Subgroups — C₂×C₃²×C₁₁×D₇₁ #43244708

Order 28116.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×D₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₁×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₁×D₇₁	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₁×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×D₇₁	C₂×C₃	1	8	yes	direct product factor
6	C₂×C₃×C₁₁×C₇₁	C₂×C₃	1	4	yes	complemented
7	C₂×C₁₁×D₇₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃²×D₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁×C₇₁	C₂²×C₃	1	4	yes	complemented
10	C₂×C₁₁×C₇₁	C₂×C₃²	1	1	yes	characteristic, complemented
11	C₁₁×D₇₁	C₂×C₃²	1	2	yes	direct product factor
12	C₂×C₃²×C₇₁	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₃²×D₇₁	C₂×C₁₁	1	2	yes	direct product factor
14	C₂×C₃×D₇₁	C₃×C₁₁	1	4	yes	direct product factor
15	C₁₁×C₇₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇₁	C₂×C₃×C₁₁	1	4	yes	complemented
18	C₃×D₇₁	C₂×C₃×C₁₁	1	8	yes	direct product factor
19	C₂²×C₃²×C₁₁	—	71	1	no	maximal, Hall
20	C₂×D₇₁	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₇₁	C₂²×C₃×C₁₁	1	4	yes	complemented
22	C₂×C₃²×C₁₁	—	71	2	no	—
23	C₂×C₃²×C₁₁	D₇₁	1	1	yes	characteristic, direct product factor
24	C₂×C₇₁	C₂×C₃²×C₁₁	1	1	yes	characteristic, complemented
25	D₇₁	C₂×C₃²×C₁₁	1	2	yes	direct product factor
26	C₂²×C₃×C₁₁	—	71	4	no	—
27	C₃²×C₁₁	C₂×D₇₁	1	1	yes	characteristic, direct product factor, Hall
28	C₇₁	C₂²×C₃²×C₁₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃×C₁₁	—	71	8	no	—
30	C₂×C₃×C₁₁	C₃×D₇₁	1	4	yes	direct product factor
31	C₂²×C₁₁	—	71	1	no	Hall
32	C₂²×C₃²	—	71	1	no	Hall
33	C₃×C₁₁	C₂×C₃×D₇₁	1	4	yes	direct product factor
34	C₂×C₁₁	—	71	2	no	—
35	C₂×C₁₁	C₃²×D₇₁	1	1	yes	characteristic, direct product factor
36	C₂×C₃²	—	71	2	no	—
37	C₂×C₃²	C₁₁×D₇₁	1	1	yes	characteristic, direct product factor
38	C₂²×C₃	—	71	4	no	—
39	C₁₁	C₂×C₃²×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₃²	C₂×C₁₁×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	71	8	no	—
42	C₂×C₃	C₃×C₁₁×D₇₁	1	4	yes	direct product factor
43	C₂²	—	71	1	no	Sylow
44	C₃	C₂×C₃×C₁₁×D₇₁	1	4	yes	direct product factor
45	C₂	—	71	2	no	—
46	C₂	C₃²×C₁₁×D₇₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₁	D₇₁
commutator, cosocle, hypocenter	C₇₁	C₂²×C₃²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁×C₇₁	C₂
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂×C₃²×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₁×D₇₁	C₂	direct (N × H)
2. C₂×C₃²×C₁₁×C₇₁	C₂	semidirect
3. C₂×C₃×C₁₁×D₇₁	C₃	direct (N × H)
4. C₃²×C₁₁×C₇₁	C₂²	semidirect
5. C₃×C₁₁×D₇₁	C₂×C₃	direct (N × H)
6. C₂×C₃×C₁₁×C₇₁	C₂×C₃	semidirect
7. C₂×C₁₁×D₇₁	C₃²	direct (N × H)
8. C₂×C₃²×D₇₁	C₁₁	direct (N × H)
9. C₃×C₁₁×C₇₁	C₂²×C₃	semidirect
10. C₂×C₁₁×C₇₁	C₂×C₃²	semidirect
11. C₁₁×D₇₁	C₂×C₃²	direct (N × H)
12. C₂×C₃²×C₇₁	C₂×C₁₁	semidirect
13. C₃²×D₇₁	C₂×C₁₁	direct (N × H)
14. C₂×C₃×D₇₁	C₃×C₁₁	direct (N × H)
15. C₁₁×C₇₁	C₂²×C₃²	semidirect
16. C₃²×C₇₁	C₂²×C₁₁	semidirect
17. C₂×C₃×C₇₁	C₂×C₃×C₁₁	semidirect
18. C₃×D₇₁	C₂×C₃×C₁₁	direct (N × H)
20. C₂×D₇₁	C₃²×C₁₁	direct (N × H)
21. C₃×C₇₁	C₂²×C₃×C₁₁	semidirect
23. C₂×C₃²×C₁₁	D₇₁	direct (N × H)
24. C₂×C₇₁	C₂×C₃²×C₁₁	semidirect
25. D₇₁	C₂×C₃²×C₁₁	direct (N × H)
27. C₃²×C₁₁	C₂×D₇₁	direct (N × H)
28. C₇₁	C₂²×C₃²×C₁₁	semidirect
30. C₂×C₃×C₁₁	C₃×D₇₁	direct (N × H)
33. C₃×C₁₁	C₂×C₃×D₇₁	direct (N × H)
35. C₂×C₁₁	C₃²×D₇₁	direct (N × H)
37. C₂×C₃²	C₁₁×D₇₁	direct (N × H)
39. C₁₁	C₂×C₃²×D₇₁	direct (N × H)
40. C₃²	C₂×C₁₁×D₇₁	direct (N × H)
42. C₂×C₃	C₃×C₁₁×D₇₁	direct (N × H)
44. C₃	C₂×C₃×C₁₁×D₇₁	direct (N × H)
46. C₂	C₃²×C₁₁×D₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₁×D₇₁	2
C₂×C₃²×C₁₁×C₇₁	2
C₂×C₃×C₁₁×D₇₁	3
C₂×C₃²×D₇₁	11
C₂²×C₃²×C₁₁	71

Subgroups — C2×C32×C11×D71 #43244708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₁×D₇₁ #43244708