Subgroups — D₁₆×D₄₆₁ #44442495

Order 29504.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₄₆₁	C₂	1	2	yes	maximal, complemented
2	D₇₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#28414059	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₄₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₄₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₄₆₁	—	2	2	no	—
7	D₃₆₈₈	C₂²	1	2	yes	complemented
8	#20301486	—	2	2	no	—
9	C₈×D₄₆₁	C₂²	1	1	yes	characteristic
10	#20301476	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₄₆₁	C₂²	1	2	yes	complemented
12	C₁₆×C₄₆₁	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₄₆₁	—	4	2	no	—
14	D₁₈₄₄	—	2	2	no	—
15	C₂²⋊D₄₆₁	—	4	2	no	—
16	C₄×D₄₆₁	D₄	1	1	yes	characteristic
17	#16814779	D₄	1	1	yes	characteristic
18	D₄×C₄₆₁	—	2	2	no	—
19	C₈×C₄₆₁	C₂³	1	1	yes	characteristic
20	C₂²×C₄₆₁	—	4	2	no	—
21	C₂×D₄₆₁	—	4	2	no	—
22	C₂×D₄₆₁	—	8	4	no	—
23	C₂×D₄₆₁	D₈	1	1	yes	characteristic
24	C₄×C₄₆₁	C₂×D₄	1	1	yes	characteristic
25	Dic₄₆₁	D₈	1	1	yes	characteristic
26	C₂×C₄₆₁	—	8	2	no	—
27	C₂×C₄₆₁	C₂×D₈	1	1	yes	characteristic
28	D₄₆₁	—	8	2	no	—
29	D₄₆₁	D₁₆	1	2	yes	direct product factor
30	C₄₆₁	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	461	1	no	maximal, Sylow
32	C₂×D₈	—	461	2	no	—
33	D₁₆	—	461	2	no	—
34	D₁₆	—	461	1	no	—
35	D₁₆	D₄₆₁	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	461	1	no	—
37	C₂×D₄	—	922	2	no	—
38	D₈	—	922	2	no	—
39	D₈	—	461	2	no	—
40	D₈	C₂×D₄₆₁	1	2	yes	complemented
41	C₂×C₈	—	461	1	no	—
42	C₁₆	—	461	1	no	—
43	C₁₆	C₂×D₄₆₁	1	1	yes	characteristic, complemented
44	C₂³	—	1844	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	1844	2	no	—
47	D₄	—	922	2	no	—
48	C₂×C₄	—	461	1	no	—
49	C₈	—	461	1	no	—
50	C₈	C₂²×D₄₆₁	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	1844	2	no	—
53	C₂²	—	3688	4	no	—
54	C₂²	—	461	1	no	—
55	C₄	—	461	1	no	—
56	C₄	D₄×D₄₆₁	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	3688	2	no	—
59	C₂	—	461	2	no	—
60	C₂	D₈×D₄₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₆₁
commutator, cosocle	C₈×C₄₆₁	C₂³
Frattini	C₈	C₂²×D₄₆₁
Fitting	D₁₆×C₄₆₁	C₂
socle	C₂×C₄₆₁	C₂×D₈
hypercenter	D₁₆	D₄₆₁
hypocenter	C₄₆₁	C₂×D₁₆
LCS	G ▷ C₈×C₄₆₁ ▷ C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₄₆₁	C₂	semidirect
2. D₇₃₇₆	C₂	semidirect
3. #28414059	C₂	semidirect
4. C₁₆×D₄₆₁	C₂	semidirect
5. D₁₆×C₄₆₁	C₂	semidirect
7. D₃₆₈₈	C₂²	semidirect
10. #20301476	C₂²	semidirect
11. D₈×C₄₆₁	C₂²	semidirect
12. C₁₆×C₄₆₁	C₂²	semidirect
29. D₄₆₁	D₁₆	direct (N × H)
30. C₄₆₁	C₂×D₁₆	semidirect
35. D₁₆	D₄₆₁	direct (N × H)
40. D₈	C₂×D₄₆₁	semidirect
43. C₁₆	C₂×D₄₆₁	semidirect

Maximal subgroups

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

subgroup	index
D₈×D₄₆₁	2
D₇₃₇₆	2
#28414059	2
C₁₆×D₄₆₁	2
D₁₆×C₄₆₁	2
C₂×D₁₆	461

Subgroups — D16×D461 #44442495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆×D₄₆₁ #44442495