Subgroups — C₉×#2002 #11766723

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2002	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#41	C₂²	1	1	yes	characteristic
10	C₂²×D₄×C₉	—	2	2	no	—
11	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
13	C₉×AGL(1,ℤ/8)	—	2	2	no	—
14	C₉×AGL(1,ℤ/8)	—	2	2	no	—
15	C₂×C₉×SD₁₆	—	2	1	no	—
16	C₂×C₉×D₈	—	2	1	no	—
17	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
19	C₉×#127	—	2	2	no	—
20	C₉×#127	—	2	1	no	—
21	C₉×#127	—	2	2	no	—
22	C₉×#124	—	2	1	no	—
23	C₉×#121	—	2	2	no	—
24	C₉×#120	—	2	2	no	—
25	C₉×#117	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
27	C₉×#104	—	2	2	no	—
28	C₉×#102	—	2	2	no	—
29	C₉×#100	—	2	2	no	—
30	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
31	C₃×#535	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×#127	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×#104	C₂×C₃	1	1	yes	characteristic
34	C₃×#418	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×#100	C₂×C₃	1	1	yes	characteristic
36	C₃×#339	C₂×C₃	1	1	yes	characteristic
37	C₂⁴×C₉	—	2	1	no	—
38	C₂⁴×C₉	D₄	1	2	yes	—
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	C₂×Q₈×C₉	D₄	1	1	yes	characteristic, complemented
44	C₂×D₄×C₉	—	2	8	no	—
45	C₂×D₄×C₉	—	2	1	no	—
46	C₂×D₄×C₉	—	2	4	no	—
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	—	2	1	no	—
49	C₂×D₄×C₉	—	2	1	no	—
50	C₂×D₄×C₉	—	2	1	no	—
51	C₂×D₄×C₉	—	2	1	no	—
52	C₂×D₄×C₉	—	2	1	no	—
53	C₂×D₄×C₉	—	2	1	no	—
54	C₂×D₄×C₉	—	2	1	no	—
55	C₂×D₄×C₉	—	2	1	no	—
56	C₂×D₄×C₉	—	2	1	no	—
57	C₂×D₄×C₉	—	2	1	no	—
58	C₂×D₄×C₉	—	4	8	no	—
59	C₂×D₄×C₉	D₄	1	1	yes	characteristic, complemented
60	C₂×D₄×C₉	D₄	1	2	yes	complemented
61	C₂²×C₄×C₉	—	2	1	no	—
62	C₂²×C₄×C₉	—	2	1	no	—
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₉×SD₁₆	—	2	4	no	—
65	C₉×D₈	—	2	4	no	—
66	C₉×M₁₆	—	2	1	no	—
67	C₉×M₁₆	—	2	1	no	—
68	C₉×M₁₆	—	2	1	no	—
69	C₉×M₁₆	D₄	1	2	yes	complemented
70	C₂×C₈×C₉	—	2	1	no	—
71	C₂×C₈×C₉	—	2	1	no	—
72	C₉×C₄⋊C₄	D₄	1	2	yes	complemented
73	C₉×C₂²⋊C₄	—	2	4	no	—
74	C₉×C₂²⋊C₄	—	2	1	no	—
75	C₄²×C₉	—	2	1	no	—
76	C₄²×C₉	—	2	1	no	—
77	C₄²×C₉	D₄	1	2	yes	complemented
78	#2002	C₉	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₃×D₄	—	2	2	no	—
81	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₃×AGL(1,ℤ/8)	—	2	2	no	—
84	C₃×AGL(1,ℤ/8)	—	2	2	no	—
85	C₂×C₃×SD₁₆	—	2	1	no	—
86	C₂×C₃×D₈	—	2	1	no	—
87	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
89	C₃×#127	—	2	2	no	—
90	C₃×#127	—	2	1	no	—
91	C₃×#127	—	2	2	no	—
92	C₃×#124	—	2	1	no	—
93	C₃×#121	—	2	2	no	—
94	C₃×#120	—	2	2	no	—
95	C₃×#117	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
97	C₃×#104	—	2	2	no	—
98	C₃×#102	—	2	2	no	—
99	C₃×#100	—	2	2	no	—
100	C₂³×C₉	—	2	2	no	—
101	C₂³×C₉	—	2	2	no	—
102	C₂³×C₉	—	2	2	no	—
103	C₂³×C₉	—	2	1	no	—
104	C₂³×C₉	—	2	2	no	—
105	C₂³×C₉	—	4	4	no	—
106	C₂³×C₉	—	4	4	no	—
107	C₂³×C₉	—	4	1	no	—
108	C₂³×C₉	—	4	1	no	—
109	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
110	Q₈×C₉	—	2	1	no	—
111	Q₈×C₉	—	2	1	no	—
112	D₄×C₉	—	2	1	no	—
113	D₄×C₉	—	2	2	no	—
114	D₄×C₉	—	2	2	no	—
115	D₄×C₉	—	2	1	no	—
116	D₄×C₉	—	4	16	no	—
117	D₄×C₉	—	4	1	no	—
118	D₄×C₉	—	4	1	no	—
119	D₄×C₉	—	4	1	no	—
120	D₄×C₉	—	4	1	no	—
121	D₄×C₉	—	4	1	no	—
122	D₄×C₉	—	4	1	no	—
123	D₄×C₉	—	4	1	no	—
124	D₄×C₉	—	4	1	no	—
125	D₄×C₉	—	8	4	no	—
126	C₂×C₄×C₉	—	2	4	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	—	4	1	no	—
131	C₂×C₄×C₉	—	4	1	no	—
132	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₉	#41	1	1	yes	characteristic
138	C₈×C₉	—	2	2	no	—
139	C₈×C₉	—	4	1	no	—
140	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
141	#535	C₂×C₉	1	1	yes	characteristic, complemented
142	C₂×#127	C₂×C₉	1	1	yes	characteristic, complemented
143	C₂×#104	C₂×C₉	1	1	yes	characteristic, complemented
144	#418	C₂×C₉	1	1	yes	characteristic, complemented
145	C₂×#100	C₂×C₉	1	1	yes	characteristic, complemented
146	#339	C₂×C₉	1	1	yes	characteristic, complemented
147	C₂⁴×C₃	—	2	1	no	—
148	C₂⁴×C₃	C₃×D₄	1	2	yes	—
149	C₃×#41	—	2	1	no	—
150	C₃×#41	—	2	1	no	—
151	C₃×#41	—	2	1	no	—
152	C₃×#41	—	2	1	no	—
153	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
154	C₂×C₃×D₄	—	2	8	no	—
155	C₂×C₃×D₄	—	2	1	no	—
156	C₂×C₃×D₄	—	2	4	no	—
157	C₂×C₃×D₄	—	2	1	no	—
158	C₂×C₃×D₄	—	2	1	no	—
159	C₂×C₃×D₄	—	2	1	no	—
160	C₂×C₃×D₄	—	2	1	no	—
161	C₂×C₃×D₄	—	2	1	no	—
162	C₂×C₃×D₄	—	2	1	no	—
163	C₂×C₃×D₄	—	2	1	no	—
164	C₂×C₃×D₄	—	2	1	no	—
165	C₂×C₃×D₄	—	2	1	no	—
166	C₂×C₃×D₄	—	2	1	no	—
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	—	4	8	no	—
169	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
170	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
174	C₃×SD₁₆	—	2	4	no	—
175	C₃×D₈	—	2	4	no	—
176	C₃×M₁₆	—	2	1	no	—
177	C₃×M₁₆	—	2	1	no	—
178	C₃×M₁₆	—	2	1	no	—
179	C₃×M₁₆	C₃×D₄	1	2	yes	—
180	C₂×C₃×C₈	—	2	1	no	—
181	C₂×C₃×C₈	—	2	1	no	—
182	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
183	C₃×C₂²⋊C₄	—	2	4	no	—
184	C₃×C₂²⋊C₄	—	2	1	no	—
185	C₃×C₄²	—	2	1	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	C₃×D₄	1	2	yes	—
188	C₂²×C₉	—	2	2	no	—
189	C₂²×C₉	—	4	4	no	—
190	C₂²×C₉	—	4	4	no	—
191	C₂²×C₉	—	4	1	no	—
192	C₂²×C₉	—	4	2	no	—
193	C₂²×C₉	—	4	2	no	—
194	C₂²×C₉	—	4	2	no	—
195	C₂²×C₉	—	4	4	no	—
196	C₂²×C₉	—	8	2	no	—
197	C₂²×C₉	—	8	2	no	—
198	C₂²×C₉	—	8	2	no	—
199	C₂²×C₉	#120	1	1	yes	characteristic
200	C₂²×C₉	#120	1	1	yes	characteristic
201	C₂²×C₉	#121	1	1	yes	characteristic
202	C₄×C₉	—	2	4	no	—
203	C₄×C₉	—	4	1	no	—
204	C₄×C₉	—	4	2	no	—
205	C₄×C₉	#120	1	1	yes	characteristic
206	C₄×C₉	#121	1	1	yes	characteristic
207	C₄×C₉	#121	1	1	yes	characteristic
208	C₄×C₉	#127	1	1	yes	characteristic
209	C₂×#41	C₂²×C₉	1	1	yes	characteristic
210	C₂²×D₄	—	2	2	no	—
211	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
212	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
213	AGL(1,ℤ/8)	—	2	2	no	—
214	AGL(1,ℤ/8)	—	2	2	no	—
215	C₂×SD₁₆	—	2	1	no	—
216	C₂×D₈	—	2	1	no	—
217	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
218	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
219	#127	—	2	2	no	—
220	#127	—	2	1	no	—
221	#127	—	2	2	no	—
222	#124	—	2	1	no	—
223	#121	—	2	2	no	—
224	#120	—	2	2	no	—
225	#117	C₂²×C₉	1	1	yes	characteristic
226	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
227	#104	—	2	2	no	—
228	#102	—	2	2	no	—
229	#100	—	2	2	no	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	—	2	2	no	—
233	C₂³×C₃	—	2	2	no	—
234	C₂³×C₃	—	2	2	no	—
235	C₂³×C₃	—	4	4	no	—
236	C₂³×C₃	—	4	4	no	—
237	C₂³×C₃	—	4	1	no	—
238	C₂³×C₃	—	4	1	no	—
239	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
240	C₃×Q₈	—	2	1	no	—
241	C₃×Q₈	—	2	1	no	—
242	C₃×D₄	—	2	1	no	—
243	C₃×D₄	—	2	2	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	2	1	no	—
246	C₃×D₄	—	4	16	no	—
247	C₃×D₄	—	4	1	no	—
248	C₃×D₄	—	4	1	no	—
249	C₃×D₄	—	4	1	no	—
250	C₃×D₄	—	4	1	no	—
251	C₃×D₄	—	4	1	no	—
252	C₃×D₄	—	4	1	no	—
253	C₃×D₄	—	4	1	no	—
254	C₃×D₄	—	4	1	no	—
255	C₃×D₄	—	8	4	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	—	4	1	no	—
262	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
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	C₃×#41	1	1	yes	characteristic
268	C₃×C₈	—	2	2	no	—
269	C₃×C₈	—	4	1	no	—
270	C₂×C₉	—	2	1	no	—
271	C₂×C₉	—	2	1	no	—
272	C₂×C₉	—	8	1	no	—
273	C₂×C₉	—	8	2	no	—
274	C₂×C₉	—	8	2	no	—
275	C₂×C₉	#392	1	1	yes	characteristic
276	C₂×C₉	#453	1	2	yes	—
277	C₂⁴	—	2	1	no	—
278	C₂⁴	D₄×C₉	1	2	yes	—
279	#41	—	2	1	no	—
280	#41	—	2	1	no	—
281	#41	—	2	1	no	—
282	#41	—	2	1	no	—
283	C₂×Q₈	D₄×C₉	1	1	yes	characteristic, complemented
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	4	8	no	—
299	C₂×D₄	D₄×C₉	1	1	yes	characteristic, complemented
300	C₂×D₄	D₄×C₉	1	2	yes	complemented
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
304	SD₁₆	—	2	4	no	—
305	D₈	—	2	4	no	—
306	M₁₆	—	2	1	no	—
307	M₁₆	—	2	1	no	—
308	M₁₆	—	2	1	no	—
309	M₁₆	D₄×C₉	1	2	yes	complemented
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₄⋊C₄	D₄×C₉	1	2	yes	complemented
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	2	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	D₄×C₉	1	2	yes	complemented
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	4	4	no	—
320	C₂²×C₃	—	4	4	no	—
321	C₂²×C₃	—	4	1	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	—	4	2	no	—
325	C₂²×C₃	—	4	4	no	—
326	C₂²×C₃	—	8	2	no	—
327	C₂²×C₃	—	8	2	no	—
328	C₂²×C₃	—	8	2	no	—
329	C₂²×C₃	C₃×#120	1	1	yes	characteristic
330	C₂²×C₃	C₃×#120	1	1	yes	characteristic
331	C₂²×C₃	C₃×#121	1	1	yes	characteristic
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	4	1	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	C₃×#120	1	1	yes	characteristic
336	C₃×C₄	C₃×#121	1	1	yes	characteristic
337	C₃×C₄	C₃×#121	1	1	yes	characteristic
338	C₃×C₄	C₃×#127	1	1	yes	characteristic
339	C₉	#2002	1	1	yes	characteristic, direct product factor, Sylow
340	C₂³	—	2	2	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
350	Q₈	—	2	1	no	—
351	Q₈	—	2	1	no	—
352	D₄	—	2	1	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	1	no	—
356	D₄	—	4	16	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	8	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
373	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
375	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
377	C₂×C₄	C₉×#41	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	4	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	—	8	2	no	—
383	C₂×C₃	—	8	2	no	—
384	C₂×C₃	—	8	1	no	—
385	C₂×C₃	C₃×#392	1	1	yes	characteristic
386	C₂×C₃	C₃×#453	1	2	yes	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	C₉×#120	1	1	yes	characteristic
399	C₂²	C₉×#120	1	1	yes	characteristic
400	C₂²	C₉×#121	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	2	no	—
404	C₄	C₉×#120	1	1	yes	characteristic
405	C₄	C₉×#121	1	1	yes	characteristic
406	C₄	C₉×#121	1	1	yes	characteristic
407	C₄	C₉×#127	1	1	yes	characteristic
408	C₃	C₃×#2002	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	8	2	no	—
412	C₂	—	8	2	no	—
413	C₂	—	8	1	no	—
414	C₂	C₉×#392	1	1	yes	characteristic
415	C₂	C₉×#453	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	#120
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₃×#120
prime radical	C₃×#2002	C₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₉×#535	C₂	semidirect
3. C₂×C₉×#127	C₂	semidirect
4. C₂×C₉×#104	C₂	semidirect
5. C₉×#418	C₂	semidirect
6. C₂×C₉×#100	C₂	semidirect
7. C₉×#339	C₂	semidirect
43. C₂×Q₈×C₉	D₄	semidirect
59. C₂×D₄×C₉	D₄	semidirect
60. C₂×D₄×C₉	D₄	semidirect
69. C₉×M₁₆	D₄	semidirect
72. C₉×C₄⋊C₄	D₄	semidirect
77. C₄²×C₉	D₄	semidirect
78. #2002	C₉	direct (N × H)
140. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
141. #535	C₂×C₉	semidirect
142. C₂×#127	C₂×C₉	semidirect
143. C₂×#104	C₂×C₉	semidirect
144. #418	C₂×C₉	semidirect
145. C₂×#100	C₂×C₉	semidirect
146. #339	C₂×C₉	semidirect
283. C₂×Q₈	D₄×C₉	semidirect
299. C₂×D₄	D₄×C₉	semidirect
300. C₂×D₄	D₄×C₉	semidirect
309. M₁₆	D₄×C₉	semidirect
312. C₄⋊C₄	D₄×C₉	semidirect
317. C₄²	D₄×C₉	semidirect
339. C₉	#2002	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×AGL(1,ℤ/8)	2
C₉×#535	2
C₂×C₉×#127	2
C₂×C₉×#104	2
C₉×#418	2
C₂×C₉×#100	2
C₉×#339	2
C₃×#2002	3

Subgroups — C9×#2002 #11766723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2002 #11766723