Subgroups — D₁₆×D₂₄₁ #29508136

Order 15424.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₂₄₁	C₂	1	2	yes	maximal, complemented
2	D₃₈₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#21440583	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₂₄₁	—	2	2	no	—
7	D₁₉₂₈	C₂²	1	2	yes	complemented
8	#16838755	—	2	2	no	—
9	C₈×D₂₄₁	C₂²	1	1	yes	characteristic
10	#16838745	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₂₄₁	C₂²	1	2	yes	complemented
12	C₁₆×C₂₄₁	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₂₄₁	—	4	2	no	—
14	D₉₆₄	—	2	2	no	—
15	C₂²⋊D₂₄₁	—	4	2	no	—
16	C₄×D₂₄₁	D₄	1	1	yes	characteristic
17	#14515349	D₄	1	1	yes	characteristic
18	D₄×C₂₄₁	—	2	2	no	—
19	C₈×C₂₄₁	C₂³	1	1	yes	characteristic
20	C₂²×C₂₄₁	—	4	2	no	—
21	C₂×D₂₄₁	—	4	2	no	—
22	C₂×D₂₄₁	—	8	4	no	—
23	C₂×D₂₄₁	D₈	1	1	yes	characteristic
24	C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
25	Dic₂₄₁	D₈	1	1	yes	characteristic
26	C₂×C₂₄₁	—	8	2	no	—
27	C₂×C₂₄₁	C₂×D₈	1	1	yes	characteristic
28	D₂₄₁	—	8	2	no	—
29	D₂₄₁	D₁₆	1	2	yes	direct product factor
30	C₂₄₁	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	241	1	no	maximal, Sylow
32	C₂×D₈	—	241	2	no	—
33	D₁₆	—	241	2	no	—
34	D₁₆	—	241	1	no	—
35	D₁₆	D₂₄₁	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	241	1	no	—
37	C₂×D₄	—	482	2	no	—
38	D₈	—	482	2	no	—
39	D₈	—	241	2	no	—
40	D₈	C₂×D₂₄₁	1	2	yes	complemented
41	C₂×C₈	—	241	1	no	—
42	C₁₆	—	241	1	no	—
43	C₁₆	C₂×D₂₄₁	1	1	yes	characteristic, complemented
44	C₂³	—	964	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	964	2	no	—
47	D₄	—	482	2	no	—
48	C₂×C₄	—	241	1	no	—
49	C₈	—	241	1	no	—
50	C₈	C₂²×D₂₄₁	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	1928	4	no	—
53	C₂²	—	964	2	no	—
54	C₂²	—	241	1	no	—
55	C₄	—	241	1	no	—
56	C₄	D₄×D₂₄₁	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	1928	2	no	—
59	C₂	—	241	2	no	—
60	C₂	D₈×D₂₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₂₄₁
commutator, cosocle	C₈×C₂₄₁	C₂³
Frattini	C₈	C₂²×D₂₄₁
Fitting	D₁₆×C₂₄₁	C₂
socle	C₂×C₂₄₁	C₂×D₈
hypercenter	D₁₆	D₂₄₁
hypocenter	C₂₄₁	C₂×D₁₆
LCS	G ▷ C₈×C₂₄₁ ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₂₄₁	C₂	semidirect
2. D₃₈₅₆	C₂	semidirect
3. #21440583	C₂	semidirect
4. C₁₆×D₂₄₁	C₂	semidirect
5. D₁₆×C₂₄₁	C₂	semidirect
7. D₁₉₂₈	C₂²	semidirect
10. #16838745	C₂²	semidirect
11. D₈×C₂₄₁	C₂²	semidirect
12. C₁₆×C₂₄₁	C₂²	semidirect
29. D₂₄₁	D₁₆	direct (N × H)
30. C₂₄₁	C₂×D₁₆	semidirect
35. D₁₆	D₂₄₁	direct (N × H)
40. D₈	C₂×D₂₄₁	semidirect
43. C₁₆	C₂×D₂₄₁	semidirect

Maximal subgroups

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

subgroup	index
D₈×D₂₄₁	2
D₃₈₅₆	2
#21440583	2
C₁₆×D₂₄₁	2
D₁₆×C₂₄₁	2
C₂×D₁₆	241

Subgroups — D16×D241 #29508136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆×D₂₄₁ #29508136