Subgroups — C₂×C₃²×D₁₆₁ #19154019

Order 5796.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₆₁	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₂₃	C₂×C₃	1	4	yes	complemented
6	C₃×D₁₆₁	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃²×D₂₃	—	7	1	no	maximal, Hall
8	C₂×D₁₆₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₂₃	C₂²×C₃	1	4	yes	complemented
10	C₂×C₃²×C₂₃	D₇	1	1	yes	characteristic, complemented
11	C₃²×D₂₃	—	7	2	no	—
12	C₂×C₇×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
13	D₁₆₁	C₂×C₃²	1	2	yes	direct product factor
14	C₂×C₃×D₂₃	—	7	4	no	—
15	C₂×C₃²×D₇	—	23	1	no	maximal, Hall
16	C₃²×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₂₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₂₃	C₃×D₇	1	4	yes	complemented
19	C₃×D₂₃	—	7	8	no	—
20	C₂×C₃²×C₇	D₂₃	1	1	yes	characteristic, complemented
21	C₃²×D₇	—	23	2	no	—
22	C₂×D₂₃	—	7	1	no	Hall
23	C₂×C₃×D₇	—	23	4	no	—
24	C₃×C₂₃	C₂×C₃×D₇	1	4	yes	complemented
25	C₃²×C₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₂₃	C₃²×D₇	1	1	yes	characteristic, complemented
27	D₂₃	—	7	2	no	—
28	C₂×C₃×C₇	C₃×D₂₃	1	4	yes	complemented
29	C₃×D₇	—	23	8	no	—
30	C₂²×C₃²	—	161	1	no	Hall
31	C₂×D₇	—	23	1	no	Hall
32	C₂₃	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
33	C₃×C₇	C₂×C₃×D₂₃	1	4	yes	complemented
34	C₂×C₃²	—	161	2	no	—
35	C₂×C₃²	D₁₆₁	1	1	yes	characteristic, direct product factor
36	C₂×C₇	C₃²×D₂₃	1	1	yes	characteristic, complemented
37	D₇	—	23	2	no	—
38	C₂²×C₃	—	161	4	no	—
39	C₃²	C₂×D₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₇	C₂×C₃²×D₂₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	161	8	no	—
42	C₂×C₃	C₃×D₁₆₁	1	4	yes	direct product factor
43	C₂²	—	161	1	no	Sylow
44	C₃	C₂×C₃×D₁₆₁	1	4	yes	direct product factor
45	C₂	—	161	2	no	—
46	C₂	C₃²×D₁₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₁₆₁
commutator, hypocenter	C₇×C₂₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₂₃	C₂
LCS	G ▷ C₇×C₂₃
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₆₁	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₂₃	C₂	semidirect
3. C₂×C₃×D₁₆₁	C₃	direct (N × H)
4. C₃²×C₇×C₂₃	C₂²	semidirect
5. C₂×C₃×C₇×C₂₃	C₂×C₃	semidirect
6. C₃×D₁₆₁	C₂×C₃	direct (N × H)
8. C₂×D₁₆₁	C₃²	direct (N × H)
9. C₃×C₇×C₂₃	C₂²×C₃	semidirect
10. C₂×C₃²×C₂₃	D₇	semidirect
12. C₂×C₇×C₂₃	C₂×C₃²	semidirect
13. D₁₆₁	C₂×C₃²	direct (N × H)
16. C₃²×C₂₃	C₂×D₇	semidirect
17. C₇×C₂₃	C₂²×C₃²	semidirect
18. C₂×C₃×C₂₃	C₃×D₇	semidirect
20. C₂×C₃²×C₇	D₂₃	semidirect
24. C₃×C₂₃	C₂×C₃×D₇	semidirect
25. C₃²×C₇	C₂×D₂₃	semidirect
26. C₂×C₂₃	C₃²×D₇	semidirect
28. C₂×C₃×C₇	C₃×D₂₃	semidirect
32. C₂₃	C₂×C₃²×D₇	semidirect
33. C₃×C₇	C₂×C₃×D₂₃	semidirect
35. C₂×C₃²	D₁₆₁	direct (N × H)
36. C₂×C₇	C₃²×D₂₃	semidirect
39. C₃²	C₂×D₁₆₁	direct (N × H)
40. C₇	C₂×C₃²×D₂₃	semidirect
42. C₂×C₃	C₃×D₁₆₁	direct (N × H)
44. C₃	C₂×C₃×D₁₆₁	direct (N × H)
46. C₂	C₃²×D₁₆₁	direct (N × H)

Subgroups — C2×C32×D161 #19154019

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×D₁₆₁ #19154019