Subgroups — C₉×#3217 #11767938

Order 1152.

735 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#496	C₂	1	2	yes	maximal, complemented
4	C₉×#490	C₂	1	2	yes	maximal, complemented
5	C₉×#460	C₂	1	2	yes	maximal, complemented
6	C₉×#459	C₂	1	2	yes	maximal, complemented
7	C₉×#450	C₂	1	2	yes	maximal, complemented
8	C₉×#447	C₂	1	2	yes	maximal, complemented
9	C₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3217	C₃	1	1	yes	maximal, characteristic
11	C₂²×D₄×C₉	—	2	1	no	—
12	C₂²×D₄×C₉	—	2	1	no	—
13	C₂²×D₄×C₉	C₂²	1	2	yes	—
14	C₂×C₉×SD₁₆	C₂²	1	4	yes	complemented
15	C₂×C₉×D₈	C₂²	1	4	yes	complemented
16	C₉×#127	—	2	1	no	—
17	C₉×#127	—	2	1	no	—
18	C₉×#127	C₂²	1	2	yes	—
19	C₉×#127	C₂²	1	2	yes	—
20	C₉×#126	—	2	1	no	—
21	C₉×#125	C₂²	1	1	yes	characteristic, complemented
22	C₉×#124	C₂²	1	1	yes	characteristic, complemented
23	C₉×#123	—	2	1	no	—
24	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₉×#121	C₂²	1	1	yes	characteristic
26	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₄×C₉	—	2	1	no	—
28	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
29	C₉×#117	—	2	1	no	—
30	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
32	C₉×#102	C₂²	1	4	yes	complemented
33	C₉×#102	C₂²	1	4	yes	complemented
34	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₉×#97	C₂²	1	2	yes	complemented
36	C₂×C₃×#127	C₂×C₃	1	1	yes	characteristic
37	C₃×#529	C₂×C₃	1	1	yes	characteristic
38	C₃×#496	C₂×C₃	1	2	yes	—
39	C₃×#490	C₂×C₃	1	2	yes	—
40	C₃×#460	C₂×C₃	1	2	yes	—
41	C₃×#459	C₂×C₃	1	2	yes	—
42	C₃×#450	C₂×C₃	1	2	yes	—
43	C₃×#447	C₂×C₃	1	2	yes	—
44	C₃×#432	C₂×C₃	1	1	yes	characteristic
45	C₂⁴×C₉	—	2	2	no	—
46	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	—	2	2	no	—
49	C₂×D₄×C₉	—	2	2	no	—
50	C₂×D₄×C₉	—	2	2	no	—
51	C₂×D₄×C₉	—	2	2	no	—
52	C₂×D₄×C₉	—	2	2	no	—
53	C₂×D₄×C₉	—	4	4	no	—
54	C₂×D₄×C₉	—	4	4	no	—
55	C₂×D₄×C₉	—	4	4	no	—
56	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
57	C₂×D₄×C₉	C₂³	1	4	yes	—
58	C₂²×C₄×C₉	—	2	1	no	—
59	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
60	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₉×SD₁₆	—	4	4	no	—
63	C₉×D₈	—	4	4	no	—
64	C₂×C₈×C₉	C₂³	1	4	yes	—
65	C₉×C₄⋊C₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
70	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₉×C₂²⋊C₄	—	2	1	no	—
72	C₉×C₂²⋊C₄	—	2	1	no	—
73	C₉×C₂²⋊C₄	—	2	1	no	—
74	C₉×C₂²⋊C₄	—	2	1	no	—
75	C₉×C₂²⋊C₄	—	2	1	no	—
76	C₄²×C₉	—	2	1	no	—
77	C₄²×C₉	D₄	1	1	yes	characteristic
78	C₄²×C₉	D₄	1	1	yes	characteristic
79	C₄²×C₉	C₂³	1	1	yes	characteristic
80	C₄²×C₉	C₂³	1	1	yes	characteristic
81	#3217	C₉	1	1	yes	characteristic, direct product factor, Sylow
82	C₂²×C₃×D₄	—	2	1	no	—
83	C₂²×C₃×D₄	—	2	1	no	—
84	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
85	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
86	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
87	C₃×#127	—	2	1	no	—
88	C₃×#127	—	2	1	no	—
89	C₃×#127	C₂²×C₃	1	2	yes	—
90	C₃×#127	C₂²×C₃	1	2	yes	—
91	C₃×#126	—	2	1	no	—
92	C₃×#125	C₂²×C₃	1	1	yes	characteristic
93	C₃×#124	C₂²×C₃	1	1	yes	characteristic
94	C₃×#123	—	2	1	no	—
95	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
96	C₃×#121	C₂²×C₃	1	1	yes	characteristic
97	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₃×C₄×D₄	—	2	1	no	—
99	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
100	C₃×#117	—	2	1	no	—
101	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
103	C₃×#102	C₂²×C₃	1	4	yes	—
104	C₃×#102	C₂²×C₃	1	4	yes	—
105	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₃×#97	C₂²×C₃	1	2	yes	—
107	C₂³×C₉	—	2	1	no	—
108	C₂³×C₉	—	2	4	no	—
109	C₂³×C₉	—	4	4	no	—
110	C₂³×C₉	—	4	4	no	—
111	C₂³×C₉	—	4	4	no	—
112	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
113	Q₈×C₉	—	2	2	no	—
114	D₄×C₉	—	2	2	no	—
115	D₄×C₉	—	2	4	no	—
116	D₄×C₉	—	2	4	no	—
117	D₄×C₉	—	4	4	no	—
118	D₄×C₉	—	4	4	no	—
119	D₄×C₉	—	4	4	no	—
120	D₄×C₉	—	4	4	no	—
121	D₄×C₉	—	4	2	no	—
122	D₄×C₉	—	4	4	no	—
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	2	2	no	—
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	1	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	4	2	no	—
130	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
136	C₈×C₉	—	2	4	no	—
137	C₂×#127	C₂×C₉	1	1	yes	characteristic, complemented
138	#529	C₂×C₉	1	1	yes	characteristic, complemented
139	#496	C₂×C₉	1	2	yes	complemented
140	#490	C₂×C₉	1	2	yes	complemented
141	#460	C₂×C₉	1	2	yes	complemented
142	#459	C₂×C₉	1	2	yes	complemented
143	#450	C₂×C₉	1	2	yes	complemented
144	#447	C₂×C₉	1	2	yes	complemented
145	#432	C₂×C₉	1	1	yes	characteristic, complemented
146	C₂⁴×C₃	—	2	2	no	—
147	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₃×D₄	—	2	1	no	—
149	C₂×C₃×D₄	—	2	2	no	—
150	C₂×C₃×D₄	—	2	2	no	—
151	C₂×C₃×D₄	—	2	2	no	—
152	C₂×C₃×D₄	—	2	2	no	—
153	C₂×C₃×D₄	—	2	2	no	—
154	C₂×C₃×D₄	—	4	4	no	—
155	C₂×C₃×D₄	—	4	4	no	—
156	C₂×C₃×D₄	—	4	4	no	—
157	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
158	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₃×C₄	—	2	1	no	—
160	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₃×SD₁₆	—	4	4	no	—
164	C₃×D₈	—	4	4	no	—
165	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
166	C₃×C₄⋊C₄	—	2	1	no	—
167	C₃×C₄⋊C₄	—	2	1	no	—
168	C₃×C₄⋊C₄	—	2	1	no	—
169	C₃×C₄⋊C₄	—	2	1	no	—
170	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
171	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
172	C₃×C₂²⋊C₄	—	2	1	no	—
173	C₃×C₂²⋊C₄	—	2	1	no	—
174	C₃×C₂²⋊C₄	—	2	1	no	—
175	C₃×C₂²⋊C₄	—	2	1	no	—
176	C₃×C₂²⋊C₄	—	2	1	no	—
177	C₃×C₄²	—	2	1	no	—
178	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
179	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
180	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
181	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₉	—	2	1	no	—
183	C₂²×C₉	—	2	1	no	—
184	C₂²×C₉	—	4	4	no	—
185	C₂²×C₉	—	4	1	no	—
186	C₂²×C₉	—	4	1	no	—
187	C₂²×C₉	—	4	4	no	—
188	C₂²×C₉	—	4	4	no	—
189	C₂²×C₉	—	4	1	no	—
190	C₂²×C₉	—	8	8	no	—
191	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
192	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
193	C₄×C₉	—	2	1	no	—
194	C₄×C₉	—	2	1	no	—
195	C₄×C₉	—	2	1	no	—
196	C₄×C₉	—	2	1	no	—
197	C₄×C₉	—	4	1	no	—
198	C₄×C₉	—	4	1	no	—
199	C₄×C₉	—	4	1	no	—
200	C₄×C₉	AGL(1,ℤ/8)	1	2	yes	—
201	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
202	C₂²×D₄	—	2	1	no	—
203	C₂²×D₄	—	2	1	no	—
204	C₂²×D₄	C₂²×C₉	1	2	yes	—
205	C₂×SD₁₆	C₂²×C₉	1	4	yes	complemented
206	C₂×D₈	C₂²×C₉	1	4	yes	complemented
207	#127	—	2	1	no	—
208	#127	—	2	1	no	—
209	#127	C₂²×C₉	1	2	yes	—
210	#127	C₂²×C₉	1	2	yes	—
211	#126	—	2	1	no	—
212	#125	C₂²×C₉	1	1	yes	characteristic, complemented
213	#124	C₂²×C₉	1	1	yes	characteristic, complemented
214	#123	—	2	1	no	—
215	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
216	#121	C₂²×C₉	1	1	yes	characteristic
217	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
220	#117	—	2	1	no	—
221	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
222	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
223	#102	C₂²×C₉	1	4	yes	complemented
224	#102	C₂²×C₉	1	4	yes	complemented
225	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
226	#97	C₂²×C₉	1	2	yes	complemented
227	C₂³×C₃	—	2	1	no	—
228	C₂³×C₃	—	2	4	no	—
229	C₂³×C₃	—	4	4	no	—
230	C₂³×C₃	—	4	4	no	—
231	C₂³×C₃	—	4	4	no	—
232	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
233	C₃×Q₈	—	2	2	no	—
234	C₃×D₄	—	2	2	no	—
235	C₃×D₄	—	2	4	no	—
236	C₃×D₄	—	2	4	no	—
237	C₃×D₄	—	4	4	no	—
238	C₃×D₄	—	4	4	no	—
239	C₃×D₄	—	4	4	no	—
240	C₃×D₄	—	4	4	no	—
241	C₃×D₄	—	4	2	no	—
242	C₃×D₄	—	4	4	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	4	2	no	—
250	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
256	C₃×C₈	—	2	4	no	—
257	C₂×C₉	—	2	2	no	—
258	C₂×C₉	—	8	1	no	—
259	C₂×C₉	—	8	4	no	—
260	C₂×C₉	#535	1	1	yes	characteristic
261	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂⁴	—	2	2	no	—
264	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	C₂³×C₉	1	4	yes	—
275	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
278	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
279	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
280	SD₁₆	—	4	4	no	—
281	D₈	—	4	4	no	—
282	C₂×C₈	C₂³×C₉	1	4	yes	—
283	C₄⋊C₄	—	2	1	no	—
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
288	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	D₄×C₉	1	1	yes	characteristic
296	C₄²	D₄×C₉	1	1	yes	characteristic
297	C₄²	C₂³×C₉	1	1	yes	characteristic
298	C₄²	C₂³×C₉	1	1	yes	characteristic
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	4	4	no	—
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	—	4	1	no	—
305	C₂²×C₃	—	4	4	no	—
306	C₂²×C₃	—	4	1	no	—
307	C₂²×C₃	—	8	8	no	—
308	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
309	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	4	1	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	1	no	—
317	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
318	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
319	C₉	#3217	1	1	yes	characteristic, direct product factor, Sylow
320	C₂³	—	2	1	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	2	4	no	—
329	D₄	—	2	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
344	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
345	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
347	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
348	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
349	C₈	—	2	4	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	8	4	no	—
352	C₂×C₃	—	8	1	no	—
353	C₂×C₃	C₃×#535	1	1	yes	characteristic
354	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
355	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	8	8	no	—
365	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
366	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	C₉×AGL(1,ℤ/8)	1	2	yes	—
375	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
376	C₃	C₃×#3217	1	1	yes	characteristic
377	C₂	—	2	2	no	—
378	C₂	—	8	4	no	—
379	C₂	—	8	1	no	—
380	C₂	C₉×#535	1	1	yes	characteristic
381	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂	C₂×C₉×AGL(1,ℤ/8)	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×#3217	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. C₂×C₉×#127	C₂	semidirect
2. C₉×#529	C₂	semidirect
3. C₉×#496	C₂	semidirect
4. C₉×#490	C₂	semidirect
5. C₉×#460	C₂	semidirect
6. C₉×#459	C₂	semidirect
7. C₉×#450	C₂	semidirect
8. C₉×#447	C₂	semidirect
9. C₉×#432	C₂	semidirect
14. C₂×C₉×SD₁₆	C₂²	semidirect
15. C₂×C₉×D₈	C₂²	semidirect
21. C₉×#125	C₂²	semidirect
22. C₉×#124	C₂²	semidirect
26. C₄×Q₈×C₉	C₂²	semidirect
28. C₄×D₄×C₉	C₂²	semidirect
31. C₉×C₄⋊C₈	C₂²	semidirect
32. C₉×#102	C₂²	semidirect
33. C₉×#102	C₂²	semidirect
35. C₉×#97	C₂²	semidirect
81. #3217	C₉	direct (N × H)
137. C₂×#127	C₂×C₉	semidirect
138. #529	C₂×C₉	semidirect
139. #496	C₂×C₉	semidirect
140. #490	C₂×C₉	semidirect
141. #460	C₂×C₉	semidirect
142. #459	C₂×C₉	semidirect
143. #450	C₂×C₉	semidirect
144. #447	C₂×C₉	semidirect
145. #432	C₂×C₉	semidirect
205. C₂×SD₁₆	C₂²×C₉	semidirect
206. C₂×D₈	C₂²×C₉	semidirect
212. #125	C₂²×C₉	semidirect
213. #124	C₂²×C₉	semidirect
217. C₄×Q₈	C₂²×C₉	semidirect
219. C₄×D₄	C₂²×C₉	semidirect
222. C₄⋊C₈	C₂²×C₉	semidirect
223. #102	C₂²×C₉	semidirect
224. #102	C₂²×C₉	semidirect
226. #97	C₂²×C₉	semidirect
319. C₉	#3217	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×#127	2
C₉×#529	2
C₉×#496	2
C₉×#490	2
C₉×#460	2
C₉×#459	2
C₉×#450	2
C₉×#447	2
C₉×#432	2
C₃×#3217	3

Subgroups — C9×#3217 #11767938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3217 #11767938