Subgroups — C₂₃×#11925898 #42123723

Order 27830.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#10597244	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₁₁×C₂₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂₃×AGL(1,𝔽₁₁)	—	11	1	no	maximal
5	C₂×C₂₃×C₁₁⋊C₅	—	11	1	no	maximal
6	C₂₃×C₁₁⋊C₅	—	11	1	no	—
7	C₂₃×C₁₁⋊C₅	—	11	1	no	—
8	#11925898	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	#10597244	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₂₃	—	11	1	no	—
11	D₁₁×C₂₃	C₁₁⋊C₅	1	1	yes	characteristic, complemented
12	C₁₁×C₂₃	—	10	1	no	—
13	C₁₁×C₂₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
14	C₁₁×C₂₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
15	C₁₁×D₁₁	C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₂₃	—	121	1	no	Hall
17	C₁₁²	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
18	C₅×C₂₃	—	121	1	no	Hall
19	C₂×C₁₁⋊C₅	—	11	1	no	—
20	AGL(1,𝔽₁₁)	—	11	1	no	—
21	C₁₁⋊C₅	—	11	1	no	—
22	C₁₁⋊C₅	—	11	1	no	—
23	C₂×C₂₃	—	11	1	no	Hall
24	C₂₃	#11925898	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₁	—	11	1	no	—
26	D₁₁	C₂₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
27	C₁₁	—	10	1	no	—
28	C₁₁	C₂×C₂₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
29	C₁₁	C₂₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
30	C₂×C₅	—	121	1	no	Hall
31	C₅	—	121	1	no	Sylow
32	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	#11925898
commutator, cosocle, hypocenter	C₁₁²	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₁²×C₂₃	C₂×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×#10597244	C₂	semidirect
2. C₁₁×D₁₁×C₂₃	C₅	semidirect
3. C₁₁²×C₂₃	C₂×C₅	semidirect
8. #11925898	C₂₃	direct (N × H)
9. #10597244	C₂×C₂₃	semidirect
11. D₁₁×C₂₃	C₁₁⋊C₅	semidirect
13. C₁₁×C₂₃	AGL(1,𝔽₁₁)	semidirect
14. C₁₁×C₂₃	C₂×C₁₁⋊C₅	semidirect
15. C₁₁×D₁₁	C₅×C₂₃	semidirect
17. C₁₁²	C₂×C₅×C₂₃	semidirect
24. C₂₃	#11925898	direct (N × H)
26. D₁₁	C₂₃×C₁₁⋊C₅	semidirect
28. C₁₁	C₂×C₂₃×C₁₁⋊C₅	semidirect
29. C₁₁	C₂₃×AGL(1,𝔽₁₁)	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#10597244	2
C₁₁×D₁₁×C₂₃	5
C₂₃×AGL(1,𝔽₁₁)	11
C₂×C₂₃×C₁₁⋊C₅	11
#11925898	23

Subgroups — C23×#11925898 #42123723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11925898 #42123723