Subgroups — C₉×#1906 #11766627

Order 1152.

498 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#575	C₂	1	1	yes	maximal, characteristic
2	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1906	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#41	C₂²	1	1	yes	characteristic
10	C₂×C₉×#41	C₂²	1	1	yes	characteristic
11	C₉×#137	—	2	1	no	—
12	C₉×#137	C₄	1	2	yes	complemented
13	C₉×AGL(1,ℤ/8)	—	2	1	no	—
14	C₉×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
15	C₉×#135	—	2	2	no	—
16	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
18	C₄×Q₈×C₉	—	2	1	no	—
19	C₄×D₄×C₉	—	2	1	no	—
20	C₄×D₄×C₉	—	2	2	no	—
21	C₉×#117	—	2	1	no	—
22	C₉×#117	C₂²	1	1	yes	characteristic
23	C₉×#117	C₂²	1	1	yes	characteristic
24	C₂×C₄²×C₉	—	2	1	no	—
25	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
26	C₉×#104	—	2	2	no	—
27	C₉×#104	—	2	1	no	—
28	C₉×#104	—	2	1	no	—
29	C₉×#99	—	2	2	no	—
30	C₃×#575	C₂×C₃	1	1	yes	characteristic
31	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
32	C₃×#421	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×#104	C₂×C₃	1	1	yes	characteristic
34	C₃×#410	C₂×C₃	1	1	yes	characteristic
35	C₃×#344	C₂×C₃	1	1	yes	characteristic
36	C₃×#339	C₂×C₃	1	1	yes	characteristic
37	C₉×#41	—	2	1	no	—
38	C₉×#41	—	2	1	no	—
39	C₉×#41	—	2	1	no	—
40	C₉×#41	—	2	1	no	—
41	C₉×#41	—	2	1	no	—
42	C₉×#41	—	2	1	no	—
43	C₉×#41	C₂×C₄	1	2	yes	—
44	C₉×#41	D₄	1	2	yes	—
45	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic, complemented
46	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	—	2	1	no	—
49	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×D₄×C₉	D₄	1	1	yes	characteristic
51	C₂²×C₄×C₉	—	2	1	no	—
52	C₂²×C₄×C₉	—	2	2	no	—
53	C₂²×C₄×C₉	—	2	1	no	—
54	C₂²×C₄×C₉	—	2	1	no	—
55	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
56	C₉×Q₁₆	—	2	2	no	—
57	C₉×SD₁₆	—	2	2	no	—
58	C₉×SD₁₆	—	2	2	no	—
59	C₉×D₈	—	2	2	no	—
60	C₉×M₁₆	—	2	1	no	—
61	C₉×M₁₆	—	2	1	no	—
62	C₉×M₁₆	—	2	1	no	—
63	C₉×M₁₆	C₂×C₄	1	2	yes	complemented
64	C₂×C₈×C₉	—	2	1	no	—
65	C₂×C₈×C₉	—	2	1	no	—
66	C₉×C₄⋊C₄	—	2	2	no	—
67	C₉×C₄⋊C₄	—	2	1	no	—
68	C₉×C₄⋊C₄	—	2	1	no	—
69	C₉×C₂²⋊C₄	—	2	2	no	—
70	C₉×C₂²⋊C₄	—	2	1	no	—
71	C₉×C₂²⋊C₄	D₄	1	2	yes	—
72	C₄²×C₉	—	2	2	no	—
73	C₄²×C₉	—	2	1	no	—
74	C₄²×C₉	—	2	1	no	—
75	C₄²×C₉	—	2	1	no	—
76	C₄²×C₉	D₄	1	1	yes	characteristic
77	C₄²×C₉	D₄	1	1	yes	characteristic
78	#1906	C₉	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
81	C₃×#137	—	2	1	no	—
82	C₃×#137	C₃×C₄	1	2	yes	—
83	C₃×AGL(1,ℤ/8)	—	2	1	no	—
84	C₃×AGL(1,ℤ/8)	C₃×C₄	1	2	yes	—
85	C₃×#135	—	2	2	no	—
86	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
88	C₃×C₄×Q₈	—	2	1	no	—
89	C₃×C₄×D₄	—	2	1	no	—
90	C₃×C₄×D₄	—	2	2	no	—
91	C₃×#117	—	2	1	no	—
92	C₃×#117	C₂²×C₃	1	1	yes	characteristic
93	C₃×#117	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄²	—	2	1	no	—
95	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
96	C₃×#104	—	2	2	no	—
97	C₃×#104	—	2	1	no	—
98	C₃×#104	—	2	1	no	—
99	C₃×#99	—	2	2	no	—
100	C₂³×C₉	—	2	1	no	—
101	C₂³×C₉	—	2	1	no	—
102	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
103	Q₈×C₉	—	2	1	no	—
104	Q₈×C₉	—	2	1	no	—
105	Q₈×C₉	—	2	1	no	—
106	Q₈×C₉	C₂²⋊C₄	1	2	yes	—
107	D₄×C₉	—	2	2	no	—
108	D₄×C₉	—	2	2	no	—
109	D₄×C₉	—	2	1	no	—
110	D₄×C₉	—	2	1	no	—
111	D₄×C₉	—	2	1	no	—
112	D₄×C₉	—	4	1	no	—
113	D₄×C₉	—	4	1	no	—
114	D₄×C₉	C₂²⋊C₄	1	2	yes	—
115	C₂×C₄×C₉	—	2	1	no	—
116	C₂×C₄×C₉	—	2	1	no	—
117	C₂×C₄×C₉	—	2	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	1	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	1	no	—
122	C₂×C₄×C₉	—	4	2	no	—
123	C₂×C₄×C₉	—	4	4	no	—
124	C₂×C₄×C₉	—	4	1	no	—
125	C₂×C₄×C₉	—	4	1	no	—
126	C₂×C₄×C₉	—	4	1	no	—
127	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₉	#41	1	1	yes	characteristic
132	C₂×C₄×C₉	#41	1	1	yes	characteristic
133	C₈×C₉	—	2	2	no	—
134	C₈×C₉	—	4	1	no	—
135	#575	C₂×C₉	1	1	yes	characteristic
136	C₄×#41	C₂×C₉	1	1	yes	characteristic, complemented
137	#421	C₂×C₉	1	1	yes	characteristic, complemented
138	C₂×#104	C₂×C₉	1	1	yes	characteristic, complemented
139	#410	C₂×C₉	1	1	yes	characteristic, complemented
140	#344	C₂×C₉	1	1	yes	characteristic, complemented
141	#339	C₂×C₉	1	1	yes	characteristic, complemented
142	C₃×#41	—	2	1	no	—
143	C₃×#41	—	2	1	no	—
144	C₃×#41	—	2	1	no	—
145	C₃×#41	—	2	1	no	—
146	C₃×#41	—	2	1	no	—
147	C₃×#41	—	2	1	no	—
148	C₃×#41	C₂×C₃×C₄	1	2	yes	—
149	C₃×#41	C₃×D₄	1	2	yes	—
150	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
152	C₂×C₃×D₄	—	2	1	no	—
153	C₂×C₃×D₄	—	2	1	no	—
154	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	—	2	1	no	—
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	—	2	1	no	—
160	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₃×Q₁₆	—	2	2	no	—
162	C₃×SD₁₆	—	2	2	no	—
163	C₃×SD₁₆	—	2	2	no	—
164	C₃×D₈	—	2	2	no	—
165	C₃×M₁₆	—	2	1	no	—
166	C₃×M₁₆	—	2	1	no	—
167	C₃×M₁₆	—	2	1	no	—
168	C₃×M₁₆	C₂×C₃×C₄	1	2	yes	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	1	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	1	no	—
174	C₃×C₂²⋊C₄	—	2	2	no	—
175	C₃×C₂²⋊C₄	—	2	1	no	—
176	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
177	C₃×C₄²	—	2	2	no	—
178	C₃×C₄²	—	2	1	no	—
179	C₃×C₄²	—	2	1	no	—
180	C₃×C₄²	—	2	1	no	—
181	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
182	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₉	—	2	2	no	—
184	C₂²×C₉	—	4	1	no	—
185	C₂²×C₉	—	4	2	no	—
186	C₂²×C₉	—	4	1	no	—
187	C₂²×C₉	—	8	1	no	—
188	C₂²×C₉	C₄×D₄	1	1	yes	characteristic
189	C₂²×C₉	#120	1	1	yes	characteristic
190	C₂²×C₉	#121	1	1	yes	characteristic
191	C₄×C₉	—	2	2	no	—
192	C₄×C₉	—	2	2	no	—
193	C₄×C₉	—	4	2	no	—
194	C₄×C₉	—	4	1	no	—
195	C₄×C₉	—	4	1	no	—
196	C₄×C₉	—	8	1	no	—
197	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₄×C₉	C₄×D₄	1	1	yes	characteristic
199	C₄×C₉	#121	1	1	yes	characteristic
200	C₄×C₉	#123	1	1	yes	characteristic
201	C₂×#41	C₂²×C₉	1	1	yes	characteristic
202	C₂×#41	C₂²×C₉	1	1	yes	characteristic
203	#137	—	2	1	no	—
204	#137	C₄×C₉	1	2	yes	complemented
205	AGL(1,ℤ/8)	—	2	1	no	—
206	AGL(1,ℤ/8)	C₄×C₉	1	2	yes	complemented
207	#135	—	2	2	no	—
208	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
209	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
210	C₄×Q₈	—	2	1	no	—
211	C₄×D₄	—	2	1	no	—
212	C₄×D₄	—	2	2	no	—
213	#117	—	2	1	no	—
214	#117	C₂²×C₉	1	1	yes	characteristic
215	#117	C₂²×C₉	1	1	yes	characteristic
216	C₂×C₄²	—	2	1	no	—
217	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
218	#104	—	2	2	no	—
219	#104	—	2	1	no	—
220	#104	—	2	1	no	—
221	#99	—	2	2	no	—
222	C₂³×C₃	—	2	1	no	—
223	C₂³×C₃	—	2	1	no	—
224	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
225	C₃×Q₈	—	2	1	no	—
226	C₃×Q₈	—	2	1	no	—
227	C₃×Q₈	—	2	1	no	—
228	C₃×Q₈	C₃×C₂²⋊C₄	1	2	yes	—
229	C₃×D₄	—	2	2	no	—
230	C₃×D₄	—	2	2	no	—
231	C₃×D₄	—	2	1	no	—
232	C₃×D₄	—	2	1	no	—
233	C₃×D₄	—	2	1	no	—
234	C₃×D₄	—	4	1	no	—
235	C₃×D₄	—	4	1	no	—
236	C₃×D₄	C₃×C₂²⋊C₄	1	2	yes	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	4	2	no	—
245	C₂×C₃×C₄	—	4	4	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	4	1	no	—
248	C₂×C₃×C₄	—	4	1	no	—
249	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
254	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
255	C₃×C₈	—	2	2	no	—
256	C₃×C₈	—	4	1	no	—
257	C₂×C₉	—	2	1	no	—
258	C₂×C₉	—	2	1	no	—
259	C₂×C₉	—	2	1	no	—
260	C₂×C₉	—	4	2	no	—
261	C₂×C₉	—	8	1	no	—
262	C₂×C₉	#386	1	1	yes	characteristic
263	#41	—	2	1	no	—
264	#41	—	2	1	no	—
265	#41	—	2	1	no	—
266	#41	—	2	1	no	—
267	#41	—	2	1	no	—
268	#41	—	2	1	no	—
269	#41	C₂×C₄×C₉	1	2	yes	—
270	#41	D₄×C₉	1	2	yes	—
271	C₂×Q₈	C₂×C₄×C₉	1	1	yes	characteristic, complemented
272	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic, complemented
276	C₂×D₄	D₄×C₉	1	1	yes	characteristic
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
282	Q₁₆	—	2	2	no	—
283	SD₁₆	—	2	2	no	—
284	SD₁₆	—	2	2	no	—
285	D₈	—	2	2	no	—
286	M₁₆	—	2	1	no	—
287	M₁₆	—	2	1	no	—
288	M₁₆	—	2	1	no	—
289	M₁₆	C₂×C₄×C₉	1	2	yes	complemented
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	1	no	—
297	C₂²⋊C₄	D₄×C₉	1	2	yes	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	D₄×C₉	1	1	yes	characteristic
303	C₄²	D₄×C₉	1	1	yes	characteristic
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	4	1	no	—
306	C₂²×C₃	—	4	2	no	—
307	C₂²×C₃	—	4	1	no	—
308	C₂²×C₃	—	8	1	no	—
309	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₃	C₃×#120	1	1	yes	characteristic
311	C₂²×C₃	C₃×#121	1	1	yes	characteristic
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	4	2	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	1	no	—
317	C₃×C₄	—	8	1	no	—
318	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
319	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
320	C₃×C₄	C₃×#121	1	1	yes	characteristic
321	C₃×C₄	C₃×#123	1	1	yes	characteristic
322	C₉	#1906	1	1	yes	characteristic, direct product factor, Sylow
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
326	Q₈	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	C₉×C₂²⋊C₄	1	2	yes	—
330	D₄	—	2	2	no	—
331	D₄	—	2	2	no	—
332	D₄	—	2	1	no	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	4	1	no	—
336	D₄	—	4	1	no	—
337	D₄	C₉×C₂²⋊C₄	1	2	yes	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
351	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
352	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
353	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
354	C₂×C₄	C₉×#41	1	1	yes	characteristic
355	C₂×C₄	C₉×#41	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	4	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	4	2	no	—
362	C₂×C₃	—	8	1	no	—
363	C₂×C₃	C₃×#386	1	1	yes	characteristic
364	C₂²	—	2	2	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₄×D₄×C₉	1	1	yes	characteristic
370	C₂²	C₉×#120	1	1	yes	characteristic
371	C₂²	C₉×#121	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	8	1	no	—
378	C₄	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
379	C₄	C₄×D₄×C₉	1	1	yes	characteristic
380	C₄	C₉×#121	1	1	yes	characteristic
381	C₄	C₉×#123	1	1	yes	characteristic
382	C₃	C₃×#1906	1	1	yes	characteristic
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	4	2	no	—
387	C₂	—	8	1	no	—
388	C₂	C₉×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	#121
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#386
prime radical	C₃×#575	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₉×#41	C₂	semidirect
3. C₉×#421	C₂	semidirect
4. C₂×C₉×#104	C₂	semidirect
5. C₉×#410	C₂	semidirect
6. C₉×#344	C₂	semidirect
7. C₉×#339	C₂	semidirect
12. C₉×#137	C₄	semidirect
14. C₉×AGL(1,ℤ/8)	C₄	semidirect
45. C₂×Q₈×C₉	C₂×C₄	semidirect
49. C₂×D₄×C₉	C₂×C₄	semidirect
63. C₉×M₁₆	C₂×C₄	semidirect
78. #1906	C₉	direct (N × H)
136. C₄×#41	C₂×C₉	semidirect
137. #421	C₂×C₉	semidirect
138. C₂×#104	C₂×C₉	semidirect
139. #410	C₂×C₉	semidirect
140. #344	C₂×C₉	semidirect
141. #339	C₂×C₉	semidirect
204. #137	C₄×C₉	semidirect
206. AGL(1,ℤ/8)	C₄×C₉	semidirect
271. C₂×Q₈	C₂×C₄×C₉	semidirect
275. C₂×D₄	C₂×C₄×C₉	semidirect
289. M₁₆	C₂×C₄×C₉	semidirect
322. C₉	#1906	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×#575	2
C₄×C₉×#41	2
C₉×#421	2
C₂×C₉×#104	2
C₉×#410	2
C₉×#344	2
C₉×#339	2
C₃×#1906	3

Subgroups — C9×#1906 #11766627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1906 #11766627