Subgroups — C₂×A₄×C₁₇ #88005

Order 408.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₁₇	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₃×C₁₇	—	4	1	no	maximal
4	C₂²×C₁₇	—	3	1	no	—
5	C₂²×C₁₇	—	3	1	no	—
6	C₂²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₁₇	—	4	1	no	Hall
8	C₂×C₁₇	—	3	1	no	—
9	C₂×C₁₇	—	3	1	no	—
10	C₂×C₁₇	A₄	1	1	yes	characteristic, direct product factor
11	C₂×A₄	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₇	C₂×A₄	1	1	yes	characteristic, direct product factor, Sylow
13	A₄	C₂×C₁₇	1	1	yes	characteristic, direct product factor
14	C₂³	C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃	—	4	1	no	—
16	C₂²	—	3	1	no	—
17	C₂²	—	3	1	no	—
18	C₂²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
19	C₃	—	4	1	no	Sylow
20	C₂	—	3	1	no	—
21	C₂	—	3	1	no	—
22	C₂	A₄×C₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	A₄
commutator, cosocle, hypocenter	C₂²	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂³×C₁₇	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₁₇

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.