Subgroups — C₃₁⋊H(3,ℤ/9) #36379541

Order 22599.

174 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419296	C₃	1	3	yes	maximal
2	C₃₁×#6887	C₃	1	1	yes	maximal, characteristic
3	#14578887	—	3	3	no	—
4	#14578886	—	3	3	no	—
5	C₃²⋊(C₃₁⋊C₉)	—	3	3	no	—
6	C₉×C₃₁⋊C₉	C₉	1	9	yes	complemented
7	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
8	C₃₁×C₉⋊C₉	—	3	2	no	—
9	C₃₁×C₃²⋊C₉	—	3	1	no	—
10	C₉²×C₃₁	C₉	1	3	yes	complemented
11	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₉×C₃₁	—	3	3	no	—
13	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
14	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₃₁	3₋¹⁺²	1	3	yes	—
16	C₃×C₉×C₃₁	3₋¹⁺²	1	3	yes	—
17	C₃×C₉×C₃₁	3₋¹⁺²	1	2	yes	—
18	C₃×C₃₁⋊C₉	—	3	9	no	—
19	H(3,ℤ/9)	—	31	1	no	maximal, Sylow
20	C₃²×C₃₁	—	9	1	no	—
21	C₃²×C₃₁	C₃²⋊C₉	1	3	yes	—
22	C₃²×C₃₁	C₃²⋊C₉	1	1	yes	characteristic
23	C₉×C₃₁	—	9	3	no	—
24	C₉×C₃₁	C₉²	1	1	yes	characteristic
25	C₉×C₃₁	C₉⋊C₉	1	6	yes	—
26	C₉×C₃₁	C₉⋊C₉	1	1	yes	characteristic
27	C₉×C₃₁	C₉⋊C₉	1	1	yes	characteristic
28	C₃₁⋊C₉	—	9	9	no	—
29	#6887	—	31	3	no	—
30	#6887	C₃₁⋊C₃	1	1	yes	characteristic
31	C₃×C₃₁	—	3	3	no	—
32	C₃×C₃₁	—	3	1	no	—
33	C₃×C₃₁	#6855	1	1	yes	characteristic
34	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
35	C₉⋊C₉	—	3	2	no	—
36	C₉⋊C₉	—	93	3	no	—
37	C₉⋊C₉	—	93	3	no	—
38	C₃²⋊C₉	—	3	1	no	—
39	C₃²⋊C₉	—	93	3	no	—
40	C₉²	—	31	9	no	—
41	C₉²	C₃₁⋊C₉	1	3	yes	complemented
42	C₃₁	H(3,ℤ/9)	1	1	yes	characteristic, complemented, Sylow
43	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
44	C₃×C₉	—	3	3	no	—
45	C₃×C₉	—	93	9	no	—
46	C₃×C₉	C₉×C₃₁⋊C₃	1	3	yes	—
47	C₃×C₉	#11719686	1	3	yes	—
48	C₃×C₉	#11719687	1	3	yes	—
49	C₃×C₉	C₃×C₃₁⋊C₉	1	1	yes	characteristic
50	C₃×C₉	#11719689	1	2	yes	—
51	C₃²	—	9	1	no	—
52	C₃²	(C₃×C₃₁⋊C₃)⋊C₉	1	3	yes	—
53	C₃²	C₃²⋊(C₃₁⋊C₉)	1	1	yes	characteristic
54	C₉	—	9	3	no	—
55	C₉	—	279	9	no	—
56	C₉	C₉×C₃₁⋊C₉	1	1	yes	characteristic
57	C₉	(C₃₁⋊C₉)⋊C₉	1	6	yes	—
58	C₉	#14578886	1	1	yes	characteristic
59	C₉	#14578887	1	1	yes	characteristic
60	C₃	—	3	1	no	—
61	C₃	—	3	3	no	—
62	C₃	C₃₁⋊#6855	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₉×C₃₁⋊C₉
commutator	C₉×C₃₁	C₉²
Frattini	C₃²×C₉	C₃×C₃₁⋊C₃
Fitting	C₃₁×#6887	C₃
socle	C₃×C₃₁	#6855
prime radical	C₃³×C₃₁	H(3,𝔽₃)
cosocle	C₃²×C₉×C₃₁	C₃²
hypercenter	#6887	C₃₁⋊C₃
hypocenter	C₃₁	H(3,ℤ/9)
LCS	G ▷ C₉×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
6. C₉×C₃₁⋊C₉	C₉	semidirect
10. C₉²×C₃₁	C₉	semidirect
41. C₉²	C₃₁⋊C₉	semidirect
42. C₃₁	H(3,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
#21419296	3
C₃₁×#6887	3
H(3,ℤ/9)	31

Subgroups — C31⋊H(3,ℤ/9) #36379541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁⋊H(3,ℤ/9) #36379541