Subgroups — C₂×D₄₁×C₄₉⋊C₃ #37563012

Order 24108.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×C₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₁×C₄₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄₉×D₄₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₁×C₄₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₄₉×D₄₁	C₂×C₃	1	2	yes	complemented
6	C₂×C₄₁×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×ΓL(1,𝔽₈)×D₄₁	—	7	1	no	maximal
8	C₄₁×C₄₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×ΓL(1,𝔽₈)×C₄₁	—	7	1	no	—
10	ΓL(1,𝔽₈)×D₄₁	—	7	2	no	—
11	C₂×C₇×D₄₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	ΓL(1,𝔽₈)×C₄₁	—	7	1	no	—
13	C₂²×C₄₉⋊C₃	—	41	1	no	maximal, Hall
14	C₂×C₇×C₄₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₇×D₄₁	C₂×ΓL(1,𝔽₈)	1	2	yes	—
16	C₂×C₃×D₄₁	—	49	1	no	Hall
17	C₂×C₄₉⋊C₃	—	41	2	no	—
18	C₂×C₄₉⋊C₃	D₄₁	1	1	yes	characteristic, direct product factor
19	C₇×C₄₁	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
20	C₂×C₃×C₄₁	—	49	1	no	—
21	C₃×D₄₁	—	49	2	no	—
22	C₂²×C₄₉	—	41	1	no	Hall
23	C₂×D₄₁	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₄₉⋊C₃	C₂×D₄₁	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₄₁	—	49	1	no	Hall
26	C₂×C₄₉	—	41	2	no	—
27	C₂×C₄₉	C₃×D₄₁	1	1	yes	characteristic, complemented
28	C₂²×ΓL(1,𝔽₈)	—	287	1	no	—
29	C₂×C₄₁	C₂×C₄₉⋊C₃	1	1	yes	characteristic, complemented
30	D₄₁	C₂×C₄₉⋊C₃	1	2	yes	direct product factor
31	C₄₉	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
32	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
33	C₂×ΓL(1,𝔽₈)	—	287	2	no	—
34	C₄₁	C₂²×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₇	—	41	1	no	—
36	ΓL(1,𝔽₈)	—	7	1	no	—
37	C₂×C₇	—	41	2	no	—
38	C₂×C₇	ΓL(1,𝔽₈)×D₄₁	1	1	yes	characteristic
39	C₂²×C₃	—	2009	1	no	Hall
40	C₇	C₂×ΓL(1,𝔽₈)×D₄₁	1	1	yes	characteristic
41	C₂×C₃	—	49	1	no	—
42	C₂×C₃	—	2009	2	no	—
43	C₂²	—	41	1	no	Sylow
44	C₃	—	49	1	no	Sylow
45	C₂	—	41	2	no	—
46	C₂	D₄₁×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₄₁×C₄₉⋊C₃
commutator, cosocle, hypocenter	C₄₁×C₄₉	C₂²×C₃
Frattini	C₇	C₂×ΓL(1,𝔽₈)×D₄₁
Fitting	C₂×C₄₁×C₄₉	C₂×C₃
socle	C₂×C₇×C₄₁	C₂×ΓL(1,𝔽₈)
LCS	G ▷ C₄₁×C₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×C₄₉⋊C₃	C₂	semidirect
2. D₄₁×C₄₉⋊C₃	C₂	direct (N × H)
3. C₂×C₄₉×D₄₁	C₃	semidirect
4. C₄₁×C₄₉⋊C₃	C₂²	semidirect
5. C₄₉×D₄₁	C₂×C₃	semidirect
6. C₂×C₄₁×C₄₉	C₂×C₃	semidirect
8. C₄₁×C₄₉	C₂²×C₃	semidirect
18. C₂×C₄₉⋊C₃	D₄₁	direct (N × H)
23. C₂×D₄₁	C₄₉⋊C₃	direct (N × H)
24. C₄₉⋊C₃	C₂×D₄₁	direct (N × H)
27. C₂×C₄₉	C₃×D₄₁	semidirect
29. C₂×C₄₁	C₂×C₄₉⋊C₃	semidirect
30. D₄₁	C₂×C₄₉⋊C₃	direct (N × H)
31. C₄₉	C₂×C₃×D₄₁	semidirect
34. C₄₁	C₂²×C₄₉⋊C₃	semidirect
46. C₂	D₄₁×C₄₉⋊C₃	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×C₄₁×C₄₉⋊C₃	2
D₄₁×C₄₉⋊C₃	2
C₂×C₄₉×D₄₁	3
C₂×ΓL(1,𝔽₈)×D₄₁	7
C₂²×C₄₉⋊C₃	41

Subgroups — C2×D41×C49⋊C3 #37563012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₁×C₄₉⋊C₃ #37563012