Subgroups — C₄₉×Dic₁₂₃ #37563003

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	C₄₉×Dic₄₁	—	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×Dic₁₂₃	C₇	1	1	yes	maximal, characteristic
6	C₄₁×C₄₉	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₇×C₄₁	C₂×C₇	1	1	yes	characteristic
8	C₇×Dic₄₁	—	3	1	no	—
9	C₃×C₇×C₄₁	C₄×C₇	1	1	yes	characteristic
10	Dic₃×C₄₉	—	41	1	no	maximal, Hall
11	C₂×C₇×C₄₁	D₃×C₇	1	1	yes	characteristic
12	Dic₁₂₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₄₉	D₄₁	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	—	123	1	no	Hall
17	Dic₄₁	—	3	1	no	Hall
18	C₃×C₄₉	Dic₄₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄₁	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₄₉	D₁₂₃	1	1	yes	characteristic
21	C₇×Dic₃	—	41	1	no	—
22	C₂×C₄₁	D₃×C₄₉	1	1	yes	characteristic
23	C₄₉	Dic₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃×C₇	C₇×D₄₁	1	1	yes	characteristic
25	C₄₁	Dic₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
26	C₄×C₇	—	123	1	no	—
27	C₃×C₇	C₇×Dic₄₁	1	1	yes	characteristic
28	C₂×C₇	C₇×D₁₂₃	1	1	yes	characteristic
29	Dic₃	—	41	1	no	Hall
30	C₇	C₇×Dic₁₂₃	1	1	yes	characteristic
31	C₂×C₃	C₄₉×D₄₁	1	1	yes	characteristic
32	C₄	—	123	1	no	Sylow
33	C₃	C₄₉×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₄₉×D₁₂₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄₉	D₁₂₃
commutator, hypocenter	C₃×C₄₁	C₄×C₄₉
Frattini	C₂×C₇	C₇×D₁₂₃
Fitting	C₂×C₃×C₄₁×C₄₉	C₂
socle, prime radical, cosocle	C₂×C₃×C₇×C₄₁	C₂×C₇
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₂×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	semidirect
12. Dic₁₂₃	C₄₉	direct (N × H)
18. C₃×C₄₉	Dic₄₁	semidirect
19. C₃×C₄₁	C₄×C₄₉	semidirect
23. C₄₉	Dic₁₂₃	direct (N × H)
25. C₄₁	Dic₃×C₄₉	semidirect
33. C₃	C₄₉×Dic₄₁	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
C₄₉×Dic₄₁	3
C₇×Dic₁₂₃	7
Dic₃×C₄₉	41

Subgroups — C49×Dic123 #37563003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₉×Dic₁₂₃ #37563003