Subgroups — A₄×#14579731 #44535744

Order 31356.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579731	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×C₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#14579731	C₃	1	2	yes	maximal, complemented
4	C₃×#14579731	—	4	1	no	maximal, Hall
5	C₂×#14579731	—	3	1	no	—
6	C₂²×C₁₃×C₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃×C₆₇	—	4	1	no	—
8	#14579731	—	4	2	no	—
9	#14579731	A₄	1	1	yes	characteristic, direct product factor
10	A₄×C₆₇⋊C₃	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₆₇	—	3	1	no	—
12	C₁₃×C₆₇	C₃×A₄	1	1	yes	characteristic, complemented, Hall
13	C₂²⋊(C₆₇⋊C₃)	—	13	2	no	—
14	A₄×C₆₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₂²×C₆₇⋊C₃	—	13	1	no	—
16	C₃×C₆₇⋊C₃	—	52	1	no	Hall
17	A₄×C₁₃⋊C₃	—	67	1	no	maximal, Hall
18	C₂×C₆₇⋊C₃	—	39	1	no	—
19	C₂²×C₆₇	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₆₇	—	4	1	no	—
21	C₆₇⋊C₃	—	13	1	no	—
22	C₆₇⋊C₃	—	52	2	no	—
23	C₂²⋊(C₁₃⋊C₃)	—	67	2	no	—
24	A₄×C₁₃	C₆₇⋊C₃	1	1	yes	characteristic, complemented
25	C₂²×C₁₃⋊C₃	—	67	1	no	—
26	C₂×C₆₇	—	3	1	no	—
27	C₃×C₁₃⋊C₃	—	268	1	no	Hall
28	C₂×C₁₃⋊C₃	—	201	1	no	—
29	C₆₇	A₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₁₃	C₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₃	—	4	1	no	—
32	C₁₃⋊C₃	—	268	2	no	—
33	C₁₃⋊C₃	—	67	1	no	—
34	C₃×A₄	—	871	1	no	Hall
35	C₂×C₁₃	—	3	1	no	—
36	C₁₃	A₄×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₃	—	871	1	no	—
38	A₄	—	871	2	no	—
39	A₄	#14579731	1	1	yes	characteristic, direct product factor
40	C₃²	—	3484	1	no	Sylow
41	C₂×C₃	—	2613	1	no	—
42	C₂²	C₃×#14579731	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	4	1	no	—
44	C₃	—	871	1	no	—
45	C₃	—	3484	2	no	—
46	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₁₃×C₆₇	C₃²
LCS	G ▷ C₂²×C₁₃×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#14579731	C₃	semidirect
2. A₄×C₁₃×C₆₇	C₃	semidirect
3. C₂²⋊#14579731	C₃	semidirect
6. C₂²×C₁₃×C₆₇	C₃²	semidirect
9. #14579731	A₄	direct (N × H)
12. C₁₃×C₆₇	C₃×A₄	semidirect
14. A₄×C₆₇	C₁₃⋊C₃	semidirect
19. C₂²×C₆₇	C₃×C₁₃⋊C₃	semidirect
24. A₄×C₁₃	C₆₇⋊C₃	semidirect
29. C₆₇	A₄×C₁₃⋊C₃	semidirect
30. C₂²×C₁₃	C₃×C₆₇⋊C₃	semidirect
36. C₁₃	A₄×C₆₇⋊C₃	semidirect
39. A₄	#14579731	direct (N × H)
42. C₂²	C₃×#14579731	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14579731	3
A₄×C₁₃×C₆₇	3
C₂²⋊#14579731	3
C₃×#14579731	4
A₄×C₆₇⋊C₃	13
A₄×C₁₃⋊C₃	67

Subgroups — A4×#14579731 #44535744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×#14579731 #44535744