Subgroups — (C₇⋊C₉)⋊D₂₈₉ #49138709

Order 36414.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊C₉×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₂₀₂₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₂₈₉	C₂×C₃	1	1	yes	characteristic
4	C₉×D₂₈₉	—	7	1	no	maximal, Hall
5	D₂₀₂₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₉×C₂₈₉	—	7	1	no	Hall
7	C₁₇⋊(D₇⋊C₉)	—	17	1	no	maximal
8	C₇×C₂₈₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×D₂₈₉	—	7	1	no	—
10	C₁₇×C₇⋊C₉	D₁₇	1	1	yes	characteristic
11	C₃×C₂₈₉	AGL(1,𝔽₇)	1	1	yes	characteristic
12	C₃×D₁₁₉	—	17	1	no	—
13	D₂₈₉	—	7	1	no	Hall
14	C₃×C₇×C₁₇	C₃×D₁₇	1	1	yes	characteristic
15	C₉×D₁₇	—	119	1	no	—
16	C₂₈₉	D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
17	D₁₁₉	—	17	1	no	—
18	C₉×C₁₇	—	7	1	no	—
19	D₇⋊C₉	—	289	1	no	Hall
20	C₇×C₁₇	C₉×D₁₇	1	1	yes	characteristic
21	C₃×D₁₇	—	119	1	no	—
22	C₇⋊C₉	D₂₈₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₇	C₁₇⋊AGL(1,𝔽₇)	1	1	yes	characteristic
24	C₃×D₇	—	289	1	no	—
25	D₁₇	—	119	1	no	—
26	C₃×C₇	C₃×D₂₈₉	1	1	yes	characteristic
27	C₂×C₉	—	2023	1	no	Hall
28	C₁₇	C₁₇⋊(D₇⋊C₉)	1	1	yes	characteristic
29	D₇	—	289	1	no	Hall
30	C₉	—	7	1	no	Sylow
31	C₇	C₉×D₂₈₉	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃	—	2023	1	no	—
33	C₃	ΓL(1,𝔽₈)⋊D₂₈₉	1	1	yes	characteristic
34	C₂	—	2023	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.