Subgroups — Q₈×D₂₁ #66731

Order 336.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₂₁	C₂	1	3	yes	maximal
3	Dic₄₂	C₂	1	3	yes	maximal, complemented
4	Q₈×D₇	—	3	1	no	maximal, Hall
5	C₂×D₂₁	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₇	C₂²	1	3	yes	—
7	Dic₂₁	C₂²	1	3	yes	—
8	C₇×Q₈	D₃	1	1	yes	characteristic, complemented
9	C₄×D₇	—	3	3	no	—
10	Dic₁₄	—	3	3	no	—
11	D₃×Q₈	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	C₂³	1	1	yes	characteristic
13	D₂₁	Q₈	1	2	yes	direct product factor
14	C₂×D₇	—	3	1	no	—
15	C₄×C₇	C₂×D₃	1	3	yes	—
16	Dic₇	—	3	3	no	—
17	C₃×Q₈	D₇	1	1	yes	characteristic, complemented
18	C₄×D₃	—	7	3	no	—
19	Dic₆	—	7	3	no	—
20	C₃×C₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
21	C₂×Q₈	—	21	1	no	Sylow
22	C₂×C₇	C₂²×D₃	1	1	yes	characteristic
23	D₇	—	3	2	no	—
24	C₂×D₃	—	7	1	no	—
25	C₃×C₄	C₂×D₇	1	3	yes	—
26	Dic₃	—	7	3	no	—
27	Q₈	—	21	3	no	—
28	Q₈	D₂₁	1	1	yes	characteristic, direct product factor
29	C₂×C₄	—	21	3	no	—
30	C₇	D₃×Q₈	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₂²×D₇	1	1	yes	characteristic
32	D₃	—	7	2	no	—
33	C₂²	—	21	1	no	—
34	C₄	—	21	3	no	—
35	C₄	C₂×D₂₁	1	3	yes	—
36	C₃	Q₈×D₇	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	21	2	no	—
38	C₂	C₂²×D₂₁	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.