Subgroups — D₃₃×D₂₅₁ #45684029

Order 33132.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₃×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₂₅₁	—	3	1	no	maximal, Hall
5	C₃×C₁₁×C₂₅₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₇₆₁	—	3	1	no	—
7	C₁₁×D₂₅₁	D₃	1	1	yes	characteristic, complemented
8	D₁₁×C₂₅₁	—	3	1	no	—
9	D₃×D₂₅₁	—	11	1	no	maximal, Hall
10	C₁₁×C₂₅₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₇₅₃	—	11	1	no	—
12	C₃×D₂₅₁	D₁₁	1	1	yes	characteristic, complemented
13	D₃×C₂₅₁	—	11	1	no	—
14	C₂×D₂₅₁	—	33	1	no	Hall
15	C₃×C₂₅₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₂₅₁	—	33	1	no	—
17	D₂₅₁	—	33	1	no	—
18	D₂₅₁	D₃₃	1	1	yes	characteristic, direct product factor
19	C₂₅₁	C₂×D₃₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₃₃	—	251	1	no	maximal, Hall
21	C₂×C₃×C₁₁	—	251	1	no	—
22	D₃₃	—	251	1	no	—
23	D₃₃	D₂₅₁	1	1	yes	characteristic, direct product factor
24	C₂×D₁₁	—	753	1	no	Hall
25	C₃×C₁₁	C₂×D₂₅₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁	—	251	1	no	—
27	D₁₁	—	3	1	no	—
28	D₁₁	—	753	1	no	—
29	C₂×D₃	—	2761	1	no	Hall
30	C₁₁	D₃×D₂₅₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	251	1	no	—
32	D₃	—	11	1	no	—
33	D₃	—	2761	1	no	—
34	C₂²	—	8283	1	no	Sylow
35	C₃	D₁₁×D₂₅₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	33	1	no	—
37	C₂	—	8283	1	no	—
38	C₂	—	251	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₂₅₁	C₂²
LCS	G ▷ C₃×C₁₁×C₂₅₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₂₈₃	C₂	semidirect
2. D₃₃×C₂₅₁	C₂	semidirect
3. C₃×C₁₁×D₂₅₁	C₂	semidirect
5. C₃×C₁₁×C₂₅₁	C₂²	semidirect
7. C₁₁×D₂₅₁	D₃	semidirect
10. C₁₁×C₂₅₁	C₂×D₃	semidirect
12. C₃×D₂₅₁	D₁₁	semidirect
15. C₃×C₂₅₁	C₂×D₁₁	semidirect
18. D₂₅₁	D₃₃	direct (N × H)
19. C₂₅₁	C₂×D₃₃	semidirect
23. D₃₃	D₂₅₁	direct (N × H)
25. C₃×C₁₁	C₂×D₂₅₁	semidirect
30. C₁₁	D₃×D₂₅₁	semidirect
35. C₃	D₁₁×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
D₈₂₈₃	2
D₃₃×C₂₅₁	2
C₃×C₁₁×D₂₅₁	2
D₁₁×D₂₅₁	3
D₃×D₂₅₁	11
C₂×D₃₃	251

Subgroups — D33×D251 #45684029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₃×D₂₅₁ #45684029