Subgroups — Q₁₆×#87938 #20266215

Order 6464.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#87938	C₂	1	2	yes	maximal
2	#15692324	C₂	1	1	yes	maximal, characteristic
3	#15692318	C₂	1	2	yes	maximal
4	C₈×#87938	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₁₀₁	C₂	1	1	yes	maximal, characteristic
6	D₁₀₁⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊#87938	—	2	2	no	—
8	C₄⋊#87938	C₂²	1	2	yes	—
9	C₄×#87938	—	2	2	no	—
10	C₄×#87938	C₂²	1	1	yes	characteristic
11	Q₈×D₁₀₁	C₂²	1	2	yes	—
12	Dic₄₀₄	C₄	1	1	yes	characteristic, complemented
13	#13108064	C₄	1	2	yes	complemented
14	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
15	Q₁₆×C₁₀₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#87938	—	2	2	no	—
17	C₂×#87938	D₄	1	1	yes	characteristic
18	C₂×#87938	D₄	1	1	yes	characteristic
19	Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
20	C₄×D₁₀₁	—	2	2	no	—
21	C₄×D₁₀₁	C₂³	1	1	yes	characteristic
22	Dic₂₀₂	—	2	2	no	—
23	Dic₂₀₂	C₂×C₄	1	2	yes	—
24	#11717581	—	2	1	no	—
25	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
26	#11717579	C₂×C₄	1	1	yes	characteristic
27	C₂×D₁₀₁	C₂×D₄	1	1	yes	characteristic
28	#87938	—	2	1	no	—
29	#87938	—	4	2	no	—
30	#87938	Q₁₆	1	2	yes	direct product factor
31	C₄×C₁₀₁	—	2	2	no	—
32	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
33	Dic₁₀₁	—	2	2	no	—
34	Dic₁₀₁	#41	1	1	yes	characteristic
35	C₂×C₁₀₁	C₄×D₄	1	1	yes	characteristic
36	D₁₀₁	C₂×Q₁₆	1	1	yes	characteristic
37	D₁₀₁	#135	1	1	yes	characteristic
38	C₁₀₁	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₄×Q₁₆	—	101	1	no	maximal, Sylow
40	C₂×Q₁₆	—	101	1	no	—
41	C₄×Q₈	—	101	2	no	—
42	#107	—	101	1	no	—
43	#103	—	101	2	no	—
44	C₄×C₈	—	101	1	no	—
45	C₂×Q₈	—	101	2	no	—
46	Q₁₆	—	101	2	no	—
47	Q₁₆	—	101	1	no	—
48	Q₁₆	#87938	1	1	yes	characteristic, direct product factor
49	C₂×C₈	—	101	1	no	—
50	C₂×C₈	—	101	1	no	—
51	C₄⋊C₄	—	101	2	no	—
52	C₄⋊C₄	—	202	2	no	—
53	C₄²	—	101	1	no	—
54	C₄²	—	202	2	no	—
55	Q₈	—	101	2	no	—
56	Q₈	—	202	2	no	—
57	Q₈	C₂×#87938	1	2	yes	—
58	C₂×C₄	—	101	1	no	—
59	C₂×C₄	—	101	1	no	—
60	C₂×C₄	—	101	1	no	—
61	C₂×C₄	—	202	2	no	—
62	C₂×C₄	—	202	2	no	—
63	C₈	—	101	1	no	—
64	C₈	—	202	1	no	—
65	C₈	C₂×#87938	1	1	yes	characteristic
66	C₂²	—	101	1	no	—
67	C₄	—	2	2	no	—
68	C₄	—	101	2	no	—
69	C₄	—	101	1	no	—
70	C₄	—	404	2	no	—
71	C₄	—	202	1	no	—
72	C₄	—	202	2	no	—
73	C₄	C₂²×#87938	1	1	yes	characteristic
74	C₂	—	101	1	no	—
75	C₂	—	101	1	no	—
76	C₂	D₄×#87938	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#87938
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₄	C₂²×#87938
Fitting	Q₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	C₄×D₄
hypercenter	Q₁₆	#87938
hypocenter	C₁₀₁	C₄×Q₁₆
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Dic₄₀₄	C₄	semidirect
13. #13108064	C₄	semidirect
15. Q₁₆×C₁₀₁	C₄	semidirect
30. #87938	Q₁₆	direct (N × H)
38. C₁₀₁	C₄×Q₁₆	semidirect
48. Q₁₆	#87938	direct (N × H)

Subgroups — Q16×#87938 #20266215

Conjugacy classes of subgroups

Complements

Subgroups — Q₁₆×#87938 #20266215