Subgroups — #23780935

Order 10404.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₁₇⋊D₁₇))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃⋊(C₁₇⋊D₁₇)	—	6	2	no	—
4	#11923883	—	9	1	no	maximal, Hall
5	C₃×C₁₇²	—	2	2	no	—
6	#10597479	—	17	18	no	maximal
7	C₁₇⋊D₁₇	—	9	1	no	—
8	C₃⋊D₅₁	—	17	18	no	—
9	C₁₇²	#157	1	1	yes	characteristic, complemented, Sylow
10	C₃²×C₁₇	#595	1	18	yes	complemented
11	D₅₁	—	102	36	no	—
12	#595	—	153	18	no	—
13	C₃×C₁₇	—	2	36	no	—
14	#157	—	289	1	no	Hall
15	D₁₇	—	153	18	no	—
16	C₃⋊D₃	—	289	1	no	—
17	C₁₇	#10597479	1	18	yes	complemented
18	C₃²	#11923883	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	1734	2	no	—
20	C₄	—	2601	1	no	Sylow
21	C₃	—	2	2	no	—
22	C₂	—	2601	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₇²	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₁₇⋊D₁₇))	C₂
LCS	G ▷ C₃²×C₁₇²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.