Subgroups — C₄×C₁₃×ΓL(1,𝔽₈)×C₂₉ #44539709

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×ΓL(1,𝔽₈)×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₁₃×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×ΓL(1,𝔽₈)×C₂₉	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₃×C₂₉	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₄×ΓL(1,𝔽₈)×C₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₃×C₂₉	—	7	1	no	—
9	C₄×C₁₃×C₂₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
10	C₂×ΓL(1,𝔽₈)×C₂₉	C₂×C₁₃	1	1	yes	characteristic
11	C₃×C₁₃×C₂₉	—	7	1	no	Hall
12	C₄×C₁₃×ΓL(1,𝔽₈)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₄×C₇×C₂₉	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₂₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	ΓL(1,𝔽₈)×C₂₉	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃×ΓL(1,𝔽₈)	C₂×C₂₉	1	1	yes	characteristic
17	C₂×C₇×C₂₉	C₂×C₃×C₁₃	1	1	yes	characteristic
18	C₁₃×C₂₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
19	C₄×C₇×C₁₃	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₄×C₂₉	—	7	1	no	Hall
21	C₁₃×ΓL(1,𝔽₈)	C₄×C₂₉	1	1	yes	characteristic, direct product factor, Hall
22	C₇×C₂₉	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	C₂×C₃×C₂₉	1	1	yes	characteristic
24	C₂×C₃×C₂₉	—	7	1	no	—
25	C₃×C₄×C₁₃	—	7	1	no	Hall
26	C₄×C₂₉	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
27	C₇×C₁₃	C₃×C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
28	C₃×C₂₉	—	7	1	no	Hall
29	C₄×ΓL(1,𝔽₈)	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₁₃	—	7	1	no	—
31	C₂×C₂₉	C₂×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
32	C₄×C₁₃	ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic, direct product factor, Hall
33	C₂×ΓL(1,𝔽₈)	C₂×C₁₃×C₂₉	1	1	yes	characteristic
34	C₃×C₁₃	—	7	1	no	Hall
35	C₂₉	C₄×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₇	C₃×C₁₃×C₂₉	1	1	yes	characteristic, complemented, Hall
37	C₂×C₁₃	C₂×ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic
38	ΓL(1,𝔽₈)	C₄×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇	C₂×C₃×C₁₃×C₂₉	1	1	yes	characteristic
40	C₁₃	C₄×ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₃×C₄	—	7	1	no	Hall
42	C₇	C₃×C₄×C₁₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	7	1	no	—
44	C₄	C₁₃×ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	7	1	no	Sylow
46	C₂	C₂×C₁₃×ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₁₃×C₂₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₃×C₄×C₁₃×C₂₉
Frattini	C₂	C₂×C₁₃×ΓL(1,𝔽₈)×C₂₉
Fitting	C₄×C₇×C₁₃×C₂₉	C₃
socle	C₂×C₇×C₁₃×C₂₉	C₂×C₃
prime radical	C₂×C₁₃×ΓL(1,𝔽₈)×C₂₉	C₂
cosocle	C₂×C₇	C₂×C₃×C₁₃×C₂₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₄×C₁₃×C₂₉

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₁₃×C₂₉	C₃	semidirect
3. C₁₃×ΓL(1,𝔽₈)×C₂₉	C₄	direct (N × H)
6. C₇×C₁₃×C₂₉	C₃×C₄	semidirect
7. C₄×ΓL(1,𝔽₈)×C₂₉	C₁₃	direct (N × H)
9. C₄×C₁₃×C₂₉	ΓL(1,𝔽₈)	direct (N × H)
12. C₄×C₁₃×ΓL(1,𝔽₈)	C₂₉	direct (N × H)
13. C₄×C₇×C₂₉	C₃×C₁₃	semidirect
15. ΓL(1,𝔽₈)×C₂₉	C₄×C₁₃	direct (N × H)
18. C₁₃×C₂₉	C₄×ΓL(1,𝔽₈)	direct (N × H)
19. C₄×C₇×C₁₃	C₃×C₂₉	semidirect
21. C₁₃×ΓL(1,𝔽₈)	C₄×C₂₉	direct (N × H)
22. C₇×C₂₉	C₃×C₄×C₁₃	semidirect
26. C₄×C₂₉	C₁₃×ΓL(1,𝔽₈)	direct (N × H)
27. C₇×C₁₃	C₃×C₄×C₂₉	semidirect
29. C₄×ΓL(1,𝔽₈)	C₁₃×C₂₉	direct (N × H)
32. C₄×C₁₃	ΓL(1,𝔽₈)×C₂₉	direct (N × H)
35. C₂₉	C₄×C₁₃×ΓL(1,𝔽₈)	direct (N × H)
36. C₄×C₇	C₃×C₁₃×C₂₉	semidirect
38. ΓL(1,𝔽₈)	C₄×C₁₃×C₂₉	direct (N × H)
40. C₁₃	C₄×ΓL(1,𝔽₈)×C₂₉	direct (N × H)
42. C₇	C₃×C₄×C₁₃×C₂₉	semidirect
44. C₄	C₁₃×ΓL(1,𝔽₈)×C₂₉	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×C₁₃×ΓL(1,𝔽₈)×C₂₉	2
C₄×C₇×C₁₃×C₂₉	3
C₃×C₄×C₁₃×C₂₉	7
C₄×ΓL(1,𝔽₈)×C₂₉	13
C₄×C₁₃×ΓL(1,𝔽₈)	29

Subgroups — C4×C13×ΓL(1,𝔽8)×C29 #44539709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×ΓL(1,𝔽₈)×C₂₉ #44539709