Subgroups — C₂²×C₇×C₁₁×C₇₉ #37566645

Order 24332.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₇₉	C₂	1	3	yes	maximal, direct product factor
2	C₇×C₁₁×C₇₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₁×C₇₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₇×C₇₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₇₉	C₂×C₇	1	3	yes	direct product factor
6	C₂×C₇×C₇₉	C₂×C₁₁	1	3	yes	direct product factor
7	C₁₁×C₇₉	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₇₉	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂²×C₇₉	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₇×C₁₁	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇₉	C₂×C₇×C₁₁	1	3	yes	direct product factor
12	C₂×C₇×C₁₁	C₂×C₇₉	1	3	yes	direct product factor
13	C₇₉	C₂²×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₇×C₁₁	C₂²×C₇₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₁₁	C₇×C₇₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₇	C₁₁×C₇₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₁	C₂×C₇×C₇₉	1	3	yes	direct product factor
18	C₂×C₇	C₂×C₁₁×C₇₉	1	3	yes	direct product factor
19	C₁₁	C₂²×C₇×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₂²×C₁₁×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₇×C₁₁×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₇×C₁₁×C₇₉	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×C₇×C₁₁×C₇₉	C₂	direct (N × H)
2. C₇×C₁₁×C₇₉	C₂²	direct (N × H)
3. C₂²×C₁₁×C₇₉	C₇	direct (N × H)
4. C₂²×C₇×C₇₉	C₁₁	direct (N × H)
5. C₂×C₁₁×C₇₉	C₂×C₇	direct (N × H)
6. C₂×C₇×C₇₉	C₂×C₁₁	direct (N × H)
7. C₁₁×C₇₉	C₂²×C₇	direct (N × H)
8. C₇×C₇₉	C₂²×C₁₁	direct (N × H)
9. C₂²×C₇₉	C₇×C₁₁	direct (N × H)
10. C₂²×C₇×C₁₁	C₇₉	direct (N × H)
11. C₂×C₇₉	C₂×C₇×C₁₁	direct (N × H)
12. C₂×C₇×C₁₁	C₂×C₇₉	direct (N × H)
13. C₇₉	C₂²×C₇×C₁₁	direct (N × H)
14. C₇×C₁₁	C₂²×C₇₉	direct (N × H)
15. C₂²×C₁₁	C₇×C₇₉	direct (N × H)
16. C₂²×C₇	C₁₁×C₇₉	direct (N × H)
17. C₂×C₁₁	C₂×C₇×C₇₉	direct (N × H)
18. C₂×C₇	C₂×C₁₁×C₇₉	direct (N × H)
19. C₁₁	C₂²×C₇×C₇₉	direct (N × H)
20. C₇	C₂²×C₁₁×C₇₉	direct (N × H)
21. C₂²	C₇×C₁₁×C₇₉	direct (N × H)
22. C₂	C₂×C₇×C₁₁×C₇₉	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×C₇×C₁₁×C₇₉	2
C₂²×C₁₁×C₇₉	7
C₂²×C₇×C₇₉	11
C₂²×C₇×C₁₁	79

Subgroups — C22×C7×C11×C79 #37566645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×C₁₁×C₇₉ #37566645