Group #44534815 — subgroups

Subgroups — #44534815

Order 31347.

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

normal subgroups only

This group has 716 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	#23782845	C₃	1	9	yes	maximal, complemented
2	#23782838	C₃	1	18	yes	maximal, complemented
3	#23782822	C₃	1	6	yes	maximal, complemented
4	#23782798	C₃	1	3	yes	maximal
5	#23782782	C₃	1	3	yes	maximal, complemented
6	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
7	C₃×#11923958	C₃²	1	9	yes	—
8	#16812500	C₃²	1	9	yes	complemented
9	#16812499	C₃²	1	9	yes	complemented
10	(C₄₃⋊C₉)⋊C₉	C₃²	1	54	yes	complemented
11	C₃²⋊(C₄₃⋊C₉)	C₃²	1	9	yes	—
12	C₃²⋊(C₄₃⋊C₉)	C₃²	1	18	yes	—
13	C₉×C₄₃⋊C₉	C₃²	1	9	yes	complemented
14	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
15	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
16	C₃×3₋¹⁺²×C₄₃	C₃²	1	6	yes	—
17	C₃×3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
18	C₃²×C₉×C₄₃	C₃²	1	2	yes	—
19	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
20	#11923958	—	9	9	no	—
21	C₃×C₄₃⋊C₉	C₃³	1	27	yes	—
22	C₃³×C₄₃	—	3	3	no	—
23	C₃³×C₄₃	—	9	3	no	—
24	C₃³×C₄₃	C₃³	1	2	yes	—
25	C₃³×C₄₃	C₃³	1	1	yes	characteristic
26	C₃³×C₄₃	C₃³	1	1	yes	characteristic
27	3₋¹⁺²×C₄₃	—	3	18	no	—
28	3₋¹⁺²×C₄₃	—	3	9	no	—
29	C₃×C₉×C₄₃	—	3	6	no	—
30	C₃×C₉×C₄₃	3₋¹⁺²	1	9	yes	complemented
31	C₃×C₉×C₄₃	C₃³	1	6	yes	—
32	C₃×C₉×C₄₃	C₃³	1	3	yes	—
33	#10624884	—	43	1	no	maximal, Sylow
34	C₃²×C₄₃	—	3	3	no	—
35	C₃²×C₄₃	—	3	2	no	—
36	C₃²×C₄₃	—	3	1	no	—
37	C₃²×C₄₃	—	3	6	no	—
38	C₃²×C₄₃	—	3	3	no	—
39	C₃²×C₄₃	—	9	9	no	—
40	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
41	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
42	C₉×C₄₃	—	3	6	no	—
43	C₉×C₄₃	C₃×3₋¹⁺²	1	9	yes	—
44	C₄₃⋊C₉	—	3	27	no	—
45	C₃²×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
46	#6900	—	43	9	no	—
47	#6899	—	43	18	no	—
48	#6895	—	43	6	no	—
49	#6891	—	43	3	no	—
50	#6887	—	43	3	no	—
51	C₃×C₄₃	—	3	3	no	—
52	C₃×C₄₃	—	9	2	no	—
53	C₃×C₄₃	—	9	1	no	—
54	C₃×C₄₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
55	C₃×C₄₃	3₋¹⁺⁴	1	3	yes	—
56	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
57	C₃×3₋¹⁺²	—	3	9	no	—
58	C₃×3₋¹⁺²	—	43	9	no	—
59	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	6	yes	—
60	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
61	C₃²×C₉	C₃×C₄₃⋊C₃	1	2	yes	—
62	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
63	C₉⋊C₉	—	43	54	no	—
64	C₉⋊C₉	—	43	9	no	—
65	C₉⋊C₉	—	43	9	no	—
66	C₃²⋊C₉	—	43	9	no	—
67	C₃²⋊C₉	—	43	18	no	—
68	C₉²	—	43	9	no	—
69	C₄₃	#10624884	1	1	yes	characteristic, complemented, Sylow
70	C₃³	—	3	3	no	—
71	C₃³	—	9	3	no	—
72	C₃³	C₃²×C₄₃⋊C₃	1	2	yes	—
73	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
74	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
75	3₋¹⁺²	—	3	18	no	—
76	3₋¹⁺²	—	3	9	no	—
77	3₋¹⁺²	—	387	9	no	—
78	C₃×C₉	—	3	6	no	—
79	C₃×C₉	—	43	27	no	—
80	C₃×C₉	#11923958	1	9	yes	complemented
81	C₃×C₉	C₃²×C₄₃⋊C₃	1	6	yes	—
82	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
83	C₃²	—	3	3	no	—
84	C₃²	—	3	2	no	—
85	C₃²	—	3	1	no	—
86	C₃²	—	3	3	no	—
87	C₃²	—	3	6	no	—
88	C₃²	—	9	9	no	—
89	C₃²	C₃×#11923958	1	3	yes	—
90	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
91	C₉	—	3	6	no	—
92	C₉	—	129	27	no	—
93	C₉	C₃×#11923958	1	9	yes	—
94	C₃	—	3	3	no	—
95	C₃	—	9	1	no	—
96	C₃	—	9	2	no	—
97	C₃	C₃²×#11923958	1	1	yes	characteristic
98	C₃	#23782923	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23782845

C₃

yes

maximal, complemented

#23782838

C₃

yes

maximal, complemented

#23782822

C₃

yes

maximal, complemented

#23782798

C₃

yes

maximal

#23782782

C₃

yes

maximal, complemented

C₃²×3₋¹⁺²×C₄₃

C₃

yes

maximal, characteristic

C₃×#11923958

C₃²

yes

—

#16812500

C₃²

yes

complemented

#16812499

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

—

C₃×3₋¹⁺²×C₄₃

C₃²

yes

—

C₃×3₋¹⁺²×C₄₃

C₃²

yes

—

C₃²×C₉×C₄₃

C₃²

yes

—

C₃²×C₉×C₄₃

C₃²

yes

characteristic

#11923958

—

C₃×C₄₃⋊C₉

C₃³

yes

—

C₃³×C₄₃

—

C₃³×C₄₃

—

C₃³×C₄₃

C₃³

yes

—

C₃³×C₄₃

C₃³

yes

characteristic

C₃³×C₄₃

C₃³

yes

characteristic

3₋¹⁺²×C₄₃

—

3₋¹⁺²×C₄₃

—

C₃×C₉×C₄₃

—

C₃×C₉×C₄₃

3₋¹⁺²

yes

complemented

C₃×C₉×C₄₃

C₃³

yes

—

C₃×C₉×C₄₃

C₃³

yes

—

#10624884

—

maximal, Sylow

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

—

C₉×C₄₃

C₃×3₋¹⁺²

yes

—

C₄₃⋊C₉

—

C₃²×3₋¹⁺²

C₄₃⋊C₃

yes

—

—

—

—

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

—

C₃×C₄₃

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₄₃

3₋¹⁺⁴

yes

—

C₃⁴

C₃×C₄₃⋊C₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃×C₄₃⋊C₃

yes

—

C₃×3₋¹⁺²

C₃×C₄₃⋊C₃

yes

—

C₃²×C₉

C₃×C₄₃⋊C₃

yes

—

C₃²×C₉

C₃×C₄₃⋊C₃

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₉²

—

C₄₃

#10624884

yes

characteristic, complemented, Sylow

C₃³

—

C₃³

—

C₃³

C₃²×C₄₃⋊C₃

yes

—

C₃³

C₃²×C₄₃⋊C₃

yes

characteristic

C₃³

C₃²×C₄₃⋊C₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

387

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

#11923958

yes

complemented

C₃×C₉

C₃²×C₄₃⋊C₃

yes

—

C₃×C₉

C₃²×C₄₃⋊C₃

yes

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃×#11923958

yes

—

C₃²

C₃³×C₄₃⋊C₃

yes

characteristic

C₉

—

C₉

—

129

—

C₉

C₃×#11923958

yes

—

C₃

—

C₃

—

C₃

—

C₃

C₃²×#11923958

yes

characteristic

C₃

#23782923

yes

—

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₃²×3₋¹⁺²×C₄₃	C₃
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	C₃²×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624884
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃²×3₋¹⁺²

subgroup

G/H

center, Frattini

C₃²

C₃³×C₄₃⋊C₃

commutator, socle, cosocle

C₃²×C₄₃

C₃⁴

Fitting

C₃²×3₋¹⁺²×C₄₃

C₃

prime radical

C₃⁴×C₄₃

C₃²

hypercenter

C₃²×3₋¹⁺²

C₄₃⋊C₃

C₄₃

G ▷ C₃²×C₄₃ ▷ C₄₃

C₁ ◁ C₃² ◁ C₃²×3₋¹⁺²

N	H ≅ G/N	type
1. #23782845	C₃	semidirect
2. #23782838	C₃	semidirect
3. #23782822	C₃	semidirect
5. #23782782	C₃	semidirect
8. #16812500	C₃²	semidirect
9. #16812499	C₃²	semidirect
10. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
13. C₉×C₄₃⋊C₉	C₃²	semidirect
30. C₃×C₉×C₄₃	3₋¹⁺²	semidirect
69. C₄₃	#10624884	semidirect
80. C₃×C₉	#11923958	semidirect

H ≅ G/N

type

1. #23782845

C₃

semidirect

2. #23782838

C₃

semidirect

3. #23782822

C₃

semidirect

5. #23782782

C₃

semidirect

8. #16812500

C₃²

semidirect

9. #16812499

C₃²

semidirect

10. (C₄₃⋊C₉)⋊C₉

C₃²

semidirect

13. C₉×C₄₃⋊C₉

C₃²

semidirect

30. C₃×C₉×C₄₃

3₋¹⁺²

semidirect

69. C₄₃

#10624884

semidirect

80. C₃×C₉

#11923958

semidirect

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

subgroup	index
#23782845	3
#23782838	3
#23782822	3
#23782798	3
#23782782	3
C₃²×3₋¹⁺²×C₄₃	3
#10624884	43

subgroup

index

C₃²×3₋¹⁺²×C₄₃

Subgroups — #44534815

Conjugacy classes of subgroups

Complements

Maximal subgroups