Subgroups — C₃×#21419349 #36382346

Order 22599.

692 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419349	C₃	1	27	yes	maximal, direct product factor
2	C₃×(C₃₁⋊C₉)⋊C₉	C₃	1	8	yes	maximal, complemented
3	C₃×(C₃×C₃₁⋊C₃)⋊C₉	C₃	1	4	yes	maximal
4	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
6	C₃²×C₃₁⋊C₉	C₃²	1	8	yes	—
7	(C₃₁⋊C₉)⋊C₉	C₃²	1	72	yes	complemented
8	(C₃×C₃₁⋊C₃)⋊C₉	C₃²	1	36	yes	—
9	C₃²×C₉×C₃₁	C₃²	1	4	yes	—
10	C₉²×C₃₁	C₃²	1	9	yes	complemented
11	C₃³×C₃₁	C₃³	1	1	yes	characteristic
12	C₃²×C₃₁⋊C₃	—	3	12	no	—
13	C₃²×C₃₁⋊C₃	C₃³	1	3	yes	—
14	C₃×C₉×C₃₁	—	3	12	no	—
15	C₃×C₉×C₃₁	C₃³	1	12	yes	—
16	C₃×C₃₁⋊C₉	—	3	24	no	—
17	C₃×C₃₁⋊C₉	C₃³	1	24	yes	—
18	C₃×#6898	—	31	1	no	maximal, Sylow
19	C₃²×C₃₁	#737	1	12	yes	—
20	C₃²×C₃₁	C₃⁴	1	1	yes	characteristic
21	C₃×C₃₁⋊C₃	—	3	12	no	—
22	C₃×C₃₁⋊C₃	—	9	9	no	—
23	C₉×C₃₁	—	3	12	no	—
24	C₃₁⋊C₉	—	3	24	no	—
25	#6898	—	31	27	no	—
26	C₃×C₉⋊C₉	—	31	8	no	—
27	C₃×C₃²⋊C₉	—	31	4	no	—
28	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic, complemented
29	C₃×C₃₁	#6898	1	9	yes	complemented
30	C₃×C₃₁	C₃×#737	1	4	yes	—
31	C₃₁⋊C₃	—	9	3	no	—
32	C₃⁴	—	31	1	no	—
33	C₃²×C₉	—	31	8	no	—
34	C₃²×C₉	C₃×C₃₁⋊C₃	1	4	yes	—
35	C₉⋊C₉	—	31	72	no	—
36	C₃²⋊C₉	—	31	36	no	—
37	C₉²	C₃×C₃₁⋊C₃	1	9	yes	complemented
38	C₃₁	C₃×#6898	1	1	yes	characteristic, complemented, Sylow
39	C₃³	—	31	3	no	—
40	C₃³	—	93	12	no	—
41	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
42	C₃×C₉	—	3	12	no	—
43	C₃×C₉	—	31	24	no	—
44	C₃×C₉	—	93	24	no	—
45	C₃×C₉	C₃²×C₃₁⋊C₃	1	12	yes	—
46	C₃²	—	279	9	no	—
47	C₃²	—	93	12	no	—
48	C₃²	#14578912	1	12	yes	—
49	C₃²	C₃³×C₃₁⋊C₃	1	1	yes	characteristic
50	C₉	—	3	12	no	—
51	C₉	—	93	24	no	—
52	C₃	—	279	3	no	—
53	C₃	#21419349	1	9	yes	direct product factor
54	C₃	C₃×#14578912	1	4	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₃₁⋊C₃
commutator, cosocle	C₃²×C₃₁	C₃⁴
Frattini	C₃²	C₃³×C₃₁⋊C₃
Fitting	C₃×C₉²×C₃₁	C₃
socle	C₃³×C₃₁	C₃³
prime radical	C₃³×C₃₁⋊C₃	C₃²
hypercenter	C₃×C₉²	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#6898
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
1. #21419349	C₃	direct (N × H)
2. C₃×(C₃₁⋊C₉)⋊C₉	C₃	semidirect
4. C₃×C₉²×C₃₁	C₃	semidirect
7. (C₃₁⋊C₉)⋊C₉	C₃²	semidirect
10. C₉²×C₃₁	C₃²	semidirect
28. C₃×C₉²	C₃₁⋊C₃	semidirect
29. C₃×C₃₁	#6898	semidirect
37. C₉²	C₃×C₃₁⋊C₃	semidirect
38. C₃₁	C₃×#6898	semidirect
53. C₃	#21419349	direct (N × H)

Maximal subgroups

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

subgroup	index
#21419349	3
C₃×(C₃₁⋊C₉)⋊C₉	3
C₃×(C₃×C₃₁⋊C₃)⋊C₉	3
C₃×C₉²×C₃₁	3
C₃×#6898	31

Subgroups — C3×#21419349 #36382346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21419349 #36382346