Subgroups — D₄×Dic₁₁ #66987

Order 352.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₁	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Dic₁₁	C₂	1	2	yes	maximal, complemented
4	C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₁₁	C₂²	1	2	yes	—
7	D₄×C₁₁	C₄	1	4	yes	complemented
8	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₁	—	2	4	no	—
10	C₂×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₁	C₂²	1	2	yes	—
12	C₂×Dic₁₁	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁	—	2	2	no	—
14	C₂²×C₁₁	—	2	2	no	—
15	C₂²×C₁₁	C₂×C₄	1	4	yes	complemented
16	C₂²×C₁₁	C₂³	1	1	yes	characteristic
17	C₄×C₁₁	C₂×C₄	1	2	yes	complemented
18	Dic₁₁	—	2	2	no	—
19	Dic₁₁	—	2	1	no	—
20	Dic₁₁	D₄	1	2	yes	direct product factor
21	C₄×D₄	—	11	1	no	maximal, Sylow
22	C₂×C₁₁	—	2	4	no	—
23	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
25	C₂×C₁₁	#41	1	1	yes	characteristic
26	C₂×D₄	D₁₁	1	1	yes	characteristic
27	C₂²×C₄	—	11	2	no	—
28	C₄⋊C₄	—	11	1	no	—
29	C₂²⋊C₄	—	11	2	no	—
30	C₄²	—	11	1	no	—
31	C₁₁	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
32	C₂³	C₂×D₁₁	1	2	yes	—
33	D₄	Dic₁₁	1	4	yes	direct product factor
34	C₂×C₄	—	11	1	no	—
35	C₂×C₄	—	11	1	no	—
36	C₂×C₄	—	11	2	no	—
37	C₂×C₄	—	22	4	no	—
38	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
39	C₂²	—	2	2	no	—
40	C₂²	—	2	2	no	—
41	C₂²	C₂×Dic₁₁	1	4	yes	complemented
42	C₂²	C₂²×D₁₁	1	1	yes	characteristic
43	C₄	—	11	2	no	—
44	C₄	—	22	2	no	—
45	C₄	—	22	1	no	—
46	C₄	C₂×Dic₁₁	1	2	yes	complemented
47	C₂	—	2	4	no	—
48	C₂	D₄×D₁₁	1	1	yes	characteristic
49	C₂	#4341	1	1	yes	characteristic
50	C₂	C₂²×Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₁
commutator	C₂×C₁₁	C₂²×C₄
Fitting, prime radical	C₂×D₄×C₁₁	C₂
socle, cosocle	C₂²×C₁₁	C₂³
hypercenter	C₂×D₄	D₁₁
hypocenter	C₁₁	C₄×D₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₁₁	C₂	semidirect
3. C₂²⋊Dic₁₁	C₂	semidirect
4. C₄⋊Dic₁₁	C₂	semidirect
5. C₄×Dic₁₁	C₂	semidirect
7. D₄×C₁₁	C₄	semidirect
15. C₂²×C₁₁	C₂×C₄	semidirect
17. C₄×C₁₁	C₂×C₄	semidirect
20. Dic₁₁	D₄	direct (N × H)
31. C₁₁	C₄×D₄	semidirect
33. D₄	Dic₁₁	direct (N × H)
41. C₂²	C₂×Dic₁₁	semidirect
46. C₄	C₂×Dic₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₁₁	2
C₂²×Dic₁₁	2
C₂²⋊Dic₁₁	2
C₄⋊Dic₁₁	2
C₄×Dic₁₁	2
C₄×D₄	11

Subgroups — D4×Dic11 #66987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×Dic₁₁ #66987