Subgroups — Q₈×C₇⋊C₉ #92595

Order 504.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇⋊C₉	C₂	1	3	yes	maximal
2	C₃×C₇×Q₈	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇⋊C₉	C₂²	1	1	yes	characteristic
4	C₃×C₄×C₇	C₂×C₃	1	3	yes	—
5	Q₈×C₉	—	7	1	no	maximal, Hall
6	C₇⋊C₉	Q₈	1	1	yes	characteristic, direct product factor, Hall
7	C₇×Q₈	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
9	C₄×C₉	—	7	3	no	—
10	C₄×C₇	C₂×C₉	1	3	yes	—
11	C₃×Q₈	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₃×C₇	C₃×Q₈	1	1	yes	characteristic
13	C₂×C₉	—	7	1	no	—
14	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
15	C₃×C₄	C₂×ΓL(1,𝔽₈)	1	3	yes	—
16	C₉	—	7	1	no	Sylow
17	Q₈	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₇	Q₈×C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
20	C₄	C₂×C₇⋊C₉	1	3	yes	—
21	C₃	Q₈×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₂	C₂²×C₇⋊C₉	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.