Subgroups — C₄₃⋊C₃×#6894 #44534706

Order 31347.

932 conjugacy classes of subgroups.

The subgroup lattice has 240 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	#23782818	C₃	1	2	yes	maximal, complemented
4	#23782817	C₃	1	2	yes	maximal, complemented
5	#23782816	C₃	1	1	yes	maximal, characteristic, complemented
6	#23782815	C₃	1	1	yes	maximal, characteristic, complemented
7	#23782814	C₃	1	6	yes	maximal, complemented
8	#23782813	C₃	1	6	yes	maximal, complemented
9	#23782812	C₃	1	2	yes	maximal, complemented
10	#23782811	C₃	1	3	yes	maximal, complemented
11	#23782810	C₃	1	3	yes	maximal, complemented
12	C₉⋊C₉×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
13	C₉⋊C₉×C₄₃⋊C₃	C₃	1	6	yes	maximal, complemented
14	C₃²⋊C₉×C₄₃⋊C₃	C₃	1	2	yes	maximal
15	C₄₃×#6894	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
17	C₃×#11923958	C₃²	1	1	yes	characteristic
18	C₃×#11923958	C₃²	1	1	yes	characteristic
19	C₃×#11923957	C₃²	1	3	yes	—
20	C₃×#11923956	C₃²	1	3	yes	—
21	3₋¹⁺²×C₄₃⋊C₃	—	3	9	no	—
22	C₃²×C₄₃⋊C₉	C₃²	1	2	yes	—
23	C₃×C₉×C₄₃⋊C₃	—	3	9	no	—
24	C₃×C₉×C₄₃⋊C₃	C₃²	1	3	yes	—
25	C₃×C₉×C₄₃⋊C₃	C₃²	1	6	yes	—
26	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	—
27	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
28	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
29	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	—
30	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	—
31	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
32	#16812500	C₃²	1	3	yes	complemented
33	#16812500	C₃²	1	6	yes	complemented
34	#16812499	C₃²	1	3	yes	complemented
35	#16812499	C₃²	1	6	yes	complemented
36	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
37	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
38	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
39	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
40	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
41	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
42	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
43	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
44	(C₄₃⋊C₉)⋊C₉	C₃²	1	6	yes	complemented
45	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	—
46	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	—
47	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	6	yes	—
48	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	6	yes	—
49	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
50	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
51	C₄₃×C₉⋊C₉	C₃²	1	3	yes	complemented
52	C₄₃×C₉⋊C₉	C₃²	1	6	yes	complemented
53	C₄₃×C₃²⋊C₉	C₃²	1	2	yes	—
54	C₃²×C₄₃⋊C₃	—	3	3	no	—
55	C₃²×C₄₃⋊C₃	—	3	6	no	—
56	C₃²×C₄₃⋊C₃	3₋¹⁺²	1	9	yes	—
57	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
58	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
59	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
60	#11923958	—	3	3	no	—
61	#11923958	—	3	3	no	—
62	#11923957	—	3	9	no	—
63	#11923956	—	3	9	no	—
64	C₃×C₄₃⋊C₉	—	3	6	no	—
65	C₃×C₄₃⋊C₉	C₃³	1	6	yes	—
66	C₃×C₄₃⋊C₉	C₃³	1	6	yes	—
67	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
68	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
69	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
70	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
71	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
72	C₉×C₄₃⋊C₃	—	3	6	no	—
73	C₉×C₄₃⋊C₃	—	3	9	no	—
74	C₉×C₄₃⋊C₃	—	3	18	no	—
75	C₉×C₄₃⋊C₃	—	3	3	no	—
76	C₉×C₄₃⋊C₃	—	3	3	no	—
77	C₉×C₄₃⋊C₃	—	3	6	no	—
78	C₉×C₄₃⋊C₃	—	3	6	no	—
79	C₉×C₄₃⋊C₃	3₋¹⁺²	1	9	yes	complemented
80	C₃³×C₄₃	C₃³	1	1	yes	characteristic
81	3₋¹⁺²×C₄₃	—	3	3	no	—
82	C₃×C₉×C₄₃	—	3	3	no	—
83	C₃×C₉×C₄₃	C₃³	1	6	yes	—
84	C₃×C₉×C₄₃	C₃³	1	2	yes	—
85	C₃×C₉×C₄₃	C₃³	1	3	yes	—
86	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
87	C₃×#6894	—	43	1	no	maximal, Sylow
88	C₃²×C₄₃	—	3	1	no	—
89	C₃²×C₄₃	—	3	2	no	—
90	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
91	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
92	C₃×C₄₃⋊C₃	—	3	1	no	—
93	C₃×C₄₃⋊C₃	—	3	1	no	—
94	C₃×C₄₃⋊C₃	—	3	2	no	—
95	C₃×C₄₃⋊C₃	—	3	2	no	—
96	C₃×C₄₃⋊C₃	—	3	27	no	—
97	C₃×C₄₃⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
98	C₃×C₄₃⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
99	C₃×C₄₃⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
100	C₃×C₄₃⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
101	C₃×C₄₃⋊C₃	#737	1	6	yes	—
102	C₉×C₄₃	—	3	2	no	—
103	C₉×C₄₃	—	3	3	no	—
104	C₉×C₄₃	—	3	6	no	—
105	C₉×C₄₃	C₃×3₋¹⁺²	1	3	yes	complemented
106	C₄₃⋊C₉	—	3	2	no	—
107	C₄₃⋊C₉	—	3	2	no	—
108	C₄₃⋊C₉	—	3	3	no	—
109	C₄₃⋊C₉	—	3	3	no	—
110	C₄₃⋊C₉	—	3	6	no	—
111	C₄₃⋊C₉	—	3	6	no	—
112	C₄₃⋊C₉	C₃×3₋¹⁺²	1	6	yes	complemented
113	C₃²×3₋¹⁺²	—	43	1	no	—
114	C₃³×C₉	—	43	1	no	—
115	#6894	—	43	2	no	—
116	#6894	—	43	1	no	—
117	#6894	—	43	1	no	—
118	#6894	—	43	3	no	—
119	#6894	—	43	3	no	—
120	#6894	—	43	6	no	—
121	#6894	—	43	6	no	—
122	#6894	—	43	2	no	—
123	#6894	—	43	2	no	—
124	#6894	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
125	C₃×C₉⋊C₉	—	43	3	no	—
126	C₃×C₉⋊C₉	—	43	6	no	—
127	C₃×C₃²⋊C₉	—	43	2	no	—
128	C₃×C₄₃	—	3	3	no	—
129	C₃×C₄₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
130	C₃×C₄₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
131	C₃×C₄₃	C₃×#737	1	2	yes	—
132	C₄₃⋊C₃	—	3	3	no	—
133	C₄₃⋊C₃	—	3	3	no	—
134	C₄₃⋊C₃	#6894	1	9	yes	direct product factor
135	C₃⁴	—	43	1	no	—
136	C₃×3₋¹⁺²	—	43	1	no	—
137	C₃×3₋¹⁺²	—	43	1	no	—
138	C₃×3₋¹⁺²	—	43	3	no	—
139	C₃×3₋¹⁺²	—	43	3	no	—
140	C₃×3₋¹⁺²	—	129	9	no	—
141	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
142	C₃²×C₉	—	43	1	no	—
143	C₃²×C₉	—	43	2	no	—
144	C₃²×C₉	—	43	2	no	—
145	C₃²×C₉	—	43	2	no	—
146	C₃²×C₉	—	43	2	no	—
147	C₃²×C₉	—	43	1	no	—
148	C₃²×C₉	—	43	1	no	—
149	C₃²×C₉	—	43	3	no	—
150	C₃²×C₉	—	43	6	no	—
151	C₃²×C₉	—	129	9	no	—
152	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
153	C₉⋊C₉	—	43	6	no	—
154	C₉⋊C₉	—	43	6	no	—
155	C₉⋊C₉	—	43	6	no	—
156	C₉⋊C₉	—	43	6	no	—
157	C₉⋊C₉	—	43	6	no	—
158	C₉⋊C₉	—	43	6	no	—
159	C₉⋊C₉	—	43	6	no	—
160	C₉⋊C₉	—	43	6	no	—
161	C₉⋊C₉	—	43	6	no	—
162	C₉⋊C₉	—	43	3	no	—
163	C₉⋊C₉	—	43	6	no	—
164	C₉⋊C₉	—	43	3	no	—
165	C₉⋊C₉	—	43	6	no	—
166	C₉⋊C₉	C₃×C₄₃⋊C₃	1	6	yes	complemented
167	C₉⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	complemented
168	C₃²⋊C₉	—	43	2	no	—
169	C₃²⋊C₉	—	43	2	no	—
170	C₃²⋊C₉	—	43	6	no	—
171	C₃²⋊C₉	—	43	6	no	—
172	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
173	C₄₃	C₃×#6894	1	1	yes	characteristic, complemented, Sylow
174	C₃³	—	43	1	no	—
175	C₃³	—	43	9	no	—
176	C₃³	—	43	1	no	—
177	C₃³	—	43	1	no	—
178	C₃³	—	129	3	no	—
179	C₃³	—	129	6	no	—
180	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
181	3₋¹⁺²	—	3	3	no	—
182	3₋¹⁺²	—	129	9	no	—
183	3₋¹⁺²	—	129	9	no	—
184	3₋¹⁺²	—	129	3	no	—
185	3₋¹⁺²	—	129	3	no	—
186	C₃×C₉	—	3	3	no	—
187	C₃×C₉	—	43	2	no	—
188	C₃×C₉	—	43	9	no	—
189	C₃×C₉	—	43	6	no	—
190	C₃×C₉	—	43	6	no	—
191	C₃×C₉	—	43	2	no	—
192	C₃×C₉	—	43	2	no	—
193	C₃×C₉	—	43	3	no	—
194	C₃×C₉	—	43	3	no	—
195	C₃×C₉	—	129	6	no	—
196	C₃×C₉	—	129	6	no	—
197	C₃×C₉	—	129	6	no	—
198	C₃×C₉	—	129	9	no	—
199	C₃×C₉	—	129	18	no	—
200	C₃×C₉	—	129	6	no	—
201	C₃×C₉	—	129	3	no	—
202	C₃×C₉	—	129	3	no	—
203	C₃×C₉	C₃²×C₄₃⋊C₃	1	6	yes	—
204	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
205	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
206	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
207	C₃²	—	3	1	no	—
208	C₃²	—	3	2	no	—
209	C₃²	—	43	3	no	—
210	C₃²	—	43	3	no	—
211	C₃²	—	43	6	no	—
212	C₃²	—	43	3	no	—
213	C₃²	—	43	3	no	—
214	C₃²	—	129	27	no	—
215	C₃²	—	129	1	no	—
216	C₃²	—	129	1	no	—
217	C₃²	—	129	2	no	—
218	C₃²	—	129	2	no	—
219	C₃²	3₋¹⁺²×C₄₃⋊C₃	1	3	yes	—
220	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
221	C₉	—	3	2	no	—
222	C₉	—	3	3	no	—
223	C₉	—	3	6	no	—
224	C₉	—	43	6	no	—
225	C₉	—	129	2	no	—
226	C₉	—	129	2	no	—
227	C₉	—	129	3	no	—
228	C₉	—	129	3	no	—
229	C₉	—	129	6	no	—
230	C₉	—	129	6	no	—
231	C₉	3₋¹⁺²×C₄₃⋊C₃	1	3	yes	complemented
232	C₃	—	3	3	no	—
233	C₃	—	43	9	no	—
234	C₃	—	129	3	no	—
235	C₃	—	129	3	no	—
236	C₃	C₃×3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
237	C₃	C₃×3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
238	C₃	#737×C₄₃⋊C₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₄₃×#6894	C₃
prime radical	C₃³×C₄₃⋊C₃	C₃²
hypercenter	#6894	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#6894
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ #6894

Complements

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

N	H ≅ G/N	type
3. #23782818	C₃	semidirect
4. #23782817	C₃	semidirect
5. #23782816	C₃	semidirect
6. #23782815	C₃	semidirect
7. #23782814	C₃	semidirect
8. #23782813	C₃	semidirect
9. #23782812	C₃	semidirect
10. #23782811	C₃	semidirect
11. #23782810	C₃	semidirect
12. C₉⋊C₉×C₄₃⋊C₃	C₃	semidirect
13. C₉⋊C₉×C₄₃⋊C₃	C₃	semidirect
15. C₄₃×#6894	C₃	semidirect
32. #16812500	C₃²	semidirect
33. #16812500	C₃²	semidirect
34. #16812499	C₃²	semidirect
35. #16812499	C₃²	semidirect
36. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
37. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
38. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
39. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
40. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
41. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
42. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
43. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
44. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
51. C₄₃×C₉⋊C₉	C₃²	semidirect
52. C₄₃×C₉⋊C₉	C₃²	semidirect
79. C₉×C₄₃⋊C₃	3₋¹⁺²	semidirect
105. C₉×C₄₃	C₃×3₋¹⁺²	semidirect
112. C₄₃⋊C₉	C₃×3₋¹⁺²	semidirect
124. #6894	C₄₃⋊C₃	direct (N × H)
134. C₄₃⋊C₃	#6894	direct (N × H)
166. C₉⋊C₉	C₃×C₄₃⋊C₃	semidirect
167. C₉⋊C₉	C₃×C₄₃⋊C₃	semidirect
173. C₄₃	C₃×#6894	semidirect
231. C₉	3₋¹⁺²×C₄₃⋊C₃	semidirect

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
#23782818	3
#23782817	3
#23782816	3
#23782815	3
#23782814	3
#23782813	3
#23782812	3
#23782811	3
#23782810	3
C₉⋊C₉×C₄₃⋊C₃	3
C₃²⋊C₉×C₄₃⋊C₃	3
C₄₃×#6894	3
C₃×#6894	43

Subgroups — C43⋊C3×#6894 #44534706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃⋊C₃×#6894 #44534706