Subgroups — C₃×#26042797 #46853513

Order 34914.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19154123	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#26042797	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	#19154123	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₂₃²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₂₃⋊C₁₁	—	23	1	no	maximal
7	C₃×AGL(1,𝔽₂₃)	—	23	1	no	maximal
8	C₂₃×D₂₃	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₃×C₂₃⋊C₁₁	—	23	1	no	—
10	C₃×C₂₃⋊C₁₁	—	23	1	no	—
11	C₂₃²	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₂₃⋊C₁₁	—	23	1	no	—
13	AGL(1,𝔽₂₃)	—	23	1	no	—
14	C₂₃⋊C₁₁	—	23	1	no	—
15	C₂₃⋊C₁₁	—	23	1	no	—
16	C₂×C₃×C₂₃	—	23	1	no	—
17	C₃×D₂₃	C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
18	C₃×C₂₃	—	22	1	no	—
19	C₃×C₂₃	AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented
20	C₃×C₂₃	C₂×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
21	C₂×C₃×C₁₁	—	529	1	no	Hall
22	C₂×C₂₃	—	23	1	no	—
23	D₂₃	C₃×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
24	C₃×C₁₁	—	529	1	no	Hall
25	C₂₃	—	22	1	no	—
26	C₂₃	C₃×AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented
27	C₂₃	C₂×C₃×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
28	C₂×C₁₁	—	529	1	no	Hall
29	C₁₁	—	529	1	no	Sylow
30	C₂×C₃	—	23	1	no	Hall
31	C₃	#26042797	1	1	yes	characteristic, direct product factor, Sylow
32	C₂	—	23	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#26042797
commutator, cosocle, hypocenter	C₂₃²	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₂₃²	C₂×C₁₁
LCS	G ▷ C₂₃²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#19154123	C₂	semidirect
2. #26042797	C₃	direct (N × H)
3. #19154123	C₂×C₃	semidirect
4. C₃×C₂₃×D₂₃	C₁₁	semidirect
5. C₃×C₂₃²	C₂×C₁₁	semidirect
8. C₂₃×D₂₃	C₃×C₁₁	semidirect
11. C₂₃²	C₂×C₃×C₁₁	semidirect
17. C₃×D₂₃	C₂₃⋊C₁₁	semidirect
19. C₃×C₂₃	AGL(1,𝔽₂₃)	semidirect
20. C₃×C₂₃	C₂×C₂₃⋊C₁₁	semidirect
23. D₂₃	C₃×C₂₃⋊C₁₁	semidirect
26. C₂₃	C₃×AGL(1,𝔽₂₃)	semidirect
27. C₂₃	C₂×C₃×C₂₃⋊C₁₁	semidirect
31. C₃	#26042797	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×#19154123	2
#26042797	3
C₃×C₂₃×D₂₃	11
C₂×C₃×C₂₃⋊C₁₁	23
C₃×AGL(1,𝔽₂₃)	23

Subgroups — C3×#26042797 #46853513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#26042797 #46853513