Subgroups — D₃₃⋊D₁₈₁ #37560682

Order 23892.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₃×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₅₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₉₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₁₈₁	—	3	1	no	maximal, Hall
5	C₃×C₁₁×C₁₈₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉₉₁	D₃	1	1	yes	characteristic, complemented
7	C₁₁×D₁₈₁	—	3	1	no	—
8	D₁₁×C₁₈₁	—	3	1	no	—
9	D₃×D₁₈₁	—	11	1	no	maximal, Hall
10	C₁₁×C₁₈₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₅₄₃	D₁₁	1	1	yes	characteristic, complemented
12	C₃×D₁₈₁	—	11	1	no	—
13	D₃×C₁₈₁	—	11	1	no	—
14	C₂×D₁₈₁	—	33	1	no	Hall
15	C₃×C₁₈₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₈₁	—	33	1	no	—
17	D₁₈₁	—	3	1	no	—
18	D₁₈₁	—	11	1	no	—
19	C₁₈₁	D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₁₁	—	181	1	no	maximal, Hall
21	D₃₃	D₁₈₁	1	1	yes	characteristic, complemented
22	C₃×D₁₁	—	181	1	no	—
23	D₃×C₁₁	—	181	1	no	—
24	C₂×D₁₁	—	543	1	no	Hall
25	C₃×C₁₁	C₂×D₁₈₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁	—	543	1	no	—
27	D₁₁	—	3	1	no	—
28	D₁₁	—	181	1	no	—
29	C₂×D₃	—	1991	1	no	Hall
30	C₁₁	D₃×D₁₈₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	1991	1	no	—
32	D₃	—	11	1	no	—
33	D₃	—	181	1	no	—
34	C₂²	—	5973	1	no	Sylow
35	C₃	D₁₁×D₁₈₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	543	1	no	—
37	C₂	—	33	1	no	—
38	C₂	—	1991	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₈₁	C₂²
LCS	G ▷ C₃×C₁₁×C₁₈₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃₃×C₁₈₁	C₂	semidirect
2. C₁₁×D₅₄₃	C₂	semidirect
3. C₃×D₁₉₉₁	C₂	semidirect
5. C₃×C₁₁×C₁₈₁	C₂²	semidirect
6. D₁₉₉₁	D₃	semidirect
10. C₁₁×C₁₈₁	C₂×D₃	semidirect
11. D₅₄₃	D₁₁	semidirect
15. C₃×C₁₈₁	C₂×D₁₁	semidirect
19. C₁₈₁	D₃×D₁₁	semidirect
21. D₃₃	D₁₈₁	semidirect
25. C₃×C₁₁	C₂×D₁₈₁	semidirect
30. C₁₁	D₃×D₁₈₁	semidirect
35. C₃	D₁₁×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
D₃₃×C₁₈₁	2
C₁₁×D₅₄₃	2
C₃×D₁₉₉₁	2
D₁₁×D₁₈₁	3
D₃×D₁₈₁	11
D₃×D₁₁	181

Subgroups — D33⋊D181 #37560682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₃⋊D₁₈₁ #37560682