Group #44534983 — subgroups

Subgroups — #44534983

Order 31347.

836 conjugacy classes of subgroups; only the 298 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 298 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	#23782845	C₃	1	9	yes	maximal, complemented
3	#23782823	C₃	1	9	yes	maximal, complemented
4	#23782818	C₃	1	6	yes	maximal, complemented
5	#23782817	C₃	1	6	yes	maximal, complemented
6	#23782798	C₃	1	1	yes	maximal, characteristic
7	#23782792	C₃	1	6	yes	maximal, complemented
8	C₄₃×#6891	C₃	1	1	yes	maximal, characteristic
9	C₃×#11923958	—	3	18	no	—
10	C₃×#11923958	C₃²	1	2	yes	—
11	C₃×#11923958	C₃²	1	2	yes	—
12	C₃×#11923958	C₃²	1	6	yes	—
13	C₃×#11923958	C₃²	1	6	yes	—
14	C₃×#11923958	C₃²	1	3	yes	—
15	C₃×#11923958	C₃²	1	2	yes	—
16	C₃²×C₄₃⋊C₉	C₃²	1	6	yes	—
17	#16812500	C₃²	1	9	yes	complemented
18	#16812499	C₃²	1	9	yes	complemented
19	(C₄₃⋊C₉)⋊C₉	C₃²	1	18	yes	complemented
20	(C₄₃⋊C₉)⋊C₉	C₃²	1	18	yes	complemented
21	(C₄₃⋊C₉)⋊C₉	C₃²	1	18	yes	complemented
22	C₃²⋊(C₄₃⋊C₉)	C₃²	1	6	yes	—
23	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	—
24	C₉×C₄₃⋊C₉	C₃²	1	9	yes	complemented
25	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
26	C₃×3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
27	C₄₃×C₃²⋊C₉	C₃²	1	6	yes	—
28	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	—
29	#11923958	—	3	6	no	—
30	#11923958	—	3	6	no	—
31	#11923958	—	3	18	no	—
32	#11923958	—	3	18	no	—
33	#11923958	—	9	3	no	—
34	#11923958	3₋¹⁺²	1	18	yes	complemented
35	C₃×C₄₃⋊C₉	—	3	18	no	—
36	C₃×C₄₃⋊C₉	C₃³	1	9	yes	—
37	C₃×C₄₃⋊C₉	C₃³	1	6	yes	—
38	C₃×C₄₃⋊C₉	C₃³	1	6	yes	—
39	C₃×C₄₃⋊C₉	C₃³	1	6	yes	—
40	C₃³×C₄₃	—	3	6	no	—
41	C₃³×C₄₃	—	9	1	no	—
42	C₃³×C₄₃	—	9	1	no	—
43	C₃³×C₄₃	C₃³	1	1	yes	characteristic
44	C₃³×C₄₃	C₃³	1	1	yes	characteristic
45	C₃³×C₄₃	C₃³	1	2	yes	—
46	3₋¹⁺²×C₄₃	—	9	3	no	—
47	C₃×C₉×C₄₃	C₃³	1	9	yes	—
48	3₋¹⁺²²	—	43	1	no	maximal, Sylow
49	C₃²×C₄₃	—	3	2	no	—
50	C₃²×C₄₃	—	3	2	no	—
51	C₃²×C₄₃	—	3	2	no	—
52	C₃²×C₄₃	—	3	2	no	—
53	C₃²×C₄₃	—	3	2	no	—
54	C₃²×C₄₃	—	3	1	no	—
55	C₃²×C₄₃	—	3	1	no	—
56	C₃²×C₄₃	—	3	1	no	—
57	C₃²×C₄₃	—	3	1	no	—
58	C₃²×C₄₃	—	9	9	no	—
59	C₃²×C₄₃	C₃×3₋¹⁺²	1	6	yes	—
60	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
61	C₉×C₄₃	—	3	9	no	—
62	C₄₃⋊C₉	—	3	6	no	—
63	C₄₃⋊C₉	—	3	6	no	—
64	C₄₃⋊C₉	—	3	9	no	—
65	C₄₃⋊C₉	C₃×3₋¹⁺²	1	18	yes	complemented
66	C₃²×3₋¹⁺²	—	43	2	no	—
67	#6900	—	43	9	no	—
68	#6896	—	43	9	no	—
69	#6894	—	43	6	no	—
70	#6894	—	43	6	no	—
71	#6891	—	43	1	no	—
72	#6891	C₄₃⋊C₃	1	1	yes	characteristic
73	C₉×3₋¹⁺²	—	43	6	no	—
74	C₃×C₄₃	—	3	6	no	—
75	C₃×C₄₃	—	9	1	no	—
76	C₃×C₄₃	—	9	1	no	—
77	C₃×C₄₃	C₃²×3₋¹⁺²	1	2	yes	—
78	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
79	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
80	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
81	C₃×3₋¹⁺²	—	43	2	no	—
82	C₃×3₋¹⁺²	—	43	2	no	—
83	C₃×3₋¹⁺²	—	43	2	no	—
84	C₃×3₋¹⁺²	—	43	6	no	—
85	C₃×3₋¹⁺²	—	43	6	no	—
86	C₃×3₋¹⁺²	—	43	3	no	—
87	C₃×3₋¹⁺²	—	129	18	no	—
88	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
89	C₃²×C₉	—	43	6	no	—
90	C₉⋊C₉	—	43	18	no	—
91	C₉⋊C₉	—	43	18	no	—
92	C₉⋊C₉	—	43	18	no	—
93	C₉⋊C₉	—	43	9	no	—
94	C₉⋊C₉	—	43	9	no	—
95	C₃²⋊C₉	—	43	6	no	—
96	C₃²⋊C₉	—	43	3	no	—
97	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	6	yes	—
98	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
99	C₉²	—	43	9	no	—
100	C₄₃	3₋¹⁺²²	1	1	yes	characteristic, complemented, Sylow
101	C₃³	—	3	6	no	—
102	C₃³	—	9	1	no	—
103	C₃³	—	9	1	no	—
104	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
105	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
106	C₃³	C₃²×C₄₃⋊C₃	1	2	yes	—
107	3₋¹⁺²	—	9	3	no	—
108	3₋¹⁺²	—	43	18	no	—
109	3₋¹⁺²	—	129	18	no	—
110	3₋¹⁺²	—	129	18	no	—
111	3₋¹⁺²	—	129	6	no	—
112	3₋¹⁺²	—	129	6	no	—
113	3₋¹⁺²	—	387	3	no	—
114	C₃×C₉	—	43	6	no	—
115	C₃×C₉	—	43	9	no	—
116	C₃×C₉	—	43	6	no	—
117	C₃×C₉	—	43	6	no	—
118	C₃×C₉	—	129	18	no	—
119	C₃×C₉	C₃²×C₄₃⋊C₃	1	9	yes	—
120	C₃²	—	3	2	no	—
121	C₃²	—	3	2	no	—
122	C₃²	—	3	2	no	—
123	C₃²	—	3	2	no	—
124	C₃²	—	3	2	no	—
125	C₃²	—	3	1	no	—
126	C₃²	—	3	1	no	—
127	C₃²	—	3	1	no	—
128	C₃²	—	3	1	no	—
129	C₃²	—	9	9	no	—
130	C₃²	3₋¹⁺²×C₄₃⋊C₃	1	6	yes	—
131	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
132	C₉	—	3	9	no	—
133	C₉	—	43	18	no	—
134	C₉	—	129	6	no	—
135	C₉	—	129	6	no	—
136	C₉	—	129	9	no	—
137	C₃	—	3	6	no	—
138	C₃	—	9	1	no	—
139	C₃	—	9	1	no	—
140	C₃	C₃×3₋¹⁺²×C₄₃⋊C₃	1	2	yes	—
141	C₃	#23782923	1	1	yes	characteristic
142	C₃	#23782924	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#11923958

C₃

yes

maximal

#23782845

C₃

yes

maximal, complemented

#23782823

C₃

yes

maximal, complemented

#23782818

C₃

yes

maximal, complemented

#23782817

C₃

yes

maximal, complemented

#23782798

C₃

yes

maximal, characteristic

#23782792

C₃

yes

maximal, complemented

C₄₃×#6891

C₃

yes

maximal, characteristic

C₃×#11923958

—

C₃×#11923958

C₃²

yes

—

C₃×#11923958

C₃²

yes

—

C₃×#11923958

C₃²

yes

—

C₃×#11923958

C₃²

yes

—

C₃×#11923958

C₃²

yes

—

C₃×#11923958

C₃²

yes

—

C₃²×C₄₃⋊C₉

C₃²

yes

—

#16812500

C₃²

yes

complemented

#16812499

C₃²

yes

complemented

(C₄₃⋊C₉)⋊C₉

C₃²

yes

complemented

(C₄₃⋊C₉)⋊C₉

C₃²

yes

complemented

(C₄₃⋊C₉)⋊C₉

C₃²

yes

complemented

C₃²⋊(C₄₃⋊C₉)

C₃²

yes

—

C₃²⋊(C₄₃⋊C₉)

C₃²

yes

—

C₉×C₄₃⋊C₉

C₃²

yes

complemented

C₃⁴×C₄₃

C₃²

yes

characteristic

C₃×3₋¹⁺²×C₄₃

C₃²

yes

—

C₄₃×C₃²⋊C₉

C₃²

yes

—

C₄₃×C₃²⋊C₉

C₃²

yes

—

—

—

—

—

—

3₋¹⁺²

yes

complemented

C₃×C₄₃⋊C₉

—

C₃×C₄₃⋊C₉

C₃³

yes

—

C₃×C₄₃⋊C₉

C₃³

yes

—

C₃×C₄₃⋊C₉

C₃³

yes

—

C₃×C₄₃⋊C₉

C₃³

yes

—

C₃³×C₄₃

—

C₃³×C₄₃

—

C₃³×C₄₃

—

C₃³×C₄₃

C₃³

yes

characteristic

C₃³×C₄₃

C₃³

yes

characteristic

C₃³×C₄₃

C₃³

yes

—

3₋¹⁺²×C₄₃

—

C₃×C₉×C₄₃

C₃³

yes

—

3₋¹⁺²²

—

maximal, Sylow

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

C₃×3₋¹⁺²

yes

—

C₃²×C₄₃

C₃⁴

yes

characteristic

C₉×C₄₃

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

C₃×3₋¹⁺²

yes

complemented

C₃²×3₋¹⁺²

—

—

—

—

—

—

C₄₃⋊C₃

yes

characteristic

C₉×3₋¹⁺²

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

C₃²×3₋¹⁺²

yes

—

C₃×C₄₃

3₋¹⁺⁴

yes

characteristic

C₃×C₄₃

3₋¹⁺⁴

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

—

C₃×3₋¹⁺²

—

129

—

C₃×3₋¹⁺²

C₃×C₄₃⋊C₃

yes

—

C₃²×C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃×C₄₃⋊C₃

yes

—

C₃²⋊C₉

C₃×C₄₃⋊C₃

yes

—

C₉²

—

100

C₄₃

3₋¹⁺²²

yes

characteristic, complemented, Sylow

101

C₃³

—

102

C₃³

—

103

C₃³

—

104

C₃³

C₃²×C₄₃⋊C₃

yes

characteristic

105

C₃³

C₃²×C₄₃⋊C₃

yes

characteristic

106

C₃³

C₃²×C₄₃⋊C₃

yes

—

107

3₋¹⁺²

—

108

3₋¹⁺²

—

109

3₋¹⁺²

—

129

—

110

3₋¹⁺²

—

129

—

111

3₋¹⁺²

—

129

—

112

3₋¹⁺²

—

129

—

113

3₋¹⁺²

—

387

—

114

C₃×C₉

—

115

C₃×C₉

—

116

C₃×C₉

—

117

C₃×C₉

—

118

C₃×C₉

—

129

—

119

C₃×C₉

C₃²×C₄₃⋊C₃

yes

—

120

C₃²

—

121

C₃²

—

122

C₃²

—

123

C₃²

—

124

C₃²

—

125

C₃²

—

126

C₃²

—

127

C₃²

—

128

C₃²

—

129

C₃²

—

130

C₃²

3₋¹⁺²×C₄₃⋊C₃

yes

—

131

C₃²

C₃³×C₄₃⋊C₃

yes

characteristic

132

C₉

—

133

C₉

—

134

C₉

—

129

—

135

C₉

—

129

—

136

C₉

—

129

—

137

C₃

—

138

C₃

—

139

C₃

—

140

C₃

C₃×3₋¹⁺²×C₄₃⋊C₃

yes

—

141

C₃

#23782923

yes

characteristic

142

C₃

#23782924

yes

characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₄₃×#6891	C₃
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	#6891	C₄₃⋊C₃
hypocenter	C₄₃	3₋¹⁺²²
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ #6891

subgroup

G/H

center, Frattini

C₃²

C₃³×C₄₃⋊C₃

commutator, socle, cosocle

C₃²×C₄₃

C₃⁴

Fitting

C₄₃×#6891

C₃

prime radical

C₃⁴×C₄₃

C₃²

hypercenter

#6891

C₄₃⋊C₃

hypocenter

C₄₃

3₋¹⁺²²

LCS

G ▷ C₃²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₃² ◁ #6891

N	H ≅ G/N	type
2. #23782845	C₃	semidirect
3. #23782823	C₃	semidirect
4. #23782818	C₃	semidirect
5. #23782817	C₃	semidirect
7. #23782792	C₃	semidirect
17. #16812500	C₃²	semidirect
18. #16812499	C₃²	semidirect
19. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
20. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
21. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
24. C₉×C₄₃⋊C₉	C₃²	semidirect
34. #11923958	3₋¹⁺²	semidirect
65. C₄₃⋊C₉	C₃×3₋¹⁺²	semidirect
100. C₄₃	3₋¹⁺²²	semidirect

H ≅ G/N

type

2. #23782845

C₃

semidirect

3. #23782823

C₃

semidirect

4. #23782818

C₃

semidirect

5. #23782817

C₃

semidirect

7. #23782792

C₃

semidirect

17. #16812500

C₃²

semidirect

18. #16812499

C₃²

semidirect

19. (C₄₃⋊C₉)⋊C₉

C₃²

semidirect

20. (C₄₃⋊C₉)⋊C₉

C₃²

semidirect

21. (C₄₃⋊C₉)⋊C₉

C₃²

semidirect

24. C₉×C₄₃⋊C₉

C₃²

semidirect

34. #11923958

3₋¹⁺²

semidirect

65. C₄₃⋊C₉

C₃×3₋¹⁺²

semidirect

100. C₄₃

3₋¹⁺²²

semidirect

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

subgroup	index
C₃²×#11923958	3
#23782845	3
#23782823	3
#23782818	3
#23782817	3
#23782798	3
#23782792	3
C₄₃×#6891	3
3₋¹⁺²²	43

subgroup

index

C₄₃×#6891

3₋¹⁺²²

Subgroups — #44534983

Conjugacy classes of subgroups

Complements

Maximal subgroups