Subgroups — C₁₁⋊#11744607 #23754792

Order 9900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₆₅	—	3	1	no	maximal
3	C₁₁×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₅²×C₁₁	D₃	1	1	yes	characteristic
5	C₅×Dic₅₅	—	9	1	no	Hall
6	#11744607	—	11	1	no	maximal, Hall
7	C₃×C₅²×C₁₁	Dic₃	1	1	yes	characteristic
8	Dic₁₆₅	—	3	1	no	—
9	C₅×Dic₃₃	—	15	1	no	—
10	C₂×C₅²×C₁₁	D₉	1	1	yes	characteristic
11	C₂×C₅²⋊C₉	D₁₁	1	1	yes	characteristic
12	Dic₉₉	—	25	1	no	maximal, Hall
13	C₂×C₃×C₅×C₁₁	—	3	1	no	—
14	C₂×C₃×C₅×C₁₁	—	3	1	no	—
15	C₅×Dic₁₅	—	33	1	no	—
16	C₅²×C₁₁	Dic₉	1	1	yes	characteristic, complemented, Hall
17	C₅²⋊C₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
18	Dic₅₅	—	9	1	no	—
19	C₅×Dic₁₁	—	45	1	no	—
20	C₂×C₉×C₁₁	—	25	1	no	—
21	C₃×C₅×C₁₁	—	3	1	no	—
22	C₃×C₅×C₁₁	—	3	1	no	—
23	C₂×C₃×C₅²	D₃₃	1	1	yes	characteristic
24	Dic₃₃	—	15	1	no	—
25	C₂×C₅×C₁₁	—	3	1	no	—
26	C₂×C₅×C₁₁	—	3	1	no	—
27	C₅×Dic₅	—	99	1	no	Hall
28	C₉×C₁₁	—	25	1	no	Hall
29	C₃×C₅²	Dic₃₃	1	1	yes	characteristic
30	C₂×C₃×C₁₁	#3874	1	1	yes	characteristic
31	Dic₁₅	—	33	1	no	—
32	C₅×Dic₃	—	165	1	no	—
33	C₅×C₁₁	—	3	1	no	—
34	C₅×C₁₁	—	3	1	no	—
35	C₂×C₅²	D₉₉	1	1	yes	characteristic
36	Dic₁₁	—	45	1	no	Hall
37	Dic₉	—	275	1	no	Hall
38	C₃×C₁₁	#64470	1	1	yes	characteristic
39	C₂×C₃×C₅	—	3	1	no	—
40	C₂×C₃×C₅	—	3	1	no	—
41	C₅²	Dic₉₉	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₁₁	#90646	1	1	yes	characteristic
43	C₄×C₅	—	495	1	no	—
44	Dic₅	—	99	1	no	—
45	C₂×C₉	—	25	1	no	—
46	C₃×C₅	—	3	1	no	—
47	C₃×C₅	—	3	1	no	—
48	Dic₃	—	165	1	no	—
49	C₁₁	#11744607	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅	—	3	1	no	—
51	C₂×C₅	—	3	1	no	—
52	C₉	—	25	1	no	Sylow
53	C₂×C₃	C₁₁⋊#3874	1	1	yes	characteristic
54	C₅	—	3	1	no	—
55	C₅	—	3	1	no	—
56	C₄	—	495	1	no	Sylow
57	C₃	C₁₁⋊#64470	1	1	yes	characteristic
58	C₂	C₁₁⋊#90646	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	C₁₁⋊#90646
commutator, hypocenter	C₁₁×C₅²⋊C₉	C₄
Frattini	C₂×C₃	C₁₁⋊#3874
Fitting, socle, prime radical	C₂×C₃×C₅²×C₁₁	D₃
cosocle	C₂×C₁₁×C₅²⋊C₉	C₂
LCS	G ▷ C₁₁×C₅²⋊C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₁₁×C₅²⋊C₉	C₄	semidirect
16. C₅²×C₁₁	Dic₉	semidirect
17. C₅²⋊C₉	Dic₁₁	semidirect
41. C₅²	Dic₉₉	semidirect
49. C₁₁	#11744607	semidirect

Subgroups — C11⋊#11744607 #23754792

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁⋊#11744607 #23754792