Subgroups — C₂×D₃×C₁₁×C₁₂₇ #30660939

Order 16764.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₁×C₁₂₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁×C₁₂₇	—	3	1	no	maximal, Hall
4	C₃×C₁₁×C₁₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₁₂₇	—	3	2	no	—
6	C₂×C₁₁×C₁₂₇	D₃	1	1	yes	characteristic, direct product factor
7	C₂×D₃×C₁₂₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₁₂₇	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₁₂₇	C₂×C₁₁	1	1	yes	characteristic, complemented
10	D₃×C₁₂₇	C₂×C₁₁	1	2	yes	direct product factor
11	C₂²×C₁₂₇	—	3	1	no	Hall
12	C₃×C₁₂₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₂₇	—	3	2	no	—
14	C₂×C₁₂₇	D₃×C₁₁	1	1	yes	characteristic, direct product factor
15	C₂×D₃×C₁₁	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₂₇	C₂×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃×C₁₁	C₂×C₁₂₇	1	1	yes	characteristic, complemented
18	D₃×C₁₁	C₂×C₁₂₇	1	2	yes	direct product factor
19	C₂²×C₁₁	—	3	1	no	Hall
20	C₃×C₁₁	C₂²×C₁₂₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₁	—	3	2	no	—
22	C₂×C₁₁	D₃×C₁₂₇	1	1	yes	characteristic, direct product factor
23	C₂×D₃	C₁₁×C₁₂₇	1	1	yes	characteristic, direct product factor, Hall
24	C₁₁	C₂×D₃×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	C₂×C₁₁×C₁₂₇	1	1	yes	characteristic, complemented
26	D₃	C₂×C₁₁×C₁₂₇	1	2	yes	direct product factor
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₁₁×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	D₃×C₁₁×C₁₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₂₇	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₁₁×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁×C₁₂₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₁×C₁₂₇

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₁×C₁₂₇	C₂	direct (N × H)
2. C₂×C₃×C₁₁×C₁₂₇	C₂	semidirect
4. C₃×C₁₁×C₁₂₇	C₂²	semidirect
6. C₂×C₁₁×C₁₂₇	D₃	direct (N × H)
7. C₂×D₃×C₁₂₇	C₁₁	direct (N × H)
8. C₁₁×C₁₂₇	C₂×D₃	direct (N × H)
9. C₂×C₃×C₁₂₇	C₂×C₁₁	semidirect
10. D₃×C₁₂₇	C₂×C₁₁	direct (N × H)
12. C₃×C₁₂₇	C₂²×C₁₁	semidirect
14. C₂×C₁₂₇	D₃×C₁₁	direct (N × H)
15. C₂×D₃×C₁₁	C₁₂₇	direct (N × H)
16. C₁₂₇	C₂×D₃×C₁₁	direct (N × H)
17. C₂×C₃×C₁₁	C₂×C₁₂₇	semidirect
18. D₃×C₁₁	C₂×C₁₂₇	direct (N × H)
20. C₃×C₁₁	C₂²×C₁₂₇	semidirect
22. C₂×C₁₁	D₃×C₁₂₇	direct (N × H)
23. C₂×D₃	C₁₁×C₁₂₇	direct (N × H)
24. C₁₁	C₂×D₃×C₁₂₇	direct (N × H)
25. C₂×C₃	C₂×C₁₁×C₁₂₇	semidirect
26. D₃	C₂×C₁₁×C₁₂₇	direct (N × H)
28. C₃	C₂²×C₁₁×C₁₂₇	semidirect
30. C₂	D₃×C₁₁×C₁₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃×C₁₁×C₁₂₇	2
C₂×C₃×C₁₁×C₁₂₇	2
C₂²×C₁₁×C₁₂₇	3
C₂×D₃×C₁₂₇	11
C₂×D₃×C₁₁	127

Subgroups — C2×D3×C11×C127 #30660939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₁₁×C₁₂₇ #30660939