Subgroups — C₃×#21419248 #36381065

Order 22599.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁⋊C₂₇	C₃	1	3	yes	maximal
2	#21419248	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₃×C₃₁⋊C₂₇	—	3	9	no	—
5	C₃×C₃₁⋊C₂₇	C₃²	1	9	yes	—
6	C₃²×C₉×C₃₁	C₉	1	2	yes	—
7	C₃²×C₉×C₃₁	C₉	1	1	yes	characteristic
8	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
9	C₉²×C₃₁	C₉	1	6	yes	—
10	C₉²×C₃₁	C₃²	1	3	yes	—
11	C₃³×C₃₁	C₃×C₉	1	1	yes	characteristic
12	C₃×C₉×C₃₁	—	3	6	no	—
13	C₃×C₉×C₃₁	C₂₇	1	9	yes	complemented
14	C₃×C₉×C₃₁	C₃×C₉	1	6	yes	—
15	C₃×C₉×C₃₁	C₃×C₉	1	2	yes	—
16	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
17	C₃×C₉×C₃₁	3₋¹⁺²	1	9	yes	—
18	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
19	C₃₁⋊C₂₇	—	3	9	no	—
20	C₃×C₉⋊C₂₇	—	31	1	no	maximal, Sylow
21	C₃²×C₃₁	C₉⋊C₉	1	3	yes	—
22	C₃²×C₃₁	C₃×C₂₇	1	3	yes	—
23	C₃²×C₃₁	C₂₇⋊C₃	1	6	yes	—
24	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
25	C₉×C₃₁	—	3	6	no	—
26	C₉×C₃₁	C₉⋊C₉	1	6	yes	—
27	C₉×C₃₁	C₃×C₂₇	1	9	yes	complemented
28	C₉×C₃₁	C₃×3₋¹⁺²	1	3	yes	—
29	C₃²×C₂₇	—	31	3	no	—
30	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic
31	C₉⋊C₂₇	—	31	9	no	—
32	C₃×C₃₁	C₉⋊C₂₇	1	9	yes	complemented
33	C₃×C₃₁	C₃×C₉⋊C₉	1	1	yes	characteristic
34	C₃×C₃₁	C₃²×C₂₇	1	1	yes	characteristic
35	C₃×C₃₁	C₃×C₂₇⋊C₃	1	2	yes	—
36	C₃²×C₉	C₃₁⋊C₉	1	2	yes	—
37	C₃²×C₉	C₃₁⋊C₉	1	1	yes	characteristic
38	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
39	C₃×C₂₇	—	31	9	no	—
40	C₃×C₂₇	—	93	9	no	—
41	C₉²	C₃₁⋊C₉	1	6	yes	—
42	C₉²	C₃×C₃₁⋊C₃	1	3	yes	—
43	C₃₁	C₃×C₉⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
44	C₃³	C₃×C₃₁⋊C₉	1	1	yes	characteristic
45	C₃×C₉	—	3	6	no	—
46	C₃×C₉	C₃₁⋊C₂₇	1	9	yes	complemented
47	C₃×C₉	#11719687	1	9	yes	—
48	C₃×C₉	C₃×C₃₁⋊C₉	1	6	yes	—
49	C₃×C₉	C₃×C₃₁⋊C₉	1	2	yes	—
50	C₃×C₉	C₃×C₃₁⋊C₉	1	3	yes	—
51	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
52	C₂₇	—	93	9	no	—
53	C₃²	#14578887	1	3	yes	—
54	C₃²	C₃×C₃₁⋊C₂₇	1	3	yes	—
55	C₃²	#14578892	1	6	yes	—
56	C₃²	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
57	C₉	—	3	6	no	—
58	C₉	#14578887	1	6	yes	—
59	C₉	C₃×C₃₁⋊C₂₇	1	9	yes	complemented
60	C₉	C₃×#11719687	1	3	yes	—
61	C₃	#21419248	1	9	yes	direct product factor
62	C₃	C₃×#14578887	1	1	yes	characteristic
63	C₃	C₃²×C₃₁⋊C₂₇	1	1	yes	characteristic
64	C₃	C₃×#14578892	1	2	yes	—

	subgroup	G/H
center	C₃²×C₉	C₃×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃²×C₂₇
Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
Fitting	C₃×C₉²×C₃₁	C₃
socle, prime radical	C₃³×C₃₁	C₃×C₉
cosocle	C₃×C₉×C₃₁	C₃³
hypercenter	C₃×C₉²	C₃₁⋊C₃
hypocenter	C₃₁	C₃×C₉⋊C₂₇
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃²×C₉ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. #21419248	C₃	direct (N × H)
13. C₃×C₉×C₃₁	C₂₇	semidirect
27. C₉×C₃₁	C₃×C₂₇	semidirect
32. C₃×C₃₁	C₉⋊C₂₇	semidirect
43. C₃₁	C₃×C₉⋊C₂₇	semidirect
46. C₃×C₉	C₃₁⋊C₂₇	semidirect
59. C₉	C₃×C₃₁⋊C₂₇	semidirect
61. C₃	#21419248	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₃₁⋊C₂₇	3
#21419248	3
C₃×C₉²×C₃₁	3
C₃×C₉⋊C₂₇	31

Subgroups — C3×#21419248 #36381065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21419248 #36381065