Subgroups — C₇×C₉×C₁₇×C₂₃ #37590146

Order 24633.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₂₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₇×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₇×C₂₃	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₇×C₉×C₂₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×C₂₃	C₃×C₇	1	1	yes	characteristic
6	C₇×C₉×C₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇×C₂₃	C₃×C₁₇	1	1	yes	characteristic
8	C₁₇×C₂₃	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₁₇	C₃×C₂₃	1	1	yes	characteristic
10	C₉×C₂₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₂₃	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₉×C₁₇	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₁₇	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₂₃	C₃×C₇×C₁₇	1	1	yes	characteristic
15	C₇×C₉	C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₇	C₃×C₇×C₂₃	1	1	yes	characteristic
17	C₂₃	C₇×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₇	C₃×C₁₇×C₂₃	1	1	yes	characteristic
19	C₁₇	C₇×C₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₉	C₇×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₇	C₉×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₇×C₁₇×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₇×C₁₇×C₂₃
socle, prime radical	C₃×C₇×C₁₇×C₂₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₇×C₂₃	C₇	direct (N × H)
3. C₇×C₁₇×C₂₃	C₉	direct (N × H)
4. C₇×C₉×C₂₃	C₁₇	direct (N × H)
6. C₇×C₉×C₁₇	C₂₃	direct (N × H)
8. C₁₇×C₂₃	C₇×C₉	direct (N × H)
10. C₉×C₂₃	C₇×C₁₇	direct (N × H)
11. C₇×C₂₃	C₉×C₁₇	direct (N × H)
12. C₉×C₁₇	C₇×C₂₃	direct (N × H)
13. C₇×C₁₇	C₉×C₂₃	direct (N × H)
15. C₇×C₉	C₁₇×C₂₃	direct (N × H)
17. C₂₃	C₇×C₉×C₁₇	direct (N × H)
19. C₁₇	C₇×C₉×C₂₃	direct (N × H)
20. C₉	C₇×C₁₇×C₂₃	direct (N × H)
21. C₇	C₉×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
C₃×C₇×C₁₇×C₂₃	3
C₉×C₁₇×C₂₃	7
C₇×C₉×C₂₃	17
C₇×C₉×C₁₇	23

Subgroups — C7×C9×C17×C23 #37590146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×C₁₇×C₂₃ #37590146