Subgroups — C₂⁴×C₃⋊D₃ #64396

Order 288.

2244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃⋊D₃	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×D₃	—	3	4	no	maximal
4	C₂³×C₃²	C₂²	1	15	yes	complemented
5	C₂²×C₃⋊D₃	C₂²	1	140	yes	direct product factor
6	C₂⁴×C₃	D₃	1	4	yes	complemented
7	C₂³×D₃	—	3	120	no	—
8	C₂²×C₃²	C₂³	1	35	yes	complemented
9	C₂×C₃⋊D₃	C₂³	1	120	yes	direct product factor
10	C₂⁵	—	9	1	no	Sylow
11	C₂³×C₃	C₂×D₃	1	60	yes	complemented
12	C₂²×D₃	—	3	560	no	—
13	C₂×C₃²	C₂⁴	1	15	yes	complemented
14	C₃⋊D₃	C₂⁴	1	16	yes	direct product factor
15	C₂⁴	—	9	30	no	—
16	C₂⁴	C₃⋊D₃	1	1	yes	characteristic, direct product factor
17	C₂²×C₃	C₂²×D₃	1	140	yes	complemented
18	C₂×D₃	—	3	480	no	—
19	C₃²	C₂⁵	1	1	yes	characteristic, complemented, Sylow
20	C₂³	—	9	140	no	—
21	C₂³	C₂×C₃⋊D₃	1	15	yes	direct product factor
22	C₂×C₃	C₂³×D₃	1	60	yes	complemented
23	D₃	—	3	64	no	—
24	C₂²	—	9	120	no	—
25	C₂²	C₂²×C₃⋊D₃	1	35	yes	direct product factor
26	C₃	C₂⁴×D₃	1	4	yes	complemented
27	C₂	—	9	16	no	—
28	C₂	C₂³×C₃⋊D₃	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂⁴

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.