Subgroups — C₉₇×C₃⋊D₅₁ #44445895

Order 29682.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₉₇×D₅₁	—	3	4	no	maximal
3	C₃×C₁₇×C₉₇	D₃	1	4	yes	complemented
4	D₁₇×C₉₇	—	9	1	no	Hall
5	C₃⋊D₃×C₉₇	—	17	1	no	maximal, Hall
6	C₁₇×C₉₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₉₇	D₁₇	1	1	yes	characteristic, complemented, Hall
8	D₃×C₉₇	—	51	4	no	—
9	C₃⋊D₅₁	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₉₇	D₅₁	1	4	yes	complemented
11	C₂×C₉₇	—	153	1	no	Hall
12	C₃²×C₁₇	C₂×C₉₇	1	1	yes	characteristic, complemented, Hall
13	D₅₁	—	3	4	no	—
14	C₉₇	C₃⋊D₅₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₇	D₃×C₉₇	1	4	yes	complemented
16	D₁₇	—	9	1	no	Hall
17	C₃⋊D₃	—	17	1	no	Hall
18	C₁₇	C₃⋊D₃×C₉₇	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₇×C₉₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	51	4	no	—
21	C₃	C₉₇×D₅₁	1	4	yes	complemented
22	C₂	—	153	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉₇	C₃⋊D₅₁
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂×C₉₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₉₇	C₂
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₉₇

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.