Subgroups — C₃×#16813404 #24925508

Order 10836.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#11744748	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#16813404	C₃	1	3	yes	maximal, direct product factor
4	C₃×#11744748	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₄₃	C₂×C₃	1	1	yes	characteristic
6	C₂×#11744748	C₂×C₃	1	3	yes	—
7	C₃×C₄×C₄₃⋊C₃	—	7	1	no	maximal, Hall
8	Dic₇×C₄₃	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented
10	#11744748	C₃×C₄	1	3	yes	complemented
11	C₂×C₃×C₄₃⋊C₃	—	7	1	no	—
12	C₂×C₇×C₄₃	C₂×C₃²	1	1	yes	characteristic
13	C₃×C₄×C₄₃	—	7	1	no	—
14	C₄×C₄₃⋊C₃	—	7	3	no	—
15	C₃×C₄₃⋊C₃	—	7	1	no	Hall
16	C₇×C₄₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic
18	C₂×C₄₃⋊C₃	—	7	3	no	—
19	C₃×ΓL(1,𝔽₈)⋊C₄	—	43	1	no	maximal, Hall
20	C₄×C₄₃	—	7	1	no	Hall
21	C₃×C₄₃	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented
22	C₄₃⋊C₃	—	7	3	no	—
23	C₂×C₃×ΓL(1,𝔽₈)	—	43	1	no	—
24	C₂×C₄₃	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic
25	C₃×Dic₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented
26	ΓL(1,𝔽₈)⋊C₄	—	43	3	no	—
27	C₃×ΓL(1,𝔽₈)	—	43	1	no	Hall
28	C₄₃	C₃×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃×C₇	C₂×C₄₃⋊C₃	1	1	yes	characteristic
30	C₂×ΓL(1,𝔽₈)	—	43	3	no	—
31	C₃²×C₄	—	301	1	no	Hall
32	Dic₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₇	C₄×C₄₃⋊C₃	1	1	yes	characteristic, complemented
34	ΓL(1,𝔽₈)	—	43	3	no	—
35	C₂×C₃²	—	301	1	no	—
36	C₂×C₇	C₂×C₃×C₄₃⋊C₃	1	1	yes	characteristic
37	C₃×C₄	—	7	1	no	—
38	C₃×C₄	—	301	3	no	—
39	C₃²	—	301	1	no	Sylow
40	C₇	C₃×C₄×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	301	3	no	—
42	C₂×C₃	#14268591	1	1	yes	characteristic
43	C₄	—	7	1	no	Sylow
44	C₃	—	301	3	no	—
45	C₃	#16813404	1	1	yes	characteristic, direct product factor
46	C₂	C₃×#14268591	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#14268591
commutator, hypocenter	C₇×C₄₃	C₃²×C₄
Frattini	C₂	C₃×#14268591
Fitting, socle	C₂×C₃×C₇×C₄₃	C₂×C₃
prime radical	C₂×C₃×#11744748	C₂
cosocle	C₂×C₇×C₄₃	C₂×C₃²
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₇×C₄₃	C₃	semidirect
3. #16813404	C₃	direct (N × H)
4. C₃×#11744748	C₄	semidirect
8. Dic₇×C₄₃	C₃²	semidirect
9. C₃×C₇×C₄₃	C₃×C₄	semidirect
10. #11744748	C₃×C₄	semidirect
16. C₇×C₄₃	C₃²×C₄	semidirect
21. C₃×C₄₃	ΓL(1,𝔽₈)⋊C₄	semidirect
25. C₃×Dic₇	C₄₃⋊C₃	semidirect
28. C₄₃	C₃×ΓL(1,𝔽₈)⋊C₄	semidirect
32. Dic₇	C₃×C₄₃⋊C₃	semidirect
33. C₃×C₇	C₄×C₄₃⋊C₃	semidirect
40. C₇	C₃×C₄×C₄₃⋊C₃	semidirect
45. C₃	#16813404	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×#11744748	2
C₃×Dic₇×C₄₃	3
#16813404	3
C₃×C₄×C₄₃⋊C₃	7
C₃×ΓL(1,𝔽₈)⋊C₄	43

Subgroups — C3×#16813404 #24925508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#16813404 #24925508