Group #23744843 — subgroups

Subgroups — C₁₃×#10624692 #23744843

Order 9477.

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

normal subgroups only

This group has 362 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	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6887	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6868	C₃	1	3	yes	maximal, complemented
4	C₁₃×#6867	C₃	1	3	yes	maximal, complemented
5	C₁₃×#6866	C₃	1	3	yes	maximal
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
8	C₃×C₁₃×3₋¹⁺²	—	3	6	no	—
9	C₃×C₁₃×3₋¹⁺²	C₉	1	9	yes	complemented
10	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
13	C₁₃×C₉⋊C₉	—	3	6	no	—
14	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
15	C₉²×C₁₃	—	3	3	no	—
16	#10624692	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	—	3	1	no	—
18	C₃³×C₁₃	—	3	2	no	—
19	C₃³×C₁₃	—	9	3	no	—
20	C₃³×C₁₃	C₃×C₉	1	3	yes	—
21	C₃³×C₁₃	C₃³	1	1	yes	characteristic
22	C₁₃×3₋¹⁺²	—	3	27	no	—
23	C₃×C₉×C₁₃	—	3	1	no	—
24	C₃×C₉×C₁₃	—	3	1	no	—
25	C₃×C₉×C₁₃	—	3	2	no	—
26	C₃×C₉×C₁₃	—	3	2	no	—
27	C₃×C₉×C₁₃	—	3	9	no	—
28	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
29	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
30	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
31	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
32	C₃×C₉×C₁₃	3₋¹⁺²	1	6	yes	—
33	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
34	#6887	C₃×C₁₃	1	3	yes	complemented
35	#6868	C₃×C₁₃	1	3	yes	complemented
36	#6867	C₃×C₁₃	1	3	yes	complemented
37	#6866	C₃×C₁₃	1	3	yes	—
38	C₃²×C₁₃	—	3	3	no	—
39	C₃²×C₁₃	—	3	3	no	—
40	C₃²×C₁₃	—	9	3	no	—
41	C₃²×C₁₃	—	9	6	no	—
42	C₃²×C₁₃	—	9	3	no	—
43	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
44	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
45	C₃²×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
46	C₉×C₁₃	—	3	3	no	—
47	C₉×C₁₃	—	3	3	no	—
48	C₉×C₁₃	—	9	9	no	—
49	C₉×C₁₃	C₃²⋊C₉	1	9	yes	—
50	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
51	C₃×3₋¹⁺²	—	3	3	no	—
52	C₃×3₋¹⁺²	—	3	6	no	—
53	C₃×3₋¹⁺²	C₉×C₁₃	1	9	yes	complemented
54	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
55	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
56	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
57	C₉⋊C₉	—	3	6	no	—
58	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
59	C₉²	—	3	3	no	—
60	C₃×C₁₃	—	3	1	no	—
61	C₃×C₁₃	—	3	2	no	—
62	C₃×C₁₃	—	9	3	no	—
63	C₃×C₁₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
64	C₃×C₁₃	#6913	1	3	yes	—
65	C₃³	—	3	1	no	—
66	C₃³	—	3	2	no	—
67	C₃³	—	9	3	no	—
68	C₃³	C₃×C₉×C₁₃	1	3	yes	—
69	C₃³	C₃³×C₁₃	1	1	yes	characteristic
70	3₋¹⁺²	—	3	27	no	—
71	C₃×C₉	—	3	1	no	—
72	C₃×C₉	—	3	1	no	—
73	C₃×C₉	—	3	2	no	—
74	C₃×C₉	—	3	2	no	—
75	C₃×C₉	—	3	9	no	—
76	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
77	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
78	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
79	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
80	C₃×C₉	C₁₃×3₋¹⁺²	1	6	yes	—
81	C₁₃	#10624692	1	1	yes	characteristic, direct product factor, Sylow
82	C₃²	—	3	3	no	—
83	C₃²	—	3	3	no	—
84	C₃²	—	9	3	no	—
85	C₃²	—	9	6	no	—
86	C₃²	—	9	3	no	—
87	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
88	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
89	C₃²	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
90	C₉	—	3	3	no	—
91	C₉	—	3	3	no	—
92	C₉	—	9	9	no	—
93	C₉	C₁₃×C₃²⋊C₉	1	9	yes	—
94	C₃	—	3	1	no	—
95	C₃	—	3	2	no	—
96	C₃	—	9	3	no	—
97	C₃	C₃×C₁₃×C₃²⋊C₉	1	1	yes	characteristic
98	C₃	C₁₃×#6913	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₁₃×#6887

C₃

yes

maximal, complemented

C₁₃×#6868

C₃

yes

maximal, complemented

C₁₃×#6867

C₃

yes

maximal, complemented

C₁₃×#6866

C₃

yes

maximal

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

C₉

yes

complemented

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₉²×C₁₃

—

#10624692

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

C₃×C₉

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

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃²×3₋¹⁺²

C₃×C₁₃

yes

characteristic

#6887

C₃×C₁₃

yes

complemented

#6868

C₃×C₁₃

yes

complemented

#6867

C₃×C₁₃

yes

complemented

#6866

C₃×C₁₃

yes

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃²×C₉

yes

characteristic

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

C₃²⋊C₉

yes

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₉×C₁₃

yes

complemented

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₉²

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

C₃×C₃²⋊C₉

yes

characteristic

C₃×C₁₃

#6913

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₃×C₉×C₁₃

yes

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

C₁₃

#10624692

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃²×C₉×C₁₃

yes

characteristic

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₉

—

C₉

—

C₉

—

C₉

C₁₃×C₃²⋊C₉

yes

—

C₃

—

C₃

—

C₃

—

C₃

C₃×C₁₃×C₃²⋊C₉

yes

characteristic

C₃

C₁₃×#6913

yes

—

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

subgroup

G/H

center, socle

C₃²×C₁₃

C₃×H(3,𝔽₃)

commutator

C₃²

C₃²×C₉×C₁₃

Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃⁴×C₁₃

C₃²

LCS

G ▷ C₃² ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₁₃×#6887	C₃	semidirect
3. C₁₃×#6868	C₃	semidirect
4. C₁₃×#6867	C₃	semidirect
9. C₃×C₁₃×3₋¹⁺²	C₉	semidirect
16. #10624692	C₁₃	direct (N × H)
34. #6887	C₃×C₁₃	semidirect
35. #6868	C₃×C₁₃	semidirect
36. #6867	C₃×C₁₃	semidirect
53. C₃×3₋¹⁺²	C₉×C₁₃	semidirect
81. C₁₃	#10624692	direct (N × H)

H ≅ G/N

type

2. C₁₃×#6887

C₃

semidirect

3. C₁₃×#6868

C₃

semidirect

4. C₁₃×#6867

C₃

semidirect

9. C₃×C₁₃×3₋¹⁺²

C₉

semidirect

16. #10624692

C₁₃

direct (N × H)

34. #6887

C₃×C₁₃

semidirect

35. #6868

C₃×C₁₃

semidirect

36. #6867

C₃×C₁₃

semidirect

53. C₃×3₋¹⁺²

C₉×C₁₃

semidirect

81. C₁₃

#10624692

direct (N × H)

Subgroups — C₁₃×#10624692 #23744843

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624692 #23744843

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624692 #23744843