Subgroups — C₂²×D₅₁ #88008

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×D₅₁	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₁₇	—	3	1	no	maximal, Hall
4	C₂×C₃×C₁₇	C₂²	1	3	yes	complemented
5	D₅₁	C₂²	1	4	yes	direct product factor
6	C₂²×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₂×D₁₇	—	3	6	no	—
8	C₃×C₁₇	C₂³	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₇	C₂×D₃	1	3	yes	complemented
10	D₁₇	—	3	4	no	—
11	C₂²×D₃	—	17	1	no	maximal, Hall
12	C₁₇	C₂²×D₃	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₃	D₁₇	1	1	yes	characteristic, complemented
14	C₂×D₃	—	17	6	no	—
15	C₂³	—	51	1	no	Sylow
16	C₂×C₃	C₂×D₁₇	1	3	yes	complemented
17	D₃	—	17	4	no	—
18	C₂²	—	51	6	no	—
19	C₂²	D₅₁	1	1	yes	characteristic, direct product factor
20	C₃	C₂²×D₁₇	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	51	4	no	—
22	C₂	C₂×D₅₁	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₂²

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.