Subgroups — C₃×C₂²⋊#87705 #18012325

Order 4788.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊#87705	C₃	1	3	yes	maximal, direct product factor
3	C₃×#87705	—	4	1	no	maximal, Hall
4	C₂×C₃×C₇×C₁₉	—	3	1	no	—
5	C₃×C₂²⋊(C₁₉⋊C₃)	—	7	1	no	maximal, Hall
6	C₂²×C₇×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₁₉	A₄	1	1	yes	characteristic, complemented
8	#87705	—	4	3	no	—
9	C₂×C₇×C₁₉	—	3	1	no	—
10	C₃×C₂²⋊ΓL(1,𝔽₈)	—	19	1	no	maximal, Hall
11	C₂²×C₃×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
12	C₂²⋊(C₁₉⋊C₃)	—	7	3	no	—
13	C₃×C₁₉⋊C₃	—	28	1	no	Hall
14	C₇×C₁₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₉	—	3	1	no	—
16	C₂²×C₃×C₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
17	C₂²⋊ΓL(1,𝔽₈)	—	19	3	no	—
18	C₂²×C₁₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
19	C₃×ΓL(1,𝔽₈)	—	76	1	no	Hall
20	C₃×C₁₉	C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
21	C₁₉⋊C₃	—	28	3	no	—
22	C₂×C₃×C₇	—	3	1	no	—
23	C₂×C₁₉	—	3	1	no	—
24	C₃×A₄	—	133	1	no	Hall
25	C₂²×C₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, complemented
27	ΓL(1,𝔽₈)	—	76	3	no	—
28	C₁₉	C₃×C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₇	—	3	1	no	—
30	C₂²×C₃	#87705	1	1	yes	characteristic, complemented
31	A₄	—	133	3	no	—
32	C₃²	—	532	1	no	Sylow
33	C₇	C₃×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂²	C₃×#87705	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	532	3	no	—
37	C₃	C₂²⋊#87705	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₂²⋊#87705
commutator, cosocle, hypocenter	C₂²×C₇×C₁₉	C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇×C₁₉	C₃
LCS	G ▷ C₂²×C₇×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₇×C₁₉	C₃	semidirect
2. C₂²⋊#87705	C₃	direct (N × H)
6. C₂²×C₇×C₁₉	C₃²	semidirect
7. C₃×C₇×C₁₉	A₄	semidirect
11. C₂²×C₃×C₁₉	ΓL(1,𝔽₈)	semidirect
14. C₇×C₁₉	C₃×A₄	semidirect
16. C₂²×C₃×C₇	C₁₉⋊C₃	semidirect
18. C₂²×C₁₉	C₃×ΓL(1,𝔽₈)	semidirect
20. C₃×C₁₉	C₂²⋊ΓL(1,𝔽₈)	semidirect
25. C₂²×C₇	C₃×C₁₉⋊C₃	semidirect
26. C₃×C₇	C₂²⋊(C₁₉⋊C₃)	semidirect
28. C₁₉	C₃×C₂²⋊ΓL(1,𝔽₈)	semidirect
30. C₂²×C₃	#87705	semidirect
33. C₇	C₃×C₂²⋊(C₁₉⋊C₃)	semidirect
35. C₂²	C₃×#87705	semidirect
37. C₃	C₂²⋊#87705	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₇×C₁₉	3
C₂²⋊#87705	3
C₃×#87705	4
C₃×C₂²⋊(C₁₉⋊C₃)	7
C₃×C₂²⋊ΓL(1,𝔽₈)	19

Subgroups — C3×C22⋊#87705 #18012325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊#87705 #18012325