Subgroups — C₄₃×C₃⋊(C₃⋊#595) #39911708

Order 26316.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₇×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×C₃⋊#595	—	3	4	no	maximal
3	C₃²×C₁₇×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₇×C₄₃	D₃	1	4	yes	—
5	C₄₃×#595	—	9	1	no	Hall
6	C₃×C₁₇×C₄₃	Dic₃	1	4	yes	complemented
7	C₃⋊Dic₃×C₄₃	—	17	1	no	maximal, Hall
8	D₁₇×C₄₃	C₃⋊D₃	1	1	yes	characteristic
9	C₂×C₃²×C₄₃	—	17	1	no	—
10	C₁₇×C₄₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
11	C₃⋊(C₃⋊#595)	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	Dic₃×C₄₃	—	51	4	no	—
13	C₃²×C₄₃	#595	1	1	yes	characteristic, complemented, Hall
14	C₃²×D₁₇	C₂×C₄₃	1	1	yes	characteristic
15	C₂×C₃×C₄₃	—	17	4	no	—
16	C₃⋊#595	—	3	4	no	—
17	C₄×C₄₃	—	153	1	no	Hall
18	C₃²×C₁₇	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄₃	C₃⋊#595	1	4	yes	complemented
20	C₃×D₁₇	D₃×C₄₃	1	4	yes	—
21	C₂×C₄₃	—	17	1	no	—
22	#595	—	9	1	no	Hall
23	C₃×C₁₇	Dic₃×C₄₃	1	4	yes	complemented
24	C₄₃	C₃⋊(C₃⋊#595)	1	1	yes	characteristic, direct product factor, Sylow
25	C₃⋊Dic₃	—	17	1	no	Hall
26	D₁₇	C₃⋊D₃×C₄₃	1	1	yes	characteristic
27	C₂×C₃²	—	17	1	no	—
28	C₁₇	C₃⋊Dic₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	51	4	no	—
30	C₃²	C₄₃×#595	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	17	4	no	—
32	C₄	—	153	1	no	Sylow
33	C₃	C₄₃×C₃⋊#595	1	4	yes	complemented
34	C₂	—	17	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.