Subgroups — #44534835

Order 31347.

698 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812526	C₃	1	1	yes	maximal, characteristic
2	#23782849	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782848	C₃	1	1	yes	maximal, characteristic, complemented
4	#23782845	C₃	1	1	yes	maximal, characteristic, complemented
5	#23782842	C₃	1	1	yes	maximal, characteristic, complemented
6	#23782842	C₃	1	1	yes	maximal, characteristic, complemented
7	#23782841	C₃	1	1	yes	maximal, characteristic, complemented
8	#23782841	C₃	1	1	yes	maximal, characteristic, complemented
9	#23782837	C₃	1	1	yes	maximal, characteristic, complemented
10	#23782837	C₃	1	1	yes	maximal, characteristic, complemented
11	#23782828	C₃	1	1	yes	maximal, characteristic, complemented
12	#23782828	C₃	1	1	yes	maximal, characteristic, complemented
13	#23782827	C₃	1	1	yes	maximal, characteristic, complemented
14	#23782827	C₃	1	1	yes	maximal, characteristic, complemented
15	#23782825	C₃	1	1	yes	maximal, characteristic, complemented
16	#23782825	C₃	1	1	yes	maximal, characteristic, complemented
17	#23782824	C₃	1	1	yes	maximal, characteristic, complemented
18	#23782824	C₃	1	1	yes	maximal, characteristic, complemented
19	#23782818	C₃	1	1	yes	maximal, characteristic, complemented
20	#23782817	C₃	1	1	yes	maximal, characteristic, complemented
21	#23782814	C₃	1	1	yes	maximal, characteristic, complemented
22	#23782814	C₃	1	1	yes	maximal, characteristic, complemented
23	#23782814	C₃	1	1	yes	maximal, characteristic, complemented
24	#23782814	C₃	1	1	yes	maximal, characteristic, complemented
25	#23782814	C₃	1	1	yes	maximal, characteristic, complemented
26	#23782813	C₃	1	1	yes	maximal, characteristic, complemented
27	#23782813	C₃	1	1	yes	maximal, characteristic, complemented
28	#23782813	C₃	1	1	yes	maximal, characteristic, complemented
29	#23782813	C₃	1	1	yes	maximal, characteristic, complemented
30	#23782813	C₃	1	1	yes	maximal, characteristic, complemented
31	#23782812	C₃	1	1	yes	maximal, characteristic, complemented
32	#23782811	C₃	1	1	yes	maximal, characteristic, complemented
33	#23782810	C₃	1	1	yes	maximal, characteristic, complemented
34	#23782801	C₃	1	1	yes	maximal, characteristic
35	#23782801	C₃	1	1	yes	maximal, characteristic
36	#23782799	C₃	1	1	yes	maximal, characteristic
37	#23782781	C₃	1	1	yes	maximal, characteristic, complemented
38	#23782780	C₃	1	1	yes	maximal, characteristic, complemented
39	C₉⋊C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
40	C₄₃×#6896	C₃	1	1	yes	maximal, characteristic, complemented
41	#16812526	—	3	9	no	—
42	C₃×#11923958	C₃²	1	1	yes	characteristic
43	C₃×#11923958	C₃²	1	1	yes	characteristic
44	C₃×#11923958	C₃²	1	1	yes	characteristic
45	C₃×#11923957	C₃²	1	1	yes	characteristic
46	C₃×#11923957	C₃²	1	1	yes	characteristic
47	C₃×#11923957	C₃²	1	1	yes	characteristic
48	C₃×#11923957	C₃²	1	1	yes	characteristic
49	C₃×#11923957	C₃²	1	1	yes	characteristic
50	C₃×#11923957	C₃²	1	1	yes	characteristic
51	C₃×#11923956	C₃²	1	1	yes	characteristic
52	C₃×#11923956	C₃²	1	1	yes	characteristic
53	C₃×#11923956	C₃²	1	1	yes	characteristic
54	C₃×#11923956	C₃²	1	1	yes	characteristic
55	C₃×#11923956	C₃²	1	1	yes	characteristic
56	C₃×#11923956	C₃²	1	1	yes	characteristic
57	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
58	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
59	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
60	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
61	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
62	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
63	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
64	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
65	#16812500	C₃²	1	1	yes	characteristic
66	#16812500	C₃²	1	1	yes	characteristic
67	#16812500	C₃²	1	1	yes	characteristic
68	#16812500	C₃²	1	1	yes	characteristic
69	#16812500	C₃²	1	1	yes	characteristic
70	#16812500	C₃²	1	1	yes	characteristic
71	#16812500	C₃²	1	1	yes	characteristic
72	#16812500	C₃²	1	1	yes	characteristic
73	#16812499	C₃²	1	1	yes	characteristic
74	#16812499	C₃²	1	1	yes	characteristic
75	#16812499	C₃²	1	1	yes	characteristic
76	#16812499	C₃²	1	1	yes	characteristic
77	#16812499	C₃²	1	1	yes	characteristic
78	#16812499	C₃²	1	1	yes	characteristic
79	#16812499	C₃²	1	1	yes	characteristic
80	#16812499	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	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
116	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
117	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
118	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
119	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
120	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
121	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
122	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
123	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
124	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
125	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
126	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
127	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
128	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
129	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
130	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
131	(C₄₃⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
132	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
133	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
134	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
135	C₃²⋊(C₄₃⋊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	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
147	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
148	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
149	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
150	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
151	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
152	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
153	(C₃×C₄₃⋊C₃)⋊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	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
159	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
160	C₃×3₋¹⁺²×C₄₃	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×C₉⋊C₉	C₃²	1	1	yes	characteristic
167	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
168	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
169	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
170	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
171	C₉²×C₄₃	C₃²	1	1	yes	characteristic
172	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
173	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
174	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
175	#11923958	—	3	3	no	—
176	#11923958	—	9	1	no	—
177	#11923958	—	9	1	no	—
178	#11923957	—	3	3	no	—
179	#11923957	—	3	3	no	—
180	#11923957	—	3	3	no	—
181	#11923957	—	9	1	no	—
182	#11923957	—	9	1	no	—
183	#11923957	—	9	1	no	—
184	#11923956	—	3	3	no	—
185	#11923956	—	3	3	no	—
186	#11923956	—	3	3	no	—
187	#11923956	—	9	1	no	—
188	#11923956	—	9	1	no	—
189	#11923956	—	9	1	no	—
190	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
191	C₃×C₄₃⋊C₉	—	3	3	no	—
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	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
207	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
208	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
209	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
210	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
211	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
212	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
213	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
214	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
215	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
216	C₉×C₄₃⋊C₃	—	3	3	no	—
217	C₉×C₄₃⋊C₃	—	3	3	no	—
218	C₉×C₄₃⋊C₃	—	9	1	no	—
219	C₉×C₄₃⋊C₃	—	9	1	no	—
220	C₉×C₄₃⋊C₃	—	9	1	no	—
221	C₉×C₄₃⋊C₃	3₋¹⁺²	1	9	yes	complemented
222	C₃³×C₄₃	C₃³	1	1	yes	characteristic
223	3₋¹⁺²×C₄₃	—	3	3	no	—
224	3₋¹⁺²×C₄₃	—	9	1	no	—
225	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
226	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
227	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
228	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
229	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
230	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
231	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
232	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
233	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
234	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
235	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
236	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
237	#10624887	—	43	1	no	maximal, Sylow
238	C₃²×C₄₃	—	3	1	no	—
239	C₃²×C₄₃	—	3	1	no	—
240	C₃²×C₄₃	—	3	1	no	—
241	C₃²×C₄₃	—	3	1	no	—
242	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
243	C₃×C₄₃⋊C₃	—	3	1	no	—
244	C₃×C₄₃⋊C₃	—	3	1	no	—
245	C₃×C₄₃⋊C₃	—	3	1	no	—
246	C₃×C₄₃⋊C₃	—	3	1	no	—
247	C₃×C₄₃⋊C₃	—	3	1	no	—
248	C₃×C₄₃⋊C₃	—	3	1	no	—
249	C₃×C₄₃⋊C₃	—	3	1	no	—
250	C₃×C₄₃⋊C₃	—	3	1	no	—
251	C₃×C₄₃⋊C₃	—	3	1	no	—
252	C₃×C₄₃⋊C₃	—	3	1	no	—
253	C₃×C₄₃⋊C₃	—	3	1	no	—
254	C₃×C₄₃⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
255	C₉×C₄₃	—	3	1	no	—
256	C₉×C₄₃	—	3	1	no	—
257	C₉×C₄₃	—	3	1	no	—
258	C₉×C₄₃	—	3	1	no	—
259	C₉×C₄₃	—	3	1	no	—
260	C₉×C₄₃	—	3	1	no	—
261	C₉×C₄₃	—	3	1	no	—
262	C₉×C₄₃	—	3	1	no	—
263	C₉×C₄₃	—	3	1	no	—
264	C₉×C₄₃	—	3	1	no	—
265	C₉×C₄₃	—	3	1	no	—
266	C₉×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
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	—	3	1	no	—
281	C₄₃⋊C₉	—	3	1	no	—
282	C₄₃⋊C₉	—	3	1	no	—
283	C₄₃⋊C₉	—	3	1	no	—
284	C₄₃⋊C₉	—	3	1	no	—
285	C₄₃⋊C₉	—	3	1	no	—
286	C₄₃⋊C₉	—	3	1	no	—
287	C₄₃⋊C₉	—	3	1	no	—
288	C₄₃⋊C₉	—	3	1	no	—
289	C₄₃⋊C₉	C₃×3₋¹⁺²	1	3	yes	—
290	C₄₃⋊C₉	C₃×3₋¹⁺²	1	3	yes	—
291	C₃×#737	—	43	1	no	—
292	#6900	—	43	1	no	—
293	#6900	—	43	1	no	—
294	#6900	—	43	1	no	—
295	#6899	—	43	1	no	—
296	#6899	—	43	1	no	—
297	#6899	—	43	1	no	—
298	#6899	—	43	1	no	—
299	#6899	—	43	1	no	—
300	#6899	—	43	1	no	—
301	#6896	—	43	1	no	—
302	#6896	—	43	1	no	—
303	#6896	—	43	1	no	—
304	#6896	—	43	1	no	—
305	#6896	—	43	1	no	—
306	#6896	—	43	1	no	—
307	#6896	—	43	1	no	—
308	#6896	—	43	1	no	—
309	#6896	C₄₃⋊C₃	1	1	yes	characteristic, complemented
310	#6894	—	43	1	no	—
311	#6894	—	43	1	no	—
312	#6894	—	43	1	no	—
313	#6894	—	43	1	no	—
314	#6894	—	43	1	no	—
315	#6894	—	43	1	no	—
316	#6894	—	43	1	no	—
317	#6894	—	43	1	no	—
318	#6894	—	43	1	no	—
319	#6894	—	43	1	no	—
320	#6894	—	43	1	no	—
321	#6894	—	43	1	no	—
322	#6894	—	43	1	no	—
323	#6894	—	43	1	no	—
324	#6894	—	43	1	no	—
325	C₉⋊H(3,𝔽₃)	—	43	1	no	—
326	C₉⋊H(3,𝔽₃)	—	43	1	no	—
327	C₉⋊H(3,𝔽₃)	—	43	1	no	—
328	#6887	—	43	1	no	—
329	#6887	—	43	1	no	—
330	C₃×C₉⋊C₉	—	43	1	no	—
331	C₃×C₄₃	—	9	1	no	—
332	C₃×C₄₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
333	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
334	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
335	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
336	C₄₃⋊C₃	—	3	3	no	—
337	C₄₃⋊C₃	—	9	1	no	—
338	C₄₃⋊C₃	—	9	1	no	—
339	#737	—	129	9	no	—
340	C₃×3₋¹⁺²	—	43	1	no	—
341	C₃×3₋¹⁺²	—	43	1	no	—
342	C₃×3₋¹⁺²	—	43	1	no	—
343	C₃×3₋¹⁺²	—	43	1	no	—
344	C₃×3₋¹⁺²	—	43	1	no	—
345	C₃×3₋¹⁺²	—	43	1	no	—
346	C₃×3₋¹⁺²	—	43	1	no	—
347	C₃×3₋¹⁺²	—	43	1	no	—
348	C₃×3₋¹⁺²	—	43	1	no	—
349	C₃×3₋¹⁺²	—	43	1	no	—
350	C₃×3₋¹⁺²	—	43	1	no	—
351	C₃×3₋¹⁺²	—	43	1	no	—
352	C₃×3₋¹⁺²	—	43	1	no	—
353	C₃×3₋¹⁺²	—	43	1	no	—
354	C₃×3₋¹⁺²	—	43	1	no	—
355	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
356	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
357	C₃×H(3,𝔽₃)	—	43	1	no	—
358	C₃²×C₉	—	43	1	no	—
359	C₃²×C₉	—	43	1	no	—
360	C₃²×C₉	—	43	1	no	—
361	C₃²×C₉	—	43	1	no	—
362	C₃²×C₉	—	43	1	no	—
363	C₃²×C₉	—	43	1	no	—
364	C₃²×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	—	43	1	no	—
406	C₉⋊C₉	—	43	1	no	—
407	C₉⋊C₉	—	43	1	no	—
408	C₉⋊C₉	—	43	1	no	—
409	C₉⋊C₉	—	43	1	no	—
410	C₉⋊C₉	—	43	1	no	—
411	C₉⋊C₉	—	43	1	no	—
412	C₉⋊C₉	—	43	1	no	—
413	C₉⋊C₉	—	43	1	no	—
414	C₉⋊C₉	—	43	1	no	—
415	C₉⋊C₉	—	43	1	no	—
416	C₉⋊C₉	—	43	1	no	—
417	C₉⋊C₉	—	43	1	no	—
418	C₉⋊C₉	—	43	1	no	—
419	C₉⋊C₉	—	43	1	no	—
420	C₉⋊C₉	—	43	1	no	—
421	C₉⋊C₉	—	43	1	no	—
422	C₉⋊C₉	—	43	1	no	—
423	C₉⋊C₉	—	43	1	no	—
424	C₉⋊C₉	—	43	1	no	—
425	C₉⋊C₉	—	43	1	no	—
426	C₉⋊C₉	—	43	1	no	—
427	C₉⋊C₉	—	43	1	no	—
428	C₉⋊C₉	—	43	1	no	—
429	C₉⋊C₉	—	43	1	no	—
430	C₉⋊C₉	—	43	1	no	—
431	C₉⋊C₉	—	43	1	no	—
432	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
433	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
434	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
435	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
436	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
437	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
438	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
439	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
440	C₃²⋊C₉	—	43	1	no	—
441	C₃²⋊C₉	—	43	1	no	—
442	C₃²⋊C₉	—	43	1	no	—
443	C₃²⋊C₉	—	43	1	no	—
444	C₃²⋊C₉	—	43	1	no	—
445	C₃²⋊C₉	—	43	1	no	—
446	C₃²⋊C₉	—	43	1	no	—
447	C₃²⋊C₉	—	43	1	no	—
448	C₃²⋊C₉	—	43	1	no	—
449	C₃²⋊C₉	—	43	1	no	—
450	C₃²⋊C₉	—	43	1	no	—
451	C₃²⋊C₉	—	43	1	no	—
452	C₃²⋊C₉	—	43	1	no	—
453	C₃²⋊C₉	—	43	1	no	—
454	C₃²⋊C₉	—	43	1	no	—
455	C₃²⋊C₉	—	43	1	no	—
456	C₃²⋊C₉	—	43	1	no	—
457	C₃²⋊C₉	—	43	1	no	—
458	C₃²⋊C₉	—	43	1	no	—
459	C₃²⋊C₉	—	43	1	no	—
460	C₃²⋊C₉	—	43	1	no	—
461	C₃²⋊C₉	—	43	1	no	—
462	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
463	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
464	C₉²	—	43	1	no	—
465	C₉²	—	43	1	no	—
466	C₉²	—	43	1	no	—
467	C₉²	—	43	1	no	—
468	C₉²	—	43	1	no	—
469	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
470	C₄₃	#10624887	1	1	yes	characteristic, complemented, Sylow
471	C₃³	—	43	1	no	—
472	C₃³	—	43	1	no	—
473	C₃³	—	43	1	no	—
474	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
475	3₋¹⁺²	—	3	3	no	—
476	3₋¹⁺²	—	9	1	no	—
477	3₋¹⁺²	—	129	3	no	—
478	3₋¹⁺²	—	129	3	no	—
479	3₋¹⁺²	—	129	3	no	—
480	3₋¹⁺²	—	129	3	no	—
481	3₋¹⁺²	—	129	3	no	—
482	3₋¹⁺²	—	129	3	no	—
483	3₋¹⁺²	—	129	3	no	—
484	3₋¹⁺²	—	387	1	no	—
485	3₋¹⁺²	—	387	1	no	—
486	3₋¹⁺²	—	387	1	no	—
487	3₋¹⁺²	—	387	1	no	—
488	3₋¹⁺²	—	387	1	no	—
489	3₋¹⁺²	—	387	1	no	—
490	3₋¹⁺²	—	387	1	no	—
491	3₋¹⁺²	—	387	1	no	—
492	H(3,𝔽₃)	—	129	3	no	—
493	C₃×C₉	—	43	1	no	—
494	C₃×C₉	—	43	1	no	—
495	C₃×C₉	—	43	9	no	—
496	C₃×C₉	—	43	1	no	—
497	C₃×C₉	—	43	1	no	—
498	C₃×C₉	—	43	1	no	—
499	C₃×C₉	—	43	1	no	—
500	C₃×C₉	—	43	1	no	—
501	C₃×C₉	—	43	1	no	—
502	C₃×C₉	—	43	1	no	—
503	C₃×C₉	—	43	1	no	—
504	C₃×C₉	—	43	1	no	—
505	C₃×C₉	—	43	1	no	—
506	C₃×C₉	—	43	1	no	—
507	C₃×C₉	—	43	1	no	—
508	C₃×C₉	—	43	1	no	—
509	C₃×C₉	—	43	1	no	—
510	C₃×C₉	—	43	1	no	—
511	C₃×C₉	—	43	1	no	—
512	C₃×C₉	—	43	1	no	—
513	C₃×C₉	—	43	1	no	—
514	C₃×C₉	—	43	1	no	—
515	C₃×C₉	—	43	1	no	—
516	C₃×C₉	—	43	1	no	—
517	C₃×C₉	—	43	1	no	—
518	C₃×C₉	—	129	3	no	—
519	C₃×C₉	—	129	3	no	—
520	C₃×C₉	—	129	3	no	—
521	C₃×C₉	—	387	1	no	—
522	C₃×C₉	—	387	1	no	—
523	C₃×C₉	—	387	1	no	—
524	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
525	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
526	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
527	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
528	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
529	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
530	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
531	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
532	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
533	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
534	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
535	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
536	C₃²	—	3	1	no	—
537	C₃²	—	3	1	no	—
538	C₃²	—	3	1	no	—
539	C₃²	—	3	1	no	—
540	C₃²	—	43	3	no	—
541	C₃²	—	129	1	no	—
542	C₃²	—	129	1	no	—
543	C₃²	—	129	1	no	—
544	C₃²	—	129	1	no	—
545	C₃²	—	129	1	no	—
546	C₃²	—	129	1	no	—
547	C₃²	—	129	1	no	—
548	C₃²	—	129	1	no	—
549	C₃²	—	129	1	no	—
550	C₃²	—	129	1	no	—
551	C₃²	—	129	1	no	—
552	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
553	C₉	—	3	1	no	—
554	C₉	—	3	1	no	—
555	C₉	—	3	1	no	—
556	C₉	—	3	1	no	—
557	C₉	—	3	1	no	—
558	C₉	—	3	1	no	—
559	C₉	—	3	1	no	—
560	C₉	—	3	1	no	—
561	C₉	—	3	1	no	—
562	C₉	—	3	1	no	—
563	C₉	—	3	1	no	—
564	C₉	—	43	3	no	—
565	C₉	—	43	3	no	—
566	C₉	—	129	1	no	—
567	C₉	—	129	1	no	—
568	C₉	—	129	1	no	—
569	C₉	—	129	1	no	—
570	C₉	—	129	1	no	—
571	C₉	—	129	1	no	—
572	C₉	—	129	1	no	—
573	C₉	—	129	1	no	—
574	C₉	—	129	1	no	—
575	C₉	—	129	1	no	—
576	C₉	—	129	1	no	—
577	C₉	—	129	1	no	—
578	C₉	—	129	1	no	—
579	C₉	—	129	1	no	—
580	C₉	—	129	1	no	—
581	C₉	—	129	1	no	—
582	C₉	—	129	1	no	—
583	C₉	—	129	1	no	—
584	C₉	—	129	1	no	—
585	C₉	—	129	1	no	—
586	C₉	—	129	1	no	—
587	C₉	—	129	1	no	—
588	C₉	3₋¹⁺²×C₄₃⋊C₃	1	3	yes	—
589	C₃	—	9	1	no	—
590	C₃	—	129	3	no	—
591	C₃	—	387	1	no	—
592	C₃	—	387	1	no	—
593	C₃	C₃×3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
594	C₃	#23782921	1	1	yes	characteristic
595	C₃	#23782922	1	1	yes	characteristic
596	C₃	#23782923	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₄₃×#6896	C₃
prime radical	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²
hypercenter	#6896	C₄₃⋊C₃
hypocenter	C₄₃	#10624887
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ #6896

Complements

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

N	H ≅ G/N	type
2. #23782849	C₃	semidirect
3. #23782848	C₃	semidirect
4. #23782845	C₃	semidirect
5. #23782842	C₃	semidirect
6. #23782842	C₃	semidirect
7. #23782841	C₃	semidirect
8. #23782841	C₃	semidirect
9. #23782837	C₃	semidirect
10. #23782837	C₃	semidirect
11. #23782828	C₃	semidirect
12. #23782828	C₃	semidirect
13. #23782827	C₃	semidirect
14. #23782827	C₃	semidirect
15. #23782825	C₃	semidirect
16. #23782825	C₃	semidirect
17. #23782824	C₃	semidirect
18. #23782824	C₃	semidirect
19. #23782818	C₃	semidirect
20. #23782817	C₃	semidirect
21. #23782814	C₃	semidirect
22. #23782814	C₃	semidirect
23. #23782814	C₃	semidirect
24. #23782814	C₃	semidirect
25. #23782814	C₃	semidirect
26. #23782813	C₃	semidirect
27. #23782813	C₃	semidirect
28. #23782813	C₃	semidirect
29. #23782813	C₃	semidirect
30. #23782813	C₃	semidirect
31. #23782812	C₃	semidirect
32. #23782811	C₃	semidirect
33. #23782810	C₃	semidirect
37. #23782781	C₃	semidirect
38. #23782780	C₃	semidirect
39. C₉⋊C₉×C₄₃⋊C₃	C₃	semidirect
40. C₄₃×#6896	C₃	semidirect
221. C₉×C₄₃⋊C₃	3₋¹⁺²	semidirect
309. #6896	C₄₃⋊C₃	semidirect
470. C₄₃	#10624887	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812526	3
#23782849	3
#23782848	3
#23782845	3
#23782842	3
#23782841	3
#23782837	3
#23782828	3
#23782827	3
#23782825	3
#23782824	3
#23782818	3
#23782817	3
#23782814	3
#23782813	3
#23782812	3
#23782811	3
#23782810	3
#23782801	3
#23782799	3
#23782781	3
#23782780	3
C₉⋊C₉×C₄₃⋊C₃	3
C₄₃×#6896	3
#10624887	43