Subgroups — D₁₁×D₅₅₉ #37589708

Order 24596.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₁₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₅₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅₅₉	—	11	1	no	maximal, Hall
6	D₁₁×D₄₃	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₄₃	—	11	1	no	—
8	D₅₅₉	—	11	1	no	—
9	D₅₅₉	D₁₁	1	1	yes	characteristic, direct product factor
10	D₄₇₃	—	13	1	no	—
11	C₁₁×D₄₃	—	13	1	no	—
12	D₁₁×C₄₃	D₁₃	1	1	yes	characteristic, complemented
13	D₁₁×D₁₃	—	43	1	no	maximal, Hall
14	C₁₃×C₄₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₄₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	D₁₄₃	—	43	1	no	—
17	C₁₁×D₁₃	—	43	1	no	—
18	C₁₃×D₁₁	D₄₃	1	1	yes	characteristic, complemented
19	C₂×D₄₃	—	143	1	no	Hall
20	C₁₁×C₁₃	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₄₃	—	11	1	no	—
22	D₄₃	—	13	1	no	—
23	D₄₃	—	143	1	no	—
24	C₂×D₁₃	—	473	1	no	Hall
25	C₂×D₁₁	—	559	1	no	Hall
26	C₄₃	D₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₃	—	11	1	no	—
28	D₁₃	—	43	1	no	—
29	D₁₃	—	473	1	no	—
30	C₂×C₁₁	—	559	1	no	—
31	D₁₁	—	559	1	no	—
32	D₁₁	D₅₅₉	1	1	yes	characteristic, direct product factor
33	C₁₃	D₁₁×D₄₃	1	1	yes	characteristic, complemented, Sylow
34	C₁₁	C₂×D₅₅₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	6149	1	no	Sylow
36	C₂	—	6149	1	no	—
37	C₂	—	11	1	no	—
38	C₂	—	559	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃×C₄₃	C₂²
LCS	G ▷ C₁₁×C₁₃×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₁₄₉	C₂	semidirect
2. C₁₃×D₁₁×C₄₃	C₂	semidirect
3. C₁₁×D₅₅₉	C₂	semidirect
4. C₁₁×C₁₃×C₄₃	C₂²	semidirect
9. D₅₅₉	D₁₁	direct (N × H)
12. D₁₁×C₄₃	D₁₃	semidirect
14. C₁₃×C₄₃	C₂×D₁₁	semidirect
15. C₁₁×C₄₃	C₂×D₁₃	semidirect
18. C₁₃×D₁₁	D₄₃	semidirect
20. C₁₁×C₁₃	C₂×D₄₃	semidirect
26. C₄₃	D₁₁×D₁₃	semidirect
32. D₁₁	D₅₅₉	direct (N × H)
33. C₁₃	D₁₁×D₄₃	semidirect
34. C₁₁	C₂×D₅₅₉	semidirect

Maximal subgroups

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

subgroup	index
D₆₁₄₉	2
C₁₃×D₁₁×C₄₃	2
C₁₁×D₅₅₉	2
C₂×D₅₅₉	11
D₁₁×D₄₃	13
D₁₁×D₁₃	43

Subgroups — D11×D559 #37589708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×D₅₅₉ #37589708