Subgroups — C₂×C₃×C₂²⋊A₄ #64394

Order 288.

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

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂²⋊A₄
commutator, cosocle, hypocenter	C₂⁴	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂⁵×C₃	C₃
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂×C₃

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.