Subgroups — C₁₁×Dic₉⋊C₄ #13096891

Order 1584.

78 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	C₂×C₁₁×Dic₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×Dic₉	C₂	1	1	yes	maximal, characteristic
4	C₁₁×Dic₃⋊C₄	—	3	1	no	maximal
5	C₂²×C₉×C₁₁	C₂²	1	1	yes	characteristic
6	C₄×C₉×C₁₁	—	2	1	no	—
7	C₁₁×Dic₉	—	2	1	no	—
8	C₁₁×Dic₉	C₄	1	2	yes	complemented
9	C₂×C₃×C₄×C₁₁	D₃	1	1	yes	characteristic
10	C₂×C₁₁×Dic₃	—	3	1	no	—
11	C₂×C₁₁×Dic₃	—	3	1	no	—
12	C₂×C₉×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₉×C₁₁	D₄	1	1	yes	characteristic
14	C₂×C₉×C₁₁	Q₈	1	1	yes	characteristic
15	C₁₁×C₄⋊C₄	—	9	1	no	Hall
16	Dic₉⋊C₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₁₁	C₂×D₃	1	1	yes	characteristic
18	C₃×C₄×C₁₁	—	2	1	no	—
19	C₁₁×Dic₃	—	3	2	no	—
20	C₁₁×Dic₃	—	6	1	no	—
21	C₉×C₁₁	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
22	C₂×C₄×C₁₁	—	9	1	no	—
23	C₂×C₄×C₁₁	—	9	1	no	—
24	C₂×C₄×C₁₁	D₉	1	1	yes	characteristic
25	C₂×C₄×C₉	C₂×C₁₁	1	1	yes	characteristic
26	C₂×Dic₉	C₂×C₁₁	1	1	yes	characteristic
27	C₂×Dic₉	C₂×C₁₁	1	1	yes	characteristic
28	C₂×C₃×C₁₁	Dic₆	1	1	yes	characteristic
29	C₂×C₃×C₁₁	C₄×D₃	1	1	yes	characteristic
30	C₂×C₃×C₁₁	#67	1	1	yes	characteristic
31	Dic₃⋊C₄	—	3	1	no	—
32	C₂²×C₁₁	C₂×D₉	1	1	yes	characteristic
33	C₄×C₁₁	—	2	1	no	—
34	C₄×C₁₁	—	9	2	no	—
35	C₄×C₁₁	—	18	1	no	—
36	C₂²×C₉	C₂²×C₁₁	1	1	yes	characteristic
37	C₄×C₉	—	2	1	no	—
38	Dic₉	—	2	1	no	—
39	Dic₉	C₄×C₁₁	1	2	yes	complemented
40	C₃×C₁₁	Dic₃⋊C₄	1	1	yes	characteristic
41	C₂×C₃×C₄	D₃×C₁₁	1	1	yes	characteristic
42	C₂×Dic₃	—	3	1	no	—
43	C₂×Dic₃	—	3	1	no	—
44	C₂×C₁₁	Dic₁₈	1	1	yes	characteristic
45	C₂×C₁₁	C₄×D₉	1	1	yes	characteristic
46	C₂×C₁₁	#611	1	1	yes	characteristic
47	C₂×C₉	C₂×C₄×C₁₁	1	1	yes	characteristic
48	C₂×C₉	D₄×C₁₁	1	1	yes	characteristic
49	C₂×C₉	Q₈×C₁₁	1	1	yes	characteristic
50	C₄⋊C₄	—	9	1	no	Sylow
51	C₂²×C₃	C₂×D₃×C₁₁	1	1	yes	characteristic
52	C₃×C₄	—	2	1	no	—
53	Dic₃	—	3	2	no	—
54	Dic₃	—	6	1	no	—
55	C₁₁	Dic₉⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
56	C₉	C₁₁×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄	—	9	1	no	—
58	C₂×C₄	—	9	1	no	—
59	C₂×C₄	C₁₁×D₉	1	1	yes	characteristic
60	C₂×C₃	C₁₁×Dic₆	1	1	yes	characteristic
61	C₂×C₃	C₄×D₃×C₁₁	1	1	yes	characteristic
62	C₂×C₃	C₁₁×#67	1	1	yes	characteristic
63	C₂²	C₂×C₁₁×D₉	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	9	2	no	—
66	C₄	—	18	1	no	—
67	C₃	C₁₁×Dic₃⋊C₄	1	1	yes	characteristic
68	C₂	C₁₁×Dic₁₈	1	1	yes	characteristic
69	C₂	C₄×C₁₁×D₉	1	1	yes	characteristic
70	C₂	C₁₁×#611	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
8. C₁₁×Dic₉	C₄	semidirect
16. Dic₉⋊C₄	C₁₁	direct (N × H)
21. C₉×C₁₁	C₄⋊C₄	semidirect
39. Dic₉	C₄×C₁₁	semidirect
55. C₁₁	Dic₉⋊C₄	direct (N × H)
56. C₉	C₁₁×C₄⋊C₄	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
C₂×C₁₁×Dic₉	2
C₁₁×Dic₃⋊C₄	3
Dic₉⋊C₄	11

Subgroups — C11×Dic9⋊C4 #13096891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×Dic₉⋊C₄ #13096891