Subgroups — C₉×#3232 #11767953

Order 1152.

501 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#499	C₂	1	2	yes	maximal, complemented
4	C₉×#488	C₂	1	2	yes	maximal, complemented
5	C₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#481	C₂	1	1	yes	maximal, characteristic
8	C₉×#480	C₂	1	1	yes	maximal, characteristic
9	C₉×#479	C₂	1	2	yes	maximal, complemented
10	C₉×#478	C₂	1	2	yes	maximal, complemented
11	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3232	C₃	1	1	yes	maximal, characteristic
13	C₉×#126	—	2	1	no	—
14	C₉×#125	—	2	1	no	—
15	C₉×#125	—	2	1	no	—
16	C₉×#125	C₂²	1	2	yes	—
17	C₉×#125	C₂²	1	2	yes	—
18	C₉×#125	C₂²	1	1	yes	characteristic
19	C₉×#124	C₂²	1	1	yes	characteristic
20	C₉×#123	—	2	1	no	—
21	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₉×#121	C₂²	1	1	yes	characteristic
23	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
24	C₄×D₄×C₉	—	2	1	no	—
25	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
26	C₉×#117	—	2	1	no	—
27	C₂×C₉×C₄⋊C₄	—	2	1	no	—
28	C₂×C₉×C₄⋊C₄	—	2	1	no	—
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
32	C₉×#107	C₂²	1	2	yes	—
33	C₉×#107	C₂²	1	2	yes	—
34	C₉×#106	C₂²	1	2	yes	—
35	C₉×#106	C₂²	1	2	yes	—
36	C₉×C₄⋊C₈	C₂²	1	2	yes	—
37	C₉×#103	C₂²	1	2	yes	—
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#102	C₂²	1	2	yes	—
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₄×C₈×C₉	C₂²	1	2	yes	—
44	C₃×#529	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
46	C₃×#499	C₂×C₃	1	2	yes	—
47	C₃×#488	C₂×C₃	1	2	yes	—
48	C₃×#484	C₂×C₃	1	1	yes	characteristic
49	C₃×#483	C₂×C₃	1	1	yes	characteristic
50	C₃×#481	C₂×C₃	1	1	yes	characteristic
51	C₃×#480	C₂×C₃	1	1	yes	characteristic
52	C₃×#479	C₂×C₃	1	2	yes	—
53	C₃×#478	C₂×C₃	1	2	yes	—
54	C₃×#431	C₂×C₃	1	1	yes	characteristic
55	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
56	C₂×D₄×C₉	—	2	1	no	—
57	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₉	—	2	1	no	—
59	C₂²×C₄×C₉	—	2	1	no	—
60	C₂²×C₄×C₉	—	2	1	no	—
61	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
62	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₈×C₉	C₂³	1	2	yes	—
65	C₂×C₈×C₉	C₂³	1	2	yes	—
66	C₉×C₄⋊C₄	—	2	2	no	—
67	C₉×C₄⋊C₄	—	2	2	no	—
68	C₉×C₄⋊C₄	—	2	2	no	—
69	C₉×C₄⋊C₄	—	2	2	no	—
70	C₉×C₄⋊C₄	—	2	1	no	—
71	C₉×C₄⋊C₄	—	2	1	no	—
72	C₉×C₄⋊C₄	—	2	1	no	—
73	C₉×C₄⋊C₄	—	2	1	no	—
74	C₉×C₄⋊C₄	—	2	1	no	—
75	C₉×C₄⋊C₄	—	2	1	no	—
76	C₉×C₄⋊C₄	C₂³	1	2	yes	—
77	C₉×C₄⋊C₄	C₂³	1	2	yes	—
78	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₉×C₂²⋊C₄	—	2	1	no	—
81	C₉×C₂²⋊C₄	—	2	1	no	—
82	C₉×C₂²⋊C₄	—	2	1	no	—
83	C₉×C₂²⋊C₄	—	2	1	no	—
84	C₉×C₂²⋊C₄	—	2	1	no	—
85	C₄²×C₉	—	2	1	no	—
86	C₄²×C₉	D₄	1	1	yes	characteristic
87	C₄²×C₉	D₄	1	1	yes	characteristic
88	C₄²×C₉	C₂³	1	1	yes	characteristic
89	C₄²×C₉	C₂³	1	1	yes	characteristic
90	#3232	C₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₃×#126	—	2	1	no	—
92	C₃×#125	—	2	1	no	—
93	C₃×#125	—	2	1	no	—
94	C₃×#125	C₂²×C₃	1	2	yes	—
95	C₃×#125	C₂²×C₃	1	2	yes	—
96	C₃×#125	C₂²×C₃	1	1	yes	characteristic
97	C₃×#124	C₂²×C₃	1	1	yes	characteristic
98	C₃×#123	—	2	1	no	—
99	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₃×#121	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄×D₄	—	2	1	no	—
103	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
104	C₃×#117	—	2	1	no	—
105	C₂×C₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
110	C₃×#107	C₂²×C₃	1	2	yes	—
111	C₃×#107	C₂²×C₃	1	2	yes	—
112	C₃×#106	C₂²×C₃	1	2	yes	—
113	C₃×#106	C₂²×C₃	1	2	yes	—
114	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
115	C₃×#103	C₂²×C₃	1	2	yes	—
116	C₃×#103	C₂²×C₃	1	2	yes	—
117	C₃×#102	C₂²×C₃	1	2	yes	—
118	C₃×#102	C₂²×C₃	1	2	yes	—
119	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
122	C₂³×C₉	—	2	1	no	—
123	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
124	Q₈×C₉	—	2	2	no	—
125	D₄×C₉	—	2	2	no	—
126	D₄×C₉	—	4	2	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	1	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	4	1	no	—
135	C₂×C₄×C₉	—	4	2	no	—
136	C₂×C₄×C₉	—	4	2	no	—
137	C₂×C₄×C₉	—	4	2	no	—
138	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
144	C₈×C₉	—	2	2	no	—
145	C₈×C₉	—	2	2	no	—
146	#529	C₂×C₉	1	1	yes	characteristic
147	C₂×#125	C₂×C₉	1	1	yes	characteristic, complemented
148	#499	C₂×C₉	1	2	yes	complemented
149	#488	C₂×C₉	1	2	yes	complemented
150	#484	C₂×C₉	1	1	yes	characteristic, complemented
151	#483	C₂×C₉	1	1	yes	characteristic, complemented
152	#481	C₂×C₉	1	1	yes	characteristic
153	#480	C₂×C₉	1	1	yes	characteristic
154	#479	C₂×C₉	1	2	yes	complemented
155	#478	C₂×C₉	1	2	yes	complemented
156	#431	C₂×C₉	1	1	yes	characteristic, complemented
157	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₃×D₄	—	2	1	no	—
159	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	2	1	no	—
162	C₂²×C₃×C₄	—	2	1	no	—
163	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
167	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	1	no	—
174	C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×C₄⋊C₄	—	2	1	no	—
176	C₃×C₄⋊C₄	—	2	1	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
179	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
180	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
181	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
182	C₃×C₂²⋊C₄	—	2	1	no	—
183	C₃×C₂²⋊C₄	—	2	1	no	—
184	C₃×C₂²⋊C₄	—	2	1	no	—
185	C₃×C₂²⋊C₄	—	2	1	no	—
186	C₃×C₂²⋊C₄	—	2	1	no	—
187	C₃×C₄²	—	2	1	no	—
188	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
189	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
190	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
191	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₉	—	2	1	no	—
193	C₂²×C₉	—	2	1	no	—
194	C₂²×C₉	—	4	1	no	—
195	C₂²×C₉	—	4	1	no	—
196	C₂²×C₉	—	4	1	no	—
197	C₂²×C₉	#135	1	2	yes	—
198	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₉	—	2	1	no	—
200	C₄×C₉	—	2	1	no	—
201	C₄×C₉	—	2	1	no	—
202	C₄×C₉	—	2	1	no	—
203	C₄×C₉	—	2	1	no	—
204	C₄×C₉	—	4	1	no	—
205	C₄×C₉	—	4	2	no	—
206	C₄×C₉	—	4	1	no	—
207	C₄×C₉	—	4	1	no	—
208	C₄×C₉	—	4	2	no	—
209	C₄×C₉	2₋¹⁺⁴	1	2	yes	—
210	#126	—	2	1	no	—
211	#125	—	2	1	no	—
212	#125	—	2	1	no	—
213	#125	C₂²×C₉	1	2	yes	—
214	#125	C₂²×C₉	1	2	yes	—
215	#125	C₂²×C₉	1	1	yes	characteristic
216	#124	C₂²×C₉	1	1	yes	characteristic
217	#123	—	2	1	no	—
218	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
219	#121	C₂²×C₉	1	1	yes	characteristic
220	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
223	#117	—	2	1	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
228	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
229	#107	C₂²×C₉	1	2	yes	—
230	#107	C₂²×C₉	1	2	yes	—
231	#106	C₂²×C₉	1	2	yes	—
232	#106	C₂²×C₉	1	2	yes	—
233	C₄⋊C₈	C₂²×C₉	1	2	yes	—
234	#103	C₂²×C₉	1	2	yes	—
235	#103	C₂²×C₉	1	2	yes	—
236	#102	C₂²×C₉	1	2	yes	—
237	#102	C₂²×C₉	1	2	yes	—
238	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
239	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
240	C₄×C₈	C₂²×C₉	1	2	yes	—
241	C₂³×C₃	—	2	1	no	—
242	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
243	C₃×Q₈	—	2	2	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	4	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	4	1	no	—
254	C₂×C₃×C₄	—	4	2	no	—
255	C₂×C₃×C₄	—	4	2	no	—
256	C₂×C₃×C₄	—	4	2	no	—
257	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
263	C₃×C₈	—	2	2	no	—
264	C₃×C₈	—	2	2	no	—
265	C₂×C₉	—	2	2	no	—
266	C₂×C₉	—	8	1	no	—
267	C₂×C₉	#536	1	1	yes	characteristic
268	C₂×C₉	C₂×#135	1	1	yes	characteristic
269	C₂×C₉	#575	1	1	yes	characteristic
270	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
277	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
279	C₂×C₈	C₂³×C₉	1	2	yes	—
280	C₂×C₈	C₂³×C₉	1	2	yes	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	C₂³×C₉	1	2	yes	—
292	C₄⋊C₄	C₂³×C₉	1	2	yes	—
293	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
294	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
295	C₂²⋊C₄	—	2	1	no	—
296	C₂²⋊C₄	—	2	1	no	—
297	C₂²⋊C₄	—	2	1	no	—
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	D₄×C₉	1	1	yes	characteristic
302	C₄²	D₄×C₉	1	1	yes	characteristic
303	C₄²	C₂³×C₉	1	1	yes	characteristic
304	C₄²	C₂³×C₉	1	1	yes	characteristic
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	4	1	no	—
308	C₂²×C₃	—	4	1	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	C₃×#135	1	2	yes	—
311	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	—	4	1	no	—
322	C₃×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
323	C₉	#3232	1	1	yes	characteristic, direct product factor, Sylow
324	C₂³	—	2	1	no	—
325	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
341	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
342	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
343	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
344	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
345	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₂×C₃	—	2	2	no	—
349	C₂×C₃	—	8	1	no	—
350	C₂×C₃	C₃×#536	1	1	yes	characteristic
351	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
352	C₂×C₃	C₃×#575	1	1	yes	characteristic
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	C₉×#135	1	2	yes	—
359	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	2	no	—
370	C₄	C₉×2₋¹⁺⁴	1	2	yes	—
371	C₃	C₃×#3232	1	1	yes	characteristic
372	C₂	—	2	2	no	—
373	C₂	—	8	1	no	—
374	C₂	C₉×#536	1	1	yes	characteristic
375	C₂	C₂×C₉×#135	1	1	yes	characteristic
376	C₂	C₉×#575	1	1	yes	characteristic

	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×#121	C₂²×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×#125	C₂	semidirect
3. C₉×#499	C₂	semidirect
4. C₉×#488	C₂	semidirect
5. C₉×#484	C₂	semidirect
6. C₉×#483	C₂	semidirect
9. C₉×#479	C₂	semidirect
10. C₉×#478	C₂	semidirect
11. C₉×#431	C₂	semidirect
90. #3232	C₉	direct (N × H)
147. C₂×#125	C₂×C₉	semidirect
148. #499	C₂×C₉	semidirect
149. #488	C₂×C₉	semidirect
150. #484	C₂×C₉	semidirect
151. #483	C₂×C₉	semidirect
154. #479	C₂×C₉	semidirect
155. #478	C₂×C₉	semidirect
156. #431	C₂×C₉	semidirect
323. C₉	#3232	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×#529	2
C₂×C₉×#125	2
C₉×#499	2
C₉×#488	2
C₉×#484	2
C₉×#483	2
C₉×#481	2
C₉×#480	2
C₉×#479	2
C₉×#478	2
C₉×#431	2
C₃×#3232	3

Subgroups — C9×#3232 #11767953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3232 #11767953