Subgroups — C₇₁×C₂²⋊(C₇⋊C₉) #31822020

Order 17892.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇×C₇₁	C₃	1	1	yes	maximal, characteristic
2	C₇⋊C₉×C₇₁	—	4	1	no	maximal, Hall
3	C₂×C₃×C₇×C₇₁	—	3	1	no	—
4	C₂²⋊C₉×C₇₁	—	7	1	no	maximal, Hall
5	C₂²×C₇×C₇₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×C₇₁	A₄	1	1	yes	characteristic
7	C₂×C₇×C₇₁	—	3	1	no	—
8	C₂²×C₃×C₇₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
9	C₉×C₇₁	—	28	1	no	Hall
10	C₇×C₇₁	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇₁	—	3	1	no	—
12	C₂²×C₇₁	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
13	C₂²⋊(C₇⋊C₉)	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₇₁	C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₂×C₇₁	—	3	1	no	—
16	C₂²×C₃×C₇	C₃×C₇₁	1	1	yes	characteristic
17	C₇₁	C₂²⋊(C₇⋊C₉)	1	1	yes	characteristic, direct product factor, Sylow
18	C₇⋊C₉	—	4	1	no	Hall
19	C₂×C₃×C₇	—	3	1	no	—
20	C₂²⋊C₉	—	7	1	no	Hall
21	C₂²×C₇	C₉×C₇₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇	A₄×C₇₁	1	1	yes	characteristic
23	C₂×C₇	—	3	1	no	—
24	C₂²×C₃	ΓL(1,𝔽₈)×C₇₁	1	1	yes	characteristic
25	C₉	—	28	1	no	Sylow
26	C₇	C₂²⋊C₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	C₇⋊C₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₇₁×C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₂	—	3	1	no	—

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.