Subgroups — D₁₉×C₃⋊D₁₄₁ #44565345

Order 32148.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×C₃⋊D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₆₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₁₄₁	—	3	4	no	maximal
5	C₃²×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₆₇₉	—	3	4	no	—
7	C₁₉×D₁₄₁	—	3	4	no	—
8	C₃×D₁₉×C₄₇	D₃	1	4	yes	complemented
9	D₁₉×D₄₇	—	9	1	no	Hall
10	C₃×C₁₉×C₄₇	C₂×D₃	1	4	yes	complemented
11	D₈₉₃	—	9	1	no	—
12	C₁₉×D₄₇	—	9	1	no	—
13	D₁₉×C₄₇	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₂×C₃⋊D₁₄₁	—	19	1	no	maximal, Hall
15	C₁₉×C₄₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃²×C₄₇	—	19	1	no	—
17	C₃⋊D₁₄₁	—	19	1	no	—
18	C₃⋊D₁₄₁	D₁₉	1	1	yes	characteristic, direct product factor
19	C₃⋊D₃×D₁₉	—	47	1	no	maximal, Hall
20	C₂×D₁₄₁	—	57	4	no	—
21	C₃²×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
22	C₃⋊D₅₇	—	47	1	no	—
23	C₃⋊D₃×C₁₉	—	47	1	no	—
24	C₃²×D₁₉	D₄₇	1	1	yes	characteristic, complemented
25	C₂×C₃×C₄₇	—	19	4	no	—
26	D₁₄₁	—	3	4	no	—
27	D₁₄₁	—	57	4	no	—
28	D₃×D₁₉	—	141	4	no	—
29	C₂×D₄₇	—	171	1	no	Hall
30	C₃²×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄₇	D₃×D₁₉	1	4	yes	complemented
32	D₅₇	—	141	4	no	—
33	C₃×D₁₉	D₁₄₁	1	4	yes	complemented
34	D₃×C₁₉	—	141	4	no	—
35	C₂×C₄₇	—	19	1	no	—
36	D₄₇	—	9	1	no	—
37	D₄₇	—	171	1	no	—
38	C₂×D₁₉	—	423	1	no	Hall
39	C₃×C₁₉	C₂×D₁₄₁	1	4	yes	complemented
40	C₄₇	C₃⋊D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₉	—	423	1	no	—
42	D₁₉	—	423	1	no	—
43	D₁₉	C₃⋊D₁₄₁	1	1	yes	characteristic, direct product factor
44	C₂×C₃⋊D₃	—	893	1	no	Hall
45	C₁₉	C₂×C₃⋊D₁₄₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃²	—	19	1	no	—
47	C₃⋊D₃	—	47	1	no	—
48	C₃⋊D₃	—	893	1	no	—
49	C₂×D₃	—	2679	4	no	—
50	C₃²	D₁₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	19	4	no	—
52	D₃	—	2679	4	no	—
53	D₃	—	141	4	no	—
54	C₂²	—	8037	1	no	Sylow
55	C₃	D₁₉×D₁₄₁	1	4	yes	complemented
56	C₂	—	19	1	no	—
57	C₂	—	8037	1	no	—
58	C₂	—	423	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₉×C₄₇	C₂²
LCS	G ▷ C₃²×C₁₉×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₉×C₄₇	C₂	semidirect
2. C₁₉×C₃⋊D₁₄₁	C₂	semidirect
3. C₃⋊D₂₆₇₉	C₂	semidirect
5. C₃²×C₁₉×C₄₇	C₂²	semidirect
8. C₃×D₁₉×C₄₇	D₃	semidirect
10. C₃×C₁₉×C₄₇	C₂×D₃	semidirect
13. D₁₉×C₄₇	C₃⋊D₃	semidirect
15. C₁₉×C₄₇	C₂×C₃⋊D₃	semidirect
18. C₃⋊D₁₄₁	D₁₉	direct (N × H)
21. C₃²×C₄₇	C₂×D₁₉	semidirect
24. C₃²×D₁₉	D₄₇	semidirect
30. C₃²×C₁₉	C₂×D₄₇	semidirect
31. C₃×C₄₇	D₃×D₁₉	semidirect
33. C₃×D₁₉	D₁₄₁	semidirect
39. C₃×C₁₉	C₂×D₁₄₁	semidirect
40. C₄₇	C₃⋊D₃×D₁₉	semidirect
43. D₁₉	C₃⋊D₁₄₁	direct (N × H)
45. C₁₉	C₂×C₃⋊D₁₄₁	semidirect
50. C₃²	D₁₉×D₄₇	semidirect
55. C₃	D₁₉×D₁₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₁₉×C₄₇	2
C₁₉×C₃⋊D₁₄₁	2
C₃⋊D₂₆₇₉	2
D₁₉×D₁₄₁	3
C₂×C₃⋊D₁₄₁	19
C₃⋊D₃×D₁₉	47

Subgroups — D19×C3⋊D141 #44565345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×C₃⋊D₁₄₁ #44565345