Group #44533619 — subgroups

Subgroups — #44533619

Order 31347.

192 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 103 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	C₃×#16812505	C₃	1	1	yes	maximal, characteristic
2	#23782734	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782734	C₃	1	2	yes	maximal, complemented
4	#23782733	C₃	1	1	yes	maximal, characteristic, complemented
5	#23782733	C₃	1	2	yes	maximal, complemented
6	C₃²⋊(C₄₃⋊C₂₇)	C₃	1	2	yes	maximal
7	#23782708	C₃	1	2	yes	maximal, complemented
8	C₉×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
9	C₉×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
10	#16812505	—	3	3	no	—
11	C₃×C₄₃⋊C₂₇	C₃²	1	2	yes	—
12	C₃×C₄₃⋊C₂₇	C₃²	1	2	yes	—
13	C₃×C₄₃⋊C₂₇	C₃²	1	2	yes	—
14	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
15	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
16	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
17	C₃×3₋¹⁺²×C₄₃	C₉	1	1	yes	characteristic
18	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
19	C₄₃×C₉⋊C₉	C₉	1	4	yes	—
20	C₄₃×C₉⋊C₉	C₉	1	2	yes	—
21	C₄₃×C₃²⋊C₉	C₉	1	2	yes	—
22	C₉²×C₄₃	C₃²	1	1	yes	characteristic
23	C₉²×C₄₃	C₃²	1	2	yes	—
24	C₄₃⋊C₂₇	—	3	1	no	—
25	C₄₃⋊C₂₇	—	3	1	no	—
26	C₄₃⋊C₂₇	—	3	2	no	—
27	C₄₃⋊C₂₇	—	3	2	no	—
28	C₄₃⋊C₂₇	—	3	2	no	—
29	C₄₃⋊C₂₇	3₋¹⁺²	1	3	yes	complemented
30	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
31	3₋¹⁺²×C₄₃	—	3	3	no	—
32	C₃×C₉×C₄₃	—	3	1	no	—
33	C₃×C₉×C₄₃	—	3	2	no	—
34	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
35	C₃×C₉×C₄₃	C₃×C₉	1	4	yes	—
36	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
37	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
38	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
39	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
40	#10624728	—	43	1	no	maximal, Sylow
41	C₃²×C₄₃	—	3	1	no	—
42	C₃²×C₄₃	—	3	1	no	—
43	C₃²×C₄₃	—	3	2	no	—
44	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
45	C₉×C₄₃	—	3	2	no	—
46	C₉×C₄₃	—	3	2	no	—
47	C₉×C₄₃	—	3	2	no	—
48	C₉×C₄₃	—	3	4	no	—
49	C₉×C₄₃	C₂₇⋊C₃	1	3	yes	complemented
50	C₉×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
51	C₉×C₄₃	#737	1	2	yes	—
52	C₃×C₂₇⋊C₃	—	43	1	no	—
53	C₉×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
54	C₉⋊C₂₇	—	43	1	no	—
55	C₉⋊C₂₇	—	43	2	no	—
56	C₉⋊C₂₇	—	43	1	no	—
57	C₉⋊C₂₇	—	43	2	no	—
58	C₃²⋊C₂₇	—	43	2	no	—
59	#6864	—	43	2	no	—
60	C₉×C₂₇	—	43	1	no	—
61	C₃×C₄₃	—	9	1	no	—
62	C₃×C₄₃	C₉×3₋¹⁺²	1	1	yes	characteristic
63	C₃×C₄₃	C₃×C₂₇⋊C₃	1	1	yes	characteristic
64	C₃×C₄₃	#6903	1	2	yes	—
65	C₃×3₋¹⁺²	C₄₃⋊C₉	1	1	yes	characteristic
66	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
67	C₂₇⋊C₃	—	129	3	no	—
68	C₃×C₂₇	—	43	1	no	—
69	C₃×C₂₇	—	43	2	no	—
70	C₃×C₂₇	—	43	2	no	—
71	C₃×C₂₇	—	43	2	no	—
72	C₃×C₂₇	—	43	1	no	—
73	C₃×C₂₇	—	43	1	no	—
74	C₉⋊C₉	C₄₃⋊C₉	1	4	yes	—
75	C₉⋊C₉	C₄₃⋊C₉	1	2	yes	—
76	C₃²⋊C₉	C₄₃⋊C₉	1	2	yes	—
77	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
78	C₉²	C₃×C₄₃⋊C₃	1	2	yes	—
79	C₄₃	#10624728	1	1	yes	characteristic, complemented, Sylow
80	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
81	3₋¹⁺²	—	3	3	no	—
82	C₃×C₉	—	3	1	no	—
83	C₃×C₉	—	3	2	no	—
84	C₃×C₉	C₃×C₄₃⋊C₉	1	2	yes	—
85	C₃×C₉	C₃×C₄₃⋊C₉	1	4	yes	—
86	C₃×C₉	C₃×C₄₃⋊C₉	1	2	yes	—
87	C₃×C₉	C₃×C₄₃⋊C₉	1	2	yes	—
88	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
89	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
90	C₂₇	—	43	3	no	—
91	C₂₇	—	129	1	no	—
92	C₂₇	—	129	1	no	—
93	C₂₇	—	129	2	no	—
94	C₂₇	—	129	2	no	—
95	C₂₇	—	129	2	no	—
96	C₃²	—	3	1	no	—
97	C₃²	—	3	1	no	—
98	C₃²	—	3	2	no	—
99	C₃²	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
100	C₉	—	3	2	no	—
101	C₉	—	3	2	no	—
102	C₉	—	3	2	no	—
103	C₉	—	3	4	no	—
104	C₉	#16812505	1	3	yes	complemented
105	C₉	3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
106	C₉	#16812526	1	2	yes	—
107	C₃	—	9	1	no	—
108	C₃	3₋¹⁺²×C₄₃⋊C₉	1	1	yes	characteristic
109	C₃	C₃×#16812505	1	1	yes	characteristic
110	C₃	#23782857	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#16812505

C₃

yes

maximal, characteristic

#23782734

C₃

yes

maximal, characteristic, complemented

#23782734

C₃

yes

maximal, complemented

#23782733

C₃

yes

maximal, characteristic, complemented

#23782733

C₃

yes

maximal, complemented

C₃²⋊(C₄₃⋊C₂₇)

C₃

yes

maximal

#23782708

C₃

yes

maximal, complemented

C₉×C₄₃⋊C₂₇

C₃

yes

maximal, characteristic, complemented

C₉×3₋¹⁺²×C₄₃

C₃

yes

maximal, characteristic

#16812505

—

C₃×C₄₃⋊C₂₇

C₃²

yes

—

C₃×C₄₃⋊C₂₇

C₃²

yes

—

C₃×C₄₃⋊C₂₇

C₃²

yes

—

C₃×C₄₃⋊C₂₇

C₃²

yes

characteristic

C₃×C₄₃⋊C₂₇

C₃²

yes

characteristic

C₃×C₄₃⋊C₂₇

C₃²

yes

characteristic

C₃×3₋¹⁺²×C₄₃

C₉

yes

characteristic

C₃²×C₉×C₄₃

C₃²

yes

characteristic

C₄₃×C₉⋊C₉

C₉

yes

—

C₄₃×C₉⋊C₉

C₉

yes

—

C₄₃×C₃²⋊C₉

C₉

yes

—

C₉²×C₄₃

C₃²

yes

characteristic

C₉²×C₄₃

C₃²

yes

—

C₄₃⋊C₂₇

—

C₄₃⋊C₂₇

—

C₄₃⋊C₂₇

—

C₄₃⋊C₂₇

—

C₄₃⋊C₂₇

—

C₄₃⋊C₂₇

3₋¹⁺²

yes

complemented

C₃³×C₄₃

C₃×C₉

yes

characteristic

3₋¹⁺²×C₄₃

—

C₃×C₉×C₄₃

—

C₃×C₉×C₄₃

—

C₃×C₉×C₄₃

C₃×C₉

yes

—

C₃×C₉×C₄₃

C₃×C₉

yes

—

C₃×C₉×C₄₃

C₃×C₉

yes

—

C₃×C₉×C₄₃

C₃×C₉

yes

—

C₃×C₉×C₄₃

C₃×C₉

yes

characteristic

C₃×C₉×C₄₃

C₃³

yes

characteristic

#10624728

—

maximal, Sylow

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

—

C₃²×C₄₃

C₃²×C₉

yes

characteristic

C₉×C₄₃

—

C₉×C₄₃

—

C₉×C₄₃

—

C₉×C₄₃

—

C₉×C₄₃

C₂₇⋊C₃

yes

complemented

C₉×C₄₃

C₃×3₋¹⁺²

yes

characteristic

C₉×C₄₃

#737

yes

—

C₃×C₂₇⋊C₃

—

C₉×3₋¹⁺²

C₄₃⋊C₃

yes

characteristic

C₉⋊C₂₇

—

C₉⋊C₂₇

—

C₉⋊C₂₇

—

C₉⋊C₂₇

—

C₃²⋊C₂₇

—

#6864

—

C₉×C₂₇

—

C₃×C₄₃

—

C₃×C₄₃

C₉×3₋¹⁺²

yes

characteristic

C₃×C₄₃

C₃×C₂₇⋊C₃

yes

characteristic

C₃×C₄₃

#6903

yes

—

C₃×3₋¹⁺²

C₄₃⋊C₉

yes

characteristic

C₃²×C₉

C₃×C₄₃⋊C₃

yes

characteristic

C₂₇⋊C₃

—

129

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

—

C₉⋊C₉

C₄₃⋊C₉

yes

—

C₉⋊C₉

C₄₃⋊C₉

yes

—

C₃²⋊C₉

C₄₃⋊C₉

yes

—

C₉²

C₃×C₄₃⋊C₃

yes

characteristic

C₉²

C₃×C₄₃⋊C₃

yes

—

C₄₃

#10624728

yes

characteristic, complemented, Sylow

C₃³

C₃×C₄₃⋊C₉

yes

characteristic

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₄₃⋊C₉

yes

—

C₃×C₉

C₃×C₄₃⋊C₉

yes

—

C₃×C₉

C₃×C₄₃⋊C₉

yes

—

C₃×C₉

C₃×C₄₃⋊C₉

yes

—

C₃×C₉

C₃×C₄₃⋊C₉

yes

characteristic

C₃×C₉

C₃²×C₄₃⋊C₃

yes

characteristic

C₂₇

—

C₂₇

—

129

—

C₂₇

—

129

—

C₂₇

—

129

—

C₂₇

—

129

—

C₂₇

—

129

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃²×C₄₃⋊C₉

yes

characteristic

100

C₉

—

101

C₉

—

102

C₉

—

103

C₉

—

104

C₉

#16812505

yes

complemented

105

C₉

3₋¹⁺²×C₄₃⋊C₃

yes

characteristic

106

C₉

#16812526

yes

—

107

C₃

—

108

C₃

3₋¹⁺²×C₄₃⋊C₉

yes

characteristic

109

C₃

C₃×#16812505

yes

characteristic

110

C₃

#23782857

yes

—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
commutator, socle	C₃²×C₄₃	C₃²×C₉
Fitting	C₉×3₋¹⁺²×C₄₃	C₃
prime radical	C₃³×C₄₃	C₃×C₉
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	C₉×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624728
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₉×3₋¹⁺²

subgroup

G/H

center, Frattini

C₃×C₉

C₃²×C₄₃⋊C₃

commutator, socle

C₃²×C₄₃

C₃²×C₉

Fitting

C₉×3₋¹⁺²×C₄₃

C₃

prime radical

C₃³×C₄₃

C₃×C₉

cosocle

C₃×C₉×C₄₃

C₃³

hypercenter

C₉×3₋¹⁺²

C₄₃⋊C₃

C₄₃

G ▷ C₃²×C₄₃ ▷ C₄₃

C₁ ◁ C₃×C₉ ◁ C₉×3₋¹⁺²

N	H ≅ G/N	type
2. #23782734	C₃	semidirect
3. #23782734	C₃	semidirect
4. #23782733	C₃	semidirect
5. #23782733	C₃	semidirect
7. #23782708	C₃	semidirect
8. C₉×C₄₃⋊C₂₇	C₃	semidirect
29. C₄₃⋊C₂₇	3₋¹⁺²	semidirect
49. C₉×C₄₃	C₂₇⋊C₃	semidirect
79. C₄₃	#10624728	semidirect
104. C₉	#16812505	semidirect

H ≅ G/N

type

2. #23782734

C₃

semidirect

3. #23782734

C₃

semidirect

4. #23782733

C₃

semidirect

5. #23782733

C₃

semidirect

7. #23782708

C₃

semidirect

8. C₉×C₄₃⋊C₂₇

C₃

semidirect

29. C₄₃⋊C₂₇

3₋¹⁺²

semidirect

49. C₉×C₄₃

C₂₇⋊C₃

semidirect

79. C₄₃

#10624728

semidirect

104. C₉

#16812505

semidirect

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

subgroup	index
C₃×#16812505	3
#23782734	3
#23782733	3
C₃²⋊(C₄₃⋊C₂₇)	3
#23782708	3
C₉×C₄₃⋊C₂₇	3
C₉×3₋¹⁺²×C₄₃	3
#10624728	43

subgroup

index

C₃²⋊(C₄₃⋊C₂₇)

C₉×C₄₃⋊C₂₇

C₉×3₋¹⁺²×C₄₃

#10624728

Subgroups — #44533619

Conjugacy classes of subgroups

Complements

Maximal subgroups