Subgroups — #14552530

Order 2187.

760 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624570	C₃	1	1	yes	maximal, characteristic, complemented
2	#10624568	C₃	1	1	yes	maximal, characteristic, complemented
3	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
4	#10624566	C₃	1	1	yes	maximal, characteristic, complemented
5	#10624566	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	#10624565	C₃	1	1	yes	maximal, characteristic, complemented
16	#10624565	C₃	1	1	yes	maximal, characteristic, complemented
17	#10624563	C₃	1	1	yes	maximal, characteristic
18	#10624563	C₃	1	1	yes	maximal, characteristic
19	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
20	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
21	#10624558	C₃	1	1	yes	maximal, characteristic, complemented
22	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
23	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
24	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
25	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
26	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
27	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
28	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
29	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
30	#10624557	C₃	1	1	yes	maximal, characteristic, complemented
31	#10624557	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	#10624556	C₃	1	1	yes	maximal, characteristic, complemented
35	#10624555	C₃	1	1	yes	maximal, characteristic
36	#10624555	C₃	1	1	yes	maximal, characteristic
37	#10624549	C₃	1	1	yes	maximal, characteristic, complemented
38	#10624548	C₃	1	1	yes	maximal, characteristic, complemented
39	C₉×C₃²⋊C₉	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×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
44	C₃³×C₉	C₃²	1	1	yes	characteristic
45	C₃³×C₉	C₃²	1	1	yes	characteristic
46	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
47	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
48	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
49	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
50	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
51	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
52	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
53	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
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×C₃²⋊C₉	C₃²	1	1	yes	characteristic
66	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
67	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
68	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
69	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
70	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
71	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
73	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
74	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
75	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
76	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
77	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
78	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
79	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
80	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
81	C₃×C₃²⋊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×C₉²	C₃²	1	1	yes	characteristic
110	C₃×C₉²	C₃²	1	1	yes	characteristic
111	C₃×C₉²	C₃²	1	1	yes	characteristic
112	C₃×C₉²	C₃²	1	1	yes	characteristic
113	C₃×C₉²	C₃²	1	1	yes	characteristic
114	#6855	C₃²	1	1	yes	characteristic
115	#6855	C₃²	1	1	yes	characteristic
116	#6855	C₃²	1	1	yes	characteristic
117	#6855	C₃²	1	1	yes	characteristic
118	#6855	C₃²	1	1	yes	characteristic
119	#6855	C₃²	1	1	yes	characteristic
120	#6855	C₃²	1	1	yes	characteristic
121	#6855	C₃²	1	1	yes	characteristic
122	#6855	C₃²	1	1	yes	characteristic
123	#6855	C₃²	1	1	yes	characteristic
124	#6855	C₃²	1	1	yes	characteristic
125	#6855	C₃²	1	1	yes	characteristic
126	#6855	C₃²	1	1	yes	characteristic
127	#6855	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	C₃⁴	C₃³	1	1	yes	characteristic
172	C₃⁴	C₃³	1	1	yes	characteristic
173	C₃⁴	C₃³	1	1	yes	characteristic
174	C₃⁴	C₃³	1	1	yes	characteristic
175	C₃×3₋¹⁺²	—	3	3	no	—
176	C₃×3₋¹⁺²	—	3	3	no	—
177	C₃×3₋¹⁺²	—	3	3	no	—
178	C₃×3₋¹⁺²	—	9	1	no	—
179	C₃×3₋¹⁺²	—	9	1	no	—
180	C₃×3₋¹⁺²	—	9	1	no	—
181	C₃×3₋¹⁺²	—	9	1	no	—
182	C₃×3₋¹⁺²	—	9	1	no	—
183	C₃×H(3,𝔽₃)	—	3	3	no	—
184	C₃×H(3,𝔽₃)	—	3	3	no	—
185	C₃×H(3,𝔽₃)	—	9	1	no	—
186	C₃×H(3,𝔽₃)	—	9	1	no	—
187	C₃²×C₉	—	3	3	no	—
188	C₃²×C₉	—	3	3	no	—
189	C₃²×C₉	—	3	3	no	—
190	C₃²×C₉	—	3	3	no	—
191	C₃²×C₉	—	9	1	no	—
192	C₃²×C₉	—	9	1	no	—
193	C₃²×C₉	—	9	1	no	—
194	C₃²×C₉	—	9	1	no	—
195	C₃²×C₉	C₃³	1	1	yes	characteristic
196	C₃²×C₉	C₃³	1	1	yes	characteristic
197	C₃²×C₉	C₃³	1	1	yes	characteristic
198	C₃²×C₉	C₃³	1	1	yes	characteristic
199	C₃²×C₉	C₃³	1	1	yes	characteristic
200	C₃²×C₉	C₃³	1	1	yes	characteristic
201	C₃²×C₉	C₃³	1	1	yes	characteristic
202	C₃²×C₉	C₃³	1	1	yes	characteristic
203	C₃²×C₉	C₃³	1	1	yes	characteristic
204	C₃²×C₉	C₃³	1	1	yes	characteristic
205	C₃²×C₉	C₃³	1	1	yes	characteristic
206	C₃²×C₉	C₃³	1	1	yes	characteristic
207	C₃²×C₉	C₃³	1	1	yes	characteristic
208	C₃²×C₉	C₃³	1	1	yes	characteristic
209	C₃²×C₉	C₃³	1	1	yes	characteristic
210	C₃²×C₉	C₃³	1	1	yes	characteristic
211	C₃²×C₉	C₃³	1	1	yes	characteristic
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	C₉⋊C₉	—	9	1	no	—
232	C₉⋊C₉	—	9	1	no	—
233	C₉⋊C₉	—	9	1	no	—
234	C₉⋊C₉	—	9	1	no	—
235	C₉⋊C₉	—	9	1	no	—
236	C₉⋊C₉	—	9	1	no	—
237	C₉⋊C₉	—	9	1	no	—
238	C₉⋊C₉	—	9	1	no	—
239	C₉⋊C₉	—	9	1	no	—
240	C₉⋊C₉	—	9	1	no	—
241	C₉⋊C₉	—	9	1	no	—
242	C₉⋊C₉	—	9	1	no	—
243	C₉⋊C₉	—	9	1	no	—
244	C₉⋊C₉	—	9	1	no	—
245	C₉⋊C₉	—	9	1	no	—
246	C₉⋊C₉	—	9	1	no	—
247	C₉⋊C₉	—	9	1	no	—
248	C₉⋊C₉	—	9	1	no	—
249	C₉⋊C₉	—	9	1	no	—
250	C₃²⋊C₉	—	3	3	no	—
251	C₃²⋊C₉	—	3	3	no	—
252	C₃²⋊C₉	—	3	3	no	—
253	C₃²⋊C₉	—	3	3	no	—
254	C₃²⋊C₉	—	3	3	no	—
255	C₃²⋊C₉	—	3	3	no	—
256	C₃²⋊C₉	—	3	3	no	—
257	C₃²⋊C₉	—	3	3	no	—
258	C₃²⋊C₉	—	3	3	no	—
259	C₃²⋊C₉	—	3	3	no	—
260	C₃²⋊C₉	—	3	3	no	—
261	C₃²⋊C₉	—	3	3	no	—
262	C₃²⋊C₉	—	3	3	no	—
263	C₃²⋊C₉	—	3	3	no	—
264	C₃²⋊C₉	—	3	3	no	—
265	C₃²⋊C₉	—	3	3	no	—
266	C₃²⋊C₉	—	3	3	no	—
267	C₃²⋊C₉	—	3	3	no	—
268	C₃²⋊C₉	—	3	3	no	—
269	C₃²⋊C₉	—	9	1	no	—
270	C₃²⋊C₉	—	9	1	no	—
271	C₃²⋊C₉	—	9	1	no	—
272	C₃²⋊C₉	—	9	1	no	—
273	C₃²⋊C₉	—	9	1	no	—
274	C₃²⋊C₉	—	9	1	no	—
275	C₃²⋊C₉	—	9	1	no	—
276	C₃²⋊C₉	—	9	1	no	—
277	C₃²⋊C₉	—	9	1	no	—
278	C₃²⋊C₉	—	9	1	no	—
279	C₃²⋊C₉	—	9	1	no	—
280	C₃²⋊C₉	—	9	1	no	—
281	C₃²⋊C₉	—	9	1	no	—
282	C₃²⋊C₉	—	9	1	no	—
283	C₃²⋊C₉	—	9	1	no	—
284	C₃²⋊C₉	—	9	1	no	—
285	C₃²⋊C₉	—	9	1	no	—
286	C₃²⋊C₉	—	9	1	no	—
287	C₃²⋊C₉	—	9	1	no	—
288	C₃²⋊C₉	—	9	1	no	—
289	C₃²⋊C₉	—	9	1	no	—
290	C₃²⋊C₉	—	9	1	no	—
291	C₃²⋊C₉	—	9	1	no	—
292	C₃²⋊C₉	—	9	1	no	—
293	C₃²⋊C₉	—	9	1	no	—
294	C₉²	—	9	1	no	—
295	C₉²	—	9	1	no	—
296	C₉²	—	9	1	no	—
297	C₉²	—	9	1	no	—
298	C₉²	—	9	1	no	—
299	C₃³	—	3	1	no	—
300	C₃³	—	3	1	no	—
301	C₃³	—	3	1	no	—
302	C₃³	—	3	1	no	—
303	C₃³	—	3	1	no	—
304	C₃³	—	3	1	no	—
305	C₃³	—	3	1	no	—
306	C₃³	—	3	1	no	—
307	C₃³	—	3	1	no	—
308	C₃³	—	3	1	no	—
309	C₃³	—	3	1	no	—
310	C₃³	—	3	1	no	—
311	C₃³	—	3	1	no	—
312	C₃³	—	3	1	no	—
313	C₃³	—	3	1	no	—
314	C₃³	—	3	1	no	—
315	C₃³	—	3	1	no	—
316	C₃³	—	3	1	no	—
317	C₃³	—	3	1	no	—
318	C₃³	—	3	1	no	—
319	C₃³	—	3	1	no	—
320	C₃³	—	3	1	no	—
321	C₃³	—	3	1	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	#737	1	3	yes	—
350	C₃³	#737	1	3	yes	—
351	C₃³	C₃⁴	1	1	yes	characteristic
352	3₋¹⁺²	—	9	9	no	—
353	3₋¹⁺²	—	9	9	no	—
354	H(3,𝔽₃)	—	9	9	no	—
355	C₃×C₉	—	3	1	no	—
356	C₃×C₉	—	3	1	no	—
357	C₃×C₉	—	3	1	no	—
358	C₃×C₉	—	3	1	no	—
359	C₃×C₉	—	3	1	no	—
360	C₃×C₉	—	3	1	no	—
361	C₃×C₉	—	3	1	no	—
362	C₃×C₉	—	3	1	no	—
363	C₃×C₉	—	3	1	no	—
364	C₃×C₉	—	3	1	no	—
365	C₃×C₉	—	3	1	no	—
366	C₃×C₉	—	3	1	no	—
367	C₃×C₉	—	3	1	no	—
368	C₃×C₉	—	3	1	no	—
369	C₃×C₉	—	3	1	no	—
370	C₃×C₉	—	3	1	no	—
371	C₃×C₉	—	3	1	no	—
372	C₃×C₉	—	3	1	no	—
373	C₃×C₉	—	3	1	no	—
374	C₃×C₉	—	3	1	no	—
375	C₃×C₉	—	3	1	no	—
376	C₃×C₉	—	3	1	no	—
377	C₃×C₉	—	3	1	no	—
378	C₃×C₉	—	3	1	no	—
379	C₃×C₉	—	3	1	no	—
380	C₃×C₉	—	3	1	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	—	9	9	no	—
495	C₃×C₉	—	9	9	no	—
496	C₃×C₉	#737	1	3	yes	—
497	C₃×C₉	#737	1	3	yes	—
498	C₃×C₉	#737	1	3	yes	—
499	C₃×C₉	#737	1	3	yes	—
500	C₃×C₉	#737	1	3	yes	—
501	C₃²	—	3	3	no	—
502	C₃²	—	3	3	no	—
503	C₃²	—	3	3	no	—
504	C₃²	—	3	3	no	—
505	C₃²	—	3	3	no	—
506	C₃²	—	3	3	no	—
507	C₃²	—	3	3	no	—
508	C₃²	—	3	3	no	—
509	C₃²	—	9	1	no	—
510	C₃²	—	9	1	no	—
511	C₃²	—	9	1	no	—
512	C₃²	—	9	1	no	—
513	C₃²	—	9	1	no	—
514	C₃²	—	9	1	no	—
515	C₃²	—	9	1	no	—
516	C₃²	—	9	1	no	—
517	C₃²	—	9	1	no	—
518	C₃²	—	9	1	no	—
519	C₃²	—	9	1	no	—
520	C₃²	—	9	1	no	—
521	C₃²	—	9	1	no	—
522	C₃²	—	9	1	no	—
523	C₃²	—	9	1	no	—
524	C₃²	—	9	1	no	—
525	C₃²	—	9	1	no	—
526	C₃²	—	9	1	no	—
527	C₃²	—	9	1	no	—
528	C₃²	—	9	1	no	—
529	C₃²	—	9	1	no	—
530	C₃²	—	9	1	no	—
531	C₃²	—	9	1	no	—
532	C₃²	—	9	1	no	—
533	C₃²	—	9	1	no	—
534	C₃²	—	9	1	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	C₃×#737	1	1	yes	characteristic
554	C₃²	C₃×#737	1	1	yes	characteristic
555	C₃²	C₃×#737	1	1	yes	characteristic
556	C₃²	C₃×#737	1	1	yes	characteristic
557	C₃²	C₃×#737	1	1	yes	characteristic
558	C₃²	C₃×#737	1	1	yes	characteristic
559	C₃²	C₃×#737	1	1	yes	characteristic
560	C₃²	H(5,𝔽₃)	1	1	yes	characteristic
561	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
562	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
563	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
564	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
565	C₃²	3₋¹⁺⁴	1	1	yes	characteristic
566	C₉	—	3	3	no	—
567	C₉	—	3	3	no	—
568	C₉	—	3	3	no	—
569	C₉	—	3	3	no	—
570	C₉	—	3	3	no	—
571	C₉	—	9	1	no	—
572	C₉	—	9	1	no	—
573	C₉	—	9	1	no	—
574	C₉	—	9	1	no	—
575	C₉	—	9	1	no	—
576	C₉	—	9	1	no	—
577	C₉	—	9	1	no	—
578	C₉	—	9	1	no	—
579	C₉	—	9	1	no	—
580	C₉	—	9	1	no	—
581	C₉	—	9	1	no	—
582	C₉	—	9	1	no	—
583	C₉	—	9	1	no	—
584	C₉	—	9	1	no	—
585	C₉	—	9	1	no	—
586	C₉	—	9	1	no	—
587	C₉	—	9	1	no	—
588	C₉	—	9	1	no	—
589	C₉	—	9	1	no	—
590	C₉	—	9	1	no	—
591	C₉	—	9	1	no	—
592	C₉	—	9	1	no	—
593	C₉	—	9	1	no	—
594	C₉	—	9	1	no	—
595	C₉	—	9	1	no	—
596	C₉	—	9	1	no	—
597	C₉	—	9	1	no	—
598	C₉	—	9	1	no	—
599	C₉	—	9	1	no	—
600	C₉	—	9	1	no	—
601	C₉	—	9	1	no	—
602	C₃	—	9	3	no	—
603	C₃	—	9	3	no	—
604	C₃	—	27	1	no	—
605	C₃	—	27	1	no	—
606	C₃	#10624877	1	1	yes	characteristic
607	C₃	#10624877	1	1	yes	characteristic
608	C₃	#10624888	1	1	yes	characteristic
609	C₃	#10624892	1	1	yes	characteristic
610	C₃	#10624903	1	1	yes	characteristic
611	C₃	#10624904	1	1	yes	characteristic
612	C₃	#10624905	1	1	yes	characteristic
613	C₃	#10624905	1	1	yes	characteristic
614	C₃	#10624905	1	1	yes	characteristic
615	C₃	#10624907	1	1	yes	characteristic
616	C₃	#10624908	1	1	yes	characteristic
617	C₃	#10624908	1	1	yes	characteristic
618	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. #10624570	C₃	semidirect
2. #10624568	C₃	semidirect
3. #10624566	C₃	semidirect
4. #10624566	C₃	semidirect
5. #10624566	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. #10624565	C₃	semidirect
16. #10624565	C₃	semidirect
19. #10624560	C₃	semidirect
20. #10624560	C₃	semidirect
21. #10624558	C₃	semidirect
22. #10624557	C₃	semidirect
23. #10624557	C₃	semidirect
24. #10624557	C₃	semidirect
25. #10624557	C₃	semidirect
26. #10624557	C₃	semidirect
27. #10624557	C₃	semidirect
28. #10624557	C₃	semidirect
29. #10624557	C₃	semidirect
30. #10624557	C₃	semidirect
31. #10624557	C₃	semidirect
32. #10624557	C₃	semidirect
33. #10624557	C₃	semidirect
34. #10624556	C₃	semidirect
37. #10624549	C₃	semidirect
38. #10624548	C₃	semidirect
39. C₉×C₃²⋊C₉	C₃	semidirect
40. C₉×C₃²⋊C₉	C₃	semidirect

Maximal subgroups

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

subgroup	index
#10624570	3
#10624568	3
#10624566	3
#10624565	3
#10624563	3
#10624560	3
#10624558	3
#10624557	3
#10624556	3
#10624555	3
#10624549	3
#10624548	3
C₉×C₃²⋊C₉	3