Subgroups — C₃×C₄²×C₄₇ #72182201

Order 2256.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₄₇	C₂	1	3	yes	maximal
2	C₄²×C₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂²×C₃×C₄₇	C₂²	1	1	yes	characteristic
4	C₃×C₄×C₄₇	C₄	1	6	yes	direct product factor
5	C₂×C₄×C₄₇	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₄₇	C₂×C₄	1	3	yes	—
7	C₂²×C₄₇	C₂²×C₃	1	1	yes	characteristic
8	C₄×C₄₇	C₃×C₄	1	6	yes	direct product factor
9	C₃×C₄₇	C₄²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₄₇	C₂×C₃×C₄	1	3	yes	—
11	C₃×C₄²	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₄₇	C₃×C₄²	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₄	C₂×C₄₇	1	3	yes	—
14	C₄²	C₃×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₂²×C₃	C₂²×C₄₇	1	1	yes	characteristic
16	C₃×C₄	C₄×C₄₇	1	6	yes	direct product factor
17	C₂×C₄	C₂×C₃×C₄₇	1	3	yes	—
18	C₂×C₃	C₂×C₄×C₄₇	1	3	yes	—
19	C₂²	C₂²×C₃×C₄₇	1	1	yes	characteristic
20	C₄	C₃×C₄×C₄₇	1	6	yes	direct product factor
21	C₃	C₄²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₄×C₄₇	1	3	yes	—

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.