Subgroups — C₂×C₃×#13181892 #23780899

Order 10404.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#13181892	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₇×D₁₇	—	3	1	no	maximal
4	C₂×#13181892	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₁₇²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₇²	D₃	1	1	yes	characteristic, complemented
7	C₃×C₁₇×D₁₇	—	3	2	no	—
8	C₂×C₁₇²⋊C₃	—	2	1	no	—
9	C₂×C₁₇²⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	#13181892	C₂×C₃	1	2	yes	direct product factor
11	C₂×C₁₇×D₁₇	—	3	1	no	Hall
12	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
13	C₁₇²⋊C₃	—	2	1	no	—
14	C₁₇²⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₁₇²	C₃×D₃	1	1	yes	characteristic, complemented
16	C₁₇×D₁₇	—	3	2	no	—
17	C₁₇²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₃×C₁₇	—	51	1	no	—
19	C₂×C₃×D₁₇	—	3	1	no	—
20	C₂×C₃×C₁₇	—	3	1	no	—
21	C₂×C₃×C₁₇	—	3	1	no	—
22	C₂×C₃×C₁₇	—	6	2	no	—
23	C₂×C₃×C₁₇	—	51	2	no	—
24	C₃×D₁₇	—	3	2	no	—
25	C₂²×C₁₇	—	51	1	no	—
26	C₂×D₁₇	—	3	1	no	—
27	C₃×C₁₇	—	3	1	no	—
28	C₃×C₁₇	—	3	1	no	—
29	C₃×C₁₇	—	6	2	no	—
30	C₂×C₃×D₃	—	289	1	no	maximal, Hall
31	C₂×C₁₇	—	3	1	no	—
32	C₂×C₁₇	—	3	1	no	—
33	C₂×C₁₇	—	6	2	no	—
34	C₂×C₁₇	—	51	2	no	—
35	D₁₇	—	3	2	no	—
36	C₂×C₃²	—	289	1	no	—
37	C₃×D₃	—	289	2	no	—
38	C₁₇	—	3	1	no	—
39	C₁₇	—	3	1	no	—
40	C₁₇	—	6	2	no	—
41	C₂²×C₃	—	51	1	no	—
42	C₂×D₃	—	289	1	no	—
43	C₃²	—	289	1	no	Sylow
44	C₂×C₃	—	289	1	no	—
45	C₂×C₃	—	51	2	no	—
46	C₂×C₃	—	578	1	no	—
47	C₂×C₃	#13181892	1	1	yes	characteristic, direct product factor
48	D₃	—	289	2	no	—
49	C₂²	—	51	1	no	Sylow
50	C₃	—	289	1	no	—
51	C₃	—	578	1	no	—
52	C₃	C₂×#13181892	1	1	yes	characteristic, direct product factor
53	C₂	—	51	2	no	—
54	C₂	C₃×#13181892	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#13181892
commutator, cosocle, hypocenter	C₁₇²⋊C₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₇²	D₃
LCS	G ▷ C₁₇²⋊C₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₇²⋊C₃	C₂	semidirect
2. C₃×#13181892	C₂	direct (N × H)
4. C₂×#13181892	C₃	direct (N × H)
5. C₃×C₁₇²⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₇²	D₃	semidirect
9. C₂×C₁₇²⋊C₃	C₂×C₃	semidirect
10. #13181892	C₂×C₃	direct (N × H)
12. C₃×C₁₇²	C₂×D₃	semidirect
14. C₁₇²⋊C₃	C₂²×C₃	semidirect
15. C₂×C₁₇²	C₃×D₃	semidirect
17. C₁₇²	C₂×C₃×D₃	semidirect
47. C₂×C₃	#13181892	direct (N × H)
52. C₃	C₂×#13181892	direct (N × H)
54. C₂	C₃×#13181892	direct (N × H)

Subgroups — C2×C3×#13181892 #23780899

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×#13181892 #23780899