Subgroups — C₄×D₄×C₁₁ #67011

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×C₄×C₁₁	C₂	1	2	yes	maximal, complemented
3	C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₁₁	C₂²	1	2	yes	—
7	D₄×C₁₁	C₄	1	4	yes	direct product factor
8	C₂×C₄×C₁₁	—	2	4	no	—
9	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₁	C₂²	1	2	yes	—
11	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₁	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	—	2	2	no	—
18	C₄×C₁₁	—	2	1	no	—
19	C₄×C₁₁	C₂×C₄	1	2	yes	complemented
20	C₄×C₁₁	D₄	1	2	yes	direct product factor
21	C₄×D₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, 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	C₂×C₁₁	1	1	yes	characteristic
27	C₂²×C₄	C₂×C₁₁	1	2	yes	complemented
28	C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
29	C₂²⋊C₄	C₂×C₁₁	1	2	yes	complemented
30	C₄²	C₂×C₁₁	1	1	yes	characteristic, complemented
31	C₁₁	C₄×D₄	1	1	yes	characteristic, direct product factor, Sylow
32	C₂³	C₂²×C₁₁	1	2	yes	—
33	D₄	C₄×C₁₁	1	4	yes	direct product factor
34	C₂×C₄	—	2	4	no	—
35	C₂×C₄	C₂²×C₁₁	1	1	yes	characteristic
36	C₂×C₄	C₂²×C₁₁	1	2	yes	—
37	C₂×C₄	C₂²×C₁₁	1	1	yes	characteristic
38	C₂×C₄	C₂²×C₁₁	1	1	yes	characteristic
39	C₂²	—	2	2	no	—
40	C₂²	—	2	2	no	—
41	C₂²	C₂×C₄×C₁₁	1	4	yes	complemented
42	C₂²	C₂³×C₁₁	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	2	1	no	—
45	C₄	C₂×C₄×C₁₁	1	2	yes	complemented
46	C₄	D₄×C₁₁	1	2	yes	direct product factor
47	C₂	—	2	4	no	—
48	C₂	C₂²×C₄×C₁₁	1	1	yes	characteristic
49	C₂	C₂×D₄×C₁₁	1	1	yes	characteristic
50	C₂	C₁₁×#41	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₁₁	C₂	semidirect
3. C₁₁×C₄⋊C₄	C₂	semidirect
4. C₁₁×C₂²⋊C₄	C₂	semidirect
5. C₄²×C₁₁	C₂	semidirect
7. D₄×C₁₁	C₄	direct (N × H)
15. C₂²×C₁₁	C₂×C₄	semidirect
19. C₄×C₁₁	C₂×C₄	semidirect
20. C₄×C₁₁	D₄	direct (N × H)
21. C₄×D₄	C₁₁	direct (N × H)
27. C₂²×C₄	C₂×C₁₁	semidirect
28. C₄⋊C₄	C₂×C₁₁	semidirect
29. C₂²⋊C₄	C₂×C₁₁	semidirect
30. C₄²	C₂×C₁₁	semidirect
31. C₁₁	C₄×D₄	direct (N × H)
33. D₄	C₄×C₁₁	direct (N × H)
41. C₂²	C₂×C₄×C₁₁	semidirect
45. C₄	C₂×C₄×C₁₁	semidirect
46. C₄	D₄×C₁₁	direct (N × H)

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×C₄×C₁₁	2
C₁₁×C₄⋊C₄	2
C₁₁×C₂²⋊C₄	2
C₄²×C₁₁	2
C₄×D₄	11

Subgroups — C4×D4×C11 #67011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₄×C₁₁ #67011