Subgroups — C₂×C₃⋊(C₃⋊(C₁₇⋊D₁₇)) #23780942

Order 10404.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(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)	—	3	4	no	maximal
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₇²	D₃	1	4	yes	complemented
6	C₃⋊(C₁₇⋊D₁₇)	—	3	8	no	—
7	C₂×C₁₇⋊D₁₇	—	9	1	no	Hall
8	C₃×C₁₇²	C₂×D₃	1	4	yes	complemented
9	C₂×C₃⋊D₅₁	—	17	18	no	maximal
10	C₂×C₁₇²	C₃⋊D₃	1	1	yes	characteristic, complemented
11	C₁₇⋊D₁₇	—	9	2	no	—
12	C₂×C₃²×C₁₇	D₁₇	1	18	yes	complemented
13	C₃⋊D₅₁	—	17	36	no	—
14	C₁₇²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
15	C₂×D₅₁	—	51	72	no	—
16	C₃²×C₁₇	C₂×D₁₇	1	18	yes	complemented
17	C₂×C₃×C₁₇	D₅₁	1	72	yes	complemented
18	D₅₁	—	51	144	no	—
19	C₂×D₁₇	—	153	18	no	—
20	C₃×C₁₇	C₂×D₅₁	1	72	yes	complemented
21	C₂×C₃⋊D₃	—	289	1	no	Hall
22	C₂×C₁₇	C₃⋊D₅₁	1	18	yes	complemented
23	D₁₇	—	153	36	no	—
24	C₂×C₃²	C₁₇⋊D₁₇	1	1	yes	characteristic, complemented
25	C₃⋊D₃	—	289	2	no	—
26	C₁₇	C₂×C₃⋊D₅₁	1	18	yes	complemented
27	C₂×D₃	—	867	4	no	—
28	C₃²	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	C₃⋊(C₁₇⋊D₁₇)	1	4	yes	complemented
30	D₃	—	867	8	no	—
31	C₂²	—	2601	1	no	Sylow
32	C₃	C₂×C₃⋊(C₁₇⋊D₁₇)	1	4	yes	complemented
33	C₂	—	2601	2	no	—
34	C₂	C₃⋊(C₃⋊(C₁₇⋊D₁₇))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₃⋊(C₁₇⋊D₁₇))
commutator, cosocle, hypocenter	C₃²×C₁₇²	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇²	C₂
LCS	G ▷ C₃²×C₁₇²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃⋊(C₁₇⋊D₁₇))	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
10. C₂×C₁₇²	C₃⋊D₃	semidirect
12. C₂×C₃²×C₁₇	D₁₇	semidirect
14. C₁₇²	C₂×C₃⋊D₃	semidirect
16. C₃²×C₁₇	C₂×D₁₇	semidirect
17. C₂×C₃×C₁₇	D₅₁	semidirect
20. C₃×C₁₇	C₂×D₅₁	semidirect
22. C₂×C₁₇	C₃⋊D₅₁	semidirect
24. C₂×C₃²	C₁₇⋊D₁₇	semidirect
26. C₁₇	C₂×C₃⋊D₅₁	semidirect
28. C₃²	C₂×C₁₇⋊D₁₇	semidirect
29. C₂×C₃	C₃⋊(C₁₇⋊D₁₇)	semidirect
32. C₃	C₂×C₃⋊(C₁₇⋊D₁₇)	semidirect
34. C₂	C₃⋊(C₃⋊(C₁₇⋊D₁₇))	direct (N × H)

Subgroups — C2×C3⋊(C3⋊(C17⋊D17)) #23780942

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊(C₃⋊(C₁₇⋊D₁₇)) #23780942