Subgroups — C₃×#21419215 #36380050

Order 22599.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₃₁⋊C₉)	C₃	1	1	yes	maximal, characteristic
2	C₃×C₃²⋊(C₃₁⋊C₉)	C₃	1	2	yes	maximal
3	#21419215	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₃₁×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₃²×C₃₁⋊C₉	—	3	1	no	—
6	C₃²×C₃₁⋊C₉	—	3	2	no	—
7	C₃²⋊(C₃₁⋊C₉)	—	3	2	no	—
8	C₃²⋊(C₃₁⋊C₉)	—	3	4	no	—
9	C₃²⋊(C₃₁⋊C₉)	C₃²	1	3	yes	—
10	C₃²⋊(C₃₁⋊C₉)	C₃²	1	6	yes	—
11	C₃⁴×C₃₁	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₃₁	—	3	1	no	—
13	C₃₁×C₃²⋊C₉	—	3	2	no	—
14	C₃₁×C₃²⋊C₉	C₃²	1	3	yes	—
15	C₃³×C₃₁	—	3	3	no	—
16	C₃³×C₃₁	—	3	3	no	—
17	C₃³×C₃₁	—	3	6	no	—
18	C₃³×C₃₁	H(3,𝔽₃)	1	2	yes	—
19	C₃³×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃³×C₃₁	C₃³	1	1	yes	characteristic
21	C₃×C₉×C₃₁	—	3	3	no	—
22	C₃×C₉×C₃₁	—	9	3	no	—
23	C₃×C₃₁⋊C₉	—	3	3	no	—
24	C₃×C₃₁⋊C₉	—	3	6	no	—
25	C₃×C₃₁⋊C₉	—	9	3	no	—
26	C₃×C₃₁⋊C₉	—	9	6	no	—
27	C₃×#6861	—	31	1	no	maximal, Sylow
28	C₃²×C₃₁	—	3	2	no	—
29	C₃²×C₃₁	—	3	1	no	—
30	C₃²×C₃₁	—	3	2	no	—
31	C₃²×C₃₁	—	3	1	no	—
32	C₃²×C₃₁	—	3	4	no	—
33	C₃²×C₃₁	—	3	2	no	—
34	C₃²×C₃₁	—	9	9	no	—
35	C₃²×C₃₁	#731	1	3	yes	—
36	C₃²×C₃₁	#732	1	3	yes	—
37	C₃²×C₃₁	#733	1	6	yes	—
38	C₃²×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
39	C₉×C₃₁	—	9	3	no	—
40	C₃₁⋊C₉	—	9	3	no	—
41	C₃₁⋊C₉	—	9	6	no	—
42	C₃×C₃²⋊C₉	—	31	1	no	—
43	C₃×C₃²⋊C₉	—	31	2	no	—
44	C₃×C₃²⋊C₉	C₃₁⋊C₃	1	1	yes	characteristic
45	#6861	—	31	9	no	—
46	C₃×C₃₁	—	9	2	no	—
47	C₃×C₃₁	—	9	1	no	—
48	C₃×C₃₁	#6861	1	9	yes	complemented
49	C₃×C₃₁	C₃×#731	1	1	yes	characteristic
50	C₃×C₃₁	C₃×#732	1	1	yes	characteristic
51	C₃×C₃₁	C₃×#733	1	2	yes	—
52	C₃⁴	C₃×C₃₁⋊C₃	1	1	yes	characteristic
53	C₃²×C₉	—	3	1	no	—
54	C₃²×C₉	—	93	1	no	—
55	C₃²×C₉	—	93	2	no	—
56	C₃²⋊C₉	—	3	2	no	—
57	C₃²⋊C₉	—	31	3	no	—
58	C₃²⋊C₉	—	31	6	no	—
59	C₃²⋊C₉	—	93	2	no	—
60	C₃²⋊C₉	—	93	4	no	—
61	C₃²⋊C₉	C₃×C₃₁⋊C₃	1	3	yes	—
62	C₃₁	C₃×#6861	1	1	yes	characteristic, complemented, Sylow
63	C₃³	—	3	3	no	—
64	C₃³	—	3	3	no	—
65	C₃³	—	3	6	no	—
66	C₃³	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
67	C₃³	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
68	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
69	C₃×C₉	—	3	3	no	—
70	C₃×C₉	—	9	3	no	—
71	C₃×C₉	—	279	3	no	—
72	C₃×C₉	—	279	6	no	—
73	C₃×C₉	—	93	3	no	—
74	C₃×C₉	—	93	6	no	—
75	C₃²	—	3	2	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	3	2	no	—
78	C₃²	—	3	1	no	—
79	C₃²	—	3	4	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	9	9	no	—
82	C₃²	#14578897	1	3	yes	—
83	C₃²	#14578899	1	3	yes	—
84	C₃²	#14578901	1	6	yes	—
85	C₃²	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
86	C₉	—	9	3	no	—
87	C₉	—	279	3	no	—
88	C₉	—	279	6	no	—
89	C₃	—	9	2	no	—
90	C₃	—	9	1	no	—
91	C₃	#21419215	1	9	yes	direct product factor
92	C₃	C₃×#14578897	1	1	yes	characteristic
93	C₃	C₃×#14578899	1	1	yes	characteristic
94	C₃	C₃×#14578901	1	2	yes	—

	subgroup	G/H
center	C₃³	C₃²⋊(C₃₁⋊C₃)
commutator, cosocle	C₃³×C₃₁	C₃³
Frattini	C₃³	C₃²×C₃₁⋊C₃
Fitting	C₃×C₃₁×C₃²⋊C₉	C₃
socle	C₃³×C₃₁	H(3,𝔽₃)
prime radical	C₃⁴×C₃₁	C₃²
hypercenter	C₃×C₃²⋊C₉	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#6861
LCS	G ▷ C₃³×C₃₁ ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃³ ◁ C₃⁴ ◁ C₃×C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. #21419215	C₃	direct (N × H)
48. C₃×C₃₁	#6861	semidirect
62. C₃₁	C₃×#6861	semidirect
91. C₃	#21419215	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×C₃²⋊(C₃₁⋊C₉)	3
#21419215	3
C₃×C₃₁×C₃²⋊C₉	3
C₃×#6861	31

Subgroups — C3×#21419215 #36380050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21419215 #36380050