Subgroups — D₉×D₄₂₁ #29503003

Order 15156.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₉×C₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₄₂₁	—	3	1	no	maximal
5	C₉×C₄₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₂₆₃	—	3	1	no	—
7	C₃×D₄₂₁	D₃	1	1	yes	characteristic
8	D₃×C₄₂₁	—	3	1	no	—
9	C₂×D₄₂₁	—	9	1	no	Hall
10	C₃×C₄₂₁	C₂×D₃	1	1	yes	characteristic
11	C₂×C₄₂₁	—	9	1	no	—
12	D₄₂₁	—	9	1	no	—
13	D₄₂₁	D₉	1	1	yes	characteristic, direct product factor
14	C₄₂₁	C₂×D₉	1	1	yes	characteristic, complemented, Sylow
15	C₂×D₉	—	421	1	no	maximal, Hall
16	C₂×C₉	—	421	1	no	—
17	D₉	—	421	1	no	—
18	D₉	D₄₂₁	1	1	yes	characteristic, direct product factor
19	C₂×D₃	—	1263	1	no	—
20	C₉	C₂×D₄₂₁	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃	—	421	1	no	—
22	D₃	—	3	1	no	—
23	D₃	—	1263	1	no	—
24	C₂²	—	3789	1	no	Sylow
25	C₃	D₃×D₄₂₁	1	1	yes	characteristic
26	C₂	—	9	1	no	—
27	C₂	—	421	1	no	—
28	C₂	—	3789	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₄₂₁	C₂²
Frattini	C₃	D₃×D₄₂₁
socle	C₃×C₄₂₁	C₂×D₃
LCS	G ▷ C₉×C₄₂₁
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.