Subgroups — C₇²×C₁₉×C₃⋊Dic₃ #45691964

Order 33516.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₇²×Dic₃×C₁₉	—	3	4	no	maximal
3	C₃²×C₇²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	D₃	1	4	yes	—
5	C₇×C₁₉×C₃⋊Dic₃	C₇	1	8	yes	maximal, direct product factor
6	C₄×C₇²×C₁₉	—	9	1	no	Hall
7	C₃×C₇²×C₁₉	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₇×C₁₉	C₂×C₇	1	8	yes	—
9	C₂×C₇²×C₁₉	C₃⋊D₃	1	1	yes	characteristic
10	C₇²×C₃⋊Dic₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×Dic₃×C₁₉	—	3	32	no	—
12	C₃²×C₇×C₁₉	C₄×C₇	1	8	yes	complemented
13	C₇²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃²×C₇²	C₂×C₁₉	1	1	yes	characteristic
15	C₂×C₃×C₇×C₁₉	D₃×C₇	1	32	yes	—
16	C₁₉×C₃⋊Dic₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	C₇²×Dic₃	—	3	4	no	—
18	C₄×C₇×C₁₉	—	9	8	no	—
19	C₃²×C₇²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₇×C₁₉	C₇×Dic₃	1	32	yes	complemented
21	C₂×C₃²×C₁₉	C₂×C₇²	1	1	yes	characteristic
22	C₂×C₃×C₇²	D₃×C₁₉	1	4	yes	—
23	C₂×C₇×C₁₉	C₇×C₃⋊D₃	1	8	yes	—
24	C₇×C₃⋊Dic₃	C₇×C₁₉	1	8	yes	direct product factor
25	Dic₃×C₁₉	—	3	4	no	—
26	C₄×C₇²	—	9	1	no	Hall
27	C₃²×C₁₉	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
28	C₃×C₇²	Dic₃×C₁₉	1	4	yes	complemented
29	C₇×C₁₉	C₇×C₃⋊Dic₃	1	8	yes	direct product factor
30	C₂×C₃²×C₇	C₂×C₇×C₁₉	1	8	yes	—
31	C₂×C₃×C₁₉	D₃×C₇²	1	4	yes	—
32	C₂×C₇²	C₃⋊D₃×C₁₉	1	1	yes	characteristic
33	C₇×Dic₃	—	3	32	no	—
34	C₄×C₁₉	—	9	1	no	Hall
35	C₃²×C₇	C₄×C₇×C₁₉	1	8	yes	complemented
36	C₃×C₁₉	C₇²×Dic₃	1	4	yes	complemented
37	C₇²	C₁₉×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₃×C₇	D₃×C₇×C₁₉	1	32	yes	—
39	C₂×C₁₉	C₇²×C₃⋊D₃	1	1	yes	characteristic
40	C₃⋊Dic₃	C₇²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
41	C₄×C₇	—	9	8	no	—
42	C₃×C₇	C₇×Dic₃×C₁₉	1	32	yes	complemented
43	C₁₉	C₇²×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃²	C₂×C₇²×C₁₉	1	1	yes	characteristic
45	C₂×C₇	C₇×C₃⋊D₃×C₁₉	1	8	yes	—
46	Dic₃	—	3	4	no	—
47	C₃²	C₄×C₇²×C₁₉	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₇×C₁₉×C₃⋊Dic₃	1	8	yes	direct product factor
49	C₂×C₃	D₃×C₇²×C₁₉	1	4	yes	—
50	C₄	—	9	1	no	Sylow
51	C₃	C₇²×Dic₃×C₁₉	1	4	yes	complemented
52	C₂	C₇²×C₃⋊D₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇²×C₁₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₇²×C₁₉
Frattini	C₂	C₇²×C₃⋊D₃×C₁₉
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₃²	C₂×C₇²×C₁₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₇²×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇²×C₁₉	C₄	semidirect
5. C₇×C₁₉×C₃⋊Dic₃	C₇	direct (N × H)
7. C₃×C₇²×C₁₉	Dic₃	semidirect
10. C₇²×C₃⋊Dic₃	C₁₉	direct (N × H)
12. C₃²×C₇×C₁₉	C₄×C₇	semidirect
13. C₇²×C₁₉	C₃⋊Dic₃	direct (N × H)
16. C₁₉×C₃⋊Dic₃	C₇²	direct (N × H)
19. C₃²×C₇²	C₄×C₁₉	semidirect
20. C₃×C₇×C₁₉	C₇×Dic₃	semidirect
24. C₇×C₃⋊Dic₃	C₇×C₁₉	direct (N × H)
27. C₃²×C₁₉	C₄×C₇²	semidirect
28. C₃×C₇²	Dic₃×C₁₉	semidirect
29. C₇×C₁₉	C₇×C₃⋊Dic₃	direct (N × H)
35. C₃²×C₇	C₄×C₇×C₁₉	semidirect
36. C₃×C₁₉	C₇²×Dic₃	semidirect
37. C₇²	C₁₉×C₃⋊Dic₃	direct (N × H)
40. C₃⋊Dic₃	C₇²×C₁₉	direct (N × H)
42. C₃×C₇	C₇×Dic₃×C₁₉	semidirect
43. C₁₉	C₇²×C₃⋊Dic₃	direct (N × H)
47. C₃²	C₄×C₇²×C₁₉	semidirect
48. C₇	C₇×C₁₉×C₃⋊Dic₃	direct (N × H)
51. C₃	C₇²×Dic₃×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇²×C₁₉	2
C₇²×Dic₃×C₁₉	3
C₇×C₁₉×C₃⋊Dic₃	7
C₇²×C₃⋊Dic₃	19

Subgroups — C72×C19×C3⋊Dic3 #45691964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₁₉×C₃⋊Dic₃ #45691964