Subgroups — D₂₁⋊D₃₇₃ #44531299

Order 31332.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₁×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₁₁₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₆₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₇₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₃₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₆₁₁	D₃	1	1	yes	characteristic, complemented
7	C₇×D₃₇₃	—	3	1	no	—
8	D₇×C₃₇₃	—	3	1	no	—
9	D₃×D₃₇₃	—	7	1	no	maximal, Hall
10	C₇×C₃₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₁₁₉	D₇	1	1	yes	characteristic, complemented
12	C₃×D₃₇₃	—	7	1	no	—
13	D₃×C₃₇₃	—	7	1	no	—
14	C₂×D₃₇₃	—	21	1	no	Hall
15	C₃×C₃₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₇₃	—	21	1	no	—
17	D₃₇₃	—	3	1	no	—
18	D₃₇₃	—	7	1	no	—
19	C₃₇₃	D₃×D₇	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₇	—	373	1	no	maximal, Hall
21	D₂₁	D₃₇₃	1	1	yes	characteristic, complemented
22	C₃×D₇	—	373	1	no	—
23	D₃×C₇	—	373	1	no	—
24	C₂×D₇	—	1119	1	no	Hall
25	C₃×C₇	C₂×D₃₇₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	1119	1	no	—
27	D₇	—	3	1	no	—
28	D₇	—	373	1	no	—
29	C₂×D₃	—	2611	1	no	Hall
30	C₇	D₃×D₃₇₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	2611	1	no	—
32	D₃	—	7	1	no	—
33	D₃	—	373	1	no	—
34	C₂²	—	7833	1	no	Sylow
35	C₃	D₇×D₃₇₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	21	1	no	—
37	C₂	—	2611	1	no	—
38	C₂	—	1119	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₃₇₃	C₂²
LCS	G ▷ C₃×C₇×C₃₇₃
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.