Subgroups — C₂×C₃²×D₆₄₁ #37528091

Order 23076.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₆₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₆₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₆₄₁	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₆₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₆₄₁	C₂×C₃	1	4	yes	complemented
6	C₃×D₆₄₁	C₂×C₃	1	8	yes	direct product factor
7	C₂×D₆₄₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₆₄₁	C₂²×C₃	1	4	yes	complemented
9	C₂×C₆₄₁	C₂×C₃²	1	1	yes	characteristic, complemented
10	D₆₄₁	C₂×C₃²	1	2	yes	direct product factor
11	C₆₄₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₃²	—	641	1	no	maximal, Hall
13	C₂×C₃²	—	641	2	no	—
14	C₂×C₃²	D₆₄₁	1	1	yes	characteristic, direct product factor
15	C₂²×C₃	—	641	4	no	—
16	C₃²	C₂×D₆₄₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃	—	641	8	no	—
18	C₂×C₃	C₃×D₆₄₁	1	4	yes	direct product factor
19	C₂²	—	641	1	no	Sylow
20	C₃	C₂×C₃×D₆₄₁	1	4	yes	direct product factor
21	C₂	—	641	2	no	—
22	C₂	C₃²×D₆₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₆₄₁
commutator, cosocle, hypocenter	C₆₄₁	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₆₄₁	C₂
LCS	G ▷ C₆₄₁
UCS	C₁ ◁ C₂×C₃²

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.