Subgroups — D₃×C₂²⋊A₄ #64390

Order 288.

303 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂²⋊A₄	—	3	1	no	maximal
4	D₃×A₄	—	4	5	no	maximal
5	C₂⁴×C₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂³×D₃	—	3	5	no	—
7	C₂³×D₃	—	3	5	no	—
8	C₂²⋊A₄	—	2	1	no	—
9	C₂²⋊A₄	D₃	1	1	yes	characteristic, direct product factor
10	C₃×A₄	—	4	5	no	—
11	C₂⁵	—	3	1	no	Sylow
12	C₂³×C₃	—	3	5	no	—
13	C₂²×D₃	—	3	30	no	—
14	C₂²×D₃	—	3	10	no	—
15	C₂²×D₃	—	3	5	no	—
16	C₂²×D₃	A₄	1	5	yes	complemented
17	C₂×A₄	—	12	5	no	—
18	C₃×D₃	—	16	1	no	—
19	C₂⁴	—	9	5	no	—
20	C₂⁴	—	9	5	no	—
21	C₂⁴	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂²×C₃	—	3	10	no	—
23	C₂²×C₃	C₂×A₄	1	5	yes	complemented
24	C₂×D₃	—	3	30	no	—
25	C₂×D₃	—	3	5	no	—
26	C₂×D₃	—	3	5	no	—
27	A₄	—	4	5	no	—
28	A₄	—	8	5	no	—
29	C₃²	—	16	1	no	Sylow
30	C₂³	—	3	5	no	—
31	C₂³	—	3	5	no	—
32	C₂³	—	9	10	no	—
33	C₂³	—	9	30	no	—
34	C₂³	—	9	5	no	—
35	C₂×C₃	—	3	5	no	—
36	C₂×C₃	—	48	1	no	—
37	D₃	—	3	5	no	—
38	D₃	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
39	C₂²	—	3	10	no	—
40	C₂²	—	9	5	no	—
41	C₂²	—	9	5	no	—
42	C₂²	—	9	30	no	—
43	C₂²	D₃×A₄	1	5	yes	complemented
44	C₃	—	16	1	no	—
45	C₃	—	32	1	no	—
46	C₃	C₂×C₂²⋊A₄	1	1	yes	characteristic, complemented
47	C₂	—	3	5	no	—
48	C₂	—	3	1	no	—
49	C₂	—	9	5	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂⁴×C₃	C₂×C₃
LCS	G ▷ C₂⁴×C₃
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.