Subgroups — #44534761

Order 31347.

662 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782844	C₃	1	1	yes	maximal, characteristic, complemented
2	#23782843	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782842	C₃	1	1	yes	maximal, characteristic, complemented
4	#23782841	C₃	1	1	yes	maximal, characteristic, complemented
5	#23782838	C₃	1	1	yes	maximal, characteristic, complemented
6	#23782837	C₃	1	1	yes	maximal, characteristic, complemented
7	#23782836	C₃	1	1	yes	maximal, characteristic, complemented
8	#23782836	C₃	1	1	yes	maximal, characteristic, complemented
9	#23782834	C₃	1	1	yes	maximal, characteristic, complemented
10	#23782833	C₃	1	1	yes	maximal, characteristic, complemented
11	#23782833	C₃	1	1	yes	maximal, characteristic, complemented
12	#23782832	C₃	1	1	yes	maximal, characteristic, complemented
13	#23782832	C₃	1	1	yes	maximal, characteristic, complemented
14	#23782829	C₃	1	1	yes	maximal, characteristic, complemented
15	#23782829	C₃	1	1	yes	maximal, characteristic, complemented
16	#23782828	C₃	1	1	yes	maximal, characteristic, complemented
17	#23782827	C₃	1	1	yes	maximal, characteristic, complemented
18	#23782824	C₃	1	1	yes	maximal, characteristic, complemented
19	#23782821	C₃	1	1	yes	maximal, characteristic, complemented
20	#23782821	C₃	1	1	yes	maximal, characteristic, complemented
21	#23782814	C₃	1	1	yes	maximal, characteristic, complemented
22	#23782813	C₃	1	1	yes	maximal, characteristic, complemented
23	#23782811	C₃	1	1	yes	maximal, characteristic, complemented
24	#23782810	C₃	1	1	yes	maximal, characteristic, complemented
25	#23782807	C₃	1	1	yes	maximal, characteristic
26	#23782801	C₃	1	1	yes	maximal, characteristic
27	#23782799	C₃	1	1	yes	maximal, characteristic
28	C₉×#11923956	C₃	1	1	yes	maximal, characteristic, complemented
29	C₉×#11923956	C₃	1	1	yes	maximal, characteristic, complemented
30	C₉×#11923956	C₃	1	1	yes	maximal, characteristic, complemented
31	C₉×#11923957	C₃	1	1	yes	maximal, characteristic, complemented
32	C₉×#11923957	C₃	1	1	yes	maximal, characteristic, complemented
33	C₉×#11923957	C₃	1	1	yes	maximal, characteristic, complemented
34	C₉×#11923958	C₃	1	1	yes	maximal, characteristic, complemented
35	C₉×C₃²⋊(C₄₃⋊C₃)	C₃	1	1	yes	maximal, characteristic
36	#23782782	C₃	1	1	yes	maximal, characteristic, complemented
37	#23782780	C₃	1	1	yes	maximal, characteristic, complemented
38	#23782780	C₃	1	1	yes	maximal, characteristic, complemented
39	C₉²×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
40	C₉×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
41	C₃×#11923958	C₃²	1	1	yes	characteristic
42	C₃×#11923957	C₃²	1	1	yes	characteristic
43	C₃×#11923957	C₃²	1	1	yes	characteristic
44	C₃×#11923957	C₃²	1	1	yes	characteristic
45	C₃×#11923956	C₃²	1	1	yes	characteristic
46	C₃×#11923956	C₃²	1	1	yes	characteristic
47	C₃×#11923956	C₃²	1	1	yes	characteristic
48	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
49	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
50	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
51	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
52	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
53	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
54	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
55	#16812500	C₃²	1	1	yes	characteristic
56	#16812500	C₃²	1	1	yes	characteristic
57	#16812500	C₃²	1	1	yes	characteristic
58	#16812500	C₃²	1	1	yes	characteristic
59	#16812500	C₃²	1	1	yes	characteristic
60	#16812500	C₃²	1	1	yes	characteristic
61	#16812500	C₃²	1	1	yes	characteristic
62	#16812500	C₃²	1	1	yes	characteristic
63	#16812500	C₃²	1	1	yes	characteristic
64	#16812499	C₃²	1	1	yes	characteristic
65	#16812499	C₃²	1	1	yes	characteristic
66	#16812499	C₃²	1	1	yes	characteristic
67	#16812499	C₃²	1	1	yes	characteristic
68	#16812499	C₃²	1	1	yes	characteristic
69	#16812499	C₃²	1	1	yes	characteristic
70	#16812499	C₃²	1	1	yes	characteristic
71	#16812499	C₃²	1	1	yes	characteristic
72	#16812499	C₃²	1	1	yes	characteristic
73	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
74	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
75	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
76	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
77	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
78	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
79	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
80	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
81	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
82	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
83	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
84	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
85	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
86	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
87	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
88	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
89	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
90	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
91	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
92	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
93	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
94	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
95	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
96	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
97	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
98	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
99	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
100	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
101	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
102	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
103	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
104	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
105	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
106	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
107	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
108	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
109	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
110	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
111	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
112	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
113	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
114	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
115	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
116	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
117	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
118	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
119	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
120	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
121	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
122	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
123	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
124	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
125	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
126	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
127	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
128	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
129	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
130	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
131	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
132	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
133	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
134	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
135	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
136	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
137	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
138	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
139	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
140	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
141	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
142	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
143	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
144	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
145	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
146	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
147	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
148	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
149	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
150	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
151	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
152	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
153	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
154	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
155	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
156	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
157	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
158	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
159	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
160	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
161	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
162	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
163	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
164	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
165	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
166	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
167	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
168	C₉²×C₄₃	C₃²	1	1	yes	characteristic
169	C₉²×C₄₃	C₃²	1	1	yes	characteristic
170	C₉²×C₄₃	C₃²	1	1	yes	characteristic
171	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
172	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
173	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
174	#11923958	—	3	3	no	—
175	#11923957	—	3	3	no	—
176	#11923957	—	3	3	no	—
177	#11923957	—	3	3	no	—
178	#11923956	—	3	3	no	—
179	#11923956	—	3	3	no	—
180	#11923956	—	3	3	no	—
181	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
182	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
183	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
184	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
185	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
186	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
187	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
188	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
189	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
190	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
191	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
192	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
193	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
194	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
195	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
196	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
197	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
198	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
199	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
200	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
201	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
202	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
203	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
204	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
205	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
206	C₉×C₄₃⋊C₃	—	3	3	no	—
207	C₉×C₄₃⋊C₃	—	3	3	no	—
208	C₉×C₄₃⋊C₃	—	3	3	no	—
209	C₉×C₄₃⋊C₃	—	3	3	no	—
210	C₉×C₄₃⋊C₃	—	3	3	no	—
211	C₉×C₄₃⋊C₃	—	3	3	no	—
212	C₃³×C₄₃	C₃³	1	1	yes	characteristic
213	3₋¹⁺²×C₄₃	—	3	3	no	—
214	C₃×C₉×C₄₃	—	3	3	no	—
215	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
216	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
217	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
218	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
219	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
220	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
221	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
222	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
223	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
224	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
225	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
226	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
227	#10624877	—	43	1	no	maximal, Sylow
228	C₃²×C₄₃	—	3	1	no	—
229	C₃²×C₄₃	—	3	1	no	—
230	C₃²×C₄₃	—	3	1	no	—
231	C₃²×C₄₃	—	3	1	no	—
232	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
233	C₃×C₄₃⋊C₃	—	3	1	no	—
234	C₃×C₄₃⋊C₃	—	3	1	no	—
235	C₃×C₄₃⋊C₃	—	3	1	no	—
236	C₃×C₄₃⋊C₃	—	3	1	no	—
237	C₃×C₄₃⋊C₃	—	3	1	no	—
238	C₃×C₄₃⋊C₃	—	3	1	no	—
239	C₃×C₄₃⋊C₃	—	3	1	no	—
240	C₃×C₄₃⋊C₃	—	3	1	no	—
241	C₃×C₄₃⋊C₃	—	3	1	no	—
242	C₃×C₄₃⋊C₃	—	3	1	no	—
243	C₃×C₄₃⋊C₃	—	3	1	no	—
244	C₃×C₄₃⋊C₃	#737	1	3	yes	—
245	C₉×C₄₃	—	3	1	no	—
246	C₉×C₄₃	—	3	1	no	—
247	C₉×C₄₃	—	3	1	no	—
248	C₉×C₄₃	—	3	1	no	—
249	C₉×C₄₃	—	3	1	no	—
250	C₉×C₄₃	—	3	1	no	—
251	C₉×C₄₃	—	3	1	no	—
252	C₉×C₄₃	—	3	1	no	—
253	C₉×C₄₃	—	3	1	no	—
254	C₉×C₄₃	—	3	1	no	—
255	C₉×C₄₃	#737	1	3	yes	—
256	C₉×C₄₃	#737	1	3	yes	—
257	C₄₃⋊C₉	—	3	1	no	—
258	C₄₃⋊C₉	—	3	1	no	—
259	C₄₃⋊C₉	—	3	1	no	—
260	C₄₃⋊C₉	—	3	1	no	—
261	C₄₃⋊C₉	—	3	1	no	—
262	C₄₃⋊C₉	—	3	1	no	—
263	C₄₃⋊C₉	—	3	1	no	—
264	C₄₃⋊C₉	—	3	1	no	—
265	C₄₃⋊C₉	—	3	1	no	—
266	C₄₃⋊C₉	—	3	1	no	—
267	C₄₃⋊C₉	—	3	1	no	—
268	C₄₃⋊C₉	—	3	1	no	—
269	C₄₃⋊C₉	—	3	1	no	—
270	C₄₃⋊C₉	—	3	1	no	—
271	C₄₃⋊C₉	—	3	1	no	—
272	C₄₃⋊C₉	—	3	1	no	—
273	C₄₃⋊C₉	—	3	1	no	—
274	C₄₃⋊C₉	—	3	1	no	—
275	C₄₃⋊C₉	—	3	1	no	—
276	C₄₃⋊C₉	—	3	1	no	—
277	C₄₃⋊C₉	—	3	1	no	—
278	C₄₃⋊C₉	—	3	1	no	—
279	C₄₃⋊C₉	—	3	1	no	—
280	C₄₃⋊C₉	#737	1	3	yes	—
281	#6899	—	43	1	no	—
282	#6899	—	43	1	no	—
283	#6899	—	43	1	no	—
284	#6899	—	43	1	no	—
285	#6899	—	43	1	no	—
286	#6899	—	43	1	no	—
287	#6898	—	43	1	no	—
288	#6898	—	43	1	no	—
289	#6898	—	43	1	no	—
290	#6897	—	43	1	no	—
291	#6897	—	43	1	no	—
292	#6897	—	43	1	no	—
293	#6897	—	43	1	no	—
294	#6897	—	43	1	no	—
295	#6897	—	43	1	no	—
296	#6896	—	43	1	no	—
297	#6896	—	43	1	no	—
298	#6896	—	43	1	no	—
299	#6895	—	43	1	no	—
300	#6895	—	43	1	no	—
301	#6894	—	43	1	no	—
302	#6894	—	43	1	no	—
303	#6894	—	43	1	no	—
304	#6894	—	43	1	no	—
305	#6893	—	43	1	no	—
306	C₉⋊H(3,𝔽₃)	—	43	1	no	—
307	C₉⋊H(3,𝔽₃)	—	43	1	no	—
308	C₉×3₋¹⁺²	—	43	1	no	—
309	C₉×3₋¹⁺²	—	43	1	no	—
310	C₉×3₋¹⁺²	—	43	1	no	—
311	C₉×3₋¹⁺²	—	43	1	no	—
312	C₉×3₋¹⁺²	—	43	1	no	—
313	C₉×3₋¹⁺²	—	43	1	no	—
314	C₉×3₋¹⁺²	—	43	1	no	—
315	C₉×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic, complemented
316	C₉×H(3,𝔽₃)	—	43	1	no	—
317	#6887	—	43	1	no	—
318	#6887	—	43	1	no	—
319	#6887	—	43	1	no	—
320	C₃×C₉²	—	43	1	no	—
321	C₃×C₄₃	—	9	1	no	—
322	C₃×C₄₃	C₃×#737	1	1	yes	characteristic
323	C₃×C₄₃	C₃×#737	1	1	yes	characteristic
324	C₃×C₄₃	C₃×#737	1	1	yes	characteristic
325	C₃×C₄₃	C₃×#737	1	1	yes	characteristic
326	C₄₃⋊C₃	—	3	3	no	—
327	C₄₃⋊C₃	—	9	1	no	—
328	C₄₃⋊C₃	—	9	1	no	—
329	C₃×3₋¹⁺²	—	43	1	no	—
330	C₃×3₋¹⁺²	—	43	1	no	—
331	C₃×3₋¹⁺²	—	43	1	no	—
332	C₃×3₋¹⁺²	—	43	1	no	—
333	C₃×3₋¹⁺²	—	43	1	no	—
334	C₃×3₋¹⁺²	—	43	1	no	—
335	C₃×3₋¹⁺²	—	43	1	no	—
336	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
337	C₃×H(3,𝔽₃)	—	43	1	no	—
338	C₃²×C₉	—	43	1	no	—
339	C₃²×C₉	—	43	1	no	—
340	C₃²×C₉	—	43	1	no	—
341	C₃²×C₉	—	43	1	no	—
342	C₃²×C₉	—	43	1	no	—
343	C₃²×C₉	—	43	1	no	—
344	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
345	C₉⋊C₉	—	43	1	no	—
346	C₉⋊C₉	—	43	1	no	—
347	C₉⋊C₉	—	43	1	no	—
348	C₉⋊C₉	—	43	1	no	—
349	C₉⋊C₉	—	43	1	no	—
350	C₉⋊C₉	—	43	1	no	—
351	C₉⋊C₉	—	43	1	no	—
352	C₉⋊C₉	—	43	1	no	—
353	C₉⋊C₉	—	43	1	no	—
354	C₉⋊C₉	—	43	1	no	—
355	C₉⋊C₉	—	43	1	no	—
356	C₉⋊C₉	—	43	1	no	—
357	C₉⋊C₉	—	43	1	no	—
358	C₉⋊C₉	—	43	1	no	—
359	C₉⋊C₉	—	43	1	no	—
360	C₉⋊C₉	—	43	1	no	—
361	C₉⋊C₉	—	43	1	no	—
362	C₉⋊C₉	—	43	1	no	—
363	C₉⋊C₉	—	43	1	no	—
364	C₉⋊C₉	—	43	1	no	—
365	C₉⋊C₉	—	43	1	no	—
366	C₉⋊C₉	—	43	1	no	—
367	C₉⋊C₉	—	43	1	no	—
368	C₉⋊C₉	—	43	1	no	—
369	C₉⋊C₉	—	43	1	no	—
370	C₉⋊C₉	—	43	1	no	—
371	C₉⋊C₉	—	43	1	no	—
372	C₉⋊C₉	—	43	1	no	—
373	C₉⋊C₉	—	43	1	no	—
374	C₉⋊C₉	—	43	1	no	—
375	C₉⋊C₉	—	43	1	no	—
376	C₉⋊C₉	—	43	1	no	—
377	C₉⋊C₉	—	43	1	no	—
378	C₉⋊C₉	—	43	1	no	—
379	C₉⋊C₉	—	43	1	no	—
380	C₉⋊C₉	—	43	1	no	—
381	C₉⋊C₉	—	43	1	no	—
382	C₉⋊C₉	—	43	1	no	—
383	C₉⋊C₉	—	43	1	no	—
384	C₉⋊C₉	—	43	1	no	—
385	C₉⋊C₉	—	43	1	no	—
386	C₉⋊C₉	—	43	1	no	—
387	C₉⋊C₉	—	43	1	no	—
388	C₉⋊C₉	—	43	1	no	—
389	C₉⋊C₉	—	43	1	no	—
390	C₉⋊C₉	—	43	1	no	—
391	C₉⋊C₉	—	43	1	no	—
392	C₉⋊C₉	—	43	1	no	—
393	C₉⋊C₉	—	43	1	no	—
394	C₉⋊C₉	—	43	1	no	—
395	C₉⋊C₉	—	43	1	no	—
396	C₉⋊C₉	—	43	1	no	—
397	C₉⋊C₉	—	43	1	no	—
398	C₉⋊C₉	—	43	1	no	—
399	C₉⋊C₉	—	43	1	no	—
400	C₉⋊C₉	—	43	1	no	—
401	C₉⋊C₉	—	43	1	no	—
402	C₉⋊C₉	—	43	1	no	—
403	C₉⋊C₉	—	43	1	no	—
404	C₉⋊C₉	—	43	1	no	—
405	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
406	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
407	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
408	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
409	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
410	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
411	C₃²⋊C₉	—	43	1	no	—
412	C₃²⋊C₉	—	43	1	no	—
413	C₃²⋊C₉	—	43	1	no	—
414	C₃²⋊C₉	—	43	1	no	—
415	C₃²⋊C₉	—	43	1	no	—
416	C₃²⋊C₉	—	43	1	no	—
417	C₃²⋊C₉	—	43	1	no	—
418	C₃²⋊C₉	—	43	1	no	—
419	C₃²⋊C₉	—	43	1	no	—
420	C₃²⋊C₉	—	43	1	no	—
421	C₃²⋊C₉	—	43	1	no	—
422	C₃²⋊C₉	—	43	1	no	—
423	C₃²⋊C₉	—	43	1	no	—
424	C₃²⋊C₉	—	43	1	no	—
425	C₃²⋊C₉	—	43	1	no	—
426	C₃²⋊C₉	—	43	1	no	—
427	C₃²⋊C₉	—	43	1	no	—
428	C₃²⋊C₉	—	43	1	no	—
429	C₃²⋊C₉	—	43	1	no	—
430	C₃²⋊C₉	—	43	1	no	—
431	C₃²⋊C₉	—	43	1	no	—
432	C₃²⋊C₉	—	43	1	no	—
433	C₃²⋊C₉	—	43	1	no	—
434	C₃²⋊C₉	—	43	1	no	—
435	C₃²⋊C₉	—	43	1	no	—
436	C₃²⋊C₉	—	43	1	no	—
437	C₃²⋊C₉	—	43	1	no	—
438	C₃²⋊C₉	—	43	1	no	—
439	C₃²⋊C₉	—	43	1	no	—
440	C₃²⋊C₉	—	43	1	no	—
441	C₃²⋊C₉	—	43	1	no	—
442	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
443	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
444	C₉²	—	43	1	no	—
445	C₉²	—	43	1	no	—
446	C₉²	—	43	1	no	—
447	C₉²	—	43	1	no	—
448	C₉²	—	43	1	no	—
449	C₉²	—	43	1	no	—
450	C₉²	—	43	1	no	—
451	C₉²	—	43	1	no	—
452	C₉²	—	43	1	no	—
453	C₉²	—	43	1	no	—
454	C₉²	—	43	1	no	—
455	C₉²	—	43	1	no	—
456	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
457	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
458	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
459	C₄₃	#10624877	1	1	yes	characteristic, complemented, Sylow
460	C₃³	—	43	1	no	—
461	C₃³	—	43	1	no	—
462	C₃³	—	43	1	no	—
463	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
464	3₋¹⁺²	—	3	3	no	—
465	3₋¹⁺²	—	129	3	no	—
466	3₋¹⁺²	—	129	3	no	—
467	3₋¹⁺²	—	129	3	no	—
468	3₋¹⁺²	—	129	3	no	—
469	3₋¹⁺²	—	129	3	no	—
470	3₋¹⁺²	—	129	3	no	—
471	3₋¹⁺²	—	129	3	no	—
472	H(3,𝔽₃)	—	129	3	no	—
473	C₃×C₉	—	3	3	no	—
474	C₃×C₉	—	43	1	no	—
475	C₃×C₉	—	43	1	no	—
476	C₃×C₉	—	43	1	no	—
477	C₃×C₉	—	43	1	no	—
478	C₃×C₉	—	43	1	no	—
479	C₃×C₉	—	43	1	no	—
480	C₃×C₉	—	43	1	no	—
481	C₃×C₉	—	43	1	no	—
482	C₃×C₉	—	43	1	no	—
483	C₃×C₉	—	43	1	no	—
484	C₃×C₉	—	43	1	no	—
485	C₃×C₉	—	43	1	no	—
486	C₃×C₉	—	43	1	no	—
487	C₃×C₉	—	43	1	no	—
488	C₃×C₉	—	43	1	no	—
489	C₃×C₉	—	43	1	no	—
490	C₃×C₉	—	43	1	no	—
491	C₃×C₉	—	43	1	no	—
492	C₃×C₉	—	43	1	no	—
493	C₃×C₉	—	43	1	no	—
494	C₃×C₉	—	43	1	no	—
495	C₃×C₉	—	43	1	no	—
496	C₃×C₉	—	43	1	no	—
497	C₃×C₉	—	43	1	no	—
498	C₃×C₉	—	129	3	no	—
499	C₃×C₉	—	129	3	no	—
500	C₃×C₉	—	129	3	no	—
501	C₃×C₉	—	129	3	no	—
502	C₃×C₉	—	129	3	no	—
503	C₃×C₉	—	129	3	no	—
504	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
505	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
506	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
507	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
508	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
509	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
510	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
511	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
512	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
513	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
514	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
515	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
516	C₃²	—	3	1	no	—
517	C₃²	—	3	1	no	—
518	C₃²	—	3	1	no	—
519	C₃²	—	3	1	no	—
520	C₃²	—	43	3	no	—
521	C₃²	—	129	1	no	—
522	C₃²	—	129	1	no	—
523	C₃²	—	129	1	no	—
524	C₃²	—	129	1	no	—
525	C₃²	—	129	1	no	—
526	C₃²	—	129	1	no	—
527	C₃²	—	129	1	no	—
528	C₃²	—	129	1	no	—
529	C₃²	—	129	1	no	—
530	C₃²	—	129	1	no	—
531	C₃²	—	129	1	no	—
532	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
533	C₉	—	3	1	no	—
534	C₉	—	3	1	no	—
535	C₉	—	3	1	no	—
536	C₉	—	3	1	no	—
537	C₉	—	3	1	no	—
538	C₉	—	3	1	no	—
539	C₉	—	3	1	no	—
540	C₉	—	3	1	no	—
541	C₉	—	3	1	no	—
542	C₉	—	3	1	no	—
543	C₉	—	43	3	no	—
544	C₉	—	129	1	no	—
545	C₉	—	129	1	no	—
546	C₉	—	129	1	no	—
547	C₉	—	129	1	no	—
548	C₉	—	129	1	no	—
549	C₉	—	129	1	no	—
550	C₉	—	129	1	no	—
551	C₉	—	129	1	no	—
552	C₉	—	129	1	no	—
553	C₉	—	129	1	no	—
554	C₉	—	129	1	no	—
555	C₉	—	129	1	no	—
556	C₉	—	129	1	no	—
557	C₉	—	129	1	no	—
558	C₉	—	129	1	no	—
559	C₉	—	129	1	no	—
560	C₉	—	129	1	no	—
561	C₉	—	129	1	no	—
562	C₉	—	129	1	no	—
563	C₉	—	129	1	no	—
564	C₉	—	129	1	no	—
565	C₉	—	129	1	no	—
566	C₉	—	129	1	no	—
567	C₉	#16812525	1	3	yes	—
568	C₉	#16812526	1	3	yes	—
569	C₃	—	9	1	no	—
570	C₃	—	129	3	no	—
571	C₃	—	387	1	no	—
572	C₃	—	387	1	no	—
573	C₃	#737×C₄₃⋊C₃	1	1	yes	characteristic
574	C₃	#737×C₄₃⋊C₃	1	1	yes	characteristic
575	C₃	C₃×#16812525	1	1	yes	characteristic
576	C₃	C₃×#16812526	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting	C₉×3₋¹⁺²×C₄₃	C₃
prime radical	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²
hypercenter	C₉×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624877
LCS	G ▷ C₃²×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
1. #23782844	C₃	semidirect
2. #23782843	C₃	semidirect
3. #23782842	C₃	semidirect
4. #23782841	C₃	semidirect
5. #23782838	C₃	semidirect
6. #23782837	C₃	semidirect
7. #23782836	C₃	semidirect
8. #23782836	C₃	semidirect
9. #23782834	C₃	semidirect
10. #23782833	C₃	semidirect
11. #23782833	C₃	semidirect
12. #23782832	C₃	semidirect
13. #23782832	C₃	semidirect
14. #23782829	C₃	semidirect
15. #23782829	C₃	semidirect
16. #23782828	C₃	semidirect
17. #23782827	C₃	semidirect
18. #23782824	C₃	semidirect
19. #23782821	C₃	semidirect
20. #23782821	C₃	semidirect
21. #23782814	C₃	semidirect
22. #23782813	C₃	semidirect
23. #23782811	C₃	semidirect
24. #23782810	C₃	semidirect
28. C₉×#11923956	C₃	semidirect
29. C₉×#11923956	C₃	semidirect
30. C₉×#11923956	C₃	semidirect
31. C₉×#11923957	C₃	semidirect
32. C₉×#11923957	C₃	semidirect
33. C₉×#11923957	C₃	semidirect
34. C₉×#11923958	C₃	semidirect
36. #23782782	C₃	semidirect
37. #23782780	C₃	semidirect
38. #23782780	C₃	semidirect
39. C₉²×C₄₃⋊C₃	C₃	semidirect
40. C₉×3₋¹⁺²×C₄₃	C₃	semidirect
315. C₉×3₋¹⁺²	C₄₃⋊C₃	semidirect
459. C₄₃	#10624877	semidirect

Maximal subgroups

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

subgroup	index
#23782844	3
#23782843	3
#23782842	3
#23782841	3
#23782838	3
#23782837	3
#23782836	3
#23782834	3
#23782833	3
#23782832	3
#23782829	3
#23782828	3
#23782827	3
#23782824	3
#23782821	3
#23782814	3
#23782813	3
#23782811	3
#23782810	3
#23782807	3
#23782801	3
#23782799	3
C₉×#11923956	3
C₉×#11923957	3
C₉×#11923958	3
C₉×C₃²⋊(C₄₃⋊C₃)	3
#23782782	3
#23782780	3
C₉²×C₄₃⋊C₃	3
C₉×3₋¹⁺²×C₄₃	3
#10624877	43