Subgroups — C₂²×C₁₁×C₁₉×C₂₃ #34063646

Order 19228.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₉×C₂₃	C₂	1	3	yes	maximal, direct product factor
2	C₁₁×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₉×C₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₁₁×C₂₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₉×C₂₃	C₂×C₁₁	1	3	yes	direct product factor
6	C₂²×C₁₁×C₁₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₂₃	C₂×C₁₉	1	3	yes	direct product factor
8	C₁₉×C₂₃	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₁×C₁₉	C₂×C₂₃	1	3	yes	direct product factor
10	C₁₁×C₂₃	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₁₉	C₂²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₂₃	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₁₉	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₂₃	C₂×C₁₁×C₁₉	1	3	yes	direct product factor
15	C₂²×C₁₁	C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₉	C₂×C₁₁×C₂₃	1	3	yes	direct product factor
17	C₂₃	C₂²×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₁₁	C₂×C₁₉×C₂₃	1	3	yes	direct product factor
19	C₁₉	C₂²×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₂²×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₁₁×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₁₁×C₁₉×C₂₃	1	3	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. C₂×C₁₁×C₁₉×C₂₃	C₂	direct (N × H)
2. C₁₁×C₁₉×C₂₃	C₂²	direct (N × H)
3. C₂²×C₁₉×C₂₃	C₁₁	direct (N × H)
4. C₂²×C₁₁×C₂₃	C₁₉	direct (N × H)
5. C₂×C₁₉×C₂₃	C₂×C₁₁	direct (N × H)
6. C₂²×C₁₁×C₁₉	C₂₃	direct (N × H)
7. C₂×C₁₁×C₂₃	C₂×C₁₉	direct (N × H)
8. C₁₉×C₂₃	C₂²×C₁₁	direct (N × H)
9. C₂×C₁₁×C₁₉	C₂×C₂₃	direct (N × H)
10. C₁₁×C₂₃	C₂²×C₁₉	direct (N × H)
11. C₁₁×C₁₉	C₂²×C₂₃	direct (N × H)
12. C₂²×C₂₃	C₁₁×C₁₉	direct (N × H)
13. C₂²×C₁₉	C₁₁×C₂₃	direct (N × H)
14. C₂×C₂₃	C₂×C₁₁×C₁₉	direct (N × H)
15. C₂²×C₁₁	C₁₉×C₂₃	direct (N × H)
16. C₂×C₁₉	C₂×C₁₁×C₂₃	direct (N × H)
17. C₂₃	C₂²×C₁₁×C₁₉	direct (N × H)
18. C₂×C₁₁	C₂×C₁₉×C₂₃	direct (N × H)
19. C₁₉	C₂²×C₁₁×C₂₃	direct (N × H)
20. C₁₁	C₂²×C₁₉×C₂₃	direct (N × H)
21. C₂²	C₁₁×C₁₉×C₂₃	direct (N × H)
22. C₂	C₂×C₁₁×C₁₉×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
C₂×C₁₁×C₁₉×C₂₃	2
C₂²×C₁₉×C₂₃	11
C₂²×C₁₁×C₂₃	19
C₂²×C₁₁×C₁₉	23

Subgroups — C22×C11×C19×C23 #34063646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×C₁₉×C₂₃ #34063646