Group #44532873 — subgroups

Subgroups — #44532873

Order 31347.

344 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 58 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	#23782798	C₃	1	1	yes	maximal, characteristic
2	#23782798	C₃	1	2	yes	maximal
3	#23782691	C₃	1	9	yes	maximal, complemented
4	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
5	C₃×#11923958	—	3	2	no	—
6	C₃×#11923958	—	3	1	no	—
7	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
8	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
9	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
10	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
11	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	—
12	C₃²⋊(C₄₃⋊C₉)	C₃²	1	6	yes	—
13	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
14	C₃×3₋¹⁺²×C₄₃	—	3	1	no	—
15	C₃×3₋¹⁺²×C₄₃	—	3	1	no	—
16	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
17	C₃×3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
18	C₃²×C₉×C₄₃	—	3	1	no	—
19	#11923958	—	9	6	no	—
20	#11923958	—	9	3	no	—
21	C₃×C₄₃⋊C₉	—	3	3	no	—
22	C₃×C₄₃⋊C₉	—	3	6	no	—
23	C₃³×C₄₃	—	3	3	no	—
24	C₃³×C₄₃	—	9	1	no	—
25	C₃³×C₄₃	—	9	2	no	—
26	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
28	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
29	C₃³×C₄₃	C₃³	1	1	yes	characteristic
30	3₋¹⁺²×C₄₃	—	3	9	no	—
31	3₋¹⁺²×C₄₃	—	3	9	no	—
32	3₋¹⁺²×C₄₃	—	3	9	no	—
33	C₃×C₉×C₄₃	—	3	9	no	—
34	C₃×C₉×C₄₃	—	3	3	no	—
35	#10624631	—	43	1	no	maximal, Sylow
36	C₃²×C₄₃	—	3	1	no	—
37	C₃²×C₄₃	—	3	2	no	—
38	C₃²×C₄₃	—	3	1	no	—
39	C₃²×C₄₃	—	3	1	no	—
40	C₃²×C₄₃	—	3	1	no	—
41	C₃²×C₄₃	—	3	1	no	—
42	C₃²×C₄₃	—	3	1	no	—
43	C₃²×C₄₃	—	3	1	no	—
44	C₃²×C₄₃	—	3	2	no	—
45	C₃²×C₄₃	—	3	2	no	—
46	C₃²×C₄₃	—	3	2	no	—
47	C₃²×C₄₃	—	9	9	no	—
48	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	3	yes	—
49	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
50	C₉×C₄₃	—	3	9	no	—
51	C₄₃⋊C₉	—	9	3	no	—
52	C₄₃⋊C₉	—	9	6	no	—
53	C₃²×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
54	#6891	—	43	1	no	—
55	#6891	—	43	2	no	—
56	#6858	—	43	9	no	—
57	C₃×C₄₃	—	3	3	no	—
58	C₃×C₄₃	—	9	1	no	—
59	C₃×C₄₃	—	9	1	no	—
60	C₃×C₄₃	—	9	1	no	—
61	C₃×C₄₃	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
62	C₃×C₄₃	#6910	1	2	yes	—
63	C₃×C₄₃	#6912	1	1	yes	characteristic
64	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
65	C₃×3₋¹⁺²	—	3	1	no	—
66	C₃×3₋¹⁺²	—	3	1	no	—
67	C₃×3₋¹⁺²	—	3	9	no	—
68	C₃×3₋¹⁺²	—	129	2	no	—
69	C₃×3₋¹⁺²	—	129	1	no	—
70	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
71	C₃²×C₉	—	3	1	no	—
72	C₃²⋊C₉	—	43	3	no	—
73	C₃²⋊C₉	—	43	6	no	—
74	C₃²⋊C₉	—	129	1	no	—
75	C₃²⋊C₉	—	129	2	no	—
76	C₃²⋊C₉	—	129	1	no	—
77	C₃²⋊C₉	—	129	2	no	—
78	C₄₃	#10624631	1	1	yes	characteristic, complemented, Sylow
79	C₃³	—	3	3	no	—
80	C₃³	—	9	2	no	—
81	C₃³	—	9	1	no	—
82	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
83	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
84	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
85	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
86	3₋¹⁺²	—	3	9	no	—
87	3₋¹⁺²	—	3	9	no	—
88	3₋¹⁺²	—	3	9	no	—
89	3₋¹⁺²	—	387	6	no	—
90	3₋¹⁺²	—	387	3	no	—
91	C₃×C₉	—	3	9	no	—
92	C₃×C₉	—	3	3	no	—
93	C₃×C₉	—	129	3	no	—
94	C₃×C₉	—	129	6	no	—
95	C₃²	—	3	2	no	—
96	C₃²	—	3	1	no	—
97	C₃²	—	3	1	no	—
98	C₃²	—	3	1	no	—
99	C₃²	—	3	1	no	—
100	C₃²	—	3	2	no	—
101	C₃²	—	3	2	no	—
102	C₃²	—	3	2	no	—
103	C₃²	—	3	1	no	—
104	C₃²	—	3	1	no	—
105	C₃²	—	3	1	no	—
106	C₃²	—	9	9	no	—
107	C₃²	#16812507	1	3	yes	—
108	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
109	C₉	—	3	9	no	—
110	C₉	—	387	3	no	—
111	C₉	—	387	6	no	—
112	C₃	—	3	3	no	—
113	C₃	—	9	1	no	—
114	C₃	—	9	1	no	—
115	C₃	—	9	1	no	—
116	C₃	C₃×#16812507	1	1	yes	characteristic
117	C₃	#23782888	1	2	yes	—
118	C₃	#23782895	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23782798

C₃

yes

maximal, characteristic

#23782798

C₃

yes

maximal

#23782691

C₃

yes

maximal, complemented

C₃²×3₋¹⁺²×C₄₃

C₃

yes

maximal, characteristic

C₃×#11923958

—

C₃×#11923958

—

C₃²⋊(C₄₃⋊C₉)

—

C₃²⋊(C₄₃⋊C₉)

—

C₃²⋊(C₄₃⋊C₉)

—

C₃²⋊(C₄₃⋊C₉)

—

C₃²⋊(C₄₃⋊C₉)

C₃²

yes

—

C₃²⋊(C₄₃⋊C₉)

C₃²

yes

—

C₃⁴×C₄₃

C₃²

yes

characteristic

C₃×3₋¹⁺²×C₄₃

—

C₃×3₋¹⁺²×C₄₃

—

C₃×3₋¹⁺²×C₄₃

—

C₃×3₋¹⁺²×C₄₃

C₃²

yes

—

C₃²×C₉×C₄₃

—

#11923958

—

#11923958

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

—

C₃³×C₄₃

—

C₃³×C₄₃

—

C₃³×C₄₃

—

C₃³×C₄₃

yes

C₃³×C₄₃

yes

C₃³×C₄₃

yes

C₃³×C₄₃

C₃³

yes

characteristic

3₋¹⁺²×C₄₃

—

3₋¹⁺²×C₄₃

—

3₋¹⁺²×C₄₃

—

C₃×C₉×C₄₃

—

C₃×C₉×C₄₃

—

#10624631

—

maximal, Sylow

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

AΣL(1,𝔽₂₇)

yes

—

C₃²×C₄₃

C₃×H(3,𝔽₃)

yes

characteristic

C₉×C₄₃

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₃²×3₋¹⁺²

C₄₃⋊C₃

yes

—

—

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

C₃×AΣL(1,𝔽₂₇)

yes

characteristic

C₃×C₄₃

#6910

yes

—

C₃×C₄₃

#6912

yes

characteristic

C₃⁴

C₃×C₄₃⋊C₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

C₃×C₄₃⋊C₃

yes

—

C₃²×C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

129

—

C₃²⋊C₉

—

129

—

C₃²⋊C₉

—

129

—

C₃²⋊C₉

—

129

—

C₄₃

#10624631

yes

characteristic, complemented, Sylow

C₃³

—

C₃³

—

C₃³

—

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

characteristic

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

characteristic

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

characteristic

C₃³

C₃²×C₄₃⋊C₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

387

—

3₋¹⁺²

—

387

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

129

—

C₃×C₉

—

129

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

100

C₃²

—

101

C₃²

—

102

C₃²

—

103

C₃²

—

104

C₃²

—

105

C₃²

—

106

C₃²

—

107

C₃²

#16812507

yes

—

108

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

yes

characteristic

109

C₉

—

110

C₉

—

387

—

111

C₉

—

387

—

112

C₃

—

113

C₃

—

114

C₃

—

115

C₃

—

116

C₃

C₃×#16812507

yes

characteristic

117

C₃

#23782888

yes

—

118

C₃

#23782895

yes

characteristic

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₃²×3₋¹⁺²×C₄₃	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	C₃²×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624631
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃²×3₋¹⁺²

subgroup

G/H

center

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

commutator, cosocle

C₃³×C₄₃

C₃³

Frattini

C₃³

C₃²×C₄₃⋊C₃

Fitting

C₃²×3₋¹⁺²×C₄₃

C₃

socle

C₃²×C₄₃

C₃×H(3,𝔽₃)

prime radical

C₃⁴×C₄₃

C₃²

hypercenter

C₃²×3₋¹⁺²

C₄₃⋊C₃

hypocenter

C₄₃

#10624631

LCS

G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃²×3₋¹⁺²

N	H ≅ G/N	type
3. #23782691	C₃	semidirect
78. C₄₃	#10624631	semidirect

H ≅ G/N

type

3. #23782691

C₃

semidirect

78. C₄₃

#10624631

semidirect

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

subgroup	index
#23782798	3
#23782691	3
C₃²×3₋¹⁺²×C₄₃	3
#10624631	43

subgroup

index

#23782798

#23782691

C₃²×3₋¹⁺²×C₄₃

#10624631

Subgroups — #44532873

Conjugacy classes of subgroups

Complements

Maximal subgroups