Subgroups — C₂×C₁₁×D₅₅₁ #37564622

Order 24244.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₅₅₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅₅₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×D₂₉	—	19	1	no	maximal, Hall
6	C₂×C₁₉×C₂₉	C₂×C₁₁	1	1	yes	characteristic, complemented
7	D₅₅₁	C₂×C₁₁	1	2	yes	direct product factor
8	C₂×C₁₁×D₁₉	—	29	1	no	maximal, Hall
9	C₂×C₁₁×C₂₉	D₁₉	1	1	yes	characteristic, complemented
10	C₁₁×D₂₉	—	19	2	no	—
11	C₁₉×C₂₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₉	D₂₉	1	1	yes	characteristic, complemented
13	C₁₁×D₁₉	—	29	2	no	—
14	C₁₁×C₂₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
16	C₂×D₂₉	—	19	1	no	Hall
17	C₂×D₁₉	—	29	1	no	Hall
18	C₂×C₂₉	C₁₁×D₁₉	1	1	yes	characteristic, complemented
19	D₂₉	—	19	2	no	—
20	C₂²×C₁₁	—	551	1	no	Hall
21	C₂×C₁₉	C₁₁×D₂₉	1	1	yes	characteristic, complemented
22	D₁₉	—	29	2	no	—
23	C₂₉	C₂×C₁₁×D₁₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₁₁	—	551	2	no	—
25	C₂×C₁₁	D₅₅₁	1	1	yes	characteristic, direct product factor
26	C₁₉	C₂×C₁₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₂×D₅₅₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	551	1	no	Sylow
29	C₂	—	551	2	no	—
30	C₂	C₁₁×D₅₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₅₅₁
commutator, cosocle, hypocenter	C₁₉×C₂₉	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₉×C₂₉	C₂
LCS	G ▷ C₁₉×C₂₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₅₅₁	C₂	direct (N × H)
2. C₂×C₁₁×C₁₉×C₂₉	C₂	semidirect
3. C₁₁×C₁₉×C₂₉	C₂²	semidirect
4. C₂×D₅₅₁	C₁₁	direct (N × H)
6. C₂×C₁₉×C₂₉	C₂×C₁₁	semidirect
7. D₅₅₁	C₂×C₁₁	direct (N × H)
9. C₂×C₁₁×C₂₉	D₁₉	semidirect
11. C₁₉×C₂₉	C₂²×C₁₁	semidirect
12. C₂×C₁₁×C₁₉	D₂₉	semidirect
14. C₁₁×C₂₉	C₂×D₁₉	semidirect
15. C₁₁×C₁₉	C₂×D₂₉	semidirect
18. C₂×C₂₉	C₁₁×D₁₉	semidirect
21. C₂×C₁₉	C₁₁×D₂₉	semidirect
23. C₂₉	C₂×C₁₁×D₁₉	semidirect
25. C₂×C₁₁	D₅₅₁	direct (N × H)
26. C₁₉	C₂×C₁₁×D₂₉	semidirect
27. C₁₁	C₂×D₅₅₁	direct (N × H)
30. C₂	C₁₁×D₅₅₁	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×D₅₅₁	2
C₂×C₁₁×C₁₉×C₂₉	2
C₂×D₅₅₁	11
C₂×C₁₁×D₂₉	19
C₂×C₁₁×D₁₉	29

Subgroups — C2×C11×D551 #37564622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₅₅₁ #37564622