Subgroups — C₃×C₄×D₁₇ #87979

Order 408.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₁₇	C₂²	1	1	yes	characteristic
6	C₃×D₁₇	C₄	1	2	yes	direct product factor
7	C₂×D₁₇	C₂×C₃	1	1	yes	characteristic
8	C₄×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
9	Dic₁₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₁₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇	C₂²×C₃	1	1	yes	characteristic
12	D₁₇	C₃×C₄	1	2	yes	direct product factor
13	C₂×C₃×C₄	—	17	1	no	maximal, Hall
14	C₁₇	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₃	—	17	1	no	—
16	C₃×C₄	—	17	1	no	—
17	C₃×C₄	D₁₇	1	1	yes	characteristic, direct product factor
18	C₂×C₄	—	17	1	no	Sylow
19	C₂×C₃	—	17	2	no	—
20	C₂×C₃	C₂×D₁₇	1	1	yes	characteristic
21	C₂²	—	17	1	no	—
22	C₄	—	17	1	no	—
23	C₄	C₃×D₁₇	1	1	yes	characteristic, direct product factor
24	C₃	C₄×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂	—	17	2	no	—
26	C₂	C₂×C₃×D₁₇	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.