Subgroups — C₉×#3233 #11767954

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×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#529	C₂	1	1	yes	maximal, characteristic
3	C₉×#499	C₂	1	2	yes	maximal, complemented
4	C₉×#488	C₂	1	2	yes	maximal, complemented
5	C₉×#485	C₂	1	2	yes	maximal, complemented
6	C₉×#482	C₂	1	2	yes	maximal
7	C₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#474	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3233	C₃	1	1	yes	maximal, characteristic
13	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₉×#126	—	2	1	no	—
16	C₉×#125	C₂²	1	1	yes	characteristic
17	C₉×#125	C₂²	1	2	yes	—
18	C₉×#124	C₂²	1	1	yes	characteristic
19	C₉×#123	—	2	1	no	—
20	C₉×C₂²⋊Q₈	—	2	1	no	—
21	C₉×C₂²⋊Q₈	—	2	1	no	—
22	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₉×#121	C₂²	1	1	yes	characteristic
24	C₄×Q₈×C₉	—	2	1	no	—
25	C₄×Q₈×C₉	—	2	1	no	—
26	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₉	—	2	1	no	—
28	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
29	C₉×#117	—	2	1	no	—
30	C₉×#117	C₂²	1	2	yes	—
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	1	yes	characteristic
37	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#103	C₂²	1	2	yes	—
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×#102	C₂²	1	2	yes	—
42	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₄×C₈×C₉	C₂²	1	2	yes	—
44	C₃×#533	C₂×C₃	1	1	yes	characteristic
45	C₃×#529	C₂×C₃	1	1	yes	characteristic
46	C₃×#499	C₂×C₃	1	2	yes	—
47	C₃×#488	C₂×C₃	1	2	yes	—
48	C₃×#485	C₂×C₃	1	2	yes	—
49	C₃×#482	C₂×C₃	1	2	yes	—
50	C₃×#477	C₂×C₃	1	1	yes	characteristic
51	C₃×#476	C₂×C₃	1	1	yes	characteristic
52	C₃×#475	C₂×C₃	1	1	yes	characteristic
53	C₃×#474	C₂×C₃	1	1	yes	characteristic
54	C₃×#431	C₂×C₃	1	1	yes	characteristic
55	C₂×Q₈×C₉	—	2	1	no	—
56	C₂×Q₈×C₉	—	2	1	no	—
57	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
58	C₂×D₄×C₉	—	2	1	no	—
59	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
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	1	no	—
67	C₉×C₄⋊C₄	—	2	1	no	—
68	C₉×C₄⋊C₄	—	2	1	no	—
69	C₉×C₄⋊C₄	—	2	2	no	—
70	C₉×C₄⋊C₄	—	2	2	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	C₂³	1	2	yes	—
75	C₉×C₄⋊C₄	C₂³	1	2	yes	—
76	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₉×C₂²⋊C₄	—	2	2	no	—
79	C₉×C₂²⋊C₄	—	2	1	no	—
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	C₄²×C₉	—	2	1	no	—
85	C₄²×C₉	—	2	2	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	#3233	C₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₃×#126	—	2	1	no	—
94	C₃×#125	C₂²×C₃	1	1	yes	characteristic
95	C₃×#125	C₂²×C₃	1	2	yes	—
96	C₃×#124	C₂²×C₃	1	1	yes	characteristic
97	C₃×#123	—	2	1	no	—
98	C₃×C₂²⋊Q₈	—	2	1	no	—
99	C₃×C₂²⋊Q₈	—	2	1	no	—
100	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
101	C₃×#121	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄×Q₈	—	2	1	no	—
103	C₃×C₄×Q₈	—	2	1	no	—
104	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₃×C₄×D₄	—	2	1	no	—
106	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
107	C₃×#117	—	2	1	no	—
108	C₃×#117	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
115	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
116	C₃×#103	C₂²×C₃	1	2	yes	—
117	C₃×#103	C₂²×C₃	1	2	yes	—
118	C₃×#102	C₂²×C₃	1	2	yes	—
119	C₃×#102	C₂²×C₃	1	2	yes	—
120	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
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	1	no	—
125	Q₈×C₉	—	2	1	no	—
126	Q₈×C₉	—	4	2	no	—
127	Q₈×C₉	—	4	2	no	—
128	D₄×C₉	—	2	1	no	—
129	D₄×C₉	—	2	1	no	—
130	D₄×C₉	—	4	2	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	4	1	no	—
140	C₂×C₄×C₉	—	4	2	no	—
141	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
147	C₈×C₉	—	2	2	no	—
148	C₈×C₉	—	2	2	no	—
149	#533	C₂×C₉	1	1	yes	characteristic, complemented
150	#529	C₂×C₉	1	1	yes	characteristic
151	#499	C₂×C₉	1	2	yes	complemented
152	#488	C₂×C₉	1	2	yes	complemented
153	#485	C₂×C₉	1	2	yes	complemented
154	#482	C₂×C₉	1	2	yes	—
155	#477	C₂×C₉	1	1	yes	characteristic, complemented
156	#476	C₂×C₉	1	1	yes	characteristic, complemented
157	#475	C₂×C₉	1	1	yes	characteristic, complemented
158	#474	C₂×C₉	1	1	yes	characteristic, complemented
159	#431	C₂×C₉	1	1	yes	characteristic, complemented
160	C₂×C₃×Q₈	—	2	1	no	—
161	C₂×C₃×Q₈	—	2	1	no	—
162	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₃×D₄	—	2	1	no	—
164	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₃×C₄	—	2	1	no	—
166	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
170	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
171	C₃×C₄⋊C₄	—	2	1	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	1	no	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	—	2	1	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	2	1	no	—
179	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
180	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₄	—	2	2	no	—
184	C₃×C₂²⋊C₄	—	2	1	no	—
185	C₃×C₂²⋊C₄	—	2	1	no	—
186	C₃×C₂²⋊C₄	—	2	1	no	—
187	C₃×C₂²⋊C₄	—	2	1	no	—
188	C₃×C₂²⋊C₄	—	2	1	no	—
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	—	2	2	no	—
191	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
192	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
193	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
194	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₉	—	2	1	no	—
196	C₂²×C₉	—	2	1	no	—
197	C₂²×C₉	—	2	1	no	—
198	C₂²×C₉	—	4	1	no	—
199	C₂²×C₉	—	4	1	no	—
200	C₂²×C₉	—	4	1	no	—
201	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₉	—	2	1	no	—
203	C₄×C₉	—	2	1	no	—
204	C₄×C₉	—	2	1	no	—
205	C₄×C₉	—	2	1	no	—
206	C₄×C₉	—	4	1	no	—
207	C₄×C₉	—	4	1	no	—
208	C₄×C₉	—	4	2	no	—
209	C₄×C₉	—	4	1	no	—
210	C₄×C₉	—	4	2	no	—
211	C₄×C₉	#135	1	2	yes	—
212	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
213	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
214	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
215	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
216	#126	—	2	1	no	—
217	#125	C₂²×C₉	1	1	yes	characteristic
218	#125	C₂²×C₉	1	2	yes	—
219	#124	C₂²×C₉	1	1	yes	characteristic
220	#123	—	2	1	no	—
221	C₂²⋊Q₈	—	2	1	no	—
222	C₂²⋊Q₈	—	2	1	no	—
223	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
224	#121	C₂²×C₉	1	1	yes	characteristic
225	C₄×Q₈	—	2	1	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
230	#117	—	2	1	no	—
231	#117	C₂²×C₉	1	2	yes	—
232	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
233	#107	C₂²×C₉	1	2	yes	—
234	#107	C₂²×C₉	1	2	yes	—
235	#106	C₂²×C₉	1	2	yes	—
236	#106	C₂²×C₉	1	2	yes	—
237	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
238	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
239	#103	C₂²×C₉	1	2	yes	—
240	#103	C₂²×C₉	1	2	yes	—
241	#102	C₂²×C₉	1	2	yes	—
242	#102	C₂²×C₉	1	2	yes	—
243	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
244	C₄×C₈	C₂²×C₉	1	2	yes	—
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
247	C₃×Q₈	—	2	1	no	—
248	C₃×Q₈	—	2	1	no	—
249	C₃×Q₈	—	4	2	no	—
250	C₃×Q₈	—	4	2	no	—
251	C₃×D₄	—	2	1	no	—
252	C₃×D₄	—	2	1	no	—
253	C₃×D₄	—	4	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	4	1	no	—
263	C₂×C₃×C₄	—	4	2	no	—
264	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
270	C₃×C₈	—	2	2	no	—
271	C₃×C₈	—	2	2	no	—
272	C₂×C₉	—	4	1	no	—
273	C₂×C₉	—	8	1	no	—
274	C₂×C₉	#536	1	1	yes	characteristic
275	C₂×C₉	C₂×#135	1	1	yes	characteristic
276	C₂×C₉	#575	1	1	yes	characteristic
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
284	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
285	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
286	C₂×C₈	C₂³×C₉	1	2	yes	—
287	C₂×C₈	C₂³×C₉	1	2	yes	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	C₂³×C₉	1	2	yes	—
297	C₄⋊C₄	C₂³×C₉	1	2	yes	—
298	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
299	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	2	no	—
308	C₄²	D₄×C₉	1	1	yes	characteristic
309	C₄²	D₄×C₉	1	1	yes	characteristic
310	C₄²	C₂³×C₉	1	1	yes	characteristic
311	C₄²	C₂³×C₉	1	1	yes	characteristic
312	C₂²×C₃	—	2	1	no	—
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	—	4	1	no	—
317	C₂²×C₃	—	4	1	no	—
318	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
319	C₃×C₄	—	2	1	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	4	1	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	—	4	1	no	—
326	C₃×C₄	—	4	2	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	C₃×#135	1	2	yes	—
329	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
330	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
331	C₉	#3233	1	1	yes	characteristic, direct product factor, Sylow
332	C₂³	—	2	1	no	—
333	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	2	1	no	—
339	D₄	—	2	1	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
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	C₂×D₄×C₉	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
356	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₂×C₃	—	4	1	no	—
360	C₂×C₃	—	8	1	no	—
361	C₂×C₃	C₃×#536	1	1	yes	characteristic
362	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
363	C₂×C₃	C₃×#575	1	1	yes	characteristic
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	2	no	—
380	C₄	C₉×#135	1	2	yes	—
381	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
382	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
383	C₃	C₃×#3233	1	1	yes	characteristic
384	C₂	—	4	1	no	—
385	C₂	—	8	1	no	—
386	C₂	C₉×#536	1	1	yes	characteristic
387	C₂	C₂×C₉×#135	1	1	yes	characteristic
388	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
1. C₉×#533	C₂	semidirect
3. C₉×#499	C₂	semidirect
4. C₉×#488	C₂	semidirect
5. C₉×#485	C₂	semidirect
7. C₉×#477	C₂	semidirect
8. C₉×#476	C₂	semidirect
9. C₉×#475	C₂	semidirect
10. C₉×#474	C₂	semidirect
11. C₉×#431	C₂	semidirect
90. #3233	C₉	direct (N × H)
149. #533	C₂×C₉	semidirect
151. #499	C₂×C₉	semidirect
152. #488	C₂×C₉	semidirect
153. #485	C₂×C₉	semidirect
155. #477	C₂×C₉	semidirect
156. #476	C₂×C₉	semidirect
157. #475	C₂×C₉	semidirect
158. #474	C₂×C₉	semidirect
159. #431	C₂×C₉	semidirect
331. C₉	#3233	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×#533	2
C₉×#529	2
C₉×#499	2
C₉×#488	2
C₉×#485	2
C₉×#482	2
C₉×#477	2
C₉×#476	2
C₉×#475	2
C₉×#474	2
C₉×#431	2
C₃×#3233	3

Subgroups — C9×#3233 #11767954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3233 #11767954