Subgroups — C₂⁴×3₋¹⁺² #88917

Order 432.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×3₋¹⁺²	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₃²	C₃	1	1	yes	maximal, characteristic
3	C₂⁴×C₉	C₃	1	3	yes	maximal, complemented
4	C₂²×3₋¹⁺²	C₂²	1	35	yes	direct product factor
5	C₂³×C₃²	C₂×C₃	1	15	yes	—
6	C₂³×C₉	C₂×C₃	1	45	yes	complemented
7	C₂×3₋¹⁺²	C₂³	1	15	yes	direct product factor
8	C₂⁴×C₃	—	3	1	no	—
9	C₂⁴×C₃	C₃²	1	1	yes	characteristic
10	C₂²×C₃²	C₂²×C₃	1	35	yes	—
11	C₂²×C₉	C₂²×C₃	1	105	yes	complemented
12	3₋¹⁺²	C₂⁴	1	1	yes	characteristic, direct product factor, Sylow
13	C₂³×C₃	—	3	15	no	—
14	C₂³×C₃	C₂×C₃²	1	15	yes	—
15	C₂×C₃²	C₂³×C₃	1	15	yes	—
16	C₂×C₉	C₂³×C₃	1	45	yes	complemented
17	C₂⁴	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₃	—	3	35	no	—
19	C₂²×C₃	C₂²×C₃²	1	35	yes	—
20	C₃²	C₂⁴×C₃	1	1	yes	characteristic
21	C₉	C₂⁴×C₃	1	3	yes	complemented
22	C₂³	C₂×3₋¹⁺²	1	15	yes	direct product factor
23	C₂×C₃	—	3	15	no	—
24	C₂×C₃	C₂³×C₃²	1	15	yes	—
25	C₂²	C₂²×3₋¹⁺²	1	35	yes	direct product factor
26	C₃	—	3	1	no	—
27	C₃	C₂⁴×C₃²	1	1	yes	characteristic
28	C₂	C₂³×3₋¹⁺²	1	15	yes	direct product factor

	subgroup	G/H
center, socle	C₂⁴×C₃	C₃²
commutator, Frattini, cosocle	C₃	C₂⁴×C₃²
prime radical	C₂⁴×C₃²	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ G

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.