Subgroups — C₂×C₁₁×D₅₃₃ #37553005

Order 23452.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₅₃₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅₃₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×D₄₁	—	13	1	no	maximal, Hall
6	C₂×C₁₃×C₄₁	C₂×C₁₁	1	1	yes	characteristic, complemented
7	D₅₃₃	C₂×C₁₁	1	2	yes	direct product factor
8	C₂×C₁₁×C₄₁	D₁₃	1	1	yes	characteristic, complemented
9	C₁₁×D₄₁	—	13	2	no	—
10	C₂×C₁₁×D₁₃	—	41	1	no	maximal, Hall
11	C₁₃×C₄₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₄₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁×C₁₃	D₄₁	1	1	yes	characteristic, complemented
14	C₁₁×D₁₃	—	41	2	no	—
15	C₂×D₄₁	—	13	1	no	Hall
16	C₁₁×C₁₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄₁	C₁₁×D₁₃	1	1	yes	characteristic, complemented
18	D₄₁	—	13	2	no	—
19	C₂×D₁₃	—	41	1	no	Hall
20	C₂²×C₁₁	—	533	1	no	Hall
21	C₄₁	C₂×C₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₃	C₁₁×D₄₁	1	1	yes	characteristic, complemented
23	D₁₃	—	41	2	no	—
24	C₂×C₁₁	—	533	2	no	—
25	C₂×C₁₁	D₅₃₃	1	1	yes	characteristic, direct product factor
26	C₁₃	C₂×C₁₁×D₄₁	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₂×D₅₃₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	533	1	no	Sylow
29	C₂	—	533	2	no	—
30	C₂	C₁₁×D₅₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₅₃₃
commutator, cosocle, hypocenter	C₁₃×C₄₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃×C₄₁	C₂
LCS	G ▷ C₁₃×C₄₁
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₅₃₃	C₂	direct (N × H)
2. C₂×C₁₁×C₁₃×C₄₁	C₂	semidirect
3. C₁₁×C₁₃×C₄₁	C₂²	semidirect
4. C₂×D₅₃₃	C₁₁	direct (N × H)
6. C₂×C₁₃×C₄₁	C₂×C₁₁	semidirect
7. D₅₃₃	C₂×C₁₁	direct (N × H)
8. C₂×C₁₁×C₄₁	D₁₃	semidirect
11. C₁₃×C₄₁	C₂²×C₁₁	semidirect
12. C₁₁×C₄₁	C₂×D₁₃	semidirect
13. C₂×C₁₁×C₁₃	D₄₁	semidirect
16. C₁₁×C₁₃	C₂×D₄₁	semidirect
17. C₂×C₄₁	C₁₁×D₁₃	semidirect
21. C₄₁	C₂×C₁₁×D₁₃	semidirect
22. C₂×C₁₃	C₁₁×D₄₁	semidirect
25. C₂×C₁₁	D₅₃₃	direct (N × H)
26. C₁₃	C₂×C₁₁×D₄₁	semidirect
27. C₁₁	C₂×D₅₃₃	direct (N × H)
30. C₂	C₁₁×D₅₃₃	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×D₅₃₃	2
C₂×C₁₁×C₁₃×C₄₁	2
C₂×D₅₃₃	11
C₂×C₁₁×D₄₁	13
C₂×C₁₁×D₁₃	41

Subgroups — C2×C11×D533 #37553005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₅₃₃ #37553005