Subgroups — C₁₇×D₉×C₇₃ #36375232

Order 22338.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₇×C₇₃	—	3	1	no	maximal
3	C₃×C₁₇×C₇₃	D₃	1	1	yes	characteristic
4	C₂×C₁₇×C₇₃	—	9	1	no	Hall
5	D₉×C₇₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₇₃	D₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₇₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
8	D₃×C₇₃	—	3	1	no	—
9	C₁₇×D₉	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇₃	D₃×C₁₇	1	1	yes	characteristic
11	C₉×C₁₇	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇₃	—	9	1	no	Hall
13	D₃×C₁₇	—	3	1	no	—
14	C₇₃	C₁₇×D₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₇	D₃×C₇₃	1	1	yes	characteristic
16	C₂×C₁₇	—	9	1	no	Hall
17	D₉	C₁₇×C₇₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₇	D₉×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₉	C₂×C₁₇×C₇₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3	1	no	—
21	C₃	D₃×C₁₇×C₇₃	1	1	yes	characteristic
22	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₇₃	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₇×C₇₃
Frattini	C₃	D₃×C₁₇×C₇₃
Fitting	C₉×C₁₇×C₇₃	C₂
socle	C₃×C₁₇×C₇₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₇×C₇₃

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.