Subgroups — C₉×#3222 #11767943

Order 1152.

594 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#535	C₂	1	1	yes	maximal, characteristic
3	C₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#464	C₂	1	2	yes	maximal, complemented
8	C₉×#460	C₂	1	2	yes	maximal, complemented
9	C₉×#452	C₂	1	2	yes	maximal, complemented
10	C₉×#450	C₂	1	2	yes	maximal, complemented
11	C₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3222	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×Q₁₆	C₂²	1	2	yes	complemented
16	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
19	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₉×#127	C₂²	1	1	yes	characteristic
21	C₉×#127	C₂²	1	1	yes	characteristic
22	C₉×#126	—	2	2	no	—
23	C₉×#125	—	2	2	no	—
24	C₉×#125	C₂²	1	1	yes	characteristic, complemented
25	C₉×#124	C₂²	1	1	yes	characteristic
26	C₉×#124	C₂²	1	1	yes	characteristic
27	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₉×#121	—	2	2	no	—
29	C₉×#120	—	2	2	no	—
30	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
31	C₉×#117	C₂²	1	1	yes	characteristic
32	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
33	C₉×#103	C₂²	1	2	yes	complemented
34	C₉×#102	C₂²	1	2	yes	—
35	C₉×#102	C₂²	1	2	yes	—
36	C₉×#102	C₂²	1	2	yes	complemented
37	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₉×#97	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
40	C₃×#541	C₂×C₃	1	1	yes	characteristic
41	C₃×#535	C₂×C₃	1	1	yes	characteristic
42	C₃×#497	C₂×C₃	1	1	yes	characteristic
43	C₃×#492	C₂×C₃	1	1	yes	characteristic
44	C₃×#490	C₂×C₃	1	1	yes	characteristic
45	C₃×#488	C₂×C₃	1	1	yes	characteristic
46	C₃×#464	C₂×C₃	1	2	yes	—
47	C₃×#460	C₂×C₃	1	2	yes	—
48	C₃×#452	C₂×C₃	1	2	yes	—
49	C₃×#450	C₂×C₃	1	2	yes	—
50	C₃×#433	C₂×C₃	1	1	yes	characteristic
51	C₂⁴×C₉	—	2	1	no	—
52	C₉×#41	—	4	2	no	—
53	C₂×Q₈×C₉	C₂³	1	2	yes	—
54	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
55	C₂×D₄×C₉	—	2	1	no	—
56	C₂×D₄×C₉	—	2	1	no	—
57	C₂×D₄×C₉	—	2	2	no	—
58	C₂×D₄×C₉	—	2	2	no	—
59	C₂×D₄×C₉	—	4	2	no	—
60	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₉	—	2	1	no	—
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₉×Q₁₆	—	4	2	no	—
66	C₉×SD₁₆	—	4	2	no	—
67	C₉×SD₁₆	—	4	2	no	—
68	C₉×SD₁₆	—	4	2	no	—
69	C₂×C₈×C₉	C₂³	1	2	yes	—
70	C₂×C₈×C₉	C₂³	1	2	yes	—
71	C₉×C₄⋊C₄	—	2	2	no	—
72	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	—	2	2	no	—
74	C₉×C₄⋊C₄	—	2	2	no	—
75	C₉×C₄⋊C₄	D₄	1	2	yes	—
76	C₉×C₄⋊C₄	C₂³	1	2	yes	—
77	C₉×C₂²⋊C₄	—	2	2	no	—
78	C₉×C₂²⋊C₄	—	2	2	no	—
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	D₄	1	2	yes	—
81	C₄²×C₉	—	2	2	no	—
82	C₄²×C₉	C₂³	1	1	yes	characteristic
83	C₄²×C₉	C₂³	1	1	yes	characteristic
84	#3222	C₉	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
88	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
89	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
90	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
91	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₃×#127	C₂²×C₃	1	1	yes	characteristic
93	C₃×#127	C₂²×C₃	1	1	yes	characteristic
94	C₃×#126	—	2	2	no	—
95	C₃×#125	—	2	2	no	—
96	C₃×#125	C₂²×C₃	1	1	yes	characteristic
97	C₃×#124	C₂²×C₃	1	1	yes	characteristic
98	C₃×#124	C₂²×C₃	1	1	yes	characteristic
99	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
100	C₃×#121	—	2	2	no	—
101	C₃×#120	—	2	2	no	—
102	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
103	C₃×#117	C₂²×C₃	1	1	yes	characteristic
104	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
105	C₃×#103	C₂²×C₃	1	2	yes	—
106	C₃×#102	C₂²×C₃	1	2	yes	—
107	C₃×#102	C₂²×C₃	1	2	yes	—
108	C₃×#102	C₂²×C₃	1	2	yes	—
109	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
110	C₃×#97	C₂²×C₃	1	1	yes	characteristic
111	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
112	C₂³×C₉	—	2	1	no	—
113	C₂³×C₉	—	2	1	no	—
114	C₂³×C₉	—	2	1	no	—
115	C₂³×C₉	—	4	2	no	—
116	C₂³×C₉	—	8	2	no	—
117	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
118	Q₈×C₉	—	2	2	no	—
119	Q₈×C₉	—	2	2	no	—
120	Q₈×C₉	—	2	2	no	—
121	D₄×C₉	—	2	2	no	—
122	D₄×C₉	—	2	2	no	—
123	D₄×C₉	—	2	2	no	—
124	D₄×C₉	—	4	2	no	—
125	D₄×C₉	—	4	2	no	—
126	D₄×C₉	—	8	2	no	—
127	D₄×C₉	—	8	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	4	2	no	—
133	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
134	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
135	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
137	C₈×C₉	—	2	2	no	—
138	C₈×C₉	—	2	2	no	—
139	#541	C₂×C₉	1	1	yes	characteristic, complemented
140	#535	C₂×C₉	1	1	yes	characteristic
141	#497	C₂×C₉	1	1	yes	characteristic, complemented
142	#492	C₂×C₉	1	1	yes	characteristic, complemented
143	#490	C₂×C₉	1	1	yes	characteristic, complemented
144	#488	C₂×C₉	1	1	yes	characteristic, complemented
145	#464	C₂×C₉	1	2	yes	complemented
146	#460	C₂×C₉	1	2	yes	complemented
147	#452	C₂×C₉	1	2	yes	complemented
148	#450	C₂×C₉	1	2	yes	complemented
149	#433	C₂×C₉	1	1	yes	characteristic, complemented
150	C₂⁴×C₃	—	2	1	no	—
151	C₃×#41	—	4	2	no	—
152	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
153	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
154	C₂×C₃×D₄	—	2	1	no	—
155	C₂×C₃×D₄	—	2	1	no	—
156	C₂×C₃×D₄	—	2	2	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	4	2	no	—
159	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₃×C₄	—	2	1	no	—
163	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₃×Q₁₆	—	4	2	no	—
165	C₃×SD₁₆	—	4	2	no	—
166	C₃×SD₁₆	—	4	2	no	—
167	C₃×SD₁₆	—	4	2	no	—
168	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
169	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	2	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
175	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
176	C₃×C₂²⋊C₄	—	2	2	no	—
177	C₃×C₂²⋊C₄	—	2	2	no	—
178	C₃×C₂²⋊C₄	—	2	2	no	—
179	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
180	C₃×C₄²	—	2	2	no	—
181	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
182	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₉	—	2	1	no	—
184	C₂²×C₉	—	2	2	no	—
185	C₂²×C₉	—	4	1	no	—
186	C₂²×C₉	—	4	1	no	—
187	C₂²×C₉	—	4	1	no	—
188	C₂²×C₉	—	4	2	no	—
189	C₂²×C₉	—	4	2	no	—
190	C₂²×C₉	—	4	2	no	—
191	C₂²×C₉	—	8	4	no	—
192	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
193	C₄×C₉	—	2	1	no	—
194	C₄×C₉	—	2	2	no	—
195	C₄×C₉	—	2	2	no	—
196	C₄×C₉	—	4	1	no	—
197	C₄×C₉	—	4	2	no	—
198	C₄×C₉	—	4	2	no	—
199	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
200	C₂×#41	C₂²×C₉	1	1	yes	characteristic
201	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
202	C₂×Q₁₆	C₂²×C₉	1	2	yes	complemented
203	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
204	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
205	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
206	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
207	#127	C₂²×C₉	1	1	yes	characteristic
208	#127	C₂²×C₉	1	1	yes	characteristic
209	#126	—	2	2	no	—
210	#125	—	2	2	no	—
211	#125	C₂²×C₉	1	1	yes	characteristic, complemented
212	#124	C₂²×C₉	1	1	yes	characteristic
213	#124	C₂²×C₉	1	1	yes	characteristic
214	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
215	#121	—	2	2	no	—
216	#120	—	2	2	no	—
217	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
218	#117	C₂²×C₉	1	1	yes	characteristic
219	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
220	#103	C₂²×C₉	1	2	yes	complemented
221	#102	C₂²×C₉	1	2	yes	—
222	#102	C₂²×C₉	1	2	yes	—
223	#102	C₂²×C₉	1	2	yes	complemented
224	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
225	#97	C₂²×C₉	1	1	yes	characteristic, complemented
226	C₄×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
227	C₂³×C₃	—	2	1	no	—
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	4	2	no	—
231	C₂³×C₃	—	8	2	no	—
232	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
233	C₃×Q₈	—	2	2	no	—
234	C₃×Q₈	—	2	2	no	—
235	C₃×Q₈	—	2	2	no	—
236	C₃×D₄	—	2	2	no	—
237	C₃×D₄	—	2	2	no	—
238	C₃×D₄	—	2	2	no	—
239	C₃×D₄	—	4	2	no	—
240	C₃×D₄	—	4	2	no	—
241	C₃×D₄	—	8	2	no	—
242	C₃×D₄	—	8	2	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	—	4	2	no	—
248	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
249	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
252	C₃×C₈	—	2	2	no	—
253	C₃×C₈	—	2	2	no	—
254	C₂×C₉	—	4	1	no	—
255	C₂×C₉	—	8	1	no	—
256	C₂×C₉	—	8	1	no	—
257	C₂×C₉	—	8	1	no	—
258	C₂×C₉	#535	1	1	yes	characteristic
259	C₂×C₉	#577	1	2	yes	—
260	C₂⁴	—	2	1	no	—
261	#41	—	4	2	no	—
262	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
263	C₂×Q₈	C₂³×C₉	1	2	yes	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
270	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
271	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
274	Q₁₆	—	4	2	no	—
275	SD₁₆	—	4	2	no	—
276	SD₁₆	—	4	2	no	—
277	SD₁₆	—	4	2	no	—
278	C₂×C₈	C₂³×C₉	1	2	yes	—
279	C₂×C₈	C₂³×C₉	1	2	yes	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	D₄×C₉	1	2	yes	—
285	C₄⋊C₄	C₂³×C₉	1	2	yes	—
286	C₂²⋊C₄	—	2	2	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	D₄×C₉	1	2	yes	—
290	C₄²	—	2	2	no	—
291	C₄²	C₂³×C₉	1	1	yes	characteristic
292	C₄²	C₂³×C₉	1	1	yes	characteristic
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	4	2	no	—
297	C₂²×C₃	—	4	2	no	—
298	C₂²×C₃	—	4	1	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	8	4	no	—
302	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	4	2	no	—
307	C₃×C₄	—	4	1	no	—
308	C₃×C₄	—	4	2	no	—
309	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
310	C₉	#3222	1	1	yes	characteristic, direct product factor, Sylow
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	8	2	no	—
316	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
317	Q₈	—	2	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	D₄	—	2	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	2	2	no	—
323	D₄	—	4	2	no	—
324	D₄	—	4	2	no	—
325	D₄	—	8	2	no	—
326	D₄	—	8	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
333	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
334	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
335	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₂×C₃	—	4	1	no	—
339	C₂×C₃	—	8	1	no	—
340	C₂×C₃	—	8	1	no	—
341	C₂×C₃	—	8	1	no	—
342	C₂×C₃	C₃×#535	1	1	yes	characteristic
343	C₂×C₃	C₃×#577	1	2	yes	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	8	4	no	—
353	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
354	C₄	—	2	1	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	2	no	—
360	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
361	C₃	C₃×#3222	1	1	yes	characteristic
362	C₂	—	4	1	no	—
363	C₂	—	8	1	no	—
364	C₂	—	8	1	no	—
365	C₂	—	8	1	no	—
366	C₂	C₉×#535	1	1	yes	characteristic
367	C₂	C₉×#577	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×#535	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#541	C₂	semidirect
3. C₉×#497	C₂	semidirect
4. C₉×#492	C₂	semidirect
5. C₉×#490	C₂	semidirect
6. C₉×#488	C₂	semidirect
7. C₉×#464	C₂	semidirect
8. C₉×#460	C₂	semidirect
9. C₉×#452	C₂	semidirect
10. C₉×#450	C₂	semidirect
11. C₉×#433	C₂	semidirect
15. C₂×C₉×Q₁₆	C₂²	semidirect
18. C₂×C₉×SD₁₆	C₂²	semidirect
19. C₉×C₄⋊Q₈	C₂²	semidirect
24. C₉×#125	C₂²	semidirect
30. C₄×Q₈×C₉	C₂²	semidirect
32. C₉×C₄⋊C₈	C₂²	semidirect
33. C₉×#103	C₂²	semidirect
36. C₉×#102	C₂²	semidirect
38. C₉×#97	C₂²	semidirect
39. C₄×C₈×C₉	C₂²	semidirect
84. #3222	C₉	direct (N × H)
139. #541	C₂×C₉	semidirect
141. #497	C₂×C₉	semidirect
142. #492	C₂×C₉	semidirect
143. #490	C₂×C₉	semidirect
144. #488	C₂×C₉	semidirect
145. #464	C₂×C₉	semidirect
146. #460	C₂×C₉	semidirect
147. #452	C₂×C₉	semidirect
148. #450	C₂×C₉	semidirect
149. #433	C₂×C₉	semidirect
202. C₂×Q₁₆	C₂²×C₉	semidirect
205. C₂×SD₁₆	C₂²×C₉	semidirect
206. C₄⋊Q₈	C₂²×C₉	semidirect
211. #125	C₂²×C₉	semidirect
217. C₄×Q₈	C₂²×C₉	semidirect
219. C₄⋊C₈	C₂²×C₉	semidirect
220. #103	C₂²×C₉	semidirect
223. #102	C₂²×C₉	semidirect
225. #97	C₂²×C₉	semidirect
226. C₄×C₈	C₂²×C₉	semidirect
310. C₉	#3222	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×#541	2
C₉×#535	2
C₉×#497	2
C₉×#492	2
C₉×#490	2
C₉×#488	2
C₉×#464	2
C₉×#460	2
C₉×#452	2
C₉×#450	2
C₉×#433	2
C₃×#3222	3

Subgroups — C9×#3222 #11767943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3222 #11767943