Subgroups — C₄₉×D₃₂₁ #44538020

Order 31458.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₉×D₁₀₇	—	3	1	no	maximal, Hall
3	C₄₉×C₁₀₇	D₃	1	1	yes	characteristic, complemented, Hall
4	C₇×D₃₂₁	C₇	1	1	yes	maximal, characteristic
5	C₃×C₇×C₁₀₇	C₂×C₇	1	1	yes	characteristic
6	C₇×D₁₀₇	—	3	1	no	—
7	C₇×C₁₀₇	D₃×C₇	1	1	yes	characteristic
8	D₃₂₁	C₄₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₀₇	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
10	D₃×C₄₉	—	107	1	no	maximal, Hall
11	D₁₀₇	—	3	1	no	Hall
12	C₃×C₄₉	D₁₀₇	1	1	yes	characteristic, complemented, Hall
13	C₁₀₇	D₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₄₉	—	321	1	no	Hall
15	C₄₉	D₃₂₁	1	1	yes	characteristic, direct product factor, Sylow
16	D₃×C₇	—	107	1	no	—
17	C₃×C₇	C₇×D₁₀₇	1	1	yes	characteristic
18	C₂×C₇	—	321	1	no	—
19	C₇	C₇×D₃₂₁	1	1	yes	characteristic
20	D₃	—	107	1	no	Hall
21	C₃	C₄₉×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	321	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.