Subgroups — C₉×3₋¹⁺²×C₄₃⋊C₃ #44534650

Order 31347.

1148 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#23782792	C₃	1	4	yes	maximal, complemented
4	3₋¹⁺²×C₄₃⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₉×#11923956	C₃	1	3	yes	maximal, complemented
6	C₉×#11923957	C₃	1	3	yes	maximal, complemented
7	C₉×#11923958	C₃	1	2	yes	maximal, complemented
8	#11923957⋊C₉	C₃	1	6	yes	maximal, complemented
9	#11923956⋊C₉	C₃	1	6	yes	maximal, complemented
10	C₉⋊C₉×C₄₃⋊C₃	C₃	1	6	yes	maximal, complemented
11	C₃²⋊C₉×C₄₃⋊C₃	C₃	1	2	yes	maximal
12	C₉²×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
13	C₉×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
14	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
15	C₃×#11923958	C₃²	1	2	yes	—
16	C₃×#11923957	C₃²	1	3	yes	—
17	C₃×#11923956	C₃²	1	3	yes	—
18	3₋¹⁺²×C₄₃⋊C₃	C₉	1	27	yes	direct product factor
19	C₃²×C₄₃⋊C₉	C₃²	1	2	yes	—
20	C₃×C₉×C₄₃⋊C₃	—	3	9	no	—
21	C₃×C₉×C₄₃⋊C₃	C₃²	1	6	yes	—
22	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	—
23	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	—
24	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	—
25	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
26	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
27	C₃×C₉×C₄₃⋊C₃	C₃²	1	3	yes	—
28	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
29	#16812500	C₃²	1	6	yes	complemented
30	#16812499	C₃²	1	6	yes	complemented
31	(C₄₃⋊C₉)⋊C₉	C₃²	1	12	yes	complemented
32	(C₄₃⋊C₉)⋊C₉	C₃²	1	12	yes	complemented
33	(C₄₃⋊C₉)⋊C₉	C₃²	1	12	yes	complemented
34	C₃²⋊(C₄₃⋊C₉)	C₃²	1	4	yes	—
35	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	6	yes	—
36	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	6	yes	—
37	C₉×C₄₃⋊C₉	C₃²	1	6	yes	complemented
38	C₉×C₄₃⋊C₉	C₃²	1	12	yes	complemented
39	C₉×C₄₃⋊C₉	C₃²	1	6	yes	complemented
40	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
41	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
42	C₄₃×C₉⋊C₉	C₃²	1	6	yes	complemented
43	C₄₃×C₃²⋊C₉	C₃²	1	2	yes	—
44	C₉²×C₄₃	C₃²	1	3	yes	complemented
45	C₃²×C₄₃⋊C₃	—	3	3	no	—
46	C₃²×C₄₃⋊C₃	—	3	6	no	—
47	C₃²×C₄₃⋊C₃	C₃×C₉	1	9	yes	—
48	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
49	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
50	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
51	#11923958	C₃×C₉	1	18	yes	complemented
52	#11923957	C₃×C₉	1	27	yes	complemented
53	#11923956	C₃×C₉	1	27	yes	complemented
54	C₃×C₄₃⋊C₉	—	3	6	no	—
55	C₃×C₄₃⋊C₉	C₃³	1	12	yes	—
56	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
57	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
58	C₃×C₄₃⋊C₉	C₃³	1	6	yes	—
59	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
60	C₉×C₄₃⋊C₃	—	3	6	no	—
61	C₉×C₄₃⋊C₃	—	3	18	no	—
62	C₉×C₄₃⋊C₃	—	3	3	no	—
63	C₉×C₄₃⋊C₃	—	3	3	no	—
64	C₉×C₄₃⋊C₃	—	3	6	no	—
65	C₉×C₄₃⋊C₃	—	3	6	no	—
66	C₉×C₄₃⋊C₃	C₃×C₉	1	27	yes	complemented
67	C₉×C₄₃⋊C₃	3₋¹⁺²	1	9	yes	direct product factor
68	C₃³×C₄₃	C₃³	1	1	yes	characteristic
69	3₋¹⁺²×C₄₃	C₃×C₉	1	9	yes	complemented
70	C₃×C₉×C₄₃	—	3	3	no	—
71	C₃×C₉×C₄₃	C₃³	1	6	yes	—
72	C₃×C₉×C₄₃	C₃³	1	2	yes	—
73	C₃×C₉×C₄₃	C₃³	1	3	yes	—
74	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
75	C₃×C₉×3₋¹⁺²	—	43	1	no	maximal, Sylow
76	C₃²×C₄₃	—	3	1	no	—
77	C₃²×C₄₃	—	3	2	no	—
78	C₃²×C₄₃	C₃²×C₉	1	3	yes	—
79	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
80	C₃×C₄₃⋊C₃	—	3	1	no	—
81	C₃×C₄₃⋊C₃	—	3	1	no	—
82	C₃×C₄₃⋊C₃	—	3	2	no	—
83	C₃×C₄₃⋊C₃	—	3	2	no	—
84	C₃×C₄₃⋊C₃	—	3	27	no	—
85	C₃×C₄₃⋊C₃	C₃²×C₉	1	3	yes	—
86	C₃×C₄₃⋊C₃	C₃²×C₉	1	3	yes	—
87	C₃×C₄₃⋊C₃	C₃²×C₉	1	3	yes	—
88	C₃×C₄₃⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
89	C₃×C₄₃⋊C₃	#737	1	6	yes	—
90	C₉×C₄₃	—	3	2	no	—
91	C₉×C₄₃	—	3	6	no	—
92	C₉×C₄₃	C₃²×C₉	1	9	yes	complemented
93	C₉×C₄₃	C₃×3₋¹⁺²	1	3	yes	complemented
94	C₄₃⋊C₉	—	3	2	no	—
95	C₄₃⋊C₉	—	3	2	no	—
96	C₄₃⋊C₉	—	3	12	no	—
97	C₄₃⋊C₉	C₃²×C₉	1	18	yes	complemented
98	C₄₃⋊C₉	C₃×3₋¹⁺²	1	6	yes	complemented
99	C₃²×3₋¹⁺²	—	43	1	no	—
100	C₃³×C₉	—	43	1	no	—
101	C₉×3₋¹⁺²	—	43	2	no	—
102	C₉×3₋¹⁺²	—	43	2	no	—
103	C₉×3₋¹⁺²	—	43	6	no	—
104	C₉×3₋¹⁺²	—	43	6	no	—
105	C₉×3₋¹⁺²	—	43	4	no	—
106	C₉×3₋¹⁺²	—	43	3	no	—
107	C₉×3₋¹⁺²	—	43	3	no	—
108	C₉×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
109	C₃×C₉⋊C₉	—	43	6	no	—
110	C₃×C₃²⋊C₉	—	43	2	no	—
111	C₃×C₉²	—	43	3	no	—
112	C₃×C₄₃	—	3	3	no	—
113	C₃×C₄₃	C₃³×C₉	1	1	yes	characteristic
114	C₃×C₄₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
115	C₃×C₄₃	C₃×#737	1	2	yes	—
116	C₄₃⋊C₃	—	3	3	no	—
117	C₄₃⋊C₃	—	3	3	no	—
118	C₄₃⋊C₃	C₉×3₋¹⁺²	1	9	yes	direct product factor
119	C₃⁴	—	43	1	no	—
120	C₃×3₋¹⁺²	—	43	2	no	—
121	C₃×3₋¹⁺²	—	43	27	no	—
122	C₃×3₋¹⁺²	—	43	3	no	—
123	C₃×3₋¹⁺²	—	43	3	no	—
124	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
125	C₃²×C₉	—	43	3	no	—
126	C₃²×C₉	—	43	1	no	—
127	C₃²×C₉	—	43	2	no	—
128	C₃²×C₉	—	43	2	no	—
129	C₃²×C₉	—	43	2	no	—
130	C₃²×C₉	—	43	2	no	—
131	C₃²×C₉	—	43	6	no	—
132	C₃²×C₉	—	43	1	no	—
133	C₃²×C₉	—	43	1	no	—
134	C₃²×C₉	—	129	9	no	—
135	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
136	C₉⋊C₉	—	43	12	no	—
137	C₉⋊C₉	—	43	12	no	—
138	C₉⋊C₉	—	43	12	no	—
139	C₉⋊C₉	—	43	6	no	—
140	C₉⋊C₉	—	43	6	no	—
141	C₉⋊C₉	C₃×C₄₃⋊C₃	1	6	yes	complemented
142	C₃²⋊C₉	—	43	4	no	—
143	C₃²⋊C₉	—	43	6	no	—
144	C₃²⋊C₉	—	43	6	no	—
145	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
146	C₉²	—	43	12	no	—
147	C₉²	—	43	6	no	—
148	C₉²	—	43	6	no	—
149	C₉²	C₃×C₄₃⋊C₃	1	3	yes	complemented
150	C₄₃	C₃×C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
151	C₃³	—	43	1	no	—
152	C₃³	—	43	9	no	—
153	C₃³	—	43	1	no	—
154	C₃³	—	43	1	no	—
155	C₃³	—	129	3	no	—
156	C₃³	—	129	6	no	—
157	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
158	3₋¹⁺²	—	43	18	no	—
159	3₋¹⁺²	—	43	27	no	—
160	3₋¹⁺²	—	43	27	no	—
161	3₋¹⁺²	C₉×C₄₃⋊C₃	1	9	yes	direct product factor
162	C₃×C₉	—	3	3	no	—
163	C₃×C₉	—	43	2	no	—
164	C₃×C₉	—	43	6	no	—
165	C₃×C₉	—	43	27	no	—
166	C₃×C₉	—	43	9	no	—
167	C₃×C₉	—	43	12	no	—
168	C₃×C₉	—	43	2	no	—
169	C₃×C₉	—	43	2	no	—
170	C₃×C₉	—	129	6	no	—
171	C₃×C₉	—	129	6	no	—
172	C₃×C₉	—	129	6	no	—
173	C₃×C₉	—	129	18	no	—
174	C₃×C₉	—	129	6	no	—
175	C₃×C₉	—	129	3	no	—
176	C₃×C₉	—	129	3	no	—
177	C₃×C₉	C₃²×C₄₃⋊C₃	1	6	yes	—
178	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
179	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
180	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
181	C₃²	—	3	1	no	—
182	C₃²	—	3	2	no	—
183	C₃²	—	43	3	no	—
184	C₃²	—	43	6	no	—
185	C₃²	—	43	3	no	—
186	C₃²	—	43	3	no	—
187	C₃²	—	43	3	no	—
188	C₃²	—	129	27	no	—
189	C₃²	—	129	1	no	—
190	C₃²	—	129	1	no	—
191	C₃²	—	129	2	no	—
192	C₃²	—	129	2	no	—
193	C₃²	C₃×C₉×C₄₃⋊C₃	1	3	yes	—
194	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
195	C₉	—	3	2	no	—
196	C₉	—	3	6	no	—
197	C₉	—	43	6	no	—
198	C₉	—	43	18	no	—
199	C₉	—	129	2	no	—
200	C₉	—	129	2	no	—
201	C₉	—	129	12	no	—
202	C₉	C₃×C₉×C₄₃⋊C₃	1	9	yes	complemented
203	C₉	3₋¹⁺²×C₄₃⋊C₃	1	3	yes	direct product factor
204	C₃	—	3	3	no	—
205	C₃	—	43	9	no	—
206	C₃	—	129	3	no	—
207	C₃	—	129	3	no	—
208	C₃	C₃²×C₉×C₄₃⋊C₃	1	1	yes	characteristic
209	C₃	C₃×3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
210	C₃	#737×C₄₃⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃³×C₉
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting	C₉×3₋¹⁺²×C₄₃	C₃
socle, cosocle	C₃²×C₄₃	C₃⁴
prime radical	C₃³×C₄₃⋊C₃	C₃²
hypercenter	C₉×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	C₃×C₉×3₋¹⁺²
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₉×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
3. #23782792	C₃	semidirect
4. 3₋¹⁺²×C₄₃⋊C₉	C₃	semidirect
5. C₉×#11923956	C₃	semidirect
6. C₉×#11923957	C₃	semidirect
7. C₉×#11923958	C₃	semidirect
8. #11923957⋊C₉	C₃	semidirect
9. #11923956⋊C₉	C₃	semidirect
10. C₉⋊C₉×C₄₃⋊C₃	C₃	semidirect
12. C₉²×C₄₃⋊C₃	C₃	semidirect
13. C₉×3₋¹⁺²×C₄₃	C₃	semidirect
18. 3₋¹⁺²×C₄₃⋊C₃	C₉	direct (N × H)
29. #16812500	C₃²	semidirect
30. #16812499	C₃²	semidirect
31. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
32. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
33. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
37. C₉×C₄₃⋊C₉	C₃²	semidirect
38. C₉×C₄₃⋊C₉	C₃²	semidirect
39. C₉×C₄₃⋊C₉	C₃²	semidirect
42. C₄₃×C₉⋊C₉	C₃²	semidirect
44. C₉²×C₄₃	C₃²	semidirect
51. #11923958	C₃×C₉	semidirect
52. #11923957	C₃×C₉	semidirect
53. #11923956	C₃×C₉	semidirect
66. C₉×C₄₃⋊C₃	C₃×C₉	semidirect
67. C₉×C₄₃⋊C₃	3₋¹⁺²	direct (N × H)
69. 3₋¹⁺²×C₄₃	C₃×C₉	semidirect
92. C₉×C₄₃	C₃²×C₉	semidirect
93. C₉×C₄₃	C₃×3₋¹⁺²	semidirect
97. C₄₃⋊C₉	C₃²×C₉	semidirect
98. C₄₃⋊C₉	C₃×3₋¹⁺²	semidirect
108. C₉×3₋¹⁺²	C₄₃⋊C₃	direct (N × H)
118. C₄₃⋊C₃	C₉×3₋¹⁺²	direct (N × H)
141. C₉⋊C₉	C₃×C₄₃⋊C₃	semidirect
149. C₉²	C₃×C₄₃⋊C₃	semidirect
150. C₄₃	C₃×C₉×3₋¹⁺²	semidirect
161. 3₋¹⁺²	C₉×C₄₃⋊C₃	direct (N × H)
202. C₉	C₃×C₉×C₄₃⋊C₃	semidirect
203. C₉	3₋¹⁺²×C₄₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×3₋¹⁺²×C₄₃⋊C₃	3
C₃²×C₉×C₄₃⋊C₃	3
#23782792	3
3₋¹⁺²×C₄₃⋊C₉	3
C₉×#11923956	3
C₉×#11923957	3
C₉×#11923958	3
#11923957⋊C₉	3
#11923956⋊C₉	3
C₉⋊C₉×C₄₃⋊C₃	3
C₃²⋊C₉×C₄₃⋊C₃	3
C₉²×C₄₃⋊C₃	3
C₉×3₋¹⁺²×C₄₃	3
C₃×C₉×3₋¹⁺²	43

Subgroups — C9×3−1+2×C43⋊C3 #44534650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×3₋¹⁺²×C₄₃⋊C₃ #44534650