Subgroups — C₄₁⋊(D₄₉⋊C₉) #49116262

Order 36162.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₄₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₂₀₀₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₁×C₄₉	C₂×C₃	1	1	yes	characteristic
4	C₄₁⋊(D₇⋊C₉)	—	7	1	no	maximal
5	D₂₀₀₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₄₁×C₇⋊C₉	—	7	1	no	—
7	C₄₁×C₄₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₂₈₇	—	7	1	no	—
9	D₄₉⋊C₉	—	41	1	no	maximal, Hall
10	C₃×C₇×C₄₁	AGL(1,𝔽₇)	1	1	yes	characteristic
11	C₉×D₄₁	—	49	1	no	Hall
12	D₂₈₇	—	7	1	no	—
13	C₄₉⋊C₉	D₄₁	1	1	yes	characteristic, complemented, Hall
14	C₉×C₄₁	—	49	1	no	Hall
15	C₃×D₄₉	—	41	1	no	—
16	C₇×C₄₁	D₇⋊C₉	1	1	yes	characteristic
17	C₃×D₄₁	—	49	1	no	—
18	C₃×C₄₉	C₃×D₄₁	1	1	yes	characteristic
19	D₇⋊C₉	—	287	1	no	—
20	C₃×C₄₁	D₄₉⋊C₃	1	1	yes	characteristic
21	D₄₉	—	41	1	no	Hall
22	D₄₁	—	49	1	no	Hall
23	C₇⋊C₉	—	7	1	no	—
24	C₄₉	C₉×D₄₁	1	1	yes	characteristic, complemented, Sylow
25	C₃×D₇	—	287	1	no	—
26	C₄₁	D₄₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₇	ΓL(1,𝔽₈)⋊D₄₁	1	1	yes	characteristic
28	C₂×C₉	—	2009	1	no	Hall
29	D₇	—	287	1	no	—
30	C₉	—	49	1	no	Sylow
31	C₇	C₄₁⋊(D₇⋊C₉)	1	1	yes	characteristic
32	C₂×C₃	—	2009	1	no	—
33	C₃	C₄₁⋊(D₄₉⋊C₃)	1	1	yes	characteristic
34	C₂	—	2009	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.