Subgroups — #44534778

Order 31347.

758 conjugacy classes of subgroups.

The subgroup lattice has 398 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	2	yes	maximal, complemented
6	#23782841	C₃	1	2	yes	maximal, complemented
7	#23782837	C₃	1	2	yes	maximal, complemented
8	#23782828	C₃	1	2	yes	maximal, complemented
9	#23782827	C₃	1	2	yes	maximal, complemented
10	#23782825	C₃	1	1	yes	maximal, characteristic, complemented
11	#23782825	C₃	1	1	yes	maximal, characteristic, complemented
12	#23782824	C₃	1	2	yes	maximal, complemented
13	#23782814	C₃	1	2	yes	maximal, complemented
14	#23782813	C₃	1	2	yes	maximal, complemented
15	#23782811	C₃	1	1	yes	maximal, characteristic, complemented
16	#23782810	C₃	1	1	yes	maximal, characteristic, complemented
17	#23782801	C₃	1	2	yes	maximal
18	#23782799	C₃	1	1	yes	maximal, characteristic
19	#23782792	C₃	1	2	yes	maximal, complemented
20	3₋¹⁺²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
21	#11923957⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
22	#11923957⋊C₉	C₃	1	2	yes	maximal, complemented
23	#11923956⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
24	#11923956⋊C₉	C₃	1	2	yes	maximal, complemented
25	#23782781	C₃	1	2	yes	maximal, complemented
26	C₉²×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
27	C₄₃×#6896	C₃	1	1	yes	maximal, characteristic, complemented
28	#16812526	—	3	9	no	—
29	C₃×#11923958	C₃²	1	1	yes	characteristic
30	C₃×#11923958	C₃²	1	2	yes	—
31	C₃×#11923957	C₃²	1	1	yes	characteristic
32	C₃×#11923957	C₃²	1	1	yes	characteristic
33	C₃×#11923957	C₃²	1	1	yes	characteristic
34	C₃×#11923957	C₃²	1	1	yes	characteristic
35	C₃×#11923957	C₃²	1	2	yes	—
36	C₃×#11923956	C₃²	1	1	yes	characteristic
37	C₃×#11923956	C₃²	1	1	yes	characteristic
38	C₃×#11923956	C₃²	1	1	yes	characteristic
39	C₃×#11923956	C₃²	1	1	yes	characteristic
40	C₃×#11923956	C₃²	1	2	yes	—
41	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
42	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
43	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
44	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
45	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
46	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	—
47	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
48	#16812500	C₃²	1	2	yes	—
49	#16812500	C₃²	1	1	yes	characteristic
50	#16812500	C₃²	1	2	yes	—
51	#16812500	C₃²	1	1	yes	characteristic
52	#16812500	C₃²	1	2	yes	—
53	#16812499	C₃²	1	2	yes	—
54	#16812499	C₃²	1	1	yes	characteristic
55	#16812499	C₃²	1	2	yes	—
56	#16812499	C₃²	1	1	yes	characteristic
57	#16812499	C₃²	1	2	yes	—
58	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
59	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
60	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
61	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
62	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
63	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
64	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
65	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
66	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
67	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
68	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
69	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
70	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
71	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
72	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
73	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
74	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
75	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
76	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
77	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
78	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
79	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	—
80	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	—
81	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
82	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
83	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
84	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
85	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
86	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
87	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
88	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
89	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
90	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
91	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
92	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
93	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
94	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
95	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
96	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
97	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
98	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
99	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
100	C₄₃×C₉⋊C₉	C₃²	1	2	yes	—
101	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
102	C₄₃×C₉⋊C₉	C₃²	1	2	yes	—
103	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
104	C₄₃×C₉⋊C₉	C₃²	1	2	yes	—
105	C₄₃×C₃²⋊C₉	C₃²	1	2	yes	—
106	C₉²×C₄₃	C₃²	1	1	yes	characteristic
107	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
108	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
109	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
110	#11923958	—	3	3	no	—
111	#11923958	—	3	6	no	—
112	#11923957	—	3	3	no	—
113	#11923957	—	3	3	no	—
114	#11923957	—	3	3	no	—
115	#11923957	—	3	3	no	—
116	#11923957	—	3	6	no	—
117	#11923956	—	3	3	no	—
118	#11923956	—	3	3	no	—
119	#11923956	—	3	3	no	—
120	#11923956	—	3	3	no	—
121	#11923956	—	3	6	no	—
122	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
123	C₃×C₄₃⋊C₉	—	3	3	no	—
124	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
125	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
126	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
127	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
128	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
129	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
130	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
131	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
132	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
133	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
134	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
135	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
136	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
137	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
138	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
139	C₉×C₄₃⋊C₃	—	3	3	no	—
140	C₉×C₄₃⋊C₃	—	3	3	no	—
141	C₉×C₄₃⋊C₃	—	3	3	no	—
142	C₉×C₄₃⋊C₃	—	3	6	no	—
143	C₉×C₄₃⋊C₃	3₋¹⁺²	1	9	yes	complemented
144	C₃³×C₄₃	C₃³	1	1	yes	characteristic
145	3₋¹⁺²×C₄₃	—	3	3	no	—
146	3₋¹⁺²×C₄₃	—	3	3	no	—
147	C₃×C₉×C₄₃	C₃³	1	2	yes	—
148	C₃×C₉×C₄₃	C₃³	1	2	yes	—
149	C₃×C₉×C₄₃	C₃³	1	2	yes	—
150	C₃×C₉×C₄₃	C₃³	1	2	yes	—
151	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
152	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
153	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
154	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
155	#10624879	—	43	1	no	maximal, Sylow
156	C₃²×C₄₃	—	3	1	no	—
157	C₃²×C₄₃	—	3	1	no	—
158	C₃²×C₄₃	—	3	2	no	—
159	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
160	C₃×C₄₃⋊C₃	—	3	2	no	—
161	C₃×C₄₃⋊C₃	—	3	1	no	—
162	C₃×C₄₃⋊C₃	—	3	1	no	—
163	C₃×C₄₃⋊C₃	—	3	1	no	—
164	C₃×C₄₃⋊C₃	—	3	2	no	—
165	C₃×C₄₃⋊C₃	—	3	1	no	—
166	C₃×C₄₃⋊C₃	—	3	2	no	—
167	C₃×C₄₃⋊C₃	—	3	1	no	—
168	C₃×C₄₃⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
169	C₉×C₄₃	—	3	1	no	—
170	C₉×C₄₃	—	3	1	no	—
171	C₉×C₄₃	—	3	2	no	—
172	C₉×C₄₃	—	3	2	no	—
173	C₉×C₄₃	—	3	2	no	—
174	C₉×C₄₃	—	3	2	no	—
175	C₉×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
176	C₉×C₄₃	#737	1	3	yes	complemented
177	C₄₃⋊C₉	—	3	1	no	—
178	C₄₃⋊C₉	—	3	1	no	—
179	C₄₃⋊C₉	—	3	1	no	—
180	C₄₃⋊C₉	—	3	1	no	—
181	C₄₃⋊C₉	—	3	2	no	—
182	C₄₃⋊C₉	—	3	2	no	—
183	C₄₃⋊C₉	—	3	2	no	—
184	C₄₃⋊C₉	—	3	2	no	—
185	C₄₃⋊C₉	—	3	2	no	—
186	C₄₃⋊C₉	—	3	2	no	—
187	C₄₃⋊C₉	—	3	2	no	—
188	C₄₃⋊C₉	—	3	2	no	—
189	C₄₃⋊C₉	C₃×3₋¹⁺²	1	3	yes	—
190	C₄₃⋊C₉	C₃×3₋¹⁺²	1	3	yes	—
191	C₄₃⋊C₉	#737	1	6	yes	complemented
192	C₃×#737	—	43	1	no	—
193	#6900	—	43	1	no	—
194	#6900	—	43	1	no	—
195	#6900	—	43	1	no	—
196	#6899	—	43	2	no	—
197	#6899	—	43	2	no	—
198	#6899	—	43	2	no	—
199	#6896	—	43	2	no	—
200	#6896	—	43	2	no	—
201	#6896	—	43	2	no	—
202	#6896	—	43	1	no	—
203	#6896	—	43	1	no	—
204	#6896	C₄₃⋊C₃	1	1	yes	characteristic, complemented
205	#6894	—	43	1	no	—
206	#6894	—	43	1	no	—
207	#6894	—	43	2	no	—
208	#6894	—	43	2	no	—
209	C₉⋊H(3,𝔽₃)	—	43	1	no	—
210	C₉⋊H(3,𝔽₃)	—	43	2	no	—
211	C₉×3₋¹⁺²	—	43	1	no	—
212	C₉×3₋¹⁺²	—	43	1	no	—
213	C₉×3₋¹⁺²	—	43	2	no	—
214	C₉×3₋¹⁺²	—	43	1	no	—
215	C₉×3₋¹⁺²	—	43	2	no	—
216	C₉×3₋¹⁺²	—	43	2	no	—
217	#6887	—	43	2	no	—
218	C₃×C₉²	—	43	1	no	—
219	C₃×C₄₃	—	9	1	no	—
220	C₃×C₄₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
221	C₃×C₄₃	C₃×#737	1	2	yes	—
222	C₃×C₄₃	C₃×#737	1	1	yes	characteristic
223	C₄₃⋊C₃	—	3	3	no	—
224	C₄₃⋊C₃	—	9	1	no	—
225	C₄₃⋊C₃	—	9	1	no	—
226	#737	—	129	9	no	—
227	C₃×3₋¹⁺²	—	43	1	no	—
228	C₃×3₋¹⁺²	—	43	2	no	—
229	C₃×3₋¹⁺²	—	43	1	no	—
230	C₃×3₋¹⁺²	—	43	1	no	—
231	C₃×3₋¹⁺²	—	43	1	no	—
232	C₃×3₋¹⁺²	—	43	1	no	—
233	C₃×3₋¹⁺²	—	43	1	no	—
234	C₃×3₋¹⁺²	—	43	1	no	—
235	C₃×3₋¹⁺²	—	43	2	no	—
236	C₃×3₋¹⁺²	—	43	1	no	—
237	C₃×3₋¹⁺²	—	43	2	no	—
238	C₃×3₋¹⁺²	—	43	1	no	—
239	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
240	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
241	C₃×H(3,𝔽₃)	—	43	1	no	—
242	C₃²×C₉	—	43	1	no	—
243	C₃²×C₉	—	43	1	no	—
244	C₃²×C₉	—	43	1	no	—
245	C₃²×C₉	—	43	1	no	—
246	C₃²×C₉	—	43	2	no	—
247	C₃²×C₉	—	43	1	no	—
248	C₉⋊C₉	—	43	2	no	—
249	C₉⋊C₉	—	43	2	no	—
250	C₉⋊C₉	—	43	2	no	—
251	C₉⋊C₉	—	43	2	no	—
252	C₉⋊C₉	—	43	2	no	—
253	C₉⋊C₉	—	43	2	no	—
254	C₉⋊C₉	—	43	2	no	—
255	C₉⋊C₉	—	43	2	no	—
256	C₉⋊C₉	—	43	2	no	—
257	C₉⋊C₉	—	43	2	no	—
258	C₉⋊C₉	—	43	2	no	—
259	C₉⋊C₉	—	43	2	no	—
260	C₉⋊C₉	—	43	2	no	—
261	C₉⋊C₉	—	43	2	no	—
262	C₉⋊C₉	—	43	2	no	—
263	C₉⋊C₉	—	43	2	no	—
264	C₉⋊C₉	—	43	2	no	—
265	C₉⋊C₉	—	43	2	no	—
266	C₉⋊C₉	—	43	2	no	—
267	C₉⋊C₉	—	43	2	no	—
268	C₉⋊C₉	—	43	2	no	—
269	C₉⋊C₉	—	43	2	no	—
270	C₉⋊C₉	—	43	2	no	—
271	C₉⋊C₉	—	43	2	no	—
272	C₉⋊C₉	—	43	1	no	—
273	C₉⋊C₉	—	43	1	no	—
274	C₉⋊C₉	—	43	2	no	—
275	C₉⋊C₉	—	43	2	no	—
276	C₉⋊C₉	—	43	2	no	—
277	C₉⋊C₉	—	43	1	no	—
278	C₉⋊C₉	—	43	1	no	—
279	C₉⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
280	C₉⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
281	C₉⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
282	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
283	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
284	C₃²⋊C₉	—	43	2	no	—
285	C₃²⋊C₉	—	43	2	no	—
286	C₃²⋊C₉	—	43	2	no	—
287	C₃²⋊C₉	—	43	2	no	—
288	C₃²⋊C₉	—	43	2	no	—
289	C₃²⋊C₉	—	43	2	no	—
290	C₃²⋊C₉	—	43	2	no	—
291	C₃²⋊C₉	—	43	2	no	—
292	C₃²⋊C₉	—	43	2	no	—
293	C₃²⋊C₉	—	43	2	no	—
294	C₃²⋊C₉	—	43	2	no	—
295	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
296	C₉²	—	43	2	no	—
297	C₉²	—	43	1	no	—
298	C₉²	—	43	2	no	—
299	C₉²	—	43	2	no	—
300	C₉²	—	43	1	no	—
301	C₉²	—	43	2	no	—
302	C₉²	—	43	2	no	—
303	C₉²	—	43	2	no	—
304	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
305	C₄₃	#10624879	1	1	yes	characteristic, complemented, Sylow
306	C₃³	—	43	1	no	—
307	C₃³	—	43	1	no	—
308	C₃³	—	43	1	no	—
309	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
310	3₋¹⁺²	—	3	3	no	—
311	3₋¹⁺²	—	3	3	no	—
312	3₋¹⁺²	—	129	3	no	—
313	3₋¹⁺²	—	129	3	no	—
314	3₋¹⁺²	—	129	6	no	—
315	3₋¹⁺²	—	129	6	no	—
316	3₋¹⁺²	—	129	3	no	—
317	3₋¹⁺²	—	129	3	no	—
318	3₋¹⁺²	—	129	3	no	—
319	3₋¹⁺²	—	129	6	no	—
320	3₋¹⁺²	—	129	3	no	—
321	3₋¹⁺²	—	129	3	no	—
322	3₋¹⁺²	—	129	3	no	—
323	3₋¹⁺²	—	129	3	no	—
324	H(3,𝔽₃)	—	129	3	no	—
325	C₃×C₉	—	43	1	no	—
326	C₃×C₉	—	43	1	no	—
327	C₃×C₉	—	43	2	no	—
328	C₃×C₉	—	43	9	no	—
329	C₃×C₉	—	43	2	no	—
330	C₃×C₉	—	43	2	no	—
331	C₃×C₉	—	43	2	no	—
332	C₃×C₉	—	43	2	no	—
333	C₃×C₉	—	43	2	no	—
334	C₃×C₉	—	43	2	no	—
335	C₃×C₉	—	43	2	no	—
336	C₃×C₉	—	43	2	no	—
337	C₃×C₉	—	43	1	no	—
338	C₃×C₉	—	43	1	no	—
339	C₃×C₉	—	43	1	no	—
340	C₃×C₉	—	43	1	no	—
341	C₃×C₉	—	129	3	no	—
342	C₃×C₉	—	129	3	no	—
343	C₃×C₉	—	129	6	no	—
344	C₃×C₉	—	129	3	no	—
345	C₃×C₉	—	129	3	no	—
346	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
347	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
348	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
349	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
350	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
351	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
352	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
353	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
354	C₃²	—	3	1	no	—
355	C₃²	—	3	2	no	—
356	C₃²	—	3	1	no	—
357	C₃²	—	43	3	no	—
358	C₃²	—	129	2	no	—
359	C₃²	—	129	1	no	—
360	C₃²	—	129	1	no	—
361	C₃²	—	129	1	no	—
362	C₃²	—	129	2	no	—
363	C₃²	—	129	2	no	—
364	C₃²	—	129	1	no	—
365	C₃²	—	129	1	no	—
366	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
367	C₉	—	3	1	no	—
368	C₉	—	3	1	no	—
369	C₉	—	3	2	no	—
370	C₉	—	3	2	no	—
371	C₉	—	3	2	no	—
372	C₉	—	3	2	no	—
373	C₉	—	43	3	no	—
374	C₉	—	43	3	no	—
375	C₉	—	43	6	no	—
376	C₉	—	129	1	no	—
377	C₉	—	129	1	no	—
378	C₉	—	129	1	no	—
379	C₉	—	129	1	no	—
380	C₉	—	129	2	no	—
381	C₉	—	129	2	no	—
382	C₉	—	129	2	no	—
383	C₉	—	129	2	no	—
384	C₉	—	129	2	no	—
385	C₉	—	129	2	no	—
386	C₉	—	129	2	no	—
387	C₉	—	129	2	no	—
388	C₉	3₋¹⁺²×C₄₃⋊C₃	1	3	yes	—
389	C₉	#16812526	1	3	yes	complemented
390	C₃	—	9	1	no	—
391	C₃	—	129	3	no	—
392	C₃	—	387	1	no	—
393	C₃	—	387	1	no	—
394	C₃	C₃×3₋¹⁺²×C₄₃⋊C₃	1	1	yes	characteristic
395	C₃	#737×C₄₃⋊C₃	1	2	yes	—
396	C₃	C₃×#16812526	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	#10624879
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. #23782841	C₃	semidirect
7. #23782837	C₃	semidirect
8. #23782828	C₃	semidirect
9. #23782827	C₃	semidirect
10. #23782825	C₃	semidirect
11. #23782825	C₃	semidirect
12. #23782824	C₃	semidirect
13. #23782814	C₃	semidirect
14. #23782813	C₃	semidirect
15. #23782811	C₃	semidirect
16. #23782810	C₃	semidirect
19. #23782792	C₃	semidirect
20. 3₋¹⁺²×C₄₃⋊C₉	C₃	semidirect
21. #11923957⋊C₉	C₃	semidirect
22. #11923957⋊C₉	C₃	semidirect
23. #11923956⋊C₉	C₃	semidirect
24. #11923956⋊C₉	C₃	semidirect
25. #23782781	C₃	semidirect
26. C₉²×C₄₃⋊C₃	C₃	semidirect
27. C₄₃×#6896	C₃	semidirect
143. C₉×C₄₃⋊C₃	3₋¹⁺²	semidirect
176. C₉×C₄₃	#737	semidirect
191. C₄₃⋊C₉	#737	semidirect
204. #6896	C₄₃⋊C₃	semidirect
305. C₄₃	#10624879	semidirect
389. C₉	#16812526	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
#23782814	3
#23782813	3
#23782811	3
#23782810	3
#23782801	3
#23782799	3
#23782792	3
3₋¹⁺²×C₄₃⋊C₉	3
#11923957⋊C₉	3
#11923956⋊C₉	3
#23782781	3
C₉²×C₄₃⋊C₃	3
C₄₃×#6896	3
#10624879	43