Subgroups — D₁₁×S₄ #10587290

Order 528.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁⋊S₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×S₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×D₁₁	—	3	1	no	maximal, Hall
5	C₁₁×A₄	C₂²	1	1	yes	characteristic, complemented
6	D₃×D₁₁	—	4	1	no	maximal
7	C₂²×D₁₁	—	3	1	no	—
8	C₂²×D₁₁	D₃	1	1	yes	characteristic, complemented
9	D₄×C₁₁	—	3	1	no	—
10	C₂²⋊D₁₁	—	3	1	no	—
11	C₂²⋊D₁₁	—	3	1	no	—
12	D₄₄	—	3	1	no	—
13	C₄×D₁₁	—	3	1	no	—
14	D₃₃	—	4	1	no	—
15	C₃×D₁₁	—	4	1	no	—
16	D₃×C₁₁	—	4	1	no	—
17	C₂×S₄	—	11	1	no	maximal, Hall
18	C₂²×C₁₁	—	3	1	no	—
19	C₂²×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented
20	C₂×D₁₁	—	3	1	no	—
21	C₂×D₁₁	—	3	1	no	—
22	C₂×D₁₁	—	3	1	no	—
23	C₂×D₁₁	—	6	1	no	—
24	C₂×D₁₁	—	6	1	no	—
25	C₄×C₁₁	—	3	1	no	—
26	Dic₁₁	—	3	1	no	—
27	C₃×C₁₁	—	4	1	no	Hall
28	C₂×A₄	—	11	1	no	—
29	S₄	—	11	1	no	—
30	S₄	D₁₁	1	1	yes	characteristic, direct product factor
31	C₂×C₁₁	—	3	1	no	—
32	C₂×C₁₁	—	6	1	no	—
33	D₁₁	—	3	1	no	—
34	D₁₁	—	6	1	no	—
35	D₁₁	S₄	1	1	yes	characteristic, direct product factor
36	C₂×D₄	—	33	1	no	Sylow
37	C₂×D₃	—	44	1	no	—
38	A₄	C₂×D₁₁	1	1	yes	characteristic, complemented
39	C₁₁	C₂×S₄	1	1	yes	characteristic, complemented, Sylow
40	C₂³	—	11	1	no	—
41	C₂³	—	33	1	no	—
42	D₄	—	3	1	no	—
43	D₄	—	33	1	no	—
44	D₄	—	33	1	no	—
45	D₄	—	33	1	no	—
46	C₂×C₄	—	33	1	no	—
47	C₂×C₃	—	44	1	no	—
48	D₃	—	4	1	no	—
49	D₃	—	44	1	no	—
50	C₂²	—	3	1	no	—
51	C₂²	—	33	1	no	—
52	C₂²	—	33	1	no	—
53	C₂²	—	33	1	no	—
54	C₂²	—	66	1	no	—
55	C₂²	—	66	1	no	—
56	C₂²	D₃×D₁₁	1	1	yes	characteristic, complemented
57	C₄	—	3	1	no	—
58	C₄	—	33	1	no	—
59	C₃	—	4	1	no	Sylow
60	C₂	—	3	1	no	—
61	C₂	—	6	1	no	—
62	C₂	—	11	1	no	—
63	C₂	—	33	1	no	—
64	C₂	—	66	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₁×A₄	C₂²
Fitting, socle	C₂²×C₁₁	C₂×D₃
LCS	G ▷ C₁₁×A₄
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. A₄×D₁₁	C₂	semidirect
2. C₁₁⋊S₄	C₂	semidirect
3. C₁₁×S₄	C₂	semidirect
5. C₁₁×A₄	C₂²	semidirect
8. C₂²×D₁₁	D₃	semidirect
19. C₂²×C₁₁	C₂×D₃	semidirect
30. S₄	D₁₁	direct (N × H)
35. D₁₁	S₄	direct (N × H)
38. A₄	C₂×D₁₁	semidirect
39. C₁₁	C₂×S₄	semidirect
56. C₂²	D₃×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
A₄×D₁₁	2
C₁₁⋊S₄	2
C₁₁×S₄	2
D₄×D₁₁	3
D₃×D₁₁	4
C₂×S₄	11

Subgroups — D11×S4 #10587290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×S₄ #10587290