Subgroups — C₃×C₂₃×D₁₇₇ #37567671

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	C₂₃×D₁₇₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂₃×D₅₉	—	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	C₂₃×D₅₉	—	3	1	no	Hall
8	C₂₃×C₅₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₇₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₅₉	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₃×D₃×C₂₃	—	59	1	no	maximal, Hall
12	D₁₇₇	C₃×C₂₃	1	1	yes	characteristic, direct product factor
13	C₃×D₅₉	—	3	1	no	—
14	C₃²×C₂₃	D₅₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅₉	—	2	1	no	—
16	C₃×C₅₉	D₃×C₂₃	1	1	yes	characteristic, complemented
17	C₃×C₅₉	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
18	C₂×C₃×C₂₃	—	177	1	no	—
19	D₃×C₂₃	—	59	1	no	—
20	D₅₉	—	3	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, direct product factor
24	C₅₉	C₃×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₂₃	—	177	1	no	Hall
26	C₂₃	C₃×D₁₇₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×D₃	—	59	1	no	Hall
28	C₃²	C₂₃×D₅₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	177	1	no	—
30	D₃	—	59	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×C₂₃×D₅₉	1	1	yes	characteristic, complemented
33	C₃	C₂₃×D₁₇₇	1	1	yes	characteristic, direct product factor
34	C₂	—	177	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₁₇₇
commutator, cosocle, hypocenter	C₃×C₅₉	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃×C₅₉	C₂
LCS	G ▷ C₃×C₅₉
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₃×C₅₉	C₂	semidirect
2. C₂₃×D₁₇₇	C₃	direct (N × H)
5. C₃×C₂₃×C₅₉	D₃	semidirect
6. C₃×C₂₃×C₅₉	C₂×C₃	semidirect
8. C₂₃×C₅₉	C₃×D₃	semidirect
9. C₃×D₁₇₇	C₂₃	direct (N × H)
10. C₃²×C₅₉	C₂×C₂₃	semidirect
12. D₁₇₇	C₃×C₂₃	direct (N × H)
14. C₃²×C₂₃	D₅₉	semidirect
16. C₃×C₅₉	D₃×C₂₃	semidirect
17. C₃×C₅₉	C₂×C₃×C₂₃	semidirect
22. C₃×C₂₃	C₃×D₅₉	semidirect
23. C₃×C₂₃	D₁₇₇	direct (N × H)
24. C₅₉	C₃×D₃×C₂₃	semidirect
26. C₂₃	C₃×D₁₇₇	direct (N × H)
28. C₃²	C₂₃×D₅₉	semidirect
32. C₃	C₃×C₂₃×D₅₉	semidirect
33. C₃	C₂₃×D₁₇₇	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
C₂₃×D₁₇₇	3
C₃×C₂₃×D₅₉	3
C₃×D₁₇₇	23
C₃×D₃×C₂₃	59

Subgroups — C3×C23×D177 #37567671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₃×D₁₇₇ #37567671