Subgroups — #72243549

Order 4374.

672 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14552359	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#92265	C₃	1	1	yes	maximal, characteristic
3	D₃×#6896	—	3	1	no	maximal
4	C₃×#92264	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	(C₃×AGL(1,ℤ/9))⋊C₉	C₃	1	1	yes	maximal, characteristic
13	(C₃×AGL(1,ℤ/9))⋊C₉	C₃	1	1	yes	maximal, characteristic
14	C₉×D₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
15	D₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×#6900	C₂×C₃	1	1	yes	characteristic
17	C₃×#6896	D₃	1	1	yes	characteristic
18	C₃×#6896	C₂×C₃	1	1	yes	characteristic
19	#10624575	—	2	1	no	—
20	#10624575	—	2	1	no	—
21	#10624574	—	2	1	no	—
22	#10624574	—	2	1	no	—
23	#10624573	—	2	1	no	—
24	#10624573	—	2	1	no	—
25	#10624567	—	2	1	no	—
26	#10624565	—	2	1	no	—
27	#10624565	—	2	1	no	—
28	#10624561	—	2	1	no	—
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	#10624560	—	2	1	no	—
37	#10624560	C₂×C₃	1	1	yes	characteristic
38	#10624560	C₂×C₃	1	1	yes	characteristic
39	#10624559	—	2	1	no	—
40	#10624559	—	2	1	no	—
41	C₉×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
42	C₉×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×D₃×3₋¹⁺²	—	3	1	no	—
44	C₃×D₃×3₋¹⁺²	—	3	1	no	—
45	C₃²×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
46	C₂×#6896	—	9	1	no	—
47	#92265	—	3	1	no	—
48	#92265	—	3	2	no	—
49	#92264	—	3	1	no	—
50	#92264	—	3	1	no	—
51	#92264	—	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	D₃×C₉⋊C₉	—	3	1	no	—
58	D₃×C₉⋊C₉	—	3	1	no	—
59	D₃×C₉⋊C₉	—	3	1	no	—
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	D₃×C₉²	—	3	1	no	—
71	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
72	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
73	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
74	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
75	C₃²×3₋¹⁺²	—	2	1	no	—
76	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
77	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
78	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
79	#6900	—	3	1	no	—
80	#6900	—	3	2	no	—
81	#6900	—	6	1	no	—
82	#6900	—	6	2	no	—
83	#6896	—	3	1	no	—
84	#6896	—	3	1	no	—
85	#6896	—	3	1	no	—
86	#6896	—	6	1	no	—
87	#6896	—	6	1	no	—
88	#6896	—	6	1	no	—
89	#6896	—	6	1	no	—
90	#6896	—	6	1	no	—
91	#6896	—	6	1	no	—
92	#6896	—	6	1	no	—
93	#6896	—	6	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	—	2	1	no	—
100	C₃×C₉⋊C₉	—	2	1	no	—
101	C₃×C₉⋊C₉	—	2	1	no	—
102	C₃×C₉⋊C₉	—	2	1	no	—
103	C₃×C₉⋊C₉	—	2	1	no	—
104	C₃×C₉⋊C₉	—	2	1	no	—
105	C₃×C₉⋊C₉	—	2	1	no	—
106	C₃×C₉⋊C₉	—	2	1	no	—
107	C₃×C₉⋊C₉	—	2	1	no	—
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	C₃×D₃	1	1	yes	characteristic
113	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
114	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
115	C₃×C₉⋊C₉	C₃×D₃	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×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
122	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
123	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
124	C₃×C₃²⋊C₉	—	2	1	no	—
125	C₃×C₃²⋊C₉	—	2	1	no	—
126	C₃×C₃²⋊C₉	—	2	1	no	—
127	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
128	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
129	C₃×C₉²	—	2	1	no	—
130	C₃×C₉²	C₃×D₃	1	1	yes	characteristic
131	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
132	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
133	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
134	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
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	#6855	—	2	1	no	—
163	#6855	—	2	1	no	—
164	#6855	—	2	1	no	—
165	#6855	—	2	1	no	—
166	#6855	—	2	1	no	—
167	#6855	—	2	1	no	—
168	C₃³×D₃	—	3	1	no	—
169	C₂×C₃×3₋¹⁺²	—	9	1	no	—
170	C₂×C₃×3₋¹⁺²	—	9	1	no	—
171	D₃×3₋¹⁺²	—	9	1	no	—
172	D₃×3₋¹⁺²	—	9	1	no	—
173	D₃×3₋¹⁺²	—	9	1	no	—
174	D₃×3₋¹⁺²	—	9	1	no	—
175	D₃×3₋¹⁺²	—	9	2	no	—
176	C₃×AGL(1,ℤ/9)	—	3	1	no	—
177	C₃×AGL(1,ℤ/9)	—	3	1	no	—
178	C₃×AGL(1,ℤ/9)	—	3	1	no	—
179	C₃×AGL(1,ℤ/9)	—	3	1	no	—
180	C₃×D₃×C₉	—	3	1	no	—
181	C₃×D₃×C₉	—	3	1	no	—
182	C₃×D₃×C₉	—	3	1	no	—
183	C₃×D₃×C₉	—	3	1	no	—
184	C₃×D₃×C₉	—	3	1	no	—
185	C₃×D₃×C₉	—	3	1	no	—
186	C₃×D₃×C₉	—	3	1	no	—
187	C₃×D₃×C₉	—	3	1	no	—
188	C₃×D₃×C₉	—	3	1	no	—
189	C₃×D₃×C₉	—	3	1	no	—
190	C₃×D₃×C₉	—	3	1	no	—
191	C₃×D₃×C₉	—	3	1	no	—
192	C₃²×D₉	C₃³	1	1	yes	characteristic
193	C₂×C₉⋊C₉	—	9	1	no	—
194	C₂×C₉⋊C₉	—	9	1	no	—
195	C₂×C₉⋊C₉	—	9	1	no	—
196	C₂×C₉⋊C₉	—	9	1	no	—
197	C₂×C₉⋊C₉	—	9	1	no	—
198	C₂×C₉⋊C₉	—	9	1	no	—
199	C₂×C₉⋊C₉	—	9	1	no	—
200	C₂×C₉⋊C₉	—	9	1	no	—
201	C₂×C₃²⋊C₉	—	9	1	no	—
202	C₂×C₃²⋊C₉	—	9	1	no	—
203	C₂×C₉²	—	9	1	no	—
204	D₉⋊C₉	—	3	1	no	—
205	D₉⋊C₉	—	3	1	no	—
206	D₉⋊C₉	—	3	1	no	—
207	D₉⋊C₉	—	3	1	no	—
208	D₉⋊C₉	—	3	1	no	—
209	D₉⋊C₉	—	3	1	no	—
210	D₉⋊C₉	3₋¹⁺²	1	1	yes	characteristic, complemented
211	D₉⋊C₉	3₋¹⁺²	1	1	yes	characteristic, complemented
212	D₉⋊C₉	3₋¹⁺²	1	1	yes	characteristic, complemented
213	D₉⋊C₉	3₋¹⁺²	1	1	yes	characteristic, complemented
214	D₉⋊C₉	3₋¹⁺²	1	2	yes	complemented
215	C₉×D₉	—	3	1	no	—
216	C₉×D₉	—	3	1	no	—
217	C₉×D₉	—	3	1	no	—
218	C₉×D₉	—	3	1	no	—
219	C₃⁴	C₃²×D₃	1	1	yes	characteristic
220	C₃×3₋¹⁺²	—	3	1	no	—
221	C₃×3₋¹⁺²	—	3	1	no	—
222	C₃×3₋¹⁺²	—	3	1	no	—
223	C₃×3₋¹⁺²	—	3	1	no	—
224	C₃×3₋¹⁺²	—	3	2	no	—
225	C₃×3₋¹⁺²	—	3	1	no	—
226	C₃×3₋¹⁺²	—	3	1	no	—
227	C₃×3₋¹⁺²	—	3	1	no	—
228	C₃×3₋¹⁺²	—	3	1	no	—
229	C₃×3₋¹⁺²	—	6	1	no	—
230	C₃×3₋¹⁺²	—	6	1	no	—
231	C₃×3₋¹⁺²	—	6	2	no	—
232	C₃×3₋¹⁺²	—	6	3	no	—
233	C₃×3₋¹⁺²	—	6	1	no	—
234	C₃×3₋¹⁺²	—	6	1	no	—
235	C₃×3₋¹⁺²	—	6	1	no	—
236	C₃×3₋¹⁺²	—	6	1	no	—
237	C₃×3₋¹⁺²	—	6	1	no	—
238	C₃×3₋¹⁺²	—	6	1	no	—
239	C₃×3₋¹⁺²	—	6	1	no	—
240	C₃×3₋¹⁺²	—	18	1	no	—
241	C₃×3₋¹⁺²	—	18	1	no	—
242	C₃×3₋¹⁺²	—	18	1	no	—
243	C₃×3₋¹⁺²	—	18	1	no	—
244	C₃²×C₉	—	2	1	no	—
245	C₃²×C₉	—	2	1	no	—
246	C₃²×C₉	—	2	1	no	—
247	C₃²×C₉	—	2	1	no	—
248	C₃²×C₉	—	2	1	no	—
249	C₃²×C₉	—	2	1	no	—
250	C₃²×C₉	—	2	1	no	—
251	C₃²×C₉	—	2	1	no	—
252	C₃²×C₉	—	2	1	no	—
253	C₃²×C₉	—	2	1	no	—
254	C₃²×C₉	—	2	1	no	—
255	C₃²×C₉	—	2	1	no	—
256	C₃²×C₉	—	2	1	no	—
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	C₃²×D₃	1	1	yes	characteristic
261	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
262	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
263	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
264	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
265	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
266	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
267	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
268	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
269	C₃²×C₉	C₂×C₃³	1	1	yes	characteristic
270	C₉⋊C₉	—	2	1	no	—
271	C₉⋊C₉	—	2	1	no	—
272	C₉⋊C₉	—	2	1	no	—
273	C₉⋊C₉	—	2	1	no	—
274	C₉⋊C₉	—	2	1	no	—
275	C₉⋊C₉	—	2	1	no	—
276	C₉⋊C₉	—	2	1	no	—
277	C₉⋊C₉	—	2	1	no	—
278	C₉⋊C₉	—	2	2	no	—
279	C₉⋊C₉	—	3	1	no	—
280	C₉⋊C₉	—	3	1	no	—
281	C₉⋊C₉	—	3	1	no	—
282	C₉⋊C₉	—	3	1	no	—
283	C₉⋊C₉	—	3	1	no	—
284	C₉⋊C₉	—	3	1	no	—
285	C₉⋊C₉	—	3	1	no	—
286	C₉⋊C₉	—	6	1	no	—
287	C₉⋊C₉	—	6	1	no	—
288	C₉⋊C₉	—	6	1	no	—
289	C₉⋊C₉	—	6	1	no	—
290	C₉⋊C₉	—	6	1	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	2	no	—
303	C₉⋊C₉	—	6	1	no	—
304	C₉⋊C₉	—	6	2	no	—
305	C₉⋊C₉	—	6	1	no	—
306	C₉⋊C₉	—	6	1	no	—
307	C₉⋊C₉	—	6	3	no	—
308	C₉⋊C₉	—	6	3	no	—
309	C₉⋊C₉	—	6	3	no	—
310	C₉⋊C₉	—	6	1	no	—
311	C₉⋊C₉	—	6	1	no	—
312	C₉⋊C₉	—	6	1	no	—
313	C₉⋊C₉	—	6	1	no	—
314	C₉⋊C₉	—	6	1	no	—
315	C₉⋊C₉	—	6	1	no	—
316	C₉⋊C₉	—	6	1	no	—
317	C₉⋊C₉	—	6	1	no	—
318	C₉⋊C₉	—	6	1	no	—
319	C₉⋊C₉	—	6	1	no	—
320	C₉⋊C₉	—	6	1	no	—
321	C₉⋊C₉	—	6	1	no	—
322	C₉⋊C₉	—	6	2	no	—
323	C₉⋊C₉	—	18	1	no	—
324	C₉⋊C₉	—	18	1	no	—
325	C₉⋊C₉	—	18	1	no	—
326	C₉⋊C₉	—	18	1	no	—
327	C₉⋊C₉	—	18	1	no	—
328	C₉⋊C₉	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
329	C₉⋊C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
330	C₉⋊C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
331	C₉⋊C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
332	C₉⋊C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
333	C₉⋊C₉	C₂×3₋¹⁺²	1	2	yes	complemented
334	C₃²⋊C₉	—	3	1	no	—
335	C₃²⋊C₉	—	3	1	no	—
336	C₃²⋊C₉	—	6	1	no	—
337	C₃²⋊C₉	—	6	1	no	—
338	C₃²⋊C₉	—	6	1	no	—
339	C₃²⋊C₉	—	6	1	no	—
340	C₃²⋊C₉	—	6	1	no	—
341	C₃²⋊C₉	—	18	1	no	—
342	C₃²⋊C₉	—	18	1	no	—
343	C₉²	—	3	1	no	—
344	C₉²	—	3	1	no	—
345	C₉²	—	3	1	no	—
346	C₉²	—	3	1	no	—
347	C₉²	—	3	1	no	—
348	C₉²	—	6	1	no	—
349	C₉²	—	6	1	no	—
350	C₉²	—	6	1	no	—
351	C₉²	—	6	1	no	—
352	C₉²	—	6	1	no	—
353	C₉²	—	18	1	no	—
354	C₂×C₃³	—	9	1	no	—
355	C₃²×D₃	—	3	1	no	—
356	C₃²×D₃	—	9	1	no	—
357	C₃²×D₃	—	9	1	no	—
358	C₃²×D₃	—	9	1	no	—
359	C₃²×D₃	—	9	1	no	—
360	C₂×3₋¹⁺²	—	27	1	no	—
361	C₂×3₋¹⁺²	—	27	1	no	—
362	C₂×3₋¹⁺²	—	27	1	no	—
363	C₂×3₋¹⁺²	—	27	1	no	—
364	C₂×3₋¹⁺²	—	27	2	no	—
365	C₂×C₃×C₉	—	9	1	no	—
366	C₂×C₃×C₉	—	9	1	no	—
367	C₂×C₃×C₉	—	9	1	no	—
368	C₂×C₃×C₉	—	9	1	no	—
369	C₂×C₃×C₉	—	9	1	no	—
370	C₂×C₃×C₉	—	9	1	no	—
371	C₂×C₃×C₉	—	9	1	no	—
372	C₂×C₃×C₉	—	9	1	no	—
373	C₂×C₃×C₉	—	9	1	no	—
374	C₂×C₃×C₉	—	9	1	no	—
375	C₂×C₃×C₉	—	9	1	no	—
376	C₂×C₃×C₉	—	9	1	no	—
377	AGL(1,ℤ/9)	—	9	1	no	—
378	D₃×C₉	—	3	1	no	—
379	D₃×C₉	—	3	1	no	—
380	D₃×C₉	—	3	1	no	—
381	D₃×C₉	—	3	1	no	—
382	D₃×C₉	—	3	2	no	—
383	D₃×C₉	—	9	1	no	—
384	D₃×C₉	—	9	1	no	—
385	D₃×C₉	—	9	1	no	—
386	D₃×C₉	—	9	1	no	—
387	D₃×C₉	—	9	1	no	—
388	D₃×C₉	—	9	1	no	—
389	D₃×C₉	—	9	1	no	—
390	D₃×C₉	—	9	1	no	—
391	D₃×C₉	—	9	1	no	—
392	D₃×C₉	—	9	1	no	—
393	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
394	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
395	C₃×D₉	#737	1	1	yes	characteristic
396	C₃×D₉	#737	1	1	yes	characteristic
397	C₃³	—	3	1	no	—
398	C₃³	—	3	1	no	—
399	C₃³	—	3	1	no	—
400	C₃³	—	3	1	no	—
401	C₃³	—	6	1	no	—
402	C₃³	—	6	1	no	—
403	C₃³	—	6	1	no	—
404	C₃³	—	6	1	no	—
405	C₃³	—	6	1	no	—
406	C₃³	C₃³×D₃	1	1	yes	characteristic
407	3₋¹⁺²	—	9	1	no	—
408	3₋¹⁺²	—	9	1	no	—
409	3₋¹⁺²	—	9	1	no	—
410	3₋¹⁺²	—	9	1	no	—
411	3₋¹⁺²	—	18	1	no	—
412	3₋¹⁺²	—	18	1	no	—
413	3₋¹⁺²	—	18	1	no	—
414	3₋¹⁺²	—	18	1	no	—
415	3₋¹⁺²	—	18	1	no	—
416	3₋¹⁺²	—	18	2	no	—
417	3₋¹⁺²	—	18	1	no	—
418	3₋¹⁺²	—	18	1	no	—
419	3₋¹⁺²	—	18	1	no	—
420	3₋¹⁺²	—	18	2	no	—
421	3₋¹⁺²	—	18	1	no	—
422	3₋¹⁺²	—	18	3	no	—
423	3₋¹⁺²	—	18	6	no	—
424	C₃×C₉	—	2	1	no	—
425	C₃×C₉	—	2	1	no	—
426	C₃×C₉	—	2	1	no	—
427	C₃×C₉	—	2	1	no	—
428	C₃×C₉	—	2	3	no	—
429	C₃×C₉	—	2	1	no	—
430	C₃×C₉	—	2	1	no	—
431	C₃×C₉	—	2	1	no	—
432	C₃×C₉	—	2	1	no	—
433	C₃×C₉	—	2	1	no	—
434	C₃×C₉	—	2	1	no	—
435	C₃×C₉	—	2	1	no	—
436	C₃×C₉	—	2	2	no	—
437	C₃×C₉	—	2	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	—	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	—	6	1	no	—
483	C₃×C₉	—	6	1	no	—
484	C₃×C₉	—	6	1	no	—
485	C₃×C₉	—	6	1	no	—
486	C₃×C₉	—	6	1	no	—
487	C₃×C₉	—	6	1	no	—
488	C₃×C₉	—	6	1	no	—
489	C₃×C₉	—	6	1	no	—
490	C₃×C₉	—	6	1	no	—
491	C₃×C₉	—	6	1	no	—
492	C₃×C₉	—	6	1	no	—
493	C₃×C₉	—	6	1	no	—
494	C₃×C₉	—	6	1	no	—
495	C₃×C₉	—	6	1	no	—
496	C₃×C₉	—	6	1	no	—
497	C₃×C₉	—	6	1	no	—
498	C₃×C₉	—	6	1	no	—
499	C₃×C₉	—	6	1	no	—
500	C₃×C₉	—	6	1	no	—
501	C₃×C₉	—	6	1	no	—
502	C₃×C₉	—	6	1	no	—
503	C₃×C₉	—	6	1	no	—
504	C₃×C₉	—	6	1	no	—
505	C₃×C₉	—	6	1	no	—
506	C₃×C₉	—	6	1	no	—
507	C₃×C₉	—	6	1	no	—
508	C₃×C₉	—	6	1	no	—
509	C₃×C₉	—	6	1	no	—
510	C₃×C₉	—	6	1	no	—
511	C₃×C₉	—	6	1	no	—
512	C₃×C₉	—	6	1	no	—
513	C₃×C₉	—	6	1	no	—
514	C₃×C₉	—	6	1	no	—
515	C₃×C₉	—	6	1	no	—
516	C₃×C₉	—	6	1	no	—
517	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
518	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
519	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
520	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
521	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
522	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
523	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
524	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
525	C₃×C₉	D₃×3₋¹⁺²	1	2	yes	—
526	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
527	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
528	C₃×C₉	C₂×#737	1	1	yes	characteristic
529	C₃×C₉	C₂×#737	1	1	yes	characteristic
530	C₂×C₃²	—	9	1	no	—
531	C₂×C₃²	—	27	1	no	—
532	C₂×C₃²	—	27	1	no	—
533	C₂×C₃²	—	27	1	no	—
534	C₂×C₃²	—	27	1	no	—
535	C₃×D₃	—	3	1	no	—
536	C₃×D₃	—	3	1	no	—
537	C₃×D₃	—	3	1	no	—
538	C₃×D₃	—	3	1	no	—
539	C₃×D₃	—	27	1	no	—
540	C₂×C₉	—	9	1	no	—
541	C₂×C₉	—	9	1	no	—
542	C₂×C₉	—	9	1	no	—
543	C₂×C₉	—	9	1	no	—
544	C₂×C₉	—	9	2	no	—
545	C₂×C₉	—	27	1	no	—
546	C₂×C₉	—	27	1	no	—
547	C₂×C₉	—	27	1	no	—
548	C₂×C₉	—	27	1	no	—
549	C₂×C₉	—	27	1	no	—
550	C₂×C₉	—	27	1	no	—
551	C₂×C₉	—	27	1	no	—
552	C₂×C₉	—	27	1	no	—
553	C₂×C₉	—	27	1	no	—
554	C₂×C₉	—	27	1	no	—
555	D₉	#6896	1	1	yes	characteristic, complemented
556	C₃²	—	2	1	no	—
557	C₃²	—	2	1	no	—
558	C₃²	—	2	1	no	—
559	C₃²	—	2	1	no	—
560	C₃²	—	9	1	no	—
561	C₃²	—	18	1	no	—
562	C₃²	—	18	1	no	—
563	C₃²	—	18	1	no	—
564	C₃²	—	18	1	no	—
565	C₃²	—	18	1	no	—
566	C₃²	—	18	1	no	—
567	C₃²	—	18	1	no	—
568	C₃²	—	18	1	no	—
569	C₃²	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
570	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
571	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
572	C₃²	D₃×#737	1	1	yes	characteristic
573	C₃²	D₃×#737	1	1	yes	characteristic
574	C₉	—	2	1	no	—
575	C₉	—	2	1	no	—
576	C₉	—	2	1	no	—
577	C₉	—	2	1	no	—
578	C₉	—	3	1	no	—
579	C₉	—	3	1	no	—
580	C₉	—	3	1	no	—
581	C₉	—	3	1	no	—
582	C₉	—	3	1	no	—
583	C₉	—	3	1	no	—
584	C₉	—	6	1	no	—
585	C₉	—	6	1	no	—
586	C₉	—	6	1	no	—
587	C₉	—	6	3	no	—
588	C₉	—	6	2	no	—
589	C₉	—	6	1	no	—
590	C₉	—	6	1	no	—
591	C₉	—	6	1	no	—
592	C₉	—	6	1	no	—
593	C₉	—	6	2	no	—
594	C₉	—	6	1	no	—
595	C₉	—	6	1	no	—
596	C₉	—	6	1	no	—
597	C₉	—	9	1	no	—
598	C₉	—	18	1	no	—
599	C₉	—	18	1	no	—
600	C₉	—	18	1	no	—
601	C₉	—	18	1	no	—
602	C₉	—	18	1	no	—
603	C₉	—	18	1	no	—
604	C₉	—	18	1	no	—
605	C₉	—	18	1	no	—
606	C₉	—	18	1	no	—
607	C₉	—	18	1	no	—
608	C₉	—	18	1	no	—
609	C₉	—	18	1	no	—
610	C₉	—	18	1	no	—
611	C₉	—	18	1	no	—
612	C₉	—	18	1	no	—
613	C₉	C₂×#6896	1	1	yes	characteristic, complemented
614	C₂×C₃	—	9	1	no	—
615	C₂×C₃	—	9	1	no	—
616	C₂×C₃	—	9	1	no	—
617	C₂×C₃	—	9	1	no	—
618	C₂×C₃	—	81	1	no	—
619	D₃	—	3	1	no	—
620	C₃	—	2	1	no	—
621	C₃	—	2	1	no	—
622	C₃	—	2	1	no	—
623	C₃	—	2	1	no	—
624	C₃	—	27	1	no	—
625	C₃	D₃×#6896	1	1	yes	characteristic
626	C₃	#13091462	1	1	yes	characteristic
627	C₃	3₋¹⁺²×AGL(1,ℤ/9)	1	1	yes	characteristic
628	C₃	3₋¹⁺²×AGL(1,ℤ/9)	1	1	yes	characteristic
629	C₃	#10624901⋊C₂	1	1	yes	characteristic
630	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	#14552359	C₂
prime radical	C₃²×AGL(1,ℤ/9)	C₃²
hypercenter	C₉⋊C₉	AGL(1,ℤ/9)
hypocenter	C₉	C₂×#6896
LCS	G ▷ C₃²×C₉ ▷ C₉
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
1. #14552359	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
14. C₉×D₉⋊C₉	C₃	semidirect
15. D₉×C₉⋊C₉	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
41. C₉×C₉⋊C₉	C₂×C₃	semidirect
42. C₉×C₉⋊C₉	C₂×C₃	semidirect
210. D₉⋊C₉	3₋¹⁺²	semidirect
211. D₉⋊C₉	3₋¹⁺²	semidirect
212. D₉⋊C₉	3₋¹⁺²	semidirect
213. D₉⋊C₉	3₋¹⁺²	semidirect
214. D₉⋊C₉	3₋¹⁺²	semidirect
328. C₉⋊C₉	AGL(1,ℤ/9)	semidirect
329. C₉⋊C₉	C₂×3₋¹⁺²	semidirect
330. C₉⋊C₉	C₂×3₋¹⁺²	semidirect
331. C₉⋊C₉	C₂×3₋¹⁺²	semidirect
332. C₉⋊C₉	C₂×3₋¹⁺²	semidirect
333. C₉⋊C₉	C₂×3₋¹⁺²	semidirect
555. D₉	#6896	semidirect
613. C₉	C₂×#6896	semidirect

Maximal subgroups

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

subgroup	index
#14552359	2
C₃×#92265	3
D₃×#6896	3
C₃×#92264	3
(D₉⋊C₉)⋊C₉	3
(C₃×AGL(1,ℤ/9))⋊C₉	3
C₉×D₉⋊C₉	3
D₉×C₉⋊C₉	3