Subgroups — C₃×D₅₂₁₇ #44531084

Order 31302.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₇₃₉	—	3	1	no	maximal
4	C₃×C₃₇×C₄₇	—	2	1	no	—
5	C₃×C₃₇×C₄₇	D₃	1	1	yes	characteristic, complemented
6	C₃×C₃₇×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₇₃₉	—	3	1	no	Hall
8	C₃₇×C₄₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₄₁	—	37	1	no	maximal, Hall
10	C₃×D₁₁₁	—	47	1	no	maximal, Hall
11	C₃²×C₄₇	D₃₇	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₃₇	D₄₇	1	1	yes	characteristic, complemented, Hall
13	D₁₄₁	—	37	1	no	—
14	C₃×D₄₇	—	111	1	no	—
15	D₁₁₁	—	47	1	no	—
16	C₃×D₃₇	—	141	1	no	—
17	C₃×C₄₇	—	2	1	no	—
18	C₃×C₄₇	C₃×D₃₇	1	1	yes	characteristic, complemented
19	C₃×C₄₇	D₁₁₁	1	1	yes	characteristic, complemented
20	C₃×C₃₇	—	2	1	no	—
21	C₃×C₃₇	C₃×D₄₇	1	1	yes	characteristic, complemented
22	C₃×C₃₇	D₁₄₁	1	1	yes	characteristic, complemented
23	D₄₇	—	111	1	no	Hall
24	D₃₇	—	141	1	no	Hall
25	C₄₇	C₃×D₁₁₁	1	1	yes	characteristic, complemented, Sylow
26	C₃₇	C₃×D₁₄₁	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1739	1	no	Hall
28	C₃²	D₁₇₃₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	5217	1	no	—
30	D₃	—	1739	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₇₃₉	1	1	yes	characteristic, complemented
33	C₃	D₅₂₁₇	1	1	yes	characteristic, direct product factor
34	C₂	—	5217	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₂₁₇
commutator, cosocle, hypocenter	C₃×C₃₇×C₄₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₃₇×C₄₇	C₂
LCS	G ▷ C₃×C₃₇×C₄₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃₇×C₄₇	C₂	semidirect
2. D₅₂₁₇	C₃	direct (N × H)
5. C₃×C₃₇×C₄₇	D₃	semidirect
6. C₃×C₃₇×C₄₇	C₂×C₃	semidirect
8. C₃₇×C₄₇	C₃×D₃	semidirect
11. C₃²×C₄₇	D₃₇	semidirect
12. C₃²×C₃₇	D₄₇	semidirect
18. C₃×C₄₇	C₃×D₃₇	semidirect
19. C₃×C₄₇	D₁₁₁	semidirect
21. C₃×C₃₇	C₃×D₄₇	semidirect
22. C₃×C₃₇	D₁₄₁	semidirect
25. C₄₇	C₃×D₁₁₁	semidirect
26. C₃₇	C₃×D₁₄₁	semidirect
28. C₃²	D₁₇₃₉	semidirect
32. C₃	C₃×D₁₇₃₉	semidirect
33. C₃	D₅₂₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₃₇×C₄₇	2
D₅₂₁₇	3
C₃×D₁₇₃₉	3
C₃×D₁₄₁	37
C₃×D₁₁₁	47

Subgroups — C3×D5217 #44531084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₂₁₇ #44531084