Subgroups — C₉×#3220 #11767941

Order 1152.

630 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#463	C₂	1	2	yes	maximal, complemented
8	C₉×#459	C₂	1	2	yes	maximal, complemented
9	C₉×#449	C₂	1	2	yes	maximal, complemented
10	C₉×#447	C₂	1	2	yes	maximal, complemented
11	C₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3220	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
16	C₂×C₉×D₈	C₂²	1	2	yes	—
17	C₂×C₉×D₈	C₂²	1	2	yes	—
18	C₂×C₉×D₈	C₂²	1	2	yes	complemented
19	C₉×#127	C₂²	1	1	yes	characteristic
20	C₉×#127	C₂²	1	1	yes	characteristic
21	C₉×#127	C₂²	1	1	yes	characteristic, complemented
22	C₉×#125	C₂²	1	1	yes	characteristic, complemented
23	C₉×#124	C₂²	1	1	yes	characteristic
24	C₉×#124	C₂²	1	1	yes	characteristic
25	C₉×#123	—	2	2	no	—
26	C₉×#121	—	2	2	no	—
27	C₉×#121	—	2	2	no	—
28	C₉×#121	C₂²	1	2	yes	—
29	C₉×#120	—	2	2	no	—
30	C₄×D₄×C₉	C₂²	1	2	yes	complemented
31	C₉×#117	C₂²	1	1	yes	characteristic
32	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
33	C₉×#103	C₂²	1	2	yes	complemented
34	C₉×#102	C₂²	1	2	yes	—
35	C₉×#102	C₂²	1	2	yes	—
36	C₉×#102	C₂²	1	2	yes	complemented
37	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₉×#97	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
40	C₃×#540	C₂×C₃	1	1	yes	characteristic
41	C₃×#535	C₂×C₃	1	1	yes	characteristic
42	C₃×#496	C₂×C₃	1	1	yes	characteristic
43	C₃×#493	C₂×C₃	1	1	yes	characteristic
44	C₃×#490	C₂×C₃	1	1	yes	characteristic
45	C₃×#488	C₂×C₃	1	1	yes	characteristic
46	C₃×#463	C₂×C₃	1	2	yes	—
47	C₃×#459	C₂×C₃	1	2	yes	—
48	C₃×#449	C₂×C₃	1	2	yes	—
49	C₃×#447	C₂×C₃	1	2	yes	—
50	C₃×#433	C₂×C₃	1	1	yes	characteristic
51	C₂⁴×C₉	—	2	1	no	—
52	C₉×#41	—	4	2	no	—
53	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
54	C₂×D₄×C₉	—	2	1	no	—
55	C₂×D₄×C₉	—	2	2	no	—
56	C₂×D₄×C₉	—	2	1	no	—
57	C₂×D₄×C₉	—	2	2	no	—
58	C₂×D₄×C₉	—	2	2	no	—
59	C₂×D₄×C₉	—	2	2	no	—
60	C₂×D₄×C₉	—	4	2	no	—
61	C₂×D₄×C₉	C₂³	1	2	yes	—
62	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	—	2	1	no	—
66	C₂²×C₄×C₉	—	2	2	no	—
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₉×SD₁₆	—	4	2	no	—
69	C₉×D₈	—	4	2	no	—
70	C₉×D₈	—	4	2	no	—
71	C₉×D₈	—	4	2	no	—
72	C₂×C₈×C₉	C₂³	1	2	yes	—
73	C₂×C₈×C₉	C₂³	1	2	yes	—
74	C₉×C₄⋊C₄	—	2	2	no	—
75	C₉×C₄⋊C₄	D₄	1	2	yes	—
76	C₉×C₄⋊C₄	C₂³	1	2	yes	—
77	C₉×C₂²⋊C₄	—	2	2	no	—
78	C₉×C₂²⋊C₄	—	2	2	no	—
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	—	2	2	no	—
81	C₉×C₂²⋊C₄	D₄	1	2	yes	—
82	C₄²×C₉	C₂³	1	1	yes	characteristic
83	C₄²×C₉	C₂³	1	1	yes	characteristic
84	#3220	C₉	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
88	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
89	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
90	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
91	C₃×#127	C₂²×C₃	1	1	yes	characteristic
92	C₃×#127	C₂²×C₃	1	1	yes	characteristic
93	C₃×#127	C₂²×C₃	1	1	yes	characteristic
94	C₃×#125	C₂²×C₃	1	1	yes	characteristic
95	C₃×#124	C₂²×C₃	1	1	yes	characteristic
96	C₃×#124	C₂²×C₃	1	1	yes	characteristic
97	C₃×#123	—	2	2	no	—
98	C₃×#121	—	2	2	no	—
99	C₃×#121	—	2	2	no	—
100	C₃×#121	C₂²×C₃	1	2	yes	—
101	C₃×#120	—	2	2	no	—
102	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
103	C₃×#117	C₂²×C₃	1	1	yes	characteristic
104	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
105	C₃×#103	C₂²×C₃	1	2	yes	—
106	C₃×#102	C₂²×C₃	1	2	yes	—
107	C₃×#102	C₂²×C₃	1	2	yes	—
108	C₃×#102	C₂²×C₃	1	2	yes	—
109	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
110	C₃×#97	C₂²×C₃	1	1	yes	characteristic
111	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
112	C₂³×C₉	—	2	2	no	—
113	C₂³×C₉	—	2	1	no	—
114	C₂³×C₉	—	2	1	no	—
115	C₂³×C₉	—	2	1	no	—
116	C₂³×C₉	—	4	2	no	—
117	C₂³×C₉	—	8	2	no	—
118	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
119	Q₈×C₉	—	2	2	no	—
120	D₄×C₉	—	2	2	no	—
121	D₄×C₉	—	2	2	no	—
122	D₄×C₉	—	2	2	no	—
123	D₄×C₉	—	2	2	no	—
124	D₄×C₉	—	2	2	no	—
125	D₄×C₉	—	4	2	no	—
126	D₄×C₉	—	4	2	no	—
127	D₄×C₉	—	8	2	no	—
128	D₄×C₉	—	8	2	no	—
129	D₄×C₉	—	8	2	no	—
130	D₄×C₉	—	8	2	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	4	2	no	—
135	C₂×C₄×C₉	—	8	2	no	—
136	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
137	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
140	C₈×C₉	—	2	2	no	—
141	C₈×C₉	—	2	2	no	—
142	#540	C₂×C₉	1	1	yes	characteristic, complemented
143	#535	C₂×C₉	1	1	yes	characteristic, complemented
144	#496	C₂×C₉	1	1	yes	characteristic, complemented
145	#493	C₂×C₉	1	1	yes	characteristic, complemented
146	#490	C₂×C₉	1	1	yes	characteristic, complemented
147	#488	C₂×C₉	1	1	yes	characteristic, complemented
148	#463	C₂×C₉	1	2	yes	complemented
149	#459	C₂×C₉	1	2	yes	complemented
150	#449	C₂×C₉	1	2	yes	complemented
151	#447	C₂×C₉	1	2	yes	complemented
152	#433	C₂×C₉	1	1	yes	characteristic, complemented
153	C₂⁴×C₃	—	2	1	no	—
154	C₃×#41	—	4	2	no	—
155	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₃×D₄	—	2	1	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	1	no	—
159	C₂×C₃×D₄	—	2	2	no	—
160	C₂×C₃×D₄	—	2	2	no	—
161	C₂×C₃×D₄	—	2	2	no	—
162	C₂×C₃×D₄	—	4	2	no	—
163	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	2	2	no	—
169	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
170	C₃×SD₁₆	—	4	2	no	—
171	C₃×D₈	—	4	2	no	—
172	C₃×D₈	—	4	2	no	—
173	C₃×D₈	—	4	2	no	—
174	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
175	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
176	C₃×C₄⋊C₄	—	2	2	no	—
177	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
178	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
179	C₃×C₂²⋊C₄	—	2	2	no	—
180	C₃×C₂²⋊C₄	—	2	2	no	—
181	C₃×C₂²⋊C₄	—	2	2	no	—
182	C₃×C₂²⋊C₄	—	2	2	no	—
183	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
184	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
185	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
186	C₂²×C₉	—	2	1	no	—
187	C₂²×C₉	—	2	2	no	—
188	C₂²×C₉	—	4	1	no	—
189	C₂²×C₉	—	4	1	no	—
190	C₂²×C₉	—	4	1	no	—
191	C₂²×C₉	—	4	2	no	—
192	C₂²×C₉	—	4	2	no	—
193	C₂²×C₉	—	4	2	no	—
194	C₂²×C₉	—	4	2	no	—
195	C₂²×C₉	—	4	2	no	—
196	C₂²×C₉	—	4	2	no	—
197	C₂²×C₉	—	8	4	no	—
198	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₉	—	2	1	no	—
200	C₄×C₉	—	2	2	no	—
201	C₄×C₉	—	2	2	no	—
202	C₄×C₉	—	4	1	no	—
203	C₄×C₉	—	4	2	no	—
204	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
205	C₂×#41	C₂²×C₉	1	1	yes	characteristic
206	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
208	C₂×D₈	C₂²×C₉	1	2	yes	—
209	C₂×D₈	C₂²×C₉	1	2	yes	—
210	C₂×D₈	C₂²×C₉	1	2	yes	complemented
211	#127	C₂²×C₉	1	1	yes	characteristic
212	#127	C₂²×C₉	1	1	yes	characteristic
213	#127	C₂²×C₉	1	1	yes	characteristic, complemented
214	#125	C₂²×C₉	1	1	yes	characteristic, complemented
215	#124	C₂²×C₉	1	1	yes	characteristic
216	#124	C₂²×C₉	1	1	yes	characteristic
217	#123	—	2	2	no	—
218	#121	—	2	2	no	—
219	#121	—	2	2	no	—
220	#121	C₂²×C₉	1	2	yes	—
221	#120	—	2	2	no	—
222	C₄×D₄	C₂²×C₉	1	2	yes	complemented
223	#117	C₂²×C₉	1	1	yes	characteristic
224	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
225	#103	C₂²×C₉	1	2	yes	complemented
226	#102	C₂²×C₉	1	2	yes	—
227	#102	C₂²×C₉	1	2	yes	—
228	#102	C₂²×C₉	1	2	yes	complemented
229	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
230	#97	C₂²×C₉	1	1	yes	characteristic, complemented
231	C₄×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
232	C₂³×C₃	—	2	2	no	—
233	C₂³×C₃	—	2	1	no	—
234	C₂³×C₃	—	2	1	no	—
235	C₂³×C₃	—	2	1	no	—
236	C₂³×C₃	—	4	2	no	—
237	C₂³×C₃	—	8	2	no	—
238	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
239	C₃×Q₈	—	2	2	no	—
240	C₃×D₄	—	2	2	no	—
241	C₃×D₄	—	2	2	no	—
242	C₃×D₄	—	2	2	no	—
243	C₃×D₄	—	2	2	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	4	2	no	—
246	C₃×D₄	—	4	2	no	—
247	C₃×D₄	—	8	2	no	—
248	C₃×D₄	—	8	2	no	—
249	C₃×D₄	—	8	2	no	—
250	C₃×D₄	—	8	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	4	2	no	—
255	C₂×C₃×C₄	—	8	2	no	—
256	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
260	C₃×C₈	—	2	2	no	—
261	C₃×C₈	—	2	2	no	—
262	C₂×C₉	—	4	1	no	—
263	C₂×C₉	—	8	1	no	—
264	C₂×C₉	—	8	2	no	—
265	C₂×C₉	—	8	1	no	—
266	C₂×C₉	—	8	1	no	—
267	C₂×C₉	#535	1	1	yes	characteristic
268	C₂×C₉	#576	1	2	yes	—
269	C₂⁴	—	2	1	no	—
270	#41	—	4	2	no	—
271	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
280	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
281	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
282	C₂×D₄	C₂³×C₉	1	2	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
286	SD₁₆	—	4	2	no	—
287	D₈	—	4	2	no	—
288	D₈	—	4	2	no	—
289	D₈	—	4	2	no	—
290	C₂×C₈	C₂³×C₉	1	2	yes	—
291	C₂×C₈	C₂³×C₉	1	2	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	D₄×C₉	1	2	yes	—
294	C₄⋊C₄	C₂³×C₉	1	2	yes	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	D₄×C₉	1	2	yes	—
300	C₄²	C₂³×C₉	1	1	yes	characteristic
301	C₄²	C₂³×C₉	1	1	yes	characteristic
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	—	4	2	no	—
306	C₂²×C₃	—	4	2	no	—
307	C₂²×C₃	—	4	2	no	—
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	4	1	no	—
311	C₂²×C₃	—	4	1	no	—
312	C₂²×C₃	—	4	2	no	—
313	C₂²×C₃	—	8	4	no	—
314	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	4	2	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
321	C₉	#3220	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³	—	2	2	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	8	2	no	—
328	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
329	Q₈	—	2	2	no	—
330	D₄	—	2	2	no	—
331	D₄	—	2	2	no	—
332	D₄	—	2	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	8	2	no	—
338	D₄	—	8	2	no	—
339	D₄	—	8	2	no	—
340	D₄	—	8	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
347	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
348	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
349	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	2	2	no	—
352	C₂×C₃	—	4	1	no	—
353	C₂×C₃	—	8	1	no	—
354	C₂×C₃	—	8	1	no	—
355	C₂×C₃	—	8	2	no	—
356	C₂×C₃	—	8	1	no	—
357	C₂×C₃	C₃×#535	1	1	yes	characteristic
358	C₂×C₃	C₃×#576	1	2	yes	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	8	4	no	—
371	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
378	C₃	C₃×#3220	1	1	yes	characteristic
379	C₂	—	4	1	no	—
380	C₂	—	8	1	no	—
381	C₂	—	8	1	no	—
382	C₂	—	8	1	no	—
383	C₂	—	8	2	no	—
384	C₂	C₉×#535	1	1	yes	characteristic
385	C₂	C₉×#576	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#3220	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#540	C₂	semidirect
2. C₉×#535	C₂	semidirect
3. C₉×#496	C₂	semidirect
4. C₉×#493	C₂	semidirect
5. C₉×#490	C₂	semidirect
6. C₉×#488	C₂	semidirect
7. C₉×#463	C₂	semidirect
8. C₉×#459	C₂	semidirect
9. C₉×#449	C₂	semidirect
10. C₉×#447	C₂	semidirect
11. C₉×#433	C₂	semidirect
15. C₂×C₉×SD₁₆	C₂²	semidirect
18. C₂×C₉×D₈	C₂²	semidirect
21. C₉×#127	C₂²	semidirect
22. C₉×#125	C₂²	semidirect
30. C₄×D₄×C₉	C₂²	semidirect
32. C₉×C₄⋊C₈	C₂²	semidirect
33. C₉×#103	C₂²	semidirect
36. C₉×#102	C₂²	semidirect
38. C₉×#97	C₂²	semidirect
39. C₄×C₈×C₉	C₂²	semidirect
84. #3220	C₉	direct (N × H)
142. #540	C₂×C₉	semidirect
143. #535	C₂×C₉	semidirect
144. #496	C₂×C₉	semidirect
145. #493	C₂×C₉	semidirect
146. #490	C₂×C₉	semidirect
147. #488	C₂×C₉	semidirect
148. #463	C₂×C₉	semidirect
149. #459	C₂×C₉	semidirect
150. #449	C₂×C₉	semidirect
151. #447	C₂×C₉	semidirect
152. #433	C₂×C₉	semidirect
207. C₂×SD₁₆	C₂²×C₉	semidirect
210. C₂×D₈	C₂²×C₉	semidirect
213. #127	C₂²×C₉	semidirect
214. #125	C₂²×C₉	semidirect
222. C₄×D₄	C₂²×C₉	semidirect
224. C₄⋊C₈	C₂²×C₉	semidirect
225. #103	C₂²×C₉	semidirect
228. #102	C₂²×C₉	semidirect
230. #97	C₂²×C₉	semidirect
231. C₄×C₈	C₂²×C₉	semidirect
321. C₉	#3220	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×#540	2
C₉×#535	2
C₉×#496	2
C₉×#493	2
C₉×#490	2
C₉×#488	2
C₉×#463	2
C₉×#459	2
C₉×#449	2
C₉×#447	2
C₉×#433	2
C₃×#3220	3

Subgroups — C9×#3220 #11767941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3220 #11767941