Subgroups — C₃×#21462844 #37552885

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16840847	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#21462844	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₁×C₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	#16840847	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇₁⋊C₅	—	11	1	no	maximal, Hall
7	D₁₁×C₇₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇₁⋊C₅	—	11	1	no	Hall
9	C₁₁×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇₁⋊C₅	—	11	1	no	Hall
11	C₂×C₃×C₇₁	—	55	1	no	Hall
12	C₇₁⋊C₅	—	11	1	no	Hall
13	C₃×AGL(1,𝔽₁₁)	—	71	1	no	maximal, Hall
14	C₃×C₇₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁⋊C₅	—	71	1	no	Hall
16	C₂×C₇₁	—	55	1	no	Hall
17	AGL(1,𝔽₁₁)	—	71	1	no	Hall
18	C₇₁	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₁₁	C₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
20	C₁₁⋊C₅	—	71	1	no	Hall
21	C₃×C₁₁	C₂×C₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅	—	781	1	no	Hall
23	D₁₁	C₃×C₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅	—	781	1	no	Hall
25	C₁₁	C₂×C₃×C₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	781	1	no	Hall
27	C₂×C₃	—	55	1	no	Hall
28	C₅	—	781	1	no	Sylow
29	C₃	#21462844	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#21462844
commutator, cosocle, hypocenter	C₁₁×C₇₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₇₁	C₂×C₅
LCS	G ▷ C₁₁×C₇₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#16840847	C₂	semidirect
2. #21462844	C₃	direct (N × H)
3. C₃×D₁₁×C₇₁	C₅	semidirect
4. #16840847	C₂×C₃	semidirect
5. C₃×C₁₁×C₇₁	C₂×C₅	semidirect
7. D₁₁×C₇₁	C₃×C₅	semidirect
9. C₁₁×C₇₁	C₂×C₃×C₅	semidirect
14. C₃×C₇₁	AGL(1,𝔽₁₁)	semidirect
18. C₇₁	C₃×AGL(1,𝔽₁₁)	semidirect
19. C₃×D₁₁	C₇₁⋊C₅	semidirect
21. C₃×C₁₁	C₂×C₇₁⋊C₅	semidirect
23. D₁₁	C₃×C₇₁⋊C₅	semidirect
25. C₁₁	C₂×C₃×C₇₁⋊C₅	semidirect
29. C₃	#21462844	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×#16840847	2
#21462844	3
C₃×D₁₁×C₇₁	5
C₂×C₃×C₇₁⋊C₅	11
C₃×AGL(1,𝔽₁₁)	71

Subgroups — C3×#21462844 #37552885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21462844 #37552885