Subgroups — C₃×C₂²⋊D₄₉ #11924113

Order 1176.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊D₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄₉	—	2	1	no	—
6	C₂×C₃×C₄₉	C₂²	1	1	yes	characteristic
7	C₃×D₄₉	—	2	1	no	—
8	C₂²×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×D₄₉	C₂×C₃	1	1	yes	characteristic, complemented
10	Dic₄₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×C₂²⋊D₇	—	7	1	no	maximal
12	C₃×C₄₉	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₉	—	2	1	no	—
14	C₂×C₄₉	C₂²×C₃	1	1	yes	characteristic
15	D₄₉	—	2	1	no	—
16	C₂²×C₃×C₇	D₇	1	1	yes	characteristic
17	C₂×C₃×D₇	—	7	1	no	—
18	C₃×Dic₇	—	7	1	no	—
19	C₂²⋊D₇	—	7	1	no	—
20	C₄₉	C₃×D₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₇	—	2	1	no	—
22	C₂×C₃×C₇	C₂×D₇	1	1	yes	characteristic
23	C₃×D₇	—	14	1	no	—
24	C₂²×C₇	C₃×D₇	1	1	yes	characteristic
25	C₂×D₇	—	7	1	no	—
26	Dic₇	—	7	1	no	—
27	C₃×D₄	—	49	1	no	Hall
28	C₃×C₇	C₂²⋊D₇	1	1	yes	characteristic
29	C₂×C₇	—	2	1	no	—
30	C₂×C₇	C₂×C₃×D₇	1	1	yes	characteristic
31	D₇	—	14	1	no	—
32	C₂²×C₃	—	49	1	no	—
33	C₂²×C₃	D₄₉	1	1	yes	characteristic, complemented
34	C₃×C₄	—	49	1	no	—
35	D₄	—	49	1	no	Sylow
36	C₇	C₃×C₂²⋊D₇	1	1	yes	characteristic
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	—	98	1	no	—
39	C₂×C₃	C₂×D₄₉	1	1	yes	characteristic
40	C₂²	—	49	1	no	—
41	C₂²	C₃×D₄₉	1	1	yes	characteristic, complemented
42	C₄	—	49	1	no	—
43	C₃	C₂²⋊D₄₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₂	—	2	1	no	—
45	C₂	—	98	1	no	—
46	C₂	C₂×C₃×D₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄₉
commutator, cosocle	C₂×C₄₉	C₂²×C₃
Frattini	C₂×C₇	C₂×C₃×D₇
Fitting	C₂²×C₃×C₄₉	C₂
socle	C₂×C₃×C₇	C₂×D₇
hypercenter	C₂²×C₃	D₄₉
hypocenter	C₄₉	C₃×D₄
LCS	G ▷ C₂×C₄₉ ▷ C₄₉
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₄₉	C₂	semidirect
2. C₂×C₃×D₄₉	C₂	semidirect
3. C₃×Dic₄₉	C₂	semidirect
4. C₂²⋊D₄₉	C₃	direct (N × H)
8. C₂²×C₄₉	C₂×C₃	semidirect
9. C₂×D₄₉	C₂×C₃	semidirect
10. Dic₄₉	C₂×C₃	semidirect
12. C₃×C₄₉	D₄	semidirect
20. C₄₉	C₃×D₄	semidirect
33. C₂²×C₃	D₄₉	semidirect
41. C₂²	C₃×D₄₉	semidirect
43. C₃	C₂²⋊D₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄₉	2
C₂×C₃×D₄₉	2
C₃×Dic₄₉	2
C₂²⋊D₄₉	3
C₃×C₂²⋊D₇	7

Subgroups — C3×C22⋊D49 #11924113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊D₄₉ #11924113