Subgroups — C₂×C₃×D₃₃ #87695

Order 396.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₁₁	—	3	1	no	maximal
5	C₃²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₁	—	2	1	no	—
7	C₂×C₃×C₁₁	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃₃	C₂×C₃	1	2	yes	direct product factor
10	C₃×D₁₁	—	3	2	no	—
11	C₂×D₁₁	—	3	1	no	Hall
12	C₂×C₃×D₃	—	11	1	no	maximal, Hall
13	C₃×C₁₁	—	2	1	no	—
14	C₃×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented
15	C₃×C₁₁	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₁₁	C₃×D₃	1	1	yes	characteristic, complemented
17	D₁₁	—	3	2	no	—
18	C₂×C₃²	D₁₁	1	1	yes	characteristic, complemented
19	C₃×D₃	—	11	2	no	—
20	C₂²×C₃	—	33	1	no	—
21	C₂×D₃	—	11	1	no	—
22	C₁₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
23	C₃²	C₂×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	—	2	1	no	—
25	C₂×C₃	—	33	2	no	—
26	C₂×C₃	C₃×D₁₁	1	1	yes	characteristic, complemented
27	C₂×C₃	D₃₃	1	1	yes	characteristic, direct product factor
28	D₃	—	11	2	no	—
29	C₂²	—	33	1	no	Sylow
30	C₃	—	2	1	no	—
31	C₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented
32	C₃	C₂×D₃₃	1	1	yes	characteristic, direct product factor
33	C₂	—	33	2	no	—
34	C₂	C₃×D₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₁₁	C₂	semidirect
2. C₃×D₃₃	C₂	direct (N × H)
3. C₂×D₃₃	C₃	direct (N × H)
5. C₃²×C₁₁	C₂²	semidirect
7. C₂×C₃×C₁₁	D₃	semidirect
8. C₂×C₃×C₁₁	C₂×C₃	semidirect
9. D₃₃	C₂×C₃	direct (N × H)
14. C₃×C₁₁	C₂×D₃	semidirect
15. C₃×C₁₁	C₂²×C₃	semidirect
16. C₂×C₁₁	C₃×D₃	semidirect
18. C₂×C₃²	D₁₁	semidirect
22. C₁₁	C₂×C₃×D₃	semidirect
23. C₃²	C₂×D₁₁	semidirect
26. C₂×C₃	C₃×D₁₁	semidirect
27. C₂×C₃	D₃₃	direct (N × H)
31. C₃	C₂×C₃×D₁₁	semidirect
32. C₃	C₂×D₃₃	direct (N × H)
34. C₂	C₃×D₃₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₁	2
C₃×D₃₃	2
C₂×D₃₃	3
C₂×C₃×D₁₁	3
C₂×C₃×D₃	11

Subgroups — C2×C3×D33 #87695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃₃ #87695