Subgroups — C₃×C₁₁×D₃₃ #14546113

Order 2178.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₃₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₁×D₁₁	—	3	1	no	maximal
4	C₃×C₁₁²	—	2	1	no	—
5	C₃×C₁₁²	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁×D₁₁	—	3	1	no	Hall
8	C₃×D₃₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor
9	C₃×D₃×C₁₁	—	11	1	no	maximal
10	C₁₁²	C₃×D₃	1	1	yes	characteristic, complemented, Sylow
11	C₃²×C₁₁	—	2	5	no	—
12	C₃²×C₁₁	D₁₁	1	1	yes	characteristic, complemented
13	C₃²×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₂×C₃×C₁₁	—	33	1	no	—
15	D₃₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor
16	C₃×D₁₁	—	3	1	no	—
17	D₃×C₁₁	—	11	1	no	—
18	C₃×C₁₁	—	2	10	no	—
19	C₃×C₁₁	—	2	1	no	—
20	C₃×C₁₁	—	2	1	no	—
21	C₃×C₁₁	—	2	5	no	—
22	C₃×C₁₁	—	2	5	no	—
23	C₃×C₁₁	D₃×C₁₁	1	1	yes	characteristic, complemented
24	C₃×C₁₁	C₃×D₁₁	1	1	yes	characteristic, complemented
25	C₃×C₁₁	D₃₃	1	1	yes	characteristic, direct product factor
26	C₃×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
27	C₂×C₁₁	—	33	1	no	—
28	D₁₁	—	3	1	no	—
29	C₃×D₃	—	11	1	no	Hall
30	C₁₁	—	2	5	no	—
31	C₁₁	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented
32	C₁₁	C₃×D₃₃	1	1	yes	characteristic, direct product factor
33	C₃²	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃	—	33	1	no	—
35	D₃	—	11	1	no	—
36	C₃	—	2	1	no	—
37	C₃	C₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented
38	C₃	C₁₁×D₃₃	1	1	yes	characteristic, direct product factor
39	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁²	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₁²	C₂	semidirect
2. C₁₁×D₃₃	C₃	direct (N × H)
5. C₃×C₁₁²	D₃	semidirect
6. C₃×C₁₁²	C₂×C₃	semidirect
8. C₃×D₃₃	C₁₁	direct (N × H)
10. C₁₁²	C₃×D₃	semidirect
12. C₃²×C₁₁	D₁₁	semidirect
13. C₃²×C₁₁	C₂×C₁₁	semidirect
15. D₃₃	C₃×C₁₁	direct (N × H)
23. C₃×C₁₁	D₃×C₁₁	semidirect
24. C₃×C₁₁	C₃×D₁₁	semidirect
25. C₃×C₁₁	D₃₃	direct (N × H)
26. C₃×C₁₁	C₂×C₃×C₁₁	semidirect
31. C₁₁	C₃×D₃×C₁₁	semidirect
32. C₁₁	C₃×D₃₃	direct (N × H)
33. C₃²	C₁₁×D₁₁	semidirect
37. C₃	C₃×C₁₁×D₁₁	semidirect
38. C₃	C₁₁×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
C₃²×C₁₁²	2
C₁₁×D₃₃	3
C₃×C₁₁×D₁₁	3
C₃×D₃₃	11
C₃×D₃×C₁₁	11

Subgroups — C3×C11×D33 #14546113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×D₃₃ #14546113