Subgroups — D₆₁⋊M₁₆ #14519862

Order 1952.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₆₁	C₂	1	1	yes	maximal, characteristic
2	#11758217	C₂	1	2	yes	maximal, complemented
3	#11758213	C₂	1	2	yes	maximal, complemented
4	D₆₁⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂²×D₆₁	C₄	1	1	yes	characteristic
6	C₂×C₄×C₆₁	C₄	1	1	yes	characteristic
7	C₂×Dic₆₁	C₂²	1	1	yes	characteristic
8	C₄×D₆₁	C₄	1	1	yes	characteristic
9	C₄×D₆₁	C₄	1	1	yes	characteristic
10	C₄×D₆₁	C₂²	1	1	yes	characteristic
11	C₄×D₆₁	C₂²	1	1	yes	characteristic
12	#92420	C₂²	1	4	yes	complemented
13	C₂²×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×D₆₁	—	2	2	no	—
15	C₂×D₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
19	Dic₆₁	C₂×C₄	1	1	yes	characteristic
20	Dic₆₁	C₂³	1	1	yes	characteristic
21	C₂×C₆₁	—	2	1	no	—
22	C₂×C₆₁	C₂²×C₄	1	1	yes	characteristic
23	D₆₁	—	2	1	no	—
24	D₆₁	M₁₆	1	2	yes	complemented
25	C₆₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	61	1	no	maximal, Sylow
27	C₂²×C₄	—	61	1	no	—
28	M₁₆	—	61	2	no	—
29	M₁₆	—	61	2	no	—
30	C₂×C₈	—	61	2	no	—
31	C₂³	—	61	1	no	—
32	C₂×C₄	—	61	1	no	—
33	C₂×C₄	—	61	1	no	—
34	C₂×C₄	—	61	1	no	—
35	C₂×C₄	—	61	1	no	—
36	C₂×C₄	—	61	1	no	—
37	C₂×C₄	#6923	1	1	yes	characteristic
38	C₈	—	61	4	no	—
39	C₂²	—	61	1	no	—
40	C₂²	—	61	1	no	—
41	C₂²	—	122	2	no	—
42	C₂²	C₂×#6923	1	1	yes	characteristic
43	C₄	—	61	1	no	—
44	C₄	—	61	1	no	—
45	C₄	C₂×#6923	1	1	yes	characteristic
46	C₄	C₂×#6923	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	61	2	no	—
49	C₂	—	122	1	no	—
50	C₂	C₂²×#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#6923
commutator, socle	C₂×C₆₁	C₂²×C₄
Frattini	C₂	C₂²×#6923
Fitting	C₂×C₄×C₆₁	C₄
prime radical	C₂²×D₆₁	C₄
cosocle	Dic₆₁	C₂³
hypercenter	C₂×C₄	#6923
hypocenter	C₆₁	C₂×M₁₆
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #11758217	C₂	semidirect
3. #11758213	C₂	semidirect
4. D₆₁⋊C₈	C₂	semidirect
12. #92420	C₂²	semidirect
24. D₆₁	M₁₆	semidirect
25. C₆₁	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₆₁	2
#11758217	2
#11758213	2
D₆₁⋊C₈	2
C₂×M₁₆	61

Subgroups — D61⋊M16 #14519862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁⋊M₁₆ #14519862