Subgroups — A₄×#13089649 #31773014

Order 17316.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#13089649	C₃	1	2	yes	maximal, complemented
2	A₄×C₁₃×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13089649	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#13089649	—	4	1	no	maximal, Hall
5	C₂×#13089649	—	3	1	no	—
6	C₂²×C₁₃×C₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃×C₃₇	—	4	1	no	—
8	#13089649	—	4	2	no	—
9	#13089649	A₄	1	1	yes	characteristic, direct product factor
10	A₄×C₃₇⋊C₃	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₃₇	—	3	1	no	—
12	C₁₃×C₃₇	C₃×A₄	1	1	yes	characteristic, complemented, Hall
13	A₄×C₁₃⋊C₃	—	37	1	no	maximal, Hall
14	C₂²⋊(C₃₇⋊C₃)	—	13	2	no	—
15	A₄×C₃₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₂²×C₃₇⋊C₃	—	13	1	no	—
17	C₃×C₃₇⋊C₃	—	52	1	no	Hall
18	C₂×C₃₇⋊C₃	—	39	1	no	—
19	C₂²⋊(C₁₃⋊C₃)	—	37	2	no	—
20	A₄×C₁₃	C₃₇⋊C₃	1	1	yes	characteristic, complemented
21	C₂²×C₁₃⋊C₃	—	37	1	no	—
22	C₂²×C₃₇	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₃⋊C₃	—	148	1	no	Hall
24	C₃×C₃₇	—	4	1	no	—
25	C₃₇⋊C₃	—	13	1	no	—
26	C₃₇⋊C₃	—	52	2	no	—
27	C₂×C₁₃⋊C₃	—	111	1	no	—
28	C₂×C₃₇	—	3	1	no	—
29	C₂²×C₁₃	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₃×C₁₃	—	4	1	no	—
31	C₁₃⋊C₃	—	37	1	no	—
32	C₁₃⋊C₃	—	148	2	no	—
33	C₃₇	A₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₃×A₄	—	481	1	no	Hall
35	C₂×C₁₃	—	3	1	no	—
36	C₁₃	A₄×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₃	—	481	1	no	—
38	A₄	—	481	2	no	—
39	A₄	#13089649	1	1	yes	characteristic, direct product factor
40	C₃²	—	1924	1	no	Sylow
41	C₂×C₃	—	1443	1	no	—
42	C₂²	C₃×#13089649	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	4	1	no	—
44	C₃	—	1924	2	no	—
45	C₃	—	481	1	no	—
46	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₁₃×C₃₇	C₃²
LCS	G ▷ C₂²×C₁₃×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#13089649	C₃	semidirect
2. A₄×C₁₃×C₃₇	C₃	semidirect
3. C₂²×#13089649	C₃	semidirect
6. C₂²×C₁₃×C₃₇	C₃²	semidirect
9. #13089649	A₄	direct (N × H)
12. C₁₃×C₃₇	C₃×A₄	semidirect
15. A₄×C₃₇	C₁₃⋊C₃	semidirect
20. A₄×C₁₃	C₃₇⋊C₃	semidirect
22. C₂²×C₃₇	C₃×C₁₃⋊C₃	semidirect
29. C₂²×C₁₃	C₃×C₃₇⋊C₃	semidirect
33. C₃₇	A₄×C₁₃⋊C₃	semidirect
36. C₁₃	A₄×C₃₇⋊C₃	semidirect
39. A₄	#13089649	direct (N × H)
42. C₂²	C₃×#13089649	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊#13089649	3
A₄×C₁₃×C₃₇	3
C₂²×#13089649	3
C₃×#13089649	4
A₄×C₃₇⋊C₃	13
A₄×C₁₃⋊C₃	37

Subgroups — A4×#13089649 #31773014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×#13089649 #31773014