Subgroups — C₉⋊#14559051 #36344787

Order 21780.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#10597243	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#14559051	—	3	1	no	maximal
3	C₉×#10597243	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊(C₁₁⋊Dic₁₁)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×#10597243	D₃	1	1	yes	characteristic
6	#14559051	—	9	1	no	Hall
7	C₂×C₉×C₁₁²	C₂×C₅	1	1	yes	characteristic
8	C₉⋊(Dic₁₁⋊C₅)	—	11	12	no	maximal
9	C₃×#10597243	Dic₃	1	1	yes	characteristic
10	C₃⋊(C₁₁⋊Dic₁₁)	—	3	1	no	—
11	C₂×#10597243	D₉	1	1	yes	characteristic
12	C₉×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₁₁⋊C₅	—	11	12	no	—
14	C₂×C₃×C₁₁²	C₅×D₃	1	1	yes	characteristic
15	C₃⋊(Dic₁₁⋊C₅)	—	33	12	no	—
16	#10597243	Dic₉	1	1	yes	characteristic, complemented, Hall
17	C₉×C₁₁⋊C₅	—	11	12	no	—
18	C₁₁⋊Dic₁₁	—	9	1	no	Hall
19	Dic₉₉	—	11	12	no	—
20	C₃×C₁₁²	C₅×Dic₃	1	1	yes	characteristic
21	C₂×C₃×C₁₁⋊C₅	—	11	12	no	—
22	C₂×C₁₁²	C₅×D₉	1	1	yes	characteristic
23	Dic₁₁⋊C₅	—	99	12	no	—
24	C₂×C₉×C₁₁	AGL(1,𝔽₁₁)	1	12	yes	—
25	C₅×Dic₉	—	121	1	no	Hall
26	C₃×C₁₁⋊C₅	—	11	12	no	—
27	Dic₃₃	—	33	12	no	—
28	C₁₁²	C₅×Dic₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₁⋊C₅	—	11	12	no	—
30	C₉×C₁₁	Dic₁₁⋊C₅	1	12	yes	complemented
31	C₂×C₅×C₉	—	121	1	no	—
32	C₂×C₃×C₁₁	C₃⋊AGL(1,𝔽₁₁)	1	12	yes	—
33	C₅×Dic₃	—	363	1	no	—
34	C₁₁⋊C₅	—	11	12	no	—
35	C₅×C₉	—	121	1	no	Hall
36	Dic₁₁	—	99	12	no	—
37	Dic₉	—	121	1	no	Hall
38	C₃×C₁₁	C₃⋊(Dic₁₁⋊C₅)	1	12	yes	—
39	C₂×C₃×C₅	—	121	1	no	—
40	C₂×C₁₁	C₉⋊AGL(1,𝔽₁₁)	1	12	yes	—
41	C₄×C₅	—	1089	1	no	Hall
42	C₂×C₉	#11925892	1	1	yes	characteristic
43	C₃×C₅	—	121	1	no	—
44	Dic₃	—	363	1	no	—
45	C₁₁	C₉⋊(Dic₁₁⋊C₅)	1	12	yes	complemented
46	C₂×C₅	—	121	1	no	—
47	C₉	#14559051	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₃⋊#11925892	1	1	yes	characteristic
49	C₅	—	121	1	no	Sylow
50	C₄	—	1089	1	no	Sylow
51	C₃	C₃⋊#14559051	1	1	yes	characteristic
52	C₂	C₉⋊#11925892	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	C₉⋊#11925892
commutator, hypocenter	C₉×C₁₁²	C₄×C₅
Frattini	C₂×C₃	C₃⋊#11925892
Fitting, cosocle	C₂×C₉×C₁₁²	C₂×C₅
socle	C₂×C₃×C₁₁²	C₅×D₃
prime radical	C₂×C₃×#10597243	D₃
LCS	G ▷ C₉×C₁₁²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₉×#10597243	C₄	semidirect
4. C₉⋊(C₁₁⋊Dic₁₁)	C₅	semidirect
12. C₉×C₁₁²	C₄×C₅	semidirect
16. #10597243	Dic₉	semidirect
28. C₁₁²	C₅×Dic₉	semidirect
30. C₉×C₁₁	Dic₁₁⋊C₅	semidirect
45. C₁₁	C₉⋊(Dic₁₁⋊C₅)	semidirect
47. C₉	#14559051	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#10597243	2
C₃⋊#14559051	3
C₉⋊(C₁₁⋊Dic₁₁)	5
C₉⋊(Dic₁₁⋊C₅)	11

Subgroups — C9⋊#14559051 #36344787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#14559051 #36344787