Subgroups — D₇×D₉ #6969

Order 252.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₇	—	3	1	no	maximal
5	C₇×C₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁	—	3	1	no	—
7	C₃×D₇	D₃	1	1	yes	characteristic
8	D₃×C₇	—	3	1	no	—
9	C₂×D₉	—	7	1	no	maximal, Hall
10	C₂×D₇	—	9	1	no	Hall
11	C₃×C₇	C₂×D₃	1	1	yes	characteristic
12	C₂×C₉	—	7	1	no	—
13	D₉	—	7	1	no	—
14	D₉	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₇	—	9	1	no	—
16	D₇	—	9	1	no	—
17	D₇	D₉	1	1	yes	characteristic, direct product factor
18	C₂×D₃	—	21	1	no	—
19	C₉	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
20	C₇	C₂×D₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃	—	7	1	no	—
22	D₃	—	3	1	no	—
23	D₃	—	21	1	no	—
24	C₂²	—	63	1	no	Sylow
25	C₃	D₃×D₇	1	1	yes	characteristic
26	C₂	—	7	1	no	—
27	C₂	—	9	1	no	—
28	C₂	—	63	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉	C₂²
Frattini	C₃	D₃×D₇
socle	C₃×C₇	C₂×D₃
LCS	G ▷ C₇×C₉
UCS	C₁

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.