Subgroups — C₃×#23780570 #44527885

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#87704	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#23780570	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×D₂₄₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#87704	C₂×C₃	1	3	yes	complemented
5	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×(C₁₉⋊C₃)⋊D₁₃	—	7	1	no	maximal, Hall
7	C₇×D₂₄₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×#11716321	—	13	1	no	maximal, Hall
9	C₃×C₁₃×C₁₉⋊C₃	—	7	1	no	Hall
10	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×ΓL(1,𝔽₈)×D₁₃	—	19	1	no	maximal, Hall
12	C₃×D₂₄₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	(C₁₉⋊C₃)⋊D₁₃	—	7	3	no	—
14	C₃×#87704	D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₃×ΓL(1,𝔽₈)	—	19	1	no	Hall
16	C₃×C₇×D₁₉	—	13	1	no	—
17	#11716321	—	13	3	no	—
18	C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
19	C₁₃×C₁₉⋊C₃	—	7	3	no	—
20	C₃×C₇×D₁₃	—	19	1	no	—
21	ΓL(1,𝔽₈)×D₁₃	—	19	3	no	—
22	D₂₄₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented
24	#87704	C₃×D₁₃	1	3	yes	complemented
25	C₃×D₁₉⋊C₃	—	91	1	no	Hall
26	C₃×C₇×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
27	C₁₃×ΓL(1,𝔽₈)	—	19	3	no	—
28	C₇×D₁₉	—	13	1	no	Hall
29	C₁₃×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
30	C₃²×D₁₃	—	133	1	no	Hall
31	C₇×D₁₃	—	19	1	no	Hall
32	C₃×C₁₉⋊C₃	—	7	1	no	Hall
33	C₇×C₁₉	C₃²×D₁₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×ΓL(1,𝔽₈)	—	247	1	no	Hall
35	C₃²×C₁₃	—	133	1	no	Hall
36	C₃×D₁₉	—	13	1	no	—
37	D₁₉⋊C₃	—	91	3	no	—
38	C₇×C₁₃	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₃×D₁₃	—	19	1	no	—
40	C₃×D₁₃	—	133	3	no	—
41	C₃×ΓL(1,𝔽₈)	—	19	1	no	Hall
42	C₃×C₁₉	ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, complemented
43	C₁₉⋊C₃	—	7	3	no	—
44	C₂×C₃×C₇	—	247	1	no	—
45	C₂×ΓL(1,𝔽₈)	—	247	3	no	—
46	C₃×C₁₃	—	133	3	no	—
47	C₃×C₁₃	#11716321	1	1	yes	characteristic, complemented
48	D₁₉	—	13	1	no	Hall
49	D₁₃	—	19	1	no	Hall
50	C₃×C₇	(C₁₉⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₈)	—	19	3	no	—
52	C₁₉	C₃×ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃²	—	1729	1	no	Hall
54	C₂×C₇	—	247	1	no	Hall
55	C₁₃	C₃×#11716321	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	133	1	no	Sylow
57	C₇	C₃×(C₁₉⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃	—	1729	3	no	—
59	C₂×C₃	—	247	1	no	—
60	C₃	—	133	3	no	—
61	C₃	#23780570	1	1	yes	characteristic, direct product factor
62	C₂	—	247	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#23780570
commutator, cosocle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×#87704	C₂	semidirect
2. #23780570	C₃	direct (N × H)
3. C₃×C₇×D₂₄₇	C₃	semidirect
4. C₁₃×#87704	C₂×C₃	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₇×D₂₄₇	C₃²	semidirect
10. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
12. C₃×D₂₄₇	ΓL(1,𝔽₈)	semidirect
14. C₃×#87704	D₁₃	semidirect
18. C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
22. D₂₄₇	C₃×ΓL(1,𝔽₈)	semidirect
23. C₃×C₇×C₁₉	C₃×D₁₃	semidirect
24. #87704	C₃×D₁₃	semidirect
26. C₃×C₇×C₁₃	D₁₉⋊C₃	semidirect
29. C₁₃×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
33. C₇×C₁₉	C₃²×D₁₃	semidirect
38. C₇×C₁₃	C₃×D₁₉⋊C₃	semidirect
42. C₃×C₁₉	ΓL(1,𝔽₈)×D₁₃	semidirect
47. C₃×C₁₃	#11716321	semidirect
50. C₃×C₇	(C₁₉⋊C₃)⋊D₁₃	semidirect
52. C₁₉	C₃×ΓL(1,𝔽₈)×D₁₃	semidirect
55. C₁₃	C₃×#11716321	semidirect
57. C₇	C₃×(C₁₉⋊C₃)⋊D₁₃	semidirect
61. C₃	#23780570	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×C₁₃×#87704	2
#23780570	3
C₃×C₇×D₂₄₇	3
C₃×(C₁₉⋊C₃)⋊D₁₃	7
C₃×#11716321	13
C₃×ΓL(1,𝔽₈)×D₁₃	19

Subgroups — C3×#23780570 #44527885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23780570 #44527885