Subgroups — C₉×#14578911 #36382260

Order 22599.

986 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578911	C₃	1	1	yes	maximal, characteristic
2	#21419306	C₃	1	16	yes	maximal, complemented
3	C₉×#11719689	C₃	1	8	yes	maximal, complemented
4	H(3,𝔽₃)×C₃₁⋊C₉	C₃	1	2	yes	maximal
5	#21419293	C₃	1	8	yes	maximal, complemented
6	C₃×C₉×C₃₁⋊C₉	C₃	1	4	yes	maximal, complemented
7	C₉×H(3,𝔽₃)×C₃₁	C₃	1	1	yes	maximal, characteristic
8	#14578911	C₉	1	27	yes	direct product factor
9	C₃×#11719689	C₃²	1	8	yes	—
10	C₃²×C₃₁⋊C₉	C₃²	1	8	yes	—
11	C₃²×C₃₁⋊C₉	C₃²	1	4	yes	—
12	(C₃₁⋊C₉)⋊C₉	C₃²	1	48	yes	—
13	C₃²⋊(C₃₁⋊C₉)	C₃²	1	16	yes	—
14	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
15	C₉×C₃₁⋊C₉	C₃²	1	8	yes	—
16	C₉×C₃₁⋊C₉	C₃²	1	8	yes	—
17	C₉×C₃₁⋊C₉	C₃²	1	16	yes	—
18	C₃×H(3,𝔽₃)×C₃₁	C₃²	1	1	yes	characteristic
19	C₃²×C₉×C₃₁	C₃²	1	4	yes	—
20	C₃₁×C₃²⋊C₉	C₃²	1	8	yes	—
21	C₃³×C₃₁	C₃³	1	4	yes	—
22	H(3,𝔽₃)×C₃₁	C₃×C₉	1	9	yes	—
23	C₃×C₉×C₃₁	—	3	12	no	—
24	C₃×C₉×C₃₁	C₃³	1	8	yes	—
25	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
26	#11719689	C₃×C₉	1	72	yes	complemented
27	C₃×C₃₁⋊C₉	—	3	24	no	—
28	C₃×C₃₁⋊C₉	C₃×C₉	1	36	yes	complemented
29	C₃×C₃₁⋊C₉	C₃³	1	16	yes	—
30	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
31	C₃×C₃₁⋊C₉	C₃³	1	8	yes	—
32	C₃×C₃₁⋊C₉	C₃³	1	2	yes	—
33	C₉×#737	—	31	1	no	maximal, Sylow
34	C₃²×C₃₁	—	3	8	no	—
35	C₃²×C₃₁	—	3	4	no	—
36	C₃²×C₃₁	C₃²×C₉	1	12	yes	—
37	C₃²×C₃₁	C₃⁴	1	1	yes	characteristic
38	C₉×C₃₁	—	3	8	no	—
39	C₉×C₃₁	#737	1	3	yes	complemented
40	C₃₁⋊C₉	—	3	16	no	—
41	C₃₁⋊C₉	C₃²×C₉	1	3	yes	—
42	C₃₁⋊C₉	C₃²×C₉	1	24	yes	—
43	C₃₁⋊C₉	#737	1	6	yes	complemented
44	C₃×#737	—	31	1	no	—
45	C₉×3₋¹⁺²	—	31	8	no	—
46	C₉×3₋¹⁺²	—	31	16	no	—
47	C₉×H(3,𝔽₃)	—	31	2	no	—
48	C₉×H(3,𝔽₃)	C₃₁⋊C₃	1	1	yes	characteristic
49	#6887	—	31	8	no	—
50	C₃×C₉²	—	31	4	no	—
51	C₃×C₃₁	—	3	12	no	—
52	C₃×C₃₁	C₃³×C₉	1	1	yes	characteristic
53	C₃×C₃₁	C₃×#737	1	2	yes	—
54	C₃×C₃₁	C₃×#737	1	1	yes	characteristic
55	#737	—	31	27	no	—
56	C₃×3₋¹⁺²	—	31	8	no	—
57	C₃×H(3,𝔽₃)	C₃×C₃₁⋊C₃	1	1	yes	characteristic
58	C₃²×C₉	—	31	4	no	—
59	C₃²×C₉	—	31	8	no	—
60	C₃²×C₉	C₃×C₃₁⋊C₃	1	4	yes	—
61	C₉⋊C₉	—	31	48	no	—
62	C₃²⋊C₉	—	31	16	no	—
63	C₃²⋊C₉	C₃×C₃₁⋊C₃	1	8	yes	—
64	C₉²	—	31	8	no	—
65	C₉²	—	31	16	no	—
66	C₉²	—	31	1	no	—
67	C₉²	—	31	8	no	—
68	C₃₁	C₉×#737	1	1	yes	characteristic, complemented, Sylow
69	C₃³	C₃²×C₃₁⋊C₃	1	4	yes	—
70	3₋¹⁺²	—	31	72	no	—
71	H(3,𝔽₃)	C₉×C₃₁⋊C₃	1	9	yes	—
72	C₃×C₉	—	3	12	no	—
73	C₃×C₉	—	31	36	no	—
74	C₃×C₉	—	31	1	no	—
75	C₃×C₉	—	31	2	no	—
76	C₃×C₉	—	31	8	no	—
77	C₃×C₉	—	31	16	no	—
78	C₃×C₉	—	93	24	no	—
79	C₃×C₉	C₃²×C₃₁⋊C₃	1	8	yes	—
80	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
81	C₃²	—	3	8	no	—
82	C₃²	—	3	4	no	—
83	C₃²	C₃×C₉×C₃₁⋊C₃	1	12	yes	—
84	C₃²	C₃³×C₃₁⋊C₃	1	1	yes	characteristic
85	C₉	—	3	8	no	—
86	C₉	—	31	3	no	—
87	C₉	—	31	24	no	—
88	C₉	—	31	6	no	—
89	C₉	—	93	16	no	—
90	C₉	#14578911	1	3	yes	direct product factor
91	C₃	—	3	12	no	—
92	C₃	C₃²×C₉×C₃₁⋊C₃	1	1	yes	characteristic
93	C₃	#737×C₃₁⋊C₃	1	2	yes	—
94	C₃	C₃×#14578911	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃³×C₉
Frattini	C₃²	C₃³×C₃₁⋊C₃
Fitting	C₉×H(3,𝔽₃)×C₃₁	C₃
socle, cosocle	C₃²×C₃₁	C₃⁴
prime radical	C₃×H(3,𝔽₃)×C₃₁	C₃²
hypercenter	C₉×H(3,𝔽₃)	C₃₁⋊C₃
hypocenter	C₃₁	C₉×#737
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₉ ◁ C₉×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
2. #21419306	C₃	semidirect
3. C₉×#11719689	C₃	semidirect
5. #21419293	C₃	semidirect
6. C₃×C₉×C₃₁⋊C₉	C₃	semidirect
8. #14578911	C₉	direct (N × H)
26. #11719689	C₃×C₉	semidirect
28. C₃×C₃₁⋊C₉	C₃×C₉	semidirect
39. C₉×C₃₁	#737	semidirect
43. C₃₁⋊C₉	#737	semidirect
68. C₃₁	C₉×#737	semidirect
90. C₉	#14578911	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#14578911	3
#21419306	3
C₉×#11719689	3
H(3,𝔽₃)×C₃₁⋊C₉	3
#21419293	3
C₃×C₉×C₃₁⋊C₉	3
C₉×H(3,𝔽₃)×C₃₁	3
C₉×#737	31

Subgroups — C9×#14578911 #36382260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#14578911 #36382260