Subgroups — C₉×#92262 #72243687

Order 4374.

1096 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₉⋊H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#92262	C₃	1	1	yes	maximal, characteristic
3	D₃×C₉×3₋¹⁺²	—	3	1	no	maximal
4	C₃×C₉×(C₃⋊D₃)⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₉²×C₃⋊D₃	C₃	1	1	yes	maximal, characteristic, complemented
6	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
11	(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
12	#13090622	C₃	1	1	yes	maximal, characteristic, complemented
13	#13090622	C₃	1	1	yes	maximal, characteristic, complemented
14	C₉×(C₃⋊D₃)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
15	C₉×(C₃⋊D₃)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
17	C₃×C₉×3₋¹⁺²	—	2	1	no	—
18	C₃×C₉×3₋¹⁺²	D₃	1	1	yes	characteristic, complemented
19	C₃×C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
20	C₃²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
21	#10624560	—	2	1	no	—
22	#10624560	—	2	1	no	—
23	#10624560	—	2	1	no	—
24	#10624557	—	2	1	no	—
25	#10624557	—	2	1	no	—
26	#10624557	—	2	1	no	—
27	#10624557	—	2	1	no	—
28	#10624557	—	2	1	no	—
29	#10624557	—	2	1	no	—
30	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
31	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
32	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
33	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
34	#10624555	C₂×C₃	1	1	yes	characteristic
35	#10624555	C₂×C₃	1	1	yes	characteristic
36	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
37	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
38	C₉×C₃²⋊C₉	—	2	1	no	—
39	C₉×C₃²⋊C₉	—	2	1	no	—
40	C₉×C₃²⋊C₉	—	2	1	no	—
41	C₉×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
42	C₉×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
44	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
45	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
46	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
47	C₃×D₃×3₋¹⁺²	—	3	1	no	—
48	C₃²×(C₃⋊D₃)⋊C₃	C₃²	1	1	yes	characteristic
49	C₃²×D₃×C₉	—	3	1	no	—
50	C₂×C₉×3₋¹⁺²	—	9	1	no	—
51	#92262	C₉	1	2	yes	direct product factor
52	#92262	C₉	1	1	yes	characteristic, direct product factor
53	#92262	C₉	1	2	yes	direct product factor
54	#92262	C₉	1	2	yes	direct product factor
55	#92262	C₉	1	2	yes	direct product factor
56	C₉×(C₃⋊D₃)⋊C₃	—	3	1	no	—
57	C₉×(C₃⋊D₃)⋊C₃	—	3	2	no	—
58	D₃×C₉⋊C₉	—	3	1	no	—
59	D₃×C₉⋊C₉	—	3	1	no	—
60	D₃×C₉⋊C₉	—	3	1	no	—
61	D₃×C₉⋊C₉	—	3	1	no	—
62	D₃×C₉⋊C₉	—	3	1	no	—
63	D₃×C₉⋊C₉	—	3	1	no	—
64	D₃×C₃²⋊C₉	—	3	1	no	—
65	D₃×C₃²⋊C₉	—	3	1	no	—
66	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
67	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
68	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
69	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
70	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
71	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
73	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
74	D₃×C₉²	—	3	1	no	—
75	D₃×C₉²	—	3	1	no	—
76	D₃×C₉²	—	3	1	no	—
77	D₃×C₉²	—	9	1	no	—
78	C₃²×3₋¹⁺²	—	2	1	no	—
79	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
80	C₃²×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
81	C₃³×C₉	—	2	1	no	—
82	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
83	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
84	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
85	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
86	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
87	C₉⋊H(3,𝔽₃)	—	2	2	no	—
88	C₉⋊H(3,𝔽₃)	—	2	1	no	—
89	C₉⋊H(3,𝔽₃)	—	2	2	no	—
90	C₉⋊H(3,𝔽₃)	—	2	2	no	—
91	C₉⋊H(3,𝔽₃)	—	2	2	no	—
92	C₉⋊H(3,𝔽₃)	C₂×C₉	1	2	yes	complemented
93	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
94	C₉⋊H(3,𝔽₃)	C₂×C₉	1	2	yes	complemented
95	C₉⋊H(3,𝔽₃)	C₂×C₉	1	2	yes	complemented
96	C₉⋊H(3,𝔽₃)	C₂×C₉	1	2	yes	complemented
97	C₉×3₋¹⁺²	—	6	1	no	—
98	C₉×3₋¹⁺²	—	6	1	no	—
99	C₉×3₋¹⁺²	—	6	1	no	—
100	C₉×3₋¹⁺²	—	6	1	no	—
101	C₉×3₋¹⁺²	—	6	2	no	—
102	C₉×3₋¹⁺²	—	6	2	no	—
103	C₉×3₋¹⁺²	—	6	2	no	—
104	C₉×3₋¹⁺²	—	6	2	no	—
105	C₉×3₋¹⁺²	—	6	1	no	—
106	C₉×3₋¹⁺²	—	6	1	no	—
107	C₉×H(3,𝔽₃)	—	3	1	no	—
108	C₉×H(3,𝔽₃)	—	3	2	no	—
109	C₉×H(3,𝔽₃)	—	6	1	no	—
110	C₉×H(3,𝔽₃)	—	6	2	no	—
111	C₃×C₉⋊C₉	—	2	1	no	—
112	C₃×C₉⋊C₉	—	2	1	no	—
113	C₃×C₉⋊C₉	—	2	1	no	—
114	C₃×C₉⋊C₉	—	2	1	no	—
115	C₃×C₉⋊C₉	—	2	1	no	—
116	C₃×C₉⋊C₉	—	2	1	no	—
117	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
118	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
119	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
120	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
121	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
122	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
123	C₃×C₃²⋊C₉	—	2	1	no	—
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	—	2	1	no	—
128	C₃×C₃²⋊C₉	—	2	1	no	—
129	C₃×C₃²⋊C₉	—	2	1	no	—
130	C₃×C₃²⋊C₉	—	2	1	no	—
131	C₃×C₃²⋊C₉	—	2	1	no	—
132	C₃×C₃²⋊C₉	—	2	1	no	—
133	C₃×C₃²⋊C₉	—	2	1	no	—
134	C₃×C₃²⋊C₉	—	2	1	no	—
135	C₃×C₃²⋊C₉	—	2	1	no	—
136	C₃×C₃²⋊C₉	—	2	1	no	—
137	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
138	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
139	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
140	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
141	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
142	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
143	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
144	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
145	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
146	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
147	C₃×C₉²	—	2	1	no	—
148	C₃×C₉²	—	2	1	no	—
149	C₃×C₉²	—	2	1	no	—
150	C₃×C₉²	—	2	1	no	—
151	C₃×C₉²	—	2	1	no	—
152	C₃×C₉²	—	2	1	no	—
153	C₃×C₉²	—	3	1	no	—
154	C₃×C₉²	—	6	1	no	—
155	C₃×C₉²	—	6	1	no	—
156	C₃×C₉²	—	6	1	no	—
157	C₃×C₉²	—	6	1	no	—
158	C₃×C₉²	C₃×D₃	1	1	yes	characteristic
159	C₃×C₉²	C₃×D₃	1	1	yes	characteristic
160	C₃×C₉²	C₃×D₃	1	1	yes	characteristic
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	#6855	—	2	1	no	—
169	#6855	—	2	1	no	—
170	#6855	—	2	1	no	—
171	#6855	—	2	1	no	—
172	#6855	—	2	1	no	—
173	#6855	—	2	1	no	—
174	#6855	—	2	1	no	—
175	#6855	—	2	1	no	—
176	#6855	—	2	1	no	—
177	#6855	—	2	1	no	—
178	#6855	—	2	1	no	—
179	#6855	—	2	1	no	—
180	#6855	—	2	1	no	—
181	#6855	—	2	1	no	—
182	#6855	—	2	1	no	—
183	#6855	—	2	1	no	—
184	#6855	—	2	1	no	—
185	C₃²×C₃⋊D₃	C₃³	1	1	yes	characteristic
186	C₃³×D₃	—	3	1	no	—
187	C₂×C₃×3₋¹⁺²	—	9	1	no	—
188	C₂×C₃²×C₉	—	9	1	no	—
189	C₉×C₃⋊D₃	—	3	1	no	—
190	C₉×C₃⋊D₃	—	3	1	no	—
191	C₉×C₃⋊D₃	C₃×C₉	1	1	yes	characteristic, complemented
192	C₉×C₃⋊D₃	C₃×C₉	1	2	yes	complemented
193	C₉×C₃⋊D₃	3₋¹⁺²	1	1	yes	characteristic, complemented
194	C₉×C₃⋊D₃	3₋¹⁺²	1	2	yes	complemented
195	D₃×3₋¹⁺²	—	3	2	no	—
196	D₃×3₋¹⁺²	—	3	1	no	—
197	D₃×3₋¹⁺²	—	3	2	no	—
198	D₃×3₋¹⁺²	—	3	2	no	—
199	D₃×3₋¹⁺²	—	3	2	no	—
200	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
201	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
202	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
203	C₃×(C₃⋊D₃)⋊C₃	C₃×C₉	1	2	yes	—
204	C₃×(C₃⋊D₃)⋊C₃	C₃×C₉	1	1	yes	characteristic
205	C₃×D₃×C₉	—	3	1	no	—
206	C₃×D₃×C₉	—	3	1	no	—
207	C₃×D₃×C₉	—	3	1	no	—
208	C₃×D₃×C₉	—	3	1	no	—
209	C₃×D₃×C₉	—	3	1	no	—
210	C₃×D₃×C₉	—	3	1	no	—
211	C₃×D₃×C₉	—	3	1	no	—
212	C₃×D₃×C₉	—	3	1	no	—
213	C₃×D₃×C₉	—	3	1	no	—
214	C₃×D₃×C₉	—	3	1	no	—
215	C₃×D₃×C₉	—	3	1	no	—
216	C₃×D₃×C₉	—	3	1	no	—
217	C₃×D₃×C₉	—	9	1	no	—
218	C₃×D₃×C₉	—	9	2	no	—
219	C₃×D₃×C₉	—	9	1	no	—
220	C₃×D₃×C₉	—	9	1	no	—
221	C₃×D₃×C₉	—	9	1	no	—
222	C₃×D₃×C₉	—	9	1	no	—
223	C₂×C₉⋊C₉	—	9	1	no	—
224	C₂×C₉⋊C₉	—	9	1	no	—
225	C₂×C₉⋊C₉	—	9	1	no	—
226	C₂×C₉⋊C₉	—	9	1	no	—
227	C₂×C₉⋊C₉	—	9	1	no	—
228	C₂×C₉⋊C₉	—	9	1	no	—
229	C₂×C₃²⋊C₉	—	9	1	no	—
230	C₂×C₃²⋊C₉	—	9	1	no	—
231	C₂×C₉²	—	9	1	no	—
232	C₂×C₉²	—	9	1	no	—
233	C₂×C₉²	—	9	1	no	—
234	(C₃⋊D₃)⋊C₉	—	3	1	no	—
235	(C₃⋊D₃)⋊C₉	—	3	1	no	—
236	(C₃⋊D₃)⋊C₉	—	3	1	no	—
237	(C₃⋊D₃)⋊C₉	—	3	1	no	—
238	(C₃⋊D₃)⋊C₉	—	3	1	no	—
239	(C₃⋊D₃)⋊C₉	—	3	1	no	—
240	(C₃⋊D₃)⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
241	(C₃⋊D₃)⋊C₉	C₃×C₉	1	2	yes	complemented
242	(C₃⋊D₃)⋊C₉	C₃×C₉	1	2	yes	complemented
243	(C₃⋊D₃)⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
244	C₃⁴	—	2	1	no	—
245	C₃⁴	C₃²×D₃	1	1	yes	characteristic
246	C₃⁴	C₂×C₃³	1	1	yes	characteristic
247	C₃×3₋¹⁺²	—	2	2	no	—
248	C₃×3₋¹⁺²	—	2	1	no	—
249	C₃×3₋¹⁺²	—	2	2	no	—
250	C₃×3₋¹⁺²	—	2	2	no	—
251	C₃×3₋¹⁺²	—	2	2	no	—
252	C₃×3₋¹⁺²	—	6	1	no	—
253	C₃×3₋¹⁺²	—	6	2	no	—
254	C₃×3₋¹⁺²	—	6	1	no	—
255	C₃×3₋¹⁺²	—	6	1	no	—
256	C₃×3₋¹⁺²	—	6	1	no	—
257	C₃×3₋¹⁺²	—	6	2	no	—
258	C₃×3₋¹⁺²	—	6	2	no	—
259	C₃×3₋¹⁺²	—	6	2	no	—
260	C₃×3₋¹⁺²	—	6	1	no	—
261	C₃×3₋¹⁺²	—	6	1	no	—
262	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
263	C₃×3₋¹⁺²	D₃×C₉	1	2	yes	complemented
264	C₃×3₋¹⁺²	D₃×C₉	1	2	yes	complemented
265	C₃×3₋¹⁺²	D₃×C₉	1	2	yes	complemented
266	C₃×3₋¹⁺²	D₃×C₉	1	2	yes	complemented
267	C₃×H(3,𝔽₃)	—	2	2	no	—
268	C₃×H(3,𝔽₃)	—	2	1	no	—
269	C₃×H(3,𝔽₃)	—	3	1	no	—
270	C₃×H(3,𝔽₃)	—	3	1	no	—
271	C₃×H(3,𝔽₃)	—	3	1	no	—
272	C₃×H(3,𝔽₃)	—	6	1	no	—
273	C₃×H(3,𝔽₃)	—	6	1	no	—
274	C₃×H(3,𝔽₃)	—	6	1	no	—
275	C₃×H(3,𝔽₃)	C₂×C₃×C₉	1	2	yes	—
276	C₃×H(3,𝔽₃)	C₂×C₃×C₉	1	1	yes	characteristic
277	C₃²×C₉	—	2	1	no	—
278	C₃²×C₉	—	2	1	no	—
279	C₃²×C₉	—	2	1	no	—
280	C₃²×C₉	—	2	1	no	—
281	C₃²×C₉	—	2	1	no	—
282	C₃²×C₉	—	2	1	no	—
283	C₃²×C₉	—	2	1	no	—
284	C₃²×C₉	—	2	2	no	—
285	C₃²×C₉	—	2	1	no	—
286	C₃²×C₉	—	2	2	no	—
287	C₃²×C₉	—	2	1	no	—
288	C₃²×C₉	—	2	1	no	—
289	C₃²×C₉	—	2	1	no	—
290	C₃²×C₉	—	2	1	no	—
291	C₃²×C₉	—	2	1	no	—
292	C₃²×C₉	—	2	1	no	—
293	C₃²×C₉	—	3	1	no	—
294	C₃²×C₉	—	3	1	no	—
295	C₃²×C₉	—	3	1	no	—
296	C₃²×C₉	—	3	1	no	—
297	C₃²×C₉	—	3	1	no	—
298	C₃²×C₉	—	3	1	no	—
299	C₃²×C₉	—	3	1	no	—
300	C₃²×C₉	—	3	2	no	—
301	C₃²×C₉	—	3	1	no	—
302	C₃²×C₉	—	6	1	no	—
303	C₃²×C₉	—	6	2	no	—
304	C₃²×C₉	—	6	1	no	—
305	C₃²×C₉	—	6	2	no	—
306	C₃²×C₉	—	6	3	no	—
307	C₃²×C₉	—	6	3	no	—
308	C₃²×C₉	—	6	1	no	—
309	C₃²×C₉	—	6	1	no	—
310	C₃²×C₉	—	6	1	no	—
311	C₃²×C₉	—	6	1	no	—
312	C₃²×C₉	—	6	1	no	—
313	C₃²×C₉	—	6	1	no	—
314	C₃²×C₉	—	6	1	no	—
315	C₃²×C₉	—	6	1	no	—
316	C₃²×C₉	—	6	2	no	—
317	C₃²×C₉	—	6	2	no	—
318	C₃²×C₉	—	6	2	no	—
319	C₃²×C₉	—	6	2	no	—
320	C₃²×C₉	—	6	1	no	—
321	C₃²×C₉	—	6	1	no	—
322	C₃²×C₉	—	6	1	no	—
323	C₃²×C₉	—	6	1	no	—
324	C₃²×C₉	—	6	2	no	—
325	C₃²×C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
326	C₃²×C₉	C₂×C₃×C₉	1	2	yes	complemented
327	C₃²×C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
328	C₃²×C₉	C₂×3₋¹⁺²	1	2	yes	complemented
329	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
330	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
331	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
332	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
333	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
334	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
335	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
336	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
337	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
338	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
339	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
340	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
341	C₉⋊C₉	—	3	1	no	—
342	C₉⋊C₉	—	3	1	no	—
343	C₉⋊C₉	—	6	1	no	—
344	C₉⋊C₉	—	6	1	no	—
345	C₉⋊C₉	—	6	1	no	—
346	C₉⋊C₉	—	6	1	no	—
347	C₉⋊C₉	—	6	1	no	—
348	C₉⋊C₉	—	6	2	no	—
349	C₉⋊C₉	—	6	2	no	—
350	C₉⋊C₉	—	6	2	no	—
351	C₉⋊C₉	—	6	2	no	—
352	C₉⋊C₉	—	6	2	no	—
353	C₉⋊C₉	—	6	2	no	—
354	C₉⋊C₉	—	6	1	no	—
355	C₉⋊C₉	—	6	1	no	—
356	C₉⋊C₉	—	6	1	no	—
357	C₉⋊C₉	—	6	1	no	—
358	C₉⋊C₉	—	6	1	no	—
359	C₉⋊C₉	—	6	1	no	—
360	C₉⋊C₉	—	6	1	no	—
361	C₉⋊C₉	—	6	1	no	—
362	C₉⋊C₉	—	6	1	no	—
363	C₉⋊C₉	—	6	1	no	—
364	C₉⋊C₉	—	6	1	no	—
365	C₃²⋊C₉	—	2	2	no	—
366	C₃²⋊C₉	—	2	2	no	—
367	C₃²⋊C₉	—	2	2	no	—
368	C₃²⋊C₉	—	2	2	no	—
369	C₃²⋊C₉	—	2	1	no	—
370	C₃²⋊C₉	—	2	1	no	—
371	C₃²⋊C₉	—	2	2	no	—
372	C₃²⋊C₉	—	2	2	no	—
373	C₃²⋊C₉	—	2	2	no	—
374	C₃²⋊C₉	—	2	2	no	—
375	C₃²⋊C₉	—	2	2	no	—
376	C₃²⋊C₉	—	2	2	no	—
377	C₃²⋊C₉	—	2	2	no	—
378	C₃²⋊C₉	—	2	2	no	—
379	C₃²⋊C₉	—	2	1	no	—
380	C₃²⋊C₉	—	2	1	no	—
381	C₃²⋊C₉	—	2	2	no	—
382	C₃²⋊C₉	—	2	1	no	—
383	C₃²⋊C₉	—	2	2	no	—
384	C₃²⋊C₉	—	3	1	no	—
385	C₃²⋊C₉	—	3	1	no	—
386	C₃²⋊C₉	—	3	1	no	—
387	C₃²⋊C₉	—	3	1	no	—
388	C₃²⋊C₉	—	3	1	no	—
389	C₃²⋊C₉	—	3	1	no	—
390	C₃²⋊C₉	—	3	1	no	—
391	C₃²⋊C₉	—	6	1	no	—
392	C₃²⋊C₉	—	6	1	no	—
393	C₃²⋊C₉	—	6	2	no	—
394	C₃²⋊C₉	—	6	1	no	—
395	C₃²⋊C₉	—	6	2	no	—
396	C₃²⋊C₉	—	6	1	no	—
397	C₃²⋊C₉	—	6	2	no	—
398	C₃²⋊C₉	—	6	1	no	—
399	C₃²⋊C₉	—	6	3	no	—
400	C₃²⋊C₉	—	6	3	no	—
401	C₃²⋊C₉	—	6	3	no	—
402	C₃²⋊C₉	—	6	3	no	—
403	C₃²⋊C₉	—	6	3	no	—
404	C₃²⋊C₉	—	6	3	no	—
405	C₃²⋊C₉	—	6	2	no	—
406	C₃²⋊C₉	—	6	2	no	—
407	C₃²⋊C₉	—	6	1	no	—
408	C₃²⋊C₉	—	6	1	no	—
409	C₃²⋊C₉	—	6	1	no	—
410	C₃²⋊C₉	—	6	1	no	—
411	C₃²⋊C₉	—	6	1	no	—
412	C₃²⋊C₉	—	6	1	no	—
413	C₃²⋊C₉	—	6	1	no	—
414	C₃²⋊C₉	—	6	1	no	—
415	C₃²⋊C₉	—	6	1	no	—
416	C₃²⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
417	C₃²⋊C₉	C₂×C₃×C₉	1	2	yes	complemented
418	C₃²⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
419	C₃²⋊C₉	C₂×C₃×C₉	1	2	yes	complemented
420	C₉²	—	2	1	no	—
421	C₉²	—	2	1	no	—
422	C₉²	—	2	1	no	—
423	C₉²	—	2	1	no	—
424	C₉²	—	3	1	no	—
425	C₉²	—	6	1	no	—
426	C₉²	—	6	1	no	—
427	C₉²	—	6	2	no	—
428	C₉²	—	6	2	no	—
429	C₉²	—	6	2	no	—
430	C₉²	—	6	2	no	—
431	C₉²	—	6	2	no	—
432	C₉²	—	6	2	no	—
433	C₉²	—	6	1	no	—
434	C₉²	—	6	1	no	—
435	C₉²	—	6	1	no	—
436	C₉²	—	6	1	no	—
437	C₉²	—	6	1	no	—
438	C₉²	—	6	1	no	—
439	C₉²	—	6	1	no	—
440	C₉²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
441	C₂×C₃³	—	9	1	no	—
442	C₃×C₃⋊D₃	C₃²×C₉	1	1	yes	characteristic
443	C₃×C₃⋊D₃	C₃×3₋¹⁺²	1	1	yes	characteristic
444	C₃×C₃⋊D₃	#737	1	1	yes	characteristic
445	C₃×C₃⋊D₃	#737	1	1	yes	characteristic
446	C₃²×D₃	—	3	1	no	—
447	C₃²×D₃	—	3	2	no	—
448	C₃²×D₃	—	3	1	no	—
449	C₃²×D₃	—	9	1	no	—
450	C₃²×D₃	—	9	1	no	—
451	C₃²×D₃	—	9	1	no	—
452	C₃²×D₃	—	9	1	no	—
453	C₂×3₋¹⁺²	—	9	2	no	—
454	C₂×3₋¹⁺²	—	9	1	no	—
455	C₂×3₋¹⁺²	—	9	2	no	—
456	C₂×3₋¹⁺²	—	9	2	no	—
457	C₂×3₋¹⁺²	—	9	2	no	—
458	C₂×C₃×C₉	—	9	1	no	—
459	C₂×C₃×C₉	—	9	1	no	—
460	C₂×C₃×C₉	—	9	1	no	—
461	C₂×C₃×C₉	—	9	1	no	—
462	C₂×C₃×C₉	—	9	1	no	—
463	C₂×C₃×C₉	—	9	1	no	—
464	C₂×C₃×C₉	—	9	1	no	—
465	C₂×C₃×C₉	—	9	1	no	—
466	C₂×C₃×C₉	—	9	1	no	—
467	C₂×C₃×C₉	—	9	1	no	—
468	C₂×C₃×C₉	—	9	1	no	—
469	C₂×C₃×C₉	—	9	1	no	—
470	C₂×C₃×C₉	—	27	1	no	—
471	C₂×C₃×C₉	—	27	2	no	—
472	(C₃⋊D₃)⋊C₃	—	3	2	no	—
473	(C₃⋊D₃)⋊C₃	—	3	1	no	—
474	D₃×C₉	—	3	1	no	—
475	D₃×C₉	—	3	2	no	—
476	D₃×C₉	—	3	2	no	—
477	D₃×C₉	—	3	1	no	—
478	D₃×C₉	—	3	1	no	—
479	D₃×C₉	—	3	2	no	—
480	D₃×C₉	—	3	1	no	—
481	D₃×C₉	—	3	2	no	—
482	D₃×C₉	—	9	1	no	—
483	D₃×C₉	—	9	2	no	—
484	D₃×C₉	—	9	1	no	—
485	D₃×C₉	—	9	2	no	—
486	D₃×C₉	—	9	1	no	—
487	D₃×C₉	—	9	1	no	—
488	D₃×C₉	—	9	1	no	—
489	D₃×C₉	—	9	1	no	—
490	D₃×C₉	—	9	1	no	—
491	D₃×C₉	—	9	1	no	—
492	D₃×C₉	—	9	1	no	—
493	D₃×C₉	—	9	1	no	—
494	D₃×C₉	—	9	3	no	—
495	D₃×C₉	—	9	3	no	—
496	C₃³	—	2	1	no	—
497	C₃³	—	2	1	no	—
498	C₃³	—	2	1	no	—
499	C₃³	—	2	1	no	—
500	C₃³	—	2	1	no	—
501	C₃³	—	2	2	no	—
502	C₃³	—	3	1	no	—
503	C₃³	—	3	1	no	—
504	C₃³	—	3	1	no	—
505	C₃³	—	3	1	no	—
506	C₃³	—	3	1	no	—
507	C₃³	—	6	1	no	—
508	C₃³	—	6	1	no	—
509	C₃³	—	6	1	no	—
510	C₃³	—	6	1	no	—
511	C₃³	—	6	1	no	—
512	C₃³	—	6	1	no	—
513	C₃³	—	6	1	no	—
514	C₃³	—	6	1	no	—
515	C₃³	—	6	1	no	—
516	C₃³	—	6	1	no	—
517	C₃³	—	6	1	no	—
518	C₃³	—	6	1	no	—
519	C₃³	—	6	1	no	—
520	C₃³	—	6	1	no	—
521	C₃³	—	6	1	no	—
522	C₃³	—	6	1	no	—
523	C₃³	—	6	1	no	—
524	C₃³	—	6	1	no	—
525	C₃³	—	6	1	no	—
526	C₃³	—	6	1	no	—
527	C₃³	C₃×D₃×C₉	1	2	yes	—
528	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
529	C₃³	C₂×C₃²×C₉	1	1	yes	characteristic
530	C₃³	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
531	C₃³	C₂×#737	1	1	yes	characteristic
532	C₃³	C₂×#737	1	1	yes	characteristic
533	C₃³	C₃³×D₃	1	1	yes	characteristic
534	3₋¹⁺²	—	3	2	no	—
535	3₋¹⁺²	—	3	1	no	—
536	3₋¹⁺²	—	3	2	no	—
537	3₋¹⁺²	—	6	2	no	—
538	3₋¹⁺²	—	6	1	no	—
539	3₋¹⁺²	—	6	2	no	—
540	3₋¹⁺²	—	6	2	no	—
541	3₋¹⁺²	—	6	2	no	—
542	3₋¹⁺²	—	6	2	no	—
543	3₋¹⁺²	—	6	2	no	—
544	3₋¹⁺²	—	6	2	no	—
545	3₋¹⁺²	—	6	4	no	—
546	3₋¹⁺²	—	6	2	no	—
547	3₋¹⁺²	—	6	2	no	—
548	3₋¹⁺²	—	6	2	no	—
549	3₋¹⁺²	—	6	2	no	—
550	3₋¹⁺²	—	6	2	no	—
551	3₋¹⁺²	—	6	2	no	—
552	3₋¹⁺²	—	6	2	no	—
553	3₋¹⁺²	—	6	1	no	—
554	3₋¹⁺²	—	6	2	no	—
555	3₋¹⁺²	—	6	2	no	—
556	3₋¹⁺²	—	6	2	no	—
557	H(3,𝔽₃)	—	3	2	no	—
558	H(3,𝔽₃)	—	3	1	no	—
559	H(3,𝔽₃)	—	6	2	no	—
560	H(3,𝔽₃)	—	6	1	no	—
561	H(3,𝔽₃)	—	6	2	no	—
562	H(3,𝔽₃)	—	6	1	no	—
563	H(3,𝔽₃)	—	6	2	no	—
564	H(3,𝔽₃)	—	6	1	no	—
565	H(3,𝔽₃)	—	6	2	no	—
566	H(3,𝔽₃)	—	6	1	no	—
567	C₃×C₉	—	2	1	no	—
568	C₃×C₉	—	2	1	no	—
569	C₃×C₉	—	2	1	no	—
570	C₃×C₉	—	2	2	no	—
571	C₃×C₉	—	2	1	no	—
572	C₃×C₉	—	2	2	no	—
573	C₃×C₉	—	2	3	no	—
574	C₃×C₉	—	2	3	no	—
575	C₃×C₉	—	2	1	no	—
576	C₃×C₉	—	2	2	no	—
577	C₃×C₉	—	2	1	no	—
578	C₃×C₉	—	2	2	no	—
579	C₃×C₉	—	2	2	no	—
580	C₃×C₉	—	2	1	no	—
581	C₃×C₉	—	2	1	no	—
582	C₃×C₉	—	2	1	no	—
583	C₃×C₉	—	2	1	no	—
584	C₃×C₉	—	2	2	no	—
585	C₃×C₉	—	3	3	no	—
586	C₃×C₉	—	3	3	no	—
587	C₃×C₉	—	3	1	no	—
588	C₃×C₉	—	3	1	no	—
589	C₃×C₉	—	3	1	no	—
590	C₃×C₉	—	3	2	no	—
591	C₃×C₉	—	3	1	no	—
592	C₃×C₉	—	3	2	no	—
593	C₃×C₉	—	3	1	no	—
594	C₃×C₉	—	3	1	no	—
595	C₃×C₉	—	3	1	no	—
596	C₃×C₉	—	3	1	no	—
597	C₃×C₉	—	3	1	no	—
598	C₃×C₉	—	3	1	no	—
599	C₃×C₉	—	3	1	no	—
600	C₃×C₉	—	3	1	no	—
601	C₃×C₉	—	3	1	no	—
602	C₃×C₉	—	6	4	no	—
603	C₃×C₉	—	6	2	no	—
604	C₃×C₉	—	6	4	no	—
605	C₃×C₉	—	6	2	no	—
606	C₃×C₉	—	6	2	no	—
607	C₃×C₉	—	6	1	no	—
608	C₃×C₉	—	6	2	no	—
609	C₃×C₉	—	6	1	no	—
610	C₃×C₉	—	6	1	no	—
611	C₃×C₉	—	6	3	no	—
612	C₃×C₉	—	6	3	no	—
613	C₃×C₉	—	6	1	no	—
614	C₃×C₉	—	6	1	no	—
615	C₃×C₉	—	6	1	no	—
616	C₃×C₉	—	6	2	no	—
617	C₃×C₉	—	6	2	no	—
618	C₃×C₉	—	6	1	no	—
619	C₃×C₉	—	6	1	no	—
620	C₃×C₉	—	6	1	no	—
621	C₃×C₉	—	6	1	no	—
622	C₃×C₉	—	6	1	no	—
623	C₃×C₉	—	6	1	no	—
624	C₃×C₉	—	6	1	no	—
625	C₃×C₉	—	6	3	no	—
626	C₃×C₉	—	6	3	no	—
627	C₃×C₉	—	6	3	no	—
628	C₃×C₉	—	6	3	no	—
629	C₃×C₉	—	6	1	no	—
630	C₃×C₉	—	6	1	no	—
631	C₃×C₉	—	6	1	no	—
632	C₃×C₉	—	6	1	no	—
633	C₃×C₉	—	6	1	no	—
634	C₃×C₉	—	6	1	no	—
635	C₃×C₉	—	6	1	no	—
636	C₃×C₉	—	6	1	no	—
637	C₃×C₉	—	6	1	no	—
638	C₃×C₉	—	6	1	no	—
639	C₃×C₉	—	6	2	no	—
640	C₃×C₉	—	6	1	no	—
641	C₃×C₉	—	6	2	no	—
642	C₃×C₉	—	6	3	no	—
643	C₃×C₉	—	6	3	no	—
644	C₃×C₉	—	6	1	no	—
645	C₃×C₉	—	6	1	no	—
646	C₃×C₉	—	6	1	no	—
647	C₃×C₉	—	6	1	no	—
648	C₃×C₉	—	6	1	no	—
649	C₃×C₉	—	6	1	no	—
650	C₃×C₉	—	6	1	no	—
651	C₃×C₉	—	6	1	no	—
652	C₃×C₉	—	6	1	no	—
653	C₃×C₉	—	6	1	no	—
654	C₃×C₉	—	6	1	no	—
655	C₃×C₉	—	6	1	no	—
656	C₃×C₉	—	6	1	no	—
657	C₃×C₉	—	6	1	no	—
658	C₃×C₉	—	6	1	no	—
659	C₃×C₉	—	6	1	no	—
660	C₃×C₉	—	6	1	no	—
661	C₃×C₉	—	6	1	no	—
662	C₃×C₉	—	6	1	no	—
663	C₃×C₉	—	6	1	no	—
664	C₃×C₉	—	6	1	no	—
665	C₃×C₉	—	6	1	no	—
666	C₃×C₉	—	6	1	no	—
667	C₃×C₉	—	6	1	no	—
668	C₃×C₉	—	6	1	no	—
669	C₃×C₉	—	6	1	no	—
670	C₃×C₉	—	6	1	no	—
671	C₃×C₉	—	6	1	no	—
672	C₃×C₉	—	6	1	no	—
673	C₃×C₉	—	6	1	no	—
674	C₃×C₉	—	6	1	no	—
675	C₃×C₉	—	6	1	no	—
676	C₃×C₉	—	6	1	no	—
677	C₃×C₉	—	9	1	no	—
678	C₃×C₉	—	18	1	no	—
679	C₃×C₉	—	18	2	no	—
680	C₃×C₉	—	18	2	no	—
681	C₃×C₉	—	18	2	no	—
682	C₃×C₉	—	18	2	no	—
683	C₃×C₉	—	18	2	no	—
684	C₃×C₉	—	18	1	no	—
685	C₃×C₉	—	18	2	no	—
686	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
687	C₃×C₉	C₃×D₃×C₉	1	2	yes	—
688	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
689	C₃×C₉	C₃×D₃×C₉	1	2	yes	—
690	C₃×C₉	C₃×D₃×C₉	1	2	yes	—
691	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
692	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
693	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
694	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
695	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
696	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
697	C₃×C₉	D₃×3₋¹⁺²	1	2	yes	—
698	C₂×C₃²	—	9	1	no	—
699	C₂×C₃²	—	9	2	no	—
700	C₂×C₃²	—	9	1	no	—
701	C₂×C₃²	—	27	1	no	—
702	C₂×C₃²	—	27	1	no	—
703	C₂×C₃²	—	27	1	no	—
704	C₃⋊D₃	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented
705	C₃×D₃	—	3	1	no	—
706	C₃×D₃	—	3	1	no	—
707	C₃×D₃	—	3	1	no	—
708	C₃×D₃	—	3	1	no	—
709	C₃×D₃	—	9	2	no	—
710	C₃×D₃	—	9	1	no	—
711	C₃×D₃	—	9	1	no	—
712	C₃×D₃	—	9	1	no	—
713	C₃×D₃	—	9	1	no	—
714	C₃×D₃	—	9	1	no	—
715	C₂×C₉	—	9	1	no	—
716	C₂×C₉	—	9	2	no	—
717	C₂×C₉	—	9	2	no	—
718	C₂×C₉	—	9	1	no	—
719	C₂×C₉	—	9	1	no	—
720	C₂×C₉	—	9	2	no	—
721	C₂×C₉	—	9	1	no	—
722	C₂×C₉	—	9	2	no	—
723	C₂×C₉	—	27	1	no	—
724	C₂×C₉	—	27	1	no	—
725	C₂×C₉	—	27	1	no	—
726	C₂×C₉	—	27	1	no	—
727	C₂×C₉	—	27	1	no	—
728	C₂×C₉	—	27	1	no	—
729	C₂×C₉	—	27	1	no	—
730	C₂×C₉	—	27	1	no	—
731	C₃²	—	2	1	no	—
732	C₃²	—	2	1	no	—
733	C₃²	—	2	1	no	—
734	C₃²	—	2	1	no	—
735	C₃²	—	2	1	no	—
736	C₃²	—	2	1	no	—
737	C₃²	—	2	1	no	—
738	C₃²	—	2	1	no	—
739	C₃²	—	3	1	no	—
740	C₃²	—	3	1	no	—
741	C₃²	—	3	1	no	—
742	C₃²	—	3	1	no	—
743	C₃²	—	3	2	no	—
744	C₃²	—	3	1	no	—
745	C₃²	—	6	1	no	—
746	C₃²	—	6	1	no	—
747	C₃²	—	6	1	no	—
748	C₃²	—	6	1	no	—
749	C₃²	—	6	2	no	—
750	C₃²	—	6	2	no	—
751	C₃²	—	6	2	no	—
752	C₃²	—	6	2	no	—
753	C₃²	—	6	2	no	—
754	C₃²	—	6	1	no	—
755	C₃²	—	6	1	no	—
756	C₃²	—	6	2	no	—
757	C₃²	—	6	1	no	—
758	C₃²	—	6	2	no	—
759	C₃²	—	6	1	no	—
760	C₃²	—	6	1	no	—
761	C₃²	—	6	1	no	—
762	C₃²	—	6	1	no	—
763	C₃²	—	6	2	no	—
764	C₃²	—	6	1	no	—
765	C₃²	—	6	1	no	—
766	C₃²	—	6	2	no	—
767	C₃²	—	6	2	no	—
768	C₃²	—	6	1	no	—
769	C₃²	—	9	1	no	—
770	C₃²	—	18	1	no	—
771	C₃²	—	18	1	no	—
772	C₃²	—	18	1	no	—
773	C₃²	—	18	1	no	—
774	C₃²	—	18	1	no	—
775	C₃²	—	18	1	no	—
776	C₃²	—	18	1	no	—
777	C₃²	—	18	1	no	—
778	C₃²	—	18	1	no	—
779	C₃²	—	18	1	no	—
780	C₃²	—	18	1	no	—
781	C₃²	—	18	1	no	—
782	C₃²	—	18	1	no	—
783	C₃²	—	18	1	no	—
784	C₃²	C₂×C₉×3₋¹⁺²	1	1	yes	characteristic, complemented
785	C₃²	C₃²×D₃×C₉	1	1	yes	characteristic
786	C₃²	C₃²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
787	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
788	C₃²	D₃×#737	1	1	yes	characteristic
789	C₃²	D₃×#737	1	1	yes	characteristic
790	C₉	—	2	2	no	—
791	C₉	—	2	1	no	—
792	C₉	—	2	2	no	—
793	C₉	—	2	1	no	—
794	C₉	—	3	1	no	—
795	C₉	—	3	1	no	—
796	C₉	—	3	1	no	—
797	C₉	—	6	2	no	—
798	C₉	—	6	2	no	—
799	C₉	—	6	1	no	—
800	C₉	—	6	1	no	—
801	C₉	—	6	2	no	—
802	C₉	—	6	1	no	—
803	C₉	—	6	2	no	—
804	C₉	—	6	2	no	—
805	C₉	—	6	1	no	—
806	C₉	—	6	1	no	—
807	C₉	—	6	2	no	—
808	C₉	—	6	3	no	—
809	C₉	—	6	1	no	—
810	C₉	—	6	3	no	—
811	C₉	—	6	1	no	—
812	C₉	—	9	1	no	—
813	C₉	—	9	1	no	—
814	C₉	—	9	1	no	—
815	C₉	—	9	1	no	—
816	C₉	—	18	1	no	—
817	C₉	—	18	1	no	—
818	C₉	—	18	1	no	—
819	C₉	—	18	1	no	—
820	C₉	—	18	1	no	—
821	C₉	—	18	1	no	—
822	C₉	—	18	1	no	—
823	C₉	—	18	1	no	—
824	C₉	C₉×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
825	C₉	C₉×(C₃⋊D₃)⋊C₃	1	2	yes	complemented
826	C₉	#92262	1	1	yes	characteristic, direct product factor
827	C₉	#92262	1	2	yes	direct product factor
828	C₂×C₃	—	9	1	no	—
829	C₂×C₃	—	9	1	no	—
830	C₂×C₃	—	9	1	no	—
831	C₂×C₃	—	9	1	no	—
832	C₂×C₃	—	27	2	no	—
833	C₂×C₃	—	27	1	no	—
834	D₃	—	3	1	no	—
835	D₃	—	9	1	no	—
836	C₃	—	2	1	no	—
837	C₃	—	2	1	no	—
838	C₃	—	2	1	no	—
839	C₃	—	2	1	no	—
840	C₃	—	3	1	no	—
841	C₃	—	6	1	no	—
842	C₃	—	6	1	no	—
843	C₃	—	6	1	no	—
844	C₃	—	6	1	no	—
845	C₃	—	9	2	no	—
846	C₃	—	9	1	no	—
847	C₃	—	18	1	no	—
848	C₃	—	18	2	no	—
849	C₃	C₃×C₉×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
850	C₃	D₃×C₉×3₋¹⁺²	1	1	yes	characteristic
851	C₃	C₃×#92262	1	1	yes	characteristic
852	C₃	#13091420	1	1	yes	characteristic
853	C₃	#13091420	1	1	yes	characteristic
854	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃
commutator	C₃³	C₂×C₃²×C₉
Frattini, socle	C₃³	C₃³×D₃
Fitting	C₉×C₉⋊H(3,𝔽₃)	C₂
prime radical	C₃²×(C₃⋊D₃)⋊C₃	C₃²
cosocle	C₃⁴	C₂×C₃³
hypercenter	C₉²	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₂×C₉×3₋¹⁺²
LCS	G ▷ C₃³ ▷ C₃²
UCS	C₁ ◁ C₃×C₉ ◁ C₉²

Complements

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

N	H ≅ G/N	type
1. C₉×C₉⋊H(3,𝔽₃)	C₂	semidirect
5. C₉²×C₃⋊D₃	C₃	semidirect
6. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
7. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
8. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
9. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
12. #13090622	C₃	semidirect
13. #13090622	C₃	semidirect
14. C₉×(C₃⋊D₃)⋊C₉	C₃	semidirect
15. C₉×(C₃⋊D₃)⋊C₉	C₃	semidirect
18. C₃×C₉×3₋¹⁺²	D₃	semidirect
20. C₃²×C₉²	C₂×C₃	semidirect
30. #10624556	C₂×C₃	semidirect
31. #10624556	C₂×C₃	semidirect
32. #10624556	C₂×C₃	semidirect
33. #10624556	C₂×C₃	semidirect
36. #10624548	C₂×C₃	semidirect
37. #10624548	C₂×C₃	semidirect
41. C₉×C₃²⋊C₉	C₂×C₃	semidirect
42. C₉×C₃²⋊C₉	C₂×C₃	semidirect
51. #92262	C₉	direct (N × H)
52. #92262	C₉	direct (N × H)
53. #92262	C₉	direct (N × H)
54. #92262	C₉	direct (N × H)
55. #92262	C₉	direct (N × H)
92. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
93. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
94. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
95. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
96. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
191. C₉×C₃⋊D₃	C₃×C₉	semidirect
192. C₉×C₃⋊D₃	C₃×C₉	semidirect
193. C₉×C₃⋊D₃	3₋¹⁺²	semidirect
194. C₉×C₃⋊D₃	3₋¹⁺²	semidirect
240. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
241. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
242. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
243. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
262. C₃×3₋¹⁺²	D₃×C₉	semidirect
263. C₃×3₋¹⁺²	D₃×C₉	semidirect
264. C₃×3₋¹⁺²	D₃×C₉	semidirect
265. C₃×3₋¹⁺²	D₃×C₉	semidirect
266. C₃×3₋¹⁺²	D₃×C₉	semidirect
325. C₃²×C₉	C₂×C₃×C₉	semidirect
326. C₃²×C₉	C₂×C₃×C₉	semidirect
327. C₃²×C₉	C₂×3₋¹⁺²	semidirect
328. C₃²×C₉	C₂×3₋¹⁺²	semidirect
416. C₃²⋊C₉	C₂×C₃×C₉	semidirect
417. C₃²⋊C₉	C₂×C₃×C₉	semidirect
418. C₃²⋊C₉	C₂×C₃×C₉	semidirect
419. C₃²⋊C₉	C₂×C₃×C₉	semidirect
440. C₉²	(C₃⋊D₃)⋊C₃	semidirect
704. C₃⋊D₃	C₉×3₋¹⁺²	semidirect
784. C₃²	C₂×C₉×3₋¹⁺²	semidirect
824. C₉	C₉×(C₃⋊D₃)⋊C₃	semidirect
825. C₉	C₉×(C₃⋊D₃)⋊C₃	semidirect
826. C₉	#92262	direct (N × H)
827. C₉	#92262	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₉⋊H(3,𝔽₃)	2
C₃×#92262	3
D₃×C₉×3₋¹⁺²	3
C₃×C₉×(C₃⋊D₃)⋊C₃	3
C₉²×C₃⋊D₃	3
((C₃⋊D₃)⋊C₉)⋊C₉	3
(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	3
#13090622	3
C₉×(C₃⋊D₃)⋊C₉	3

Subgroups — C9×#92262 #72243687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#92262 #72243687