Subgroups — #11717849

Order 816.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#3624	C₂	1	2	yes	maximal, complemented
3	#63247	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₁₇	C₄	1	1	yes	characteristic
5	C₃×Dic₁₇	C₄	1	1	yes	characteristic
6	C₃×Dic₁₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₇	D₃	1	1	yes	characteristic
8	#3624	—	3	2	no	—
9	C₂×C₃×C₁₇	—	2	1	no	—
10	C₂×C₃×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₇	Dic₃	1	1	yes	characteristic
12	Dic₁₇	Dic₃	1	1	yes	characteristic
13	Dic₁₇	C₂×D₃	1	1	yes	characteristic
14	C₃×C₁₇	M₁₆	1	1	yes	characteristic, complemented, Hall
15	#208	—	17	1	no	maximal, Hall
16	C₂×C₁₇	—	2	1	no	—
17	C₂×C₁₇	C₂×Dic₃	1	1	yes	characteristic
18	C₂×C₃×C₄	—	17	1	no	—
19	C₃⋊C₈	—	17	2	no	—
20	C₁₇	#208	1	1	yes	characteristic, complemented, Sylow
21	M₁₆	—	51	1	no	Sylow
22	C₂²×C₃	#595	1	1	yes	characteristic
23	C₃×C₄	—	17	1	no	—
24	C₃×C₄	—	17	1	no	—
25	C₂×C₄	—	17	1	no	—
26	C₈	—	51	2	no	—
27	C₂×C₃	—	2	1	no	—
28	C₂×C₃	C₂×#595	1	1	yes	characteristic
29	C₂²	C₃⋊#595	1	1	yes	characteristic
30	C₄	—	17	1	no	—
31	C₄	—	17	1	no	—
32	C₃	#63247	1	1	yes	characteristic, complemented, Sylow
33	C₂	—	2	1	no	—
34	C₂	C₂×C₃⋊#595	1	1	yes	characteristic

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.