Group #19100269 — subgroups

Subgroups — C₃×C₇×C₉×3₋¹⁺² #19100269

Order 5103.

1148 conjugacy classes of subgroups; only the 872 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 872 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×C₇×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₇×C₉	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×3₋¹⁺²	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₇×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₃×C₇×C₃²⋊C₉	C₃	1	2	yes	maximal
6	C₃×C₇×C₉²	C₃	1	3	yes	maximal, complemented
7	C₃×C₉×3₋¹⁺²	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃⁴×C₇	C₃²	1	1	yes	characteristic
9	C₃×C₇×3₋¹⁺²	C₉	1	27	yes	direct product factor
10	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
11	C₃²×C₇×C₉	—	3	9	no	—
12	C₃²×C₇×C₉	C₃²	1	6	yes	—
13	C₃²×C₇×C₉	C₃²	1	2	yes	—
14	C₃²×C₇×C₉	C₃²	1	9	yes	—
15	C₃²×C₇×C₉	C₃²	1	3	yes	—
16	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
17	C₇×C₉⋊C₉	C₃²	1	54	yes	complemented
18	C₇×C₃²⋊C₉	C₃²	1	18	yes	—
19	C₇×C₉²	C₃²	1	27	yes	complemented
20	C₃²×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic
21	C₃³×C₉	C₃×C₇	1	1	yes	characteristic
22	C₉×3₋¹⁺²	C₃×C₇	1	27	yes	direct product factor
23	C₃×C₉⋊C₉	C₃×C₇	1	6	yes	complemented
24	C₃×C₃²⋊C₉	C₃×C₇	1	2	yes	—
25	C₃×C₉²	C₃×C₇	1	3	yes	complemented
26	C₃³×C₇	—	3	3	no	—
27	C₃³×C₇	—	3	6	no	—
28	C₃³×C₇	C₃×C₉	1	9	yes	—
29	C₃³×C₇	C₃³	1	3	yes	—
30	C₃³×C₇	C₃³	1	1	yes	characteristic
31	C₇×3₋¹⁺²	C₃×C₉	1	81	yes	direct product factor
32	C₃×C₇×C₉	—	3	6	no	—
33	C₃×C₇×C₉	—	3	18	no	—
34	C₃×C₇×C₉	—	3	27	no	—
35	C₃×C₇×C₉	C₃×C₉	1	27	yes	complemented
36	C₃×C₇×C₉	3₋¹⁺²	1	9	yes	direct product factor
37	C₃×C₇×C₉	C₃³	1	18	yes	—
38	C₃×C₇×C₉	C₃³	1	6	yes	—
39	C₃×C₇×C₉	C₃³	1	9	yes	—
40	C₃×C₇×C₉	C₃³	1	3	yes	—
41	C₃⁴	C₃²×C₇	1	1	yes	characteristic
42	C₃×3₋¹⁺²	C₇×C₉	1	27	yes	direct product factor
43	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
44	C₃²×C₉	—	3	9	no	—
45	C₃²×C₉	C₃²×C₇	1	2	yes	—
46	C₃²×C₉	C₃²×C₇	1	9	yes	—
47	C₃²×C₉	C₃²×C₇	1	6	yes	—
48	C₃²×C₉	C₃²×C₇	1	3	yes	—
49	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
50	C₉⋊C₉	C₃²×C₇	1	54	yes	complemented
51	C₃²⋊C₉	C₃²×C₇	1	18	yes	—
52	C₉²	C₃²×C₇	1	27	yes	complemented
53	C₃²×C₇	—	3	3	no	—
54	C₃²×C₇	—	3	6	no	—
55	C₃²×C₇	—	3	27	no	—
56	C₃²×C₇	C₃²×C₉	1	9	yes	—
57	C₃²×C₇	C₃²×C₉	1	3	yes	—
58	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
59	C₃²×C₇	#737	1	6	yes	—
60	C₃²×C₇	C₃⁴	1	1	yes	characteristic
61	C₇×C₉	—	3	6	no	—
62	C₇×C₉	—	3	18	no	—
63	C₇×C₉	C₃²×C₉	1	27	yes	complemented
64	C₇×C₉	C₃×3₋¹⁺²	1	9	yes	direct product factor
65	C₃³	—	3	3	no	—
66	C₃³	—	3	6	no	—
67	C₃³	C₃×C₇×C₉	1	9	yes	—
68	C₃³	C₃³×C₇	1	3	yes	—
69	C₃³	C₃³×C₇	1	1	yes	characteristic
70	3₋¹⁺²	C₃×C₇×C₉	1	81	yes	direct product factor
71	C₃×C₉	—	3	6	no	—
72	C₃×C₉	—	3	18	no	—
73	C₃×C₉	—	3	27	no	—
74	C₃×C₉	C₃×C₇×C₉	1	27	yes	complemented
75	C₃×C₉	C₇×3₋¹⁺²	1	9	yes	direct product factor
76	C₃×C₉	C₃³×C₇	1	18	yes	—
77	C₃×C₉	C₃³×C₇	1	6	yes	—
78	C₃×C₉	C₃³×C₇	1	9	yes	—
79	C₃×C₉	C₃³×C₇	1	3	yes	—
80	C₃×C₇	—	3	9	no	—
81	C₃×C₇	C₉×3₋¹⁺²	1	9	yes	direct product factor
82	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
83	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
84	C₃×C₇	C₃×#737	1	2	yes	—
85	C₃²	—	3	27	no	—
86	C₃²	—	3	3	no	—
87	C₃²	—	3	6	no	—
88	C₃²	C₃²×C₇×C₉	1	9	yes	—
89	C₃²	C₃²×C₇×C₉	1	3	yes	—
90	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
91	C₃²	C₇×#737	1	6	yes	—
92	C₃²	C₃⁴×C₇	1	1	yes	characteristic
93	C₉	—	3	6	no	—
94	C₉	—	3	18	no	—
95	C₉	C₃²×C₇×C₉	1	27	yes	complemented
96	C₉	C₃×C₇×3₋¹⁺²	1	9	yes	direct product factor
97	C₇	C₃×C₉×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
98	C₃	—	3	9	no	—
99	C₃	C₇×C₉×3₋¹⁺²	1	9	yes	direct product factor
100	C₃	C₃³×C₇×C₉	1	1	yes	characteristic
101	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
102	C₃	C₃×C₇×#737	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₇×3₋¹⁺²

C₃

yes

maximal, characteristic

C₃³×C₇×C₉

C₃

yes

maximal, characteristic

C₇×C₉×3₋¹⁺²

C₃

yes

maximal, direct product factor

C₃×C₇×C₉⋊C₉

C₃

yes

maximal, complemented

C₃×C₇×C₃²⋊C₉

C₃

yes

maximal

C₃×C₇×C₉²

C₃

yes

maximal, complemented

C₃×C₉×3₋¹⁺²

C₇

yes

maximal, characteristic, direct product factor, Sylow

C₃⁴×C₇

C₃²

yes

characteristic

C₃×C₇×3₋¹⁺²

C₉

yes

direct product factor

C₃×C₇×3₋¹⁺²

C₃²

yes

—

C₃²×C₇×C₉

—

C₃²×C₇×C₉

C₃²

yes

—

C₃²×C₇×C₉

C₃²

yes

—

C₃²×C₇×C₉

C₃²

yes

—

C₃²×C₇×C₉

C₃²

yes

—

C₃²×C₇×C₉

C₃²

yes

characteristic

C₇×C₉⋊C₉

C₃²

yes

complemented

C₇×C₃²⋊C₉

C₃²

yes

—

C₇×C₉²

C₃²

yes

complemented

C₃²×3₋¹⁺²

C₃×C₇

yes

characteristic

C₃³×C₉

C₃×C₇

yes

characteristic

C₉×3₋¹⁺²

C₃×C₇

yes

direct product factor

C₃×C₉⋊C₉

C₃×C₇

yes

complemented

C₃×C₃²⋊C₉

C₃×C₇

yes

—

C₃×C₉²

C₃×C₇

yes

complemented

C₃³×C₇

—

C₃³×C₇

—

C₃³×C₇

C₃×C₉

yes

—

C₃³×C₇

C₃³

yes

—

C₃³×C₇

C₃³

yes

characteristic

C₇×3₋¹⁺²

C₃×C₉

yes

direct product factor

C₃×C₇×C₉

—

C₃×C₇×C₉

—

C₃×C₇×C₉

—

C₃×C₇×C₉

C₃×C₉

yes

complemented

C₃×C₇×C₉

3₋¹⁺²

yes

direct product factor

C₃×C₇×C₉

C₃³

yes

—

C₃×C₇×C₉

C₃³

yes

—

C₃×C₇×C₉

C₃³

yes

—

C₃×C₇×C₉

C₃³

yes

—

C₃⁴

C₃²×C₇

yes

characteristic

C₃×3₋¹⁺²

C₇×C₉

yes

direct product factor

C₃×3₋¹⁺²

C₃²×C₇

yes

—

C₃²×C₉

—

C₃²×C₉

C₃²×C₇

yes

—

C₃²×C₉

C₃²×C₇

yes

—

C₃²×C₉

C₃²×C₇

yes

—

C₃²×C₉

C₃²×C₇

yes

—

C₃²×C₉

C₃²×C₇

yes

characteristic

C₉⋊C₉

C₃²×C₇

yes

complemented

C₃²⋊C₉

C₃²×C₇

yes

—

C₉²

C₃²×C₇

yes

complemented

C₃²×C₇

—

C₃²×C₇

—

C₃²×C₇

—

C₃²×C₇

C₃²×C₉

yes

—

C₃²×C₇

C₃²×C₉

yes

—

C₃²×C₇

C₃×3₋¹⁺²

yes

—

C₃²×C₇

#737

yes

—

C₃²×C₇

C₃⁴

yes

characteristic

C₇×C₉

—

C₇×C₉

—

C₇×C₉

C₃²×C₉

yes

complemented

C₇×C₉

C₃×3₋¹⁺²

yes

direct product factor

C₃³

—

C₃³

—

C₃³

C₃×C₇×C₉

yes

—

C₃³

C₃³×C₇

yes

—

C₃³

C₃³×C₇

yes

characteristic

3₋¹⁺²

C₃×C₇×C₉

yes

direct product factor

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₇×C₉

yes

complemented

C₃×C₉

C₇×3₋¹⁺²

yes

direct product factor

C₃×C₉

C₃³×C₇

yes

—

C₃×C₉

C₃³×C₇

yes

—

C₃×C₉

C₃³×C₇

yes

—

C₃×C₉

C₃³×C₇

yes

—

C₃×C₇

—

C₃×C₇

C₉×3₋¹⁺²

yes

direct product factor

C₃×C₇

C₃³×C₉

yes

characteristic

C₃×C₇

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₇

C₃×#737

yes

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃²×C₇×C₉

yes

—

C₃²

C₃²×C₇×C₉

yes

—

C₃²

C₃×C₇×3₋¹⁺²

yes

—

C₃²

C₇×#737

yes

—

C₃²

C₃⁴×C₇

yes

characteristic

C₉

—

C₉

—

C₉

C₃²×C₇×C₉

yes

complemented

C₉

C₃×C₇×3₋¹⁺²

yes

direct product factor

C₇

C₃×C₉×3₋¹⁺²

yes

characteristic, direct product factor, Sylow

C₃

—

C₃

C₇×C₉×3₋¹⁺²

yes

direct product factor

100

C₃

C₃³×C₇×C₉

yes

characteristic

101

C₃

C₃²×C₇×3₋¹⁺²

yes

characteristic

102

C₃

C₃×C₇×#737

yes

—

	subgroup	G/H
center	C₃²×C₇×C₉	C₃²
commutator	C₃	C₃³×C₇×C₉
Frattini	C₃²	C₃⁴×C₇
socle	C₃³×C₇	C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₇×C₉ ◁ G

subgroup

G/H

center

C₃²×C₇×C₉

C₃²

commutator

C₃

C₃³×C₇×C₉

Frattini

C₃²

C₃⁴×C₇

socle

C₃³×C₇

C₃³

LCS

G ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃²×C₇×C₉ ◁ G

N	H ≅ G/N	type
3. C₇×C₉×3₋¹⁺²	C₃	direct (N × H)
4. C₃×C₇×C₉⋊C₉	C₃	semidirect
6. C₃×C₇×C₉²	C₃	semidirect
7. C₃×C₉×3₋¹⁺²	C₇	direct (N × H)
9. C₃×C₇×3₋¹⁺²	C₉	direct (N × H)
17. C₇×C₉⋊C₉	C₃²	semidirect
19. C₇×C₉²	C₃²	semidirect
22. C₉×3₋¹⁺²	C₃×C₇	direct (N × H)
23. C₃×C₉⋊C₉	C₃×C₇	semidirect
25. C₃×C₉²	C₃×C₇	semidirect
31. C₇×3₋¹⁺²	C₃×C₉	direct (N × H)
35. C₃×C₇×C₉	C₃×C₉	semidirect
36. C₃×C₇×C₉	3₋¹⁺²	direct (N × H)
42. C₃×3₋¹⁺²	C₇×C₉	direct (N × H)
50. C₉⋊C₉	C₃²×C₇	semidirect
52. C₉²	C₃²×C₇	semidirect
63. C₇×C₉	C₃²×C₉	semidirect
64. C₇×C₉	C₃×3₋¹⁺²	direct (N × H)
70. 3₋¹⁺²	C₃×C₇×C₉	direct (N × H)
74. C₃×C₉	C₃×C₇×C₉	semidirect
75. C₃×C₉	C₇×3₋¹⁺²	direct (N × H)
81. C₃×C₇	C₉×3₋¹⁺²	direct (N × H)
95. C₉	C₃²×C₇×C₉	semidirect
96. C₉	C₃×C₇×3₋¹⁺²	direct (N × H)
97. C₇	C₃×C₉×3₋¹⁺²	direct (N × H)
99. C₃	C₇×C₉×3₋¹⁺²	direct (N × H)

H ≅ G/N

type

3. C₇×C₉×3₋¹⁺²

C₃

direct (N × H)

4. C₃×C₇×C₉⋊C₉

C₃

semidirect

6. C₃×C₇×C₉²

C₃

semidirect

7. C₃×C₉×3₋¹⁺²

C₇

direct (N × H)

9. C₃×C₇×3₋¹⁺²

C₉

direct (N × H)

17. C₇×C₉⋊C₉

C₃²

semidirect

19. C₇×C₉²

C₃²

semidirect

22. C₉×3₋¹⁺²

C₃×C₇

direct (N × H)

23. C₃×C₉⋊C₉

C₃×C₇

semidirect

25. C₃×C₉²

C₃×C₇

semidirect

31. C₇×3₋¹⁺²

C₃×C₉

direct (N × H)

35. C₃×C₇×C₉

C₃×C₉

semidirect

36. C₃×C₇×C₉

3₋¹⁺²

direct (N × H)

42. C₃×3₋¹⁺²

C₇×C₉

direct (N × H)

50. C₉⋊C₉

C₃²×C₇

semidirect

52. C₉²

C₃²×C₇

semidirect

63. C₇×C₉

C₃²×C₉

semidirect

64. C₇×C₉

C₃×3₋¹⁺²

direct (N × H)

70. 3₋¹⁺²

C₃×C₇×C₉

direct (N × H)

74. C₃×C₉

C₃×C₇×C₉

semidirect

75. C₃×C₉

C₇×3₋¹⁺²

direct (N × H)

81. C₃×C₇

C₉×3₋¹⁺²

direct (N × H)

95. C₉

C₃²×C₇×C₉

semidirect

96. C₉

C₃×C₇×3₋¹⁺²

direct (N × H)

97. C₇

C₃×C₉×3₋¹⁺²

direct (N × H)

99. C₃

C₇×C₉×3₋¹⁺²

direct (N × H)

Subgroups — C₃×C₇×C₉×3₋¹⁺² #19100269

Conjugacy classes of subgroups

Complements

Subgroups — C3×C7×C9×3−1+2 #19100269

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×C₉×3₋¹⁺² #19100269