Subgroups — (C₃⋊D₃)⋊(C₁₇⋊D₁₇) #23780929

Order 10404.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	1	2	yes	maximal, complemented
3	D₃×C₁₇⋊D₁₇	—	3	2	no	maximal
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇⋊D₁₇	—	3	2	no	—
6	D₃×C₁₇²	—	3	2	no	—
7	D₃×C₁₇²	—	6	1	no	—
8	C₃⋊(C₁₇⋊D₁₇)	D₃	1	2	yes	complemented
9	C₂×C₁₇⋊D₁₇	—	9	1	no	Hall
10	C₃×C₁₇²	—	2	1	no	—
11	C₃×C₁₇²	C₂×D₃	1	2	yes	complemented
12	(C₃⋊D₃)⋊D₁₇	—	17	18	no	maximal
13	C₂×C₁₇²	—	9	1	no	—
14	C₁₇⋊D₁₇	—	3	2	no	—
15	C₁₇×C₃⋊D₃	D₁₇	1	18	yes	complemented
16	C₃×D₅₁	—	17	36	no	—
17	C₁₇²	D₃²	1	1	yes	characteristic, complemented, Sylow
18	D₃×D₁₇	—	51	36	no	—
19	C₃²×C₁₇	C₂×D₁₇	1	18	yes	complemented
20	D₅₁	—	17	36	no	—
21	C₃×D₁₇	—	51	36	no	—
22	D₃×C₁₇	—	3	36	no	—
23	D₃×C₁₇	—	6	18	no	—
24	C₂×D₁₇	—	153	18	no	—
25	C₃×C₁₇	—	2	18	no	—
26	C₃×C₁₇	D₃×D₁₇	1	36	yes	complemented
27	D₃²	—	289	1	no	Hall
28	C₂×C₁₇	—	9	18	no	—
29	D₁₇	—	51	36	no	—
30	C₃⋊D₃	C₁₇⋊D₁₇	1	1	yes	characteristic, complemented
31	C₃×D₃	—	289	2	no	—
32	C₁₇	(C₃⋊D₃)⋊D₁₇	1	18	yes	complemented
33	C₂×D₃	—	867	2	no	—
34	C₃²	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	867	2	no	—
36	D₃	—	3	2	no	—
37	D₃	—	6	1	no	—
38	D₃	—	289	2	no	—
39	C₂²	—	2601	1	no	Sylow
40	C₃	—	2	1	no	—
41	C₃	D₃×C₁₇⋊D₁₇	1	2	yes	complemented
42	C₂	—	9	1	no	—
43	C₂	—	867	2	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. C₁₇²×C₃⋊D₃	C₂	semidirect
2. C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	semidirect
4. C₃²×C₁₇²	C₂²	semidirect
8. C₃⋊(C₁₇⋊D₁₇)	D₃	semidirect
11. C₃×C₁₇²	C₂×D₃	semidirect
15. C₁₇×C₃⋊D₃	D₁₇	semidirect
17. C₁₇²	D₃²	semidirect
19. C₃²×C₁₇	C₂×D₁₇	semidirect
26. C₃×C₁₇	D₃×D₁₇	semidirect
30. C₃⋊D₃	C₁₇⋊D₁₇	semidirect
32. C₁₇	(C₃⋊D₃)⋊D₁₇	semidirect
34. C₃²	C₂×C₁₇⋊D₁₇	semidirect
41. C₃	D₃×C₁₇⋊D₁₇	semidirect

Subgroups — (C3⋊D3)⋊(C17⋊D17) #23780929

Conjugacy classes of subgroups

Complements

Subgroups — (C₃⋊D₃)⋊(C₁₇⋊D₁₇) #23780929