Subgroups — C₃×ΓL(1,𝔽₂₅) #3727

Order 144.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×M₁₆	—	3	1	no	maximal
5	ΓL(1,𝔽₂₅)	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×D₃	C₄	1	1	yes	characteristic
7	C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₃×Dic₃	C₄	1	1	yes	characteristic
9	C₂×C₃×C₄	—	3	1	no	—
10	C₄×D₃	C₂×C₃	1	1	yes	characteristic
11	C₃×C₈	—	2	1	no	—
12	C₃×C₈	—	3	1	no	—
13	C₃×C₈	D₃	1	1	yes	characteristic, complemented
14	C₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
15	C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
17	C₃×D₃	—	2	1	no	—
18	M₁₆	—	3	1	no	Sylow
19	C₂²×C₃	—	3	1	no	—
20	C₂×D₃	C₃×C₄	1	1	yes	characteristic
21	C₃×C₄	—	2	1	no	—
22	C₃×C₄	—	3	1	no	—
23	C₃×C₄	C₂×D₃	1	1	yes	characteristic
24	C₃×C₄	C₂²×C₃	1	1	yes	characteristic
25	Dic₃	C₃×C₄	1	1	yes	characteristic
26	C₃²	M₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄	—	3	1	no	—
28	C₈	—	3	1	no	—
29	C₈	C₃×D₃	1	1	yes	characteristic, complemented
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	—	6	1	no	—
32	C₂×C₃	C₄×D₃	1	1	yes	characteristic
33	C₂×C₃	C₂×C₃×C₄	1	1	yes	characteristic
34	D₃	—	2	1	no	—
35	C₂²	—	3	1	no	—
36	C₄	—	3	1	no	—
37	C₄	C₂×C₃×D₃	1	1	yes	characteristic
38	C₃	—	2	1	no	—
39	C₃	ΓL(1,𝔽₂₅)	1	1	yes	characteristic, direct product factor
40	C₃	C₃×M₁₆	1	1	yes	characteristic, complemented
41	C₂	—	6	1	no	—
42	C₂	C₃×C₄×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₃
commutator	C₂×C₃	C₂×C₃×C₄
Frattini	C₄	C₂×C₃×D₃
Fitting	C₃²×C₈	C₂
socle	C₂×C₃²	C₂×C₄
prime radical	C₂×C₃×D₃	C₄
cosocle	C₃×C₄	C₂²×C₃
hypercenter	C₃×C₈	D₃
hypocenter	C₃	C₃×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃²×C₈	C₂	semidirect
3. C₃×C₃⋊C₈	C₂	semidirect
5. ΓL(1,𝔽₂₅)	C₃	direct (N × H)
13. C₃×C₈	D₃	semidirect
14. C₃×C₈	C₂×C₃	semidirect
15. C₃⋊C₈	C₂×C₃	semidirect
26. C₃²	M₁₆	semidirect
29. C₈	C₃×D₃	semidirect
39. C₃	ΓL(1,𝔽₂₅)	direct (N × H)
40. C₃	C₃×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₃	2
C₃²×C₈	2
C₃×C₃⋊C₈	2
C₃×M₁₆	3
ΓL(1,𝔽₂₅)	3

Subgroups — C3×ΓL(1,𝔽25) #3727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×ΓL(1,𝔽₂₅) #3727