Subgroups — C₂×C₃×C₁₁²×C₃₇ #41001739

Order 26862.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₃₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁²×C₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁²×C₃₇	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₁×C₃₇	C₁₁	1	12	yes	maximal, direct product factor
5	C₃×C₁₁×C₃₇	C₂×C₁₁	1	12	yes	direct product factor
6	C₂×C₁₁×C₃₇	C₃×C₁₁	1	12	yes	direct product factor
7	C₂×C₃×C₁₁²	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₃₇	C₂×C₃×C₁₁	1	12	yes	direct product factor
9	C₃×C₁₁²	C₂×C₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁²	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₃₇	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁²	C₂×C₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₃₇	C₂×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₇	C₃×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₁₁	C₁₁×C₃₇	1	12	yes	direct product factor
16	C₃₇	C₂×C₃×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₁₁	C₂×C₁₁×C₃₇	1	12	yes	direct product factor
18	C₂×C₁₁	C₃×C₁₁×C₃₇	1	12	yes	direct product factor
19	C₁₁	C₂×C₃×C₁₁×C₃₇	1	12	yes	direct product factor
20	C₂×C₃	C₁₁²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₁₁²×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₁₁²×C₃₇	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. C₃×C₁₁²×C₃₇	C₂	direct (N × H)
2. C₂×C₁₁²×C₃₇	C₃	direct (N × H)
3. C₁₁²×C₃₇	C₂×C₃	direct (N × H)
4. C₂×C₃×C₁₁×C₃₇	C₁₁	direct (N × H)
5. C₃×C₁₁×C₃₇	C₂×C₁₁	direct (N × H)
6. C₂×C₁₁×C₃₇	C₃×C₁₁	direct (N × H)
7. C₂×C₃×C₁₁²	C₃₇	direct (N × H)
8. C₁₁×C₃₇	C₂×C₃×C₁₁	direct (N × H)
9. C₃×C₁₁²	C₂×C₃₇	direct (N × H)
10. C₂×C₁₁²	C₃×C₃₇	direct (N × H)
11. C₂×C₃×C₃₇	C₁₁²	direct (N × H)
12. C₁₁²	C₂×C₃×C₃₇	direct (N × H)
13. C₃×C₃₇	C₂×C₁₁²	direct (N × H)
14. C₂×C₃₇	C₃×C₁₁²	direct (N × H)
15. C₂×C₃×C₁₁	C₁₁×C₃₇	direct (N × H)
16. C₃₇	C₂×C₃×C₁₁²	direct (N × H)
17. C₃×C₁₁	C₂×C₁₁×C₃₇	direct (N × H)
18. C₂×C₁₁	C₃×C₁₁×C₃₇	direct (N × H)
19. C₁₁	C₂×C₃×C₁₁×C₃₇	direct (N × H)
20. C₂×C₃	C₁₁²×C₃₇	direct (N × H)
21. C₃	C₂×C₁₁²×C₃₇	direct (N × H)
22. C₂	C₃×C₁₁²×C₃₇	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×C₁₁²×C₃₇	2
C₂×C₁₁²×C₃₇	3
C₂×C₃×C₁₁×C₃₇	11
C₂×C₃×C₁₁²	37

Subgroups — C2×C3×C112×C37 #41001739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₁²×C₃₇ #41001739