Subgroups — C₂×D₁₇×C₄₃⋊C₇ #35205960

Order 20468.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×C₄₃⋊C₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₇×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×C₄₃⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₇×C₄₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₇×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
6	D₁₇×C₄₃	C₂×C₇	1	2	yes	complemented
7	C₂²×C₄₃⋊C₇	—	17	1	no	maximal, Hall
8	C₁₇×C₄₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₄₃⋊C₇	—	17	2	no	—
10	C₂×C₄₃⋊C₇	D₁₇	1	1	yes	characteristic, direct product factor
11	C₂×C₇×D₁₇	—	43	1	no	maximal, Hall
12	C₄₃⋊C₇	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₇×C₁₇	—	43	1	no	—
14	C₇×D₁₇	—	43	2	no	—
15	C₂²×C₄₃	—	17	1	no	Hall
16	C₇×C₁₇	—	43	1	no	Hall
17	C₂×C₄₃	—	17	2	no	—
18	C₂×C₄₃	C₇×D₁₇	1	1	yes	characteristic, complemented
19	C₂×D₁₇	C₄₃⋊C₇	1	1	yes	characteristic, direct product factor, Hall
20	C₄₃	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₇	C₂×C₄₃⋊C₇	1	1	yes	characteristic, complemented
22	D₁₇	C₂×C₄₃⋊C₇	1	2	yes	direct product factor
23	C₂²×C₇	—	731	1	no	Hall
24	C₁₇	C₂²×C₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	—	43	1	no	—
26	C₂×C₇	—	731	2	no	—
27	C₇	—	43	1	no	Sylow
28	C₂²	—	17	1	no	Sylow
29	C₂	—	17	2	no	—
30	C₂	D₁₇×C₄₃⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₇×C₄₃⋊C₇
commutator, cosocle, hypocenter	C₁₇×C₄₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₄₃	C₂×C₇
LCS	G ▷ C₁₇×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₁₇×C₄₃⋊C₇	C₂	direct (N × H)
2. C₂×C₁₇×C₄₃⋊C₇	C₂	semidirect
3. C₁₇×C₄₃⋊C₇	C₂²	semidirect
4. C₂×D₁₇×C₄₃	C₇	semidirect
5. C₂×C₁₇×C₄₃	C₂×C₇	semidirect
6. D₁₇×C₄₃	C₂×C₇	semidirect
8. C₁₇×C₄₃	C₂²×C₇	semidirect
10. C₂×C₄₃⋊C₇	D₁₇	direct (N × H)
12. C₄₃⋊C₇	C₂×D₁₇	direct (N × H)
18. C₂×C₄₃	C₇×D₁₇	semidirect
19. C₂×D₁₇	C₄₃⋊C₇	direct (N × H)
20. C₄₃	C₂×C₇×D₁₇	semidirect
21. C₂×C₁₇	C₂×C₄₃⋊C₇	semidirect
22. D₁₇	C₂×C₄₃⋊C₇	direct (N × H)
24. C₁₇	C₂²×C₄₃⋊C₇	semidirect
30. C₂	D₁₇×C₄₃⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₇×C₄₃⋊C₇	2
C₂×C₁₇×C₄₃⋊C₇	2
C₂×D₁₇×C₄₃	7
C₂²×C₄₃⋊C₇	17
C₂×C₇×D₁₇	43

Subgroups — C2×D17×C43⋊C7 #35205960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₇×C₄₃⋊C₇ #35205960