Group #23744844 — subgroups

Subgroups — C₃×C₁₃×#6869 #23744844

Order 9477.

416 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 152 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	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₂₇⋊C₃	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6869	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₁₃	C₉	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	—	3	2	no	—
6	C₃²×C₉×C₁₃	—	3	1	no	—
7	C₃²×C₉×C₁₃	—	3	4	no	—
8	C₃²×C₉×C₁₃	—	3	2	no	—
9	C₃²×C₉×C₁₃	C₉	1	2	yes	—
10	C₃²×C₉×C₁₃	C₉	1	6	yes	—
11	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
13	C₁₃×C₂₇⋊C₃	—	3	6	no	—
14	C₁₃×C₂₇⋊C₃	C₃²	1	9	yes	complemented
15	C₃×C₁₃×C₂₇	—	3	3	no	—
16	C₃×#6869	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	—	3	9	no	—
18	C₃³×C₁₃	—	3	2	no	—
19	C₃³×C₁₃	—	3	1	no	—
20	C₃³×C₁₃	C₃×C₉	1	3	yes	—
21	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₉×C₁₃	—	3	4	no	—
23	C₃×C₉×C₁₃	—	3	2	no	—
24	C₃×C₉×C₁₃	—	3	12	no	—
25	C₃×C₉×C₁₃	—	3	6	no	—
26	C₃×C₉×C₁₃	—	3	3	no	—
27	C₃×C₉×C₁₃	—	3	6	no	—
28	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
29	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
30	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
31	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
32	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
33	C₃×C₉×C₁₃	3₋¹⁺²	1	4	yes	—
34	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
35	C₁₃×C₂₇	—	3	9	no	—
36	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
37	C₃×C₂₇⋊C₃	C₃×C₁₃	1	3	yes	complemented
38	#6869	C₃×C₁₃	1	9	yes	direct product factor
39	C₃²×C₁₃	—	3	9	no	—
40	C₃²×C₁₃	—	3	18	no	—
41	C₃²×C₁₃	—	3	9	no	—
42	C₃²×C₁₃	—	3	3	no	—
43	C₃²×C₁₃	—	3	3	no	—
44	C₃²×C₁₃	C₃²⋊C₉	1	2	yes	—
45	C₃²×C₁₃	C₃²⋊C₉	1	1	yes	characteristic
46	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
47	C₉×C₁₃	—	3	6	no	—
48	C₉×C₁₃	C₃²⋊C₉	1	4	yes	—
49	C₉×C₁₃	C₃²⋊C₉	1	2	yes	—
50	C₉×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
51	C₉×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
52	C₃⁴	C₉×C₁₃	1	1	yes	characteristic
53	C₃²×C₉	—	3	2	no	—
54	C₃²×C₉	—	3	1	no	—
55	C₃²×C₉	—	3	4	no	—
56	C₃²×C₉	—	3	2	no	—
57	C₃²×C₉	C₉×C₁₃	1	2	yes	—
58	C₃²×C₉	C₉×C₁₃	1	6	yes	—
59	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
60	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
61	C₂₇⋊C₃	—	3	6	no	—
62	C₂₇⋊C₃	C₃²×C₁₃	1	9	yes	complemented
63	C₃×C₂₇	—	3	3	no	—
64	C₃×C₁₃	—	3	9	no	—
65	C₃×C₁₃	—	3	2	no	—
66	C₃×C₁₃	—	3	1	no	—
67	C₃×C₁₃	#6869	1	3	yes	direct product factor
68	C₃×C₁₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
69	C₃³	—	3	9	no	—
70	C₃³	—	3	2	no	—
71	C₃³	—	3	1	no	—
72	C₃³	C₃×C₉×C₁₃	1	3	yes	—
73	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
74	C₃×C₉	—	3	4	no	—
75	C₃×C₉	—	3	2	no	—
76	C₃×C₉	—	3	12	no	—
77	C₃×C₉	—	3	6	no	—
78	C₃×C₉	—	3	3	no	—
79	C₃×C₉	—	3	6	no	—
80	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
81	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
82	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
83	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
84	C₃×C₉	C₁₃×3₋¹⁺²	1	4	yes	—
85	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
86	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
87	C₂₇	—	3	9	no	—
88	C₁₃	C₃×#6869	1	1	yes	characteristic, direct product factor, Sylow
89	C₃²	—	3	9	no	—
90	C₃²	—	3	18	no	—
91	C₃²	—	3	3	no	—
92	C₃²	—	3	9	no	—
93	C₃²	—	3	3	no	—
94	C₃²	C₁₃×C₃²⋊C₉	1	2	yes	—
95	C₃²	C₁₃×C₃²⋊C₉	1	1	yes	characteristic
96	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
97	C₉	—	3	6	no	—
98	C₉	C₁₃×C₃²⋊C₉	1	4	yes	—
99	C₉	C₁₃×C₃²⋊C₉	1	2	yes	—
100	C₉	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
101	C₉	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
102	C₃	—	3	2	no	—
103	C₃	—	3	1	no	—
104	C₃	—	3	9	no	—
105	C₃	C₁₃×#6869	1	3	yes	direct product factor
106	C₃	C₃×C₁₃×C₃²⋊C₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃³×C₉×C₁₃

C₃

yes

maximal, characteristic

C₃×C₁₃×C₂₇⋊C₃

C₃

yes

maximal, complemented

C₁₃×#6869

C₃

yes

maximal, direct product factor

C₃⁴×C₁₃

C₉

yes

characteristic

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

C₉

yes

—

C₃²×C₉×C₁₃

C₉

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₂₇⋊C₃

—

C₁₃×C₂₇⋊C₃

C₃²

yes

complemented

C₃×C₁₃×C₂₇

—

C₃×#6869

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

C₃×C₉

yes

—

C₃³×C₁₃

C₃×C₉

yes

characteristic

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

characteristic

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃×C₉×C₁₃

C₃³

yes

characteristic

C₁₃×C₂₇

—

C₃³×C₉

C₃×C₁₃

yes

characteristic

C₃×C₂₇⋊C₃

C₃×C₁₃

yes

complemented

#6869

C₃×C₁₃

yes

direct product factor

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃²⋊C₉

yes

—

C₃²×C₁₃

C₃²⋊C₉

yes

characteristic

C₃²×C₁₃

C₃²×C₉

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

C₃²⋊C₉

yes

—

C₉×C₁₃

C₃²⋊C₉

yes

—

C₉×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₉×C₁₃

C₃×3₋¹⁺²

yes

—

C₃⁴

C₉×C₁₃

yes

characteristic

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₉×C₁₃

yes

—

C₃²×C₉

C₉×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₂₇⋊C₃

—

C₂₇⋊C₃

C₃²×C₁₃

yes

complemented

C₃×C₂₇

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

#6869

yes

direct product factor

C₃×C₁₃

C₃×C₃²⋊C₉

yes

characteristic

C₃³

—

C₃³

—

C₃³

—

C₃³

C₃×C₉×C₁₃

yes

—

C₃³

C₃×C₉×C₁₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

characteristic

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

C₃×C₉

C₃³×C₁₃

yes

characteristic

C₂₇

—

C₁₃

C₃×#6869

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₁₃×C₃²⋊C₉

yes

—

C₃²

C₁₃×C₃²⋊C₉

yes

characteristic

C₃²

C₃²×C₉×C₁₃

yes

characteristic

C₉

—

C₉

C₁₃×C₃²⋊C₉

yes

—

C₉

C₁₃×C₃²⋊C₉

yes

—

100

C₉

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

101

C₉

C₃×C₁₃×3₋¹⁺²

yes

—

102

C₃

—

103

C₃

—

104

C₃

—

105

C₃

C₁₃×#6869

yes

direct product factor

106

C₃

C₃×C₁₃×C₃²⋊C₉

yes

characteristic

	subgroup	G/H
center	C₃×C₉×C₁₃	H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃²×C₁₃	C₃²⋊C₉
prime radical	C₃⁴×C₁₃	C₉
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

subgroup

G/H

center

C₃×C₉×C₁₃

H(3,𝔽₃)

commutator

C₃²

C₃²×C₉×C₁₃

Frattini, cosocle

C₃×C₉

C₃³×C₁₃

socle

C₃²×C₁₃

C₃²⋊C₉

prime radical

C₃⁴×C₁₃

C₉

LCS

G ▷ C₃² ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃×C₉×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₃×C₁₃×C₂₇⋊C₃	C₃	semidirect
3. C₁₃×#6869	C₃	direct (N × H)
14. C₁₃×C₂₇⋊C₃	C₃²	semidirect
16. C₃×#6869	C₁₃	direct (N × H)
37. C₃×C₂₇⋊C₃	C₃×C₁₃	semidirect
38. #6869	C₃×C₁₃	direct (N × H)
62. C₂₇⋊C₃	C₃²×C₁₃	semidirect
67. C₃×C₁₃	#6869	direct (N × H)
88. C₁₃	C₃×#6869	direct (N × H)
105. C₃	C₁₃×#6869	direct (N × H)

H ≅ G/N

type

2. C₃×C₁₃×C₂₇⋊C₃

C₃

semidirect

3. C₁₃×#6869

C₃

direct (N × H)

14. C₁₃×C₂₇⋊C₃

C₃²

semidirect

16. C₃×#6869

C₁₃

direct (N × H)

37. C₃×C₂₇⋊C₃

C₃×C₁₃

semidirect

38. #6869

C₃×C₁₃

direct (N × H)

62. C₂₇⋊C₃

C₃²×C₁₃

semidirect

67. C₃×C₁₃

#6869

direct (N × H)

88. C₁₃

C₃×#6869

direct (N × H)

105. C₃

C₁₃×#6869

direct (N × H)

Subgroups — C₃×C₁₃×#6869 #23744844

Conjugacy classes of subgroups

Complements

Subgroups — C3×C13×#6869 #23744844

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6869 #23744844