Subgroups — C₂×C₃²×C₁₇⋊D₁₇ #23780948

Order 10404.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇⋊D₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₇⋊D₁₇	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₇²	C₂×C₃	1	4	yes	complemented
6	C₃×C₁₇⋊D₁₇	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₁₇⋊D₁₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₇²	C₂²×C₃	1	4	yes	complemented
9	C₂×C₃²×D₁₇	—	17	18	no	maximal
10	C₂×C₁₇²	C₂×C₃²	1	1	yes	characteristic, complemented
11	C₁₇⋊D₁₇	C₂×C₃²	1	2	yes	direct product factor
12	C₂×C₃²×C₁₇	D₁₇	1	18	yes	complemented
13	C₃²×D₁₇	—	17	36	no	—
14	C₁₇²	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃×D₁₇	—	17	72	no	—
16	C₃²×C₁₇	C₂×D₁₇	1	18	yes	complemented
17	C₂×C₃×C₁₇	C₃×D₁₇	1	72	yes	complemented
18	C₃×D₁₇	—	17	144	no	—
19	C₂×D₁₇	—	17	18	no	—
20	C₃×C₁₇	C₂×C₃×D₁₇	1	72	yes	complemented
21	C₂²×C₃²	—	289	1	no	Hall
22	C₂×C₁₇	C₃²×D₁₇	1	18	yes	complemented
23	D₁₇	—	17	36	no	—
24	C₂×C₃²	—	289	2	no	—
25	C₂×C₃²	C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor
26	C₁₇	C₂×C₃²×D₁₇	1	18	yes	complemented
27	C₂²×C₃	—	289	4	no	—
28	C₃²	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃	—	289	8	no	—
30	C₂×C₃	C₃×C₁₇⋊D₁₇	1	4	yes	direct product factor
31	C₂²	—	289	1	no	Sylow
32	C₃	C₂×C₃×C₁₇⋊D₁₇	1	4	yes	direct product factor
33	C₂	—	289	2	no	—
34	C₂	C₃²×C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	C₁₇⋊D₁₇
commutator, cosocle, hypocenter	C₁₇²	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇²	C₂
LCS	G ▷ C₁₇²
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇⋊D₁₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₇²	C₂	semidirect
3. C₂×C₃×C₁₇⋊D₁₇	C₃	direct (N × H)
4. C₃²×C₁₇²	C₂²	semidirect
5. C₂×C₃×C₁₇²	C₂×C₃	semidirect
6. C₃×C₁₇⋊D₁₇	C₂×C₃	direct (N × H)
7. C₂×C₁₇⋊D₁₇	C₃²	direct (N × H)
8. C₃×C₁₇²	C₂²×C₃	semidirect
10. C₂×C₁₇²	C₂×C₃²	semidirect
11. C₁₇⋊D₁₇	C₂×C₃²	direct (N × H)
12. C₂×C₃²×C₁₇	D₁₇	semidirect
14. C₁₇²	C₂²×C₃²	semidirect
16. C₃²×C₁₇	C₂×D₁₇	semidirect
17. C₂×C₃×C₁₇	C₃×D₁₇	semidirect
20. C₃×C₁₇	C₂×C₃×D₁₇	semidirect
22. C₂×C₁₇	C₃²×D₁₇	semidirect
25. C₂×C₃²	C₁₇⋊D₁₇	direct (N × H)
26. C₁₇	C₂×C₃²×D₁₇	semidirect
28. C₃²	C₂×C₁₇⋊D₁₇	direct (N × H)
30. C₂×C₃	C₃×C₁₇⋊D₁₇	direct (N × H)
32. C₃	C₂×C₃×C₁₇⋊D₁₇	direct (N × H)
34. C₂	C₃²×C₁₇⋊D₁₇	direct (N × H)

Subgroups — C2×C32×C17⋊D17 #23780948

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×C₁₇⋊D₁₇ #23780948