Subgroups — C₉×#5701 #13153210

Order 1728.

636 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#126	C₂	1	1	yes	maximal, characteristic
2	C₉×#890	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#879	C₂	1	1	yes	maximal, characteristic
9	C₉×#879	C₂	1	1	yes	maximal, characteristic
10	C₉×#879	C₂	1	1	yes	maximal, characteristic
11	C₉×#878	C₂	1	1	yes	maximal, characteristic
12	C₉×#878	C₂	1	1	yes	maximal, characteristic
13	C₉×#877	C₂	1	1	yes	maximal, characteristic
14	C₉×#870	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5701	C₃	1	1	yes	maximal, characteristic
17	C₉×#541	—	3	1	no	maximal
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
20	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₉×#217	C₂²	1	1	yes	characteristic
29	C₉×#217	C₂²	1	1	yes	characteristic
30	C₉×#217	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
35	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
36	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
39	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
49	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
50	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
51	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
52	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
53	C₃²×#126	C₂×C₃	1	1	yes	characteristic
54	C₃×#890	C₂×C₃	1	1	yes	characteristic
55	C₃×#889	C₂×C₃	1	1	yes	characteristic
56	C₃×#889	C₂×C₃	1	1	yes	characteristic
57	C₃×#889	C₂×C₃	1	1	yes	characteristic
58	C₃×#888	C₂×C₃	1	1	yes	characteristic
59	C₃×#887	C₂×C₃	1	1	yes	characteristic
60	C₃×#879	C₂×C₃	1	1	yes	characteristic
61	C₃×#879	C₂×C₃	1	1	yes	characteristic
62	C₃×#879	C₂×C₃	1	1	yes	characteristic
63	C₃×#878	C₂×C₃	1	1	yes	characteristic
64	C₃×#878	C₂×C₃	1	1	yes	characteristic
65	C₃×#877	C₂×C₃	1	1	yes	characteristic
66	C₃×#870	C₂×C₃	1	1	yes	characteristic
67	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
68	C₉×C₄⋊Q₈	—	3	1	no	—
69	C₉×#126	—	2	1	no	—
70	C₉×#126	—	3	1	no	—
71	C₉×#126	—	3	1	no	—
72	C₉×#126	—	3	1	no	—
73	C₉×#126	D₃	1	1	yes	characteristic
74	C₉×#125	—	3	1	no	—
75	C₉×#125	—	3	1	no	—
76	C₉×#125	—	3	1	no	—
77	C₉×#125	—	3	1	no	—
78	C₉×#125	—	3	1	no	—
79	C₉×C₂²⋊Q₈	—	3	1	no	—
80	C₉×C₂²⋊Q₈	—	3	1	no	—
81	C₄×Q₈×C₉	—	3	1	no	—
82	C₄×Q₈×C₉	—	3	1	no	—
83	C₉×#117	—	3	1	no	—
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₉×Dic₃	—	2	2	no	—
92	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
93	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
95	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
96	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
97	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
99	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
100	C₉×Dic₆	—	2	2	no	—
101	C₉×Dic₆	—	2	2	no	—
102	C₃×#541	—	3	1	no	—
103	#5701	C₉	1	1	yes	characteristic, direct product factor
104	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
107	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
114	C₃×#217	C₂²×C₃	1	1	yes	characteristic
115	C₃×#217	C₂²×C₃	1	1	yes	characteristic
116	C₃×#217	C₂²×C₃	1	1	yes	characteristic
117	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
118	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
119	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
121	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
122	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
135	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
136	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
137	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
138	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
139	C₂×Q₈×C₉	—	3	1	no	—
140	C₂×Q₈×C₉	—	3	1	no	—
141	C₂²×C₄×C₉	—	3	1	no	—
142	C₉×C₄⋊C₄	—	2	1	no	—
143	C₉×C₄⋊C₄	—	2	1	no	—
144	C₉×C₄⋊C₄	—	2	1	no	—
145	C₉×C₄⋊C₄	—	3	1	no	—
146	C₉×C₄⋊C₄	—	3	1	no	—
147	C₉×C₄⋊C₄	—	3	1	no	—
148	C₉×C₄⋊C₄	—	3	1	no	—
149	C₉×C₄⋊C₄	—	3	1	no	—
150	C₉×C₄⋊C₄	—	3	1	no	—
151	C₉×C₄⋊C₄	—	3	1	no	—
152	C₉×C₄⋊C₄	—	3	1	no	—
153	C₉×C₄⋊C₄	—	3	1	no	—
154	C₉×C₄⋊C₄	—	3	1	no	—
155	C₉×C₄⋊C₄	—	3	1	no	—
156	C₉×C₄⋊C₄	—	3	1	no	—
157	C₉×C₄⋊C₄	—	3	1	no	—
158	C₉×C₄⋊C₄	—	3	1	no	—
159	C₉×C₄⋊C₄	—	3	1	no	—
160	C₉×C₄⋊C₄	—	3	1	no	—
161	C₉×C₄⋊C₄	—	3	1	no	—
162	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
163	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
164	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
165	C₉×C₂²⋊C₄	—	2	1	no	—
166	C₉×C₂²⋊C₄	—	2	1	no	—
167	C₉×C₂²⋊C₄	—	2	1	no	—
168	C₉×C₂²⋊C₄	—	3	1	no	—
169	C₉×C₂²⋊C₄	—	3	1	no	—
170	C₉×C₂²⋊C₄	—	3	1	no	—
171	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
172	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
173	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
174	C₄²×C₉	—	2	1	no	—
175	C₄²×C₉	—	3	1	no	—
176	C₄²×C₉	—	3	1	no	—
177	C₄²×C₉	—	3	1	no	—
178	C₄²×C₉	—	3	1	no	—
179	C₄²×C₉	—	3	1	no	—
180	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
181	C₂²×C₃×C₉	—	2	1	no	—
182	C₂²×C₃×C₉	—	2	1	no	—
183	C₂²×C₃×C₉	—	2	1	no	—
184	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
185	C₃×C₄×C₉	—	2	1	no	—
186	C₃×C₄×C₉	—	2	1	no	—
187	C₃×C₄×C₉	—	2	1	no	—
188	C₃×C₄×C₉	—	2	1	no	—
189	C₃×C₄×C₉	—	2	1	no	—
190	C₃×C₄×C₉	—	2	1	no	—
191	C₉×Dic₃	—	2	1	no	—
192	C₉×Dic₃	—	2	1	no	—
193	C₉×Dic₃	—	2	1	no	—
194	C₉×Dic₃	—	2	1	no	—
195	C₉×Dic₃	—	2	1	no	—
196	C₉×Dic₃	—	2	1	no	—
197	C₉×Dic₃	—	2	1	no	—
198	C₉×Dic₃	#41	1	2	yes	—
199	C₃×C₄⋊Q₈	—	3	1	no	—
200	C₃×#126	—	2	1	no	—
201	C₃×#126	—	3	1	no	—
202	C₃×#126	—	3	1	no	—
203	C₃×#126	—	3	1	no	—
204	C₃×#126	C₂×C₉	1	1	yes	characteristic
205	C₃×#126	C₃×D₃	1	1	yes	characteristic
206	C₃×#125	—	3	1	no	—
207	C₃×#125	—	3	1	no	—
208	C₃×#125	—	3	1	no	—
209	C₃×#125	—	3	1	no	—
210	C₃×#125	—	3	1	no	—
211	C₃×C₂²⋊Q₈	—	3	1	no	—
212	C₃×C₂²⋊Q₈	—	3	1	no	—
213	C₃×C₄×Q₈	—	3	1	no	—
214	C₃×C₄×Q₈	—	3	1	no	—
215	C₃×#117	—	3	1	no	—
216	#890	C₂×C₉	1	1	yes	characteristic, complemented
217	#889	C₂×C₉	1	1	yes	characteristic, complemented
218	#889	C₂×C₉	1	1	yes	characteristic, complemented
219	#889	C₂×C₉	1	1	yes	characteristic, complemented
220	#888	C₂×C₉	1	1	yes	characteristic, complemented
221	#887	C₂×C₉	1	1	yes	characteristic, complemented
222	#879	C₂×C₉	1	1	yes	characteristic
223	#879	C₂×C₉	1	1	yes	characteristic
224	#879	C₂×C₉	1	1	yes	characteristic
225	#878	C₂×C₉	1	1	yes	characteristic
226	#878	C₂×C₉	1	1	yes	characteristic
227	#877	C₂×C₉	1	1	yes	characteristic
228	#870	C₂×C₉	1	1	yes	characteristic, complemented
229	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
230	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
232	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
233	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
234	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
235	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
236	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₃×Dic₃	—	2	2	no	—
238	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
240	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
246	C₃×Dic₆	—	2	2	no	—
247	C₃×Dic₆	—	2	2	no	—
248	C₂³×C₉	—	2	1	no	—
249	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
250	Q₈×C₉	—	6	2	no	—
251	Q₈×C₉	—	6	2	no	—
252	C₂×C₄×C₉	—	2	1	no	—
253	C₂×C₄×C₉	—	2	1	no	—
254	C₂×C₄×C₉	—	2	1	no	—
255	C₂×C₄×C₉	—	2	1	no	—
256	C₂×C₄×C₉	—	2	1	no	—
257	C₂×C₄×C₉	—	2	1	no	—
258	C₂×C₄×C₉	—	3	1	no	—
259	C₂×C₄×C₉	—	3	1	no	—
260	C₂×C₄×C₉	—	3	1	no	—
261	C₂×C₄×C₉	—	3	1	no	—
262	C₂×C₄×C₉	—	3	1	no	—
263	C₂×C₄×C₉	—	3	1	no	—
264	C₂×C₄×C₉	—	3	1	no	—
265	C₂×C₄×C₉	—	3	1	no	—
266	C₂×C₄×C₉	—	6	2	no	—
267	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
269	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
271	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
272	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
273	#541	—	3	1	no	Sylow
274	C₂×C₃×C₉	—	4	1	no	—
275	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
277	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
278	C₂×C₃×Q₈	—	3	1	no	—
279	C₂×C₃×Q₈	—	3	1	no	—
280	C₂²×C₃×C₄	—	3	1	no	—
281	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
282	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
283	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
284	C₃×C₄⋊C₄	—	2	1	no	—
285	C₃×C₄⋊C₄	—	2	1	no	—
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	—	3	1	no	—
288	C₃×C₄⋊C₄	—	3	1	no	—
289	C₃×C₄⋊C₄	—	3	1	no	—
290	C₃×C₄⋊C₄	—	3	1	no	—
291	C₃×C₄⋊C₄	—	3	1	no	—
292	C₃×C₄⋊C₄	—	3	1	no	—
293	C₃×C₄⋊C₄	—	3	1	no	—
294	C₃×C₄⋊C₄	—	3	1	no	—
295	C₃×C₄⋊C₄	—	3	1	no	—
296	C₃×C₄⋊C₄	—	3	1	no	—
297	C₃×C₄⋊C₄	—	3	1	no	—
298	C₃×C₄⋊C₄	—	3	1	no	—
299	C₃×C₄⋊C₄	—	3	1	no	—
300	C₃×C₄⋊C₄	—	3	1	no	—
301	C₃×C₄⋊C₄	—	3	1	no	—
302	C₃×C₄⋊C₄	—	3	1	no	—
303	C₃×C₄⋊C₄	—	3	1	no	—
304	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
306	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
308	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
309	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
310	C₃×C₂²⋊C₄	—	2	1	no	—
311	C₃×C₂²⋊C₄	—	2	1	no	—
312	C₃×C₂²⋊C₄	—	2	1	no	—
313	C₃×C₂²⋊C₄	—	3	1	no	—
314	C₃×C₂²⋊C₄	—	3	1	no	—
315	C₃×C₂²⋊C₄	—	3	1	no	—
316	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
317	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
318	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
319	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
320	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
321	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
322	C₃×C₄²	—	2	1	no	—
323	C₃×C₄²	—	3	1	no	—
324	C₃×C₄²	—	3	1	no	—
325	C₃×C₄²	—	3	1	no	—
326	C₃×C₄²	—	3	1	no	—
327	C₃×C₄²	—	3	1	no	—
328	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
329	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
330	#217	C₂²×C₉	1	1	yes	characteristic
331	#217	C₂²×C₉	1	1	yes	characteristic
332	#217	C₂²×C₉	1	1	yes	characteristic
333	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
334	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
335	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
336	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
337	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
338	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
339	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
340	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
341	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
342	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
343	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
344	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
345	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
346	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
347	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
348	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
349	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
350	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
351	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
352	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
353	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
354	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
355	C₂²×C₃²	—	2	1	no	—
356	C₂²×C₃²	—	2	1	no	—
357	C₂²×C₃²	—	2	1	no	—
358	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
359	C₃²×C₄	—	2	1	no	—
360	C₃²×C₄	—	2	1	no	—
361	C₃²×C₄	—	2	1	no	—
362	C₃²×C₄	—	2	1	no	—
363	C₃²×C₄	—	2	1	no	—
364	C₃²×C₄	—	2	1	no	—
365	C₃×Dic₃	—	2	1	no	—
366	C₃×Dic₃	—	2	1	no	—
367	C₃×Dic₃	—	2	1	no	—
368	C₃×Dic₃	—	2	1	no	—
369	C₃×Dic₃	—	2	1	no	—
370	C₃×Dic₃	—	2	1	no	—
371	C₃×Dic₃	—	2	1	no	—
372	C₃×Dic₃	C₃×#41	1	2	yes	—
373	C₂²×C₉	—	2	1	no	—
374	C₂²×C₉	—	2	1	no	—
375	C₂²×C₉	—	2	1	no	—
376	C₂²×C₉	—	2	1	no	—
377	C₂²×C₉	—	4	1	no	—
378	C₂²×C₉	—	4	1	no	—
379	C₂²×C₉	—	4	1	no	—
380	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
381	C₄×C₉	—	2	1	no	—
382	C₄×C₉	—	2	1	no	—
383	C₄×C₉	—	2	1	no	—
384	C₄×C₉	—	2	1	no	—
385	C₄×C₉	—	2	1	no	—
386	C₄×C₉	—	2	1	no	—
387	C₄×C₉	—	3	2	no	—
388	C₄×C₉	—	4	1	no	—
389	C₄×C₉	—	4	1	no	—
390	C₄×C₉	—	4	1	no	—
391	C₄×C₉	—	4	1	no	—
392	C₄×C₉	—	4	1	no	—
393	C₄×C₉	—	4	1	no	—
394	C₄×C₉	—	6	1	no	—
395	C₄×C₉	—	6	1	no	—
396	C₄×C₉	—	6	1	no	—
397	C₄×C₉	—	6	1	no	—
398	C₄×C₉	—	6	1	no	—
399	C₄×C₉	—	6	1	no	—
400	C₄×C₉	—	6	1	no	—
401	C₄⋊Q₈	—	3	1	no	—
402	#126	—	3	1	no	—
403	#126	—	3	1	no	—
404	#126	—	3	1	no	—
405	#126	D₃×C₉	1	1	yes	characteristic
406	#125	—	3	1	no	—
407	#125	—	3	1	no	—
408	#125	—	3	1	no	—
409	#125	—	3	1	no	—
410	#125	—	3	1	no	—
411	C₂²⋊Q₈	—	3	1	no	—
412	C₂²⋊Q₈	—	3	1	no	—
413	C₄×Q₈	—	3	1	no	—
414	C₄×Q₈	—	3	1	no	—
415	#117	—	3	1	no	—
416	C₃×C₉	#541	1	1	yes	characteristic, complemented, Sylow
417	C₂³×C₃	—	2	1	no	—
418	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
419	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
420	C₃×Q₈	—	6	2	no	—
421	C₃×Q₈	—	6	2	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	1	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	3	1	no	—
429	C₂×C₃×C₄	—	3	1	no	—
430	C₂×C₃×C₄	—	3	1	no	—
431	C₂×C₃×C₄	—	3	1	no	—
432	C₂×C₃×C₄	—	3	1	no	—
433	C₂×C₃×C₄	—	3	1	no	—
434	C₂×C₃×C₄	—	3	1	no	—
435	C₂×C₃×C₄	—	3	1	no	—
436	C₂×C₃×C₄	—	6	2	no	—
437	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
440	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
442	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
444	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
445	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
446	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
447	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
448	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
449	C₂×Dic₃	—	2	2	no	—
450	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
451	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
452	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
453	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
454	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
455	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
456	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
457	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
458	Dic₆	—	2	2	no	—
459	Dic₆	—	2	2	no	—
460	C₂×C₃²	—	4	1	no	—
461	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
462	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
464	C₂×C₉	—	2	1	no	—
465	C₂×C₉	—	2	1	no	—
466	C₂×C₉	—	2	1	no	—
467	C₂×C₉	—	4	1	no	—
468	C₂×C₉	—	8	1	no	—
469	C₂×C₉	D₃×#41	1	1	yes	characteristic
470	C₂×C₉	#1010	1	1	yes	characteristic
471	C₂×C₉	#1010	1	1	yes	characteristic
472	C₂×Q₈	—	3	1	no	—
473	C₂×Q₈	—	3	1	no	—
474	C₂²×C₄	—	3	1	no	—
475	C₄⋊C₄	—	3	1	no	—
476	C₄⋊C₄	—	3	1	no	—
477	C₄⋊C₄	—	3	1	no	—
478	C₄⋊C₄	—	3	1	no	—
479	C₄⋊C₄	—	3	1	no	—
480	C₄⋊C₄	—	3	1	no	—
481	C₄⋊C₄	—	3	1	no	—
482	C₄⋊C₄	—	3	1	no	—
483	C₄⋊C₄	—	3	1	no	—
484	C₄⋊C₄	—	3	1	no	—
485	C₄⋊C₄	—	3	1	no	—
486	C₄⋊C₄	—	3	1	no	—
487	C₄⋊C₄	—	3	1	no	—
488	C₄⋊C₄	—	3	1	no	—
489	C₄⋊C₄	—	3	1	no	—
490	C₄⋊C₄	—	3	1	no	—
491	C₄⋊C₄	—	3	1	no	—
492	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
495	C₂²⋊C₄	—	3	1	no	—
496	C₂²⋊C₄	—	3	1	no	—
497	C₂²⋊C₄	—	3	1	no	—
498	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
499	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
500	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
501	C₄²	—	3	1	no	—
502	C₄²	—	3	1	no	—
503	C₄²	—	3	1	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	1	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
518	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
519	C₃×C₄	—	2	1	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	2	1	no	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	3	2	no	—
532	C₃×C₄	—	4	1	no	—
533	C₃×C₄	—	4	1	no	—
534	C₃×C₄	—	4	1	no	—
535	C₃×C₄	—	4	1	no	—
536	C₃×C₄	—	4	1	no	—
537	C₃×C₄	—	4	1	no	—
538	C₃×C₄	—	6	1	no	—
539	C₃×C₄	—	6	1	no	—
540	C₃×C₄	—	6	1	no	—
541	C₃×C₄	—	6	1	no	—
542	C₃×C₄	—	6	1	no	—
543	C₃×C₄	—	6	1	no	—
544	C₃×C₄	—	6	1	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	—	2	1	no	—
547	Dic₃	—	2	1	no	—
548	Dic₃	—	2	1	no	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	2	1	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	C₉×#41	1	2	yes	—
553	C₃²	C₃×#541	1	1	yes	characteristic
554	C₉	—	2	1	no	—
555	C₉	#5701	1	1	yes	characteristic, direct product factor
556	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
557	Q₈	—	6	2	no	—
558	Q₈	—	6	2	no	—
559	C₂×C₄	—	3	1	no	—
560	C₂×C₄	—	3	1	no	—
561	C₂×C₄	—	3	1	no	—
562	C₂×C₄	—	3	1	no	—
563	C₂×C₄	—	3	1	no	—
564	C₂×C₄	—	3	1	no	—
565	C₂×C₄	—	3	1	no	—
566	C₂×C₄	—	3	1	no	—
567	C₂×C₄	—	6	2	no	—
568	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
574	C₂×C₃	—	2	1	no	—
575	C₂×C₃	—	2	1	no	—
576	C₂×C₃	—	2	1	no	—
577	C₂×C₃	—	4	1	no	—
578	C₂×C₃	—	4	1	no	—
579	C₂×C₃	—	8	1	no	—
580	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
581	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
582	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
583	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
584	C₂×C₃	C₃×#1010	1	1	yes	characteristic
585	C₂×C₃	C₃×#1010	1	1	yes	characteristic
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	3	2	no	—
597	C₄	—	6	1	no	—
598	C₄	—	6	1	no	—
599	C₄	—	6	1	no	—
600	C₄	—	6	1	no	—
601	C₄	—	6	1	no	—
602	C₄	—	6	1	no	—
603	C₄	—	6	1	no	—
604	C₃	—	2	1	no	—
605	C₃	C₉×#541	1	1	yes	characteristic, complemented
606	C₃	C₃×#5701	1	1	yes	characteristic
607	C₂	—	4	1	no	—
608	C₂	D₃×C₉×#41	1	1	yes	characteristic
609	C₂	C₉×#1010	1	1	yes	characteristic
610	C₂	C₉×#1010	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×#126	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂³×C₃²	C₂³×C₃
hypercenter	C₉×#126	D₃
hypocenter	C₃	C₉×#541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#126

Complements

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

N	H ≅ G/N	type
2. C₉×#890	C₂	semidirect
3. C₉×#889	C₂	semidirect
4. C₉×#889	C₂	semidirect
5. C₉×#889	C₂	semidirect
6. C₉×#888	C₂	semidirect
7. C₉×#887	C₂	semidirect
14. C₉×#870	C₂	semidirect
15. C₄×C₉×Dic₆	C₂	semidirect
103. #5701	C₉	direct (N × H)
216. #890	C₂×C₉	semidirect
217. #889	C₂×C₉	semidirect
218. #889	C₂×C₉	semidirect
219. #889	C₂×C₉	semidirect
220. #888	C₂×C₉	semidirect
221. #887	C₂×C₉	semidirect
228. #870	C₂×C₉	semidirect
229. C₄×Dic₆	C₂×C₉	semidirect
416. C₃×C₉	#541	semidirect
555. C₉	#5701	direct (N × H)
605. C₃	C₉×#541	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#126	2
C₉×#890	2
C₉×#889	2
C₉×#888	2
C₉×#887	2
C₉×#879	2
C₉×#878	2
C₉×#877	2
C₉×#870	2
C₄×C₉×Dic₆	2
C₃×#5701	3
C₉×#541	3

Subgroups — C9×#5701 #13153210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5701 #13153210