Subgroups — C₃×C₇×#13095275 #44567162

Order 32193.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#13095275	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₇²×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₇₃⋊C₃	—	7	1	no	maximal
4	C₃×#13095275	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇²×C₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×C₇₃	—	3	2	no	—
7	C₃×C₇×C₇₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
8	C₃×C₇×C₇₃	C₃×C₇	1	1	yes	characteristic, complemented
9	#13095275	C₃×C₇	1	3	yes	direct product factor
10	C₇×C₇₃⋊C₃	—	7	3	no	—
11	C₃×C₇₃⋊C₃	—	7	1	no	Hall
12	C₇×C₇₃	—	3	2	no	—
13	C₇×C₇₃	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₇×C₇₃	C₃²×C₇	1	1	yes	characteristic, complemented
15	C₃×C₇×ΓL(1,𝔽₈)	—	73	1	no	maximal, Hall
16	C₃×C₇₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
17	C₇₃⋊C₃	—	7	3	no	—
18	C₃×C₇²	C₇₃⋊C₃	1	1	yes	characteristic, complemented
19	C₇×ΓL(1,𝔽₈)	—	73	3	no	—
20	C₇₃	C₃×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
21	C₃²×C₇	—	511	1	no	—
22	C₃×ΓL(1,𝔽₈)	—	73	1	no	—
23	C₇²	C₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	—	3	2	no	—
25	C₃×C₇	—	511	3	no	—
26	C₃×C₇	C₇×C₇₃⋊C₃	1	1	yes	characteristic, complemented
27	C₃×C₇	#13095275	1	1	yes	characteristic, direct product factor
28	ΓL(1,𝔽₈)	—	73	3	no	—
29	C₃²	—	511	1	no	Sylow
30	C₇	—	3	2	no	—
31	C₇	C₃×#13095275	1	1	yes	characteristic, direct product factor
32	C₇	C₃×C₇×C₇₃⋊C₃	1	1	yes	characteristic, complemented
33	C₃	—	511	3	no	—
34	C₃	C₇×#13095275	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₇	#13095275
commutator, cosocle, hypocenter	C₇×C₇₃	C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₇₃	C₃
LCS	G ▷ C₇×C₇₃
UCS	C₁ ◁ C₃×C₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#13095275	C₃	direct (N × H)
2. C₃×C₇²×C₇₃	C₃	semidirect
4. C₃×#13095275	C₇	direct (N × H)
5. C₇²×C₇₃	C₃²	semidirect
7. C₃×C₇×C₇₃	ΓL(1,𝔽₈)	semidirect
8. C₃×C₇×C₇₃	C₃×C₇	semidirect
9. #13095275	C₃×C₇	direct (N × H)
13. C₇×C₇₃	C₃×ΓL(1,𝔽₈)	semidirect
14. C₇×C₇₃	C₃²×C₇	semidirect
16. C₃×C₇₃	C₇×ΓL(1,𝔽₈)	semidirect
18. C₃×C₇²	C₇₃⋊C₃	semidirect
20. C₇₃	C₃×C₇×ΓL(1,𝔽₈)	semidirect
23. C₇²	C₃×C₇₃⋊C₃	semidirect
26. C₃×C₇	C₇×C₇₃⋊C₃	semidirect
27. C₃×C₇	#13095275	direct (N × H)
31. C₇	C₃×#13095275	direct (N × H)
32. C₇	C₃×C₇×C₇₃⋊C₃	semidirect
34. C₃	C₇×#13095275	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#13095275	3
C₃×C₇²×C₇₃	3
C₃×C₇×C₇₃⋊C₃	7
C₃×#13095275	7
C₃×C₇×ΓL(1,𝔽₈)	73

Subgroups — C3×C7×#13095275 #44567162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×#13095275 #44567162