Subgroups — C₂×C₃×#14524190 #27188564

Order 12978.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14524190	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×#14524190	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₇×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#14524190	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₁₀₃⋊C₃	—	7	1	no	maximal, Hall
7	C₂×C₇×C₁₀₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₀₃⋊C₃	—	7	1	no	Hall
9	C₇×C₁₀₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₀₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	C₂×C₁₀₃⋊C₃	—	7	3	no	—
12	C₃×C₁₀₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₁₀₃⋊C₃	—	7	3	no	—
14	C₂×C₁₀₃	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×ΓL(1,𝔽₈)	—	103	1	no	maximal, Hall
16	C₁₀₃	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
17	C₃×ΓL(1,𝔽₈)	—	103	1	no	Hall
18	C₂×C₃×C₇	C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
19	C₂×ΓL(1,𝔽₈)	—	103	3	no	—
20	C₃×C₇	C₂×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
21	ΓL(1,𝔽₈)	—	103	3	no	—
22	C₂×C₃²	—	721	1	no	Hall
23	C₂×C₇	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Hall
24	C₃²	—	721	1	no	Sylow
25	C₇	C₂×C₃×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	721	3	no	—
27	C₂×C₃	#14524190	1	1	yes	characteristic, direct product factor
28	C₃	—	721	3	no	—
29	C₃	C₂×#14524190	1	1	yes	characteristic, direct product factor
30	C₂	C₃×#14524190	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	#14524190
commutator, cosocle, hypocenter	C₇×C₁₀₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₀₃	C₃
LCS	G ▷ C₇×C₁₀₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#14524190	C₂	direct (N × H)
2. C₂×#14524190	C₃	direct (N × H)
3. C₂×C₃×C₇×C₁₀₃	C₃	semidirect
4. C₃×C₇×C₁₀₃	C₂×C₃	semidirect
5. #14524190	C₂×C₃	direct (N × H)
7. C₂×C₇×C₁₀₃	C₃²	semidirect
9. C₇×C₁₀₃	C₂×C₃²	semidirect
10. C₂×C₃×C₁₀₃	ΓL(1,𝔽₈)	semidirect
12. C₃×C₁₀₃	C₂×ΓL(1,𝔽₈)	semidirect
14. C₂×C₁₀₃	C₃×ΓL(1,𝔽₈)	semidirect
16. C₁₀₃	C₂×C₃×ΓL(1,𝔽₈)	semidirect
18. C₂×C₃×C₇	C₁₀₃⋊C₃	semidirect
20. C₃×C₇	C₂×C₁₀₃⋊C₃	semidirect
23. C₂×C₇	C₃×C₁₀₃⋊C₃	semidirect
25. C₇	C₂×C₃×C₁₀₃⋊C₃	semidirect
27. C₂×C₃	#14524190	direct (N × H)
29. C₃	C₂×#14524190	direct (N × H)
30. C₂	C₃×#14524190	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×#14524190	2
C₂×#14524190	3
C₂×C₃×C₇×C₁₀₃	3
C₂×C₃×C₁₀₃⋊C₃	7
C₂×C₃×ΓL(1,𝔽₈)	103

Subgroups — C2×C3×#14524190 #27188564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#14524190 #27188564