Subgroups — C₃²×C₁₉×C₇⋊Dic₇ #45691972

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	C₃×C₁₉×C₇⋊Dic₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	4	yes	—
5	C₃²×C₁₉×Dic₇	—	7	8	no	maximal
6	C₁₉×C₇⋊Dic₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇²×C₁₉	C₃×C₄	1	4	yes	complemented
8	C₂×C₃²×C₇×C₁₉	D₇	1	8	yes	—
9	C₂×C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic
10	C₃²×C₇⋊Dic₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₉×Dic₇	—	7	32	no	—
12	C₃²×C₇×C₁₉	Dic₇	1	8	yes	complemented
13	C₇²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₇²	C₂×C₁₉	1	1	yes	characteristic
15	C₂×C₃×C₇×C₁₉	C₃×D₇	1	32	yes	—
16	C₃²×C₄×C₁₉	—	49	1	no	Hall
17	C₃×C₇⋊Dic₇	C₃×C₁₉	1	4	yes	direct product factor
18	C₁₉×Dic₇	—	7	8	no	—
19	C₃²×C₇²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₇×C₁₉	C₃×Dic₇	1	32	yes	complemented
21	C₂×C₃²×C₁₉	C₇⋊D₇	1	1	yes	characteristic
22	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	4	yes	—
23	C₂×C₇×C₁₉	C₃²×D₇	1	8	yes	—
24	C₃²×Dic₇	—	7	8	no	—
25	C₃×C₄×C₁₉	—	49	4	no	—
26	C₇⋊Dic₇	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
27	C₃²×C₁₉	C₇⋊Dic₇	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₇²	C₃×C₄×C₁₉	1	4	yes	complemented
29	C₇×C₁₉	C₃²×Dic₇	1	8	yes	complemented
30	C₂×C₃²×C₇	D₇×C₁₉	1	8	yes	—
31	C₂×C₃×C₁₉	C₃×C₇⋊D₇	1	4	yes	—
32	C₂×C₇²	C₂×C₃²×C₁₉	1	1	yes	characteristic
33	C₃×Dic₇	—	7	32	no	—
34	C₄×C₁₉	—	49	1	no	Hall
35	C₃²×C₇	C₁₉×Dic₇	1	8	yes	complemented
36	C₃×C₁₉	C₃×C₇⋊Dic₇	1	4	yes	direct product factor
37	C₇²	C₃²×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₇	C₃×D₇×C₁₉	1	32	yes	—
39	C₂×C₁₉	C₃²×C₇⋊D₇	1	1	yes	characteristic
40	C₃²×C₄	—	49	1	no	Hall
41	Dic₇	—	7	8	no	—
42	C₃×C₇	C₃×C₁₉×Dic₇	1	32	yes	complemented
43	C₁₉	C₃²×C₇⋊Dic₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃²	C₁₉×C₇⋊D₇	1	1	yes	characteristic
45	C₂×C₇	C₃²×D₇×C₁₉	1	8	yes	—
46	C₃×C₄	—	49	4	no	—
47	C₃²	C₁₉×C₇⋊Dic₇	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₃²×C₁₉×Dic₇	1	8	yes	complemented
49	C₂×C₃	C₃×C₁₉×C₇⋊D₇	1	4	yes	—
50	C₄	—	49	1	no	Sylow
51	C₃	C₃×C₁₉×C₇⋊Dic₇	1	4	yes	direct product factor
52	C₂	C₃²×C₁₉×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₉	C₇⋊D₇
commutator, hypocenter	C₇²	C₃²×C₄×C₁₉
Frattini	C₂	C₃²×C₁₉×C₇⋊D₇
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₇²	C₂×C₃²×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃²×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉×C₇⋊Dic₇	C₃	direct (N × H)
3. C₃²×C₇²×C₁₉	C₄	semidirect
6. C₁₉×C₇⋊Dic₇	C₃²	direct (N × H)
7. C₃×C₇²×C₁₉	C₃×C₄	semidirect
10. C₃²×C₇⋊Dic₇	C₁₉	direct (N × H)
12. C₃²×C₇×C₁₉	Dic₇	semidirect
13. C₇²×C₁₉	C₃²×C₄	semidirect
17. C₃×C₇⋊Dic₇	C₃×C₁₉	direct (N × H)
19. C₃²×C₇²	C₄×C₁₉	semidirect
20. C₃×C₇×C₁₉	C₃×Dic₇	semidirect
26. C₇⋊Dic₇	C₃²×C₁₉	direct (N × H)
27. C₃²×C₁₉	C₇⋊Dic₇	direct (N × H)
28. C₃×C₇²	C₃×C₄×C₁₉	semidirect
29. C₇×C₁₉	C₃²×Dic₇	semidirect
35. C₃²×C₇	C₁₉×Dic₇	semidirect
36. C₃×C₁₉	C₃×C₇⋊Dic₇	direct (N × H)
37. C₇²	C₃²×C₄×C₁₉	semidirect
42. C₃×C₇	C₃×C₁₉×Dic₇	semidirect
43. C₁₉	C₃²×C₇⋊Dic₇	direct (N × H)
47. C₃²	C₁₉×C₇⋊Dic₇	direct (N × H)
48. C₇	C₃²×C₁₉×Dic₇	semidirect
51. C₃	C₃×C₁₉×C₇⋊Dic₇	direct (N × H)

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
C₃×C₁₉×C₇⋊Dic₇	3
C₃²×C₁₉×Dic₇	7
C₃²×C₇⋊Dic₇	19

Subgroups — C32×C19×C7⋊Dic7 #45691972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₉×C₇⋊Dic₇ #45691972