Subgroups — D₃×C₄₁²⋊C₃ #44475413

Order 30258.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₄₁²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁²⋊C₃	—	3	1	no	maximal
4	C₃×C₄₁²	C₂×C₃	1	1	yes	characteristic, complemented
5	C₄₁²⋊C₃	—	2	1	no	—
6	C₄₁²⋊C₃	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₄₁²	—	3	1	no	Hall
8	C₄₁²	C₃×D₃	1	1	yes	characteristic, complemented, Sylow
9	D₃×C₄₁	—	3	14	no	—
10	C₃×C₄₁	—	3	14	no	—
11	C₂×C₄₁	—	9	14	no	—
12	C₄₁	—	3	14	no	—
13	C₃×D₃	—	1681	1	no	maximal, Hall
14	C₃²	—	1681	1	no	Sylow
15	C₂×C₃	—	5043	1	no	—
16	D₃	C₄₁²⋊C₃	1	1	yes	characteristic, direct product factor
17	C₃	—	3362	1	no	—
18	C₃	—	1681	1	no	—
19	C₃	C₂×C₄₁²⋊C₃	1	1	yes	characteristic, complemented
20	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₄₁²	C₂×C₃
LCS	G ▷ C₃×C₄₁²
UCS	C₁

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.