Subgroups — C₂×C₃×#14268592 #24925613

Order 10836.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#11744749	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#14268592	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#14268592	C₃	1	3	yes	maximal, direct product factor
5	C₃×#11744749	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₇×C₄₃	C₂×C₃	1	2	yes	complemented
8	C₂×#11744749	C₂×C₃	1	3	yes	complemented
9	#14268592	C₂×C₃	1	6	yes	direct product factor
10	C₂²×C₃×C₄₃⋊C₃	—	7	1	no	maximal, Hall
11	C₂×D₇×C₄₃	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented
13	#11744749	C₂²×C₃	1	3	yes	complemented
14	C₂×C₃×C₄₃⋊C₃	—	7	2	no	—
15	C₂×C₃×C₄₃⋊C₃	—	7	1	no	—
16	C₂×C₇×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented
17	D₇×C₄₃	C₂×C₃²	1	2	yes	complemented
18	C₂²×C₃×C₄₃	—	7	1	no	—
19	C₂²×C₄₃⋊C₃	—	7	3	no	—
20	C₃×C₄₃⋊C₃	—	7	1	no	Hall
21	C₇×C₄₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₄₃	—	7	2	no	—
23	C₂×C₃×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
24	C₂×C₄₃⋊C₃	—	7	6	no	—
25	C₂×C₄₃⋊C₃	—	7	3	no	—
26	C₂×C₃×AGL(1,𝔽₇)	—	43	1	no	maximal, Hall
27	C₂²×C₄₃	—	7	1	no	Hall
28	C₃×C₄₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
29	C₄₃⋊C₃	—	7	3	no	—
30	C₂×C₃×ΓL(1,𝔽₈)	—	43	1	no	—
31	C₃×AGL(1,𝔽₇)	—	43	2	no	—
32	C₂×C₄₃	—	7	2	no	—
33	C₂×C₄₃	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
34	C₂×C₃×D₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented
35	C₂×AGL(1,𝔽₇)	—	43	3	no	—
36	C₃×ΓL(1,𝔽₈)	—	43	1	no	Hall
37	C₄₃	C₂×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₇	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
39	C₃×D₇	C₂×C₄₃⋊C₃	1	2	yes	complemented
40	C₂×ΓL(1,𝔽₈)	—	43	3	no	—
41	AGL(1,𝔽₇)	—	43	6	no	—
42	C₂²×C₃²	—	301	1	no	Hall
43	C₂×D₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
44	C₃×C₇	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented
45	ΓL(1,𝔽₈)	—	43	3	no	—
46	C₂×C₃²	—	301	2	no	—
47	C₂×C₃²	—	301	1	no	—
48	C₂×C₇	C₂×C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented
49	D₇	C₂×C₃×C₄₃⋊C₃	1	2	yes	complemented
50	C₂²×C₃	—	7	1	no	—
51	C₂²×C₃	—	301	3	no	—
52	C₃²	—	301	1	no	Sylow
53	C₇	C₂²×C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃	—	7	2	no	—
55	C₂×C₃	—	301	6	no	—
56	C₂×C₃	—	301	3	no	—
57	C₂×C₃	#14268592	1	1	yes	characteristic, direct product factor
58	C₂²	—	7	1	no	Sylow
59	C₃	—	301	3	no	—
60	C₃	C₂×#14268592	1	1	yes	characteristic, direct product factor
61	C₂	—	7	2	no	—
62	C₂	C₃×#14268592	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#14268592
commutator, cosocle, hypocenter	C₇×C₄₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₄₃	C₂×C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#11744749	C₂	semidirect
2. C₃×#14268592	C₂	direct (N × H)
3. C₂×C₃×D₇×C₄₃	C₃	semidirect
4. C₂×#14268592	C₃	direct (N × H)
5. C₃×#11744749	C₂²	semidirect
6. C₂×C₃×C₇×C₄₃	C₂×C₃	semidirect
7. C₃×D₇×C₄₃	C₂×C₃	semidirect
8. C₂×#11744749	C₂×C₃	semidirect
9. #14268592	C₂×C₃	direct (N × H)
11. C₂×D₇×C₄₃	C₃²	semidirect
12. C₃×C₇×C₄₃	C₂²×C₃	semidirect
13. #11744749	C₂²×C₃	semidirect
16. C₂×C₇×C₄₃	C₂×C₃²	semidirect
17. D₇×C₄₃	C₂×C₃²	semidirect
21. C₇×C₄₃	C₂²×C₃²	semidirect
23. C₂×C₃×C₄₃	AGL(1,𝔽₇)	semidirect
28. C₃×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
33. C₂×C₄₃	C₃×AGL(1,𝔽₇)	semidirect
34. C₂×C₃×D₇	C₄₃⋊C₃	semidirect
37. C₄₃	C₂×C₃×AGL(1,𝔽₇)	semidirect
38. C₂×C₃×C₇	C₂×C₄₃⋊C₃	semidirect
39. C₃×D₇	C₂×C₄₃⋊C₃	semidirect
43. C₂×D₇	C₃×C₄₃⋊C₃	semidirect
44. C₃×C₇	C₂²×C₄₃⋊C₃	semidirect
48. C₂×C₇	C₂×C₃×C₄₃⋊C₃	semidirect
49. D₇	C₂×C₃×C₄₃⋊C₃	semidirect
53. C₇	C₂²×C₃×C₄₃⋊C₃	semidirect
57. C₂×C₃	#14268592	direct (N × H)
60. C₃	C₂×#14268592	direct (N × H)
62. C₂	C₃×#14268592	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#11744749	2
C₃×#14268592	2
C₂×C₃×D₇×C₄₃	3
C₂×#14268592	3
C₂²×C₃×C₄₃⋊C₃	7
C₂×C₃×AGL(1,𝔽₇)	43

Subgroups — C2×C3×#14268592 #24925613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#14268592 #24925613