Subgroups — D₃²×C₆₄₁ #37528085

Order 23076.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₆₄₁	C₂	1	2	yes	maximal, complemented
2	C₃⋊D₃×C₆₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₆₄₁	—	3	2	no	maximal
4	C₃²×C₆₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₆₄₁	—	3	2	no	—
6	D₃×C₆₄₁	—	3	2	no	—
7	D₃×C₆₄₁	—	6	1	no	—
8	D₃×C₆₄₁	D₃	1	2	yes	direct product factor
9	C₂²×C₆₄₁	—	9	1	no	Hall
10	C₃×C₆₄₁	—	2	1	no	—
11	C₃×C₆₄₁	C₂×D₃	1	2	yes	complemented
12	C₂×C₆₄₁	—	3	2	no	—
13	C₂×C₆₄₁	—	9	1	no	—
14	C₆₄₁	D₃²	1	1	yes	characteristic, direct product factor, Sylow
15	D₃²	C₆₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃⋊D₃	C₂×C₆₄₁	1	1	yes	characteristic, complemented
17	C₃×D₃	C₂×C₆₄₁	1	2	yes	complemented
18	C₂×D₃	—	3	2	no	—
19	C₃²	C₂²×C₆₄₁	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	3	2	no	—
21	D₃	—	3	2	no	—
22	D₃	—	6	1	no	—
23	D₃	D₃×C₆₄₁	1	2	yes	direct product factor
24	C₂²	—	9	1	no	Sylow
25	C₃	—	2	1	no	—
26	C₃	C₂×D₃×C₆₄₁	1	2	yes	complemented
27	C₂	—	3	2	no	—
28	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₆₄₁	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₆₄₁
Frattini	C₁	G
Fitting, socle	C₃²×C₆₄₁	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₆₄₁

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.