Subgroups — C₃×#21419252 #36381081

Order 22599.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578892	C₃	1	1	yes	maximal, characteristic
2	C₃×#14578892	C₃	1	1	yes	maximal, characteristic
3	C₃×#14578887	C₃	1	1	yes	maximal, characteristic
4	#21419252	C₃	1	9	yes	maximal, direct product factor
5	C₃×C₃₁×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
6	C₃²×C₃₁⋊C₉	—	3	1	no	—
7	#14578892	—	3	2	no	—
8	#14578892	C₉	1	6	yes	complemented
9	#14578892	C₃²	1	3	yes	—
10	#14578892	C₃²	1	3	yes	—
11	C₃×C₃₁⋊C₂₇	—	3	1	no	—
12	C₃×C₃₁⋊C₂₇	C₉	1	3	yes	complemented
13	#14578887	—	3	2	no	—
14	#14578887	C₃²	1	3	yes	—
15	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
16	C₃₁×C₂₇⋊C₃	—	3	2	no	—
17	C₃₁×C₂₇⋊C₃	C₃²	1	3	yes	—
18	C₃×C₂₇×C₃₁	—	3	1	no	—
19	C₃³×C₃₁	3₋¹⁺²	1	1	yes	characteristic
20	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₃₁	C₃×C₉	1	2	yes	—
22	C₃×C₉×C₃₁	3₋¹⁺²	1	2	yes	—
23	C₃×C₉×C₃₁	3₋¹⁺²	1	1	yes	characteristic
24	C₃×C₉×C₃₁	3₋¹⁺²	1	2	yes	—
25	C₃×C₉×C₃₁	3₋¹⁺²	1	1	yes	characteristic
26	C₃×C₉×C₃₁	3₋¹⁺²	1	2	yes	—
27	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
28	C₃×C₃₁⋊C₉	—	3	3	no	—
29	C₃×C₃₁⋊C₉	—	9	3	no	—
30	C₂₇×C₃₁	—	3	3	no	—
31	C₃₁⋊C₂₇	—	3	3	no	—
32	C₃₁⋊C₂₇	C₃×C₉	1	9	yes	complemented
33	C₃×#6875	—	31	1	no	maximal, Sylow
34	C₃²×C₃₁	—	3	3	no	—
35	C₃²×C₃₁	C₉⋊C₉	1	2	yes	—
36	C₃²×C₃₁	C₉⋊C₉	1	1	yes	characteristic
37	C₃²×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
38	C₉×C₃₁	C₉⋊C₉	1	2	yes	—
39	C₉×C₃₁	C₉⋊C₉	1	2	yes	—
40	C₉×C₃₁	C₉⋊C₉	1	2	yes	—
41	C₉×C₃₁	C₃²×C₉	1	1	yes	characteristic
42	C₉×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
43	C₉×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
44	C₃₁⋊C₉	—	9	3	no	—
45	C₃×C₂₇⋊C₃	—	31	1	no	—
46	C₃×C₂₇⋊C₃	—	31	1	no	—
47	C₃×C₂₇⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic
48	C₃×C₉⋊C₉	—	31	1	no	—
49	#6875	—	31	9	no	—
50	C₃×C₃₁	—	3	1	no	—
51	C₃×C₃₁	—	3	2	no	—
52	C₃×C₃₁	#6875	1	3	yes	complemented
53	C₃×C₃₁	C₃×C₉⋊C₉	1	1	yes	characteristic
54	C₃²×C₉	—	93	1	no	—
55	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
56	C₂₇⋊C₃	—	3	2	no	—
57	C₂₇⋊C₃	—	31	6	no	—
58	C₂₇⋊C₃	—	31	3	no	—
59	C₂₇⋊C₃	—	31	3	no	—
60	C₂₇⋊C₃	—	93	2	no	—
61	C₂₇⋊C₃	C₃×C₃₁⋊C₃	1	3	yes	—
62	C₃×C₂₇	—	3	1	no	—
63	C₃×C₂₇	—	31	3	no	—
64	C₃×C₂₇	—	93	1	no	—
65	C₉⋊C₉	—	31	3	no	—
66	C₉⋊C₉	—	93	2	no	—
67	C₃₁	C₃×#6875	1	1	yes	characteristic, complemented, Sylow
68	C₃³	#11719687	1	1	yes	characteristic
69	C₃×C₉	—	279	3	no	—
70	C₃×C₉	—	93	3	no	—
71	C₃×C₉	C₉×C₃₁⋊C₃	1	2	yes	—
72	C₃×C₉	C₉×C₃₁⋊C₃	1	1	yes	characteristic
73	C₃×C₉	#11719686	1	2	yes	—
74	C₃×C₉	#11719686	1	1	yes	characteristic
75	C₃×C₉	#11719687	1	2	yes	—
76	C₃×C₉	#11719689	1	2	yes	—
77	C₃×C₉	#11719689	1	1	yes	characteristic
78	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
79	C₂₇	—	3	3	no	—
80	C₂₇	—	31	9	no	—
81	C₂₇	—	93	3	no	—
82	C₃²	—	3	3	no	—
83	C₃²	(C₃₁⋊C₉)⋊C₉	1	2	yes	—
84	C₃²	(C₃₁⋊C₉)⋊C₉	1	1	yes	characteristic
85	C₃²	C₃×#11719687	1	1	yes	characteristic
86	C₉	—	279	3	no	—
87	C₉	(C₃₁⋊C₉)⋊C₉	1	2	yes	—
88	C₉	(C₃₁⋊C₉)⋊C₉	1	2	yes	—
89	C₉	(C₃₁⋊C₉)⋊C₉	1	2	yes	—
90	C₉	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic
91	C₉	C₃×#11719686	1	1	yes	characteristic
92	C₉	C₃×#11719689	1	1	yes	characteristic
93	C₃	—	3	1	no	—
94	C₃	—	3	2	no	—
95	C₃	#21419252	1	3	yes	direct product factor
96	C₃	C₃×(C₃₁⋊C₉)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	(C₃₁⋊C₉)⋊C₉
commutator	C₉×C₃₁	C₃²×C₉
Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
Fitting	C₃×C₃₁×C₂₇⋊C₃	C₃
socle	C₃²×C₃₁	C₉⋊C₉
prime radical	C₃³×C₃₁	3₋¹⁺²
cosocle	C₃×C₉×C₃₁	C₃³
hypercenter	C₃×C₂₇⋊C₃	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#6875
LCS	G ▷ C₉×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
4. #21419252	C₃	direct (N × H)
8. #14578892	C₉	semidirect
12. C₃×C₃₁⋊C₂₇	C₉	semidirect
32. C₃₁⋊C₂₇	C₃×C₉	semidirect
52. C₃×C₃₁	#6875	semidirect
67. C₃₁	C₃×#6875	semidirect
95. C₃	#21419252	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×#14578892	3
C₃×#14578887	3
#21419252	3
C₃×C₃₁×C₂₇⋊C₃	3
C₃×#6875	31

Subgroups — C3×#21419252 #36381081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21419252 #36381081