Subgroups — A₄×#157 #89097

Order 432.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#157	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×A₄	C₄	1	1	yes	characteristic, complemented
4	C₃×#157	—	4	1	no	maximal
5	C₂²×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
6	C₂×#157	—	3	1	no	—
7	C₂×#157	—	3	1	no	—
8	D₃×A₄	—	6	2	no	—
9	C₃×C₃⋊D₃	—	4	1	no	—
10	C₄×A₄	—	9	1	no	maximal
11	C₂²×C₃²	C₃×C₄	1	1	yes	characteristic, complemented
12	C₂×C₃⋊D₃	—	3	1	no	—
13	C₂×C₃⋊D₃	—	3	1	no	—
14	C₃×A₄	—	2	2	no	—
15	C₃×A₄	—	4	2	no	—
16	#157	—	3	1	no	—
17	#157	A₄	1	1	yes	characteristic, direct product factor
18	C₃³	—	4	1	no	Sylow
19	C₂²×D₃	—	6	2	no	—
20	C₂×A₄	—	9	1	no	—
21	C₂×C₃²	—	3	1	no	—
22	C₃⋊D₃	—	3	1	no	—
23	C₃⋊D₃	C₂×A₄	1	1	yes	characteristic
24	C₃×D₃	—	24	2	no	—
25	C₂²×C₄	—	9	1	no	Sylow
26	C₂²×C₃	—	2	2	no	—
27	C₂×D₃	—	18	2	no	—
28	C₂×D₃	—	18	2	no	—
29	A₄	—	4	2	no	—
30	A₄	#157	1	1	yes	characteristic, direct product factor
31	C₃×C₄	—	36	1	no	—
32	C₃²	—	8	2	no	—
33	C₃²	—	16	2	no	—
34	C₃²	C₄×A₄	1	1	yes	characteristic, complemented
35	C₂³	—	9	1	no	—
36	C₂×C₄	—	27	1	no	—
37	C₂×C₄	—	27	1	no	—
38	C₂×C₃	—	6	2	no	—
39	C₂×C₃	—	36	1	no	—
40	D₃	—	6	2	no	—
41	D₃	—	18	2	no	—
42	C₂²	—	27	1	no	—
43	C₂²	—	27	1	no	—
44	C₂²	C₃×#157	1	1	yes	characteristic, complemented
45	C₄	—	9	1	no	—
46	C₄	—	27	1	no	—
47	C₃	—	2	2	no	—
48	C₃	—	4	1	no	—
49	C₃	—	16	2	no	—
50	C₂	—	3	1	no	—
51	C₂	—	9	1	no	—
52	C₂	—	27	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂²×C₃²	C₃×C₄
prime radical	A₄×C₃⋊D₃	C₂
cosocle	C₂²×C₃⋊D₃	C₂×C₃
LCS	G ▷ C₂²×C₃²
UCS	C₁

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

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