Subgroups — Q₁₆×D₁₁ #66970

Order 352.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₁₁	C₂	1	2	yes	maximal
2	C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#4326	C₂	1	2	yes	maximal, complemented
4	Dic₄₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₁₁	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₁₁	C₂²	1	2	yes	—
7	C₄×D₁₁	—	2	2	no	—
8	C₄×D₁₁	C₂²	1	1	yes	characteristic
9	Dic₂₂	—	2	2	no	—
10	Dic₂₂	C₂²	1	2	yes	—
11	C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×D₁₁	D₄	1	1	yes	characteristic
14	C₄×C₁₁	—	2	2	no	—
15	C₄×C₁₁	C₂³	1	1	yes	characteristic
16	Dic₁₁	—	2	2	no	—
17	Dic₁₁	D₄	1	1	yes	characteristic
18	C₂×Q₁₆	—	11	1	no	maximal, Sylow
19	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
20	D₁₁	Q₁₆	1	2	yes	direct product factor
21	C₂×Q₈	—	11	2	no	—
22	Q₁₆	—	11	2	no	—
23	Q₁₆	—	11	1	no	—
24	Q₁₆	D₁₁	1	1	yes	characteristic, direct product factor
25	C₂×C₈	—	11	1	no	—
26	C₁₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	11	2	no	—
28	Q₈	—	22	2	no	—
29	Q₈	C₂×D₁₁	1	2	yes	—
30	C₂×C₄	—	11	1	no	—
31	C₂×C₄	—	22	2	no	—
32	C₈	—	11	1	no	—
33	C₈	C₂×D₁₁	1	1	yes	characteristic
34	C₂²	—	11	1	no	—
35	C₄	—	2	2	no	—
36	C₄	—	11	1	no	—
37	C₄	—	22	2	no	—
38	C₄	C₂²×D₁₁	1	1	yes	characteristic
39	C₂	—	11	2	no	—
40	C₂	D₄×D₁₁	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.