Subgroups — D₄₆₁⋊M₁₆ #28414203

Order 14752.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301511	C₂	1	2	yes	maximal, complemented
2	#20301510	C₂	1	2	yes	maximal, complemented
3	D₄₆₁⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₄₆₁	C₂	1	1	yes	maximal, characteristic
5	#16814786	C₂²	1	4	yes	complemented
6	C₂²×D₄₆₁	C₄	1	1	yes	characteristic
7	C₂×Dic₄₆₁	C₂²	1	1	yes	characteristic
8	C₄×D₄₆₁	C₄	1	1	yes	characteristic
9	C₄×D₄₆₁	C₄	1	1	yes	characteristic
10	C₄×D₄₆₁	C₂²	1	1	yes	characteristic
11	C₄×D₄₆₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₄₆₁	C₄	1	1	yes	characteristic
13	C₂²×C₄₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×D₄₆₁	—	2	2	no	—
15	C₂×D₄₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×D₄₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄×C₄₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₄₆₁	C₂×C₄	1	1	yes	characteristic
19	Dic₄₆₁	C₂×C₄	1	1	yes	characteristic
20	Dic₄₆₁	C₂³	1	1	yes	characteristic
21	C₂×C₄₆₁	—	2	1	no	—
22	C₂×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
23	D₄₆₁	—	2	1	no	—
24	D₄₆₁	M₁₆	1	2	yes	complemented
25	C₄₆₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	461	1	no	maximal, Sylow
27	C₂²×C₄	—	461	1	no	—
28	M₁₆	—	461	2	no	—
29	M₁₆	—	461	2	no	—
30	C₂×C₈	—	461	2	no	—
31	C₂³	—	461	1	no	—
32	C₂×C₄	—	461	1	no	—
33	C₂×C₄	—	461	1	no	—
34	C₂×C₄	—	461	1	no	—
35	C₂×C₄	—	461	1	no	—
36	C₂×C₄	—	461	1	no	—
37	C₂×C₄	#14270406	1	1	yes	characteristic
38	C₈	—	461	4	no	—
39	C₂²	—	922	2	no	—
40	C₂²	—	461	1	no	—
41	C₂²	—	461	1	no	—
42	C₂²	C₂×#14270406	1	1	yes	characteristic
43	C₄	—	461	1	no	—
44	C₄	—	461	1	no	—
45	C₄	C₂×#14270406	1	1	yes	characteristic
46	C₄	C₂×#14270406	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	922	1	no	—
49	C₂	—	461	2	no	—
50	C₂	C₂²×#14270406	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#14270406
commutator, socle	C₂×C₄₆₁	C₂²×C₄
Frattini	C₂	C₂²×#14270406
Fitting	C₂×C₄×C₄₆₁	C₄
prime radical	C₂²×D₄₆₁	C₄
cosocle	Dic₄₆₁	C₂³
hypercenter	C₂×C₄	#14270406
hypocenter	C₄₆₁	C₂×M₁₆
LCS	G ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #20301511	C₂	semidirect
2. #20301510	C₂	semidirect
3. D₄₆₁⋊C₈	C₂	semidirect
5. #16814786	C₂²	semidirect
24. D₄₆₁	M₁₆	semidirect
25. C₄₆₁	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#20301511	2
#20301510	2
D₄₆₁⋊C₈	2
C₂×C₄×D₄₆₁	2
C₂×M₁₆	461

Subgroups — D461⋊M16 #28414203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₆₁⋊M₁₆ #28414203