Subgroups — C₉×#5593 #13152764

Order 1728.

880 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#953	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#935	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#885	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5593	C₃	1	1	yes	maximal, characteristic
17	C₉×#538	—	3	1	no	maximal
18	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
22	C₂×C₉×#67	C₂²	1	1	yes	characteristic
23	C₂×C₉×#67	C₂²	1	1	yes	characteristic
24	C₂×C₉×#67	C₂²	1	1	yes	characteristic
25	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
27	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
28	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₉×#217	C₂²	1	1	yes	characteristic
35	C₉×#217	C₂²	1	1	yes	characteristic
36	C₉×#217	C₂²	1	1	yes	characteristic
37	C₉×#217	C₂²	1	1	yes	characteristic
38	C₉×#217	C₂²	1	1	yes	characteristic
39	C₉×#217	C₂²	1	1	yes	characteristic
40	C₉×#217	C₂²	1	1	yes	characteristic
41	C₉×#217	C₂²	1	1	yes	characteristic, complemented
42	C₉×#217	C₂²	1	1	yes	characteristic, complemented
43	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
47	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₃²×#120	C₂×C₃	1	1	yes	characteristic
54	C₃×#953	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
56	C₃×#939	C₂×C₃	1	1	yes	characteristic
57	C₃×#939	C₂×C₃	1	1	yes	characteristic
58	C₃×#938	C₂×C₃	1	1	yes	characteristic
59	C₃×#936	C₂×C₃	1	1	yes	characteristic
60	C₃×#935	C₂×C₃	1	1	yes	characteristic
61	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
62	C₃×#885	C₂×C₃	1	1	yes	characteristic
63	C₃×#883	C₂×C₃	1	1	yes	characteristic
64	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
65	C₃×#879	C₂×C₃	1	1	yes	characteristic
66	C₃×#879	C₂×C₃	1	1	yes	characteristic
67	C₃×#878	C₂×C₃	1	1	yes	characteristic
68	C₉×#126	—	3	1	no	—
69	C₉×#126	—	3	1	no	—
70	C₉×#124	—	3	1	no	—
71	C₉×#124	—	3	1	no	—
72	C₉×#123	—	3	1	no	—
73	C₉×#123	—	3	1	no	—
74	C₉×C₂²⋊Q₈	—	3	1	no	—
75	C₉×#121	—	3	1	no	—
76	C₉×#121	—	3	1	no	—
77	C₉×#121	—	3	1	no	—
78	C₉×#120	—	2	1	no	—
79	C₉×#120	—	3	1	no	—
80	C₉×#120	D₃	1	1	yes	characteristic, complemented
81	C₄×D₄×C₉	—	3	1	no	—
82	C₄×D₄×C₉	—	3	1	no	—
83	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
84	C₂³×C₃×C₉	—	2	2	no	—
85	C₂³×C₃×C₉	—	4	1	no	—
86	C₂³×C₃×C₉	—	4	1	no	—
87	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
88	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
89	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
90	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
91	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
92	C₃×D₄×C₉	—	2	2	no	—
93	C₃×D₄×C₉	—	4	1	no	—
94	C₃×D₄×C₉	—	4	1	no	—
95	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
98	C₉×#67	—	2	2	no	—
99	C₉×#67	—	4	1	no	—
100	C₉×#67	—	4	1	no	—
101	C₉×#67	—	4	1	no	—
102	C₂×C₉×Dic₃	—	4	1	no	—
103	C₂×C₉×Dic₃	—	4	1	no	—
104	C₂×C₉×Dic₃	—	4	1	no	—
105	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
106	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
108	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
109	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
110	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
111	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
112	C₄×D₃×C₉	—	4	1	no	—
113	C₉×Dic₆	—	4	1	no	—
114	C₃×#538	—	3	1	no	—
115	#5593	C₉	1	1	yes	characteristic, direct product factor
116	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
124	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
125	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
129	C₂⁴×C₉	—	2	1	no	—
130	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
131	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃×#217	C₂²×C₃	1	1	yes	characteristic
135	C₃×#217	C₂²×C₃	1	1	yes	characteristic
136	C₃×#217	C₂²×C₃	1	1	yes	characteristic
137	C₃×#217	C₂²×C₃	1	1	yes	characteristic
138	C₃×#217	C₂²×C₃	1	1	yes	characteristic
139	C₃×#217	C₂²×C₃	1	1	yes	characteristic
140	C₃×#217	C₂²×C₃	1	1	yes	characteristic
141	C₃×#217	C₂²×C₃	1	1	yes	characteristic
142	C₃×#217	C₂²×C₃	1	1	yes	characteristic
143	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
146	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
147	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
152	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
153	C₂×Q₈×C₉	—	3	1	no	—
154	C₂×D₄×C₉	—	2	1	no	—
155	C₂×D₄×C₉	—	2	1	no	—
156	C₂×D₄×C₉	—	2	1	no	—
157	C₂×D₄×C₉	—	3	1	no	—
158	C₂×D₄×C₉	—	3	1	no	—
159	C₂×D₄×C₉	—	3	1	no	—
160	C₂×D₄×C₉	—	3	1	no	—
161	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
162	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
163	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
164	C₂²×C₄×C₉	—	3	1	no	—
165	C₂²×C₄×C₉	—	3	1	no	—
166	C₂²×C₄×C₉	—	3	1	no	—
167	C₂²×C₄×C₉	—	3	1	no	—
168	C₉×C₄⋊C₄	—	3	1	no	—
169	C₉×C₄⋊C₄	—	3	1	no	—
170	C₉×C₄⋊C₄	—	3	1	no	—
171	C₉×C₄⋊C₄	—	3	1	no	—
172	C₉×C₄⋊C₄	—	3	1	no	—
173	C₉×C₄⋊C₄	—	3	1	no	—
174	C₉×C₂²⋊C₄	—	2	1	no	—
175	C₉×C₂²⋊C₄	—	2	1	no	—
176	C₉×C₂²⋊C₄	—	2	1	no	—
177	C₉×C₂²⋊C₄	—	3	1	no	—
178	C₉×C₂²⋊C₄	—	3	1	no	—
179	C₉×C₂²⋊C₄	—	3	1	no	—
180	C₉×C₂²⋊C₄	—	3	1	no	—
181	C₉×C₂²⋊C₄	—	3	1	no	—
182	C₉×C₂²⋊C₄	—	3	1	no	—
183	C₉×C₂²⋊C₄	—	3	1	no	—
184	C₉×C₂²⋊C₄	—	3	1	no	—
185	C₉×C₂²⋊C₄	—	3	1	no	—
186	C₉×C₂²⋊C₄	—	3	1	no	—
187	C₉×C₂²⋊C₄	—	3	1	no	—
188	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
189	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
190	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
191	C₄²×C₉	—	3	1	no	—
192	C₄²×C₉	—	3	1	no	—
193	C₂²×C₃×C₉	—	2	1	no	—
194	C₂²×C₃×C₉	—	2	1	no	—
195	C₂²×C₃×C₉	—	2	1	no	—
196	C₂²×C₃×C₉	—	2	1	no	—
197	C₂²×C₃×C₉	—	2	1	no	—
198	C₂²×C₃×C₉	—	2	1	no	—
199	C₂²×C₃×C₉	—	2	1	no	—
200	C₂²×C₃×C₉	—	2	1	no	—
201	C₂²×C₃×C₉	—	2	1	no	—
202	C₂²×C₃×C₉	—	2	1	no	—
203	C₂²×C₃×C₉	—	2	1	no	—
204	C₂²×C₃×C₉	—	4	4	no	—
205	C₂²×C₃×C₉	#41	1	2	yes	—
206	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
207	C₂×D₃×C₉	—	2	1	no	—
208	C₂×D₃×C₉	—	2	1	no	—
209	C₂×D₃×C₉	—	2	1	no	—
210	C₃×C₄×C₉	—	2	1	no	—
211	C₃×C₄×C₉	—	2	1	no	—
212	C₃×C₄×C₉	—	2	1	no	—
213	C₉×Dic₃	—	2	1	no	—
214	C₉×Dic₃	—	2	1	no	—
215	C₉×Dic₃	—	2	1	no	—
216	C₉×Dic₃	—	2	1	no	—
217	C₉×Dic₃	—	2	1	no	—
218	C₉×Dic₃	—	2	1	no	—
219	C₉×Dic₃	—	2	1	no	—
220	C₃×#126	—	3	1	no	—
221	C₃×#126	—	3	1	no	—
222	C₃×#124	—	3	1	no	—
223	C₃×#124	—	3	1	no	—
224	C₃×#123	—	3	1	no	—
225	C₃×#123	—	3	1	no	—
226	C₃×C₂²⋊Q₈	—	3	1	no	—
227	C₃×#121	—	3	1	no	—
228	C₃×#121	—	3	1	no	—
229	C₃×#121	—	3	1	no	—
230	C₃×#120	—	2	1	no	—
231	C₃×#120	—	3	1	no	—
232	C₃×#120	C₂×C₉	1	1	yes	characteristic, complemented
233	C₃×#120	C₃×D₃	1	1	yes	characteristic
234	C₃×C₄×D₄	—	3	1	no	—
235	C₃×C₄×D₄	—	3	1	no	—
236	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
237	#953	C₂×C₉	1	1	yes	characteristic, complemented
238	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
239	#939	C₂×C₉	1	1	yes	characteristic, complemented
240	#939	C₂×C₉	1	1	yes	characteristic, complemented
241	#938	C₂×C₉	1	1	yes	characteristic, complemented
242	#936	C₂×C₉	1	1	yes	characteristic, complemented
243	#935	C₂×C₉	1	1	yes	characteristic, complemented
244	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
245	#885	C₂×C₉	1	1	yes	characteristic, complemented
246	#883	C₂×C₉	1	1	yes	characteristic, complemented
247	#67⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
248	#879	C₂×C₉	1	1	yes	characteristic, complemented
249	#879	C₂×C₉	1	1	yes	characteristic, complemented
250	#878	C₂×C₉	1	1	yes	characteristic, complemented
251	C₂³×C₃²	—	2	2	no	—
252	C₂³×C₃²	—	4	1	no	—
253	C₂³×C₃²	—	4	1	no	—
254	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
255	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
256	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
257	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
259	C₃²×D₄	—	2	2	no	—
260	C₃²×D₄	—	4	1	no	—
261	C₃²×D₄	—	4	1	no	—
262	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
265	C₃×#67	—	2	2	no	—
266	C₃×#67	—	4	1	no	—
267	C₃×#67	—	4	1	no	—
268	C₃×#67	—	4	1	no	—
269	C₂×C₃×Dic₃	—	4	1	no	—
270	C₂×C₃×Dic₃	—	4	1	no	—
271	C₂×C₃×Dic₃	—	4	1	no	—
272	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
279	C₃×C₄×D₃	—	4	1	no	—
280	C₃×Dic₆	—	4	1	no	—
281	C₂³×C₉	—	2	2	no	—
282	C₂³×C₉	—	2	1	no	—
283	C₂³×C₉	—	2	1	no	—
284	C₂³×C₉	—	2	1	no	—
285	C₂³×C₉	—	2	1	no	—
286	C₂³×C₉	—	3	1	no	—
287	C₂³×C₉	—	4	2	no	—
288	C₂³×C₉	—	4	1	no	—
289	C₂³×C₉	—	4	1	no	—
290	C₂³×C₉	—	4	2	no	—
291	C₂³×C₉	—	4	2	no	—
292	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
293	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
294	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
295	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
296	Q₈×C₉	—	12	1	no	—
297	D₄×C₉	—	2	2	no	—
298	D₄×C₉	—	4	2	no	—
299	D₄×C₉	—	4	1	no	—
300	D₄×C₉	—	4	1	no	—
301	D₄×C₉	—	4	2	no	—
302	D₄×C₉	—	4	2	no	—
303	D₄×C₉	—	6	2	no	—
304	D₄×C₉	—	12	1	no	—
305	D₄×C₉	—	12	1	no	—
306	D₄×C₉	—	12	1	no	—
307	C₂×C₄×C₉	—	2	1	no	—
308	C₂×C₄×C₉	—	2	1	no	—
309	C₂×C₄×C₉	—	2	1	no	—
310	C₂×C₄×C₉	—	3	1	no	—
311	C₂×C₄×C₉	—	3	1	no	—
312	C₂×C₄×C₉	—	3	1	no	—
313	C₂×C₄×C₉	—	3	1	no	—
314	C₂×C₄×C₉	—	3	1	no	—
315	C₂×C₄×C₉	—	3	1	no	—
316	C₂×C₄×C₉	—	3	1	no	—
317	C₂×C₄×C₉	—	12	1	no	—
318	C₂×C₄×C₉	—	12	1	no	—
319	C₂×C₄×C₉	—	12	1	no	—
320	C₂×C₄×C₉	—	12	1	no	—
321	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
322	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
323	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
324	#538	—	3	1	no	Sylow
325	C₂×C₃×C₉	—	2	2	no	—
326	C₂×C₃×C₉	—	4	1	no	—
327	C₂×C₃×C₉	—	4	1	no	—
328	C₂×C₃×C₉	—	4	1	no	—
329	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
330	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
332	D₃×C₉	—	4	1	no	—
333	C₂⁴×C₃	—	2	1	no	—
334	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
335	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
336	C₂×C₃×Q₈	—	3	1	no	—
337	C₂×C₃×D₄	—	2	1	no	—
338	C₂×C₃×D₄	—	2	1	no	—
339	C₂×C₃×D₄	—	2	1	no	—
340	C₂×C₃×D₄	—	3	1	no	—
341	C₂×C₃×D₄	—	3	1	no	—
342	C₂×C₃×D₄	—	3	1	no	—
343	C₂×C₃×D₄	—	3	1	no	—
344	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
345	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
346	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
347	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
348	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
349	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
350	C₂²×C₃×C₄	—	3	1	no	—
351	C₂²×C₃×C₄	—	3	1	no	—
352	C₂²×C₃×C₄	—	3	1	no	—
353	C₂²×C₃×C₄	—	3	1	no	—
354	C₂×#67	C₂²×C₉	1	1	yes	characteristic
355	C₂×#67	C₂²×C₉	1	1	yes	characteristic
356	C₂×#67	C₂²×C₉	1	1	yes	characteristic
357	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
358	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
359	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
360	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
361	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
362	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
363	C₃×C₄⋊C₄	—	3	1	no	—
364	C₃×C₄⋊C₄	—	3	1	no	—
365	C₃×C₄⋊C₄	—	3	1	no	—
366	C₃×C₄⋊C₄	—	3	1	no	—
367	C₃×C₄⋊C₄	—	3	1	no	—
368	C₃×C₄⋊C₄	—	3	1	no	—
369	C₃×C₂²⋊C₄	—	2	1	no	—
370	C₃×C₂²⋊C₄	—	2	1	no	—
371	C₃×C₂²⋊C₄	—	2	1	no	—
372	C₃×C₂²⋊C₄	—	3	1	no	—
373	C₃×C₂²⋊C₄	—	3	1	no	—
374	C₃×C₂²⋊C₄	—	3	1	no	—
375	C₃×C₂²⋊C₄	—	3	1	no	—
376	C₃×C₂²⋊C₄	—	3	1	no	—
377	C₃×C₂²⋊C₄	—	3	1	no	—
378	C₃×C₂²⋊C₄	—	3	1	no	—
379	C₃×C₂²⋊C₄	—	3	1	no	—
380	C₃×C₂²⋊C₄	—	3	1	no	—
381	C₃×C₂²⋊C₄	—	3	1	no	—
382	C₃×C₂²⋊C₄	—	3	1	no	—
383	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
384	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
385	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
386	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
387	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
388	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
389	C₃×C₄²	—	3	1	no	—
390	C₃×C₄²	—	3	1	no	—
391	#217	C₂²×C₉	1	1	yes	characteristic
392	#217	C₂²×C₉	1	1	yes	characteristic
393	#217	C₂²×C₉	1	1	yes	characteristic
394	#217	C₂²×C₉	1	1	yes	characteristic
395	#217	C₂²×C₉	1	1	yes	characteristic
396	#217	C₂²×C₉	1	1	yes	characteristic
397	#217	C₂²×C₉	1	1	yes	characteristic
398	#217	C₂²×C₉	1	1	yes	characteristic, complemented
399	#217	C₂²×C₉	1	1	yes	characteristic, complemented
400	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
401	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
402	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
403	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
404	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
405	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
406	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
407	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
408	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
409	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
410	C₂²×C₃²	—	2	1	no	—
411	C₂²×C₃²	—	2	1	no	—
412	C₂²×C₃²	—	2	1	no	—
413	C₂²×C₃²	—	2	1	no	—
414	C₂²×C₃²	—	2	1	no	—
415	C₂²×C₃²	—	2	1	no	—
416	C₂²×C₃²	—	2	1	no	—
417	C₂²×C₃²	—	2	1	no	—
418	C₂²×C₃²	—	2	1	no	—
419	C₂²×C₃²	—	2	1	no	—
420	C₂²×C₃²	—	2	1	no	—
421	C₂²×C₃²	—	4	4	no	—
422	C₂²×C₃²	C₃×#41	1	2	yes	—
423	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
424	C₂×C₃×D₃	—	2	1	no	—
425	C₂×C₃×D₃	—	2	1	no	—
426	C₂×C₃×D₃	—	2	1	no	—
427	C₃²×C₄	—	2	1	no	—
428	C₃²×C₄	—	2	1	no	—
429	C₃²×C₄	—	2	1	no	—
430	C₃×Dic₃	—	2	1	no	—
431	C₃×Dic₃	—	2	1	no	—
432	C₃×Dic₃	—	2	1	no	—
433	C₃×Dic₃	—	2	1	no	—
434	C₃×Dic₃	—	2	1	no	—
435	C₃×Dic₃	—	2	1	no	—
436	C₃×Dic₃	—	2	1	no	—
437	C₂²×C₉	—	2	1	no	—
438	C₂²×C₉	—	2	1	no	—
439	C₂²×C₉	—	2	2	no	—
440	C₂²×C₉	—	2	2	no	—
441	C₂²×C₉	—	2	1	no	—
442	C₂²×C₉	—	2	1	no	—
443	C₂²×C₉	—	2	1	no	—
444	C₂²×C₉	—	2	1	no	—
445	C₂²×C₉	—	2	1	no	—
446	C₂²×C₉	—	2	1	no	—
447	C₂²×C₉	—	2	1	no	—
448	C₂²×C₉	—	2	1	no	—
449	C₂²×C₉	—	2	1	no	—
450	C₂²×C₉	—	2	1	no	—
451	C₂²×C₉	—	2	2	no	—
452	C₂²×C₉	—	4	1	no	—
453	C₂²×C₉	—	4	1	no	—
454	C₂²×C₉	—	4	1	no	—
455	C₂²×C₉	—	4	1	no	—
456	C₂²×C₉	—	4	1	no	—
457	C₂²×C₉	—	4	1	no	—
458	C₂²×C₉	—	4	1	no	—
459	C₂²×C₉	—	4	1	no	—
460	C₂²×C₉	—	4	1	no	—
461	C₂²×C₉	—	4	4	no	—
462	C₂²×C₉	—	4	8	no	—
463	C₂²×C₉	—	6	1	no	—
464	C₂²×C₉	—	6	1	no	—
465	C₂²×C₉	—	6	1	no	—
466	C₂²×C₉	#237	1	2	yes	—
467	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
468	C₄×C₉	—	2	1	no	—
469	C₄×C₉	—	2	1	no	—
470	C₄×C₉	—	2	1	no	—
471	C₄×C₉	—	4	1	no	—
472	C₄×C₉	—	4	1	no	—
473	C₄×C₉	—	4	1	no	—
474	C₄×C₉	—	6	1	no	—
475	C₄×C₉	—	6	1	no	—
476	C₄×C₉	—	6	1	no	—
477	C₄×C₉	—	6	1	no	—
478	C₄×C₉	—	6	1	no	—
479	C₄×C₉	—	6	1	no	—
480	C₄×C₉	—	6	1	no	—
481	#126	—	3	1	no	—
482	#126	—	3	1	no	—
483	#124	—	3	1	no	—
484	#124	—	3	1	no	—
485	#123	—	3	1	no	—
486	#123	—	3	1	no	—
487	C₂²⋊Q₈	—	3	1	no	—
488	#121	—	3	1	no	—
489	#121	—	3	1	no	—
490	#121	—	3	1	no	—
491	#120	—	3	1	no	—
492	#120	D₃×C₉	1	1	yes	characteristic, complemented
493	C₄×D₄	—	3	1	no	—
494	C₄×D₄	—	3	1	no	—
495	C₂×C₂²⋊C₄	—	3	1	no	—
496	C₃×C₉	#538	1	1	yes	characteristic, complemented, Sylow
497	C₂³×C₃	—	2	2	no	—
498	C₂³×C₃	—	2	2	no	—
499	C₂³×C₃	—	2	1	no	—
500	C₂³×C₃	—	2	1	no	—
501	C₂³×C₃	—	2	1	no	—
502	C₂³×C₃	—	2	1	no	—
503	C₂³×C₃	—	3	1	no	—
504	C₂³×C₃	—	4	2	no	—
505	C₂³×C₃	—	4	1	no	—
506	C₂³×C₃	—	4	1	no	—
507	C₂³×C₃	—	4	1	no	—
508	C₂³×C₃	—	4	1	no	—
509	C₂³×C₃	—	4	2	no	—
510	C₂³×C₃	—	4	2	no	—
511	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
512	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
513	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
514	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
515	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
516	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
517	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
518	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
519	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
520	C₃×Q₈	—	12	1	no	—
521	C₃×D₄	—	2	2	no	—
522	C₃×D₄	—	2	2	no	—
523	C₃×D₄	—	4	2	no	—
524	C₃×D₄	—	4	1	no	—
525	C₃×D₄	—	4	1	no	—
526	C₃×D₄	—	4	1	no	—
527	C₃×D₄	—	4	1	no	—
528	C₃×D₄	—	4	2	no	—
529	C₃×D₄	—	4	2	no	—
530	C₃×D₄	—	6	2	no	—
531	C₃×D₄	—	12	1	no	—
532	C₃×D₄	—	12	1	no	—
533	C₃×D₄	—	12	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	1	no	—
537	C₂×C₃×C₄	—	3	1	no	—
538	C₂×C₃×C₄	—	3	1	no	—
539	C₂×C₃×C₄	—	3	1	no	—
540	C₂×C₃×C₄	—	3	1	no	—
541	C₂×C₃×C₄	—	3	1	no	—
542	C₂×C₃×C₄	—	3	1	no	—
543	C₂×C₃×C₄	—	3	1	no	—
544	C₂×C₃×C₄	—	12	1	no	—
545	C₂×C₃×C₄	—	12	1	no	—
546	C₂×C₃×C₄	—	12	1	no	—
547	C₂×C₃×C₄	—	12	1	no	—
548	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
549	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
550	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
551	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
552	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
553	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
554	#67	—	2	2	no	—
555	#67	—	4	1	no	—
556	#67	—	4	1	no	—
557	#67	—	4	1	no	—
558	C₂×Dic₃	—	4	1	no	—
559	C₂×Dic₃	—	4	1	no	—
560	C₂×Dic₃	—	4	1	no	—
561	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
562	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
563	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
564	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
565	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
566	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
567	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
568	C₄×D₃	—	4	1	no	—
569	Dic₆	—	4	1	no	—
570	C₂×C₃²	—	2	2	no	—
571	C₂×C₃²	—	4	1	no	—
572	C₂×C₃²	—	4	1	no	—
573	C₂×C₃²	—	4	1	no	—
574	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
575	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
577	C₃×D₃	—	4	1	no	—
578	C₂×C₉	—	2	2	no	—
579	C₂×C₉	—	2	1	no	—
580	C₂×C₉	—	2	1	no	—
581	C₂×C₉	—	2	1	no	—
582	C₂×C₉	—	4	2	no	—
583	C₂×C₉	—	4	2	no	—
584	C₂×C₉	—	4	2	no	—
585	C₂×C₉	—	4	1	no	—
586	C₂×C₉	—	4	1	no	—
587	C₂×C₉	—	4	1	no	—
588	C₂×C₉	—	8	1	no	—
589	C₂×C₉	—	12	1	no	—
590	C₂×C₉	C₂×#237	1	1	yes	characteristic
591	C₂×C₉	#1004	1	1	yes	characteristic
592	C₂×C₉	#1004	1	1	yes	characteristic
593	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
594	C₂×Q₈	—	3	1	no	—
595	C₂×D₄	—	3	1	no	—
596	C₂×D₄	—	3	1	no	—
597	C₂×D₄	—	3	1	no	—
598	C₂×D₄	—	3	1	no	—
599	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
600	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
601	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
602	C₂²×C₄	—	3	1	no	—
603	C₂²×C₄	—	3	1	no	—
604	C₂²×C₄	—	3	1	no	—
605	C₂²×C₄	—	3	1	no	—
606	C₄⋊C₄	—	3	1	no	—
607	C₄⋊C₄	—	3	1	no	—
608	C₄⋊C₄	—	3	1	no	—
609	C₄⋊C₄	—	3	1	no	—
610	C₄⋊C₄	—	3	1	no	—
611	C₄⋊C₄	—	3	1	no	—
612	C₂²⋊C₄	—	3	1	no	—
613	C₂²⋊C₄	—	3	1	no	—
614	C₂²⋊C₄	—	3	1	no	—
615	C₂²⋊C₄	—	3	1	no	—
616	C₂²⋊C₄	—	3	1	no	—
617	C₂²⋊C₄	—	3	1	no	—
618	C₂²⋊C₄	—	3	1	no	—
619	C₂²⋊C₄	—	3	1	no	—
620	C₂²⋊C₄	—	3	1	no	—
621	C₂²⋊C₄	—	3	1	no	—
622	C₂²⋊C₄	—	3	1	no	—
623	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
624	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
625	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
626	C₄²	—	3	1	no	—
627	C₄²	—	3	1	no	—
628	C₂²×C₃	—	2	1	no	—
629	C₂²×C₃	—	2	1	no	—
630	C₂²×C₃	—	2	1	no	—
631	C₂²×C₃	—	2	1	no	—
632	C₂²×C₃	—	2	2	no	—
633	C₂²×C₃	—	2	2	no	—
634	C₂²×C₃	—	2	1	no	—
635	C₂²×C₃	—	2	1	no	—
636	C₂²×C₃	—	2	1	no	—
637	C₂²×C₃	—	2	1	no	—
638	C₂²×C₃	—	2	1	no	—
639	C₂²×C₃	—	2	1	no	—
640	C₂²×C₃	—	2	1	no	—
641	C₂²×C₃	—	2	1	no	—
642	C₂²×C₃	—	2	1	no	—
643	C₂²×C₃	—	2	1	no	—
644	C₂²×C₃	—	2	1	no	—
645	C₂²×C₃	—	2	1	no	—
646	C₂²×C₃	—	2	1	no	—
647	C₂²×C₃	—	2	1	no	—
648	C₂²×C₃	—	2	1	no	—
649	C₂²×C₃	—	2	1	no	—
650	C₂²×C₃	—	2	1	no	—
651	C₂²×C₃	—	2	1	no	—
652	C₂²×C₃	—	2	1	no	—
653	C₂²×C₃	—	2	2	no	—
654	C₂²×C₃	—	4	1	no	—
655	C₂²×C₃	—	4	1	no	—
656	C₂²×C₃	—	4	1	no	—
657	C₂²×C₃	—	4	1	no	—
658	C₂²×C₃	—	4	1	no	—
659	C₂²×C₃	—	4	1	no	—
660	C₂²×C₃	—	4	1	no	—
661	C₂²×C₃	—	4	1	no	—
662	C₂²×C₃	—	4	1	no	—
663	C₂²×C₃	—	4	4	no	—
664	C₂²×C₃	—	4	4	no	—
665	C₂²×C₃	—	4	8	no	—
666	C₂²×C₃	—	6	1	no	—
667	C₂²×C₃	—	6	1	no	—
668	C₂²×C₃	—	6	1	no	—
669	C₂²×C₃	C₉×#41	1	2	yes	—
670	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
671	C₂²×C₃	C₃×#237	1	2	yes	—
672	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
673	C₂×D₃	—	2	1	no	—
674	C₂×D₃	—	2	1	no	—
675	C₂×D₃	—	2	1	no	—
676	C₃×C₄	—	2	1	no	—
677	C₃×C₄	—	2	1	no	—
678	C₃×C₄	—	2	1	no	—
679	C₃×C₄	—	2	1	no	—
680	C₃×C₄	—	2	1	no	—
681	C₃×C₄	—	2	1	no	—
682	C₃×C₄	—	4	1	no	—
683	C₃×C₄	—	4	1	no	—
684	C₃×C₄	—	4	1	no	—
685	C₃×C₄	—	6	1	no	—
686	C₃×C₄	—	6	1	no	—
687	C₃×C₄	—	6	1	no	—
688	C₃×C₄	—	6	1	no	—
689	C₃×C₄	—	6	1	no	—
690	C₃×C₄	—	6	1	no	—
691	C₃×C₄	—	6	1	no	—
692	Dic₃	—	2	1	no	—
693	Dic₃	—	2	1	no	—
694	Dic₃	—	2	1	no	—
695	Dic₃	—	2	1	no	—
696	Dic₃	—	2	1	no	—
697	Dic₃	—	2	1	no	—
698	Dic₃	—	2	1	no	—
699	C₃²	C₃×#538	1	1	yes	characteristic
700	C₉	—	2	1	no	—
701	C₉	#5593	1	1	yes	characteristic, direct product factor
702	C₂³	—	2	2	no	—
703	C₂³	—	3	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
707	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
708	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
709	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
710	Q₈	—	12	1	no	—
711	D₄	—	2	2	no	—
712	D₄	—	4	1	no	—
713	D₄	—	4	1	no	—
714	D₄	—	6	2	no	—
715	D₄	—	12	1	no	—
716	D₄	—	12	1	no	—
717	D₄	—	12	1	no	—
718	C₂×C₄	—	3	1	no	—
719	C₂×C₄	—	3	1	no	—
720	C₂×C₄	—	3	1	no	—
721	C₂×C₄	—	3	1	no	—
722	C₂×C₄	—	3	1	no	—
723	C₂×C₄	—	3	1	no	—
724	C₂×C₄	—	3	1	no	—
725	C₂×C₄	—	12	1	no	—
726	C₂×C₄	—	12	1	no	—
727	C₂×C₄	—	12	1	no	—
728	C₂×C₄	—	12	1	no	—
729	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
732	C₂×C₃	—	2	2	no	—
733	C₂×C₃	—	2	2	no	—
734	C₂×C₃	—	2	1	no	—
735	C₂×C₃	—	2	1	no	—
736	C₂×C₃	—	2	1	no	—
737	C₂×C₃	—	4	2	no	—
738	C₂×C₃	—	4	2	no	—
739	C₂×C₃	—	4	2	no	—
740	C₂×C₃	—	4	1	no	—
741	C₂×C₃	—	4	1	no	—
742	C₂×C₃	—	4	1	no	—
743	C₂×C₃	—	4	1	no	—
744	C₂×C₃	—	4	1	no	—
745	C₂×C₃	—	4	1	no	—
746	C₂×C₃	—	8	1	no	—
747	C₂×C₃	—	12	1	no	—
748	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
749	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
750	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
751	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
752	C₂×C₃	C₃×#1004	1	1	yes	characteristic
753	C₂×C₃	C₃×#1004	1	1	yes	characteristic
754	D₃	—	4	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	6	1	no	—
768	C₂²	—	6	1	no	—
769	C₂²	—	6	1	no	—
770	C₂²	C₉×#237	1	2	yes	—
771	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	1	no	—
775	C₄	—	6	1	no	—
776	C₄	—	6	1	no	—
777	C₄	—	6	1	no	—
778	C₄	—	6	1	no	—
779	C₄	—	6	1	no	—
780	C₄	—	6	1	no	—
781	C₄	—	6	1	no	—
782	C₃	—	2	1	no	—
783	C₃	C₉×#538	1	1	yes	characteristic, complemented
784	C₃	C₃×#5593	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	4	1	no	—
787	C₂	—	4	1	no	—
788	C₂	—	4	1	no	—
789	C₂	—	12	1	no	—
790	C₂	C₂×C₉×#237	1	1	yes	characteristic
791	C₂	C₉×#1004	1	1	yes	characteristic
792	C₂	C₉×#1004	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#120	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5593	C₃
hypercenter	C₉×#120	D₃
hypocenter	C₃	C₉×#538
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#120

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#120	C₂	semidirect
2. C₉×#953	C₂	semidirect
3. C₂×C₉×#217	C₂	semidirect
4. C₉×#939	C₂	semidirect
5. C₉×#939	C₂	semidirect
6. C₉×#938	C₂	semidirect
7. C₉×#936	C₂	semidirect
8. C₉×#935	C₂	semidirect
9. D₄×C₉×Dic₃	C₂	semidirect
10. C₉×#885	C₂	semidirect
11. C₉×#883	C₂	semidirect
12. C₉×#67⋊C₄	C₂	semidirect
13. C₉×#879	C₂	semidirect
14. C₉×#879	C₂	semidirect
15. C₉×#878	C₂	semidirect
25. C₂×C₉×#67	C₂²	semidirect
28. C₂²×C₉×Dic₃	C₂²	semidirect
29. C₂×C₄×D₃×C₉	C₂²	semidirect
30. C₂×C₉×Dic₆	C₂²	semidirect
41. C₉×#217	C₂²	semidirect
42. C₉×#217	C₂²	semidirect
43. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₉×C₄⋊Dic₃	C₂²	semidirect
46. C₉×C₄⋊Dic₃	C₂²	semidirect
47. C₉×Dic₃⋊C₄	C₂²	semidirect
48. C₉×Dic₃⋊C₄	C₂²	semidirect
49. C₉×Dic₃⋊C₄	C₂²	semidirect
50. C₉×Dic₃⋊C₄	C₂²	semidirect
51. C₄×C₉×Dic₃	C₂²	semidirect
52. C₄×C₉×Dic₃	C₂²	semidirect
80. C₉×#120	D₃	semidirect
115. #5593	C₉	direct (N × H)
232. C₃×#120	C₂×C₉	semidirect
237. #953	C₂×C₉	semidirect
238. C₂×#217	C₂×C₉	semidirect
239. #939	C₂×C₉	semidirect
240. #939	C₂×C₉	semidirect
241. #938	C₂×C₉	semidirect
242. #936	C₂×C₉	semidirect
243. #935	C₂×C₉	semidirect
244. D₄×Dic₃	C₂×C₉	semidirect
245. #885	C₂×C₉	semidirect
246. #883	C₂×C₉	semidirect
247. #67⋊C₄	C₂×C₉	semidirect
248. #879	C₂×C₉	semidirect
249. #879	C₂×C₉	semidirect
250. #878	C₂×C₉	semidirect
357. C₂×#67	C₂²×C₉	semidirect
360. C₂²×Dic₃	C₂²×C₉	semidirect
361. C₂×C₄×D₃	C₂²×C₉	semidirect
362. C₂×Dic₆	C₂²×C₉	semidirect
398. #217	C₂²×C₉	semidirect
399. #217	C₂²×C₉	semidirect
400. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
401. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
402. C₄⋊Dic₃	C₂²×C₉	semidirect
403. C₄⋊Dic₃	C₂²×C₉	semidirect
404. Dic₃⋊C₄	C₂²×C₉	semidirect
405. Dic₃⋊C₄	C₂²×C₉	semidirect
406. Dic₃⋊C₄	C₂²×C₉	semidirect
407. Dic₃⋊C₄	C₂²×C₉	semidirect
408. C₄×Dic₃	C₂²×C₉	semidirect
409. C₄×Dic₃	C₂²×C₉	semidirect
492. #120	D₃×C₉	semidirect
496. C₃×C₉	#538	semidirect
701. C₉	#5593	direct (N × H)
783. C₃	C₉×#538	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#120	2
C₉×#953	2
C₂×C₉×#217	2
C₉×#939	2
C₉×#938	2
C₉×#936	2
C₉×#935	2
D₄×C₉×Dic₃	2
C₉×#885	2
C₉×#883	2
C₉×#67⋊C₄	2
C₉×#879	2
C₉×#878	2
C₃×#5593	3
C₉×#538	3

Subgroups — C9×#5593 #13152764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5593 #13152764