Subgroups — M₁₆×D₁₁ #66959

Order 352.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#4318	C₂	1	1	yes	maximal, characteristic, complemented
4	#4313	C₂	1	2	yes	maximal, complemented
5	C₈×D₁₁	C₂	1	2	yes	maximal, complemented
6	C₂²×D₁₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₁	C₄	1	1	yes	characteristic
9	C₄×D₁₁	C₄	1	1	yes	characteristic
10	C₄×D₁₁	C₄	1	1	yes	characteristic
11	C₄×D₁₁	C₂²	1	1	yes	characteristic
12	C₄×D₁₁	C₂²	1	1	yes	characteristic
13	C₈×C₁₁	C₂²	1	2	yes	complemented
14	C₁₁⋊C₈	C₂²	1	2	yes	complemented
15	C₂²×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂×D₁₁	—	2	2	no	—
17	C₂×D₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×D₁₁	C₂×C₄	1	1	yes	characteristic
19	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₄×C₁₁	C₂³	1	1	yes	characteristic
21	Dic₁₁	C₂×C₄	1	1	yes	characteristic
22	Dic₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂×M₁₆	—	11	1	no	maximal, Sylow
24	C₂×C₁₁	—	2	1	no	—
25	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
26	D₁₁	—	2	1	no	—
27	D₁₁	M₁₆	1	2	yes	direct product factor
28	C₂²×C₄	—	11	1	no	—
29	M₁₆	—	11	1	no	—
30	M₁₆	—	11	2	no	—
31	M₁₆	D₁₁	1	1	yes	characteristic, direct product factor
32	C₂×C₈	—	11	2	no	—
33	C₁₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂³	—	11	1	no	—
35	C₂×C₄	—	11	1	no	—
36	C₂×C₄	—	11	1	no	—
37	C₂×C₄	—	11	1	no	—
38	C₂×C₄	—	11	1	no	—
39	C₂×C₄	—	11	1	no	—
40	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
41	C₈	—	11	2	no	—
42	C₈	C₂×D₁₁	1	2	yes	complemented
43	C₂²	—	11	1	no	—
44	C₂²	—	11	1	no	—
45	C₂²	—	22	2	no	—
46	C₂²	C₄×D₁₁	1	1	yes	characteristic
47	C₄	—	11	1	no	—
48	C₄	—	11	1	no	—
49	C₄	C₄×D₁₁	1	1	yes	characteristic
50	C₄	C₂²×D₁₁	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	—	11	2	no	—
53	C₂	—	22	1	no	—
54	C₂	C₂×C₄×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₁₁
commutator, socle	C₂×C₁₁	C₂²×C₄
Fitting	C₁₁×M₁₆	C₂
prime radical	C₂²×D₁₁	C₄
cosocle	C₄×C₁₁	C₂³
hypercenter	M₁₆	D₁₁
hypocenter	C₁₁	C₂×M₁₆
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₁₁×M₁₆	C₂	semidirect
3. #4318	C₂	semidirect
4. #4313	C₂	semidirect
5. C₈×D₁₁	C₂	semidirect
13. C₈×C₁₁	C₂²	semidirect
14. C₁₁⋊C₈	C₂²	semidirect
27. D₁₁	M₁₆	direct (N × H)
31. M₁₆	D₁₁	direct (N × H)
33. C₁₁	C₂×M₁₆	semidirect
42. C₈	C₂×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×M₁₆	2
#4318	2
#4313	2
C₈×D₁₁	2
C₂×M₁₆	11

Subgroups — M16×D11 #66959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×D₁₁ #66959