Subgroups — D₃×D₃₇₇ #17985331

Order 4524.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₇₇	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₂₉	—	3	1	no	—
7	D₃₇₇	—	3	1	no	—
8	D₃₇₇	D₃	1	1	yes	characteristic, direct product factor
9	C₁₃×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₂₉	—	13	1	no	maximal, Hall
11	D₈₇	—	13	1	no	—
12	C₃×D₂₉	—	13	1	no	—
13	D₃×C₂₉	D₁₃	1	1	yes	characteristic, complemented
14	D₃×D₁₃	—	29	1	no	maximal, Hall
15	C₂×D₂₉	—	39	1	no	Hall
16	C₃×C₂₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
17	D₃₉	—	29	1	no	—
18	C₃×D₁₃	—	29	1	no	—
19	D₃×C₁₃	D₂₉	1	1	yes	characteristic, complemented
20	C₂×C₂₉	—	3	1	no	—
21	D₂₉	—	13	1	no	—
22	D₂₉	—	39	1	no	—
23	C₂×D₁₃	—	87	1	no	Hall
24	C₃×C₁₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
25	C₂₉	D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	—	3	1	no	—
27	D₁₃	—	29	1	no	—
28	D₁₃	—	87	1	no	—
29	C₁₃	D₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	377	1	no	Hall
31	C₂×C₃	—	377	1	no	—
32	D₃	—	377	1	no	—
33	D₃	D₃₇₇	1	1	yes	characteristic, direct product factor
34	C₂²	—	1131	1	no	Sylow
35	C₃	C₂×D₃₇₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	1131	1	no	—
38	C₂	—	377	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₂₉	C₂²
LCS	G ▷ C₃×C₁₃×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₁₁₃₁	C₂	semidirect
2. D₃×C₁₃×C₂₉	C₂	semidirect
3. C₃×D₃₇₇	C₂	semidirect
5. C₃×C₁₃×C₂₉	C₂²	semidirect
8. D₃₇₇	D₃	direct (N × H)
9. C₁₃×C₂₉	C₂×D₃	semidirect
13. D₃×C₂₉	D₁₃	semidirect
16. C₃×C₂₉	C₂×D₁₃	semidirect
19. D₃×C₁₃	D₂₉	semidirect
24. C₃×C₁₃	C₂×D₂₉	semidirect
25. C₂₉	D₃×D₁₃	semidirect
29. C₁₃	D₃×D₂₉	semidirect
33. D₃	D₃₇₇	direct (N × H)
35. C₃	C₂×D₃₇₇	semidirect

Maximal subgroups

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

subgroup	index
D₁₁₃₁	2
D₃×C₁₃×C₂₉	2
C₃×D₃₇₇	2
C₂×D₃₇₇	3
D₃×D₂₉	13
D₃×D₁₃	29

Subgroups — D3×D377 #17985331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₃₇₇ #17985331