Subgroups — #14552374

Order 2187.

1012 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6899	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#6896	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#6894	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	C₃×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
6	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
7	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
8	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
9	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
10	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
11	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
12	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
13	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
14	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
15	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
16	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
17	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
18	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
19	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
20	#10624565	C₃	1	1	yes	maximal, characteristic, complemented
21	#10624565	C₃	1	1	yes	maximal, characteristic, complemented
22	#10624563	C₃	1	1	yes	maximal, characteristic
23	#10624563	C₃	1	1	yes	maximal, characteristic
24	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
25	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
26	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
27	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
28	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
29	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
30	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
31	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
32	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
33	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
34	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
35	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
36	#10624556	C₃	1	1	yes	maximal, characteristic, complemented
37	#10624555	C₃	1	1	yes	maximal, characteristic
38	#10624548	C₃	1	1	yes	maximal, characteristic, complemented
39	#10624548	C₃	1	1	yes	maximal, characteristic, complemented
40	C₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
41	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
42	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
43	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
44	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
45	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
46	C₃²×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
47	C₃³×C₉	C₃²	1	1	yes	characteristic
48	C₃³×C₉	C₃²	1	1	yes	characteristic
49	#6899	—	3	9	no	—
50	#6896	—	3	9	no	—
51	#6894	—	3	9	no	—
52	C₉⋊H(3,𝔽₃)	—	3	9	no	—
53	C₉×3₋¹⁺²	—	3	9	no	—
54	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
55	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
56	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
57	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
58	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
59	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
60	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
61	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
62	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
63	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
64	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
65	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
66	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
67	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
68	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
69	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
70	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
71	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
73	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
74	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
75	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
76	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
77	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
78	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
79	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
80	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
81	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
82	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
83	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
84	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
85	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
86	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
87	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
88	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
89	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
90	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
91	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
92	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
93	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
94	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
95	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
96	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
97	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
98	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
99	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
100	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
101	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
102	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
103	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
104	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
105	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
106	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
107	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
108	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
109	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
110	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
111	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
112	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
113	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
114	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
115	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
116	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
117	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
118	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
119	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
120	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
121	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
122	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
123	C₃×C₉²	C₃²	1	1	yes	characteristic
124	C₃×C₉²	C₃²	1	1	yes	characteristic
125	C₃×C₉²	C₃²	1	1	yes	characteristic
126	C₃×C₉²	C₃²	1	1	yes	characteristic
127	C₃×C₉²	C₃²	1	1	yes	characteristic
128	#6855	C₃²	1	1	yes	characteristic
129	#6855	C₃²	1	1	yes	characteristic
130	#6855	C₃²	1	1	yes	characteristic
131	#6855	C₃²	1	1	yes	characteristic
132	#6855	C₃²	1	1	yes	characteristic
133	#6855	C₃²	1	1	yes	characteristic
134	#6855	C₃²	1	1	yes	characteristic
135	#6855	C₃²	1	1	yes	characteristic
136	#6855	C₃²	1	1	yes	characteristic
137	#6855	C₃²	1	1	yes	characteristic
138	#6855	C₃²	1	1	yes	characteristic
139	#6855	C₃²	1	1	yes	characteristic
140	#6855	C₃²	1	1	yes	characteristic
141	#6855	C₃²	1	1	yes	characteristic
142	#6855	C₃²	1	1	yes	characteristic
143	#6855	C₃²	1	1	yes	characteristic
144	#6855	C₃²	1	1	yes	characteristic
145	#6855	C₃²	1	1	yes	characteristic
146	#6855	C₃²	1	1	yes	characteristic
147	#6855	C₃²	1	1	yes	characteristic
148	#6855	C₃²	1	1	yes	characteristic
149	#6855	C₃²	1	1	yes	characteristic
150	#6855	C₃²	1	1	yes	characteristic
151	#6855	C₃²	1	1	yes	characteristic
152	#6855	C₃²	1	1	yes	characteristic
153	#6855	C₃²	1	1	yes	characteristic
154	#6855	C₃²	1	1	yes	characteristic
155	#6855	C₃²	1	1	yes	characteristic
156	#6855	C₃²	1	1	yes	characteristic
157	#6855	C₃²	1	1	yes	characteristic
158	#6855	C₃²	1	1	yes	characteristic
159	#6855	C₃²	1	1	yes	characteristic
160	#6855	C₃²	1	1	yes	characteristic
161	#6855	C₃²	1	1	yes	characteristic
162	#6855	C₃²	1	1	yes	characteristic
163	#6855	C₃²	1	1	yes	characteristic
164	#6855	C₃²	1	1	yes	characteristic
165	#6855	C₃²	1	1	yes	characteristic
166	#6855	C₃²	1	1	yes	characteristic
167	#6855	C₃²	1	1	yes	characteristic
168	#6855	C₃²	1	1	yes	characteristic
169	#6855	C₃²	1	1	yes	characteristic
170	#6855	C₃²	1	1	yes	characteristic
171	#6855	C₃²	1	1	yes	characteristic
172	#6855	C₃²	1	1	yes	characteristic
173	#6855	C₃²	1	1	yes	characteristic
174	#6855	C₃²	1	1	yes	characteristic
175	#6855	C₃²	1	1	yes	characteristic
176	C₃⁴	C₃³	1	1	yes	characteristic
177	C₃⁴	C₃³	1	1	yes	characteristic
178	C₃⁴	C₃³	1	1	yes	characteristic
179	C₃⁴	C₃³	1	1	yes	characteristic
180	C₃×3₋¹⁺²	—	3	3	no	—
181	C₃×3₋¹⁺²	—	3	3	no	—
182	C₃×3₋¹⁺²	—	3	3	no	—
183	C₃×3₋¹⁺²	—	3	3	no	—
184	C₃×3₋¹⁺²	—	3	3	no	—
185	C₃×3₋¹⁺²	—	3	3	no	—
186	C₃×3₋¹⁺²	—	3	3	no	—
187	C₃×3₋¹⁺²	—	3	3	no	—
188	C₃×3₋¹⁺²	—	3	3	no	—
189	C₃×3₋¹⁺²	—	3	3	no	—
190	C₃×3₋¹⁺²	—	3	3	no	—
191	C₃×3₋¹⁺²	—	3	3	no	—
192	C₃×3₋¹⁺²	—	3	3	no	—
193	C₃×3₋¹⁺²	—	3	3	no	—
194	C₃×3₋¹⁺²	—	3	3	no	—
195	C₃×3₋¹⁺²	—	9	1	no	—
196	C₃×3₋¹⁺²	—	9	1	no	—
197	C₃×3₋¹⁺²	—	9	1	no	—
198	C₃×3₋¹⁺²	—	9	1	no	—
199	C₃×3₋¹⁺²	3₋¹⁺²	1	9	yes	complemented
200	C₃×H(3,𝔽₃)	—	3	3	no	—
201	C₃×H(3,𝔽₃)	—	3	3	no	—
202	C₃×H(3,𝔽₃)	—	9	1	no	—
203	C₃×H(3,𝔽₃)	—	9	1	no	—
204	C₃²×C₉	—	3	3	no	—
205	C₃²×C₉	—	3	3	no	—
206	C₃²×C₉	—	3	3	no	—
207	C₃²×C₉	—	3	3	no	—
208	C₃²×C₉	—	3	3	no	—
209	C₃²×C₉	—	3	3	no	—
210	C₃²×C₉	—	9	1	no	—
211	C₃²×C₉	—	9	1	no	—
212	C₃²×C₉	C₃³	1	1	yes	characteristic
213	C₃²×C₉	C₃³	1	1	yes	characteristic
214	C₃²×C₉	C₃³	1	1	yes	characteristic
215	C₃²×C₉	C₃³	1	1	yes	characteristic
216	C₃²×C₉	C₃³	1	1	yes	characteristic
217	C₃²×C₉	C₃³	1	1	yes	characteristic
218	C₃²×C₉	C₃³	1	1	yes	characteristic
219	C₃²×C₉	C₃³	1	1	yes	characteristic
220	C₃²×C₉	C₃³	1	1	yes	characteristic
221	C₃²×C₉	C₃³	1	1	yes	characteristic
222	C₃²×C₉	C₃³	1	1	yes	characteristic
223	C₃²×C₉	C₃³	1	1	yes	characteristic
224	C₃²×C₉	C₃³	1	1	yes	characteristic
225	C₃²×C₉	C₃³	1	1	yes	characteristic
226	C₃²×C₉	C₃³	1	1	yes	characteristic
227	C₃²×C₉	C₃³	1	1	yes	characteristic
228	C₃²×C₉	C₃³	1	1	yes	characteristic
229	C₃²×C₉	C₃³	1	1	yes	characteristic
230	C₃²×C₉	C₃³	1	1	yes	characteristic
231	C₃²×C₉	C₃³	1	1	yes	characteristic
232	C₃²×C₉	C₃³	1	1	yes	characteristic
233	C₃²×C₉	C₃³	1	1	yes	characteristic
234	C₃²×C₉	C₃³	1	1	yes	characteristic
235	C₃²×C₉	C₃³	1	1	yes	characteristic
236	C₃²×C₉	C₃³	1	1	yes	characteristic
237	C₃²×C₉	C₃³	1	1	yes	characteristic
238	C₃²×C₉	C₃³	1	1	yes	characteristic
239	C₃²×C₉	C₃³	1	1	yes	characteristic
240	C₃²×C₉	C₃³	1	1	yes	characteristic
241	C₃²×C₉	C₃³	1	1	yes	characteristic
242	C₃²×C₉	C₃³	1	1	yes	characteristic
243	C₃²×C₉	C₃³	1	1	yes	characteristic
244	C₃²×C₉	C₃³	1	1	yes	characteristic
245	C₃²×C₉	C₃³	1	1	yes	characteristic
246	C₃²×C₉	C₃³	1	1	yes	characteristic
247	C₃²×C₉	C₃³	1	1	yes	characteristic
248	C₉⋊C₉	—	3	3	no	—
249	C₉⋊C₉	—	3	3	no	—
250	C₉⋊C₉	—	3	3	no	—
251	C₉⋊C₉	—	3	3	no	—
252	C₉⋊C₉	—	3	3	no	—
253	C₉⋊C₉	—	3	3	no	—
254	C₉⋊C₉	—	3	3	no	—
255	C₉⋊C₉	—	3	3	no	—
256	C₉⋊C₉	—	3	3	no	—
257	C₉⋊C₉	—	3	3	no	—
258	C₉⋊C₉	—	3	3	no	—
259	C₉⋊C₉	—	3	3	no	—
260	C₉⋊C₉	—	3	3	no	—
261	C₉⋊C₉	—	3	3	no	—
262	C₉⋊C₉	—	3	3	no	—
263	C₉⋊C₉	—	3	3	no	—
264	C₉⋊C₉	—	3	3	no	—
265	C₉⋊C₉	—	3	3	no	—
266	C₉⋊C₉	—	3	3	no	—
267	C₉⋊C₉	—	3	3	no	—
268	C₉⋊C₉	—	3	3	no	—
269	C₉⋊C₉	—	3	3	no	—
270	C₉⋊C₉	—	3	3	no	—
271	C₉⋊C₉	—	3	3	no	—
272	C₉⋊C₉	—	3	3	no	—
273	C₉⋊C₉	—	3	3	no	—
274	C₉⋊C₉	—	3	3	no	—
275	C₉⋊C₉	H(3,𝔽₃)	1	9	yes	complemented
276	C₃²⋊C₉	—	3	3	no	—
277	C₃²⋊C₉	—	3	3	no	—
278	C₃²⋊C₉	—	3	3	no	—
279	C₃²⋊C₉	—	3	3	no	—
280	C₃²⋊C₉	—	3	3	no	—
281	C₃²⋊C₉	—	3	3	no	—
282	C₃²⋊C₉	—	3	3	no	—
283	C₃²⋊C₉	—	3	3	no	—
284	C₃²⋊C₉	—	3	3	no	—
285	C₃²⋊C₉	—	3	3	no	—
286	C₃²⋊C₉	—	3	3	no	—
287	C₃²⋊C₉	—	3	3	no	—
288	C₃²⋊C₉	—	3	3	no	—
289	C₃²⋊C₉	—	3	3	no	—
290	C₃²⋊C₉	—	3	3	no	—
291	C₃²⋊C₉	—	3	3	no	—
292	C₃²⋊C₉	—	3	3	no	—
293	C₃²⋊C₉	—	3	3	no	—
294	C₃²⋊C₉	—	3	3	no	—
295	C₃²⋊C₉	—	3	3	no	—
296	C₃²⋊C₉	—	3	3	no	—
297	C₃²⋊C₉	—	3	3	no	—
298	C₃²⋊C₉	—	3	3	no	—
299	C₃²⋊C₉	—	3	3	no	—
300	C₃²⋊C₉	—	3	3	no	—
301	C₃²⋊C₉	—	9	1	no	—
302	C₃²⋊C₉	—	9	1	no	—
303	C₃²⋊C₉	—	9	1	no	—
304	C₃²⋊C₉	—	9	1	no	—
305	C₃²⋊C₉	—	9	1	no	—
306	C₃²⋊C₉	—	9	1	no	—
307	C₃²⋊C₉	—	9	1	no	—
308	C₃²⋊C₉	—	9	1	no	—
309	C₃²⋊C₉	—	9	1	no	—
310	C₃²⋊C₉	—	9	1	no	—
311	C₃²⋊C₉	—	9	1	no	—
312	C₃²⋊C₉	—	9	1	no	—
313	C₃²⋊C₉	—	9	1	no	—
314	C₃²⋊C₉	—	9	1	no	—
315	C₃²⋊C₉	—	9	1	no	—
316	C₃²⋊C₉	—	9	1	no	—
317	C₉²	—	3	3	no	—
318	C₉²	—	3	3	no	—
319	C₉²	—	3	3	no	—
320	C₉²	—	3	3	no	—
321	C₉²	—	3	3	no	—
322	C₃³	—	3	1	no	—
323	C₃³	—	3	1	no	—
324	C₃³	—	3	1	no	—
325	C₃³	—	3	1	no	—
326	C₃³	—	3	1	no	—
327	C₃³	—	3	1	no	—
328	C₃³	—	3	1	no	—
329	C₃³	—	3	1	no	—
330	C₃³	—	3	1	no	—
331	C₃³	—	3	1	no	—
332	C₃³	—	3	1	no	—
333	C₃³	—	3	1	no	—
334	C₃³	—	3	1	no	—
335	C₃³	—	3	1	no	—
336	C₃³	—	3	1	no	—
337	C₃³	—	3	1	no	—
338	C₃³	—	3	1	no	—
339	C₃³	—	3	1	no	—
340	C₃³	—	3	1	no	—
341	C₃³	—	3	1	no	—
342	C₃³	—	3	1	no	—
343	C₃³	—	3	1	no	—
344	C₃³	—	3	1	no	—
345	C₃³	—	3	1	no	—
346	C₃³	—	3	1	no	—
347	C₃³	—	3	1	no	—
348	C₃³	—	3	1	no	—
349	C₃³	—	3	1	no	—
350	C₃³	—	3	1	no	—
351	C₃³	—	3	1	no	—
352	C₃³	—	3	1	no	—
353	C₃³	—	3	1	no	—
354	C₃³	—	3	1	no	—
355	C₃³	—	3	1	no	—
356	C₃³	—	3	1	no	—
357	C₃³	—	3	1	no	—
358	C₃³	—	3	1	no	—
359	C₃³	—	3	1	no	—
360	C₃³	—	3	1	no	—
361	C₃³	—	3	1	no	—
362	C₃³	—	3	1	no	—
363	C₃³	—	3	1	no	—
364	C₃³	—	3	1	no	—
365	C₃³	—	3	1	no	—
366	C₃³	—	3	1	no	—
367	C₃³	—	3	1	no	—
368	C₃³	—	3	1	no	—
369	C₃³	—	3	1	no	—
370	C₃³	—	3	1	no	—
371	C₃³	—	3	1	no	—
372	C₃³	C₃×3₋¹⁺²	1	3	yes	—
373	C₃³	#737	1	3	yes	—
374	C₃³	C₃⁴	1	1	yes	characteristic
375	3₋¹⁺²	—	3	27	no	—
376	3₋¹⁺²	—	9	9	no	—
377	3₋¹⁺²	—	9	9	no	—
378	3₋¹⁺²	—	9	9	no	—
379	3₋¹⁺²	—	9	9	no	—
380	H(3,𝔽₃)	—	9	9	no	—
381	C₃×C₉	—	3	1	no	—
382	C₃×C₉	—	3	1	no	—
383	C₃×C₉	—	3	1	no	—
384	C₃×C₉	—	3	1	no	—
385	C₃×C₉	—	3	1	no	—
386	C₃×C₉	—	3	1	no	—
387	C₃×C₉	—	3	1	no	—
388	C₃×C₉	—	3	1	no	—
389	C₃×C₉	—	3	1	no	—
390	C₃×C₉	—	3	1	no	—
391	C₃×C₉	—	3	1	no	—
392	C₃×C₉	—	3	1	no	—
393	C₃×C₉	—	3	1	no	—
394	C₃×C₉	—	3	1	no	—
395	C₃×C₉	—	3	1	no	—
396	C₃×C₉	—	3	1	no	—
397	C₃×C₉	—	3	1	no	—
398	C₃×C₉	—	3	1	no	—
399	C₃×C₉	—	3	1	no	—
400	C₃×C₉	—	3	1	no	—
401	C₃×C₉	—	3	1	no	—
402	C₃×C₉	—	3	1	no	—
403	C₃×C₉	—	3	1	no	—
404	C₃×C₉	—	3	1	no	—
405	C₃×C₉	—	3	1	no	—
406	C₃×C₉	—	3	1	no	—
407	C₃×C₉	—	3	1	no	—
408	C₃×C₉	—	3	1	no	—
409	C₃×C₉	—	3	1	no	—
410	C₃×C₉	—	3	1	no	—
411	C₃×C₉	—	3	1	no	—
412	C₃×C₉	—	3	1	no	—
413	C₃×C₉	—	3	1	no	—
414	C₃×C₉	—	3	1	no	—
415	C₃×C₉	—	3	1	no	—
416	C₃×C₉	—	3	1	no	—
417	C₃×C₉	—	3	1	no	—
418	C₃×C₉	—	3	1	no	—
419	C₃×C₉	—	3	1	no	—
420	C₃×C₉	—	3	1	no	—
421	C₃×C₉	—	3	1	no	—
422	C₃×C₉	—	3	1	no	—
423	C₃×C₉	—	3	1	no	—
424	C₃×C₉	—	3	1	no	—
425	C₃×C₉	—	3	1	no	—
426	C₃×C₉	—	3	1	no	—
427	C₃×C₉	—	3	1	no	—
428	C₃×C₉	—	3	1	no	—
429	C₃×C₉	—	3	1	no	—
430	C₃×C₉	—	3	1	no	—
431	C₃×C₉	—	3	1	no	—
432	C₃×C₉	—	3	1	no	—
433	C₃×C₉	—	3	1	no	—
434	C₃×C₉	—	3	1	no	—
435	C₃×C₉	—	3	1	no	—
436	C₃×C₉	—	3	1	no	—
437	C₃×C₉	—	3	1	no	—
438	C₃×C₉	—	3	1	no	—
439	C₃×C₉	—	3	1	no	—
440	C₃×C₉	—	3	1	no	—
441	C₃×C₉	—	3	1	no	—
442	C₃×C₉	—	3	1	no	—
443	C₃×C₉	—	3	1	no	—
444	C₃×C₉	—	3	1	no	—
445	C₃×C₉	—	3	1	no	—
446	C₃×C₉	—	3	1	no	—
447	C₃×C₉	—	3	1	no	—
448	C₃×C₉	—	3	1	no	—
449	C₃×C₉	—	3	1	no	—
450	C₃×C₉	—	3	1	no	—
451	C₃×C₉	—	3	1	no	—
452	C₃×C₉	—	3	1	no	—
453	C₃×C₉	—	3	1	no	—
454	C₃×C₉	—	3	1	no	—
455	C₃×C₉	—	3	1	no	—
456	C₃×C₉	—	3	1	no	—
457	C₃×C₉	—	3	1	no	—
458	C₃×C₉	—	3	1	no	—
459	C₃×C₉	—	3	1	no	—
460	C₃×C₉	—	3	1	no	—
461	C₃×C₉	—	3	1	no	—
462	C₃×C₉	—	3	1	no	—
463	C₃×C₉	—	3	1	no	—
464	C₃×C₉	—	3	1	no	—
465	C₃×C₉	—	3	1	no	—
466	C₃×C₉	—	3	1	no	—
467	C₃×C₉	—	3	1	no	—
468	C₃×C₉	—	3	1	no	—
469	C₃×C₉	—	3	1	no	—
470	C₃×C₉	—	3	1	no	—
471	C₃×C₉	—	3	1	no	—
472	C₃×C₉	—	3	1	no	—
473	C₃×C₉	—	3	1	no	—
474	C₃×C₉	—	3	1	no	—
475	C₃×C₉	—	3	1	no	—
476	C₃×C₉	—	3	1	no	—
477	C₃×C₉	—	3	1	no	—
478	C₃×C₉	—	3	1	no	—
479	C₃×C₉	—	3	1	no	—
480	C₃×C₉	—	3	1	no	—
481	C₃×C₉	—	3	1	no	—
482	C₃×C₉	—	3	1	no	—
483	C₃×C₉	—	3	1	no	—
484	C₃×C₉	—	3	1	no	—
485	C₃×C₉	—	3	1	no	—
486	C₃×C₉	—	3	1	no	—
487	C₃×C₉	—	3	1	no	—
488	C₃×C₉	—	3	1	no	—
489	C₃×C₉	—	3	1	no	—
490	C₃×C₉	—	3	1	no	—
491	C₃×C₉	—	3	1	no	—
492	C₃×C₉	—	3	1	no	—
493	C₃×C₉	—	3	1	no	—
494	C₃×C₉	—	3	1	no	—
495	C₃×C₉	—	3	1	no	—
496	C₃×C₉	—	3	1	no	—
497	C₃×C₉	—	3	1	no	—
498	C₃×C₉	—	3	1	no	—
499	C₃×C₉	—	3	1	no	—
500	C₃×C₉	—	3	1	no	—
501	C₃×C₉	—	3	1	no	—
502	C₃×C₉	—	3	1	no	—
503	C₃×C₉	—	3	1	no	—
504	C₃×C₉	—	3	1	no	—
505	C₃×C₉	—	3	1	no	—
506	C₃×C₉	—	3	1	no	—
507	C₃×C₉	—	3	1	no	—
508	C₃×C₉	—	3	1	no	—
509	C₃×C₉	—	3	1	no	—
510	C₃×C₉	—	3	1	no	—
511	C₃×C₉	—	3	1	no	—
512	C₃×C₉	—	3	1	no	—
513	C₃×C₉	—	3	1	no	—
514	C₃×C₉	—	9	9	no	—
515	C₃×C₉	—	9	9	no	—
516	C₃×C₉	C₃×H(3,𝔽₃)	1	3	yes	—
517	C₃×C₉	C₃×H(3,𝔽₃)	1	3	yes	—
518	C₃×C₉	C₃×H(3,𝔽₃)	1	3	yes	—
519	C₃×C₉	C₃×H(3,𝔽₃)	1	3	yes	—
520	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
521	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
522	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
523	C₃×C₉	#737	1	3	yes	—
524	C₃×C₉	#737	1	3	yes	—
525	C₃×C₉	#737	1	3	yes	—
526	C₃×C₉	#737	1	3	yes	—
527	C₃²	—	3	3	no	—
528	C₃²	—	3	3	no	—
529	C₃²	—	3	3	no	—
530	C₃²	—	3	3	no	—
531	C₃²	—	3	3	no	—
532	C₃²	—	3	3	no	—
533	C₃²	—	3	3	no	—
534	C₃²	—	3	3	no	—
535	C₃²	—	9	1	no	—
536	C₃²	—	9	1	no	—
537	C₃²	—	9	1	no	—
538	C₃²	—	9	1	no	—
539	C₃²	—	9	1	no	—
540	C₃²	—	9	1	no	—
541	C₃²	—	9	1	no	—
542	C₃²	—	9	1	no	—
543	C₃²	—	9	1	no	—
544	C₃²	—	9	1	no	—
545	C₃²	—	9	1	no	—
546	C₃²	—	9	1	no	—
547	C₃²	—	9	1	no	—
548	C₃²	—	9	1	no	—
549	C₃²	—	9	1	no	—
550	C₃²	—	9	1	no	—
551	C₃²	—	9	1	no	—
552	C₃²	—	9	1	no	—
553	C₃²	—	9	1	no	—
554	C₃²	—	9	1	no	—
555	C₃²	—	9	1	no	—
556	C₃²	—	9	1	no	—
557	C₃²	—	9	1	no	—
558	C₃²	—	9	1	no	—
559	C₃²	—	9	1	no	—
560	C₃²	—	9	1	no	—
561	C₃²	—	9	1	no	—
562	C₃²	—	9	1	no	—
563	C₃²	—	9	1	no	—
564	C₃²	—	9	1	no	—
565	C₃²	—	9	1	no	—
566	C₃²	—	9	1	no	—
567	C₃²	—	9	1	no	—
568	C₃²	—	9	1	no	—
569	C₃²	—	9	1	no	—
570	C₃²	—	9	1	no	—
571	C₃²	—	9	1	no	—
572	C₃²	—	9	1	no	—
573	C₃²	—	9	1	no	—
574	C₃²	—	9	1	no	—
575	C₃²	—	9	1	no	—
576	C₃²	—	9	1	no	—
577	C₃²	—	9	1	no	—
578	C₃²	—	9	1	no	—
579	C₃²	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
580	C₃²	C₃²×3₋¹⁺²	1	1	yes	characteristic
581	C₃²	C₃×#737	1	1	yes	characteristic
582	C₃²	C₃×#737	1	1	yes	characteristic
583	C₃²	C₃×#737	1	1	yes	characteristic
584	C₃²	C₃×#737	1	1	yes	characteristic
585	C₃²	C₃×#737	1	1	yes	characteristic
586	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
587	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
588	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
589	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
590	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
591	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
592	C₉	—	3	3	no	—
593	C₉	—	3	3	no	—
594	C₉	—	3	3	no	—
595	C₉	—	3	3	no	—
596	C₉	—	3	3	no	—
597	C₉	—	3	3	no	—
598	C₉	—	3	3	no	—
599	C₉	—	9	1	no	—
600	C₉	—	9	1	no	—
601	C₉	—	9	1	no	—
602	C₉	—	9	1	no	—
603	C₉	—	9	1	no	—
604	C₉	—	9	1	no	—
605	C₉	—	9	1	no	—
606	C₉	—	9	1	no	—
607	C₉	—	9	1	no	—
608	C₉	—	9	1	no	—
609	C₉	—	9	1	no	—
610	C₉	—	9	1	no	—
611	C₉	—	9	1	no	—
612	C₉	—	9	1	no	—
613	C₉	—	9	1	no	—
614	C₉	—	9	1	no	—
615	C₉	—	9	1	no	—
616	C₉	—	9	1	no	—
617	C₉	—	9	1	no	—
618	C₉	—	9	1	no	—
619	C₉	—	9	1	no	—
620	C₉	—	9	1	no	—
621	C₉	—	9	1	no	—
622	C₉	—	9	1	no	—
623	C₉	—	9	1	no	—
624	C₉	—	9	1	no	—
625	C₉	—	9	1	no	—
626	C₉	—	9	1	no	—
627	C₉	C₉⋊H(3,𝔽₃)	1	9	yes	—
628	C₃	—	9	3	no	—
629	C₃	—	9	3	no	—
630	C₃	—	27	1	no	—
631	C₃	—	27	1	no	—
632	C₃	C₃×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
633	C₃	#10624877	1	1	yes	characteristic
634	C₃	#10624892	1	1	yes	characteristic
635	C₃	#10624892	1	1	yes	characteristic
636	C₃	#10624896	1	1	yes	characteristic
637	C₃	#10624896	1	1	yes	characteristic
638	C₃	#10624896	1	1	yes	characteristic
639	C₃	#10624899	1	1	yes	characteristic
640	C₃	#10624901	1	1	yes	characteristic
641	C₃	#10624901	1	1	yes	characteristic
642	C₃	#10624907	1	1	yes	characteristic
643	C₃	#10624908	1	1	yes	characteristic
644	C₃	#10624908	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₃³	C₃⁴
prime radical	C₃²×H(3,𝔽₃)	C₃²
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³ ◁ G
LECS	G ▷ C₃³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₃×#6899	C₃	semidirect
2. C₃×#6896	C₃	semidirect
3. C₃×#6894	C₃	semidirect
5. C₃×C₉×3₋¹⁺²	C₃	semidirect
6. #10624566	C₃	semidirect
7. #10624566	C₃	semidirect
8. #10624566	C₃	semidirect
9. #10624566	C₃	semidirect
10. #10624566	C₃	semidirect
11. #10624566	C₃	semidirect
12. #10624566	C₃	semidirect
13. #10624566	C₃	semidirect
14. #10624566	C₃	semidirect
15. #10624566	C₃	semidirect
16. #10624566	C₃	semidirect
17. #10624566	C₃	semidirect
18. #10624566	C₃	semidirect
19. #10624566	C₃	semidirect
20. #10624565	C₃	semidirect
21. #10624565	C₃	semidirect
24. #10624560	C₃	semidirect
25. #10624560	C₃	semidirect
26. #10624560	C₃	semidirect
27. #10624560	C₃	semidirect
28. #10624560	C₃	semidirect
29. #10624560	C₃	semidirect
30. #10624560	C₃	semidirect
31. #10624560	C₃	semidirect
32. #10624557	C₃	semidirect
33. #10624557	C₃	semidirect
34. #10624557	C₃	semidirect
35. #10624557	C₃	semidirect
36. #10624556	C₃	semidirect
38. #10624548	C₃	semidirect
39. #10624548	C₃	semidirect
40. C₉×C₃²⋊C₉	C₃	semidirect
199. C₃×3₋¹⁺²	3₋¹⁺²	semidirect
275. C₉⋊C₉	H(3,𝔽₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6899	3
C₃×#6896	3
C₃×#6894	3
C₃×C₉⋊H(3,𝔽₃)	3
C₃×C₉×3₋¹⁺²	3
#10624566	3
#10624565	3
#10624563	3
#10624560	3
#10624557	3
#10624556	3
#10624555	3
#10624548	3
C₉×C₃²⋊C₉	3