Subgroups — D₂₂₁⋊D₃₇ #45658474

Order 32708.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×D₂₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×D₄₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₆₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₁₇×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₇×D₃₇	—	13	1	no	maximal, Hall
6	D₁₃×D₃₇	—	17	1	no	maximal, Hall
7	D₆₂₉	D₁₃	1	1	yes	characteristic, complemented
8	C₁₇×D₃₇	—	13	1	no	—
9	D₁₇×C₃₇	—	13	1	no	—
10	D₄₈₁	D₁₇	1	1	yes	characteristic, complemented
11	C₁₃×D₃₇	—	17	1	no	—
12	D₁₃×C₃₇	—	17	1	no	—
13	D₁₃×D₁₇	—	37	1	no	maximal, Hall
14	C₁₇×C₃₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₁₃×C₃₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
16	D₂₂₁	D₃₇	1	1	yes	characteristic, complemented
17	C₁₃×D₁₇	—	37	1	no	—
18	C₁₇×D₁₃	—	37	1	no	—
19	C₁₃×C₁₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₇	—	221	1	no	Hall
21	C₂×C₃₇	—	221	1	no	—
22	D₃₇	—	13	1	no	—
23	D₃₇	—	17	1	no	—
24	C₂×D₁₇	—	481	1	no	Hall
25	C₂×D₁₃	—	629	1	no	Hall
26	C₃₇	D₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₇	—	481	1	no	—
28	D₁₇	—	13	1	no	—
29	D₁₇	—	37	1	no	—
30	C₂×C₁₃	—	629	1	no	—
31	D₁₃	—	17	1	no	—
32	D₁₃	—	37	1	no	—
33	C₁₇	D₁₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
34	C₁₃	D₁₇×D₃₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8177	1	no	Sylow
36	C₂	—	629	1	no	—
37	C₂	—	221	1	no	—
38	C₂	—	481	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₇×C₃₇	C₂²
LCS	G ▷ C₁₃×C₁₇×C₃₇
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₇×D₂₂₁	C₂	semidirect
2. C₁₇×D₄₈₁	C₂	semidirect
3. C₁₃×D₆₂₉	C₂	semidirect
4. C₁₃×C₁₇×C₃₇	C₂²	semidirect
7. D₆₂₉	D₁₃	semidirect
10. D₄₈₁	D₁₇	semidirect
14. C₁₇×C₃₇	C₂×D₁₃	semidirect
15. C₁₃×C₃₇	C₂×D₁₇	semidirect
16. D₂₂₁	D₃₇	semidirect
19. C₁₃×C₁₇	C₂×D₃₇	semidirect
26. C₃₇	D₁₃×D₁₇	semidirect
33. C₁₇	D₁₃×D₃₇	semidirect
34. C₁₃	D₁₇×D₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₇×D₂₂₁	2
C₁₇×D₄₈₁	2
C₁₃×D₆₂₉	2
D₁₇×D₃₇	13
D₁₃×D₃₇	17
D₁₃×D₁₇	37

Subgroups — D221⋊D37 #45658474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₂₁⋊D₃₇ #45658474