Subgroups — C₂×C₃×(C₁₇⋊D₁₇)⋊C₃ #23780900

Order 10404.

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

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₁₇⋊D₁₇)⋊C₃
commutator, cosocle, hypocenter	C₁₇²	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₇²	C₂×C₃
LCS	G ▷ C₁₇²
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×(C₁₇⋊D₁₇)⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₁₇⋊D₁₇	C₃	semidirect
4. C₂×(C₁₇⋊D₁₇)⋊C₃	C₃	direct (N × H)
5. C₃×C₁₇²⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₇²	C₂×C₃	semidirect
7. C₃×C₁₇⋊D₁₇	C₂×C₃	semidirect
8. C₂×C₁₇²⋊C₃	C₂×C₃	semidirect
9. (C₁₇⋊D₁₇)⋊C₃	C₂×C₃	direct (N × H)
10. C₂×C₁₇⋊D₁₇	C₃²	semidirect
11. C₃×C₁₇²	C₂²×C₃	semidirect
12. C₁₇²⋊C₃	C₂²×C₃	semidirect
13. C₂×C₁₇²	C₂×C₃²	semidirect
14. C₁₇⋊D₁₇	C₂×C₃²	semidirect
15. C₁₇²	C₂²×C₃²	semidirect
33. C₂×C₃	(C₁₇⋊D₁₇)⋊C₃	direct (N × H)
36. C₃	C₂×(C₁₇⋊D₁₇)⋊C₃	direct (N × H)
38. C₂	C₃×(C₁₇⋊D₁₇)⋊C₃	direct (N × H)

Subgroups — C2×C3×(C17⋊D17)⋊C3 #23780900

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×(C₁₇⋊D₁₇)⋊C₃ #23780900