Subgroups — C₂×C₃⋊#13181892 #23780901

Order 10404.

88 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×C₁₇×D₅₁	—	3	1	no	maximal
4	C₂×#13181892	—	3	3	no	maximal
5	C₃×C₁₇²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₇²	D₃	1	1	yes	characteristic, complemented
7	C₁₇×D₅₁	—	3	2	no	—
8	C₂×C₁₇²⋊C₃	D₃	1	3	yes	complemented
9	#13181892	—	3	6	no	—
10	C₂×C₁₇×D₁₇	—	9	1	no	Hall
11	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
12	C₁₇²⋊C₃	C₂×D₃	1	3	yes	complemented
13	C₂×C₁₇²	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₁₇×D₁₇	—	9	2	no	—
15	C₁₇²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₅₁	—	3	1	no	—
17	C₂×D₃×C₁₇	—	51	1	no	—
18	C₂×C₃×C₁₇	—	3	1	no	—
19	C₂×C₃×C₁₇	—	3	1	no	—
20	C₂×C₃×C₁₇	—	6	2	no	—
21	D₅₁	—	3	2	no	—
22	D₃×C₁₇	—	51	2	no	—
23	C₂²×C₁₇	—	153	1	no	—
24	C₂×D₁₇	—	9	1	no	—
25	C₃×C₁₇	—	3	1	no	—
26	C₃×C₁₇	—	3	1	no	—
27	C₃×C₁₇	—	6	2	no	—
28	C₂×C₃⋊D₃	—	289	1	no	maximal, Hall
29	C₂×C₁₇	—	3	1	no	—
30	C₂×C₁₇	—	3	1	no	—
31	C₂×C₁₇	—	6	2	no	—
32	C₂×C₁₇	—	153	2	no	—
33	D₁₇	—	9	2	no	—
34	C₂×C₃²	—	289	1	no	—
35	C₃⋊D₃	—	289	2	no	—
36	C₁₇	—	3	1	no	—
37	C₁₇	—	3	1	no	—
38	C₁₇	—	6	2	no	—
39	C₂×D₃	—	51	1	no	—
40	C₂×D₃	—	867	3	no	—
41	C₃²	—	289	1	no	Sylow
42	C₂×C₃	—	289	3	no	—
43	C₂×C₃	#13181892	1	1	yes	characteristic, complemented
44	D₃	—	51	2	no	—
45	D₃	—	867	6	no	—
46	C₂²	—	153	1	no	Sylow
47	C₃	—	289	3	no	—
48	C₃	C₂×#13181892	1	1	yes	characteristic, complemented
49	C₂	—	153	2	no	—
50	C₂	C₃⋊#13181892	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊#13181892
commutator, cosocle, hypocenter	C₃×C₁₇²⋊C₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₇²	D₃
LCS	G ▷ C₃×C₁₇²⋊C₃
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⋊#13181892	C₂	direct (N × H)
5. C₃×C₁₇²⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₇²	D₃	semidirect
8. C₂×C₁₇²⋊C₃	D₃	semidirect
11. C₃×C₁₇²	C₂×D₃	semidirect
12. C₁₇²⋊C₃	C₂×D₃	semidirect
13. C₂×C₁₇²	C₃⋊D₃	semidirect
15. C₁₇²	C₂×C₃⋊D₃	semidirect
43. C₂×C₃	#13181892	semidirect
48. C₃	C₂×#13181892	semidirect
50. C₂	C₃⋊#13181892	direct (N × H)

Subgroups — C2×C3⋊#13181892 #23780901

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊#13181892 #23780901