Group #23745021 — subgroups

Subgroups — C₃×C₁₃×#6894 #23745021

Order 9477.

932 conjugacy classes of subgroups; only the 548 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 548 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×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6894	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₁₃×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₃×C₁₃×C₉⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal
7	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
8	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
10	C₃²×C₉×C₁₃	—	3	9	no	—
11	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
13	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
14	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
15	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
16	C₁₃×C₉⋊C₉	C₃²	1	54	yes	complemented
17	C₁₃×C₉⋊C₉	C₃²	1	27	yes	complemented
18	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
19	C₃×#6894	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₃³×C₁₃	—	3	3	no	—
21	C₃³×C₁₃	—	3	6	no	—
22	C₃³×C₁₃	3₋¹⁺²	1	9	yes	—
23	C₃³×C₁₃	C₃³	1	3	yes	—
24	C₃³×C₁₃	C₃³	1	1	yes	characteristic
25	C₁₃×3₋¹⁺²	—	3	27	no	—
26	C₃×C₉×C₁₃	—	3	6	no	—
27	C₃×C₉×C₁₃	—	3	9	no	—
28	C₃×C₉×C₁₃	—	3	18	no	—
29	C₃×C₉×C₁₃	—	3	27	no	—
30	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
31	C₃×C₉×C₁₃	C₃³	1	18	yes	—
32	C₃×C₉×C₁₃	C₃³	1	6	yes	—
33	C₃×C₉×C₁₃	C₃³	1	9	yes	—
34	C₃×C₉×C₁₃	C₃³	1	3	yes	—
35	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
36	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
37	#6894	C₃×C₁₃	1	27	yes	direct product factor
38	C₃×C₉⋊C₉	C₃×C₁₃	1	6	yes	complemented
39	C₃×C₉⋊C₉	C₃×C₁₃	1	3	yes	complemented
40	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
41	C₃²×C₁₃	—	3	3	no	—
42	C₃²×C₁₃	—	3	6	no	—
43	C₃²×C₁₃	—	3	27	no	—
44	C₃²×C₁₃	C₃×3₋¹⁺²	1	9	yes	—
45	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
46	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
47	C₃²×C₁₃	#737	1	6	yes	—
48	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
49	C₉×C₁₃	—	3	6	no	—
50	C₉×C₁₃	—	3	9	no	—
51	C₉×C₁₃	—	3	18	no	—
52	C₉×C₁₃	C₃×3₋¹⁺²	1	9	yes	complemented
53	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
54	C₃×3₋¹⁺²	—	3	9	no	—
55	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
56	C₃²×C₉	—	3	9	no	—
57	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
58	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
59	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
60	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
61	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
62	C₉⋊C₉	C₃²×C₁₃	1	54	yes	complemented
63	C₉⋊C₉	C₃²×C₁₃	1	27	yes	complemented
64	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
65	C₃×C₁₃	—	3	9	no	—
66	C₃×C₁₃	#6894	1	9	yes	direct product factor
67	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
68	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
69	C₃×C₁₃	C₃×#737	1	2	yes	—
70	C₃³	—	3	3	no	—
71	C₃³	—	3	6	no	—
72	C₃³	C₁₃×3₋¹⁺²	1	9	yes	—
73	C₃³	C₃³×C₁₃	1	3	yes	—
74	C₃³	C₃³×C₁₃	1	1	yes	characteristic
75	3₋¹⁺²	—	3	27	no	—
76	C₃×C₉	—	3	6	no	—
77	C₃×C₉	—	3	9	no	—
78	C₃×C₉	—	3	18	no	—
79	C₃×C₉	—	3	27	no	—
80	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
81	C₃×C₉	C₃³×C₁₃	1	18	yes	—
82	C₃×C₉	C₃³×C₁₃	1	6	yes	—
83	C₃×C₉	C₃³×C₁₃	1	9	yes	—
84	C₃×C₉	C₃³×C₁₃	1	3	yes	—
85	C₁₃	C₃×#6894	1	1	yes	characteristic, direct product factor, Sylow
86	C₃²	—	3	27	no	—
87	C₃²	—	3	3	no	—
88	C₃²	—	3	6	no	—
89	C₃²	C₃×C₁₃×3₋¹⁺²	1	9	yes	—
90	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
91	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
92	C₃²	C₁₃×#737	1	6	yes	—
93	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
94	C₉	—	3	6	no	—
95	C₉	—	3	9	no	—
96	C₉	—	3	18	no	—
97	C₉	C₃×C₁₃×3₋¹⁺²	1	9	yes	complemented
98	C₃	—	3	9	no	—
99	C₃	C₁₃×#6894	1	9	yes	direct product factor
100	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
101	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
102	C₃	C₃×C₁₃×#737	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₃³×C₉×C₁₃

C₃

yes

maximal, characteristic

C₁₃×#6894

C₃

yes

maximal, direct product factor

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal, complemented

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal, complemented

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

C₃²

yes

complemented

C₁₃×C₉⋊C₉

C₃²

yes

complemented

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₃×#6894

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

3₋¹⁺²

yes

—

C₃³×C₁₃

C₃³

yes

—

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

complemented

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃²×3₋¹⁺²

C₃×C₁₃

yes

characteristic

C₃³×C₉

C₃×C₁₃

yes

characteristic

#6894

C₃×C₁₃

yes

direct product factor

C₃×C₉⋊C₉

C₃×C₁₃

yes

complemented

C₃×C₉⋊C₉

C₃×C₁₃

yes

complemented

C₃×C₃²⋊C₉

C₃×C₁₃

yes

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

#737

yes

—

C₃²×C₁₃

C₃⁴

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

C₃×3₋¹⁺²

yes

complemented

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃²×C₉

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

C₃²×C₁₃

yes

complemented

C₉⋊C₉

C₃²×C₁₃

yes

complemented

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃×C₁₃

—

C₃×C₁₃

#6894

yes

direct product factor

C₃×C₁₃

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₁₃

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₁₃

C₃×#737

yes

—

C₃³

—

C₃³

—

C₃³

C₁₃×3₋¹⁺²

yes

—

C₃³

C₃³×C₁₃

yes

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₁₃×3₋¹⁺²

yes

complemented

C₃×C₉

C₃³×C₁₃

yes

—

C₃×C₉

C₃³×C₁₃

yes

—

C₃×C₉

C₃³×C₁₃

yes

—

C₃×C₉

C₃³×C₁₃

yes

—

C₁₃

C₃×#6894

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₃²

C₁₃×#737

yes

—

C₃²

C₃⁴×C₁₃

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

C₃×C₁₃×3₋¹⁺²

yes

complemented

C₃

—

C₃

C₁₃×#6894

yes

direct product factor

100

C₃

C₃²×C₁₃×3₋¹⁺²

yes

characteristic

101

C₃

C₃²×C₁₃×3₋¹⁺²

yes

characteristic

102

C₃

C₃×C₁₃×#737

yes

—

	subgroup	G/H
center, socle	C₃³×C₁₃	C₃³
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃³×C₁₃

C₃³

commutator, Frattini, cosocle

C₃²

C₃⁴×C₁₃

prime radical

C₃⁴×C₁₃

C₃²

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃³×C₁₃ ◁ G

N	H ≅ G/N	type
3. C₁₃×#6894	C₃	direct (N × H)
4. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
5. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
16. C₁₃×C₉⋊C₉	C₃²	semidirect
17. C₁₃×C₉⋊C₉	C₃²	semidirect
19. C₃×#6894	C₁₃	direct (N × H)
30. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
37. #6894	C₃×C₁₃	direct (N × H)
38. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
39. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
52. C₉×C₁₃	C₃×3₋¹⁺²	semidirect
62. C₉⋊C₉	C₃²×C₁₃	semidirect
63. C₉⋊C₉	C₃²×C₁₃	semidirect
66. C₃×C₁₃	#6894	direct (N × H)
80. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
85. C₁₃	C₃×#6894	direct (N × H)
97. C₉	C₃×C₁₃×3₋¹⁺²	semidirect
99. C₃	C₁₃×#6894	direct (N × H)

H ≅ G/N

type

3. C₁₃×#6894

C₃

direct (N × H)

4. C₃×C₁₃×C₉⋊C₉

C₃

semidirect

5. C₃×C₁₃×C₉⋊C₉

C₃

semidirect

16. C₁₃×C₉⋊C₉

C₃²

semidirect

17. C₁₃×C₉⋊C₉

C₃²

semidirect

19. C₃×#6894

C₁₃

direct (N × H)

30. C₃×C₉×C₁₃

3₋¹⁺²

semidirect

37. #6894

C₃×C₁₃

direct (N × H)

38. C₃×C₉⋊C₉

C₃×C₁₃

semidirect

39. C₃×C₉⋊C₉

C₃×C₁₃

semidirect

52. C₉×C₁₃

C₃×3₋¹⁺²

semidirect

62. C₉⋊C₉

C₃²×C₁₃

semidirect

63. C₉⋊C₉

C₃²×C₁₃

semidirect

66. C₃×C₁₃

#6894

direct (N × H)

80. C₃×C₉

C₁₃×3₋¹⁺²

semidirect

85. C₁₃

C₃×#6894

direct (N × H)

97. C₉

C₃×C₁₃×3₋¹⁺²

semidirect

99. C₃

C₁₃×#6894

direct (N × H)

Subgroups — C₃×C₁₃×#6894 #23745021

Conjugacy classes of subgroups

Complements

Subgroups — C3×C13×#6894 #23745021

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6894 #23745021