Subgroups — C₃×#24925974 #45657520

Order 32634.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19129588	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	#24925974	C₃	1	3	yes	maximal, direct product factor
4	#19129588	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×#13095531	—	7	8	no	maximal
7	C₇²×D₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×#11715913	—	7	8	no	—
9	C₇²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×D₃₇	ΓL(1,𝔽₈)	1	8	yes	complemented
11	#13095531	—	7	24	no	—
12	C₂×C₃×#3861	—	37	1	no	maximal, Hall
13	C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
14	#11715913	—	7	24	no	—
15	C₃×D₃₇⋊C₃	—	49	1	no	Hall
16	C₇×D₃₇	C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
17	C₃×#3861	—	37	1	no	Hall
18	C₃×C₃₇⋊C₃	—	49	1	no	Hall
19	C₂×C₃×C₇²	—	37	1	no	—
20	C₂×#3861	—	37	3	no	—
21	C₇×C₃₇	C₂×C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
22	C₃×D₃₇	#3861	1	1	yes	characteristic, complemented
23	D₃₇⋊C₃	—	49	3	no	—
24	C₃×C₇²	D₃₇⋊C₃	1	1	yes	characteristic, complemented
25	#3861	—	37	3	no	—
26	C₂×C₃×ΓL(1,𝔽₈)	—	259	8	no	—
27	C₃×C₃₇	C₂×#3861	1	1	yes	characteristic, complemented
28	C₃₇⋊C₃	—	49	3	no	—
29	C₂×C₇²	—	37	1	no	Hall
30	D₃₇	C₃×#3861	1	1	yes	characteristic, complemented, Hall
31	C₃×ΓL(1,𝔽₈)	—	259	8	no	—
32	C₇²	C₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₇	—	37	8	no	—
34	C₂×ΓL(1,𝔽₈)	—	259	24	no	—
35	C₃₇	C₂×C₃×#3861	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	#13095531	1	8	yes	complemented
37	ΓL(1,𝔽₈)	—	259	24	no	—
38	C₂×C₃²	—	1813	1	no	Hall
39	C₂×C₇	—	37	8	no	—
40	C₃²	—	1813	1	no	Sylow
41	C₇	C₃×#13095531	1	8	yes	complemented
42	C₂×C₃	—	1813	3	no	—
43	C₂×C₃	—	37	1	no	—
44	C₃	—	1813	3	no	—
45	C₃	#24925974	1	1	yes	characteristic, direct product factor
46	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#24925974
commutator, cosocle, hypocenter	C₇²×C₃₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₇²×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#19129588	C₂	semidirect
2. C₃×C₇²×D₃₇	C₃	semidirect
3. #24925974	C₃	direct (N × H)
4. #19129588	C₂×C₃	semidirect
5. C₃×C₇²×C₃₇	C₂×C₃	semidirect
7. C₇²×D₃₇	C₃²	semidirect
9. C₇²×C₃₇	C₂×C₃²	semidirect
10. C₃×C₇×D₃₇	ΓL(1,𝔽₈)	semidirect
13. C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	semidirect
16. C₇×D₃₇	C₃×ΓL(1,𝔽₈)	semidirect
21. C₇×C₃₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
22. C₃×D₃₇	#3861	semidirect
24. C₃×C₇²	D₃₇⋊C₃	semidirect
27. C₃×C₃₇	C₂×#3861	semidirect
30. D₃₇	C₃×#3861	semidirect
32. C₇²	C₃×D₃₇⋊C₃	semidirect
35. C₃₇	C₂×C₃×#3861	semidirect
36. C₃×C₇	#13095531	semidirect
41. C₇	C₃×#13095531	semidirect
45. C₃	#24925974	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×#19129588	2
C₃×C₇²×D₃₇	3
#24925974	3
C₃×#13095531	7
C₂×C₃×#3861	37

Subgroups — C3×#24925974 #45657520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#24925974 #45657520