Subgroups — C₂×C₃×#15693073 #34089987

Order 19782.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15693073	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×#15693073	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₇×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
5	#15693073	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₁₅₇⋊C₃	—	7	1	no	maximal, Hall
7	C₂×C₇×C₁₅₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₅₇⋊C₃	—	7	1	no	Hall
9	C₇×C₁₅₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₅₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	C₂×C₁₅₇⋊C₃	—	7	3	no	—
12	C₃×C₁₅₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₁₅₇⋊C₃	—	7	3	no	—
14	C₂×C₁₅₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
15	C₁₅₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×ΓL(1,𝔽₈)	—	157	1	no	maximal, Hall
17	C₃×ΓL(1,𝔽₈)	—	157	1	no	Hall
18	C₂×C₃×C₇	C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
19	C₂×ΓL(1,𝔽₈)	—	157	3	no	—
20	C₃×C₇	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented
21	ΓL(1,𝔽₈)	—	157	3	no	—
22	C₂×C₃²	—	1099	1	no	Hall
23	C₂×C₇	C₃×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Hall
24	C₃²	—	1099	1	no	Sylow
25	C₇	C₂×C₃×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	1099	3	no	—
27	C₂×C₃	#15693073	1	1	yes	characteristic, direct product factor
28	C₃	—	1099	3	no	—
29	C₃	C₂×#15693073	1	1	yes	characteristic, direct product factor
30	C₂	C₃×#15693073	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	#15693073
commutator, cosocle, hypocenter	C₇×C₁₅₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₅₇	C₃
LCS	G ▷ C₇×C₁₅₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#15693073	C₂	direct (N × H)
2. C₂×#15693073	C₃	direct (N × H)
3. C₂×C₃×C₇×C₁₅₇	C₃	semidirect
4. C₃×C₇×C₁₅₇	C₂×C₃	semidirect
5. #15693073	C₂×C₃	direct (N × H)
7. C₂×C₇×C₁₅₇	C₃²	semidirect
9. C₇×C₁₅₇	C₂×C₃²	semidirect
10. C₂×C₃×C₁₅₇	ΓL(1,𝔽₈)	semidirect
12. C₃×C₁₅₇	C₂×ΓL(1,𝔽₈)	semidirect
14. C₂×C₁₅₇	C₃×ΓL(1,𝔽₈)	semidirect
15. C₁₅₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
18. C₂×C₃×C₇	C₁₅₇⋊C₃	semidirect
20. C₃×C₇	C₂×C₁₅₇⋊C₃	semidirect
23. C₂×C₇	C₃×C₁₅₇⋊C₃	semidirect
25. C₇	C₂×C₃×C₁₅₇⋊C₃	semidirect
27. C₂×C₃	#15693073	direct (N × H)
29. C₃	C₂×#15693073	direct (N × H)
30. C₂	C₃×#15693073	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#15693073	2
C₂×#15693073	3
C₂×C₃×C₇×C₁₅₇	3
C₂×C₃×C₁₅₇⋊C₃	7
C₂×C₃×ΓL(1,𝔽₈)	157

Subgroups — C2×C3×#15693073 #34089987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#15693073 #34089987