Subgroups — D₃×(C₁₇⋊D₁₇)⋊C₃ #23780895

Order 10404.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₇²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊((C₁₇⋊D₁₇)⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₁₇⋊D₁₇)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₇⋊D₁₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×(C₁₇⋊D₁₇)⋊C₃	—	3	1	no	maximal
6	C₃×C₁₇²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₇⋊D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃×C₁₇²	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃⋊(C₁₇⋊D₁₇)	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₁₇²⋊C₃	—	3	1	no	—
11	(C₁₇⋊D₁₇)⋊C₃	—	2	1	no	—
12	(C₁₇⋊D₁₇)⋊C₃	—	3	1	no	—
13	(C₁₇⋊D₁₇)⋊C₃	D₃	1	1	yes	characteristic, direct product factor
14	C₂×C₁₇⋊D₁₇	—	3	1	no	Hall
15	C₃×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₇²⋊C₃	—	2	1	no	—
17	C₁₇²⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₁₇²	—	3	1	no	—
19	C₁₇⋊D₁₇	—	3	1	no	—
20	C₁₇⋊D₁₇	C₃×D₃	1	1	yes	characteristic, complemented
21	C₁₇²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
22	D₃×D₁₇	—	51	6	no	—
23	D₅₁	—	51	6	no	—
24	C₃×D₁₇	—	51	6	no	—
25	D₃×C₁₇	—	3	6	no	—
26	C₂×D₁₇	—	153	6	no	—
27	C₃×C₁₇	—	3	6	no	—
28	C₂×C₃×D₃	—	289	1	no	maximal, Hall
29	C₂×C₁₇	—	9	6	no	—
30	D₁₇	—	51	6	no	—
31	D₁₇	—	153	6	no	—
32	C₂×C₃²	—	289	1	no	—
33	C₃×D₃	—	289	1	no	—
34	C₃×D₃	—	289	1	no	—
35	C₁₇	—	3	6	no	—
36	C₂²×C₃	—	867	1	no	—
37	C₂×D₃	—	289	1	no	—
38	C₃²	—	289	1	no	Sylow
39	C₂×C₃	—	289	1	no	—
40	C₂×C₃	—	289	1	no	—
41	C₂×C₃	—	578	1	no	—
42	C₂×C₃	—	867	1	no	—
43	C₂×C₃	—	867	1	no	—
44	D₃	—	289	1	no	—
45	D₃	(C₁₇⋊D₁₇)⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂²	—	867	1	no	Sylow
47	C₃	—	289	1	no	—
48	C₃	—	578	1	no	—
49	C₃	C₂×(C₁₇⋊D₁₇)⋊C₃	1	1	yes	characteristic, complemented
50	C₂	—	3	1	no	—
51	C₂	—	289	1	no	—
52	C₂	—	867	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₇²⋊C₃	C₂	semidirect
2. C₃⋊((C₁₇⋊D₁₇)⋊C₃)	C₂	semidirect
3. C₃×(C₁₇⋊D₁₇)⋊C₃	C₂	semidirect
4. D₃×C₁₇⋊D₁₇	C₃	semidirect
6. C₃×C₁₇²⋊C₃	C₂²	semidirect
7. C₃×C₁₇⋊D₁₇	C₂×C₃	semidirect
8. D₃×C₁₇²	C₂×C₃	semidirect
9. C₃⋊(C₁₇⋊D₁₇)	C₂×C₃	semidirect
13. (C₁₇⋊D₁₇)⋊C₃	D₃	direct (N × H)
15. C₃×C₁₇²	C₂²×C₃	semidirect
17. C₁₇²⋊C₃	C₂×D₃	semidirect
20. C₁₇⋊D₁₇	C₃×D₃	semidirect
21. C₁₇²	C₂×C₃×D₃	semidirect
45. D₃	(C₁₇⋊D₁₇)⋊C₃	direct (N × H)
49. C₃	C₂×(C₁₇⋊D₁₇)⋊C₃	semidirect

Subgroups — D3×(C17⋊D17)⋊C3 #23780895

Conjugacy classes of subgroups

Complements

Subgroups — D₃×(C₁₇⋊D₁₇)⋊C₃ #23780895