Subgroups — D₁₆₁⋊(C₃⋊D₃) #19153993

Order 5796.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₁₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₁⋊D₂₃	—	3	4	no	maximal
5	C₃²×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂₃×D₂₁	—	3	4	no	—
7	C₇×D₆₉	—	3	4	no	—
8	C₃×D₁₆₁	D₃	1	4	yes	complemented
9	C₃⋊D₃×D₂₃	—	7	1	no	maximal, Hall
10	D₇×D₂₃	—	9	1	no	Hall
11	C₃×C₇×C₂₃	C₂×D₃	1	4	yes	complemented
12	C₃⋊D₆₉	D₇	1	1	yes	characteristic, complemented
13	C₃⋊D₃×C₂₃	—	7	1	no	—
14	C₃²×D₂₃	—	7	1	no	—
15	D₁₆₁	C₃⋊D₃	1	1	yes	characteristic, complemented
16	C₇×D₂₃	—	9	1	no	—
17	D₇×C₂₃	—	9	1	no	—
18	D₃×D₂₃	—	21	4	no	—
19	D₇×C₃⋊D₃	—	23	1	no	maximal, Hall
20	C₃²×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₇×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
22	D₆₉	—	3	4	no	—
23	C₃×D₂₃	—	7	4	no	—
24	D₃×C₂₃	—	21	4	no	—
25	C₃⋊D₂₁	D₂₃	1	1	yes	characteristic, complemented
26	C₇×C₃⋊D₃	—	23	1	no	—
27	C₃²×D₇	—	23	1	no	—
28	C₂×D₂₃	—	63	1	no	Hall
29	D₃×D₇	—	69	4	no	—
30	C₃×C₂₃	D₃×D₇	1	4	yes	complemented
31	C₃²×C₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂₃	—	63	1	no	—
33	D₂₃	—	7	1	no	—
34	D₂₃	—	9	1	no	—
35	D₂₁	—	3	4	no	—
36	C₃×D₇	—	23	4	no	—
37	D₃×C₇	—	69	4	no	—
38	C₂×C₃⋊D₃	—	161	1	no	Hall
39	C₂×D₇	—	207	1	no	Hall
40	C₂₃	D₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₇	D₃×D₂₃	1	4	yes	complemented
42	C₂×C₃²	—	161	1	no	—
43	C₃⋊D₃	—	7	1	no	—
44	C₃⋊D₃	—	23	1	no	—
45	C₂×C₇	—	207	1	no	—
46	D₇	—	9	1	no	—
47	D₇	—	23	1	no	—
48	C₂×D₃	—	483	4	no	—
49	C₃²	D₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₃⋊D₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	161	4	no	—
52	D₃	—	21	4	no	—
53	D₃	—	69	4	no	—
54	C₂²	—	1449	1	no	Sylow
55	C₃	D₂₁⋊D₂₃	1	4	yes	complemented
56	C₂	—	63	1	no	—
57	C₂	—	161	1	no	—
58	C₂	—	207	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₂₃	C₂²
LCS	G ▷ C₃²×C₇×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₃⋊D₂₁	C₂	semidirect
2. C₇×C₃⋊D₆₉	C₂	semidirect
3. C₃²×D₁₆₁	C₂	semidirect
5. C₃²×C₇×C₂₃	C₂²	semidirect
8. C₃×D₁₆₁	D₃	semidirect
11. C₃×C₇×C₂₃	C₂×D₃	semidirect
12. C₃⋊D₆₉	D₇	semidirect
15. D₁₆₁	C₃⋊D₃	semidirect
20. C₃²×C₂₃	C₂×D₇	semidirect
21. C₇×C₂₃	C₂×C₃⋊D₃	semidirect
25. C₃⋊D₂₁	D₂₃	semidirect
30. C₃×C₂₃	D₃×D₇	semidirect
31. C₃²×C₇	C₂×D₂₃	semidirect
40. C₂₃	D₇×C₃⋊D₃	semidirect
41. C₃×C₇	D₃×D₂₃	semidirect
49. C₃²	D₇×D₂₃	semidirect
50. C₇	C₃⋊D₃×D₂₃	semidirect
55. C₃	D₂₁⋊D₂₃	semidirect

Subgroups — D161⋊(C3⋊D3) #19153993

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆₁⋊(C₃⋊D₃) #19153993