C₂

semidirect

3. C₄₃×#1309

C₂

semidirect

64. #1309

D₄₃

semidirect

75. C₄₃

#8130

semidirect

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

subgroup	index
#19143227	2
C₄₃⋊#1309	2
C₄₃×#1309	2
#8130	43

subgroup

index

#19143227

C₄₃⋊#1309

C₄₃×#1309

#8130

Subgroups — #24987017

Conjugacy classes of subgroups

Complements

Maximal subgroups