Subgroups — C₇₃×Dic₁₁₁ #44569408

Order 32412.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₇×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×Dic₃₇	—	3	1	no	maximal, Hall
3	C₃×C₃₇×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₇₃	D₃	1	1	yes	characteristic
5	C₃₇×C₇₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₃×C₇₃	—	37	1	no	maximal, Hall
7	Dic₁₁₁	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₇₃	D₃₇	1	1	yes	characteristic
9	C₄×C₇₃	—	111	1	no	Hall
10	C₂×C₃×C₃₇	C₂×C₇₃	1	1	yes	characteristic
11	C₃×C₇₃	Dic₃₇	1	1	yes	characteristic, complemented, Hall
12	Dic₃₇	—	3	1	no	Hall
13	C₂×C₇₃	D₁₁₁	1	1	yes	characteristic
14	C₃×C₃₇	C₄×C₇₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃₇	D₃×C₇₃	1	1	yes	characteristic
16	C₇₃	Dic₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	Dic₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	37	1	no	Hall
19	C₂×C₃	C₇₃×D₃₇	1	1	yes	characteristic
20	C₄	—	111	1	no	Sylow
21	C₃	C₇₃×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₇₃×D₁₁₁	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.