Subgroups — C₉×#3003 #11767724

Order 1152.

1491 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#450	C₂	1	4	yes	maximal, complemented
5	C₉×#447	C₂	1	4	yes	maximal, complemented
6	C₉×#418	C₂	1	2	yes	maximal, complemented
7	C₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3003	C₃	1	1	yes	maximal, characteristic
9	C₂⁵×C₉	—	2	1	no	—
10	C₂×C₉×#41	C₂²	1	1	yes	characteristic, complemented
11	C₂²×D₄×C₉	—	2	8	no	—
12	C₂²×D₄×C₉	—	2	2	no	—
13	C₂²×D₄×C₉	—	2	1	no	—
14	C₂²×D₄×C₉	C₂²	1	4	yes	—
15	C₂²×D₄×C₉	C₂²	1	2	yes	—
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₉×AGL(1,ℤ/8)	—	2	8	no	—
18	C₂×C₉×SD₁₆	C₂²	1	4	yes	complemented
19	C₂×C₉×D₈	C₂²	1	4	yes	complemented
20	C₂×C₉×M₁₆	C₂²	1	2	yes	complemented
21	C₉×#123	—	2	1	no	—
22	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
23	C₉×#121	C₂²	1	2	yes	complemented
24	C₉×#120	—	2	1	no	—
25	C₄×D₄×C₉	—	2	2	no	—
26	C₉×#117	C₂²	1	1	yes	characteristic, complemented
27	C₉×#102	C₂²	1	8	yes	complemented
28	C₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
29	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	—
31	C₃×#525	C₂×C₃	1	1	yes	characteristic
32	C₃×#450	C₂×C₃	1	4	yes	—
33	C₃×#447	C₂×C₃	1	4	yes	—
34	C₃×#418	C₂×C₃	1	2	yes	—
35	C₃×#407	C₂×C₃	1	1	yes	characteristic
36	C₂⁴×C₉	—	2	8	no	—
37	C₂⁴×C₉	—	2	4	no	—
38	C₂⁴×C₉	—	2	2	no	—
39	C₂⁴×C₉	—	4	8	no	—
40	C₂⁴×C₉	D₄	1	1	yes	characteristic
41	C₉×#41	—	2	4	no	—
42	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic, complemented
43	C₂×D₄×C₉	—	2	8	no	—
44	C₂×D₄×C₉	—	2	16	no	—
45	C₂×D₄×C₉	—	2	16	no	—
46	C₂×D₄×C₉	—	2	2	no	—
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	—	2	4	no	—
49	C₂×D₄×C₉	—	2	2	no	—
50	C₂×D₄×C₉	—	2	4	no	—
51	C₂×D₄×C₉	D₄	1	8	yes	complemented
52	C₂×D₄×C₉	C₂³	1	4	yes	—
53	C₂×D₄×C₉	C₂³	1	1	yes	characteristic, complemented
54	C₂²×C₄×C₉	—	2	4	no	—
55	C₂²×C₄×C₉	—	2	1	no	—
56	C₂²×C₄×C₉	D₄	1	2	yes	—
57	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂³	1	2	yes	—
59	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₉×SD₁₆	—	2	8	no	—
61	C₉×D₈	—	2	8	no	—
62	C₉×M₁₆	—	2	4	no	—
63	C₂×C₈×C₉	C₂³	1	4	yes	complemented
64	C₉×C₄⋊C₄	—	2	2	no	—
65	C₉×C₄⋊C₄	C₂³	1	2	yes	complemented
66	C₉×C₂²⋊C₄	—	2	1	no	—
67	C₉×C₂²⋊C₄	—	2	2	no	—
68	C₉×C₂²⋊C₄	—	2	2	no	—
69	C₄²×C₉	—	2	1	no	—
70	#3003	C₉	1	1	yes	characteristic, direct product factor, Sylow
71	C₂⁵×C₃	—	2	1	no	—
72	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₃×D₄	—	2	8	no	—
74	C₂²×C₃×D₄	—	2	2	no	—
75	C₂²×C₃×D₄	—	2	1	no	—
76	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
77	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
78	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
79	C₃×AGL(1,ℤ/8)	—	2	8	no	—
80	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
81	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
82	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
83	C₃×#123	—	2	1	no	—
84	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
85	C₃×#121	C₂²×C₃	1	2	yes	—
86	C₃×#120	—	2	1	no	—
87	C₃×C₄×D₄	—	2	2	no	—
88	C₃×#117	C₂²×C₃	1	1	yes	characteristic
89	C₃×#102	C₂²×C₃	1	8	yes	—
90	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
91	C₂³×C₉	—	2	2	no	—
92	C₂³×C₉	—	2	4	no	—
93	C₂³×C₉	—	2	16	no	—
94	C₂³×C₉	—	2	8	no	—
95	C₂³×C₉	—	2	4	no	—
96	C₂³×C₉	—	2	1	no	—
97	C₂³×C₉	—	4	32	no	—
98	C₂³×C₉	—	4	8	no	—
99	C₂³×C₉	—	4	8	no	—
100	C₂³×C₉	—	4	8	no	—
101	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
102	C₂³×C₉	C₂×D₄	1	2	yes	—
103	Q₈×C₉	—	2	2	no	—
104	D₄×C₉	—	2	16	no	—
105	D₄×C₉	—	2	8	no	—
106	D₄×C₉	—	2	4	no	—
107	D₄×C₉	—	2	2	no	—
108	D₄×C₉	—	4	2	no	—
109	D₄×C₉	—	4	4	no	—
110	D₄×C₉	C₂×D₄	1	8	yes	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	—	2	4	no	—
113	C₂×C₄×C₉	—	2	4	no	—
114	C₂×C₄×C₉	—	2	2	no	—
115	C₂×C₄×C₉	—	2	1	no	—
116	C₂×C₄×C₉	—	4	2	no	—
117	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
118	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
120	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
121	C₈×C₉	—	2	4	no	—
122	C₂³×D₄	C₂×C₉	1	1	yes	characteristic, complemented
123	C₂×AGL(1,ℤ/8)	C₂×C₉	1	2	yes	complemented
124	#525	C₂×C₉	1	1	yes	characteristic, complemented
125	#450	C₂×C₉	1	4	yes	complemented
126	#447	C₂×C₉	1	4	yes	complemented
127	#418	C₂×C₉	1	2	yes	complemented
128	#407	C₂×C₉	1	1	yes	characteristic, complemented
129	C₂⁴×C₃	—	2	8	no	—
130	C₂⁴×C₃	—	2	4	no	—
131	C₂⁴×C₃	—	2	2	no	—
132	C₂⁴×C₃	—	4	8	no	—
133	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
134	C₃×#41	—	2	4	no	—
135	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₃×D₄	—	2	8	no	—
137	C₂×C₃×D₄	—	2	16	no	—
138	C₂×C₃×D₄	—	2	16	no	—
139	C₂×C₃×D₄	—	2	2	no	—
140	C₂×C₃×D₄	—	2	1	no	—
141	C₂×C₃×D₄	—	2	4	no	—
142	C₂×C₃×D₄	—	2	2	no	—
143	C₂×C₃×D₄	—	2	4	no	—
144	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
145	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
146	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
147	C₂²×C₃×C₄	—	2	4	no	—
148	C₂²×C₃×C₄	—	2	1	no	—
149	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
150	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
152	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
153	C₃×SD₁₆	—	2	8	no	—
154	C₃×D₈	—	2	8	no	—
155	C₃×M₁₆	—	2	4	no	—
156	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
157	C₃×C₄⋊C₄	—	2	2	no	—
158	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
159	C₃×C₂²⋊C₄	—	2	1	no	—
160	C₃×C₂²⋊C₄	—	2	2	no	—
161	C₃×C₂²⋊C₄	—	2	2	no	—
162	C₃×C₄²	—	2	1	no	—
163	C₂²×C₉	—	2	8	no	—
164	C₂²×C₉	—	2	2	no	—
165	C₂²×C₉	—	2	2	no	—
166	C₂²×C₉	—	2	2	no	—
167	C₂²×C₉	—	2	8	no	—
168	C₂²×C₉	—	4	16	no	—
169	C₂²×C₉	—	4	32	no	—
170	C₂²×C₉	—	4	8	no	—
171	C₂²×C₉	—	4	1	no	—
172	C₂²×C₉	—	4	2	no	—
173	C₂²×C₉	#120	1	2	yes	—
174	C₂²×C₉	AGL(1,ℤ/8)	1	4	yes	complemented
175	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
176	C₄×C₉	—	2	2	no	—
177	C₄×C₉	—	4	1	no	—
178	C₄×C₉	—	4	2	no	—
179	C₄×C₉	#120	1	2	yes	—
180	C₄×C₉	C₂²×D₄	1	2	yes	—
181	C₂⁵	—	2	1	no	—
182	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
183	C₂²×D₄	—	2	8	no	—
184	C₂²×D₄	—	2	2	no	—
185	C₂²×D₄	—	2	1	no	—
186	C₂²×D₄	C₂²×C₉	1	4	yes	—
187	C₂²×D₄	C₂²×C₉	1	2	yes	—
188	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
189	AGL(1,ℤ/8)	—	2	8	no	—
190	C₂×SD₁₆	C₂²×C₉	1	4	yes	complemented
191	C₂×D₈	C₂²×C₉	1	4	yes	complemented
192	C₂×M₁₆	C₂²×C₉	1	2	yes	complemented
193	#123	—	2	1	no	—
194	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
195	#121	C₂²×C₉	1	2	yes	complemented
196	#120	—	2	1	no	—
197	C₄×D₄	—	2	2	no	—
198	#117	C₂²×C₉	1	1	yes	characteristic, complemented
199	#102	C₂²×C₉	1	8	yes	complemented
200	C₂²⋊C₈	C₂²×C₉	1	4	yes	complemented
201	C₂³×C₃	—	2	2	no	—
202	C₂³×C₃	—	2	4	no	—
203	C₂³×C₃	—	2	16	no	—
204	C₂³×C₃	—	2	8	no	—
205	C₂³×C₃	—	2	4	no	—
206	C₂³×C₃	—	2	1	no	—
207	C₂³×C₃	—	4	32	no	—
208	C₂³×C₃	—	4	8	no	—
209	C₂³×C₃	—	4	8	no	—
210	C₂³×C₃	—	4	8	no	—
211	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
212	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
213	C₃×Q₈	—	2	2	no	—
214	C₃×D₄	—	2	16	no	—
215	C₃×D₄	—	2	8	no	—
216	C₃×D₄	—	2	4	no	—
217	C₃×D₄	—	2	2	no	—
218	C₃×D₄	—	4	2	no	—
219	C₃×D₄	—	4	4	no	—
220	C₃×D₄	C₂×C₃×D₄	1	8	yes	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
228	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
230	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
231	C₃×C₈	—	2	4	no	—
232	C₂×C₉	—	2	2	no	—
233	C₂×C₉	—	2	4	no	—
234	C₂×C₉	—	4	8	no	—
235	C₂×C₉	—	8	1	no	—
236	C₂×C₉	C₂×#120	1	1	yes	characteristic
237	C₂×C₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	4	no	—
240	C₂⁴	—	2	2	no	—
241	C₂⁴	—	4	8	no	—
242	C₂⁴	D₄×C₉	1	1	yes	characteristic
243	#41	—	2	4	no	—
244	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic, complemented
245	C₂×D₄	—	2	8	no	—
246	C₂×D₄	—	2	16	no	—
247	C₂×D₄	—	2	16	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	—	2	1	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	D₄×C₉	1	8	yes	complemented
254	C₂×D₄	C₂³×C₉	1	4	yes	—
255	C₂×D₄	C₂³×C₉	1	1	yes	characteristic, complemented
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	D₄×C₉	1	2	yes	—
259	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
260	C₂²×C₄	C₂³×C₉	1	2	yes	—
261	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
262	SD₁₆	—	2	8	no	—
263	D₈	—	2	8	no	—
264	M₁₆	—	2	4	no	—
265	C₂×C₈	C₂³×C₉	1	4	yes	complemented
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	C₂³×C₉	1	2	yes	complemented
268	C₂²⋊C₄	—	2	1	no	—
269	C₂²⋊C₄	—	2	2	no	—
270	C₂²⋊C₄	—	2	2	no	—
271	C₄²	—	2	1	no	—
272	C₂²×C₃	—	2	8	no	—
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	2	8	no	—
277	C₂²×C₃	—	4	16	no	—
278	C₂²×C₃	—	4	32	no	—
279	C₂²×C₃	—	4	8	no	—
280	C₂²×C₃	—	4	2	no	—
281	C₂²×C₃	—	4	1	no	—
282	C₂²×C₃	C₃×#120	1	2	yes	—
283	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	4	yes	—
284	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	4	2	no	—
287	C₃×C₄	—	4	1	no	—
288	C₃×C₄	C₃×#120	1	2	yes	—
289	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
290	C₉	#3003	1	1	yes	characteristic, direct product factor, Sylow
291	C₂³	—	2	2	no	—
292	C₂³	—	2	4	no	—
293	C₂³	—	2	16	no	—
294	C₂³	—	2	8	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	4	32	no	—
298	C₂³	—	4	8	no	—
299	C₂³	—	4	8	no	—
300	C₂³	—	4	8	no	—
301	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
302	C₂³	C₂×D₄×C₉	1	2	yes	—
303	Q₈	—	2	2	no	—
304	D₄	—	2	16	no	—
305	D₄	—	2	8	no	—
306	D₄	—	2	4	no	—
307	D₄	—	2	2	no	—
308	D₄	—	4	2	no	—
309	D₄	—	4	4	no	—
310	D₄	C₂×D₄×C₉	1	8	yes	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
318	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
319	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
320	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
321	C₈	—	2	4	no	—
322	C₂×C₃	—	2	2	no	—
323	C₂×C₃	—	2	4	no	—
324	C₂×C₃	—	4	8	no	—
325	C₂×C₃	—	8	1	no	—
326	C₂×C₃	C₂×C₃×#120	1	1	yes	characteristic
327	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
328	C₂²	—	2	8	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	8	no	—
333	C₂²	—	4	16	no	—
334	C₂²	—	4	32	no	—
335	C₂²	—	4	8	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	2	no	—
338	C₂²	C₉×#120	1	2	yes	—
339	C₂²	C₉×AGL(1,ℤ/8)	1	4	yes	complemented
340	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
341	C₄	—	2	2	no	—
342	C₄	—	4	1	no	—
343	C₄	—	4	2	no	—
344	C₄	C₉×#120	1	2	yes	—
345	C₄	C₂²×D₄×C₉	1	2	yes	—
346	C₃	C₃×#3003	1	1	yes	characteristic
347	C₂	—	2	2	no	—
348	C₂	—	2	4	no	—
349	C₂	—	4	8	no	—
350	C₂	—	8	1	no	—
351	C₂	C₂×C₉×#120	1	1	yes	characteristic
352	C₂	C₂×C₉×AGL(1,ℤ/8)	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×#3003	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×C₉	C₂	semidirect
2. C₂×C₉×AGL(1,ℤ/8)	C₂	semidirect
3. C₉×#525	C₂	semidirect
4. C₉×#450	C₂	semidirect
5. C₉×#447	C₂	semidirect
6. C₉×#418	C₂	semidirect
7. C₉×#407	C₂	semidirect
10. C₂×C₉×#41	C₂²	semidirect
18. C₂×C₉×SD₁₆	C₂²	semidirect
19. C₂×C₉×D₈	C₂²	semidirect
20. C₂×C₉×M₁₆	C₂²	semidirect
22. C₉×C₂²⋊Q₈	C₂²	semidirect
23. C₉×#121	C₂²	semidirect
26. C₉×#117	C₂²	semidirect
27. C₉×#102	C₂²	semidirect
28. C₉×C₂²⋊C₈	C₂²	semidirect
42. C₂×Q₈×C₉	C₂³	semidirect
51. C₂×D₄×C₉	D₄	semidirect
53. C₂×D₄×C₉	C₂³	semidirect
63. C₂×C₈×C₉	C₂³	semidirect
65. C₉×C₄⋊C₄	C₂³	semidirect
70. #3003	C₉	direct (N × H)
122. C₂³×D₄	C₂×C₉	semidirect
123. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
124. #525	C₂×C₉	semidirect
125. #450	C₂×C₉	semidirect
126. #447	C₂×C₉	semidirect
127. #418	C₂×C₉	semidirect
128. #407	C₂×C₉	semidirect
174. C₂²×C₉	AGL(1,ℤ/8)	semidirect
182. C₂×#41	C₂²×C₉	semidirect
190. C₂×SD₁₆	C₂²×C₉	semidirect
191. C₂×D₈	C₂²×C₉	semidirect
192. C₂×M₁₆	C₂²×C₉	semidirect
194. C₂²⋊Q₈	C₂²×C₉	semidirect
195. #121	C₂²×C₉	semidirect
198. #117	C₂²×C₉	semidirect
199. #102	C₂²×C₉	semidirect
200. C₂²⋊C₈	C₂²×C₉	semidirect
244. C₂×Q₈	C₂³×C₉	semidirect
253. C₂×D₄	D₄×C₉	semidirect
255. C₂×D₄	C₂³×C₉	semidirect
265. C₂×C₈	C₂³×C₉	semidirect
267. C₄⋊C₄	C₂³×C₉	semidirect
290. C₉	#3003	direct (N × H)
339. C₂²	C₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₄×C₉	2
C₂×C₉×AGL(1,ℤ/8)	2
C₉×#525	2
C₉×#450	2
C₉×#447	2
C₉×#418	2
C₉×#407	2
C₃×#3003	3

Subgroups — C9×#3003 #11767724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3003 #11767724