Subgroups — C₃×#21419264 #36382076

Order 22599.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578900	C₃	1	2	yes	maximal, complemented
2	C₃×C₉×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#21419264	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₃₁×#732	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×C₃²⋊(C₃₁⋊C₃)	—	3	2	no	—
6	C₃²×C₃₁⋊C₉	—	3	1	no	—
7	#14578900	—	3	4	no	—
8	#14578900	C₃²	1	6	yes	complemented
9	C₉×C₃₁⋊C₉	—	3	2	no	—
10	C₉×C₃₁⋊C₉	C₃²	1	3	yes	complemented
11	C₃×H(3,𝔽₃)×C₃₁	—	3	1	no	—
12	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
13	C₃₁×#732	—	3	2	no	—
14	C₃₁×#732	C₃²	1	3	yes	complemented
15	C₃³×C₃₁	—	9	1	no	—
16	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
17	C₃²×C₃₁⋊C₃	—	9	2	no	—
18	H(3,𝔽₃)×C₃₁	—	3	3	no	—
19	H(3,𝔽₃)×C₃₁	—	9	2	no	—
20	C₃×C₉×C₃₁	—	3	2	no	—
21	C₃×C₉×C₃₁	—	3	1	no	—
22	C₃×C₉×C₃₁	H(3,𝔽₃)	1	2	yes	—
23	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
24	C₃²⋊(C₃₁⋊C₃)	—	3	6	no	—
25	C₃²⋊(C₃₁⋊C₃)	—	9	4	no	—
26	C₃×C₃₁⋊C₉	—	3	9	no	—
27	C₃×C₃₁⋊C₉	—	3	3	no	—
28	C₃×#6879	—	31	1	no	maximal, Sylow
29	C₃²×C₃₁	—	3	3	no	—
30	C₃²×C₃₁	—	9	3	no	—
31	C₃²×C₃₁	—	27	3	no	—
32	C₃²×C₃₁	#732	1	2	yes	—
33	C₃²×C₃₁	#732	1	1	yes	characteristic
34	C₃²×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃×C₃₁⋊C₃	—	9	6	no	—
36	C₃×C₃₁⋊C₃	—	27	6	no	—
37	C₉×C₃₁	—	3	2	no	—
38	C₉×C₃₁	—	3	1	no	—
39	C₃₁⋊C₉	—	3	9	no	—
40	C₃×#732	—	31	2	no	—
41	C₃×#732	C₃₁⋊C₃	1	1	yes	characteristic, complemented
42	C₃×C₉²	—	31	1	no	—
43	#6879	—	31	9	no	—
44	C₃×C₃₁	—	3	1	no	—
45	C₃×C₃₁	—	3	2	no	—
46	C₃×C₃₁	—	27	3	no	—
47	C₃×C₃₁	#6879	1	3	yes	complemented
48	C₃×C₃₁	C₃×#732	1	1	yes	characteristic
49	C₃₁⋊C₃	—	27	6	no	—
50	C₃×H(3,𝔽₃)	—	3	1	no	—
51	C₃×H(3,𝔽₃)	—	93	2	no	—
52	C₃²×C₉	—	93	1	no	—
53	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
54	#732	—	3	2	no	—
55	#732	—	31	6	no	—
56	#732	—	93	4	no	—
57	#732	C₃×C₃₁⋊C₃	1	3	yes	complemented
58	C₉²	—	31	3	no	—
59	C₉²	—	93	2	no	—
60	C₃₁	C₃×#6879	1	1	yes	characteristic, complemented, Sylow
61	C₃³	—	9	1	no	—
62	C₃³	—	279	2	no	—
63	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
64	H(3,𝔽₃)	—	3	3	no	—
65	H(3,𝔽₃)	—	9	2	no	—
66	H(3,𝔽₃)	—	279	4	no	—
67	H(3,𝔽₃)	—	93	6	no	—
68	C₃×C₉	—	3	2	no	—
69	C₃×C₉	—	3	1	no	—
70	C₃×C₉	—	93	9	no	—
71	C₃×C₉	—	93	3	no	—
72	C₃×C₉	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
73	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
74	C₃²	—	3	3	no	—
75	C₃²	—	9	3	no	—
76	C₃²	—	279	6	no	—
77	C₃²	—	27	3	no	—
78	C₃²	—	837	6	no	—
79	C₃²	#14578899	1	2	yes	—
80	C₃²	#14578899	1	1	yes	characteristic
81	C₃²	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
82	C₉	—	3	2	no	—
83	C₉	—	3	1	no	—
84	C₉	—	93	9	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	2	no	—
87	C₃	—	27	3	no	—
88	C₃	—	837	6	no	—
89	C₃	#21419264	1	3	yes	direct product factor
90	C₃	C₃×#14578899	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#14578899
commutator, cosocle	C₃×C₉×C₃₁	C₃³
Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
Fitting	C₃×C₃₁×#732	C₃
socle	C₃²×C₃₁	#732
hypercenter	C₃×#732	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#6879
LCS	G ▷ C₃×C₉×C₃₁ ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#732

Complements

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

N	H ≅ G/N	type
1. C₃×#14578900	C₃	semidirect
2. C₃×C₉×C₃₁⋊C₉	C₃	semidirect
3. #21419264	C₃	direct (N × H)
4. C₃×C₃₁×#732	C₃	semidirect
8. #14578900	C₃²	semidirect
10. C₉×C₃₁⋊C₉	C₃²	semidirect
14. C₃₁×#732	C₃²	semidirect
41. C₃×#732	C₃₁⋊C₃	semidirect
47. C₃×C₃₁	#6879	semidirect
57. #732	C₃×C₃₁⋊C₃	semidirect
60. C₃₁	C₃×#6879	semidirect
89. C₃	#21419264	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×#14578900	3
C₃×C₉×C₃₁⋊C₉	3
#21419264	3
C₃×C₃₁×#732	3
C₃×#6879	31

Subgroups — C3×#21419264 #36382076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21419264 #36382076