Subgroups — C₂×C₁₇×#11744749 #44502012

Order 30702.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#11744749	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₄₃⋊C₃	—	7	1	no	maximal, Hall
5	C₁₇×C₄₃⋊C₃	—	7	1	no	Hall
6	C₂×#11744749	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
8	#11744749	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₁₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇×ΓL(1,𝔽₈)	—	43	1	no	maximal, Hall
11	C₂×C₇×C₄₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₁₇×ΓL(1,𝔽₈)	—	43	1	no	Hall
13	C₇×C₄₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₄₃⋊C₃	—	7	1	no	Hall
15	C₂×C₇×C₁₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₄₃⋊C₃	—	7	1	no	Hall
17	C₇×C₁₇	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₇	—	301	1	no	Hall
19	C₂×C₄₃	C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₇	—	301	1	no	Hall
21	C₄₃	C₂×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
22	C₂×ΓL(1,𝔽₈)	—	43	1	no	Hall
23	C₂×C₁₇	#11744749	1	1	yes	characteristic, direct product factor, Hall
24	ΓL(1,𝔽₈)	—	43	1	no	Hall
25	C₁₇	C₂×#11744749	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	C₁₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₇	C₂×C₁₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	301	1	no	Hall
29	C₃	—	301	1	no	Sylow
30	C₂	C₁₇×#11744749	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₇	#11744749
commutator, cosocle, hypocenter	C₇×C₄₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₇×C₄₃	C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×#11744749	C₂	direct (N × H)
2. C₂×C₇×C₁₇×C₄₃	C₃	semidirect
3. C₇×C₁₇×C₄₃	C₂×C₃	semidirect
6. C₂×#11744749	C₁₇	direct (N × H)
7. C₂×C₁₇×C₄₃	ΓL(1,𝔽₈)	semidirect
8. #11744749	C₂×C₁₇	direct (N × H)
9. C₁₇×C₄₃	C₂×ΓL(1,𝔽₈)	semidirect
11. C₂×C₇×C₄₃	C₃×C₁₇	semidirect
13. C₇×C₄₃	C₂×C₃×C₁₇	semidirect
15. C₂×C₇×C₁₇	C₄₃⋊C₃	semidirect
17. C₇×C₁₇	C₂×C₄₃⋊C₃	semidirect
19. C₂×C₄₃	C₁₇×ΓL(1,𝔽₈)	semidirect
21. C₄₃	C₂×C₁₇×ΓL(1,𝔽₈)	semidirect
23. C₂×C₁₇	#11744749	direct (N × H)
25. C₁₇	C₂×#11744749	direct (N × H)
26. C₂×C₇	C₁₇×C₄₃⋊C₃	semidirect
27. C₇	C₂×C₁₇×C₄₃⋊C₃	semidirect
30. C₂	C₁₇×#11744749	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#11744749	2
C₂×C₇×C₁₇×C₄₃	3
C₂×C₁₇×C₄₃⋊C₃	7
C₂×#11744749	17
C₂×C₁₇×ΓL(1,𝔽₈)	43

Subgroups — C2×C17×#11744749 #44502012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#11744749 #44502012