Subgroups — C₂×C₁₇²×C₃⋊D₃ #23780944

Order 10404.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₃⋊D₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₇²	—	3	4	no	maximal
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₇²	D₃	1	4	yes	complemented
6	D₃×C₁₇²	—	3	8	no	—
7	C₂²×C₁₇²	—	9	1	no	Hall
8	C₃×C₁₇²	C₂×D₃	1	4	yes	complemented
9	C₂×C₁₇×C₃⋊D₃	C₁₇	1	18	yes	maximal, direct product factor
10	C₂×C₁₇²	—	9	2	no	—
11	C₂×C₁₇²	C₃⋊D₃	1	1	yes	characteristic, direct product factor
12	C₂×C₃²×C₁₇	C₂×C₁₇	1	18	yes	complemented
13	C₁₇×C₃⋊D₃	C₂×C₁₇	1	36	yes	direct product factor
14	C₁₇²	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×D₃×C₁₇	—	3	72	no	—
16	C₃²×C₁₇	C₂²×C₁₇	1	18	yes	complemented
17	C₂×C₃×C₁₇	D₃×C₁₇	1	72	yes	complemented
18	D₃×C₁₇	—	3	144	no	—
19	C₂²×C₁₇	—	9	18	no	—
20	C₃×C₁₇	C₂×D₃×C₁₇	1	72	yes	complemented
21	C₂×C₃⋊D₃	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₇	—	9	36	no	—
23	C₂×C₁₇	C₁₇×C₃⋊D₃	1	18	yes	direct product factor
24	C₂×C₃²	C₂×C₁₇²	1	1	yes	characteristic, complemented
25	C₃⋊D₃	C₂×C₁₇²	1	2	yes	direct product factor
26	C₁₇	C₂×C₁₇×C₃⋊D₃	1	18	yes	direct product factor
27	C₂×D₃	—	3	4	no	—
28	C₃²	C₂²×C₁₇²	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	D₃×C₁₇²	1	4	yes	complemented
30	D₃	—	3	8	no	—
31	C₂²	—	9	1	no	Sylow
32	C₃	C₂×D₃×C₁₇²	1	4	yes	complemented
33	C₂	—	9	2	no	—
34	C₂	C₁₇²×C₃⋊D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇²	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₇²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₇²

Complements

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

N	H ≅ G/N	type
1. C₁₇²×C₃⋊D₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₇²	C₂	semidirect
4. C₃²×C₁₇²	C₂²	semidirect
5. C₂×C₃×C₁₇²	D₃	semidirect
8. C₃×C₁₇²	C₂×D₃	semidirect
9. C₂×C₁₇×C₃⋊D₃	C₁₇	direct (N × H)
11. C₂×C₁₇²	C₃⋊D₃	direct (N × H)
12. C₂×C₃²×C₁₇	C₂×C₁₇	semidirect
13. C₁₇×C₃⋊D₃	C₂×C₁₇	direct (N × H)
14. C₁₇²	C₂×C₃⋊D₃	direct (N × H)
16. C₃²×C₁₇	C₂²×C₁₇	semidirect
17. C₂×C₃×C₁₇	D₃×C₁₇	semidirect
20. C₃×C₁₇	C₂×D₃×C₁₇	semidirect
21. C₂×C₃⋊D₃	C₁₇²	direct (N × H)
23. C₂×C₁₇	C₁₇×C₃⋊D₃	direct (N × H)
24. C₂×C₃²	C₂×C₁₇²	semidirect
25. C₃⋊D₃	C₂×C₁₇²	direct (N × H)
26. C₁₇	C₂×C₁₇×C₃⋊D₃	direct (N × H)
28. C₃²	C₂²×C₁₇²	semidirect
29. C₂×C₃	D₃×C₁₇²	semidirect
32. C₃	C₂×D₃×C₁₇²	semidirect
34. C₂	C₁₇²×C₃⋊D₃	direct (N × H)

Subgroups — C2×C172×C3⋊D3 #23780944

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₇²×C₃⋊D₃ #23780944