Subgroups — D₃×D₂₅₇₇ #44525706

Order 30924.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₈₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₅₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₅₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₅₇₇	—	3	1	no	maximal
5	D₃×D₈₅₉	—	3	1	no	maximal
6	C₃²×C₈₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₈₅₉	—	3	1	no	—
8	D₂₅₇₇	—	3	1	no	—
9	D₂₅₇₇	—	3	1	no	—
10	D₂₅₇₇	—	6	1	no	—
11	D₂₅₇₇	D₃	1	1	yes	characteristic, direct product factor
12	C₃×D₈₅₉	—	3	1	no	—
13	D₃×C₈₅₉	D₃	1	1	yes	characteristic, complemented
14	C₂×D₈₅₉	—	9	1	no	Hall
15	C₃×C₈₅₉	—	2	1	no	—
16	C₃×C₈₅₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₈₅₉	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₈₅₉	—	3	1	no	—
19	D₈₅₉	—	3	1	no	—
20	D₈₅₉	—	9	1	no	—
21	C₈₅₉	D₃²	1	1	yes	characteristic, complemented, Sylow
22	D₃²	—	859	1	no	maximal, Hall
23	C₃⋊D₃	—	859	1	no	—
24	C₃×D₃	—	859	1	no	—
25	C₃×D₃	D₈₅₉	1	1	yes	characteristic, complemented
26	C₂×D₃	—	2577	1	no	—
27	C₂×D₃	—	2577	1	no	—
28	C₃²	C₂×D₈₅₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	2577	1	no	—
31	D₃	—	2577	1	no	—
32	D₃	—	2577	1	no	—
33	D₃	—	5154	1	no	—
34	D₃	—	859	1	no	—
35	D₃	D₂₅₇₇	1	1	yes	characteristic, direct product factor
36	C₂²	—	7731	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	D₃×D₈₅₉	1	1	yes	characteristic, complemented
39	C₃	C₂×D₂₅₇₇	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	2577	1	no	—
42	C₂	—	7731	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₈₅₉	C₂²
LCS	G ▷ C₃²×C₈₅₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₈₅₉	C₂	semidirect
2. C₃×D₂₅₇₇	C₂	semidirect
3. C₃⋊D₂₅₇₇	C₂	semidirect
6. C₃²×C₈₅₉	C₂²	semidirect
11. D₂₅₇₇	D₃	direct (N × H)
13. D₃×C₈₅₉	D₃	semidirect
16. C₃×C₈₅₉	C₂×D₃	semidirect
17. C₃×C₈₅₉	C₂×D₃	semidirect
21. C₈₅₉	D₃²	semidirect
25. C₃×D₃	D₈₅₉	semidirect
28. C₃²	C₂×D₈₅₉	semidirect
35. D₃	D₂₅₇₇	direct (N × H)
38. C₃	D₃×D₈₅₉	semidirect
39. C₃	C₂×D₂₅₇₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×C₈₅₉	2
C₃×D₂₅₇₇	2
C₃⋊D₂₅₇₇	2
C₂×D₂₅₇₇	3
D₃×D₈₅₉	3
D₃²	859

Subgroups — D3×D2577 #44525706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₅₇₇ #44525706