Subgroups — Dic₃×C₄₁×C₄₉ #37563002

Order 24108.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₁×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₁×C₄₉	—	3	1	no	maximal, Hall
3	C₃×C₄₁×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₁×C₄₉	D₃	1	1	yes	characteristic
5	C₇×Dic₃×C₄₁	C₇	1	1	yes	maximal, characteristic
6	C₄₁×C₄₉	Dic₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₇×C₄₁	C₂×C₇	1	1	yes	characteristic
8	C₄×C₇×C₄₁	—	3	1	no	—
9	C₃×C₇×C₄₁	C₄×C₇	1	1	yes	characteristic
10	Dic₃×C₄₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇×C₄₁	D₃×C₇	1	1	yes	characteristic
12	Dic₃×C₄₁	C₄₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₄₉	C₂×C₄₁	1	1	yes	characteristic
14	C₇×C₄₁	C₇×Dic₃	1	1	yes	characteristic
15	C₂×C₃×C₄₁	C₂×C₄₉	1	1	yes	characteristic
16	C₄×C₄₉	—	3	1	no	Hall
17	C₄×C₄₁	—	3	1	no	Hall
18	C₃×C₄₉	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄₁	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₄₉	D₃×C₄₁	1	1	yes	characteristic
21	C₇×Dic₃	C₇×C₄₁	1	1	yes	characteristic
22	C₂×C₄₁	D₃×C₄₉	1	1	yes	characteristic
23	C₄₉	Dic₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃×C₇	C₂×C₇×C₄₁	1	1	yes	characteristic
25	C₄₁	Dic₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₄×C₇	—	3	1	no	—
27	C₃×C₇	C₄×C₇×C₄₁	1	1	yes	characteristic
28	C₂×C₇	D₃×C₇×C₄₁	1	1	yes	characteristic
29	Dic₃	C₄₁×C₄₉	1	1	yes	characteristic, direct product factor, Hall
30	C₇	C₇×Dic₃×C₄₁	1	1	yes	characteristic
31	C₂×C₃	C₂×C₄₁×C₄₉	1	1	yes	characteristic
32	C₄	—	3	1	no	Sylow
33	C₃	C₄×C₄₁×C₄₉	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₃×C₄₁×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄₁×C₄₉	D₃
commutator, hypocenter	C₃	C₄×C₄₁×C₄₉
Frattini	C₂×C₇	D₃×C₇×C₄₁
Fitting	C₂×C₃×C₄₁×C₄₉	C₂
socle, prime radical	C₂×C₃×C₇×C₄₁	C₂×C₇
cosocle	C₂×C₃×C₇	C₂×C₇×C₄₁
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₄₁×C₄₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₄₁×C₄₉	C₄	semidirect
6. C₄₁×C₄₉	Dic₃	direct (N × H)
10. Dic₃×C₄₉	C₄₁	direct (N × H)
12. Dic₃×C₄₁	C₄₉	direct (N × H)
18. C₃×C₄₉	C₄×C₄₁	semidirect
19. C₃×C₄₁	C₄×C₄₉	semidirect
23. C₄₉	Dic₃×C₄₁	direct (N × H)
25. C₄₁	Dic₃×C₄₉	direct (N × H)
29. Dic₃	C₄₁×C₄₉	direct (N × H)
33. C₃	C₄×C₄₁×C₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄₁×C₄₉	2
C₄×C₄₁×C₄₉	3
C₇×Dic₃×C₄₁	7
Dic₃×C₄₉	41

Subgroups — Dic3×C41×C49 #37563002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₄₁×C₄₉ #37563002