Subgroups — C₉×#4806 #13141885

Order 1728.

516 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#204	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#895	C₂	1	1	yes	maximal, characteristic
5	C₃×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4806	C₃	1	1	yes	maximal, characteristic
9	C₉×#448	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	D₃×Q₈×C₉	—	2	2	no	—
12	D₃×Q₈×C₉	—	2	2	no	—
13	C₂×C₉×D₁₂	—	2	1	no	—
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	—	2	1	no	—
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×Dic₆	—	2	1	no	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₉×#215	—	2	2	no	—
22	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
23	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₉×#204	—	2	2	no	—
25	C₂×C₃×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#215	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×#204	C₂×C₃	1	1	yes	characteristic
28	C₃×#895	C₂×C₃	1	1	yes	characteristic
29	C₂²×Q₈×C₉	—	3	1	no	—
30	C₃²×#103	C₂×C₃	1	1	yes	characteristic
31	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
32	C₃×#810	C₂×C₃	1	1	yes	characteristic
33	C₂×C₉×SD₁₆	—	3	1	no	—
34	C₂×C₉×SD₁₆	—	3	1	no	—
35	C₉×#121	—	3	1	no	—
36	C₉×#103	—	2	1	no	—
37	C₉×#103	—	3	1	no	—
38	C₉×#103	D₃	1	1	yes	characteristic, complemented
39	C₉×C₂²⋊C₈	—	3	1	no	—
40	C₂²×D₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
42	C₃×Q₈×C₉	—	2	1	no	—
43	C₃×Q₈×C₉	D₄	1	2	yes	complemented
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	—	2	1	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
47	C₂×C₉×Dic₃	—	2	1	no	—
48	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
49	C₉×D₁₂	—	2	1	no	—
50	C₉×D₁₂	—	2	1	no	—
51	C₉×D₁₂	—	4	2	no	—
52	C₄×D₃×C₉	—	2	4	no	—
53	C₄×D₃×C₉	—	2	1	no	—
54	C₄×D₃×C₉	—	2	1	no	—
55	C₉×Dic₆	—	2	4	no	—
56	C₉×Dic₆	—	2	1	no	—
57	C₉×Dic₆	D₄	1	2	yes	complemented
58	C₃×C₈×C₉	—	2	1	no	—
59	C₉×C₃⋊C₈	—	2	1	no	—
60	C₃×#448	—	3	1	no	—
61	#4806	C₉	1	1	yes	characteristic, direct product factor
62	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
63	C₃×D₃×Q₈	—	2	2	no	—
64	C₃×D₃×Q₈	—	2	2	no	—
65	C₂×C₃×D₁₂	—	2	1	no	—
66	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃×C₄×D₃	—	2	1	no	—
68	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×Dic₆	—	2	1	no	—
70	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
72	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
73	C₃×#215	—	2	2	no	—
74	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
75	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
76	C₃×#204	—	2	2	no	—
77	C₂×Q₈×C₉	—	2	1	no	—
78	C₂×Q₈×C₉	—	3	1	no	—
79	C₂×Q₈×C₉	—	6	1	no	—
80	C₂×Q₈×C₉	—	6	2	no	—
81	C₂×Q₈×C₉	—	6	2	no	—
82	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
83	C₂×D₄×C₉	—	3	1	no	—
84	C₂×D₄×C₉	—	6	1	no	—
85	C₂²×C₄×C₉	—	3	1	no	—
86	C₂²×C₄×C₉	—	6	1	no	—
87	C₉×SD₁₆	—	6	2	no	—
88	C₉×SD₁₆	—	6	2	no	—
89	C₂×C₈×C₉	—	2	1	no	—
90	C₂×C₈×C₉	—	3	1	no	—
91	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
92	C₉×C₄⋊C₄	—	2	1	no	—
93	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
94	C₉×C₂²⋊C₄	—	6	1	no	—
95	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
96	C₂×D₃×C₉	—	2	1	no	—
97	C₂×D₃×C₉	—	2	1	no	—
98	C₂×D₃×C₉	—	4	1	no	—
99	C₂×D₃×C₉	—	4	1	no	—
100	C₂×D₃×C₉	—	4	1	no	—
101	C₂×D₃×C₉	SD₁₆	1	2	yes	complemented
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	—	4	1	no	—
104	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
105	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
106	C₉×Dic₃	—	2	1	no	—
107	C₉×Dic₃	—	2	2	no	—
108	C₂²×C₃×Q₈	—	3	1	no	—
109	C₂×D₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
110	C₂×C₃×SD₁₆	—	3	1	no	—
111	C₂×C₃×SD₁₆	—	3	1	no	—
112	C₃×#121	—	3	1	no	—
113	C₂×#215	C₂×C₉	1	1	yes	characteristic, complemented
114	C₂×#204	C₂×C₉	1	1	yes	characteristic, complemented
115	#895	C₂×C₉	1	1	yes	characteristic
116	C₃×#103	—	2	1	no	—
117	C₃×#103	—	3	1	no	—
118	C₃×#103	C₂×C₉	1	1	yes	characteristic, complemented
119	C₃×#103	C₃×D₃	1	1	yes	characteristic
120	C₃×C₂²⋊C₈	—	3	1	no	—
121	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
122	#810	C₂×C₉	1	1	yes	characteristic, complemented
123	C₂²×C₃×D₃	—	2	1	no	—
124	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
125	C₃²×Q₈	—	2	1	no	—
126	C₃²×Q₈	C₃×D₄	1	2	yes	—
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	1	no	—
129	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
130	C₂×C₃×Dic₃	—	2	1	no	—
131	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
132	C₃×D₁₂	—	2	1	no	—
133	C₃×D₁₂	—	2	1	no	—
134	C₃×D₁₂	—	4	2	no	—
135	C₃×C₄×D₃	—	2	4	no	—
136	C₃×C₄×D₃	—	2	1	no	—
137	C₃×C₄×D₃	—	2	1	no	—
138	C₃×Dic₆	—	2	4	no	—
139	C₃×Dic₆	—	2	1	no	—
140	C₃×Dic₆	C₃×D₄	1	2	yes	—
141	C₂³×C₉	—	3	1	no	—
142	C₂³×C₉	—	6	1	no	—
143	C₃²×C₈	—	2	1	no	—
144	C₃×C₃⋊C₈	—	2	1	no	—
145	Q₈×C₉	—	2	1	no	—
146	Q₈×C₉	—	2	2	no	—
147	Q₈×C₉	—	3	2	no	—
148	Q₈×C₉	—	4	1	no	—
149	Q₈×C₉	—	6	4	no	—
150	Q₈×C₉	—	6	1	no	—
151	Q₈×C₉	D₁₂	1	2	yes	complemented
152	D₄×C₉	—	6	1	no	—
153	D₄×C₉	—	6	1	no	—
154	D₄×C₉	—	12	2	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	—	3	1	no	—
159	C₂×C₄×C₉	—	4	1	no	—
160	C₂×C₄×C₉	—	4	1	no	—
161	C₂×C₄×C₉	—	6	4	no	—
162	C₂×C₄×C₉	—	6	1	no	—
163	C₂×C₄×C₉	—	6	1	no	—
164	C₂×C₄×C₉	—	6	1	no	—
165	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
166	C₈×C₉	—	2	1	no	—
167	C₈×C₉	—	4	1	no	—
168	C₈×C₉	—	6	1	no	—
169	#448	—	3	1	no	Sylow
170	C₂×C₃×C₉	#120	1	1	yes	characteristic
171	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₃×C₉	#137	1	1	yes	characteristic
173	D₃×C₉	—	2	2	no	—
174	D₃×C₉	—	8	1	no	—
175	C₂×C₃×Q₈	—	2	1	no	—
176	C₂×C₃×Q₈	—	3	1	no	—
177	C₂×C₃×Q₈	—	6	1	no	—
178	C₂×C₃×Q₈	—	6	2	no	—
179	C₂×C₃×Q₈	—	6	2	no	—
180	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
181	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
182	C₂×C₃×D₄	—	3	1	no	—
183	C₂×C₃×D₄	—	6	1	no	—
184	C₂²×C₃×C₄	—	3	1	no	—
185	C₂²×C₃×C₄	—	6	1	no	—
186	D₃×Q₈	—	2	2	no	—
187	D₃×Q₈	—	2	2	no	—
188	C₂×D₁₂	—	2	1	no	—
189	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
190	C₂×C₄×D₃	—	2	1	no	—
191	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
192	C₂×Dic₆	—	2	1	no	—
193	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
194	C₃×SD₁₆	—	6	2	no	—
195	C₃×SD₁₆	—	6	2	no	—
196	C₂×C₃×C₈	—	2	1	no	—
197	C₂×C₃×C₈	—	3	1	no	—
198	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
199	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
200	C₃×C₄⋊C₄	—	2	1	no	—
201	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
202	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	—	6	1	no	—
204	#215	—	2	2	no	—
205	(C₂×D₃)⋊C₄	—	2	1	no	—
206	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
207	#204	—	2	2	no	—
208	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
209	C₂×C₃×D₃	—	2	1	no	—
210	C₂×C₃×D₃	—	2	1	no	—
211	C₂×C₃×D₃	—	4	1	no	—
212	C₂×C₃×D₃	—	4	1	no	—
213	C₂×C₃×D₃	—	4	1	no	—
214	C₂×C₃×D₃	C₃×SD₁₆	1	2	yes	—
215	C₃²×C₄	—	2	2	no	—
216	C₃²×C₄	—	4	1	no	—
217	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
218	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
219	C₃×Dic₃	—	2	1	no	—
220	C₃×Dic₃	—	2	2	no	—
221	C₂²×C₉	—	2	1	no	—
222	C₂²×C₉	—	3	2	no	—
223	C₂²×C₉	—	6	1	no	—
224	C₂²×C₉	—	6	1	no	—
225	C₂²×C₉	—	12	1	no	—
226	C₂²×C₉	—	12	1	no	—
227	C₂²×C₉	—	12	1	no	—
228	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
229	C₄×C₉	—	2	2	no	—
230	C₄×C₉	—	2	1	no	—
231	C₄×C₉	—	2	1	no	—
232	C₄×C₉	—	4	2	no	—
233	C₄×C₉	—	4	1	no	—
234	C₄×C₉	—	6	1	no	—
235	C₄×C₉	—	6	2	no	—
236	C₄×C₉	—	8	1	no	—
237	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
238	C₄×C₉	D₃×D₄	1	1	yes	characteristic
239	C₂²×Q₈	—	3	1	no	—
240	C₂×SD₁₆	—	3	1	no	—
241	C₂×SD₁₆	—	3	1	no	—
242	#121	—	3	1	no	—
243	#103	—	3	1	no	—
244	#103	D₃×C₉	1	1	yes	characteristic, complemented
245	C₂²⋊C₈	—	3	1	no	—
246	C₃×C₉	#448	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₃	—	3	1	no	—
248	C₂³×C₃	—	6	1	no	—
249	C₂²×D₃	—	2	1	no	—
250	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
251	C₃×Q₈	—	2	1	no	—
252	C₃×Q₈	—	2	1	no	—
253	C₃×Q₈	—	2	2	no	—
254	C₃×Q₈	—	3	2	no	—
255	C₃×Q₈	—	4	1	no	—
256	C₃×Q₈	—	6	4	no	—
257	C₃×Q₈	—	6	1	no	—
258	C₃×Q₈	D₄×C₉	1	2	yes	complemented
259	C₃×Q₈	C₃×D₁₂	1	2	yes	—
260	C₃×D₄	—	6	1	no	—
261	C₃×D₄	—	6	1	no	—
262	C₃×D₄	—	12	2	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	3	1	no	—
269	C₂×C₃×C₄	—	4	1	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	6	4	no	—
272	C₂×C₃×C₄	—	6	1	no	—
273	C₂×C₃×C₄	—	6	1	no	—
274	C₂×C₃×C₄	—	6	1	no	—
275	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
277	C₂×Dic₃	—	2	1	no	—
278	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
279	D₁₂	—	2	1	no	—
280	D₁₂	—	2	1	no	—
281	D₁₂	—	4	2	no	—
282	C₄×D₃	—	2	4	no	—
283	C₄×D₃	—	2	1	no	—
284	C₄×D₃	—	2	1	no	—
285	Dic₆	—	2	4	no	—
286	Dic₆	—	2	1	no	—
287	Dic₆	D₄×C₉	1	2	yes	complemented
288	C₃×C₈	—	2	1	no	—
289	C₃×C₈	—	2	1	no	—
290	C₃×C₈	—	4	1	no	—
291	C₃×C₈	—	6	1	no	—
292	C₃⋊C₈	—	2	1	no	—
293	C₂×C₃²	C₃×#120	1	1	yes	characteristic
294	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
295	C₂×C₃²	C₃×#137	1	1	yes	characteristic
296	C₃×D₃	—	2	2	no	—
297	C₃×D₃	—	8	1	no	—
298	C₂×C₉	—	2	1	no	—
299	C₂×C₉	—	2	1	no	—
300	C₂×C₉	—	2	1	no	—
301	C₂×C₉	—	6	2	no	—
302	C₂×C₉	—	24	1	no	—
303	C₂×C₉	#882	1	1	yes	characteristic
304	C₂×C₉	D₃×SD₁₆	1	1	yes	characteristic
305	C₂×C₉	#918	1	1	yes	characteristic
306	C₂×Q₈	—	3	1	no	—
307	C₂×Q₈	—	6	1	no	—
308	C₂×Q₈	—	6	2	no	—
309	C₂×Q₈	—	6	2	no	—
310	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
311	C₂×D₄	—	3	1	no	—
312	C₂×D₄	—	6	1	no	—
313	C₂²×C₄	—	3	1	no	—
314	C₂²×C₄	—	6	1	no	—
315	SD₁₆	—	6	2	no	—
316	SD₁₆	—	6	2	no	—
317	C₂×C₈	—	3	1	no	—
318	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
319	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
320	C₂²⋊C₄	—	6	1	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	3	2	no	—
323	C₂²×C₃	—	6	1	no	—
324	C₂²×C₃	—	6	1	no	—
325	C₂²×C₃	—	12	1	no	—
326	C₂²×C₃	—	12	1	no	—
327	C₂²×C₃	—	12	1	no	—
328	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
329	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
330	C₂×D₃	—	2	1	no	—
331	C₂×D₃	—	2	1	no	—
332	C₂×D₃	—	4	1	no	—
333	C₂×D₃	—	4	1	no	—
334	C₂×D₃	—	4	1	no	—
335	C₂×D₃	C₉×SD₁₆	1	2	yes	complemented
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	1	no	—
342	C₃×C₄	—	4	1	no	—
343	C₃×C₄	—	6	1	no	—
344	C₃×C₄	—	6	2	no	—
345	C₃×C₄	—	8	1	no	—
346	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
347	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
348	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
349	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
350	Dic₃	—	2	1	no	—
351	Dic₃	—	2	2	no	—
352	C₃²	C₃×#448	1	1	yes	characteristic
353	C₉	—	2	1	no	—
354	C₉	#4806	1	1	yes	characteristic, direct product factor
355	C₂³	—	3	1	no	—
356	C₂³	—	6	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	3	2	no	—
359	Q₈	—	6	4	no	—
360	Q₈	—	6	1	no	—
361	Q₈	C₉×D₁₂	1	2	yes	complemented
362	D₄	—	6	1	no	—
363	D₄	—	6	1	no	—
364	D₄	—	12	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	3	1	no	—
368	C₂×C₄	—	6	4	no	—
369	C₂×C₄	—	6	1	no	—
370	C₂×C₄	—	6	1	no	—
371	C₂×C₄	—	6	1	no	—
372	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
373	C₈	—	2	1	no	—
374	C₈	—	6	1	no	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	2	1	no	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	6	2	no	—
379	C₂×C₃	—	24	1	no	—
380	C₂×C₃	C₉×#120	1	1	yes	characteristic
381	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
382	C₂×C₃	C₉×#137	1	1	yes	characteristic
383	C₂×C₃	C₃×#882	1	1	yes	characteristic
384	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
385	C₂×C₃	C₃×#918	1	1	yes	characteristic
386	D₃	—	2	2	no	—
387	D₃	—	8	1	no	—
388	C₂²	—	3	2	no	—
389	C₂²	—	6	1	no	—
390	C₂²	—	6	1	no	—
391	C₂²	—	12	1	no	—
392	C₂²	—	12	1	no	—
393	C₂²	—	12	1	no	—
394	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	6	1	no	—
398	C₄	—	6	2	no	—
399	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
400	C₄	D₃×D₄×C₉	1	1	yes	characteristic
401	C₃	—	2	1	no	—
402	C₃	C₉×#448	1	1	yes	characteristic, complemented
403	C₃	C₃×#4806	1	1	yes	characteristic
404	C₂	—	6	2	no	—
405	C₂	—	24	1	no	—
406	C₂	C₉×#882	1	1	yes	characteristic
407	C₂	D₃×C₉×SD₁₆	1	1	yes	characteristic
408	C₂	C₉×#918	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#103	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₃×#895	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#103	D₃
hypocenter	C₃	C₉×#448
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#103

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×Q₈×C₉	C₂	semidirect
2. C₂×C₉×#215	C₂	semidirect
3. C₂×C₉×#204	C₂	semidirect
5. C₃×C₉×#103	C₂	semidirect
6. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₉×#810	C₂	semidirect
38. C₉×#103	D₃	semidirect
43. C₃×Q₈×C₉	D₄	semidirect
57. C₉×Dic₆	D₄	semidirect
61. #4806	C₉	direct (N × H)
101. C₂×D₃×C₉	SD₁₆	semidirect
109. C₂×D₃×Q₈	C₂×C₉	semidirect
113. C₂×#215	C₂×C₉	semidirect
114. C₂×#204	C₂×C₉	semidirect
118. C₃×#103	C₂×C₉	semidirect
121. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
122. #810	C₂×C₉	semidirect
151. Q₈×C₉	D₁₂	semidirect
244. #103	D₃×C₉	semidirect
246. C₃×C₉	#448	semidirect
258. C₃×Q₈	D₄×C₉	semidirect
287. Dic₆	D₄×C₉	semidirect
335. C₂×D₃	C₉×SD₁₆	semidirect
354. C₉	#4806	direct (N × H)
361. Q₈	C₉×D₁₂	semidirect
402. C₃	C₉×#448	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×Q₈×C₉	2
C₂×C₉×#215	2
C₂×C₉×#204	2
C₉×#895	2
C₃×C₉×#103	2
C₉×(C₂×D₃)⋊C₈	2
C₉×#810	2
C₃×#4806	3
C₉×#448	3

Subgroups — C9×#4806 #13141885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4806 #13141885