Subgroups — C₃×C₈×D₁₁ #10587161

Order 528.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×D₁₁	C₄	1	1	yes	characteristic
6	C₃×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₃×Dic₁₁	C₄	1	1	yes	characteristic
8	C₄×D₁₁	C₂×C₃	1	1	yes	characteristic
9	C₈×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₁₁⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₃×D₁₁	C₈	1	2	yes	direct product factor
13	C₂×C₃×C₈	—	11	1	no	maximal, Hall
14	C₂×D₁₁	C₃×C₄	1	1	yes	characteristic
15	C₄×C₁₁	C₂²×C₃	1	1	yes	characteristic
16	Dic₁₁	C₃×C₄	1	1	yes	characteristic
17	C₃×C₁₁	C₂×C₈	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₄	—	11	1	no	—
19	C₃×C₈	—	11	1	no	—
20	C₃×C₈	D₁₁	1	1	yes	characteristic, direct product factor
21	C₂×C₁₁	C₂×C₃×C₄	1	1	yes	characteristic
22	D₁₁	C₃×C₈	1	2	yes	direct product factor
23	C₂×C₈	—	11	1	no	Sylow
24	C₂²×C₃	—	11	1	no	—
25	C₃×C₄	—	11	1	no	—
26	C₃×C₄	C₂×D₁₁	1	1	yes	characteristic
27	C₁₁	C₂×C₃×C₈	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₄	—	11	1	no	—
29	C₈	—	11	1	no	—
30	C₈	C₃×D₁₁	1	1	yes	characteristic, direct product factor
31	C₂×C₃	—	11	2	no	—
32	C₂×C₃	C₄×D₁₁	1	1	yes	characteristic
33	C₂²	—	11	1	no	—
34	C₄	—	11	1	no	—
35	C₄	C₂×C₃×D₁₁	1	1	yes	characteristic
36	C₃	C₈×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	11	2	no	—
38	C₂	C₃×C₄×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₈	D₁₁
commutator, hypocenter	C₁₁	C₂×C₃×C₈
Frattini	C₄	C₂×C₃×D₁₁
Fitting	C₃×C₈×C₁₁	C₂
socle	C₂×C₃×C₁₁	C₂×C₄
prime radical	C₂×C₃×D₁₁	C₄
cosocle	C₄×C₁₁	C₂²×C₃
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×C₈×C₁₁	C₂	semidirect
3. C₃×C₁₁⋊C₈	C₂	semidirect
4. C₈×D₁₁	C₃	direct (N × H)
9. C₈×C₁₁	C₂×C₃	semidirect
10. C₁₁⋊C₈	C₂×C₃	semidirect
12. C₃×D₁₁	C₈	direct (N × H)
17. C₃×C₁₁	C₂×C₈	semidirect
20. C₃×C₈	D₁₁	direct (N × H)
22. D₁₁	C₃×C₈	direct (N × H)
27. C₁₁	C₂×C₃×C₈	semidirect
30. C₈	C₃×D₁₁	direct (N × H)
36. C₃	C₈×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×D₁₁	2
C₃×C₈×C₁₁	2
C₃×C₁₁⋊C₈	2
C₈×D₁₁	3
C₂×C₃×C₈	11

Subgroups — C3×C8×D11 #10587161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×D₁₁ #10587161