Subgroups — A₄×C₁₃×C₇₃⋊C₃ #46802913

Order 34164.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₇₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×C₁₃×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₂²⋊(C₇₃⋊C₃)	C₃	1	2	yes	maximal, complemented
4	C₃×C₁₃×C₇₃⋊C₃	—	4	1	no	maximal, Hall
5	C₂×C₁₃×C₇₃⋊C₃	—	3	1	no	—
6	C₂²×C₁₃×C₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃×C₇₃	—	4	1	no	—
8	C₁₃×C₇₃⋊C₃	—	4	2	no	—
9	C₁₃×C₇₃⋊C₃	A₄	1	1	yes	characteristic, direct product factor
10	A₄×C₇₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₃×C₇₃	—	3	1	no	—
12	C₁₃×C₇₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
13	C₂²⋊(C₇₃⋊C₃)	C₃×C₁₃	1	2	yes	complemented
14	A₄×C₇₃	C₃×C₁₃	1	1	yes	characteristic, complemented
15	C₂²×C₇₃⋊C₃	C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₃×C₇₃⋊C₃	—	4	1	no	Hall
17	C₃×A₄×C₁₃	—	73	1	no	maximal, Hall
18	C₂×C₇₃⋊C₃	—	3	1	no	—
19	C₂²×C₇₃	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₇₃	—	4	1	no	—
21	C₇₃⋊C₃	—	4	2	no	—
22	C₇₃⋊C₃	A₄×C₁₃	1	1	yes	characteristic, direct product factor
23	C₂²×C₃×C₁₃	—	73	1	no	—
24	A₄×C₁₃	—	73	2	no	—
25	A₄×C₁₃	C₇₃⋊C₃	1	1	yes	characteristic, direct product factor
26	C₂×C₇₃	—	3	1	no	—
27	C₃²×C₁₃	—	292	1	no	Hall
28	C₂×C₃×C₁₃	—	219	1	no	—
29	C₇₃	C₃×A₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₁₃	C₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₃	—	4	1	no	—
32	C₃×C₁₃	—	292	2	no	—
33	C₃×C₁₃	—	73	1	no	—
34	C₃×A₄	—	73	1	no	Hall
35	C₂×C₁₃	—	3	1	no	—
36	C₁₃	A₄×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃	—	73	1	no	—
38	A₄	—	73	2	no	—
39	A₄	C₁₃×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃²	—	292	1	no	Sylow
41	C₂×C₃	—	219	1	no	—
42	C₂²	C₃×C₁₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	4	1	no	—
44	C₃	—	292	2	no	—
45	C₃	—	73	1	no	—
46	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	A₄×C₇₃⋊C₃
commutator, cosocle, hypocenter	C₂²×C₇₃	C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₇₃	C₃²
LCS	G ▷ C₂²×C₇₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₇₃⋊C₃	C₃	semidirect
2. A₄×C₁₃×C₇₃	C₃	semidirect
3. C₁₃×C₂²⋊(C₇₃⋊C₃)	C₃	semidirect
6. C₂²×C₁₃×C₇₃	C₃²	semidirect
9. C₁₃×C₇₃⋊C₃	A₄	direct (N × H)
10. A₄×C₇₃⋊C₃	C₁₃	direct (N × H)
12. C₁₃×C₇₃	C₃×A₄	semidirect
13. C₂²⋊(C₇₃⋊C₃)	C₃×C₁₃	semidirect
14. A₄×C₇₃	C₃×C₁₃	semidirect
15. C₂²×C₇₃⋊C₃	C₃×C₁₃	semidirect
19. C₂²×C₇₃	C₃²×C₁₃	semidirect
22. C₇₃⋊C₃	A₄×C₁₃	direct (N × H)
25. A₄×C₁₃	C₇₃⋊C₃	direct (N × H)
29. C₇₃	C₃×A₄×C₁₃	semidirect
30. C₂²×C₁₃	C₃×C₇₃⋊C₃	semidirect
36. C₁₃	A₄×C₇₃⋊C₃	direct (N × H)
39. A₄	C₁₃×C₇₃⋊C₃	direct (N × H)
42. C₂²	C₃×C₁₃×C₇₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₇₃⋊C₃	3
A₄×C₁₃×C₇₃	3
C₁₃×C₂²⋊(C₇₃⋊C₃)	3
C₃×C₁₃×C₇₃⋊C₃	4
A₄×C₇₃⋊C₃	13
C₃×A₄×C₁₃	73

Subgroups — A4×C13×C73⋊C3 #46802913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×C₁₃×C₇₃⋊C₃ #46802913