Subgroups — C₇×Q₈⋊C₉ #92596

Order 504.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×Q₈	C₃	1	1	yes	maximal, characteristic
2	C₂×C₇×C₉	—	4	1	no	maximal
3	C₃×C₄×C₇	—	3	1	no	—
4	Q₈⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₉	—	4	1	no	Hall
6	C₇×Q₈	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₇	A₄	1	1	yes	characteristic
8	C₄×C₇	—	3	1	no	—
9	C₃×Q₈	C₃×C₇	1	1	yes	characteristic
10	C₃×C₇	SL(2,𝔽₃)	1	1	yes	characteristic
11	C₂×C₉	—	4	1	no	—
12	C₂×C₇	C₂²⋊C₉	1	1	yes	characteristic
13	C₃×C₄	—	3	1	no	—
14	C₉	—	4	1	no	Sylow
15	Q₈	C₇×C₉	1	1	yes	characteristic, complemented, Sylow
16	C₇	Q₈⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃	C₇×A₄	1	1	yes	characteristic
18	C₄	—	3	1	no	—
19	C₃	C₇×SL(2,𝔽₃)	1	1	yes	characteristic
20	C₂	C₇×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical, hypercenter	C₂×C₃×C₇	A₄
commutator, hypocenter	Q₈	C₇×C₉
Frattini	C₂×C₃	C₇×A₄
Fitting	C₃×C₇×Q₈	C₃
cosocle	C₃×Q₈	C₃×C₇
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂×C₃×C₇

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.