Subgroups — C₃×#24925951 #45657528

Order 32634.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇⋊D₂₅₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#24925951	C₃	1	3	yes	maximal, direct product factor
4	C₃₇×#3861	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×ΓL(1,𝔽₈)⋊D₃₇	—	7	8	no	maximal
7	C₇⋊D₂₅₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×ΓL(1,𝔽₈)×C₃₇	—	7	8	no	—
9	C₇²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₂₅₉	—	7	8	no	—
11	ΓL(1,𝔽₈)⋊D₃₇	—	7	24	no	—
12	C₃×#64424	—	37	1	no	maximal, Hall
13	C₃×C₇×C₃₇	AGL(1,𝔽₇)	1	8	yes	complemented
14	ΓL(1,𝔽₈)×C₃₇	—	7	24	no	—
15	C₃²×D₃₇	—	49	1	no	Hall
16	D₂₅₉	—	7	8	no	—
17	C₃×#3861	D₃₇	1	1	yes	characteristic, complemented, Hall
18	C₃²×C₃₇	—	49	1	no	Hall
19	C₃×C₇⋊D₇	—	37	1	no	—
20	#64424	—	37	3	no	—
21	C₇×C₃₇	C₃×AGL(1,𝔽₇)	1	8	yes	complemented
22	C₃×D₃₇	—	49	3	no	—
23	C₃×D₃₇	—	49	1	no	—
24	C₃×C₇²	C₃×D₃₇	1	1	yes	characteristic, complemented
25	#3861	C₃×D₃₇	1	3	yes	complemented
26	C₃×AGL(1,𝔽₇)	—	259	8	no	—
27	C₃×C₃₇	—	49	3	no	—
28	C₃×C₃₇	#64424	1	1	yes	characteristic, complemented
29	C₇⋊D₇	—	37	1	no	Hall
30	D₃₇	—	49	1	no	Hall
31	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
32	C₇²	C₃²×D₃₇	1	1	yes	characteristic, complemented, Sylow
33	C₃×D₇	—	259	8	no	—
34	AGL(1,𝔽₇)	—	259	24	no	—
35	C₃₇	C₃×#64424	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	ΓL(1,𝔽₈)⋊D₃₇	1	8	yes	complemented
37	ΓL(1,𝔽₈)	—	7	24	no	—
38	C₂×C₃²	—	1813	1	no	Hall
39	D₇	—	259	8	no	—
40	C₃²	—	49	1	no	Sylow
41	C₇	C₃×ΓL(1,𝔽₈)⋊D₃₇	1	8	yes	complemented
42	C₂×C₃	—	1813	3	no	—
43	C₂×C₃	—	1813	1	no	—
44	C₃	—	49	3	no	—
45	C₃	#24925951	1	1	yes	characteristic, direct product factor
46	C₂	—	1813	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#24925951
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×C₃₇×#3861	C₂	semidirect
2. C₃×C₇⋊D₂₅₉	C₃	semidirect
3. #24925951	C₃	direct (N × H)
4. C₃₇×#3861	C₂×C₃	semidirect
5. C₃×C₇²×C₃₇	C₂×C₃	semidirect
7. C₇⋊D₂₅₉	C₃²	semidirect
9. C₇²×C₃₇	C₂×C₃²	semidirect
13. C₃×C₇×C₃₇	AGL(1,𝔽₇)	semidirect
17. C₃×#3861	D₃₇	semidirect
21. C₇×C₃₇	C₃×AGL(1,𝔽₇)	semidirect
24. C₃×C₇²	C₃×D₃₇	semidirect
25. #3861	C₃×D₃₇	semidirect
28. C₃×C₃₇	#64424	semidirect
32. C₇²	C₃²×D₃₇	semidirect
35. C₃₇	C₃×#64424	semidirect
36. C₃×C₇	ΓL(1,𝔽₈)⋊D₃₇	semidirect
41. C₇	C₃×ΓL(1,𝔽₈)⋊D₃₇	semidirect
45. C₃	#24925951	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×C₃₇×#3861	2
C₃×C₇⋊D₂₅₉	3
#24925951	3
C₃×ΓL(1,𝔽₈)⋊D₃₇	7
C₃×#64424	37

Subgroups — C3×#24925951 #45657528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#24925951 #45657528