Subgroups — C₄⋊C₄×D₁₁ #66944

Order 352.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₁	C₂	1	2	yes	maximal
2	C₂×C₄×D₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₁⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂²×D₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₁	C₂²	1	2	yes	—
10	C₂×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₄×D₁₁	—	2	4	no	—
12	C₄×D₁₁	C₄	1	4	yes	complemented
13	C₂²×C₁₁	C₂³	1	1	yes	characteristic
14	C₂×D₁₁	C₂×C₄	1	2	yes	—
15	C₂×D₁₁	D₄	1	2	yes	—
16	C₂×D₁₁	Q₈	1	2	yes	—
17	C₄×C₁₁	—	2	2	no	—
18	C₄×C₁₁	C₂×C₄	1	2	yes	complemented
19	Dic₁₁	—	2	2	no	—
20	Dic₁₁	C₂×C₄	1	2	yes	complemented
21	C₂×C₄⋊C₄	—	11	1	no	maximal, Sylow
22	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
24	C₂×C₁₁	C₂×Q₈	1	1	yes	characteristic
25	D₁₁	C₄⋊C₄	1	4	yes	direct product factor
26	C₂²×C₄	—	11	1	no	—
27	C₂²×C₄	—	11	2	no	—
28	C₄⋊C₄	—	11	2	no	—
29	C₄⋊C₄	—	11	1	no	—
30	C₄⋊C₄	D₁₁	1	1	yes	characteristic, direct product factor
31	C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
32	C₂³	—	11	1	no	—
33	C₂×C₄	—	11	1	no	—
34	C₂×C₄	—	11	4	no	—
35	C₂×C₄	—	11	2	no	—
36	C₂×C₄	—	22	4	no	—
37	C₂×C₄	C₂×D₁₁	1	2	yes	—
38	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
39	C₂²	—	11	2	no	—
40	C₂²	—	11	2	no	—
41	C₂²	—	11	2	no	—
42	C₂²	C₂²×D₁₁	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	11	2	no	—
45	C₄	—	22	2	no	—
46	C₄	C₄×D₁₁	1	2	yes	complemented
47	C₂	—	11	4	no	—
48	C₂	C₂×C₄×D₁₁	1	1	yes	characteristic
49	C₂	D₄×D₁₁	1	1	yes	characteristic
50	C₂	Q₈×D₁₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×C₄⋊C₄	C₂	semidirect
4. C₄⋊Dic₁₁	C₂	semidirect
5. Dic₁₁⋊C₄	C₂	semidirect
12. C₄×D₁₁	C₄	semidirect
18. C₄×C₁₁	C₂×C₄	semidirect
20. Dic₁₁	C₂×C₄	semidirect
25. D₁₁	C₄⋊C₄	direct (N × H)
30. C₄⋊C₄	D₁₁	direct (N × H)
31. C₁₁	C₂×C₄⋊C₄	semidirect
46. C₄	C₄×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₁₁	2
C₁₁×C₄⋊C₄	2
C₄⋊Dic₁₁	2
Dic₁₁⋊C₄	2
C₂×C₄⋊C₄	11

Subgroups — C4⋊C4×D11 #66944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×D₁₁ #66944