Subgroups — C₂×C₇×C₁₁²×C₁₉ #44565682

Order 32186.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁²×C₁₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁²×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₇×C₁₁×C₁₉	C₁₁	1	12	yes	maximal, direct product factor
4	C₁₁²×C₁₉	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₇×C₁₁²	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₁×C₁₉	C₂×C₁₁	1	12	yes	direct product factor
7	C₇×C₁₁²	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₁×C₁₉	C₇×C₁₁	1	12	yes	direct product factor
9	C₂×C₇×C₁₉	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁²	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₁₉	C₂×C₇×C₁₁	1	12	yes	direct product factor
12	C₂×C₇×C₁₁	C₁₁×C₁₉	1	12	yes	direct product factor
13	C₇×C₁₉	C₂×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁²	C₂×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₇×C₁₁	C₂×C₁₁×C₁₉	1	12	yes	direct product factor
16	C₂×C₁₉	C₇×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₁	C₇×C₁₁×C₁₉	1	12	yes	direct product factor
18	C₁₉	C₂×C₇×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	C₁₁²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
20	C₁₁	C₂×C₇×C₁₁×C₁₉	1	12	yes	direct product factor
21	C₇	C₂×C₁₁²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₇×C₁₁²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow

	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. C₇×C₁₁²×C₁₉	C₂	direct (N × H)
2. C₂×C₁₁²×C₁₉	C₇	direct (N × H)
3. C₂×C₇×C₁₁×C₁₉	C₁₁	direct (N × H)
4. C₁₁²×C₁₉	C₂×C₇	direct (N × H)
5. C₂×C₇×C₁₁²	C₁₉	direct (N × H)
6. C₇×C₁₁×C₁₉	C₂×C₁₁	direct (N × H)
7. C₇×C₁₁²	C₂×C₁₉	direct (N × H)
8. C₂×C₁₁×C₁₉	C₇×C₁₁	direct (N × H)
9. C₂×C₇×C₁₉	C₁₁²	direct (N × H)
10. C₂×C₁₁²	C₇×C₁₉	direct (N × H)
11. C₁₁×C₁₉	C₂×C₇×C₁₁	direct (N × H)
12. C₂×C₇×C₁₁	C₁₁×C₁₉	direct (N × H)
13. C₇×C₁₉	C₂×C₁₁²	direct (N × H)
14. C₁₁²	C₂×C₇×C₁₉	direct (N × H)
15. C₇×C₁₁	C₂×C₁₁×C₁₉	direct (N × H)
16. C₂×C₁₉	C₇×C₁₁²	direct (N × H)
17. C₂×C₁₁	C₇×C₁₁×C₁₉	direct (N × H)
18. C₁₉	C₂×C₇×C₁₁²	direct (N × H)
19. C₂×C₇	C₁₁²×C₁₉	direct (N × H)
20. C₁₁	C₂×C₇×C₁₁×C₁₉	direct (N × H)
21. C₇	C₂×C₁₁²×C₁₉	direct (N × H)
22. C₂	C₇×C₁₁²×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₁²×C₁₉	2
C₂×C₁₁²×C₁₉	7
C₂×C₇×C₁₁×C₁₉	11
C₂×C₇×C₁₁²	19

Subgroups — C2×C7×C112×C19 #44565682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₁₁²×C₁₉ #44565682