Subgroups — C₂²×C₃₁×C₃₁⋊C₉ #46829331

Order 34596.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₃₁⋊C₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₃₁²	C₃	1	1	yes	maximal, characteristic
3	C₃₁×C₃₁⋊C₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₃₁²	C₂×C₃	1	3	yes	—
5	C₂²×C₃₁²	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₃₁²	C₂²×C₃	1	1	yes	characteristic
7	C₂×C₃₁²	C₂×C₉	1	3	yes	complemented
8	C₂²×C₉×C₃₁	—	31	1	no	maximal
9	C₂²×C₃₁⋊C₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor
10	C₃₁²	C₂²×C₉	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₉×C₃₁	—	31	3	no	—
12	C₂×C₃₁⋊C₉	C₂×C₃₁	1	3	yes	direct product factor
13	C₂²×C₃×C₃₁	—	3	10	no	—
14	C₂²×C₃×C₃₁	C₃₁⋊C₃	1	1	yes	characteristic
15	C₂²×C₃×C₃₁	C₃×C₃₁	1	1	yes	characteristic
16	C₉×C₃₁	—	31	1	no	—
17	C₃₁⋊C₉	C₂²×C₃₁	1	1	yes	characteristic, direct product factor
18	C₂×C₃×C₃₁	—	3	30	no	—
19	C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	1	3	yes	—
20	C₂×C₃×C₃₁	C₂×C₃×C₃₁	1	3	yes	—
21	C₂²×C₃₁	—	3	10	no	—
22	C₂²×C₃₁	C₃₁⋊C₉	1	1	yes	characteristic, direct product factor
23	C₂²×C₃₁	C₉×C₃₁	1	1	yes	characteristic, complemented
24	C₃×C₃₁	—	3	10	no	—
25	C₃×C₃₁	C₂²×C₃₁⋊C₃	1	1	yes	characteristic
26	C₃×C₃₁	C₂²×C₃×C₃₁	1	1	yes	characteristic
27	C₂×C₃₁	—	3	30	no	—
28	C₂×C₃₁	C₂×C₃₁⋊C₉	1	3	yes	direct product factor
29	C₂×C₃₁	C₂×C₉×C₃₁	1	3	yes	complemented
30	C₂²×C₉	—	31	1	no	Hall
31	C₃₁	—	3	10	no	—
32	C₃₁	C₂²×C₃₁⋊C₉	1	1	yes	characteristic, direct product factor
33	C₃₁	C₂²×C₉×C₃₁	1	1	yes	characteristic, complemented
34	C₂×C₉	—	31	3	no	—
35	C₂²×C₃	C₃₁×C₃₁⋊C₃	1	1	yes	characteristic
36	C₉	—	31	1	no	Sylow
37	C₂×C₃	C₂×C₃₁×C₃₁⋊C₃	1	3	yes	—
38	C₂²	C₃₁×C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₃	C₂²×C₃₁×C₃₁⋊C₃	1	1	yes	characteristic
40	C₂	C₂×C₃₁×C₃₁⋊C₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₃₁	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₂²×C₉×C₃₁
Frattini	C₃	C₂²×C₃₁×C₃₁⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₃₁²	C₃
cosocle	C₃×C₃₁	C₂²×C₃×C₃₁
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂²×C₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×C₃₁⋊C₉	C₂	direct (N × H)
3. C₃₁×C₃₁⋊C₉	C₂²	direct (N × H)
5. C₂²×C₃₁²	C₉	semidirect
7. C₂×C₃₁²	C₂×C₉	semidirect
9. C₂²×C₃₁⋊C₉	C₃₁	direct (N × H)
10. C₃₁²	C₂²×C₉	semidirect
12. C₂×C₃₁⋊C₉	C₂×C₃₁	direct (N × H)
17. C₃₁⋊C₉	C₂²×C₃₁	direct (N × H)
22. C₂²×C₃₁	C₃₁⋊C₉	direct (N × H)
23. C₂²×C₃₁	C₉×C₃₁	semidirect
28. C₂×C₃₁	C₂×C₃₁⋊C₉	direct (N × H)
29. C₂×C₃₁	C₂×C₉×C₃₁	semidirect
32. C₃₁	C₂²×C₃₁⋊C₉	direct (N × H)
33. C₃₁	C₂²×C₉×C₃₁	semidirect
38. C₂²	C₃₁×C₃₁⋊C₉	direct (N × H)
40. C₂	C₂×C₃₁×C₃₁⋊C₉	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×C₃₁×C₃₁⋊C₉	2
C₂²×C₃×C₃₁²	3
C₂²×C₉×C₃₁	31
C₂²×C₃₁⋊C₉	31

Subgroups — C22×C31×C31⋊C9 #46829331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×C₃₁⋊C₉ #46829331