Subgroups — C₃×C₄×#10620253 #21462952

Order 7812.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#10620253	C₂	1	1	yes	maximal, characteristic
2	C₄×#10620253	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₄×C₇×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#10620253	C₄	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₇×C₃₁	C₂×C₃	1	1	yes	characteristic
6	C₂×#10620253	C₂×C₃	1	3	yes	—
7	C₃×C₄×C₃₁⋊C₃	—	7	1	no	maximal, Hall
8	C₄×C₇×C₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented
10	#10620253	C₃×C₄	1	3	yes	direct product factor
11	C₂×C₃×C₃₁⋊C₃	—	7	1	no	—
12	C₂×C₇×C₃₁	C₂×C₃²	1	1	yes	characteristic
13	C₃×C₄×C₃₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₄×C₃₁⋊C₃	—	7	3	no	—
15	C₃×C₃₁⋊C₃	—	7	1	no	Hall
16	C₃×C₄×ΓL(1,𝔽₈)	—	31	1	no	maximal, Hall
17	C₇×C₃₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₃₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
19	C₂×C₃₁⋊C₃	—	7	3	no	—
20	C₂×C₃×ΓL(1,𝔽₈)	—	31	1	no	—
21	C₄×C₃₁	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
22	C₃×C₃₁	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₃₁⋊C₃	—	7	3	no	—
24	C₃×C₄×C₇	C₃₁⋊C₃	1	1	yes	characteristic, complemented
25	C₄×ΓL(1,𝔽₈)	—	31	3	no	—
26	C₃×ΓL(1,𝔽₈)	—	31	1	no	Hall
27	C₂×C₃₁	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	C₂×C₃×C₇	C₂×C₃₁⋊C₃	1	1	yes	characteristic
29	C₂×ΓL(1,𝔽₈)	—	31	3	no	—
30	C₃²×C₄	—	217	1	no	Hall
31	C₃₁	C₃×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
32	C₄×C₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₇	C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented
34	ΓL(1,𝔽₈)	—	31	3	no	—
35	C₂×C₃²	—	217	1	no	—
36	C₂×C₇	C₂×C₃×C₃₁⋊C₃	1	1	yes	characteristic
37	C₃×C₄	—	217	3	no	—
38	C₃×C₄	#10620253	1	1	yes	characteristic, direct product factor
39	C₃²	—	217	1	no	Sylow
40	C₇	C₃×C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	217	3	no	—
42	C₂×C₃	C₂×#10620253	1	1	yes	characteristic
43	C₄	C₃×#10620253	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	217	3	no	—
45	C₃	C₄×#10620253	1	1	yes	characteristic, direct product factor
46	C₂	C₂×C₃×#10620253	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	#10620253
commutator, hypocenter	C₇×C₃₁	C₃²×C₄
Frattini	C₂	C₂×C₃×#10620253
Fitting	C₃×C₄×C₇×C₃₁	C₃
socle	C₂×C₃×C₇×C₃₁	C₂×C₃
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#10620253	C₃	direct (N × H)
3. C₃×C₄×C₇×C₃₁	C₃	semidirect
4. C₃×#10620253	C₄	direct (N × H)
8. C₄×C₇×C₃₁	C₃²	semidirect
9. C₃×C₇×C₃₁	C₃×C₄	semidirect
10. #10620253	C₃×C₄	direct (N × H)
13. C₃×C₄×C₃₁	ΓL(1,𝔽₈)	semidirect
17. C₇×C₃₁	C₃²×C₄	semidirect
21. C₄×C₃₁	C₃×ΓL(1,𝔽₈)	semidirect
22. C₃×C₃₁	C₄×ΓL(1,𝔽₈)	semidirect
24. C₃×C₄×C₇	C₃₁⋊C₃	semidirect
31. C₃₁	C₃×C₄×ΓL(1,𝔽₈)	semidirect
32. C₄×C₇	C₃×C₃₁⋊C₃	semidirect
33. C₃×C₇	C₄×C₃₁⋊C₃	semidirect
38. C₃×C₄	#10620253	direct (N × H)
40. C₇	C₃×C₄×C₃₁⋊C₃	semidirect
43. C₄	C₃×#10620253	direct (N × H)
45. C₃	C₄×#10620253	direct (N × H)

Subgroups — C3×C4×#10620253 #21462952

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₄×#10620253 #21462952