Subgroups — #72243553

Order 4374.

715 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14552205	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₃×#6894	—	3	1	no	maximal
3	C₃×D₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
4	C₃²×D₉⋊C₉	C₃	1	1	yes	maximal, characteristic
5	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
11	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
12	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
13	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
14	#13090623	C₃	1	1	yes	maximal, characteristic
15	#13090623	C₃	1	1	yes	maximal, characteristic
16	C₃×#6894	D₃	1	1	yes	characteristic
17	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
18	C₃²×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic
19	#10624575	—	2	1	no	—
20	#10624575	—	2	1	no	—
21	#10624575	—	2	1	no	—
22	#10624574	—	2	1	no	—
23	#10624574	—	2	1	no	—
24	#10624574	—	2	1	no	—
25	#10624573	—	2	1	no	—
26	#10624573	—	2	1	no	—
27	#10624573	—	2	1	no	—
28	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
29	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
30	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
31	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
32	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
33	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
34	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
35	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
36	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
37	#10624558	—	2	1	no	—
38	#10624556	—	2	1	no	—
39	#10624556	—	2	1	no	—
40	#10624548	—	2	1	no	—
41	#10624548	C₂×C₃	1	1	yes	characteristic
42	#10624548	C₂×C₃	1	1	yes	characteristic
43	C₃×D₃×3₋¹⁺²	—	3	1	no	—
44	C₃²×D₃×C₉	—	3	1	no	—
45	C₃³×D₉	C₃²	1	1	yes	characteristic
46	C₂×#6894	—	9	1	no	—
47	D₉×3₋¹⁺²	—	3	3	no	—
48	D₃×C₉⋊C₉	—	3	1	no	—
49	D₃×C₉⋊C₉	—	3	1	no	—
50	D₃×C₉⋊C₉	—	3	1	no	—
51	D₃×C₉⋊C₉	—	3	1	no	—
52	D₃×C₉⋊C₉	—	3	1	no	—
53	D₃×C₉⋊C₉	—	3	1	no	—
54	D₃×C₉⋊C₉	—	3	1	no	—
55	D₃×C₉⋊C₉	—	3	1	no	—
56	D₃×C₉⋊C₉	—	3	1	no	—
57	C₃×D₉⋊C₉	—	3	1	no	—
58	C₃×D₉⋊C₉	—	3	2	no	—
59	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
60	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
61	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
62	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
63	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
64	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
65	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
66	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
67	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
68	D₃×C₃²⋊C₉	—	3	1	no	—
69	D₃×C₃²⋊C₉	—	3	1	no	—
70	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
71	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
72	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
73	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
74	C₃³×C₉	—	2	1	no	—
75	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
76	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
77	#6894	—	6	1	no	—
78	#6894	—	6	1	no	—
79	#6894	—	6	1	no	—
80	#6894	—	6	1	no	—
81	#6894	—	6	1	no	—
82	C₉×3₋¹⁺²	—	3	3	no	—
83	C₉×3₋¹⁺²	—	6	3	no	—
84	C₃×C₉⋊C₉	—	2	1	no	—
85	C₃×C₉⋊C₉	—	2	1	no	—
86	C₃×C₉⋊C₉	—	2	1	no	—
87	C₃×C₉⋊C₉	—	2	1	no	—
88	C₃×C₉⋊C₉	—	2	1	no	—
89	C₃×C₉⋊C₉	—	2	1	no	—
90	C₃×C₉⋊C₉	—	2	1	no	—
91	C₃×C₉⋊C₉	—	2	1	no	—
92	C₃×C₉⋊C₉	—	2	1	no	—
93	C₃×C₉⋊C₉	—	2	1	no	—
94	C₃×C₉⋊C₉	—	2	1	no	—
95	C₃×C₉⋊C₉	—	2	1	no	—
96	C₃×C₉⋊C₉	—	2	1	no	—
97	C₃×C₉⋊C₉	—	2	1	no	—
98	C₃×C₉⋊C₉	—	2	1	no	—
99	C₃×C₉⋊C₉	—	3	1	no	—
100	C₃×C₉⋊C₉	—	3	2	no	—
101	C₃×C₉⋊C₉	—	6	1	no	—
102	C₃×C₉⋊C₉	—	6	2	no	—
103	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
104	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
105	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
106	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
107	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
108	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
109	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
110	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
111	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
112	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
113	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
114	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
115	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
116	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
117	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
118	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
119	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
120	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
121	C₃×C₃²⋊C₉	—	2	1	no	—
122	C₃×C₃²⋊C₉	—	2	1	no	—
123	C₃×C₃²⋊C₉	—	2	1	no	—
124	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
125	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
126	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
127	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
128	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
129	#6855	—	2	1	no	—
130	#6855	—	2	1	no	—
131	#6855	—	2	1	no	—
132	#6855	—	2	1	no	—
133	#6855	—	2	1	no	—
134	#6855	—	2	1	no	—
135	#6855	—	2	1	no	—
136	#6855	—	2	1	no	—
137	#6855	—	2	1	no	—
138	#6855	—	2	1	no	—
139	#6855	—	2	1	no	—
140	#6855	—	2	1	no	—
141	#6855	—	2	1	no	—
142	#6855	—	2	1	no	—
143	#6855	—	2	1	no	—
144	#6855	—	2	1	no	—
145	#6855	—	2	1	no	—
146	#6855	—	2	1	no	—
147	#6855	—	2	1	no	—
148	#6855	—	2	1	no	—
149	#6855	—	2	1	no	—
150	#6855	—	2	1	no	—
151	#6855	—	2	1	no	—
152	#6855	—	2	1	no	—
153	#6855	—	2	1	no	—
154	#6855	—	2	1	no	—
155	#6855	—	2	1	no	—
156	#6855	—	2	1	no	—
157	#6855	—	2	1	no	—
158	#6855	—	2	1	no	—
159	#6855	—	2	1	no	—
160	#6855	—	2	1	no	—
161	#6855	—	2	1	no	—
162	C₃³×D₃	—	3	1	no	—
163	C₂×C₃×3₋¹⁺²	—	9	1	no	—
164	C₂×C₃²×C₉	—	9	1	no	—
165	D₃×3₋¹⁺²	—	9	3	no	—
166	C₃×D₃×C₉	—	3	1	no	—
167	C₃×D₃×C₉	—	3	1	no	—
168	C₃×D₃×C₉	—	3	1	no	—
169	C₃×D₃×C₉	—	3	1	no	—
170	C₃×D₃×C₉	—	3	1	no	—
171	C₃×D₃×C₉	—	3	1	no	—
172	C₃×D₃×C₉	—	3	1	no	—
173	C₃×D₃×C₉	—	3	1	no	—
174	C₃×D₃×C₉	—	3	1	no	—
175	C₃×D₃×C₉	—	3	1	no	—
176	C₃×D₃×C₉	—	3	1	no	—
177	C₃×D₃×C₉	—	3	1	no	—
178	C₃×D₃×C₉	—	9	1	no	—
179	C₃×D₃×C₉	—	9	2	no	—
180	C₃²×D₉	—	3	1	no	—
181	C₃²×D₉	—	3	1	no	—
182	C₃²×D₉	—	3	1	no	—
183	C₃²×D₉	3₋¹⁺²	1	3	yes	—
184	C₃²×D₉	C₃³	1	1	yes	characteristic
185	C₂×C₉⋊C₉	—	9	1	no	—
186	C₂×C₉⋊C₉	—	9	1	no	—
187	C₂×C₉⋊C₉	—	9	1	no	—
188	C₂×C₉⋊C₉	—	9	1	no	—
189	C₂×C₉⋊C₉	—	9	1	no	—
190	C₂×C₉⋊C₉	—	9	1	no	—
191	C₂×C₉⋊C₉	—	9	1	no	—
192	C₂×C₉⋊C₉	—	9	1	no	—
193	C₂×C₉⋊C₉	—	9	1	no	—
194	C₂×C₃²⋊C₉	—	9	1	no	—
195	C₂×C₃²⋊C₉	—	9	1	no	—
196	D₉⋊C₉	—	3	1	no	—
197	D₉⋊C₉	—	3	1	no	—
198	D₉⋊C₉	—	3	1	no	—
199	D₉⋊C₉	—	3	1	no	—
200	D₉⋊C₉	—	3	1	no	—
201	D₉⋊C₉	—	3	1	no	—
202	D₉⋊C₉	—	3	1	no	—
203	D₉⋊C₉	—	3	1	no	—
204	D₉⋊C₉	3₋¹⁺²	1	1	yes	characteristic, complemented
205	D₉⋊C₉	3₋¹⁺²	1	2	yes	complemented
206	C₉×D₉	—	3	1	no	—
207	C₉×D₉	—	3	1	no	—
208	C₉×D₉	—	3	1	no	—
209	C₃⁴	C₃²×D₃	1	1	yes	characteristic
210	C₃×3₋¹⁺²	—	2	1	no	—
211	C₃×3₋¹⁺²	—	2	1	no	—
212	C₃×3₋¹⁺²	—	2	1	no	—
213	C₃×3₋¹⁺²	—	2	1	no	—
214	C₃×3₋¹⁺²	—	3	3	no	—
215	C₃×3₋¹⁺²	—	6	3	no	—
216	C₃×3₋¹⁺²	AGL(1,ℤ/9)	1	1	yes	characteristic
217	C₃²×C₉	—	2	3	no	—
218	C₃²×C₉	—	2	1	no	—
219	C₃²×C₉	—	2	1	no	—
220	C₃²×C₉	—	2	1	no	—
221	C₃²×C₉	—	2	1	no	—
222	C₃²×C₉	—	2	1	no	—
223	C₃²×C₉	—	2	1	no	—
224	C₃²×C₉	—	2	1	no	—
225	C₃²×C₉	—	2	1	no	—
226	C₃²×C₉	—	2	1	no	—
227	C₃²×C₉	—	2	1	no	—
228	C₃²×C₉	—	2	1	no	—
229	C₃²×C₉	—	2	1	no	—
230	C₃²×C₉	—	2	1	no	—
231	C₃²×C₉	—	3	1	no	—
232	C₃²×C₉	—	3	1	no	—
233	C₃²×C₉	—	3	1	no	—
234	C₃²×C₉	—	3	1	no	—
235	C₃²×C₉	—	3	2	no	—
236	C₃²×C₉	—	6	1	no	—
237	C₃²×C₉	—	6	1	no	—
238	C₃²×C₉	—	6	1	no	—
239	C₃²×C₉	—	6	2	no	—
240	C₃²×C₉	—	6	1	no	—
241	C₃²×C₉	—	6	1	no	—
242	C₃²×C₉	—	6	1	no	—
243	C₃²×C₉	—	6	3	no	—
244	C₃²×C₉	—	18	1	no	—
245	C₃²×C₉	—	18	1	no	—
246	C₃²×C₉	—	18	1	no	—
247	C₃²×C₉	C₂×3₋¹⁺²	1	3	yes	—
248	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
249	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
250	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
251	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
252	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
253	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
254	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
255	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
256	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
257	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
258	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
259	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
260	C₃²×C₉	C₂×C₃³	1	1	yes	characteristic
261	C₉⋊C₉	—	2	1	no	—
262	C₉⋊C₉	—	2	2	no	—
263	C₉⋊C₉	—	3	1	no	—
264	C₉⋊C₉	—	3	1	no	—
265	C₉⋊C₉	—	3	1	no	—
266	C₉⋊C₉	—	3	1	no	—
267	C₉⋊C₉	—	3	1	no	—
268	C₉⋊C₉	—	3	1	no	—
269	C₉⋊C₉	—	3	1	no	—
270	C₉⋊C₉	—	3	1	no	—
271	C₉⋊C₉	—	3	1	no	—
272	C₉⋊C₉	—	6	1	no	—
273	C₉⋊C₉	—	6	1	no	—
274	C₉⋊C₉	—	6	1	no	—
275	C₉⋊C₉	—	6	1	no	—
276	C₉⋊C₉	—	6	1	no	—
277	C₉⋊C₉	—	6	1	no	—
278	C₉⋊C₉	—	6	1	no	—
279	C₉⋊C₉	—	6	1	no	—
280	C₉⋊C₉	—	6	1	no	—
281	C₉⋊C₉	—	6	1	no	—
282	C₉⋊C₉	—	6	1	no	—
283	C₉⋊C₉	—	6	1	no	—
284	C₉⋊C₉	—	6	2	no	—
285	C₉⋊C₉	—	6	1	no	—
286	C₉⋊C₉	—	6	2	no	—
287	C₉⋊C₉	—	6	1	no	—
288	C₉⋊C₉	—	6	3	no	—
289	C₉⋊C₉	—	6	3	no	—
290	C₉⋊C₉	—	6	3	no	—
291	C₉⋊C₉	—	6	1	no	—
292	C₉⋊C₉	—	6	1	no	—
293	C₉⋊C₉	—	6	1	no	—
294	C₉⋊C₉	—	6	1	no	—
295	C₉⋊C₉	—	6	1	no	—
296	C₉⋊C₉	—	6	1	no	—
297	C₉⋊C₉	—	6	1	no	—
298	C₉⋊C₉	—	6	1	no	—
299	C₉⋊C₉	—	6	1	no	—
300	C₉⋊C₉	—	6	1	no	—
301	C₉⋊C₉	—	6	1	no	—
302	C₉⋊C₉	—	6	1	no	—
303	C₉⋊C₉	—	6	1	no	—
304	C₉⋊C₉	—	6	1	no	—
305	C₉⋊C₉	—	6	2	no	—
306	C₉⋊C₉	—	18	1	no	—
307	C₉⋊C₉	—	18	1	no	—
308	C₉⋊C₉	—	18	1	no	—
309	C₉⋊C₉	—	18	1	no	—
310	C₉⋊C₉	—	18	1	no	—
311	C₉⋊C₉	—	18	1	no	—
312	C₉⋊C₉	—	18	1	no	—
313	C₉⋊C₉	—	18	1	no	—
314	C₉⋊C₉	—	18	1	no	—
315	C₉⋊C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
316	C₉⋊C₉	C₂×3₋¹⁺²	1	2	yes	complemented
317	C₃²⋊C₉	—	3	1	no	—
318	C₃²⋊C₉	—	6	1	no	—
319	C₃²⋊C₉	—	6	1	no	—
320	C₃²⋊C₉	—	6	3	no	—
321	C₃²⋊C₉	—	6	3	no	—
322	C₃²⋊C₉	—	6	1	no	—
323	C₃²⋊C₉	—	6	3	no	—
324	C₉²	—	3	1	no	—
325	C₉²	—	3	1	no	—
326	C₉²	—	3	1	no	—
327	C₉²	—	6	1	no	—
328	C₉²	—	6	1	no	—
329	C₉²	—	6	1	no	—
330	C₂×C₃³	—	9	1	no	—
331	C₃²×D₃	—	3	1	no	—
332	C₃²×D₃	—	3	3	no	—
333	C₃²×D₃	—	9	1	no	—
334	C₃²×D₃	—	9	1	no	—
335	C₃²×D₃	—	9	1	no	—
336	C₂×3₋¹⁺²	—	27	3	no	—
337	C₂×C₃×C₉	—	9	1	no	—
338	C₂×C₃×C₉	—	9	1	no	—
339	C₂×C₃×C₉	—	9	1	no	—
340	C₂×C₃×C₉	—	9	1	no	—
341	C₂×C₃×C₉	—	9	1	no	—
342	C₂×C₃×C₉	—	9	1	no	—
343	C₂×C₃×C₉	—	9	1	no	—
344	C₂×C₃×C₉	—	9	1	no	—
345	C₂×C₃×C₉	—	9	1	no	—
346	C₂×C₃×C₉	—	9	1	no	—
347	C₂×C₃×C₉	—	9	1	no	—
348	C₂×C₃×C₉	—	9	1	no	—
349	C₂×C₃×C₉	—	27	1	no	—
350	C₂×C₃×C₉	—	27	2	no	—
351	D₃×C₉	—	3	1	no	—
352	D₃×C₉	—	3	2	no	—
353	D₃×C₉	—	9	1	no	—
354	D₃×C₉	—	9	1	no	—
355	D₃×C₉	—	9	1	no	—
356	D₃×C₉	—	9	1	no	—
357	D₃×C₉	—	9	1	no	—
358	D₃×C₉	—	9	1	no	—
359	D₃×C₉	—	9	1	no	—
360	D₃×C₉	—	9	1	no	—
361	D₃×C₉	—	9	1	no	—
362	D₃×C₉	—	9	1	no	—
363	D₃×C₉	—	9	1	no	—
364	C₃×D₉	—	3	3	no	—
365	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
366	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
367	C₃×D₉	#737	1	1	yes	characteristic
368	C₃×D₉	#737	1	1	yes	characteristic
369	C₃³	—	2	3	no	—
370	C₃³	—	2	1	no	—
371	C₃³	—	3	1	no	—
372	C₃³	—	3	1	no	—
373	C₃³	—	3	1	no	—
374	C₃³	—	6	1	no	—
375	C₃³	—	6	1	no	—
376	C₃³	—	6	1	no	—
377	C₃³	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
378	C₃³	D₃×3₋¹⁺²	1	3	yes	—
379	C₃³	C₃³×D₃	1	1	yes	characteristic
380	3₋¹⁺²	—	3	3	no	—
381	3₋¹⁺²	—	6	3	no	—
382	3₋¹⁺²	—	6	3	no	—
383	3₋¹⁺²	—	6	3	no	—
384	3₋¹⁺²	—	6	3	no	—
385	C₃×C₉	—	2	1	no	—
386	C₃×C₉	—	2	1	no	—
387	C₃×C₉	—	2	1	no	—
388	C₃×C₉	—	2	1	no	—
389	C₃×C₉	—	2	1	no	—
390	C₃×C₉	—	2	1	no	—
391	C₃×C₉	—	2	1	no	—
392	C₃×C₉	—	2	2	no	—
393	C₃×C₉	—	2	1	no	—
394	C₃×C₉	—	2	3	no	—
395	C₃×C₉	—	3	1	no	—
396	C₃×C₉	—	3	1	no	—
397	C₃×C₉	—	3	1	no	—
398	C₃×C₉	—	3	3	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	—	6	3	no	—
412	C₃×C₉	—	6	3	no	—
413	C₃×C₉	—	6	3	no	—
414	C₃×C₉	—	6	3	no	—
415	C₃×C₉	—	6	1	no	—
416	C₃×C₉	—	6	1	no	—
417	C₃×C₉	—	6	1	no	—
418	C₃×C₉	—	6	1	no	—
419	C₃×C₉	—	6	1	no	—
420	C₃×C₉	—	6	1	no	—
421	C₃×C₉	—	6	1	no	—
422	C₃×C₉	—	6	1	no	—
423	C₃×C₉	—	6	1	no	—
424	C₃×C₉	—	6	1	no	—
425	C₃×C₉	—	6	1	no	—
426	C₃×C₉	—	6	1	no	—
427	C₃×C₉	—	6	1	no	—
428	C₃×C₉	—	6	1	no	—
429	C₃×C₉	—	6	1	no	—
430	C₃×C₉	—	6	1	no	—
431	C₃×C₉	—	6	1	no	—
432	C₃×C₉	—	6	1	no	—
433	C₃×C₉	—	6	1	no	—
434	C₃×C₉	—	6	1	no	—
435	C₃×C₉	—	6	1	no	—
436	C₃×C₉	—	6	1	no	—
437	C₃×C₉	—	6	1	no	—
438	C₃×C₉	—	6	1	no	—
439	C₃×C₉	—	6	1	no	—
440	C₃×C₉	—	6	1	no	—
441	C₃×C₉	—	6	1	no	—
442	C₃×C₉	—	6	1	no	—
443	C₃×C₉	—	6	1	no	—
444	C₃×C₉	—	6	1	no	—
445	C₃×C₉	—	6	1	no	—
446	C₃×C₉	—	6	1	no	—
447	C₃×C₉	—	6	1	no	—
448	C₃×C₉	—	6	1	no	—
449	C₃×C₉	—	6	1	no	—
450	C₃×C₉	—	6	1	no	—
451	C₃×C₉	—	6	1	no	—
452	C₃×C₉	—	6	1	no	—
453	C₃×C₉	—	6	1	no	—
454	C₃×C₉	—	6	1	no	—
455	C₃×C₉	—	6	1	no	—
456	C₃×C₉	—	6	1	no	—
457	C₃×C₉	—	6	1	no	—
458	C₃×C₉	—	6	1	no	—
459	C₃×C₉	—	6	1	no	—
460	C₃×C₉	—	6	1	no	—
461	C₃×C₉	—	6	1	no	—
462	C₃×C₉	—	6	1	no	—
463	C₃×C₉	—	6	1	no	—
464	C₃×C₉	—	6	1	no	—
465	C₃×C₉	—	6	1	no	—
466	C₃×C₉	—	6	1	no	—
467	C₃×C₉	—	6	1	no	—
468	C₃×C₉	—	6	1	no	—
469	C₃×C₉	—	6	1	no	—
470	C₃×C₉	—	6	1	no	—
471	C₃×C₉	—	6	1	no	—
472	C₃×C₉	—	6	1	no	—
473	C₃×C₉	—	6	1	no	—
474	C₃×C₉	—	6	1	no	—
475	C₃×C₉	—	6	1	no	—
476	C₃×C₉	—	6	1	no	—
477	C₃×C₉	—	6	1	no	—
478	C₃×C₉	—	6	1	no	—
479	C₃×C₉	—	6	1	no	—
480	C₃×C₉	—	6	1	no	—
481	C₃×C₉	—	6	1	no	—
482	C₃×C₉	—	18	1	no	—
483	C₃×C₉	—	18	1	no	—
484	C₃×C₉	—	18	2	no	—
485	C₃×C₉	—	18	2	no	—
486	C₃×C₉	—	18	6	no	—
487	C₃×C₉	—	18	3	no	—
488	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
489	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
490	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
491	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
492	C₃×C₉	D₃×3₋¹⁺²	1	2	yes	—
493	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
494	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
495	C₃×C₉	C₂×#737	1	1	yes	characteristic
496	C₃×C₉	C₂×#737	1	1	yes	characteristic
497	C₂×C₃²	—	9	1	no	—
498	C₂×C₃²	—	9	3	no	—
499	C₂×C₃²	—	27	1	no	—
500	C₂×C₃²	—	27	1	no	—
501	C₂×C₃²	—	27	1	no	—
502	C₃×D₃	—	3	1	no	—
503	C₃×D₃	—	3	1	no	—
504	C₃×D₃	—	3	1	no	—
505	C₃×D₃	—	3	1	no	—
506	C₃×D₃	—	9	3	no	—
507	C₂×C₉	—	9	1	no	—
508	C₂×C₉	—	9	2	no	—
509	C₂×C₉	—	27	1	no	—
510	C₂×C₉	—	27	1	no	—
511	C₂×C₉	—	27	1	no	—
512	C₂×C₉	—	27	1	no	—
513	C₂×C₉	—	27	1	no	—
514	C₂×C₉	—	27	1	no	—
515	C₂×C₉	—	27	1	no	—
516	C₂×C₉	—	27	1	no	—
517	C₂×C₉	—	27	1	no	—
518	C₂×C₉	—	27	1	no	—
519	C₂×C₉	—	27	1	no	—
520	D₉	#6894	1	1	yes	characteristic, complemented
521	C₃²	—	2	1	no	—
522	C₃²	—	2	1	no	—
523	C₃²	—	2	1	no	—
524	C₃²	—	2	1	no	—
525	C₃²	—	2	3	no	—
526	C₃²	—	3	1	no	—
527	C₃²	—	3	1	no	—
528	C₃²	—	3	1	no	—
529	C₃²	—	3	3	no	—
530	C₃²	—	6	3	no	—
531	C₃²	—	6	3	no	—
532	C₃²	—	6	3	no	—
533	C₃²	—	6	3	no	—
534	C₃²	—	6	1	no	—
535	C₃²	—	6	1	no	—
536	C₃²	—	6	1	no	—
537	C₃²	#6894⋊C₂	1	3	yes	—
538	C₃²	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
539	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
540	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
541	C₃²	D₃×#737	1	1	yes	characteristic
542	C₃²	D₃×#737	1	1	yes	characteristic
543	C₉	—	2	1	no	—
544	C₉	—	2	1	no	—
545	C₉	—	2	1	no	—
546	C₉	—	2	1	no	—
547	C₉	—	3	1	no	—
548	C₉	—	3	1	no	—
549	C₉	—	3	1	no	—
550	C₉	—	3	1	no	—
551	C₉	—	6	2	no	—
552	C₉	—	6	1	no	—
553	C₉	—	6	3	no	—
554	C₉	—	6	1	no	—
555	C₉	—	6	1	no	—
556	C₉	—	6	1	no	—
557	C₉	—	6	2	no	—
558	C₉	—	9	1	no	—
559	C₉	—	9	1	no	—
560	C₉	—	9	1	no	—
561	C₉	—	9	1	no	—
562	C₉	—	9	1	no	—
563	C₉	—	18	1	no	—
564	C₉	—	18	1	no	—
565	C₉	—	18	1	no	—
566	C₉	—	18	1	no	—
567	C₉	—	18	1	no	—
568	C₉	—	18	1	no	—
569	C₉	—	18	1	no	—
570	C₉	—	18	1	no	—
571	C₉	—	18	1	no	—
572	C₉	—	18	1	no	—
573	C₉	—	18	1	no	—
574	C₉	—	18	1	no	—
575	C₉	—	18	1	no	—
576	C₉	—	18	1	no	—
577	C₉	C₂×#6894	1	1	yes	characteristic, complemented
578	C₂×C₃	—	9	1	no	—
579	C₂×C₃	—	9	1	no	—
580	C₂×C₃	—	9	1	no	—
581	C₂×C₃	—	9	1	no	—
582	C₂×C₃	—	27	3	no	—
583	D₃	—	3	1	no	—
584	C₃	—	2	1	no	—
585	C₃	—	2	1	no	—
586	C₃	—	2	1	no	—
587	C₃	—	2	1	no	—
588	C₃	—	3	3	no	—
589	C₃	—	6	3	no	—
590	C₃	D₃×#6894	1	1	yes	characteristic
591	C₃	C₃×#6894⋊C₂	1	1	yes	characteristic
592	C₃	3₋¹⁺²×AGL(1,ℤ/9)	1	1	yes	characteristic
593	C₃	#10624901⋊C₂	1	1	yes	characteristic
594	C₃	#10624901⋊C₂	1	1	yes	characteristic
595	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃²	C₃²×AGL(1,ℤ/9)
commutator, cosocle	C₃²×C₉	C₂×C₃³
Frattini, socle	C₃³	C₃³×D₃
Fitting	#14552205	C₂
prime radical	C₃³×D₉	C₃²
hypercenter	C₃×3₋¹⁺²	AGL(1,ℤ/9)
hypocenter	C₉	C₂×#6894
LCS	G ▷ C₃²×C₉ ▷ C₉
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #14552205	C₂	semidirect
5. (D₉⋊C₉)⋊C₉	C₃	semidirect
6. (D₉⋊C₉)⋊C₉	C₃	semidirect
7. (D₉⋊C₉)⋊C₉	C₃	semidirect
8. (D₉⋊C₉)⋊C₉	C₃	semidirect
9. (D₉⋊C₉)⋊C₉	C₃	semidirect
10. (D₉⋊C₉)⋊C₉	C₃	semidirect
11. (D₉⋊C₉)⋊C₉	C₃	semidirect
12. (D₉⋊C₉)⋊C₉	C₃	semidirect
13. (D₉⋊C₉)⋊C₉	C₃	semidirect
28. #10624561	C₂×C₃	semidirect
29. #10624561	C₂×C₃	semidirect
30. #10624561	C₂×C₃	semidirect
31. #10624561	C₂×C₃	semidirect
32. #10624561	C₂×C₃	semidirect
33. #10624561	C₂×C₃	semidirect
34. #10624561	C₂×C₃	semidirect
35. #10624561	C₂×C₃	semidirect
36. #10624561	C₂×C₃	semidirect
204. D₉⋊C₉	3₋¹⁺²	semidirect
205. D₉⋊C₉	3₋¹⁺²	semidirect
315. C₉⋊C₉	C₂×3₋¹⁺²	semidirect
316. C₉⋊C₉	C₂×3₋¹⁺²	semidirect
520. D₉	#6894	semidirect
577. C₉	C₂×#6894	semidirect

Maximal subgroups

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

subgroup	index
#14552205	2
D₃×#6894	3
C₃×D₉×3₋¹⁺²	3
C₃²×D₉⋊C₉	3
(D₉⋊C₉)⋊C₉	3
#13090623	3