Subgroups — C₂×C₈×C₁₇×C₈₉ #72201511

Order 24208.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₇×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₇×C₈₉	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₁₇×C₈₉	C₄	1	1	yes	characteristic
4	C₄×C₁₇×C₈₉	C₄	1	1	yes	characteristic
5	C₄×C₁₇×C₈₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₇×C₈₉	C₈	1	2	yes	direct product factor
7	C₂×C₁₇×C₈₉	C₂×C₄	1	1	yes	characteristic
8	C₁₇×C₈₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₈×C₈₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₄×C₈₉	C₂×C₁₇	1	1	yes	characteristic
11	C₈×C₈₉	C₂×C₁₇	1	2	yes	direct product factor
12	C₂²×C₈₉	C₄×C₁₇	1	1	yes	characteristic
13	C₄×C₈₉	C₄×C₁₇	1	1	yes	characteristic
14	C₄×C₈₉	C₂²×C₁₇	1	1	yes	characteristic
15	C₂×C₈×C₁₇	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₈₉	C₈×C₁₇	1	2	yes	direct product factor
17	C₂×C₈₉	C₂×C₄×C₁₇	1	1	yes	characteristic
18	C₂×C₄×C₁₇	C₂×C₈₉	1	1	yes	characteristic
19	C₈×C₁₇	C₂×C₈₉	1	2	yes	direct product factor
20	C₈₉	C₂×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₁₇	C₄×C₈₉	1	1	yes	characteristic
22	C₄×C₁₇	C₄×C₈₉	1	1	yes	characteristic
23	C₄×C₁₇	C₂²×C₈₉	1	1	yes	characteristic
24	C₂×C₁₇	C₈×C₈₉	1	2	yes	direct product factor
25	C₂×C₁₇	C₂×C₄×C₈₉	1	1	yes	characteristic
26	C₁₇	C₂×C₈×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₈	C₁₇×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₄	C₂×C₁₇×C₈₉	1	1	yes	characteristic
29	C₈	C₂×C₁₇×C₈₉	1	2	yes	direct product factor
30	C₂²	C₄×C₁₇×C₈₉	1	1	yes	characteristic
31	C₄	C₄×C₁₇×C₈₉	1	1	yes	characteristic
32	C₄	C₂²×C₁₇×C₈₉	1	1	yes	characteristic
33	C₂	C₈×C₁₇×C₈₉	1	2	yes	direct product factor
34	C₂	C₂×C₄×C₁₇×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₁₇×C₈₉
socle, prime radical	C₂²×C₁₇×C₈₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₁₇×C₈₉	C₂	direct (N × H)
6. C₂×C₁₇×C₈₉	C₈	direct (N × H)
8. C₁₇×C₈₉	C₂×C₈	direct (N × H)
9. C₂×C₈×C₈₉	C₁₇	direct (N × H)
11. C₈×C₈₉	C₂×C₁₇	direct (N × H)
15. C₂×C₈×C₁₇	C₈₉	direct (N × H)
16. C₂×C₈₉	C₈×C₁₇	direct (N × H)
19. C₈×C₁₇	C₂×C₈₉	direct (N × H)
20. C₈₉	C₂×C₈×C₁₇	direct (N × H)
24. C₂×C₁₇	C₈×C₈₉	direct (N × H)
26. C₁₇	C₂×C₈×C₈₉	direct (N × H)
27. C₂×C₈	C₁₇×C₈₉	direct (N × H)
29. C₈	C₂×C₁₇×C₈₉	direct (N × H)
33. C₂	C₈×C₁₇×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₇×C₈₉	2
C₈×C₁₇×C₈₉	2
C₂×C₈×C₈₉	17
C₂×C₈×C₁₇	89

Subgroups — C2×C8×C17×C89 #72201511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₁₇×C₈₉ #72201511