Subgroups — D₂₁⋊D₂₂₉ #34063992

Order 19236.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₁×C₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₆₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₆₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₂₂₉	—	3	1	no	maximal, Hall
5	C₃×C₇×C₂₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₆₀₃	D₃	1	1	yes	characteristic, complemented
7	C₇×D₂₂₉	—	3	1	no	—
8	D₇×C₂₂₉	—	3	1	no	—
9	D₃×D₂₂₉	—	7	1	no	maximal, Hall
10	C₇×C₂₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₆₈₇	D₇	1	1	yes	characteristic, complemented
12	C₃×D₂₂₉	—	7	1	no	—
13	D₃×C₂₂₉	—	7	1	no	—
14	C₂×D₂₂₉	—	21	1	no	Hall
15	C₃×C₂₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₂₂₉	—	21	1	no	—
17	D₂₂₉	—	3	1	no	—
18	D₂₂₉	—	7	1	no	—
19	C₂₂₉	D₃×D₇	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₇	—	229	1	no	maximal, Hall
21	D₂₁	D₂₂₉	1	1	yes	characteristic, complemented
22	C₃×D₇	—	229	1	no	—
23	D₃×C₇	—	229	1	no	—
24	C₂×D₇	—	687	1	no	Hall
25	C₃×C₇	C₂×D₂₂₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	687	1	no	—
27	D₇	—	3	1	no	—
28	D₇	—	229	1	no	—
29	C₂×D₃	—	1603	1	no	Hall
30	C₇	D₃×D₂₂₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	1603	1	no	—
32	D₃	—	7	1	no	—
33	D₃	—	229	1	no	—
34	C₂²	—	4809	1	no	Sylow
35	C₃	D₇×D₂₂₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	21	1	no	—
37	C₂	—	1603	1	no	—
38	C₂	—	687	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₂₂₉	C₂²
LCS	G ▷ C₃×C₇×C₂₂₉
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.