Subgroups — C₉×C₁₁⋊(C₁₃⋊D₁₃) #45689554

Order 33462.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₁⋊(C₁₃⋊D₁₃)	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₁×C₁₃²	C₂×C₃	1	1	yes	characteristic
4	C₁₁⋊(C₁₃⋊D₁₃)	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₉×C₁₃⋊D₁₃	—	11	1	no	maximal, Hall
6	C₉×D₁₄₃	—	13	14	no	maximal
7	C₁₁×C₁₃²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₉×C₁₃²	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₉×C₁₁×C₁₃	D₁₃	1	14	yes	complemented
10	C₃×C₁₃⋊D₁₃	—	11	1	no	—
11	C₃×D₁₄₃	—	13	14	no	—
12	C₃×C₁₃²	C₃×D₁₁	1	1	yes	characteristic
13	C₃×C₁₁×C₁₃	C₃×D₁₃	1	14	yes	—
14	C₁₃⋊D₁₃	—	11	1	no	Hall
15	D₁₄₃	—	13	14	no	—
16	C₉×D₁₃	—	143	14	no	—
17	C₉×D₁₁	—	169	1	no	Hall
18	C₁₃²	C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₁₁×C₁₃	C₉×D₁₃	1	14	yes	complemented
20	C₉×C₁₃	D₁₄₃	1	14	yes	complemented
21	C₉×C₁₁	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
22	C₃×D₁₃	—	143	14	no	—
23	C₃×D₁₁	—	169	1	no	—
24	C₃×C₁₃	C₃×D₁₄₃	1	14	yes	—
25	C₃×C₁₁	C₃×C₁₃⋊D₁₃	1	1	yes	characteristic
26	D₁₃	—	143	14	no	—
27	D₁₁	—	169	1	no	Hall
28	C₂×C₉	—	1859	1	no	Hall
29	C₁₃	C₉×D₁₄₃	1	14	yes	complemented
30	C₁₁	C₉×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
31	C₉	C₁₁⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃	—	1859	1	no	—
33	C₃	C₃×C₁₁⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
34	C₂	—	1859	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉	C₁₁⋊(C₁₃⋊D₁₃)
commutator, hypocenter	C₁₁×C₁₃²	C₂×C₉
Frattini	C₃	C₃×C₁₁⋊(C₁₃⋊D₁₃)
Fitting	C₉×C₁₁×C₁₃²	C₂
socle, cosocle	C₃×C₁₁×C₁₃²	C₂×C₃
prime radical	C₃×C₁₁⋊(C₁₃⋊D₁₃)	C₃
LCS	G ▷ C₁₁×C₁₃²
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₁×C₁₃²	C₂	semidirect
4. C₁₁⋊(C₁₃⋊D₁₃)	C₉	direct (N × H)
7. C₁₁×C₁₃²	C₂×C₉	semidirect
8. C₉×C₁₃²	D₁₁	semidirect
9. C₉×C₁₁×C₁₃	D₁₃	semidirect
18. C₁₃²	C₉×D₁₁	semidirect
19. C₁₁×C₁₃	C₉×D₁₃	semidirect
20. C₉×C₁₃	D₁₄₃	semidirect
21. C₉×C₁₁	C₁₃⋊D₁₃	semidirect
29. C₁₃	C₉×D₁₄₃	semidirect
30. C₁₁	C₉×C₁₃⋊D₁₃	semidirect
31. C₉	C₁₁⋊(C₁₃⋊D₁₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₁×C₁₃²	2
C₃×C₁₁⋊(C₁₃⋊D₁₃)	3
C₉×C₁₃⋊D₁₃	11
C₉×D₁₄₃	13

Subgroups — C9×C11⋊(C13⋊D13) #45689554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₁⋊(C₁₃⋊D₁₃) #45689554