Group #44535316 — subgroups

Subgroups — C₃×#23782895 #44535316

Order 31347.

980 conjugacy classes of subgroups; only the 292 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 292 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	C₃²×#11923958	C₃	1	2	yes	maximal
2	C₃²×#11923958	C₃	1	1	yes	maximal, characteristic
3	#23782895	C₃	1	27	yes	maximal, direct product factor
4	C₃×#16812514	C₃	1	9	yes	maximal, complemented
5	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
6	C₃×#11923958	—	3	2	no	—
7	C₃×#11923958	—	3	1	no	—
8	C₃×#11923958	—	3	2	no	—
9	C₃×#11923958	—	3	2	no	—
10	C₃×#11923958	—	3	12	no	—
11	C₃×#11923958	—	3	6	no	—
12	C₃×#11923958	C₃²	1	6	yes	—
13	C₃×#11923958	C₃²	1	18	yes	—
14	C₃×#11923958	C₃²	1	9	yes	—
15	C₃²×C₄₃⋊C₉	—	3	2	no	—
16	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
17	#16812514	C₃²	1	81	yes	complemented
18	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
19	C₃×3₋¹⁺²×C₄₃	—	3	2	no	—
20	C₃×3₋¹⁺²×C₄₃	—	3	6	no	—
21	C₃×3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
22	C₃×3₋¹⁺²×C₄₃	C₃²	1	9	yes	—
23	C₃²×C₉×C₄₃	—	3	1	no	—
24	#11923958	—	3	18	no	—
25	#11923958	—	3	12	no	—
26	#11923958	—	3	18	no	—
27	#11923958	—	3	9	no	—
28	#11923958	—	3	18	no	—
29	#11923958	C₃³	1	18	yes	—
30	C₃×C₄₃⋊C₉	—	3	18	no	—
31	C₃×C₄₃⋊C₉	—	3	6	no	—
32	C₃×C₄₃⋊C₉	—	3	6	no	—
33	C₃×C₄₃⋊C₉	—	3	3	no	—
34	C₃×C₄₃⋊C₉	C₃³	1	9	yes	—
35	C₃³×C₄₃	—	9	3	no	—
36	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
37	C₃³×C₄₃	H(3,𝔽₃)	1	2	yes	—
38	C₃³×C₄₃	H(3,𝔽₃)	1	6	yes	—
39	C₃³×C₄₃	C₃³	1	1	yes	characteristic
40	C₃³×C₄₃	C₃³	1	3	yes	—
41	3₋¹⁺²×C₄₃	—	3	6	no	—
42	3₋¹⁺²×C₄₃	—	3	18	no	—
43	3₋¹⁺²×C₄₃	C₃³	1	9	yes	—
44	C₃×C₉×C₄₃	—	3	9	no	—
45	C₃×C₉×C₄₃	—	3	3	no	—
46	C₃×#6912	—	43	1	no	maximal, Sylow
47	C₃²×C₄₃	—	3	3	no	—
48	C₃²×C₄₃	—	3	6	no	—
49	C₃²×C₄₃	—	3	3	no	—
50	C₃²×C₄₃	—	9	6	no	—
51	C₃²×C₄₃	—	9	3	no	—
52	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	3	yes	—
53	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	6	yes	—
54	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	2	yes	—
55	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
56	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
57	C₉×C₄₃	—	3	9	no	—
58	C₄₃⋊C₉	—	3	18	no	—
59	C₄₃⋊C₉	—	3	9	no	—
60	C₃²×3₋¹⁺²	—	43	1	no	—
61	C₃²×3₋¹⁺²	—	43	2	no	—
62	C₃²×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
63	#6912	—	43	27	no	—
64	C₃×#733	—	43	9	no	—
65	C₃×C₄₃	—	3	3	no	—
66	C₃×C₄₃	—	3	6	no	—
67	C₃×C₄₃	—	3	2	no	—
68	C₃×C₄₃	—	3	1	no	—
69	C₃×C₄₃	#6912	1	3	yes	complemented
70	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
71	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
72	C₃×3₋¹⁺²	—	3	6	no	—
73	C₃×3₋¹⁺²	—	3	2	no	—
74	C₃×3₋¹⁺²	—	43	9	no	—
75	C₃×3₋¹⁺²	—	43	18	no	—
76	C₃×3₋¹⁺²	—	43	6	no	—
77	C₃×3₋¹⁺²	—	129	6	no	—
78	C₃×3₋¹⁺²	—	129	12	no	—
79	C₃×3₋¹⁺²	—	129	1	no	—
80	C₃×3₋¹⁺²	—	129	2	no	—
81	C₃×3₋¹⁺²	—	129	2	no	—
82	C₃×3₋¹⁺²	—	129	2	no	—
83	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	9	yes	—
84	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
85	C₃²×C₉	—	3	1	no	—
86	C₃²×C₉	—	43	3	no	—
87	C₃²×C₉	—	129	2	no	—
88	#733	—	43	81	no	—
89	C₄₃	C₃×#6912	1	1	yes	characteristic, complemented, Sylow
90	C₃³	—	9	3	no	—
91	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
92	C₃³	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
93	C₃³	C₃²⋊(C₄₃⋊C₃)	1	6	yes	—
94	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
95	C₃³	C₃²×C₄₃⋊C₃	1	3	yes	—
96	3₋¹⁺²	—	3	18	no	—
97	3₋¹⁺²	—	3	6	no	—
98	3₋¹⁺²	—	43	18	no	—
99	3₋¹⁺²	—	129	9	no	—
100	3₋¹⁺²	—	129	18	no	—
101	3₋¹⁺²	—	129	18	no	—
102	3₋¹⁺²	—	129	18	no	—
103	3₋¹⁺²	—	129	12	no	—
104	3₋¹⁺²	C₃²×C₄₃⋊C₃	1	9	yes	—
105	C₃×C₉	—	3	9	no	—
106	C₃×C₉	—	3	3	no	—
107	C₃×C₉	—	43	9	no	—
108	C₃×C₉	—	129	6	no	—
109	C₃×C₉	—	129	18	no	—
110	C₃×C₉	—	129	3	no	—
111	C₃×C₉	—	129	6	no	—
112	C₃²	—	3	3	no	—
113	C₃²	—	3	6	no	—
114	C₃²	—	3	3	no	—
115	C₃²	—	9	6	no	—
116	C₃²	—	9	3	no	—
117	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
118	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
119	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	6	yes	—
120	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
121	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
122	C₉	—	3	9	no	—
123	C₉	—	129	9	no	—
124	C₉	—	129	18	no	—
125	C₃	—	3	3	no	—
126	C₃	—	3	6	no	—
127	C₃	—	3	2	no	—
128	C₃	—	3	1	no	—
129	C₃	#23782895	1	3	yes	direct product factor
130	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#11923958

C₃

yes

maximal

C₃²×#11923958

C₃

yes

maximal, characteristic

#23782895

C₃

yes

maximal, direct product factor

C₃×#16812514

C₃

yes

maximal, complemented

C₃²×3₋¹⁺²×C₄₃

C₃

yes

maximal, characteristic

—

—

—

—

—

—

C₃²

yes

—

C₃×#11923958

C₃²

yes

—

C₃×#11923958

C₃²

yes

—

C₃²×C₄₃⋊C₉

—

C₃²×C₄₃⋊C₉

C₃²

yes

—

#16812514

C₃²

yes

complemented

C₃⁴×C₄₃

C₃²

yes

characteristic

C₃×3₋¹⁺²×C₄₃

—

C₃×3₋¹⁺²×C₄₃

—

C₃×3₋¹⁺²×C₄₃

C₃²

yes

—

C₃×3₋¹⁺²×C₄₃

C₃²

yes

—

C₃²×C₉×C₄₃

—

—

—

—

—

—

C₃³

yes

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

C₃³

yes

—

C₃³×C₄₃

—

C₃³×C₄₃

H(3,𝔽₃)

yes

characteristic

C₃³×C₄₃

H(3,𝔽₃)

yes

—

C₃³×C₄₃

H(3,𝔽₃)

yes

—

C₃³×C₄₃

C₃³

yes

characteristic

C₃³×C₄₃

C₃³

yes

—

3₋¹⁺²×C₄₃

—

3₋¹⁺²×C₄₃

—

3₋¹⁺²×C₄₃

C₃³

yes

—

C₃×C₉×C₄₃

—

C₃×C₉×C₄₃

—

C₃×#6912

—

maximal, Sylow

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

C₃×H(3,𝔽₃)

yes

—

C₃²×C₄₃

C₃×H(3,𝔽₃)

yes

—

C₃²×C₄₃

C₃×H(3,𝔽₃)

yes

—

C₃²×C₄₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₄₃

C₃⁴

yes

characteristic

C₉×C₄₃

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₃²×3₋¹⁺²

—

C₃²×3₋¹⁺²

—

C₃²×3₋¹⁺²

C₄₃⋊C₃

yes

characteristic

#6912

—

C₃×#733

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

#6912

yes

complemented

C₃×C₄₃

C₃²×H(3,𝔽₃)

yes

characteristic

C₃⁴

C₃×C₄₃⋊C₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

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

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

C₃×C₄₃⋊C₃

yes

—

C₃×3₋¹⁺²

C₃×C₄₃⋊C₃

yes

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

129

—

#733

—

C₄₃

C₃×#6912

yes

characteristic, complemented, Sylow

C₃³

—

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

characteristic

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

—

C₃³

C₃²⋊(C₄₃⋊C₃)

yes

—

C₃³

C₃²×C₄₃⋊C₃

yes

characteristic

C₃³

C₃²×C₄₃⋊C₃

yes

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

129

—

100

3₋¹⁺²

—

129

—

101

3₋¹⁺²

—

129

—

102

3₋¹⁺²

—

129

—

103

3₋¹⁺²

—

129

—

104

3₋¹⁺²

C₃²×C₄₃⋊C₃

yes

—

105

C₃×C₉

—

106

C₃×C₉

—

107

C₃×C₉

—

108

C₃×C₉

—

129

—

109

C₃×C₉

—

129

—

110

C₃×C₉

—

129

—

111

C₃×C₉

—

129

—

112

C₃²

—

113

C₃²

—

114

C₃²

—

115

C₃²

—

116

C₃²

—

117

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

yes

—

118

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

yes

—

119

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

yes

—

120

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

yes

characteristic

121

C₃²

C₃³×C₄₃⋊C₃

yes

characteristic

122

C₉

—

123

C₉

—

129

—

124

C₉

—

129

—

125

C₃

—

126

C₃

—

127

C₃

—

128

C₃

—

129

C₃

#23782895

yes

direct product factor

130

C₃

C₃²×C₃²⋊(C₄₃⋊C₃)

yes

characteristic

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃⁴
Frattini	C₃²	C₃³×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	C₃×#6912
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃²×3₋¹⁺²

subgroup

G/H

center

C₃²

C₃×C₃²⋊(C₄₃⋊C₃)

commutator, cosocle

C₃²×C₄₃

C₃⁴

Frattini

C₃²

C₃³×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

C₃×#6912

LCS

G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃²×3₋¹⁺²

N	H ≅ G/N	type
3. #23782895	C₃	direct (N × H)
4. C₃×#16812514	C₃	semidirect
17. #16812514	C₃²	semidirect
69. C₃×C₄₃	#6912	semidirect
89. C₄₃	C₃×#6912	semidirect
129. C₃	#23782895	direct (N × H)

H ≅ G/N

type

3. #23782895

C₃

direct (N × H)

4. C₃×#16812514

C₃

semidirect

17. #16812514

C₃²

semidirect

69. C₃×C₄₃

#6912

semidirect

89. C₄₃

C₃×#6912

semidirect

129. C₃

#23782895

direct (N × H)

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

subgroup	index
C₃²×#11923958	3
#23782895	3
C₃×#16812514	3
C₃²×3₋¹⁺²×C₄₃	3
C₃×#6912	43

subgroup

index

C₃²×3₋¹⁺²×C₄₃

Subgroups — C₃×#23782895 #44535316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#23782895 #44535316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23782895 #44535316