Subgroups — Q₁₆×Dic₁₀₃ #20267886

Order 6592.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₁₀₃	C₂	1	2	yes	maximal
2	#15692955	C₂	1	1	yes	maximal, characteristic
3	#15692945	C₂	1	2	yes	maximal
4	C₈×Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₀₃	—	2	2	no	—
8	C₄⋊Dic₁₀₃	C₂²	1	2	yes	—
9	C₄×Dic₁₀₃	—	2	2	no	—
10	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₀₃	C₂²	1	2	yes	—
12	Q₁₆×C₁₀₃	C₄	1	4	yes	complemented
13	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
14	Q₈×C₁₀₃	—	2	2	no	—
15	Q₈×C₁₀₃	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₁₀₃	—	2	2	no	—
17	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₀₃	—	2	2	no	—
19	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
20	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
21	C₈×C₁₀₃	C₂×C₄	1	2	yes	—
22	C₁₀₃⋊C₈	—	2	1	no	—
23	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₀₃	—	2	4	no	—
25	C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₁₀₃	#41	1	1	yes	characteristic
27	Dic₁₀₃	—	2	1	no	—
28	Dic₁₀₃	—	4	2	no	—
29	Dic₁₀₃	Q₁₆	1	2	yes	direct product factor
30	C₂×C₁₀₃	C₄×D₄	1	1	yes	characteristic
31	C₂×C₁₀₃	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₁₀₃	#135	1	1	yes	characteristic
33	C₁₀₃	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×Q₁₆	—	103	1	no	maximal, Sylow
35	C₂×Q₁₆	D₁₀₃	1	1	yes	characteristic
36	C₄×Q₈	—	103	2	no	—
37	#107	—	103	1	no	—
38	#103	—	103	2	no	—
39	C₄×C₈	—	103	1	no	—
40	C₂×Q₈	C₂×D₁₀₃	1	2	yes	—
41	Q₁₆	Dic₁₀₃	1	4	yes	direct product factor
42	C₂×C₈	—	103	1	no	—
43	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
44	C₄⋊C₄	—	103	2	no	—
45	C₄⋊C₄	—	206	2	no	—
46	C₄²	—	103	1	no	—
47	C₄²	—	206	2	no	—
48	Q₈	—	2	2	no	—
49	Q₈	C₂×Dic₁₀₃	1	4	yes	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	103	1	no	—
52	C₂×C₄	—	103	1	no	—
53	C₂×C₄	—	206	2	no	—
54	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
55	C₈	—	206	1	no	—
56	C₈	C₂×Dic₁₀₃	1	2	yes	—
57	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
58	C₄	—	2	4	no	—
59	C₄	—	103	2	no	—
60	C₄	—	412	2	no	—
61	C₄	—	206	1	no	—
62	C₄	C₂²×Dic₁₀₃	1	1	yes	characteristic
63	C₄	#13110104	1	1	yes	characteristic
64	C₂	D₄×Dic₁₀₃	1	1	yes	characteristic
65	C₂	Q₁₆×D₁₀₃	1	1	yes	characteristic
66	C₂	#15693044	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₄×C₁₀₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₂×Q₁₆×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₂×Q₁₆	D₁₀₃
hypocenter	C₁₀₃	C₄×Q₁₆
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
12. Q₁₆×C₁₀₃	C₄	semidirect
29. Dic₁₀₃	Q₁₆	direct (N × H)
33. C₁₀₃	C₄×Q₁₆	semidirect
41. Q₁₆	Dic₁₀₃	direct (N × H)

Subgroups — Q16×Dic103 #20267886

Conjugacy classes of subgroups

Complements

Subgroups — Q₁₆×Dic₁₀₃ #20267886