Subgroups — C₃⋊D₃×C₁₇⋊D₁₇ #23780922

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	1	yes	maximal, characteristic, complemented
2	C₁₇²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₇⋊D₁₇	—	3	4	no	maximal
5	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₇⋊D₁₇	D₃	1	4	yes	complemented
7	D₃×C₁₇²	—	3	4	no	—
8	C₃⋊(C₁₇⋊D₁₇)	—	3	4	no	—
9	C₂×C₁₇⋊D₁₇	—	9	1	no	Hall
10	C₃×C₁₇²	C₂×D₃	1	4	yes	complemented
11	C₃⋊D₃×D₁₇	—	17	18	no	maximal
12	C₂×C₁₇²	—	9	1	no	—
13	C₁₇⋊D₁₇	—	9	1	no	—
14	C₁₇⋊D₁₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃⋊D₅₁	—	17	18	no	—
16	C₁₇×C₃⋊D₃	D₁₇	1	18	yes	complemented
17	C₃²×D₁₇	—	17	18	no	—
18	C₁₇²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
19	D₃×D₁₇	—	51	72	no	—
20	C₃²×C₁₇	C₂×D₁₇	1	18	yes	complemented
21	D₅₁	—	51	72	no	—
22	C₃×D₁₇	—	17	72	no	—
23	D₃×C₁₇	—	3	72	no	—
24	C₂×D₁₇	—	153	18	no	—
25	C₃×C₁₇	D₃×D₁₇	1	72	yes	complemented
26	C₂×C₃⋊D₃	—	289	1	no	Hall
27	C₂×C₁₇	—	9	18	no	—
28	D₁₇	—	17	18	no	—
29	D₁₇	—	153	18	no	—
30	C₂×C₃²	—	289	1	no	—
31	C₃⋊D₃	—	289	1	no	—
32	C₃⋊D₃	C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor
33	C₁₇	C₃⋊D₃×D₁₇	1	18	yes	complemented
34	C₂×D₃	—	867	4	no	—
35	C₃²	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃	—	289	4	no	—
37	D₃	—	3	4	no	—
38	D₃	—	867	4	no	—
39	C₂²	—	2601	1	no	Sylow
40	C₃	D₃×C₁₇⋊D₁₇	1	4	yes	complemented
41	C₂	—	9	1	no	—
42	C₂	—	289	1	no	—
43	C₂	—	2601	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃⋊(C₁₇⋊D₁₇))	C₂	semidirect
2. C₁₇²×C₃⋊D₃	C₂	semidirect
3. C₃²×C₁₇⋊D₁₇	C₂	semidirect
5. C₃²×C₁₇²	C₂²	semidirect
6. C₃×C₁₇⋊D₁₇	D₃	semidirect
10. C₃×C₁₇²	C₂×D₃	semidirect
14. C₁₇⋊D₁₇	C₃⋊D₃	direct (N × H)
16. C₁₇×C₃⋊D₃	D₁₇	semidirect
18. C₁₇²	C₂×C₃⋊D₃	semidirect
20. C₃²×C₁₇	C₂×D₁₇	semidirect
25. C₃×C₁₇	D₃×D₁₇	semidirect
32. C₃⋊D₃	C₁₇⋊D₁₇	direct (N × H)
33. C₁₇	C₃⋊D₃×D₁₇	semidirect
35. C₃²	C₂×C₁₇⋊D₁₇	semidirect
40. C₃	D₃×C₁₇⋊D₁₇	semidirect

Subgroups — C3⋊D3×C17⋊D17 #23780922

Conjugacy classes of subgroups

Complements

Subgroups — C₃⋊D₃×C₁₇⋊D₁₇ #23780922