Subgroups — C₁₇×C₃⋊(C₃⋊#4223) #38737142

Order 25092.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×D₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₃⋊#4223	—	3	4	no	maximal
3	C₃²×C₁₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₄₁	D₃	1	4	yes	—
5	C₁₇×#4223	—	9	1	no	Hall
6	C₃×C₁₇×C₄₁	Dic₃	1	4	yes	complemented
7	C₃⋊(C₃⋊#4223)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×D₄₁	C₃⋊D₃	1	1	yes	characteristic
9	C₃²×D₄₁	C₂×C₁₇	1	1	yes	characteristic
10	C₁₇×C₄₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
11	C₁₇×C₃⋊Dic₃	—	41	1	no	maximal, Hall
12	C₃⋊#4223	—	3	4	no	—
13	C₃²×C₄₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₁₇	—	41	1	no	—
15	C₃×D₄₁	D₃×C₁₇	1	4	yes	—
16	Dic₃×C₁₇	—	123	4	no	—
17	#4223	—	9	1	no	Hall
18	C₃²×C₁₇	#4223	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄₁	Dic₃×C₁₇	1	4	yes	complemented
20	C₂×C₃×C₁₇	—	41	4	no	—
21	D₄₁	C₁₇×C₃⋊D₃	1	1	yes	characteristic
22	C₄×C₁₇	—	369	1	no	Hall
23	C₃×C₁₇	C₃⋊#4223	1	4	yes	complemented
24	C₄₁	C₁₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
25	C₃⋊Dic₃	—	41	1	no	Hall
26	C₂×C₁₇	—	41	1	no	—
27	C₂×C₃²	—	41	1	no	—
28	C₁₇	C₃⋊(C₃⋊#4223)	1	1	yes	characteristic, direct product factor, Sylow
29	Dic₃	—	123	4	no	—
30	C₃²	C₁₇×#4223	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	41	4	no	—
32	C₄	—	369	1	no	Sylow
33	C₃	C₁₇×C₃⋊#4223	1	4	yes	complemented
34	C₂	—	41	1	no	—

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.