Subgroups — C₂×C₃×C₁₁⋊D₁₄₃ #34038481

Order 18876.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁⋊D₁₄₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊D₁₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁⋊D₁₄₃	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₁₁²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×D₁₄₃	—	11	12	no	maximal
8	C₁₁²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₁⋊D₁₁	—	13	1	no	maximal, Hall
10	C₂×C₃×C₁₁×C₁₃	D₁₁	1	12	yes	complemented
11	C₃×D₁₄₃	—	11	24	no	—
12	C₂×C₃×C₁₁²	D₁₃	1	1	yes	characteristic, complemented
13	C₃×C₁₁⋊D₁₁	—	13	2	no	—
14	C₂×D₁₄₃	—	11	12	no	—
15	C₂×C₁₁⋊D₁₁	—	13	1	no	Hall
16	C₃×C₁₁×C₁₃	C₂×D₁₁	1	12	yes	complemented
17	C₃×C₁₁²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₁×C₁₃	C₃×D₁₁	1	12	yes	complemented
19	D₁₄₃	—	11	24	no	—
20	C₂×C₁₁²	C₃×D₁₃	1	1	yes	characteristic, complemented
21	C₁₁⋊D₁₁	—	13	2	no	—
22	C₂×C₃×D₁₃	—	121	1	no	Hall
23	C₁₁×C₁₃	C₂×C₃×D₁₁	1	12	yes	complemented
24	C₂×C₃×D₁₁	—	143	12	no	—
25	C₁₁²	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₁₃	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
27	C₃×D₁₃	—	121	2	no	—
28	C₂×C₃×C₁₁	D₁₄₃	1	12	yes	complemented
29	C₃×D₁₁	—	143	24	no	—
30	C₂×D₁₃	—	121	1	no	Hall
31	C₂×D₁₁	—	143	12	no	—
32	C₃×C₁₃	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₁	C₂×D₁₄₃	1	12	yes	complemented
34	C₂×C₁₃	C₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
35	D₁₃	—	121	2	no	—
36	C₂×C₁₁	C₃×D₁₄₃	1	12	yes	complemented
37	D₁₁	—	143	24	no	—
38	C₁₃	C₂×C₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	1573	1	no	Hall
40	C₁₁	C₂×C₃×D₁₄₃	1	12	yes	complemented
41	C₂×C₃	—	1573	2	no	—
42	C₂×C₃	C₁₁⋊D₁₄₃	1	1	yes	characteristic, direct product factor
43	C₂²	—	1573	1	no	Sylow
44	C₃	C₂×C₁₁⋊D₁₄₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	1573	2	no	—
46	C₂	C₃×C₁₁⋊D₁₄₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₁⋊D₁₄₃
commutator, cosocle, hypocenter	C₁₁²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁²×C₁₃	C₂
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁⋊D₁₄₃	C₂	direct (N × H)
2. C₂×C₃×C₁₁²×C₁₃	C₂	semidirect
3. C₂×C₁₁⋊D₁₄₃	C₃	direct (N × H)
4. C₃×C₁₁²×C₁₃	C₂²	semidirect
5. C₁₁⋊D₁₄₃	C₂×C₃	direct (N × H)
6. C₂×C₁₁²×C₁₃	C₂×C₃	semidirect
8. C₁₁²×C₁₃	C₂²×C₃	semidirect
10. C₂×C₃×C₁₁×C₁₃	D₁₁	semidirect
12. C₂×C₃×C₁₁²	D₁₃	semidirect
16. C₃×C₁₁×C₁₃	C₂×D₁₁	semidirect
17. C₃×C₁₁²	C₂×D₁₃	semidirect
18. C₂×C₁₁×C₁₃	C₃×D₁₁	semidirect
20. C₂×C₁₁²	C₃×D₁₃	semidirect
23. C₁₁×C₁₃	C₂×C₃×D₁₁	semidirect
25. C₁₁²	C₂×C₃×D₁₃	semidirect
26. C₂×C₃×C₁₃	C₁₁⋊D₁₁	semidirect
28. C₂×C₃×C₁₁	D₁₄₃	semidirect
32. C₃×C₁₃	C₂×C₁₁⋊D₁₁	semidirect
33. C₃×C₁₁	C₂×D₁₄₃	semidirect
34. C₂×C₁₃	C₃×C₁₁⋊D₁₁	semidirect
36. C₂×C₁₁	C₃×D₁₄₃	semidirect
38. C₁₃	C₂×C₃×C₁₁⋊D₁₁	semidirect
40. C₁₁	C₂×C₃×D₁₄₃	semidirect
42. C₂×C₃	C₁₁⋊D₁₄₃	direct (N × H)
44. C₃	C₂×C₁₁⋊D₁₄₃	direct (N × H)
46. C₂	C₃×C₁₁⋊D₁₄₃	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×C₁₁⋊D₁₄₃	2
C₂×C₃×C₁₁²×C₁₃	2
C₂×C₁₁⋊D₁₄₃	3
C₂×C₃×D₁₄₃	11
C₂×C₃×C₁₁⋊D₁₁	13

Subgroups — C2×C3×C11⋊D143 #34038481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₁⋊D₁₄₃ #34038481