Subgroups — C₂×D₃×C₁₇²⋊C₃ #23780903

Order 10404.

104 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	D₃×C₁₇²⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₁₇²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₇²⋊C₃	—	3	1	no	maximal
5	C₃×C₁₇²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₇²	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×C₁₇²	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₇²⋊C₃	—	2	1	no	—
9	C₂×C₁₇²⋊C₃	—	3	2	no	—
10	C₂×C₁₇²⋊C₃	D₃	1	1	yes	characteristic, direct product factor
11	C₂²×C₁₇²	—	3	1	no	Hall
12	C₃×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₁₇²⋊C₃	—	2	1	no	—
14	C₁₇²⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₁₇²	—	3	2	no	—
16	C₂×C₁₇²	C₃×D₃	1	1	yes	characteristic, complemented
17	C₁₇²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×D₃×C₁₇	—	3	6	no	—
19	C₂×C₃×C₁₇	—	3	6	no	—
20	D₃×C₁₇	—	3	12	no	—
21	C₂²×C₁₇	—	9	6	no	—
22	C₃×C₁₇	—	3	6	no	—
23	C₂×C₃×D₃	—	289	1	no	maximal, Hall
24	C₂×C₁₇	—	3	6	no	—
25	C₂×C₁₇	—	9	12	no	—
26	C₂×C₃²	—	289	1	no	—
27	C₃×D₃	—	289	2	no	—
28	C₁₇	—	3	6	no	—
29	C₂²×C₃	—	867	1	no	—
30	C₂×D₃	C₁₇²⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃²	—	289	1	no	Sylow
32	C₂×C₃	—	289	1	no	—
33	C₂×C₃	—	578	1	no	—
34	C₂×C₃	—	867	2	no	—
35	C₂×C₃	C₂×C₁₇²⋊C₃	1	1	yes	characteristic, complemented
36	D₃	C₂×C₁₇²⋊C₃	1	2	yes	direct product factor
37	C₂²	—	3	1	no	Sylow
38	C₃	—	289	1	no	—
39	C₃	—	578	1	no	—
40	C₃	C₂²×C₁₇²⋊C₃	1	1	yes	characteristic, complemented
41	C₂	—	3	2	no	—
42	C₂	D₃×C₁₇²⋊C₃	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₇²⋊C₃	C₂	semidirect
2. D₃×C₁₇²⋊C₃	C₂	direct (N × H)
3. C₂×D₃×C₁₇²	C₃	semidirect
5. C₃×C₁₇²⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₇²	C₂×C₃	semidirect
7. D₃×C₁₇²	C₂×C₃	semidirect
10. C₂×C₁₇²⋊C₃	D₃	direct (N × H)
12. C₃×C₁₇²	C₂²×C₃	semidirect
14. C₁₇²⋊C₃	C₂×D₃	direct (N × H)
16. C₂×C₁₇²	C₃×D₃	semidirect
17. C₁₇²	C₂×C₃×D₃	semidirect
30. C₂×D₃	C₁₇²⋊C₃	direct (N × H)
35. C₂×C₃	C₂×C₁₇²⋊C₃	semidirect
36. D₃	C₂×C₁₇²⋊C₃	direct (N × H)
40. C₃	C₂²×C₁₇²⋊C₃	semidirect
42. C₂	D₃×C₁₇²⋊C₃	direct (N × H)

Subgroups — C2×D3×C172⋊C3 #23780903

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₃×C₁₇²⋊C₃ #23780903