Subgroups — C₉×C₄₇×D₃₇ #44531056

Order 31302.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₄₇×D₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃₇×C₄₇	C₂×C₃	1	1	yes	characteristic
4	C₄₇×D₃₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₃₇×C₄₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₉×C₄₇	—	37	1	no	maximal, Hall
7	C₉×D₃₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₉×C₄₇	D₃₇	1	1	yes	characteristic, direct product factor, Hall
9	C₉×C₃₇	C₂×C₄₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₄₇	—	37	1	no	—
11	C₃×D₃₇	C₃×C₄₇	1	1	yes	characteristic
12	C₃×C₄₇	C₃×D₃₇	1	1	yes	characteristic
13	C₃×C₃₇	C₂×C₃×C₄₇	1	1	yes	characteristic
14	C₂×C₄₇	—	37	1	no	Hall
15	D₃₇	C₉×C₄₇	1	1	yes	characteristic, direct product factor, Hall
16	C₄₇	C₉×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	C₂×C₉×C₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	37	1	no	Hall
19	C₉	C₄₇×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	37	1	no	—
21	C₃	C₃×C₄₇×D₃₇	1	1	yes	characteristic
22	C₂	—	37	1	no	Sylow

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.