Subgroups — C₂×C₁₁×D₄₂₇ #34037708

Order 18788.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₄₂₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₆₁	—	7	1	no	maximal, Hall
5	C₂×D₄₂₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₁×C₆₁	D₇	1	1	yes	characteristic, complemented
7	C₁₁×D₆₁	—	7	2	no	—
8	C₂×C₇×C₆₁	C₂×C₁₁	1	1	yes	characteristic, complemented
9	D₄₂₇	C₂×C₁₁	1	2	yes	direct product factor
10	C₁₁×C₆₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₆₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×D₇	—	61	1	no	maximal, Hall
13	C₂×D₆₁	—	7	1	no	Hall
14	C₂×C₇×C₁₁	D₆₁	1	1	yes	characteristic, complemented
15	C₁₁×D₇	—	61	2	no	—
16	C₂×C₆₁	C₁₁×D₇	1	1	yes	characteristic, complemented
17	D₆₁	—	7	2	no	—
18	C₇×C₁₁	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
19	C₆₁	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₁₁	—	427	1	no	Hall
21	C₂×D₇	—	61	1	no	Hall
22	C₂×C₁₁	—	427	2	no	—
23	C₂×C₁₁	D₄₂₇	1	1	yes	characteristic, direct product factor
24	C₂×C₇	C₁₁×D₆₁	1	1	yes	characteristic, complemented
25	D₇	—	61	2	no	—
26	C₁₁	C₂×D₄₂₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₁₁×D₆₁	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	427	1	no	Sylow
29	C₂	—	427	2	no	—
30	C₂	C₁₁×D₄₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₄₂₇
commutator, cosocle, hypocenter	C₇×C₆₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₆₁	C₂
LCS	G ▷ C₇×C₆₁
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₄₂₇	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₆₁	C₂	semidirect
3. C₇×C₁₁×C₆₁	C₂²	semidirect
5. C₂×D₄₂₇	C₁₁	direct (N × H)
6. C₂×C₁₁×C₆₁	D₇	semidirect
8. C₂×C₇×C₆₁	C₂×C₁₁	semidirect
9. D₄₂₇	C₂×C₁₁	direct (N × H)
10. C₁₁×C₆₁	C₂×D₇	semidirect
11. C₇×C₆₁	C₂²×C₁₁	semidirect
14. C₂×C₇×C₁₁	D₆₁	semidirect
16. C₂×C₆₁	C₁₁×D₇	semidirect
18. C₇×C₁₁	C₂×D₆₁	semidirect
19. C₆₁	C₂×C₁₁×D₇	semidirect
23. C₂×C₁₁	D₄₂₇	direct (N × H)
24. C₂×C₇	C₁₁×D₆₁	semidirect
26. C₁₁	C₂×D₄₂₇	direct (N × H)
27. C₇	C₂×C₁₁×D₆₁	semidirect
30. C₂	C₁₁×D₄₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₄₂₇	2
C₂×C₇×C₁₁×C₆₁	2
C₂×C₁₁×D₆₁	7
C₂×D₄₂₇	11
C₂×C₁₁×D₇	61

Subgroups — C2×C11×D427 #34037708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₄₂₇ #34037708