Subgroups — D₁₁×D₆₈₉ #44476366

Order 30316.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₅₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₁₁×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₆₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₆₈₉	—	11	1	no	maximal, Hall
6	D₁₁×D₅₃	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₅₃	—	11	1	no	—
8	D₆₈₉	—	11	1	no	—
9	D₆₈₉	D₁₁	1	1	yes	characteristic, direct product factor
10	D₅₈₃	—	13	1	no	—
11	C₁₁×D₅₃	—	13	1	no	—
12	D₁₁×C₅₃	D₁₃	1	1	yes	characteristic, complemented
13	C₁₃×C₅₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₅₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	D₁₁×D₁₃	—	53	1	no	maximal, Hall
16	D₁₄₃	—	53	1	no	—
17	C₁₁×D₁₃	—	53	1	no	—
18	C₁₃×D₁₁	D₅₃	1	1	yes	characteristic, complemented
19	C₂×D₅₃	—	143	1	no	Hall
20	C₁₁×C₁₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅₃	—	11	1	no	—
22	D₅₃	—	13	1	no	—
23	D₅₃	—	143	1	no	—
24	C₅₃	D₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₁₃	—	583	1	no	Hall
26	C₂×D₁₁	—	689	1	no	Hall
27	C₂×C₁₃	—	11	1	no	—
28	D₁₃	—	53	1	no	—
29	D₁₃	—	583	1	no	—
30	C₂×C₁₁	—	689	1	no	—
31	D₁₁	—	689	1	no	—
32	D₁₁	D₆₈₉	1	1	yes	characteristic, direct product factor
33	C₁₃	D₁₁×D₅₃	1	1	yes	characteristic, complemented, Sylow
34	C₁₁	C₂×D₆₈₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	7579	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	7579	1	no	—
38	C₂	—	689	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃×C₅₃	C₂²
LCS	G ▷ C₁₁×C₁₃×C₅₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇₅₇₉	C₂	semidirect
2. C₁₃×D₁₁×C₅₃	C₂	semidirect
3. C₁₁×D₆₈₉	C₂	semidirect
4. C₁₁×C₁₃×C₅₃	C₂²	semidirect
9. D₆₈₉	D₁₁	direct (N × H)
12. D₁₁×C₅₃	D₁₃	semidirect
13. C₁₃×C₅₃	C₂×D₁₁	semidirect
14. C₁₁×C₅₃	C₂×D₁₃	semidirect
18. C₁₃×D₁₁	D₅₃	semidirect
20. C₁₁×C₁₃	C₂×D₅₃	semidirect
24. C₅₃	D₁₁×D₁₃	semidirect
32. D₁₁	D₆₈₉	direct (N × H)
33. C₁₃	D₁₁×D₅₃	semidirect
34. C₁₁	C₂×D₆₈₉	semidirect

Maximal subgroups

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

subgroup	index
D₇₅₇₉	2
C₁₃×D₁₁×C₅₃	2
C₁₁×D₆₈₉	2
C₂×D₆₈₉	11
D₁₁×D₅₃	13
D₁₁×D₁₃	53

Subgroups — D11×D689 #44476366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×D₆₈₉ #44476366