Subgroups — C₁₁×#3667 #13096889

Order 1584.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₉×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₉⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₁₁×#208	—	3	1	no	maximal
4	C₂²×C₉×C₁₁	C₄	1	1	yes	characteristic
5	C₄×C₉×C₁₁	C₄	1	1	yes	characteristic
6	C₄×C₉×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₁	D₃	1	1	yes	characteristic
8	C₁₁×C₃⋊C₈	—	3	2	no	—
9	C₂×C₉×C₁₁	—	2	1	no	—
10	C₂×C₉×C₁₁	C₂×C₄	1	1	yes	characteristic
11	C₁₁×M₁₆	—	9	1	no	Hall
12	#3667	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₁₁	Dic₃	1	1	yes	characteristic
14	C₃×C₄×C₁₁	Dic₃	1	1	yes	characteristic
15	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
16	C₉×C₁₁	M₁₆	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄×C₁₁	D₉	1	1	yes	characteristic
18	C₈×C₁₁	—	9	2	no	—
19	C₂×C₄×C₉	C₂×C₁₁	1	1	yes	characteristic
20	C₉⋊C₈	C₂×C₁₁	1	2	yes	complemented
21	C₂×C₃×C₁₁	—	2	1	no	—
22	C₂×C₃×C₁₁	C₂×Dic₃	1	1	yes	characteristic
23	#208	—	3	1	no	—
24	C₂²×C₁₁	Dic₉	1	1	yes	characteristic
25	C₄×C₁₁	Dic₉	1	1	yes	characteristic
26	C₄×C₁₁	C₂×D₉	1	1	yes	characteristic
27	C₂²×C₉	C₄×C₁₁	1	1	yes	characteristic
28	C₄×C₉	C₄×C₁₁	1	1	yes	characteristic
29	C₄×C₉	C₂²×C₁₁	1	1	yes	characteristic
30	C₃×C₁₁	#208	1	1	yes	characteristic
31	C₂×C₃×C₄	D₃×C₁₁	1	1	yes	characteristic
32	C₃⋊C₈	—	3	2	no	—
33	C₂×C₁₁	—	2	1	no	—
34	C₂×C₁₁	C₂×Dic₉	1	1	yes	characteristic
35	C₂×C₉	—	2	1	no	—
36	C₂×C₉	C₂×C₄×C₁₁	1	1	yes	characteristic
37	M₁₆	—	9	1	no	Sylow
38	C₂²×C₃	C₁₁×Dic₃	1	1	yes	characteristic
39	C₃×C₄	C₁₁×Dic₃	1	1	yes	characteristic
40	C₃×C₄	C₂×D₃×C₁₁	1	1	yes	characteristic
41	C₁₁	#3667	1	1	yes	characteristic, direct product factor, Sylow
42	C₉	C₁₁×M₁₆	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₄	C₁₁×D₉	1	1	yes	characteristic
44	C₈	—	9	2	no	—
45	C₂×C₃	—	2	1	no	—
46	C₂×C₃	C₂×C₁₁×Dic₃	1	1	yes	characteristic
47	C₂²	C₁₁×Dic₉	1	1	yes	characteristic
48	C₄	C₁₁×Dic₉	1	1	yes	characteristic
49	C₄	C₂×C₁₁×D₉	1	1	yes	characteristic
50	C₃	C₁₁×#208	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	C₂×C₁₁×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	C₂×D₉
commutator	C₂×C₉	C₂×C₄×C₁₁
Frattini	C₃×C₄	C₂×D₃×C₁₁
Fitting	C₂×C₄×C₉×C₁₁	C₂
socle	C₂×C₃×C₁₁	C₂×Dic₃
prime radical	C₂²×C₃×C₁₁	Dic₃
cosocle	C₄×C₉	C₂²×C₁₁
hypercenter	C₂×C₄×C₁₁	D₉
hypocenter	C₉	C₁₁×M₁₆
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₄×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₉⋊C₈	C₂	semidirect
12. #3667	C₁₁	direct (N × H)
16. C₉×C₁₁	M₁₆	semidirect
20. C₉⋊C₈	C₂×C₁₁	semidirect
41. C₁₁	#3667	direct (N × H)
42. C₉	C₁₁×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₉×C₁₁	2
C₁₁×C₉⋊C₈	2
C₁₁×#208	3
#3667	11

Subgroups — C11×#3667 #13096889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3667 #13096889