Subgroups — C₂×C₃⋊((C₁₇⋊D₁₇)⋊C₃) #23780902

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	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	—	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	C₃⋊(C₁₇⋊D₁₇)	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₇²⋊C₃	—	2	1	no	—
9	C₂×C₁₇²⋊C₃	D₃	1	1	yes	characteristic, complemented
10	(C₁₇⋊D₁₇)⋊C₃	—	3	2	no	—
11	C₂×C₁₇⋊D₁₇	—	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, 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	C₂×D₅₁	—	51	6	no	—
19	C₂×C₃×C₁₇	—	3	6	no	—
20	D₅₁	—	51	12	no	—
21	C₂×D₁₇	—	153	6	no	—
22	C₃×C₁₇	—	3	6	no	—
23	C₂×C₃×D₃	—	289	1	no	maximal, Hall
24	C₂×C₁₇	—	3	6	no	—
25	D₁₇	—	153	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	—	289	1	no	—
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	(C₁₇⋊D₁₇)⋊C₃	1	1	yes	characteristic, complemented
36	D₃	—	289	2	no	—
37	C₂²	—	867	1	no	Sylow
38	C₃	—	289	1	no	—
39	C₃	—	578	1	no	—
40	C₃	C₂×(C₁₇⋊D₁₇)⋊C₃	1	1	yes	characteristic, complemented
41	C₂	—	867	2	no	—
42	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	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. C₃⋊((C₁₇⋊D₁₇)⋊C₃)	C₂	direct (N × H)
3. C₂×C₃⋊(C₁₇⋊D₁₇)	C₃	semidirect
5. C₃×C₁₇²⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₇²	C₂×C₃	semidirect
7. C₃⋊(C₁₇⋊D₁₇)	C₂×C₃	semidirect
9. C₂×C₁₇²⋊C₃	D₃	semidirect
12. C₃×C₁₇²	C₂²×C₃	semidirect
14. C₁₇²⋊C₃	C₂×D₃	semidirect
15. C₂×C₁₇²	C₃×D₃	semidirect
17. C₁₇²	C₂×C₃×D₃	semidirect
35. C₂×C₃	(C₁₇⋊D₁₇)⋊C₃	semidirect
40. C₃	C₂×(C₁₇⋊D₁₇)⋊C₃	semidirect
42. C₂	C₃⋊((C₁₇⋊D₁₇)⋊C₃)	direct (N × H)

Subgroups — C2×C3⋊((C17⋊D17)⋊C3) #23780902

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊((C₁₇⋊D₁₇)⋊C₃) #23780902