Subgroups — C₉×#4822 #13141974

Order 1728.

548 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#1009	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#949	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#908	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#874	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#823	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#805	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4822	C₃	1	1	yes	maximal, characteristic
9	C₉×#453	—	3	1	no	maximal
10	C₃×C₉×#41	C₂²	1	1	yes	characteristic
11	C₉×#239	—	2	1	no	—
12	D₃×D₄×C₉	—	2	2	no	—
13	D₃×D₄×C₉	—	2	1	no	—
14	C₉×#235	—	2	1	no	—
15	C₉×#235	C₂²	1	1	yes	characteristic
16	C₂×C₉×D₁₂	—	2	1	no	—
17	C₂×C₉×D₁₂	—	2	2	no	—
18	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₉×#215	—	2	1	no	—
23	C₉×#213	—	2	1	no	—
24	C₉×#208	C₂²	1	1	yes	characteristic, complemented
25	C₉×D₂₄	—	2	1	no	—
26	C₉×#204	—	2	1	no	—
27	C₃×#1009	C₂×C₃	1	1	yes	characteristic
28	C₃×#949	C₂×C₃	1	1	yes	characteristic
29	C₃×#908	C₂×C₃	1	1	yes	characteristic
30	C₃×#874	C₂×C₃	1	1	yes	characteristic
31	C₉×H(5,𝔽₂)	—	3	1	no	—
32	C₃²×#104	C₂×C₃	1	1	yes	characteristic
33	C₃×#823	C₂×C₃	1	1	yes	characteristic
34	C₃×#805	C₂×C₃	1	1	yes	characteristic
35	C₉×AGL(1,ℤ/8)	—	3	1	no	—
36	C₉×AGL(1,ℤ/8)	—	3	1	no	—
37	C₉×#127	—	3	1	no	—
38	C₉×#104	—	2	1	no	—
39	C₉×#104	—	3	1	no	—
40	C₉×#104	D₃	1	1	yes	characteristic, complemented
41	C₉×#100	—	3	1	no	—
42	C₂²×D₃×C₉	—	2	2	no	—
43	C₂²×D₃×C₉	—	2	1	no	—
44	C₂²×D₃×C₉	D₄	1	2	yes	—
45	C₃×Q₈×C₉	D₄	1	1	yes	characteristic, complemented
46	C₃×D₄×C₉	—	2	1	no	—
47	C₃×D₄×C₉	D₄	1	1	yes	characteristic, complemented
48	C₂×C₃×C₄×C₉	—	2	1	no	—
49	C₂×C₃×C₄×C₉	—	2	1	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₉×#67	—	2	2	no	—
52	C₉×#67	—	2	1	no	—
53	C₉×D₁₂	—	2	2	no	—
54	C₉×D₁₂	—	2	1	no	—
55	C₉×D₁₂	—	2	1	no	—
56	C₉×D₁₂	—	2	1	no	—
57	C₉×D₁₂	—	2	1	no	—
58	C₉×D₁₂	—	4	4	no	—
59	C₉×D₁₂	D₄	1	1	yes	characteristic, complemented
60	C₄×D₃×C₉	—	2	2	no	—
61	C₄×D₃×C₉	—	2	1	no	—
62	C₉×Dic₆	D₄	1	1	yes	characteristic, complemented
63	C₃×C₈×C₉	—	2	1	no	—
64	C₉×C₃⋊C₈	—	2	1	no	—
65	C₃×#453	—	3	1	no	—
66	#4822	C₉	1	1	yes	characteristic, direct product factor
67	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
68	C₃×#239	—	2	1	no	—
69	C₃×D₃×D₄	—	2	2	no	—
70	C₃×D₃×D₄	—	2	1	no	—
71	C₃×#235	—	2	1	no	—
72	C₃×#235	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃×D₁₂	—	2	1	no	—
74	C₂×C₃×D₁₂	—	2	2	no	—
75	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
77	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic
78	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
79	C₃×#215	—	2	1	no	—
80	C₃×#213	—	2	1	no	—
81	C₃×#208	C₂²×C₃	1	1	yes	characteristic
82	C₃×D₂₄	—	2	1	no	—
83	C₃×#204	—	2	1	no	—
84	C₉×#41	—	2	1	no	—
85	C₉×#41	—	3	1	no	—
86	C₉×#41	—	6	1	no	—
87	C₉×#41	—	6	1	no	—
88	C₉×#41	C₂×D₃	1	1	yes	characteristic
89	C₂×D₄×C₉	—	3	1	no	—
90	C₂×D₄×C₉	—	3	1	no	—
91	C₂×D₄×C₉	—	6	1	no	—
92	C₂×D₄×C₉	—	6	2	no	—
93	C₂×D₄×C₉	—	6	2	no	—
94	C₂×D₄×C₉	—	6	1	no	—
95	C₉×SD₁₆	—	6	1	no	—
96	C₉×SD₁₆	—	6	1	no	—
97	C₉×D₈	—	6	1	no	—
98	C₉×D₈	—	6	1	no	—
99	C₉×M₁₆	—	2	1	no	—
100	C₉×M₁₆	—	3	1	no	—
101	C₉×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
102	C₄²×C₉	—	2	1	no	—
103	C₄²×C₉	C₂×D₃	1	1	yes	characteristic, complemented
104	C₂²×C₃×C₉	—	2	1	no	—
105	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
106	C₂×D₃×C₉	—	2	2	no	—
107	C₂×D₃×C₉	—	2	1	no	—
108	C₂×D₃×C₉	—	4	2	no	—
109	C₂×D₃×C₉	—	4	2	no	—
110	C₂×D₃×C₉	—	4	1	no	—
111	C₂×D₃×C₉	—	8	2	no	—
112	C₃×C₄×C₉	—	2	2	no	—
113	C₃×C₄×C₉	—	2	1	no	—
114	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
115	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
116	C₉×Dic₃	—	2	1	no	—
117	C₃×H(5,𝔽₂)	—	3	1	no	—
118	#1009	C₂×C₉	1	1	yes	characteristic, complemented
119	C₃×AGL(1,ℤ/8)	—	3	1	no	—
120	C₃×AGL(1,ℤ/8)	—	3	1	no	—
121	C₃×#127	—	3	1	no	—
122	#949	C₂×C₉	1	1	yes	characteristic, complemented
123	#908	C₂×C₉	1	1	yes	characteristic, complemented
124	#874	C₂×C₉	1	1	yes	characteristic, complemented
125	C₃×#104	—	2	1	no	—
126	C₃×#104	—	3	1	no	—
127	C₃×#104	C₂×C₉	1	1	yes	characteristic, complemented
128	C₃×#104	C₃×D₃	1	1	yes	characteristic
129	C₃×#100	—	3	1	no	—
130	#823	C₂×C₉	1	1	yes	characteristic, complemented
131	#805	C₂×C₉	1	1	yes	characteristic, complemented
132	C₂²×C₃×D₃	—	2	2	no	—
133	C₂²×C₃×D₃	—	2	1	no	—
134	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
135	C₃²×Q₈	C₃×D₄	1	1	yes	characteristic
136	C₃²×D₄	—	2	1	no	—
137	C₃²×D₄	C₃×D₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	—	2	1	no	—
139	C₂×C₃²×C₄	—	2	1	no	—
140	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
141	C₃×#67	—	2	2	no	—
142	C₃×#67	—	2	1	no	—
143	C₃×D₁₂	—	2	2	no	—
144	C₃×D₁₂	—	2	1	no	—
145	C₃×D₁₂	—	2	1	no	—
146	C₃×D₁₂	—	2	1	no	—
147	C₃×D₁₂	—	2	1	no	—
148	C₃×D₁₂	—	4	4	no	—
149	C₃×D₁₂	C₃×D₄	1	1	yes	characteristic
150	C₃×C₄×D₃	—	2	2	no	—
151	C₃×C₄×D₃	—	2	1	no	—
152	C₃×Dic₆	C₃×D₄	1	1	yes	characteristic
153	C₂³×C₉	—	3	2	no	—
154	C₂³×C₉	—	6	2	no	—
155	C₂³×C₉	—	6	1	no	—
156	C₃²×C₈	—	2	1	no	—
157	C₃×C₃⋊C₈	—	2	1	no	—
158	Q₈×C₉	—	2	1	no	—
159	Q₈×C₉	—	3	1	no	—
160	Q₈×C₉	D₁₂	1	1	yes	characteristic, complemented
161	D₄×C₉	—	2	1	no	—
162	D₄×C₉	—	2	1	no	—
163	D₄×C₉	—	3	1	no	—
164	D₄×C₉	—	4	1	no	—
165	D₄×C₉	—	6	2	no	—
166	D₄×C₉	—	6	2	no	—
167	D₄×C₉	—	6	1	no	—
168	D₄×C₉	—	6	1	no	—
169	D₄×C₉	—	6	1	no	—
170	D₄×C₉	—	6	1	no	—
171	D₄×C₉	—	6	1	no	—
172	D₄×C₉	—	12	4	no	—
173	D₄×C₉	D₁₂	1	1	yes	characteristic, complemented
174	C₂×C₄×C₉	—	2	1	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	1	no	—
177	C₂×C₄×C₉	—	4	1	no	—
178	C₂×C₄×C₉	—	4	1	no	—
179	C₂×C₄×C₉	—	6	2	no	—
180	C₂×C₄×C₉	—	6	1	no	—
181	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
182	C₈×C₉	—	2	1	no	—
183	C₈×C₉	—	4	1	no	—
184	C₈×C₉	—	6	1	no	—
185	#453	—	3	1	no	Sylow
186	C₂×C₃×C₉	—	2	1	no	—
187	C₂×C₃×C₉	—	4	1	no	—
188	C₂×C₃×C₉	#120	1	1	yes	characteristic
189	D₃×C₉	—	4	2	no	—
190	D₃×C₉	—	4	1	no	—
191	D₃×C₉	—	8	1	no	—
192	C₃×#41	—	2	1	no	—
193	C₃×#41	—	3	1	no	—
194	C₃×#41	—	6	1	no	—
195	C₃×#41	—	6	1	no	—
196	C₃×#41	C₂²×C₉	1	1	yes	characteristic
197	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
198	C₂×C₃×D₄	—	3	1	no	—
199	C₂×C₃×D₄	—	3	1	no	—
200	C₂×C₃×D₄	—	6	1	no	—
201	C₂×C₃×D₄	—	6	2	no	—
202	C₂×C₃×D₄	—	6	2	no	—
203	C₂×C₃×D₄	—	6	1	no	—
204	#239	—	2	1	no	—
205	D₃×D₄	—	2	2	no	—
206	D₃×D₄	—	2	1	no	—
207	#235	—	2	1	no	—
208	#235	C₂²×C₉	1	1	yes	characteristic
209	C₂×D₁₂	—	2	1	no	—
210	C₂×D₁₂	—	2	2	no	—
211	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
212	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
213	C₃×SD₁₆	—	6	1	no	—
214	C₃×SD₁₆	—	6	1	no	—
215	C₃×D₈	—	6	1	no	—
216	C₃×D₈	—	6	1	no	—
217	C₃×M₁₆	—	2	1	no	—
218	C₃×M₁₆	—	3	1	no	—
219	C₃×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
220	C₃×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
221	C₃×C₄²	—	2	1	no	—
222	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
223	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
224	#215	—	2	1	no	—
225	#213	—	2	1	no	—
226	#208	C₂²×C₉	1	1	yes	characteristic, complemented
227	D₂₄	—	2	1	no	—
228	#204	—	2	1	no	—
229	C₂²×C₃²	—	2	1	no	—
230	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₃×D₃	—	2	2	no	—
232	C₂×C₃×D₃	—	2	1	no	—
233	C₂×C₃×D₃	—	4	2	no	—
234	C₂×C₃×D₃	—	4	2	no	—
235	C₂×C₃×D₃	—	4	1	no	—
236	C₂×C₃×D₃	—	8	2	no	—
237	C₃²×C₄	—	2	2	no	—
238	C₃²×C₄	—	2	1	no	—
239	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
240	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
241	C₃×Dic₃	—	2	1	no	—
242	C₂²×C₉	—	2	1	no	—
243	C₂²×C₉	—	2	1	no	—
244	C₂²×C₉	—	4	1	no	—
245	C₂²×C₉	—	6	1	no	—
246	C₂²×C₉	—	6	2	no	—
247	C₂²×C₉	—	12	2	no	—
248	C₂²×C₉	—	12	2	no	—
249	C₂²×C₉	—	12	1	no	—
250	C₂²×C₉	—	24	2	no	—
251	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
252	C₄×C₉	—	2	2	no	—
253	C₄×C₉	—	2	1	no	—
254	C₄×C₉	—	2	1	no	—
255	C₄×C₉	—	2	1	no	—
256	C₄×C₉	—	4	1	no	—
257	C₄×C₉	—	4	2	no	—
258	C₄×C₉	—	6	1	no	—
259	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
260	C₄×C₉	D₃×D₄	1	1	yes	characteristic
261	H(5,𝔽₂)	—	3	1	no	—
262	AGL(1,ℤ/8)	—	3	1	no	—
263	AGL(1,ℤ/8)	—	3	1	no	—
264	#127	—	3	1	no	—
265	#104	—	3	1	no	—
266	#104	D₃×C₉	1	1	yes	characteristic, complemented
267	#100	—	3	1	no	—
268	C₃×C₉	#453	1	1	yes	characteristic, complemented, Sylow
269	C₂³×C₃	—	3	2	no	—
270	C₂³×C₃	—	6	2	no	—
271	C₂³×C₃	—	6	1	no	—
272	C₂²×D₃	—	2	2	no	—
273	C₂²×D₃	—	2	1	no	—
274	C₂²×D₃	D₄×C₉	1	2	yes	—
275	C₃×Q₈	—	2	1	no	—
276	C₃×Q₈	—	3	1	no	—
277	C₃×Q₈	D₄×C₉	1	1	yes	characteristic, complemented
278	C₃×Q₈	C₃×D₁₂	1	1	yes	characteristic
279	C₃×D₄	—	2	1	no	—
280	C₃×D₄	—	2	1	no	—
281	C₃×D₄	—	2	1	no	—
282	C₃×D₄	—	3	1	no	—
283	C₃×D₄	—	4	1	no	—
284	C₃×D₄	—	6	2	no	—
285	C₃×D₄	—	6	2	no	—
286	C₃×D₄	—	6	1	no	—
287	C₃×D₄	—	6	1	no	—
288	C₃×D₄	—	6	1	no	—
289	C₃×D₄	—	6	1	no	—
290	C₃×D₄	—	6	1	no	—
291	C₃×D₄	—	12	4	no	—
292	C₃×D₄	D₄×C₉	1	1	yes	characteristic, complemented
293	C₃×D₄	C₃×D₁₂	1	1	yes	characteristic
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	4	1	no	—
300	C₂×C₃×C₄	—	4	1	no	—
301	C₂×C₃×C₄	—	6	2	no	—
302	C₂×C₃×C₄	—	6	1	no	—
303	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
305	#67	—	2	2	no	—
306	#67	—	2	1	no	—
307	D₁₂	—	2	2	no	—
308	D₁₂	—	2	1	no	—
309	D₁₂	—	2	1	no	—
310	D₁₂	—	2	1	no	—
311	D₁₂	—	2	1	no	—
312	D₁₂	—	4	4	no	—
313	D₁₂	D₄×C₉	1	1	yes	characteristic, complemented
314	C₄×D₃	—	2	2	no	—
315	C₄×D₃	—	2	1	no	—
316	Dic₆	D₄×C₉	1	1	yes	characteristic, complemented
317	C₃×C₈	—	2	1	no	—
318	C₃×C₈	—	2	1	no	—
319	C₃×C₈	—	4	1	no	—
320	C₃×C₈	—	6	1	no	—
321	C₃⋊C₈	—	2	1	no	—
322	C₂×C₃²	—	2	1	no	—
323	C₂×C₃²	—	4	1	no	—
324	C₂×C₃²	C₃×#120	1	1	yes	characteristic
325	C₃×D₃	—	4	2	no	—
326	C₃×D₃	—	4	1	no	—
327	C₃×D₃	—	8	1	no	—
328	C₂×C₉	—	2	1	no	—
329	C₂×C₉	—	2	1	no	—
330	C₂×C₉	—	4	1	no	—
331	C₂×C₉	—	4	1	no	—
332	C₂×C₉	—	8	1	no	—
333	C₂×C₉	—	12	2	no	—
334	C₂×C₉	—	12	1	no	—
335	C₂×C₉	—	24	1	no	—
336	C₂×C₉	#882	1	1	yes	characteristic
337	#41	—	3	1	no	—
338	#41	—	6	1	no	—
339	#41	—	6	1	no	—
340	#41	C₂×D₃×C₉	1	1	yes	characteristic
341	C₂×D₄	—	3	1	no	—
342	C₂×D₄	—	3	1	no	—
343	C₂×D₄	—	6	1	no	—
344	C₂×D₄	—	6	2	no	—
345	C₂×D₄	—	6	2	no	—
346	C₂×D₄	—	6	1	no	—
347	SD₁₆	—	6	1	no	—
348	SD₁₆	—	6	1	no	—
349	D₈	—	6	1	no	—
350	D₈	—	6	1	no	—
351	M₁₆	—	3	1	no	—
352	M₁₆	C₂×D₃×C₉	1	1	yes	characteristic, complemented
353	C₄²	C₂×D₃×C₉	1	1	yes	characteristic, complemented
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	1	no	—
357	C₂²×C₃	—	4	1	no	—
358	C₂²×C₃	—	6	1	no	—
359	C₂²×C₃	—	6	2	no	—
360	C₂²×C₃	—	12	2	no	—
361	C₂²×C₃	—	12	2	no	—
362	C₂²×C₃	—	12	1	no	—
363	C₂²×C₃	—	24	2	no	—
364	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
365	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
366	C₂×D₃	—	2	2	no	—
367	C₂×D₃	—	2	1	no	—
368	C₂×D₃	—	4	2	no	—
369	C₂×D₃	—	4	2	no	—
370	C₂×D₃	—	4	1	no	—
371	C₂×D₃	—	8	2	no	—
372	C₃×C₄	—	2	2	no	—
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	4	1	no	—
379	C₃×C₄	—	4	2	no	—
380	C₃×C₄	—	6	1	no	—
381	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
382	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
383	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
384	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
385	Dic₃	—	2	1	no	—
386	C₃²	C₃×#453	1	1	yes	characteristic
387	C₉	—	2	1	no	—
388	C₉	#4822	1	1	yes	characteristic, direct product factor
389	C₂³	—	3	2	no	—
390	C₂³	—	6	2	no	—
391	C₂³	—	6	1	no	—
392	Q₈	—	3	1	no	—
393	Q₈	C₉×D₁₂	1	1	yes	characteristic, complemented
394	D₄	—	2	1	no	—
395	D₄	—	3	1	no	—
396	D₄	—	6	2	no	—
397	D₄	—	6	2	no	—
398	D₄	—	6	1	no	—
399	D₄	—	6	1	no	—
400	D₄	—	6	1	no	—
401	D₄	—	6	1	no	—
402	D₄	—	6	1	no	—
403	D₄	—	12	4	no	—
404	D₄	C₉×D₁₂	1	1	yes	characteristic, complemented
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	6	2	no	—
408	C₂×C₄	—	6	1	no	—
409	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	6	1	no	—
412	C₂×C₃	—	2	1	no	—
413	C₂×C₃	—	2	1	no	—
414	C₂×C₃	—	2	1	no	—
415	C₂×C₃	—	4	1	no	—
416	C₂×C₃	—	4	1	no	—
417	C₂×C₃	—	4	1	no	—
418	C₂×C₃	—	8	1	no	—
419	C₂×C₃	—	12	2	no	—
420	C₂×C₃	—	12	1	no	—
421	C₂×C₃	—	24	1	no	—
422	C₂×C₃	C₉×#120	1	1	yes	characteristic
423	C₂×C₃	C₃×#882	1	1	yes	characteristic
424	D₃	—	4	2	no	—
425	D₃	—	4	1	no	—
426	D₃	—	8	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	6	1	no	—
429	C₂²	—	6	2	no	—
430	C₂²	—	12	2	no	—
431	C₂²	—	12	2	no	—
432	C₂²	—	12	1	no	—
433	C₂²	—	24	2	no	—
434	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	2	1	no	—
437	C₄	—	6	1	no	—
438	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
439	C₄	D₃×D₄×C₉	1	1	yes	characteristic
440	C₃	—	2	1	no	—
441	C₃	C₉×#453	1	1	yes	characteristic, complemented
442	C₃	C₃×#4822	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	4	1	no	—
445	C₂	—	12	2	no	—
446	C₂	—	12	1	no	—
447	C₂	—	24	1	no	—
448	C₂	C₉×#882	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	#882
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#104	C₂
socle	C₂×C₃²	C₃×#120
prime radical	C₃×#4822	C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#104	D₃
hypocenter	C₃	C₉×#453
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#104

Complements

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

N	H ≅ G/N	type
1. C₉×#1009	C₂	semidirect
2. C₉×#949	C₂	semidirect
3. C₉×#908	C₂	semidirect
4. C₉×#874	C₂	semidirect
5. C₃×C₉×#104	C₂	semidirect
6. C₉×#823	C₂	semidirect
7. C₉×#805	C₂	semidirect
19. C₂×C₉×D₁₂	C₂²	semidirect
20. C₃×C₉×M₁₆	C₂²	semidirect
21. C₃×C₄²×C₉	C₂²	semidirect
24. C₉×#208	C₂²	semidirect
40. C₉×#104	D₃	semidirect
45. C₃×Q₈×C₉	D₄	semidirect
47. C₃×D₄×C₉	D₄	semidirect
59. C₉×D₁₂	D₄	semidirect
62. C₉×Dic₆	D₄	semidirect
66. #4822	C₉	direct (N × H)
101. C₉×M₁₆	C₂×D₃	semidirect
103. C₄²×C₉	C₂×D₃	semidirect
118. #1009	C₂×C₉	semidirect
122. #949	C₂×C₉	semidirect
123. #908	C₂×C₉	semidirect
124. #874	C₂×C₉	semidirect
127. C₃×#104	C₂×C₉	semidirect
130. #823	C₂×C₉	semidirect
131. #805	C₂×C₉	semidirect
160. Q₈×C₉	D₁₂	semidirect
173. D₄×C₉	D₁₂	semidirect
212. C₂×D₁₂	C₂²×C₉	semidirect
219. C₃×M₁₆	C₂²×C₉	semidirect
222. C₃×C₄²	C₂²×C₉	semidirect
226. #208	C₂²×C₉	semidirect
266. #104	D₃×C₉	semidirect
268. C₃×C₉	#453	semidirect
277. C₃×Q₈	D₄×C₉	semidirect
292. C₃×D₄	D₄×C₉	semidirect
313. D₁₂	D₄×C₉	semidirect
316. Dic₆	D₄×C₉	semidirect
352. M₁₆	C₂×D₃×C₉	semidirect
353. C₄²	C₂×D₃×C₉	semidirect
388. C₉	#4822	direct (N × H)
393. Q₈	C₉×D₁₂	semidirect
404. D₄	C₉×D₁₂	semidirect
441. C₃	C₉×#453	semidirect

Maximal subgroups

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

subgroup	index
C₉×#1009	2
C₉×#949	2
C₉×#908	2
C₉×#874	2
C₃×C₉×#104	2
C₉×#823	2
C₉×#805	2
C₃×#4822	3
C₉×#453	3

Subgroups — C9×#4822 #13141974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4822 #13141974