Subgroups — C₂³×C₇×C₁₇×C₂₃ #72199378

Order 21896.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₇×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂²×C₇×C₁₇×C₂₃	C₂	1	7	yes	maximal, direct product factor
3	C₂×C₇×C₁₇×C₂₃	C₂²	1	7	yes	direct product factor
4	C₇×C₁₇×C₂₃	C₂³	1	1	yes	characteristic, direct product factor, Hall
5	C₂²×C₁₇×C₂₃	C₂×C₇	1	7	yes	direct product factor
6	C₂³×C₇×C₂₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₇×C₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₇×C₂₃	C₂²×C₇	1	7	yes	direct product factor
9	C₂²×C₇×C₂₃	C₂×C₁₇	1	7	yes	direct product factor
10	C₂²×C₇×C₁₇	C₂×C₂₃	1	7	yes	direct product factor
11	C₁₇×C₂₃	C₂³×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₂₃	C₂²×C₁₇	1	7	yes	direct product factor
13	C₂×C₇×C₁₇	C₂²×C₂₃	1	7	yes	direct product factor
14	C₂³×C₂₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₇×C₂₃	C₂³×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂³×C₁₇	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
17	C₇×C₁₇	C₂³×C₂₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₂₃	C₂×C₇×C₁₇	1	7	yes	direct product factor
19	C₂²×C₁₇	C₂×C₇×C₂₃	1	7	yes	direct product factor
20	C₂³×C₇	C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₂₃	C₂²×C₇×C₁₇	1	7	yes	direct product factor
22	C₂×C₁₇	C₂²×C₇×C₂₃	1	7	yes	direct product factor
23	C₂²×C₇	C₂×C₁₇×C₂₃	1	7	yes	direct product factor
24	C₂₃	C₂³×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₁₇	C₂³×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	C₂²×C₁₇×C₂₃	1	7	yes	direct product factor
27	C₂³	C₇×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₇	C₂³×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	C₂×C₇×C₁₇×C₂₃	1	7	yes	direct product factor
30	C₂	C₂²×C₇×C₁₇×C₂₃	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₇×C₂₃	C₇	direct (N × H)
2. C₂²×C₇×C₁₇×C₂₃	C₂	direct (N × H)
3. C₂×C₇×C₁₇×C₂₃	C₂²	direct (N × H)
4. C₇×C₁₇×C₂₃	C₂³	direct (N × H)
5. C₂²×C₁₇×C₂₃	C₂×C₇	direct (N × H)
6. C₂³×C₇×C₂₃	C₁₇	direct (N × H)
7. C₂³×C₇×C₁₇	C₂₃	direct (N × H)
8. C₂×C₁₇×C₂₃	C₂²×C₇	direct (N × H)
9. C₂²×C₇×C₂₃	C₂×C₁₇	direct (N × H)
10. C₂²×C₇×C₁₇	C₂×C₂₃	direct (N × H)
11. C₁₇×C₂₃	C₂³×C₇	direct (N × H)
12. C₂×C₇×C₂₃	C₂²×C₁₇	direct (N × H)
13. C₂×C₇×C₁₇	C₂²×C₂₃	direct (N × H)
14. C₂³×C₂₃	C₇×C₁₇	direct (N × H)
15. C₇×C₂₃	C₂³×C₁₇	direct (N × H)
16. C₂³×C₁₇	C₇×C₂₃	direct (N × H)
17. C₇×C₁₇	C₂³×C₂₃	direct (N × H)
18. C₂²×C₂₃	C₂×C₇×C₁₇	direct (N × H)
19. C₂²×C₁₇	C₂×C₇×C₂₃	direct (N × H)
20. C₂³×C₇	C₁₇×C₂₃	direct (N × H)
21. C₂×C₂₃	C₂²×C₇×C₁₇	direct (N × H)
22. C₂×C₁₇	C₂²×C₇×C₂₃	direct (N × H)
23. C₂²×C₇	C₂×C₁₇×C₂₃	direct (N × H)
24. C₂₃	C₂³×C₇×C₁₇	direct (N × H)
25. C₁₇	C₂³×C₇×C₂₃	direct (N × H)
26. C₂×C₇	C₂²×C₁₇×C₂₃	direct (N × H)
27. C₂³	C₇×C₁₇×C₂₃	direct (N × H)
28. C₇	C₂³×C₁₇×C₂₃	direct (N × H)
29. C₂²	C₂×C₇×C₁₇×C₂₃	direct (N × H)
30. C₂	C₂²×C₇×C₁₇×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₇×C₂₃	7
C₂²×C₇×C₁₇×C₂₃	2
C₂³×C₇×C₂₃	17
C₂³×C₇×C₁₇	23

Subgroups — C23×C7×C17×C23 #72199378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₇×C₁₇×C₂₃ #72199378