Subgroups — C₃×D₄₀₇₁ #37567673

Order 24426.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₀₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₃₅₇	—	3	1	no	maximal
4	C₃×C₂₃×C₅₉	—	2	1	no	—
5	C₃×C₂₃×C₅₉	D₃	1	1	yes	characteristic, complemented
6	C₃×C₂₃×C₅₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₃₅₇	—	3	1	no	Hall
8	C₂₃×C₅₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₇₇	—	23	1	no	maximal, Hall
10	C₃²×C₅₉	D₂₃	1	1	yes	characteristic, complemented, Hall
11	C₃×D₆₉	—	59	1	no	maximal, Hall
12	D₁₇₇	—	23	1	no	—
13	C₃×D₅₉	—	69	1	no	—
14	C₃²×C₂₃	D₅₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅₉	—	2	1	no	—
16	C₃×C₅₉	C₃×D₂₃	1	1	yes	characteristic, complemented
17	C₃×C₅₉	D₆₉	1	1	yes	characteristic, complemented
18	D₆₉	—	59	1	no	—
19	C₃×D₂₃	—	177	1	no	—
20	D₅₉	—	69	1	no	Hall
21	C₃×C₂₃	—	2	1	no	—
22	C₃×C₂₃	C₃×D₅₉	1	1	yes	characteristic, complemented
23	C₃×C₂₃	D₁₇₇	1	1	yes	characteristic, complemented
24	C₅₉	C₃×D₆₉	1	1	yes	characteristic, complemented, Sylow
25	D₂₃	—	177	1	no	Hall
26	C₂₃	C₃×D₁₇₇	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1357	1	no	Hall
28	C₃²	D₁₃₅₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	4071	1	no	—
30	D₃	—	1357	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₃₅₇	1	1	yes	characteristic, complemented
33	C₃	D₄₀₇₁	1	1	yes	characteristic, direct product factor
34	C₂	—	4071	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₄₀₇₁
commutator, cosocle, hypocenter	C₃×C₂₃×C₅₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃×C₅₉	C₂
LCS	G ▷ C₃×C₂₃×C₅₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₃×C₅₉	C₂	semidirect
2. D₄₀₇₁	C₃	direct (N × H)
5. C₃×C₂₃×C₅₉	D₃	semidirect
6. C₃×C₂₃×C₅₉	C₂×C₃	semidirect
8. C₂₃×C₅₉	C₃×D₃	semidirect
10. C₃²×C₅₉	D₂₃	semidirect
14. C₃²×C₂₃	D₅₉	semidirect
16. C₃×C₅₉	C₃×D₂₃	semidirect
17. C₃×C₅₉	D₆₉	semidirect
22. C₃×C₂₃	C₃×D₅₉	semidirect
23. C₃×C₂₃	D₁₇₇	semidirect
24. C₅₉	C₃×D₆₉	semidirect
26. C₂₃	C₃×D₁₇₇	semidirect
28. C₃²	D₁₃₅₇	semidirect
32. C₃	C₃×D₁₃₅₇	semidirect
33. C₃	D₄₀₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₃×C₅₉	2
D₄₀₇₁	3
C₃×D₁₃₅₇	3
C₃×D₁₇₇	23
C₃×D₆₉	59

Subgroups — C3×D4071 #37567673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄₀₇₁ #37567673