Subgroups — C₇×C₉×C₃⋊D₃ #11765786

Order 1134.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×C₃⋊D₃	C₃	1	1	yes	maximal, characteristic
3	D₃×C₇×C₉	—	3	4	no	maximal
4	C₃³×C₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₇×C₉	—	2	4	no	—
6	C₃×C₇×C₉	D₃	1	4	yes	complemented
7	C₉×C₃⋊D₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₃⋊D₃	C₉	1	1	yes	characteristic, direct product factor
9	C₃×D₃×C₇	—	3	4	no	—
10	C₂×C₇×C₉	—	9	1	no	—
11	C₃²×C₉	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₃²×C₇	—	2	4	no	—
13	C₃²×C₇	C₂×C₉	1	1	yes	characteristic, complemented
14	C₃²×C₇	C₃×D₃	1	4	yes	—
15	C₇×C₉	—	2	4	no	—
16	C₇×C₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
17	C₃×C₃⋊D₃	C₃×C₇	1	1	yes	characteristic
18	D₃×C₉	—	3	4	no	—
19	C₂×C₃×C₇	—	9	1	no	—
20	D₃×C₇	—	3	4	no	—
21	C₃³	C₂×C₃×C₇	1	1	yes	characteristic
22	C₃×C₉	—	2	4	no	—
23	C₃×C₉	D₃×C₇	1	4	yes	complemented
24	C₃×C₇	—	2	4	no	—
25	C₃×C₇	D₃×C₉	1	4	yes	complemented
26	C₃×C₇	C₃×C₃⋊D₃	1	1	yes	characteristic
27	C₃⋊D₃	C₇×C₉	1	1	yes	characteristic, direct product factor
28	C₃×D₃	—	3	4	no	—
29	C₂×C₉	—	9	1	no	—
30	C₂×C₇	—	9	1	no	Hall
31	C₃²	—	2	4	no	—
32	C₃²	C₂×C₇×C₉	1	1	yes	characteristic, complemented
33	C₃²	C₃×D₃×C₇	1	4	yes	—
34	C₉	—	2	4	no	—
35	C₉	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
36	C₇	C₉×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃	—	9	1	no	—
38	D₃	—	3	4	no	—
39	C₃	—	2	4	no	—
40	C₃	D₃×C₇×C₉	1	4	yes	complemented
41	C₃	C₃×C₇×C₃⋊D₃	1	1	yes	characteristic
42	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×C₃⋊D₃
Fitting	C₃²×C₇×C₉	C₂
socle	C₃³×C₇	C₂×C₃
prime radical	C₃×C₇×C₃⋊D₃	C₃
cosocle	C₃³	C₂×C₃×C₇
LCS	G ▷ C₃²
UCS	C₁ ◁ C₇×C₉

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₇×C₉	C₂	semidirect
6. C₃×C₇×C₉	D₃	semidirect
7. C₉×C₃⋊D₃	C₇	direct (N × H)
8. C₇×C₃⋊D₃	C₉	direct (N × H)
11. C₃²×C₉	C₂×C₇	semidirect
13. C₃²×C₇	C₂×C₉	semidirect
16. C₇×C₉	C₃⋊D₃	direct (N × H)
23. C₃×C₉	D₃×C₇	semidirect
25. C₃×C₇	D₃×C₉	semidirect
27. C₃⋊D₃	C₇×C₉	direct (N × H)
32. C₃²	C₂×C₇×C₉	semidirect
35. C₉	C₇×C₃⋊D₃	direct (N × H)
36. C₇	C₉×C₃⋊D₃	direct (N × H)
40. C₃	D₃×C₇×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₉	2
C₃×C₇×C₃⋊D₃	3
D₃×C₇×C₉	3
C₉×C₃⋊D₃	7

Subgroups — C7×C9×C3⋊D3 #11765786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×C₃⋊D₃ #11765786