Subgroups — C₃×C₁₁×Dic₁₆₁ #36318331

Order 21252.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₁₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₁×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₁×C₂₃	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₁×Dic₂₃	—	7	1	no	maximal, Hall
6	C₃×Dic₁₆₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₁₁×C₂₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₁₁×C₂₃	D₇	1	1	yes	characteristic
9	C₁₁×Dic₂₃	—	7	1	no	Hall
10	C₂×C₃×C₇×C₂₃	C₂×C₁₁	1	1	yes	characteristic
11	C₃×C₁₁×Dic₇	—	23	1	no	maximal, Hall
12	C₃×C₁₁×C₂₃	Dic₇	1	1	yes	characteristic, complemented, Hall
13	Dic₁₆₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₁×C₂₃	C₃×D₇	1	1	yes	characteristic
15	C₃×C₇×C₂₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₇×C₁₁	D₂₃	1	1	yes	characteristic
17	C₂×C₇×C₂₃	C₂×C₃×C₁₁	1	1	yes	characteristic
18	C₁₁×Dic₇	—	23	1	no	Hall
19	C₃×Dic₂₃	—	7	1	no	Hall
20	C₁₁×C₂₃	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
21	C₃×C₇×C₁₁	Dic₂₃	1	1	yes	characteristic, complemented, Hall
22	C₇×C₂₃	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₁	C₃×D₂₃	1	1	yes	characteristic
24	C₂×C₃×C₂₃	C₁₁×D₇	1	1	yes	characteristic
25	C₃×C₄×C₁₁	—	161	1	no	Hall
26	Dic₂₃	—	7	1	no	Hall
27	C₃×Dic₇	—	23	1	no	Hall
28	C₇×C₁₁	C₃×Dic₂₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₂₃	C₁₁×Dic₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₁	D₁₆₁	1	1	yes	characteristic
31	C₂×C₂₃	C₃×C₁₁×D₇	1	1	yes	characteristic
32	C₄×C₁₁	—	161	1	no	Hall
33	C₂×C₃×C₇	C₁₁×D₂₃	1	1	yes	characteristic
34	C₃×C₁₁	Dic₁₆₁	1	1	yes	characteristic, direct product factor, Hall
35	Dic₇	—	23	1	no	Hall
36	C₂₃	C₃×C₁₁×Dic₇	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₁	C₃×D₁₆₁	1	1	yes	characteristic
38	C₃×C₇	C₁₁×Dic₂₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	C₃×C₁₁×D₂₃	1	1	yes	characteristic
40	C₃×C₄	—	161	1	no	Hall
41	C₁₁	C₃×Dic₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃×C₁₁×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	C₁₁×D₁₆₁	1	1	yes	characteristic
44	C₄	—	161	1	no	Sylow
45	C₃	C₁₁×Dic₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₁₁×D₁₆₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁	D₁₆₁
commutator, hypocenter	C₇×C₂₃	C₃×C₄×C₁₁
Frattini	C₂	C₃×C₁₁×D₁₆₁
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₁×C₂₃	C₂
cosocle	C₂×C₇×C₂₃	C₂×C₃×C₁₁
LCS	G ▷ C₇×C₂₃
UCS	C₁ ◁ C₂×C₃×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×Dic₁₆₁	C₃	direct (N × H)
3. C₃×C₇×C₁₁×C₂₃	C₄	semidirect
6. C₃×Dic₁₆₁	C₁₁	direct (N × H)
7. C₇×C₁₁×C₂₃	C₃×C₄	semidirect
12. C₃×C₁₁×C₂₃	Dic₇	semidirect
13. Dic₁₆₁	C₃×C₁₁	direct (N × H)
15. C₃×C₇×C₂₃	C₄×C₁₁	semidirect
20. C₁₁×C₂₃	C₃×Dic₇	semidirect
21. C₃×C₇×C₁₁	Dic₂₃	semidirect
22. C₇×C₂₃	C₃×C₄×C₁₁	semidirect
28. C₇×C₁₁	C₃×Dic₂₃	semidirect
29. C₃×C₂₃	C₁₁×Dic₇	semidirect
34. C₃×C₁₁	Dic₁₆₁	direct (N × H)
36. C₂₃	C₃×C₁₁×Dic₇	semidirect
38. C₃×C₇	C₁₁×Dic₂₃	semidirect
41. C₁₁	C₃×Dic₁₆₁	direct (N × H)
42. C₇	C₃×C₁₁×Dic₂₃	semidirect
45. C₃	C₁₁×Dic₁₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₁×C₂₃	2
C₁₁×Dic₁₆₁	3
C₃×C₁₁×Dic₂₃	7
C₃×Dic₁₆₁	11
C₃×C₁₁×Dic₇	23

Subgroups — C3×C11×Dic161 #36318331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×Dic₁₆₁ #36318331