Subgroups — Q₁₆×D₁₀₁ #15692271

Order 3232.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₁₀₁	C₂	1	2	yes	maximal
2	Dic₄₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#13108064	C₂	1	2	yes	maximal, complemented
4	C₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₀₁	C₂²	1	2	yes	—
7	C₄×D₁₀₁	—	2	2	no	—
8	C₄×D₁₀₁	C₂²	1	1	yes	characteristic
9	Dic₂₀₂	—	2	2	no	—
10	Dic₂₀₂	C₂²	1	2	yes	—
11	C₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	#11717579	C₂²	1	1	yes	characteristic
13	C₂×D₁₀₁	D₄	1	1	yes	characteristic
14	C₄×C₁₀₁	—	2	2	no	—
15	C₄×C₁₀₁	C₂³	1	1	yes	characteristic
16	Dic₁₀₁	—	2	2	no	—
17	Dic₁₀₁	D₄	1	1	yes	characteristic
18	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
19	D₁₀₁	Q₁₆	1	2	yes	direct product factor
20	C₁₀₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	101	1	no	maximal, Sylow
22	C₂×Q₈	—	101	2	no	—
23	Q₁₆	—	101	2	no	—
24	Q₁₆	—	101	1	no	—
25	Q₁₆	D₁₀₁	1	1	yes	characteristic, direct product factor
26	C₂×C₈	—	101	1	no	—
27	Q₈	—	101	2	no	—
28	Q₈	—	202	2	no	—
29	Q₈	C₂×D₁₀₁	1	2	yes	—
30	C₂×C₄	—	101	1	no	—
31	C₂×C₄	—	202	2	no	—
32	C₈	—	101	1	no	—
33	C₈	C₂×D₁₀₁	1	1	yes	characteristic
34	C₂²	—	101	1	no	—
35	C₄	—	2	2	no	—
36	C₄	—	101	1	no	—
37	C₄	—	202	2	no	—
38	C₄	C₂²×D₁₀₁	1	1	yes	characteristic
39	C₂	—	101	2	no	—
40	C₂	D₄×D₁₀₁	1	1	yes	characteristic

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

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