Subgroups — C₂×C₄₇×D₉₃ #31775739

Order 17484.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×D₉₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₃₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×D₃₁	—	3	1	no	maximal, Hall
4	C₃×C₃₁×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×C₄₇	D₃	1	1	yes	characteristic, complemented
6	C₄₇×D₃₁	—	3	2	no	—
7	C₃₁×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃×C₄₇	—	31	1	no	maximal, Hall
9	C₂×D₉₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₄₇	D₃₁	1	1	yes	characteristic, complemented
11	D₃×C₄₇	—	31	2	no	—
12	C₂²×C₄₇	—	93	1	no	Hall
13	C₂×C₃×C₃₁	C₂×C₄₇	1	1	yes	characteristic, complemented
14	D₉₃	C₂×C₄₇	1	2	yes	direct product factor
15	C₃×C₄₇	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₁	—	3	1	no	Hall
17	C₂×C₄₇	—	93	2	no	—
18	C₂×C₄₇	D₉₃	1	1	yes	characteristic, direct product factor
19	C₃×C₃₁	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₁	D₃×C₄₇	1	1	yes	characteristic, complemented
21	D₃₁	—	3	2	no	—
22	C₄₇	C₂×D₉₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₁	C₂×D₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	31	1	no	Hall
25	C₂×C₃	C₄₇×D₃₁	1	1	yes	characteristic, complemented
26	D₃	—	31	2	no	—
27	C₂²	—	93	1	no	Sylow
28	C₃	C₂×C₄₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	93	2	no	—
30	C₂	C₄₇×D₉₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₉₃
commutator, cosocle, hypocenter	C₃×C₃₁	C₂²×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₃₁×C₄₇	C₂
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₂×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₄₇×D₉₃	C₂	direct (N × H)
2. C₂×C₃×C₃₁×C₄₇	C₂	semidirect
4. C₃×C₃₁×C₄₇	C₂²	semidirect
5. C₂×C₃₁×C₄₇	D₃	semidirect
7. C₃₁×C₄₇	C₂×D₃	semidirect
9. C₂×D₉₃	C₄₇	direct (N × H)
10. C₂×C₃×C₄₇	D₃₁	semidirect
13. C₂×C₃×C₃₁	C₂×C₄₇	semidirect
14. D₉₃	C₂×C₄₇	direct (N × H)
15. C₃×C₄₇	C₂×D₃₁	semidirect
18. C₂×C₄₇	D₉₃	direct (N × H)
19. C₃×C₃₁	C₂²×C₄₇	semidirect
20. C₂×C₃₁	D₃×C₄₇	semidirect
22. C₄₇	C₂×D₉₃	direct (N × H)
23. C₃₁	C₂×D₃×C₄₇	semidirect
25. C₂×C₃	C₄₇×D₃₁	semidirect
28. C₃	C₂×C₄₇×D₃₁	semidirect
30. C₂	C₄₇×D₉₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×D₉₃	2
C₂×C₃×C₃₁×C₄₇	2
C₂×C₄₇×D₃₁	3
C₂×D₃×C₄₇	31
C₂×D₉₃	47

Subgroups — C2×C47×D93 #31775739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×D₉₃ #31775739