Subgroups — C₃⋊D₃×D₅₁₇ #32915939

Order 18612.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₅₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₃⋊D₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₅₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₅₁₇	—	3	4	no	maximal
5	C₃²×C₁₁×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅₅₁	—	3	4	no	—
7	D₃×C₁₁×C₄₇	—	3	4	no	—
8	C₃×D₅₁₇	D₃	1	4	yes	complemented
9	C₂×D₅₁₇	—	9	1	no	Hall
10	C₃⋊D₃×D₄₇	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₄₇	C₂×D₃	1	4	yes	complemented
12	C₂×C₁₁×C₄₇	—	9	1	no	—
13	D₅₁₇	—	9	1	no	—
14	D₅₁₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃⋊D₁₄₁	—	11	1	no	—
16	C₃⋊D₃×C₄₇	D₁₁	1	1	yes	characteristic, complemented
17	C₃²×D₄₇	—	11	1	no	—
18	D₃×D₄₇	—	33	4	no	—
19	C₁₁×C₄₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₄₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₃⋊D₃×D₁₁	—	47	1	no	maximal, Hall
22	D₁₄₁	—	33	4	no	—
23	C₃×D₄₇	—	11	4	no	—
24	D₃×C₄₇	—	3	4	no	—
25	C₃⋊D₃₃	—	47	1	no	—
26	C₁₁×C₃⋊D₃	D₄₇	1	1	yes	characteristic, complemented
27	C₃²×D₁₁	—	47	1	no	—
28	C₂×D₄₇	—	99	1	no	Hall
29	C₃×C₄₇	D₃×D₁₁	1	4	yes	complemented
30	D₃×D₁₁	—	141	4	no	—
31	C₃²×C₁₁	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
32	C₂×C₄₇	—	9	1	no	—
33	D₄₇	—	11	1	no	—
34	D₄₇	—	99	1	no	—
35	D₃₃	—	141	4	no	—
36	C₃×D₁₁	—	47	4	no	—
37	D₃×C₁₁	—	3	4	no	—
38	C₄₇	C₃⋊D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₁	—	423	1	no	Hall
40	C₂×C₃⋊D₃	—	517	1	no	Hall
41	C₃×C₁₁	D₃×D₄₇	1	4	yes	complemented
42	C₂×C₁₁	—	9	1	no	—
43	D₁₁	—	47	1	no	—
44	D₁₁	—	423	1	no	—
45	C₂×C₃²	—	517	1	no	—
46	C₃⋊D₃	—	517	1	no	—
47	C₃⋊D₃	D₅₁₇	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	1551	4	no	—
49	C₁₁	C₃⋊D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
50	C₃²	C₂×D₅₁₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	517	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	1551	4	no	—
54	C₂²	—	4653	1	no	Sylow
55	C₃	D₃×D₅₁₇	1	4	yes	complemented
56	C₂	—	517	1	no	—
57	C₂	—	9	1	no	—
58	C₂	—	4653	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁×C₄₇	C₂²
LCS	G ▷ C₃²×C₁₁×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₅₅₁	C₂	semidirect
2. C₁₁×C₃⋊D₃×C₄₇	C₂	semidirect
3. C₃²×D₅₁₇	C₂	semidirect
5. C₃²×C₁₁×C₄₇	C₂²	semidirect
8. C₃×D₅₁₇	D₃	semidirect
11. C₃×C₁₁×C₄₇	C₂×D₃	semidirect
14. D₅₁₇	C₃⋊D₃	direct (N × H)
16. C₃⋊D₃×C₄₇	D₁₁	semidirect
19. C₁₁×C₄₇	C₂×C₃⋊D₃	semidirect
20. C₃²×C₄₇	C₂×D₁₁	semidirect
26. C₁₁×C₃⋊D₃	D₄₇	semidirect
29. C₃×C₄₇	D₃×D₁₁	semidirect
31. C₃²×C₁₁	C₂×D₄₇	semidirect
38. C₄₇	C₃⋊D₃×D₁₁	semidirect
41. C₃×C₁₁	D₃×D₄₇	semidirect
47. C₃⋊D₃	D₅₁₇	direct (N × H)
49. C₁₁	C₃⋊D₃×D₄₇	semidirect
50. C₃²	C₂×D₅₁₇	semidirect
55. C₃	D₃×D₅₁₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃⋊D₁₅₅₁	2
C₁₁×C₃⋊D₃×C₄₇	2
C₃²×D₅₁₇	2
D₃×D₅₁₇	3
C₃⋊D₃×D₄₇	11
C₃⋊D₃×D₁₁	47

Subgroups — C3⋊D3×D517 #32915939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×D₅₁₇ #32915939