Subgroups — C₃×C₇×C₃⋊(C₃⋊D₃) #11765820

Order 1134.

380 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₃⋊(C₃⋊D₃)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×C₃⋊D₃	—	3	13	no	maximal
4	C₃³×C₇	—	2	13	no	—
5	C₃³×C₇	D₃	1	13	yes	complemented
6	C₃³×C₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₃⋊(C₃⋊D₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₃⋊D₃	—	3	13	no	—
9	C₃×D₃×C₇	—	9	13	no	—
10	C₃⁴	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
11	C₃²×C₇	—	2	52	no	—
12	C₃²×C₇	C₃×D₃	1	13	yes	complemented
13	C₃²×C₇	C₃⋊D₃	1	13	yes	complemented
14	C₃⋊(C₃⋊D₃)	C₃×C₇	1	1	yes	characteristic, direct product factor
15	C₃×C₃⋊D₃	—	3	13	no	—
16	C₂×C₃×C₇	—	27	1	no	—
17	D₃×C₇	—	9	13	no	—
18	C₃³	—	2	13	no	—
19	C₃³	D₃×C₇	1	13	yes	complemented
20	C₃³	C₂×C₃×C₇	1	1	yes	characteristic, complemented
21	C₃×C₇	—	2	13	no	—
22	C₃×C₇	C₃×C₃⋊D₃	1	13	yes	complemented
23	C₃×C₇	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
24	C₃⋊D₃	—	3	13	no	—
25	C₃×D₃	—	9	13	no	—
26	C₂×C₇	—	27	1	no	Hall
27	C₃²	—	2	52	no	—
28	C₃²	C₃×D₃×C₇	1	13	yes	complemented
29	C₃²	C₇×C₃⋊D₃	1	13	yes	complemented
30	C₇	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	27	1	no	—
32	D₃	—	9	13	no	—
33	C₃	—	2	13	no	—
34	C₃	C₃×C₇×C₃⋊D₃	1	13	yes	complemented
35	C₃	C₇×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
36	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	C₃⋊(C₃⋊D₃)
commutator, cosocle, hypocenter	C₃³	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃⁴×C₇	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃⁴×C₇	C₂	semidirect
2. C₇×C₃⋊(C₃⋊D₃)	C₃	direct (N × H)
5. C₃³×C₇	D₃	semidirect
6. C₃³×C₇	C₂×C₃	semidirect
7. C₃×C₃⋊(C₃⋊D₃)	C₇	direct (N × H)
10. C₃⁴	C₂×C₇	semidirect
12. C₃²×C₇	C₃×D₃	semidirect
13. C₃²×C₇	C₃⋊D₃	semidirect
14. C₃⋊(C₃⋊D₃)	C₃×C₇	direct (N × H)
19. C₃³	D₃×C₇	semidirect
20. C₃³	C₂×C₃×C₇	semidirect
22. C₃×C₇	C₃×C₃⋊D₃	semidirect
23. C₃×C₇	C₃⋊(C₃⋊D₃)	direct (N × H)
28. C₃²	C₃×D₃×C₇	semidirect
29. C₃²	C₇×C₃⋊D₃	semidirect
30. C₇	C₃×C₃⋊(C₃⋊D₃)	direct (N × H)
34. C₃	C₃×C₇×C₃⋊D₃	semidirect
35. C₃	C₇×C₃⋊(C₃⋊D₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×C₇	2
C₇×C₃⋊(C₃⋊D₃)	3
C₃×C₇×C₃⋊D₃	3
C₃×C₃⋊(C₃⋊D₃)	7

Subgroups — C3×C7×C3⋊(C3⋊D3) #11765820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₃⋊(C₃⋊D₃) #11765820