Subgroups — #23780937

Order 10404.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×D₅₁	—	6	2	no	—
4	#11923885	—	9	1	no	maximal, Hall
5	C₃×C₁₇²	—	2	2	no	—
6	#10597480	—	17	1	no	maximal
7	#10597479	—	17	1	no	maximal
8	C₁₇×D₁₇	—	9	1	no	—
9	C₃⋊D₅₁	D₁₇	1	1	yes	characteristic
10	C₁₇×C₃⋊D₃	—	17	1	no	—
11	C₁₇²	#157	1	1	yes	characteristic, complemented, Sylow
12	C₃²×C₁₇	—	4	4	no	—
13	C₃²×C₁₇	Dic₁₇	1	1	yes	characteristic, complemented
14	C₃²×C₁₇	#595	1	1	yes	characteristic, complemented
15	D₅₁	—	6	2	no	—
16	D₃×C₁₇	—	102	2	no	—
17	#595	—	153	1	no	—
18	Dic₁₇	—	153	1	no	—
19	C₃×C₁₇	—	2	2	no	—
20	C₃×C₁₇	—	2	2	no	—
21	C₃×C₁₇	—	4	16	no	—
22	#157	—	289	1	no	Hall
23	C₂×C₁₇	—	153	1	no	—
24	D₁₇	—	9	1	no	—
25	C₃⋊D₃	—	17	1	no	—
26	C₁₇	—	4	4	no	—
27	C₁₇	#10597479	1	1	yes	characteristic, complemented
28	C₁₇	#10597480	1	1	yes	characteristic, complemented
29	C₃²	#11923885	1	1	yes	characteristic, complemented, Sylow
30	D₃	—	102	2	no	—
31	C₄	—	2601	1	no	Sylow
32	C₃	—	2	2	no	—
33	C₂	—	153	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₇²	C₄
prime radical, cosocle	C₁₇×C₃⋊D₅₁	C₂
LCS	G ▷ C₃²×C₁₇²
UCS	C₁

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