Subgroups — Dic₄₈₅₁ #34084521

Order 19404.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₆₁₇	—	3	1	no	maximal
3	C₉×C₁₁×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₁×C₄₉	D₃	1	1	yes	characteristic
5	Dic₆₉₃	—	7	1	no	maximal
6	Dic₅₃₉	—	9	1	no	Hall
7	Dic₄₄₁	—	11	1	no	maximal, Hall
8	C₃×C₁₁×C₄₉	Dic₃	1	1	yes	characteristic
9	C₂×C₇×C₉×C₁₁	D₇	1	1	yes	characteristic
10	C₂×C₁₁×C₄₉	D₉	1	1	yes	characteristic
11	Dic₂₃₁	—	21	1	no	—
12	C₂×C₉×C₄₉	D₁₁	1	1	yes	characteristic
13	C₇×C₉×C₁₁	Dic₇	1	1	yes	characteristic
14	Dic₁₄₇	—	33	1	no	—
15	C₁₁×C₄₉	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₇×C₁₁	D₂₁	1	1	yes	characteristic
17	C₉×C₄₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
18	Dic₉₉	—	49	1	no	Hall
19	Dic₇₇	—	63	1	no	—
20	C₂×C₃×C₄₉	D₃₃	1	1	yes	characteristic
21	Dic₆₃	—	77	1	no	—
22	C₃×C₇×C₁₁	Dic₂₁	1	1	yes	characteristic
23	C₂×C₉×C₁₁	D₄₉	1	1	yes	characteristic
24	Dic₄₉	—	99	1	no	Hall
25	C₂×C₇×C₁₁	D₆₃	1	1	yes	characteristic
26	C₃×C₄₉	Dic₃₃	1	1	yes	characteristic
27	Dic₃₃	—	147	1	no	—
28	C₂×C₇×C₉	D₇₇	1	1	yes	characteristic
29	C₉×C₁₁	Dic₄₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₄₉	D₉₉	1	1	yes	characteristic
31	Dic₂₁	—	231	1	no	—
32	C₇×C₁₁	Dic₆₃	1	1	yes	characteristic
33	C₂×C₃×C₁₁	D₁₄₇	1	1	yes	characteristic
34	C₇×C₉	Dic₇₇	1	1	yes	characteristic
35	C₄₉	Dic₉₉	1	1	yes	characteristic, complemented, Sylow
36	Dic₁₁	—	441	1	no	Hall
37	C₂×C₃×C₇	D₂₃₁	1	1	yes	characteristic
38	Dic₉	—	539	1	no	Hall
39	C₃×C₁₁	Dic₁₄₇	1	1	yes	characteristic
40	Dic₇	—	693	1	no	—
41	C₂×C₁₁	D₄₄₁	1	1	yes	characteristic
42	C₃×C₇	Dic₂₃₁	1	1	yes	characteristic
43	C₂×C₉	D₅₃₉	1	1	yes	characteristic
44	C₂×C₇	D₆₉₃	1	1	yes	characteristic
45	Dic₃	—	1617	1	no	—
46	C₁₁	Dic₄₄₁	1	1	yes	characteristic, complemented, Sylow
47	C₉	Dic₅₃₉	1	1	yes	characteristic, complemented, Sylow
48	C₇	Dic₆₉₃	1	1	yes	characteristic
49	C₂×C₃	D₁₆₁₇	1	1	yes	characteristic
50	C₄	—	4851	1	no	Sylow
51	C₃	Dic₁₆₁₇	1	1	yes	characteristic
52	C₂	D₄₈₅₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₄₈₅₁
commutator, hypocenter	C₉×C₁₁×C₄₉	C₄
Frattini	C₂×C₃×C₇	D₂₃₁
Fitting, cosocle	C₂×C₉×C₁₁×C₄₉	C₂
socle, prime radical	C₂×C₃×C₇×C₁₁	D₂₁
LCS	G ▷ C₉×C₁₁×C₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₁×C₄₉	C₄	semidirect
15. C₁₁×C₄₉	Dic₉	semidirect
17. C₉×C₄₉	Dic₁₁	semidirect
29. C₉×C₁₁	Dic₄₉	semidirect
35. C₄₉	Dic₉₉	semidirect
46. C₁₁	Dic₄₄₁	semidirect
47. C₉	Dic₅₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₁×C₄₉	2
Dic₁₆₁₇	3
Dic₆₉₃	7
Dic₄₄₁	11

Subgroups — Dic4851 #34084521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₄₈₅₁ #34084521