Subgroups — C₂₃×#11925895 #42123720

Order 27830.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#10597243	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	C₂₃×C₁₁⋊C₅	—	22	5	no	—
9	#11925895	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	#10597243	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₁×C₂₃	—	11	1	no	—
12	D₁₁×C₂₃	C₁₁⋊C₅	1	1	yes	characteristic, complemented
13	C₁₁×C₂₃	—	2	5	no	—
14	C₁₁×C₂₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
15	C₁₁×C₂₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
16	C₁₁×D₁₁	C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₂₃	—	121	1	no	Hall
18	C₁₁²	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
19	C₅×C₂₃	—	121	1	no	Hall
20	C₂×C₁₁⋊C₅	—	11	1	no	—
21	AGL(1,𝔽₁₁)	—	11	1	no	—
22	C₁₁⋊C₅	—	11	1	no	—
23	C₁₁⋊C₅	—	11	1	no	—
24	C₁₁⋊C₅	—	22	5	no	—
25	C₂×C₂₃	—	11	1	no	Hall
26	C₂₃	#11925895	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	—	11	1	no	—
28	D₁₁	C₂₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
29	C₁₁	—	2	5	no	—
30	C₁₁	C₂×C₂₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
31	C₁₁	C₂₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
32	C₂×C₅	—	121	1	no	Hall
33	C₅	—	121	1	no	Sylow
34	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	#11925895
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×#10597243	C₂	semidirect
2. C₁₁×D₁₁×C₂₃	C₅	semidirect
3. C₁₁²×C₂₃	C₂×C₅	semidirect
9. #11925895	C₂₃	direct (N × H)
10. #10597243	C₂×C₂₃	semidirect
12. D₁₁×C₂₃	C₁₁⋊C₅	semidirect
14. C₁₁×C₂₃	AGL(1,𝔽₁₁)	semidirect
15. C₁₁×C₂₃	C₂×C₁₁⋊C₅	semidirect
16. C₁₁×D₁₁	C₅×C₂₃	semidirect
18. C₁₁²	C₂×C₅×C₂₃	semidirect
26. C₂₃	#11925895	direct (N × H)
28. D₁₁	C₂₃×C₁₁⋊C₅	semidirect
30. C₁₁	C₂×C₂₃×C₁₁⋊C₅	semidirect
31. 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×#10597243	2
C₁₁×D₁₁×C₂₃	5
C₂₃×AGL(1,𝔽₁₁)	11
C₂×C₂₃×C₁₁⋊C₅	11
#11925895	23

Subgroups — C23×#11925895 #42123720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11925895 #42123720