Subgroups — C₁₆×#87938 #20266061

Order 6464.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#87938	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	D₁₀₁⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#87938	C₄	1	1	yes	characteristic
6	#13108077	C₄	1	2	yes	complemented
7	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
8	#13108049	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₁₀₁	C₄	1	1	yes	characteristic, complemented
10	C₂×#87938	C₈	1	2	yes	—
11	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
12	#11717581	C₈	1	2	yes	—
13	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
14	#11717579	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₀₁	C₂×C₈	1	1	yes	characteristic
16	#87938	C₁₆	1	4	yes	direct product factor
17	C₄×C₁₀₁	C₄²	1	1	yes	characteristic
18	Dic₁₀₁	C₂×C₈	1	1	yes	characteristic
19	C₂×C₁₀₁	C₄×C₈	1	1	yes	characteristic
20	D₁₀₁	C₂×C₁₆	1	2	yes	—
21	C₁₀₁	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	101	1	no	maximal, Sylow
23	C₂×C₁₆	—	101	1	no	—
24	C₂×C₁₆	—	101	1	no	—
25	C₄×C₈	—	101	1	no	—
26	C₂×C₈	—	101	1	no	—
27	C₂×C₈	—	101	1	no	—
28	C₄²	—	101	1	no	—
29	C₁₆	—	101	2	no	—
30	C₁₆	—	101	1	no	—
31	C₁₆	#87938	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	101	2	no	—
33	C₂×C₄	—	101	1	no	—
34	C₈	—	101	2	no	—
35	C₈	—	101	1	no	—
36	C₈	C₂×#87938	1	1	yes	characteristic
37	C₂²	—	101	1	no	—
38	C₄	—	101	4	no	—
39	C₄	—	101	1	no	—
40	C₄	C₄×#87938	1	1	yes	characteristic
41	C₂	—	101	2	no	—
42	C₂	C₈×#87938	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#87938
commutator, hypocenter	C₁₀₁	C₄×C₁₆
Frattini	C₈	C₂×#87938
Fitting	C₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	C₄×C₈
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #13108077	C₄	semidirect
8. #13108049	C₄	semidirect
9. C₁₆×C₁₀₁	C₄	semidirect
16. #87938	C₁₆	direct (N × H)
21. C₁₀₁	C₄×C₁₆	semidirect
31. C₁₆	#87938	direct (N × H)

Subgroups — C16×#87938 #20266061

Conjugacy classes of subgroups

Complements

Subgroups — C₁₆×#87938 #20266061