Subgroups — C₂²×C₃×D₁₇ #88006

Order 408.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₁₇	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₁₇	C₂²	1	3	yes	complemented
5	C₃×D₁₇	C₂²	1	4	yes	direct product factor
6	C₂²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×D₁₇	C₂×C₃	1	6	yes	direct product factor
8	C₃×C₁₇	C₂³	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₇	C₂²×C₃	1	3	yes	complemented
10	D₁₇	C₂²×C₃	1	4	yes	direct product factor
11	C₂³×C₃	—	17	1	no	maximal, Hall
12	C₁₇	C₂³×C₃	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₃	—	17	6	no	—
14	C₂²×C₃	D₁₇	1	1	yes	characteristic, direct product factor
15	C₂³	—	17	1	no	Sylow
16	C₂×C₃	—	17	4	no	—
17	C₂×C₃	C₂×D₁₇	1	3	yes	direct product factor
18	C₂²	—	17	6	no	—
19	C₂²	C₃×D₁₇	1	1	yes	characteristic, direct product factor
20	C₃	C₂²×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	—	17	4	no	—
22	C₂	C₂×C₃×D₁₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₃

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.