Subgroups — C₁₇×D₆₅₁ #36348993

Order 22134.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₂₁₇	—	3	1	no	maximal, Hall
3	C₇×C₁₇×C₃₁	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₉₃	—	7	1	no	maximal, Hall
5	C₃×C₁₇×C₃₁	D₇	1	1	yes	characteristic, complemented, Hall
6	D₆₅₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×D₃₁	—	21	1	no	Hall
8	C₁₇×D₂₁	—	31	1	no	maximal, Hall
9	C₃×C₇×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₁₇×C₃₁	D₂₁	1	1	yes	characteristic, complemented, Hall
11	D₂₁₇	—	3	1	no	Hall
12	C₃×C₇×C₁₇	D₃₁	1	1	yes	characteristic, complemented, Hall
13	D₇×C₁₇	—	93	1	no	Hall
14	C₇×C₃₁	D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
15	D₉₃	—	7	1	no	Hall
16	C₇×C₁₇	D₉₃	1	1	yes	characteristic, complemented, Hall
17	D₃×C₁₇	—	217	1	no	Hall
18	C₃×C₃₁	D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
19	D₃₁	—	21	1	no	Hall
20	C₃×C₁₇	D₂₁₇	1	1	yes	characteristic, complemented, Hall
21	D₂₁	—	31	1	no	Hall
22	C₂×C₁₇	—	651	1	no	Hall
23	C₃₁	C₁₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	C₁₇×D₃₁	1	1	yes	characteristic, complemented, Hall
25	C₁₇	D₆₅₁	1	1	yes	characteristic, direct product factor, Sylow
26	D₇	—	93	1	no	Hall
27	C₇	C₁₇×D₉₃	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	217	1	no	Hall
29	C₃	C₁₇×D₂₁₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	651	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₆₅₁
commutator, cosocle, hypocenter	C₃×C₇×C₃₁	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₃₁	C₂
LCS	G ▷ C₃×C₇×C₃₁
UCS	C₁ ◁ 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.